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Fluorescence Microscopy

  • Alberto DiasproEmail author
  • Paolo Bianchini
  • Francesca Cella Zanacchi
  • Luca Lanzanò
  • Giuseppe Vicidomini
  • Michele Oneto
  • Luca Pesce
  • Isotta Cainero
Chapter
Part of the Springer Handbooks book series (SHB)

Abstract

In this two-part chapter, the background to confocal microscopy and two-photon fluorescence microscopy is first presented, with a detailed description of the optical setup. This is followed by a critical account of the many super-resolution techniques: coordinated stochastic fluorescence microscopy (photoactivation localization microscopy ( ), stochastic optical reconstruction microscopy ( ), point accumulation for imaging in nanoscale topography ( ), coordinate targeted fluorescence microscopy (STED, reversible saturable optical fluorescence transition ( )), structured illumination microscopy, expansion microscopy ( ), and liquid tunable microscopy ( ).

Two-photon excitation ( ) fluorescence microscopy [21.1, 21.2, 21.3] can be considered an important example of the continuing growth of interest in optical microscopy [21.4, 21.5]. In spite of its low spatial resolution compared to other modern imaging techniques, such as scanning near-field microscopy [21.6], scanning probe microscopy [21.7], or electron microscopy [21.8], light microscopy techniques, including TPE microscopy, have unique capabilities in the investigation of biological structures in a hydrated state, in living specimens, or at least under conditions that are close to physiological states [21.10, 21.11, 21.9]. This fact, coupled with advances in fluorescence labeling, permits the study of the complex and delicate relationships existing between structure and function in four-dimensional ( ) (\(x\)\(y\)\(z\)\(t\)) biological systems domain [21.12, 21.13, 21.14, 21.15]. Moreover, the advances achieved in the field of biological markers, especially the design of application-suited chromophores, the development of so-called quantum dots [21.16], visible fluorescent proteins ( s) from the green fluorescent protein ( ) and its natural homologues to specifically engineered variants of these molecules [21.17, 21.18], and the improvements in resolution by means of special optical schemes [21.19, 21.20], are enabling TPE to move from microscopy to nanoscopy [21.21, 21.22].

There is also ongoing research into using TPE in new fields where its special features can be advantageously applied to improve and to optimize existing schemes [21.23]. This covers new online detection systems such as endoscopic imaging based on gradient refractive index fibers [21.24], the development of new substrates with higher fluorescence output [21.25], as well as the use of TPE to systematically cross-link protein matrices and control diffusion [21.26]. Furthermore, the combination of TPE applications with other techniques has great potential use [21.27, 21.28, 21.29].

TPE microscopy belongs to the category of three-dimensional () optical microscopy methods, which have been widespread since the 1970s [21.30, 21.31, 21.32, 21.33, 21.34, 21.35, 21.36, 21.37, 21.38]. During the past 10 years, confocal microscopes have proved to be extremely useful research tools, notably in the life sciences. The evolution has also brought optical microscopy from 3-D (\(x\)\(y\)\(z\)) to five-dimensional ( ) (\(x\)\(y\)\(z\)\(t\)\(\lambda\)) analysis allowing researchers to probe even deeper into the intricate mechanisms of living systems [21.10, 21.11, 21.39, 21.40, 21.41, 21.9]. Here, TPE microscopy [21.1, 21.42, 21.43, 21.44], or more generally multiphoton excitation () microscopy  [21.45, 21.46], can probably be considered the most relevant advance in fluorescence optical microscopy since the introduction of confocal imaging in the 1980s [21.11, 21.36, 21.41, 21.47, 21.48, 21.49, 21.9].

TPE microscopy couples a 3-D intrinsic ability, shared with confocal microscopy, with almost five other interesting properties:
  1. 1.

    TPE greatly reduces photo interactions and allows imaging of living specimens over long time periods.

     
  2. 2.

    TPE allows operation in a high-sensitivity background-free acquisition scheme.

     
  3. 3.

    TPE microscopy can penetrate turbid and thick specimens down to a depth of a few hundred micrometers.

     
  4. 4.

    Due to the distinct character of the multiphoton absorption spectra of many of the fluorophores, TPE allows simultaneous excitation of different fluorescent molecules, reducing colocalization errors.

     
  5. 5.

    TPE can prime photochemical reactions within a subfemtoliter volume inside solutions, cells, and tissues.

     

Furthermore, this form of nonlinear microscopy also favored the development and application of several investigative techniques starting from TPE microscopy [21.1], namely, three-photon excited fluorescence [21.50, 21.51], second harmonic generation [21.52, 21.53, 21.54, 21.55], third-harmonic generation [21.56, 21.57], fluorescence correlation spectroscopy ( ) [21.58, 21.59, 21.60, 21.61, 21.62, 21.63], image correlation spectroscopy [21.64, 21.65], lifetime imaging [21.66, 21.67, 21.68, 21.69, 21.70], single-molecule detection schemes [21.71, 21.72, 21.73, 21.74, 21.75, 21.76, 21.77], photodynamic therapies [21.78], two-photon photoactivation and photoswitching of visible fluorescent proteins [21.79, 21.80, 21.81, 21.82], and others [21.10, 21.29, 21.83, 21.84, 21.85, 21.86, 21.87, 21.88, 21.89, 21.90].

21.1 Brief Chronological Notes

The important work done by Abbe indicated how to optimize the optical microscope. In 2005, the Focus on Microscopy conference, held in Jena, was dedicated to Abbe's work 100 years after his death (http://www.focusonmicroscopy.org). Abbe's approach in defining factors influencing the microscope's resolution was fundamental. Confocal and TPE microscopy show how to extend optical parameters to obtain a better resolution. In 2000, the Optical Society of America honored Paul Davidovits, M. David Egger, and Marvin Minsky with the R.W. Wood Prize for Seminal Contributions to Confocal Microscopy. The fact is that in 1975 Minsky invented a confocal microscope identical in concept to the one developed by Egger and Davidovits at Yale [21.91, 21.92], by Sheppard and Wilson at Oxford [21.35, 21.36, 21.93], and by Brakenhoff et al in Amsterdam [21.34, 21.94]. As reported by Minsky [21.95], the circumstances are also remarkable in that Minsky only published his invention as a patent (Fig. 21.1). In addition, the idea for a confocal microscope was previously presented by Naora, who built an optical setup based upon a concept of Koana, as recently indicated by Guy Cox. It was not until the end of the 1970s, with the advent of affordable computers and lasers, and the development of digital image processing software, that the first single-beam confocal laser scanning microscopes became available in a number of laboratories and were applied to biological and materials specimens. A new revolution was developing [21.96]: TPE second harmonic and fluorescence microscopy. The TPE story dates back to 1931, having its roots in the theory originally developed by Maria Göppert-Mayer [21.97]. The keystone of the TPE theory lies in the prediction that one atom or molecule can simultaneously absorb two photons in the same quantum event.

Fig. 21.1

Historical sketch of the confocal setup as reported by Marvin Minsky in his patent [21.98]

Now, to indicate the rarity of the event, consider that simultaneously here implies within a temporal window of \(E-16{-}E-15\,{\mathrm{s}}\); in bright daylight a good one or two-photon excitable fluorescent molecule absorbs a photon through a one-photon (1P ) interaction about once a second and a photon pair by two-photon (2P ) simultaneous interaction every 10 million years [21.99]. To increase the probability of the event, a very high density of photons is needed, i. e., a laser source. As in confocal microscopy, the laser is the key to the development and dissemination of the technique. In fact, it was only in the 1960s, after the development of the first laser sources [21.100, 21.101], that it was possible to find experimental evidence for Maria Göppert-Mayer's prediction. Kaiser and Garret [21.102] reported TPE of fluorescence in \(\mathrm{CaF_{2}}\):\(\mathrm{Eu^{2+}}\) and Singh and Bradley [21.103] were able to estimate the three-photon absorption cross-section for naphthalene crystals. These two results consolidated other related experimental achievements obtained by Franken et al [21.104] of second harmonic generation in a quartz crystal using a ruby laser. Later, Rentzepis et al [21.105] observed three-photon excited fluorescence from organic dyes, and Hellwarth and Christensen [21.106] collected second-harmonic generation signals from ZnSe polycrystals at a microscopic level. In 1976, Berns reported a probable two-photon effect as a result of focusing an intense pulsed laser beam onto chromosomes of living cells, and such interactions form the basis of modern nanosurgery [21.107]. However, the original idea of generating 3-D microscopic images by means of such nonlinear optical effects was first suggested and attempted in the 1970s by Sheppard, Kompfner, Gannaway, and Choudhury of the Oxford group [21.52, 21.93, 21.96]. It should also be emphasized that for many years the application of two-photon absorption was mainly related to spectroscopic studies [21.108, 21.109, 21.110, 21.111]. The real TPE boom took place at the beginning of the 1990s at the W.W. Webb laboratories (Cornell University, Ithaca, NY). However, it was the excellent and effective work done by Winfried Denk et al [21.1] that was responsible for spreading the technique and that revolutionized fluorescence microscopy imaging.

21.2 Basic Principles on Confocal and Two-Photon Excitation of Fluorescent Molecules

21.2.1 Fluorescence

Fluorescence optical microscopy is very popular for imaging in biology, since fluorescence is highly specific either as exogenous labeling or endogenous autofluorescence [21.10, 21.112, 21.12, 21.13]. Fluorescent molecules allow both spatial and functional information to be obtained through specific absorption, emission, lifetime, anisotropy, photodecay, diffusion, and other contrast mechanisms [21.11, 21.55]. This means that it is possible to efficiently study, for example, the distribution and dynamics of proteins, DNA, and chromatin as well as ion concentration, voltage, and temperature within living cells [21.113, 21.114, 21.115]. TPE of fluorescent molecules is a nonlinear process related to the simultaneous absorption of two photons whose total energy equals the energy required for conventional, one-photon excitation [21.111, 21.116, 21.117]. In any case, the energy required to prime fluorescence is the energy sufficient to produce a molecular transition to an excited electronic state. The excited fluorescent molecules then decay to an intermediate state giving off a photon of light having an energy lower than needed to prime excitation. This means that the energy \(E\) provided by photons should equal the molecule energy gap \(\Updelta E_{\mathrm{g}}\), and, considering the relationship between photon energy \(E\) and radiation wavelength \(\lambda\), it follows that
$$\Updelta E_{\mathrm{g}}=E=\frac{hc}{\lambda}\;,$$
(21.1)
where \(h={\mathrm{6.6\times 10^{-34}}}\,{\mathrm{J{\,}s}}\) is Planck's constant and \(c={\mathrm{3\times 10^{8}}}\,{\mathrm{m{\,}s^{-1}}}\) is the value of the speed of light (considered in vacuum and to a reasonable approximation). Conventional techniques for fluorescence excitation use ultraviolet ( ) or visible radiation, and excitation occurs when the absorbed photons are able to match the energy gap to the ground from the excited state. Due to energetic aspects, the fluorescence emission is shifted toward a wavelength longer than the one used for excitation. This shift typically ranges from \(\mathrm{50}\) to \({\mathrm{200}}\,{\mathrm{nm}}\) [21.116, 21.118]. For example, a fluorescent molecule that absorbs one photon at \({\mathrm{340}}\,{\mathrm{nm}}\), in the ultraviolet region, exhibits fluorescence at \({\mathrm{420}}\,{\mathrm{nm}}\) in the blue region.

A 3-D reconstruction of the distribution of fluorescence within a 3-D object such as a living cell starting with the acquisition of the two-dimensional () distribution of specific intensive properties is one of the most powerful properties of the optical microscope. In fact, this allows complete morphological analysis through volume-rendering procedures [21.115, 21.119] of living biological specimens, where the opportunity of optical slicing allows information to be obtained from different planes of the specimen without being invasive, thus preserving the structures and functionality of the different parts [21.120, 21.30, 21.31, 21.33].

21.2.2 Confocal Principle and Laser Scanning Microscopy

Conventional wide-field microscopes involve a specimen entirely bathed in the radiation from the light source, viewed directly by eye or through any capture device (charge-coupled device (CCD) camera, for instance, or photosensitive film). As reported in the paper by Minsky [21.121], an ideal microscope would examine each point of the specimen and measure the amount of light scattered, absorbed, or emitted by that point, excluding contributions from another part of the sample from the actual or adjacent planes (Fig. 21.2). Unfortunately, in trying to obtain images by making many such measurements at the same time, every focal image point will be clouded by aberrant rays of scattered light deflected from points of the specimen that are not the point of interest. This means that samples undergo continuous full excitation, leading to in and out-of-focus light points and contributing to overlapping and worsening axial resolution and producing that typical hazing in the collected images that, together with light-diffraction effects, limits the performance of the instrument. Most of those extra rays would be absent if we could illuminate only one specimen point at a time. There is no way of eliminating every undesired ray, because of multiple scattering, but it is comparatively straightforward to remove all rays not initially aimed at the focal point by using a sort of second microscope (instead of a condenser lens) to image a pinhole aperture (a small aperture in an opaque screen) on a single point of the specimen. This reduces the amount of light in the specimen by orders of magnitude without reducing the focal brightness. Even then, some of the initially focused light will be scattered by out-of-focus specimen points onto other points in the image plane affecting the clarity of the final acquisition, i. e., of the observed image \(o\). However, it is possible to reject undesired rays as well, by placing a second pinhole aperture in the image plane that lies beyond the exit side of the objective lens. We end up with an elegant, symmetrical geometry: a pinhole and an objective lens on each side of the specimen. This leads to the use of two lenses on both the excitation and detection sides of the microscope, combining the two lenses for a unique effect (Fig. 21.3).

Fig. 21.2

Comparison between conventional 1P and 2P excitation with respect to image formation. When focusing on the actual focal plane under 1P, a contribution from adjacent planes that are physically excluded in the 2P process is obtained, as happens in a confocal setup

Fig. 21.3

Equivalent optical configuration for a confocal setup

To acquire an image the excitation light has to be fully delivered to each point of the sample, and the emission signal collected and displayed. This is usually accomplished by either of two possible but different strategies.

The first one is based upon scanning the sample in a raster pattern such that over every fixed period of time, the necessary amount of information from the focal plane is collected, and the emitted light signal, usually detected through a photomultiplier tube ( ), is displayed by a mapping of each single point light emission. Sometimes, the use of a slit moving in one direction (rather than a single point) is preferred for speeding up the scanning rate, although this leads to an evident worsening of the spatial resolution and of the three-dimensional imaging capability.

A second possible approach to form confocal images consists of employing a multipinhole Nipkow spinning disk  [21.122, 21.123]. This is a disk containing multiple sets of spirally arranged holes placed in the image plane of the objective lens. A large parallel beam of light is then pointed at a particular region of the disk, and the light passing through the illuminated pinholes is focused by the objective lens straight onto the specimen. When spinning the disk at a rapid rate, the sample may undergo excitation several hundred times per second; emitted light is collected and imaged, typically by a high-resolution and high-quantum-efficiency CCD camera. Concerning optical sectioning, every architecture is built such that the sample is placed along the light path at a conjugate focal plane, and the movements along the optical axis keep the focus at a fixed distance from the objective, making it possible to effectively scan different fields of view through the specimen (due to a step-by-step motor device attached to the fine focus) and collect a series of in-focus optical slices for 3-D reconstruction.

The degree of confocality is a function of the pinhole size; the use of smaller pinholes improves the discrimination of focused light from stray light, thus involving a thinner plane in the image formation process and improving resolution, at the cost of lower light throughput, which makes things complicated when dealing with particularly dim samples.

In these architectures, \(z\)-resolution and optical sectioning thickness (which are basically the parameters involved in every optical sectioning process) depend on a number of factors, such as the numerical aperture ( ) of the objective lens, the wavelength of the excitation/emission light, the pinhole size, the refractive index of components along the light path, and, finally, the overall alignment of the instrument.

21.2.3 Theoretical Analysis

The development of an effective theoretical model for describing the properties of an optical system needs some preliminary, realistic assumptions to be made to simplify calculations.

From this point of view, a linear space invariant ( ) model is a good choice; it is pliable enough to obtain important insights and develop suitable mathematical tools for the analysis of most concrete situations. Let us consider the situation sketched in Fig. 21.3, which shows a typical confocal setup.

A monochromatic point light source is focused onto a sample in the focal plane through a lens L\({}_{1}\) (condenser), and the emitted radiation from the sample (which is also supposed to be monochromatic) is collected through a second lens L\({}_{2}\) (objective) by a point detector. Let \(h_{\mathrm{ex}}\) and \(h_{\mathrm{em}}\) be, respectively, the impulse response of L\({}_{1}\) and L\({}_{2}\), i. e., the lens response to a point-like light source. Under this hypothesis, it can be written that \(U_{\mathrm{ex}}(x)=(h_{\mathrm{ex}}\otimes\delta_{\mathrm{s}})(x)=h_{\mathrm{ex}}(x)\), where the excitation light source is modeled by a Dirac impulse.

It can be shown that with \(U_{\mathrm{ex}}\) the signal reaching the sample, the emitted signal scales with the fluorescent dye density \(D\) according to \(U_{\mathrm{em}}=D\,U_{\mathrm{ex}}\). The emitted radiation is then focused on the point detector through L\({}_{2}\).

This leads to \(U_{\mathrm{det}}(x)=[h_{\mathrm{em}}\otimes U_{\mathrm{em}})\,\delta_{\mathrm{d}}](x)\), where the point detector function is assumed to be a Dirac impulse. The overall signal collected by the detector is
$$\begin{aligned}\displaystyle I_{\mathrm{tot}}&\displaystyle=\int U_{\det}(x)\mathrm{d}x=\int\mathrm{d}x\delta_{\mathrm{d}}(x)(h_{\mathrm{em}}\otimes U_{\mathrm{em}})(x)\\ \displaystyle&\displaystyle=\int\mathrm{d}x\,\delta_{\mathrm{d}}(x)\int\mathrm{d}y\,h_{\mathrm{em}}(x-y)D(y)h_{\mathrm{ex}}(y)\\ \displaystyle&\displaystyle=\int\mathrm{d}y\,D(y)h_{\mathrm{ex}}(y)\int\mathrm{d}x\,\delta_{\mathrm{d}}(x)h_{\mathrm{em}}(x-y)\\ \displaystyle&\displaystyle=\int\mathrm{d}y\,D(y)h_{\mathrm{ex}}(y)h_{\mathrm{em}}(-y)\;.\end{aligned}$$
If we now limit ourselves to a point-like sample
$$\begin{aligned}\displaystyle\int U_{\det}(x)\,\mathrm{d}x&\displaystyle=\int\mathrm{d}y\,\delta(y)h_{\mathrm{ex}}(y)h_{\mathrm{em}}(-y)\\ \displaystyle&\displaystyle=h_{\mathrm{ex}}(0)h_{\mathrm{em}}(0)\;,\end{aligned}$$
where \(h_{\mathrm{ex}}=h_{\mathrm{em}}\) under the hypothesis of L\({}_{1}\) = L\({}_{2}\) and \(\lambda_{\mathrm{ex}}=\lambda_{\mathrm{em}}\) (The equivalence of \(h_{\mathrm{ex}}=h_{\mathrm{em}}\) is valid only for pinhole sizes \(\leq{\mathrm{0.25}}\,{\mathrm{AU}}\). is the so-called Airy unit, which represents the diameter of the Airy disk.)

Since an \(x\)\(y\)\(z\) scanning process is generally coupled to the imaging one, it is natural to write, for a general point \(P(x,y,z)\): \(I_{\mathrm{tot}}=h^{2}(x,y,z)\), which is the general expression for the point spread function ( ), that is, the system impulse response. A mathematical expression for \(h(x,y,z)\) can be obtained through the scalar electromagnetic waves theory.

The formulation, based on Fraunhofer diffraction, leads to
$$h(u,v)\propto\left|\int_{0}^{1}J_{0}(v\rho)\mathrm{e}^{-0.5\mathrm{i}u{p^{2}}}\rho\mathrm{d}\rho\right|^{2},$$
(21.2)
where \(u\) and \(v\) are suitable dimensionless variables defined according to the following
$$\begin{aligned}\displaystyle u&\displaystyle\propto z\;,\\ \displaystyle v&\displaystyle\propto\sqrt{x^{2}+y^{2}}\;.\end{aligned}$$
By limiting the discussion to the points along the optical axis and in the focal plane, we have
$$h(0,v)\propto\left(\frac{2J_{1}(v)}{v}\right)^{2},\quad h(u,0)\propto\left(\dfrac{\sin\left(\frac{u}{4}\right)}{\frac{u}{4}}\right)^{2},$$
that is,
$$\begin{aligned}\displaystyle I_{\mathrm{tot}}(0,v)&\displaystyle\propto\left(\frac{2J_{1}(v)}{v}\right)^{4},\\ \displaystyle I_{\mathrm{tot}}(u,0)&\displaystyle\propto\left(\dfrac{\sin\left(\frac{u}{4}\right)}{\frac{u}{4}}\right)^{4}.\end{aligned}$$
Compared to a conventional microscope, where \(I_{\mathrm{tot}}\approx h(u,v)\), the calculation of the full width at half-maximum ( ), representing the system resolution, leads to an improvement in resolution by a factor of \(\mathrm{1.4}\) [21.124, 21.125, 21.126, 21.34, 21.36].

21.2.4 Remarks and Comments

Comparisons between the ideal PSF in the case of strict confocality with that of conventional microscopes account for improvements in resolution. However, despite the use of this mathematical formalism for concrete situations, further drawbacks need to be highlighted. First, there is a natural relation between the pinhole size and the PSF: the more the pinhole size is increased, the more the confocal microscope response tends to fit conventional responses.

This means that in the case of dim or highly photosensitive specimens some compromise has to be found between the resolution and the amount of collected signals, according to the kind of analysis to be performed (whether a morphometric analysis or intensity analysis).

Second, the PSF is obviously dependent on many physical parameters, inter alia the refractive index of the sample, immersion medium, its turbidity, the degree of homogeneity of the sample, and the photochemical properties of the dyes used. For these reasons, the development of complicated computations often leads to poorly applicable results in practice, since conditions often change dramatically for the different measurements.

One of the most meaningful factors on which PSF depends is the refractive index mismatch between the objective immersion medium and that of the sample solution. This results in a loss of axial resolution and a corruption of the shape [21.127].

Table 21.1 reports the value of theoretical and experimental FWHM of confocal PSFs using different pinhole sizes. A sample of subresolution beads (Polyscience, diameter \(=(0.064\pm 0.009)\,{\mathrm{\upmu{}m}}\)) was imaged by means of a \(100\times\) Nikon oil-immersion objective (\(\text{NA}=1.3\); \(\text{WD}={\mathrm{0.20}}\,{\mathrm{mm}}\)) under argon laser excitation (\(\lambda={\mathrm{488}}\,{\mathrm{nm}}\)). Theoretical values are those expected (in the absence of mismatch) and are calculated by means of web-based deconvolution software (http://www.powermicroscope.com).

Table 21.1

FWHM of confocal point spread functions for different pinhole sizes

 

Oil (\(n=1.5\))

 

Lateral (nm)

Axial (nm)

 

Pinhole \({\mathrm{20}}\,{\mathrm{\upmu{}m}}\)

Pinhole \({\mathrm{50}}\,{\mathrm{\upmu{}m}}\)

Pinhole \({\mathrm{20}}\,{\mathrm{\upmu{}m}}\)

Pinhole \({\mathrm{50}}\,{\mathrm{\upmu{}m}}\)

Experimental

\({\mathrm{186}}\pm{\mathrm{6}}\)

\({\mathrm{215}}\pm{\mathrm{5}}\)

\({\mathrm{489}}\pm{\mathrm{6}}\)

\({\mathrm{596}}\pm{\mathrm{4}}\)

Theoretical

\(\mathrm{180}\)

\(\mathrm{210}\)

\(\mathrm{480}\)

\(\mathrm{560}\)

Table 21.2

Variation of lateral FWHM with focusing depth

 

Air

Glycerol

Oil

Depth

(\(\mathrm{\upmu{}m}\))

Lateral

(nm)

Axial

(nm)

Lateral

(nm)

Axial

(nm)

Lateral

(nm)

Axial

(nm)

\(\mathrm{0}\)

\({\mathrm{187}}\pm{\mathrm{8}}\)

\({\mathrm{484}}\pm{\mathrm{24}}\)

\({\mathrm{183}}\pm{\mathrm{14}}\)

\({\mathrm{495}}\pm{\mathrm{29}}\)

\({\mathrm{186}}\pm{\mathrm{6}}\)

\({\mathrm{489}}\pm{\mathrm{6}}\)

\(\mathrm{30}\)

\({\mathrm{244}}\pm{\mathrm{10}}\)

\({\mathrm{623}}\pm{\mathrm{9}}\)

\({\mathrm{221}}\pm{\mathrm{5}}\)

\({\mathrm{545}}\pm{\mathrm{12}}\)

\({\mathrm{197}}\pm{\mathrm{10}}\)

\({\mathrm{497}}\pm{\mathrm{21}}\)

\(\mathrm{60}\)

\({\mathrm{269}}\pm{\mathrm{11}}\)

\({\mathrm{798}}\pm{\mathrm{10}}\)

\({\mathrm{252}}\pm{\mathrm{7}}\)

\({\mathrm{628}}\pm{\mathrm{9}}\)

\({\mathrm{186}}\pm{\mathrm{12}}\)

\({\mathrm{496}}\pm{\mathrm{19}}\)

\(\mathrm{90}\)

\({\mathrm{277}}\pm{\mathrm{5}}\)

\({\mathrm{1063}}\pm{\mathrm{24}}\)

\({\mathrm{268}}\pm{\mathrm{8}}\)

\({\mathrm{797}}\pm{\mathrm{26}}\)

\({\mathrm{191}}\pm{\mathrm{9}}\)

\({\mathrm{484}}\pm{\mathrm{12}}\)

As can be seen from the reported values, the system resolution is worse along the optical axis and is strictly dependent on the pinhole size; these results are in accordance with what is expected from the above theory. Asymmetry of the plots in the real case is typical and becomes even more evident when focusing through different stratified media [21.127].

The theory, developed within the context of electromagnetic waves focusing across stratified media, suggests a progressive broadening of the PSF with respect to the focusing depth, becoming even more noticeable under refractive-index mismatch conditions. Furthermore, on a higher level of complexity, the coexistence of different refractive indices within the sample and the resulting artefacts can be considered.

As a consequence of this, the largest percentage of variation of the lateral FWHM, with respect to the focusing depth, goes from \({\mathrm{6}}\%\) (oil-immersed PSF), to \({\mathrm{48}}\%\) (air-immersed PSF), whereas the axial FWHM varies up to \({\mathrm{130}}\%\) (air-immersed PSF) (Table 21.2).

This phenomenon is related to a subsequent weakening of the signal with respect to the focusing depth, which turns out to be more evident in the case of refractive index mismatch. Table 21.3 gives typical observed values of the percentage of variation of the PSF intensity peak under different mismatch conditions and at different focusing depths (with reference to the coverslip).

Table 21.3

Variations in point spread function intensity with mismatch conditions and focusing depths

Medium

At \({\mathrm{30}}\,{\mathrm{\upmu{}m}}\) depth

(%)

At \({\mathrm{60}}\,{\mathrm{\upmu{}m}}\) depth

(%)

At \({\mathrm{90}}\,{\mathrm{\upmu{}m}}\) depth

(%)

Oil

\(\mathrm{3}\)

\(\mathrm{6}\)

\(\mathrm{7}\)

Glycerol

\(\mathrm{17}\)

\(\mathrm{27}\)

\(\mathrm{34}\)

Air

\(\mathrm{44}\)

\(\mathrm{51}\)

\(\mathrm{60}\)

21.2.5 Resolution and Three-Dimensional Optical Sectioning

Three-dimensional reconstruction of an object starting from the acquisition of two-dimensional (2-D) confocal slices is one of the most powerful procedures for morphological analysis and volume rendering, especially within biological sciences, where optical slicing allows information to be obtained from different planes of the specimen without being invasive, thus preserving the structure and functionality of the different parts.

Three-dimensional optical sectioning is intrinsically coupled with the axial resolution of the confocal microscope. For pinhole diameters smaller than \({\mathrm{1}}\,{\mathrm{AU}}\), the approximation of a point-like pinhole is used. For this case, the FWHM of the total PSF in the \(z\)-direction can be expressed as
$$r_{\mathrm{z}}=\frac{0.64\overline{\lambda}}{n-\sqrt{n^{2}-\text{NA}^{2}}}\;.$$
(21.3)
This expression describes the axial resolution and the effective optical slice thickness for the sectioning of the specimen. Here, \(\overline{\lambda}\) is
$$\overline{\lambda}\approx\sqrt{2}\left(\frac{\lambda_{\mathrm{em}}\lambda_{\mathrm{ex}}}{\sqrt{\lambda_{\mathrm{ex}}^{2}+\lambda_{\mathrm{em}}^{2}}}\right)$$
a mean wavelength. This technique is essentially based on an automatic fine \(z\)-stepping either of the objective or of the sample stage, coupled with the usual \(x\)\(y\) point-to-point scanning of the focal plane and image capturing.

Synchronous \(x\)\(y\)\(z\) scanning allows the collection of a set of in-focus 2-D images, which are less affected by signal cross-talk from other planes of the sample, as more strictly confocal conditions are respected.

This means that when a set of 2-D images is acquired at various focus positions and under certain conditions, in principle, the 3-D shape of the object can be recovered. However, the observed image \(o(x,y,z)\), produced by the true intensity distribution \(i(x,y,z)\), is corrupted by the characteristic PSF of the image formation system \(s(x,y,z)\), by noise stemming from different sources \(n(x,y,z)\), and by cross-information coming from different planes rather than from the focus one.

At a certain plane of focus \(z_{0}\) within the sample or, at discrete planes along the \(z\) axis, the simplest way to describe such a process for the \(j\)-th plane can be regarded as the following
$$\begin{aligned}\displaystyle o_{j}&\displaystyle=i_{j}\otimes s_{0}+i_{j-1}\otimes s_{j-1}+i_{j+1}\otimes s_{j+1}\\ \displaystyle&\displaystyle\quad+\text{(other plane contributions if relevant) }+n\;,\end{aligned}$$
(21.4)
where the subscripts on \(i\) and \(o\) refer to the \(z\) plane numbers, while the subscripts on \(s\) refer to the number of interplane spacings \(z\) away from the in-focus position at the actual \(j\)-th plane.

This relationship is usually transferred to the Fourier frequency domain, where the convolution operator becomes an algebraic multiplication [21.33]. Image restoration algorithms (deconvolution) aim to invert such equations in order to extract the true measured quantity \(i(x,y,z)\). Thus, a 3-D sample reconstruction is possible by directly piling up 2-D images. Therefore, further scale corrections are performed accounting for axial distortion phenomena linked to the refractive index mismatch.

The generic considerations for this method evidently demonstrate the crucial importance of getting to know the system performance under different working conditions, by means of its PSF. This knowledge will extend the possibilities of applying the confocal technique to a wide range of studies.

In practice, one wants to find the best estimate, according to some criterion, of \(i(x,y.z)\) through the knowledge of the observed images, the distortion or PSF of the image formation system, and the additive noise within a classical restoration scheme for space invariant linear systems [21.128, 21.129, 21.130, 21.33]. Figure 21.4a,b shows an example of digital restoration of microscopic data obtained after solving the appropriate set of equations. So far, this can be computationally done starting from any dataset of optical slices. An internet service, named power-up-your-microscope [21.127, 21.131], has become available, which produces the best estimate of \(i(x,y,z)\) according to the acquired dataset of optical slices. Interested readers can find information and check the service through the webpage http://www.power-microscope.com for free (Fig. 21.4a,b).

Fig. 21.4a,b

Comparison between 3-D views of a helicoidal biological sample before (a) and after (b) image processing utilizing 3-D deconvolution strategies

Image restoration is needed only to correct PSF distortions that are less than in the conventional case. Unfortunately, there is a drawback. In fact, during the excitation process of the fluorescent molecules, the whole thickness of the specimen is harmed by every scan, within an hourglass-shaped region [21.32]. This means that even though out-of-focus fluorescence is not detected, it is generated, with the negative effect of potential induction of those photobleaching and phototoxicity phenomena previously mentioned. The situation becomes particularly serious when there is the need for 3-D and temporal imaging coupled to the use of fluorochromes that require excitation in the ultraviolet regime [21.132, 21.133]. As earlier reported by König et al [21.66, 21.67], even using UVA (\(320{-}400\,{\mathrm{nm}}\)) photons may modify the activity of the biological system. DNA breaks, giant cell production, and cell death can be induced at radiant exposures of the order of magnitude of a few \(\mathrm{J{\,}cm^{2}}\), accumulated during 10 scans with a \({\mathrm{5}}\,{\mathrm{\upmu{}W}}\) laser scanning beam at approximately \({\mathrm{340}}\,{\mathrm{nm}}\) and a \({\mathrm{50}}\,{\mathrm{\upmu{}s}}\) pixel dwell time. In this context, TPE of fluorescent molecules provides an immediate practical advantage over confocal microscopy [21.1, 21.134, 21.135, 21.136, 21.137, 21.138, 21.139, 21.140, 21.141, 21.87]. In fact, reduced overall photobleaching and photodamage are generally acknowledged as major advantages of TPE in laser scanning microscopy of biological specimens [21.142, 21.143, 21.99], even though photobleaching in the focal plane can be accelerated [21.143]. However, the excitation intensity has to be kept low considering a regime under \({\mathrm{10}}\,{\mathrm{mW}}\) of average power as a normal operation mode. When laser power is increased above \({\mathrm{10}}\,{\mathrm{mW}}\), some nonlinear effects might arise, evidenced through abrupt rising of the signals [21.144]. Moreover, photothermal effects should be induced, especially when focusing on single-molecule detection schemes [21.145].

21.2.6 Two-Photon Excitation

Let us now move from conventional excitation of fluorescence as used in computational optical sectioning and confocal microscopy to a special case of multiphoton excitation, i. e., TPE. All considerations can be easily extended to TPE. The physical suppression of contributions from adjacent planes is realized in a completely different way, thus moving again to 3-D optical sectioning ability.

In TPE, two low-energy photons are involved in the interaction with absorbing molecules. The excitation process of a fluorescent molecule can take place only if two low-energy photons are able to interact simultaneously with the very same fluorophore. The time scale for simultaneity is the time scale of molecular energy fluctuations at photon energy scales, as determined by the Heisenberg uncertainty principle, i. e., \(E-16{-}E-15\,{\mathrm{s}}\) [21.146]. These two photons do not necessarily have to be identical, but their wavelengths, \(\lambda_{1}\) and \(\lambda_{2}\), have to be such that
$$\lambda_{\mathrm{IP}}\cong\left(\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}\right)^{-1},$$
(21.5)
where \(\lambda_{\mathrm{1P}}\) is the wavelength needed to prime fluorescence emission in a conventional one-photon absorption process according to the energy relation given in (21.1). This situation, compared to the conventional one-photon excitation process shown in Fig. 21.5a,b, is illustrated using a Perrin–Jablonski-like diagram . It is worth noting that for practical reasons the experimental choice is usually such that [21.1, 21.147, 21.148]
$$\lambda_{2\mathrm{p}}=2\lambda_{\mathrm{IP}}\;,\quad\lambda_{1}=\lambda_{2}\approx 2\lambda_{\mathrm{IP}}$$
(21.6)
and
$$\Updelta E_{\mathrm{g}}=\frac{2hc}{\lambda_{\mathrm{IP}}}\;.$$
(21.7)
Fig. 21.5a,b

Perrin–Jablonsky-like diagram illustrating the difference between conventional (a) and two-photon (b) excitation. In the second case, photons delivering one-half of the energy conventionally needed for bringing the fluorescent molecule to an excited state are used

Considering this as a nonresonant process and assuming the existence of a virtual intermediate state, the resident time, \(\tau_{\mathrm{virt}}\), in this intermediate state should be calculated using the time–energy uncertainty consideration for TPE
$$\Updelta E_{\mathrm{g}}\tau_{\text{virt}}\cong\frac{\hbar}{2}\;,$$
(21.8)
where \(\hbar=h/(2\uppi)\). It follows that
$$\tau_{\text{virt}}\cong E-15{-}E-16\,{\mathrm{s}}\;.$$
(21.9)
This is the temporal window available for two photons to coincide in the virtual state.

So far, in a TPE process it is, hence, crucial to combine sharp spatial focusing with temporal confinement of the excitation beam.

The process can be extended to \(n\)-photons requiring higher photon densities temporally and spatially confined. Thus, near-infrared ( ; circa \(680{-}1100\,{\mathrm{nm}}\)) photons can be used to excite UV and visible electronic transitions producing fluorescence. The typical photon flux densities are of the order of more than \(\mathrm{10^{24}}\) photons \(\mathrm{cm^{-2}{\,}s^{-1}}\), which implies intensities around MW–TW \(\mathrm{cm^{-2}}\) [21.97]. An elegant treatment in terms of quantum theory for two-photon transition was proposed by Nakamura [21.149] using perturbation. He clearly described the process by a time-dependent Schrödinger equation, where the Hamiltonian contains electric dipole interaction terms. Using a perturbation expansion, the first-order solution is found to be related to one-photon excitation, while higher-order solutions are related to \(n\)-photon ones [21.3]. The dependence of TPE on \(I^{2}\) should be evident and is demonstrated by using simple arguments [21.150].

The fluorescence intensity per molecule, \(I_{\mathrm{f}}(t)\), can be considered to be proportional to the molecular cross-section \(\delta_{2}(\lambda)\) and to the square of \(I(t)\) as follows
$$I_{\mathrm{f}}(t)\propto\delta_{2}I(t)^{2}\propto\delta_{2}P(t)^{2}\left(\uppi\frac{\text{NA}^{2}}{hc\lambda}\right)^{2},$$
(21.10)
where \(P(t)\) is the laser power and NA is the numerical aperture of the focusing objective lens. The last term of (21.10) simply takes care of the distribution in time and space of the photons by using the paraxial approximation in an ideal optical system [21.151].
It follows that the time-averaged two-photon fluorescence intensity per molecule within an arbitrary time interval \(T\), \(\langle I_{\mathrm{f}}(t)\rangle\), can be written as
$$\begin{aligned}\displaystyle\langle I_{\mathrm{f}}(t)\rangle&\displaystyle=\frac{1}{T}\int_{0}^{\mathrm{T}}I_{\mathrm{f}}(t)\mathrm{d}t\\ \displaystyle&\displaystyle\propto\delta_{2}\left[\uppi\frac{\text{NA}^{2}}{hc\lambda}\right]^{2}\frac{1}{T}\int_{0}^{\mathrm{T}}P(t)^{2}\mathrm{d}t\end{aligned}$$
(21.11)
in the case of continuous wave ( ) laser excitation.
Now, because the present experimental situation for TPE is related to the use of ultrafast lasers, we consider that for a pulsed laser \(T=1/f_{\mathrm{P}}\), where \(f_{\mathrm{P}}\) is the pulse repetition rate. This implies that a CW laser beam, where \(P(t)=P_{\mathrm{ave}}\), allows transformation of (21.11) into
$$\langle I_{\mathrm{f},\mathrm{cw}}(t)\rangle\propto\delta_{2}\,P_{\mathrm{ave}}^{2}\left(\uppi\frac{\text{NA}^{2}}{hc\lambda}\right)^{2}.$$
(21.12)
For a pulsed laser beam with pulse width, \(\tau_{\mathrm{p}}\), repetition rate, \(f_{\mathrm{p}}\), and average power
$$P_{\mathrm{ave}}=DP_{\text{peak}}(t)\;,$$
where \(D=\tau_{\mathrm{p}}\,f_{\mathrm{p}}\), the approximated \(P(t)\) profile can be described as
$$P(t)=\begin{cases}\frac{P_{\mathrm{ave}}}{D}&\text{for }0<t<\tau_{\mathrm{p}}\\ 0&\text{for }\tau_{\mathrm{p}}<t<\left(\frac{1}{f_{\mathrm{p}}}\right).\end{cases}$$
(21.13)
We can write (21.12) as
$$\begin{aligned}\displaystyle\langle I_{\mathrm{f},\mathrm{p}}(t)\rangle&\displaystyle\propto\delta_{2}\frac{P_{\mathrm{ave}}^{2}}{\tau_{\mathrm{p}}^{2}f_{\mathrm{P}}^{2}}\left(\uppi\frac{\text{NA}^{2}}{hc\lambda}\right)^{2}\frac{1}{T}\int_{0}^{\tau_{\mathrm{p}}}\mathrm{d}t\\ \displaystyle&\displaystyle=\delta_{2}\frac{P_{\mathrm{ave}}^{2}}{\tau_{\mathrm{p}}f_{\mathrm{P}}}\left(\uppi\frac{\text{NA}^{2}}{hc\lambda}\right)^{2}.\end{aligned} $$
(21.14)

The conclusion here is that CW and pulsed lasers operate at the very same excitation efficiency, i. e., fluorescence intensity per molecule, if the average power of the CW laser is kept higher by a factor of \(1/\sqrt{\tau\,f_{\mathrm{P}}}\). This means that \({\mathrm{10}}\,{\mathrm{W}}\) delivered by a CW laser, allowing the same efficiency of conventional excitation performed at approximately \({\mathrm{10^{-1}}}\,{\mathrm{mW}}\), is nearly equivalent to \({\mathrm{30}}\,{\mathrm{mW}}\) for a pulsed laser [21.152].

21.3 Fluorescent Molecules Under the TPE Regime

The above steps lead to the most popular relationship reported below, which is related to the practical situation of a train of beam pulses focused through a high numerical aperture objective, with a duration \(\tau_{\mathrm{p}}\) and repetition rate \(f_{\mathrm{p}}\). In this case, the probability, \(n_{\mathrm{a}}\), that a certain fluorophore simultaneously absorbs two photons during a single pulse, in the paraxial approximation, is [21.1]
$$n_{\mathrm{a}}\propto\frac{\delta_{2}\,P_{\mathrm{ave}}^{2}}{\tau_{\mathrm{p}}f_{\mathrm{p}}^{2}}\left(\frac{\text{NA}^{2}}{2hc\lambda}\right)^{2},$$
(21.15)
where \(P_{\mathrm{ave}}\) is the time-averaged power of the beam and \(\lambda\) is the excitation wavelength. Introducing \({\mathrm{1}}\,{\mathrm{GM}}\) (Goppert–Mayer) \(={\mathrm{10^{-58}}}\) (\(\mathrm{m^{4}{\,}s}\)), for a \(\delta_{2}\) of approximately \({\mathrm{10}}\,{\mathrm{GM}}\) per photon [21.1, 21.153], focusing through an objective of \(\text{NA}> 1\), an average incident laser power of \(\approx 1{-}50\,{\mathrm{mW}}\), and operating at a wavelength ranging from \(\mathrm{680}\) to \({\mathrm{1100}}\,{\mathrm{nm}}\) with \(80{-}150\,{\mathrm{fs}}\) pulse width and \(80{-}100\,{\mathrm{MHz}}\) repetition rate, would saturate the fluorescence output as for one-photon excitation. This suggests that for optimal fluorescence generation, the desirable repetition time of pulses should be on the order of a typical excited-state lifetime, which is a few nanoseconds for commonly used fluorescent molecules. For this reason, the typical repetition rate is around \({\mathrm{100}}\,{\mathrm{MHz}}\). A further condition that makes (21.15) valid is that the probability that each fluorophore will be excited during a single pulse has to be smaller than 1. The reason lies in the observation that during the pulse time (\({\mathrm{10^{-13}}}\,{\mathrm{s}}\) of duration and a typical excited-state lifetime in the \({\mathrm{10^{-9}}}\,{\mathrm{s}}\) range) the molecule has insufficient time to relax to the ground state. This can be considered a prerequisite for absorption of another photon pair. Therefore, whenever \(n_{\mathrm{a}}\) approaches unity, saturation effects start to occur. The use of (21.15) makes it possible to choose optical and laser parameters that maximize excitation efficiency without saturation. In the case of saturation, the resolution declines, and the image becomes worse [21.154]. It is also evident that the optical parameter for enhancing the process in the focal plane is the lens' numerical aperture, NA, even if the total fluorescence emitted is independent of this parameter, as was shown by Xu [21.153]. This is usually confined around \(1.3{-}1.4\) as the maximum value. Now, it is possible to estimate \(n_{\mathrm{a}}\) for a common fluorescent molecule like fluorescein, which possesses a two-photon cross-section of \({\mathrm{38}}\,{\mathrm{GM}}\) at \({\mathrm{780}}\,{\mathrm{nm}}\) [21.155].

To this end, we can use \(\text{NA}=1.4\), a repetition rate at \({\mathrm{100}}\,{\mathrm{MHz}}\), and a pulse width of \({\mathrm{100}}\,{\mathrm{fs}}\) within a range of \(P_{\mathrm{ave}}\) values of 1, 10, 20, and \({\mathrm{50}}\,{\mathrm{mW}}\), and substituting the proper values in (21.15), we obtain \(n_{\mathrm{a}}\cong 5930P^{2}_{\mathrm{ave}}\). This result for \(P_{\mathrm{ave}}=1\), 20, as a function of 1, 10, 20, and \({\mathrm{50}}\,{\mathrm{mW}}\), gives values of \(\mathrm{5.93\times 10^{-3}}\), \(\mathrm{5.93\times 10^{-1}}\), \(\mathrm{1.86}\), and \(\mathrm{2.965}\), respectively. It is evident that saturation begins to occur at \({\mathrm{10}}\,{\mathrm{mW}}\) [21.150].

The related rate of photon emission per molecule, at a nonsaturation excitation level, in the absence of photobleaching [21.143, 21.156], is given by \(n_{\mathrm{a}}\) multiplied by the repetition rate of the pulses. This means approximately \(\mathrm{5\times 10^{7}}\) photons \(\mathrm{s^{-1}}\) in both cases. It is worth noting that, when considering the effective fluorescence emission, a further factor given by the so-called quantum efficiency of the fluorescent molecules should also be considered. At present, the quantum efficiency value is usually known from conventional one-photon excitation data [21.11].

Now, even if the quantum-mechanical selection rules for TPE differ from those for one-photon excitation, several common fluorescent molecules can be used. Unfortunately, knowing the one-photon cross-section for a specific fluorescent molecule does not allow any quantitative prediction of the two-photon trend, except for a sort of rule of thumb. This simple rule states that, in general, a TPE cross-section may be expected to peak at double the wavelength needed for one-photon excitation. However, the cross-section parameter has been measured for a wide range of dyes [21.155, 21.157, 21.158]. It is worth noting that due to the increasing dissemination of TPE microscopy, new ad hoc organic molecules, endowed with large engineered two-photon absorption cross-sections, have recently been developed [21.158, 21.159, 21.160]. Figure 21.6 summarizes the properties of some commonly used fluorescent molecules under two-photon excitation [21.140, 21.157]. TPE fluorescence from NAD(P)H, flavoproteins [21.140, 21.161], tryptophan, and tyrosine in proteins [21.162] has been measured. In addition, the autofluorescent biological proteins, such as the GFP and its molecular variants, are important molecular markers [21.134, 21.163, 21.164, 21.165, 21.166]. Their TPE cross-sections are between 6 and \({\mathrm{40}}\,{\mathrm{GM}}\) [21.167]. As a comparison, consider that the cross-section for NADH, at the excitation maximum of \({\mathrm{700}}\,{\mathrm{nm}}\), is approximately \({\mathrm{0.02}}\,{\mathrm{GM}}\) [21.140]. Moving to quantum dots, there is an increase of cross-section up to \({\mathrm{2000}}\,{\mathrm{GM}}\).

Fig. 21.6

Two-photon cross-sections for popular fluorescent molecules as a function of the excitation wavelength. Bars indicate the emission range of some common laser sources utilized in TPE microscopy and spectroscopy

21.4 Optical Consequences of TPE

In terms of optical consequences, the two-photon effect limits the excitation region to within a subfemtoliter volume. The 3-D confinement of the TPE volume can be understood with the aid of optical diffraction theory [21.151]. Using excitation light with wavelength \(\lambda\), the intensity distribution at the focal region of an objective with numerical aperture \({\text{NA}}=\sin(\alpha)\) is described (see also (21.2)) in the paraxial regime [21.151, 21.168] by
$$I(u,v)=\left|2\int_{0}^{1}J_{0}(v\rho)\mathrm{e}^{-(\mathrm{i}/2)u{\rho^{2}}}\rho\mathrm{d}\rho\right|^{2},$$
(21.16)
where \(\rho\) is a dimensionless radial, \(J_{0}\) is the zeroth-order Bessel function, \(\rho\) is a radial coordinate in the pupil plane, and \(u=8\uppi\sin^{2}(\alpha/2)z/\lambda\) and \(v=2\uppi\sin(\alpha)r/\lambda\) are dimensionless axial and radial coordinates, respectively, normalized to the wavelength [21.36]. Now, the intensity of fluorescence distribution within the focal region has an \(I(u,v)\) behavior for the one-photon case and \(I^{2}(u/2,v/2)\) for the TPE case, as demonstrated above. The arguments of \(I^{2}(u/2,v/2)\) take into proper account the fact that in the latter case, wavelengths are utilized that are approximatively twice those used for one-photon excitation. As compared with the one-photon case, the TPE intensity distribution is axially confined [21.125, 21.136, 21.169]. In fact, considering the integral over \(v\), keeping \(u\) constant, its behavior is constant along \(z\) for the one-photon case and has a half-bell shape for TPE. This behavior, which is better discussed in Wilson [21.141], Torok, and Sheppard [21.126], and Jonkman and Stelzer [21.125], explains the three-dimensional discrimination property in TPE.

Now, the most interesting aspect is that the excitation power falls off as the square of the distance from the lens focal point, within the approximation of a conical illumination geometry. In practice, this means that the quadratic relationship between the excitation power and the fluorescence intensity results in the fact that TPE falls off as the fourth power of distance from the focal point of the objective. This fact implies that those regions away from the focal volume of the objective lens, directly related to the numerical aperture of the objective itself, therefore, do not suffer photobleaching or phototoxicity effects and do not contribute to the signal detected when a TPE scheme is used. Because they are simply not involved in the excitation process, a confocal-like effect is obtained without the necessity of a confocal pinhole. It is also immediately evident that in this case, an optical sectioning effect is obtained. In fact, the observed image \(o(x,y,z)\) at a plane \(j\), produced by the true fluorescence distribution \(i(x,y,z)\) at plane \(j\), distorted by the microscope through \(s\), plus noise \(n\), again corresponds to the confocal ideal situation where contributions from adjacent \(k\) planes can be set to zero, as in the confocal situation: \(o_{j}=i_{j}s_{j}+n\).

This means that TPE microscopy is intrinsically three dimensional. It is worth noting that the optical sectioning effect is obtained in a very different way with respect to the confocal solution. No fluorescence has to be removed from the detection pathway. In this case, it should be possible to collect as much fluorescence as possible. In fact, fluorescence can come only and exclusively from the small focal volume traced in Fig. 21.8a,b, which also shows a comparison with the confocal mode, that is of the order of a fraction of a femtoliter.

Fig. 21.8a,b

The two different modalities for selecting 3-D information under a confocal (a) and a TPE regime (b). In the confocal case, the selection is realized during the emission process. The different case of two-photon excitation shows how the 3-D selection can be realized during the fluorescence excitation process

In TPE, over \({\mathrm{80}}\%\) of the total intensity of fluorescence comes from a \(\mathrm{700}\) to \({\mathrm{1000}}\,{\mathrm{nm}}\)-thick region about the focal point for objectives with numerical apertures in the range of \(1.2{-}1.4\) [21.125, 21.126, 21.141, 21.34, 21.36]. This fact implies a reduction in background that allows compensation of the poorer spatial resolution compared to the single-photon confocal mode due to the longer wavelength utilized. However, the utilization of an infrared wavelength instead of UV-visible ones also allows deeper penetration than in the conventional case [21.156, 21.170, 21.171]. The long wavelengths used in TPE, or in general in multiphoton excitation, will be scattered less than the ultraviolet-visible wavelengths used for conventional excitation [21.172]. Hence, deeper targets within a thick sample can be reached. Of course, for fluorescence light, scattering on the way back can be overcome by acquiring the emitted fluorescence using a large area detector and collecting not only ballistic photons [21.148, 21.173, 21.174].

21.5 The Optical Setup

A TPE architecture including confocal modality includes the following: a high peak-power laser delivering moderate average power (femtosecond or picosecond pulsed at a relatively high repetition rate) emitting infrared or near-infrared wavelengths (\(650{-}1100\,{\mathrm{nm}}\)), CW laser sources for confocal modes, a laser beam scanning system or a confocal laser scanning head, high numerical aperture objectives (\(> {\mathrm{1}}\)), a high-throughput microscope pathway, and a high-sensitivity detection system [21.11, 21.117, 21.124, 21.135, 21.148, 21.173, 21.175, 21.176, 21.177, 21.178, 21.179, 21.180, 21.181, 21.182, 21.183, 21.184, 21.185]. Figure 21.8 shows a general scheme for a TPE microscope incorporating a confocal mode.

Fig. 21.8

Optical configuration for a TPE microscope operating in a descanned (top) and nondescanned (bottom) mode

In typical TPE or confocal microscopes, images are built by raster scanning the \(x\)\(y\) mirrors of a galvanometrically driven mechanical scanner [21.48]. This fact implies that image formation speed is mainly determined by the mechanical properties of the scanner, i. e., for single line scanning it is of the order of milliseconds. Faster beam-scanning schemes can be realized, even if the eternal triangle of compromise should be considered for sensitivity, spatial resolution, and temporal resolution. While the \(x\)\(y\) scanners provide lateral focal-point scanning, axial scanning can be achieved by means of different positioning devices, the most popular being a belt-driven system using a DC motor and a single objective piezo nanopositioner. Usually, it is possible to switch between confocal and TPE modes retaining \(x\)\(y\)\(z\) positioning on the sample being imaged [21.147, 21.155]. Acquisition and visualization are generally completely computer-controlled by dedicated software. Figure 21.9 shows a TPE microscope.

Fig. 21.9

The TPE setup at LAMBS, MicroScoBio Research Center of the University of Genoa (from left to right: Ilaria Testa, Paolo Bianchini, and Davide Mazza)

Let us now consider two popular approaches that can be used to perform TPE microscopy, namely, the descanned and non-descanned modes. They are sketched in Fig. 21.8. The former uses the very same optical pathway and mechanism employed in confocal laser scanning microscopy. The latter mainly optimizes the optical pathway by minimizing the number of optical elements encountered on the way from the sample to detectors, and increases the detector area. The TPE nondescanned mode provides very good performances giving a superior signal-to-noise ratio ( ) inside strongly scattering samples [21.135, 21.140, 21.186, 21.187].

In the descanned approach, pinholes are removed or set to their maximum aperture, and the emission signal is captured using an excitation scanning device on the back pathway. For this reason, it is called the descanned mode. In the latter, the confocal architecture has to be modified in order to increase the collection efficiency; pinholes are removed and the emitted radiation is collected using dichroic mirrors on the emission path or external detectors without passing through the galvanometric scanning mirrors. A high-sensitivity detection system is another critical issue [21.140, 21.148, 21.188].

The fluorescence emitted is collected by the objective and transferred to the detection system through a dichroic mirror along the emission path (Fig. 21.8). Due to the high excitation intensity, an additional barrier filter is needed to avoid mixing the excitation and emission light at the detection system,which is differently placed depending on the acquisition scheme being used. Photodetectors that can be used include photomultiplier tubes, avalanche photodiodes, and CCD cameras [21.117, 21.189]. Photomultiplier tubes are the most commonly used. This is due to their low cost, good sensitivity in the blue–green spectral region, high dynamic range, large size of the sensitive area, and single-photon counting mode availability [21.190]. They have a quantum efficiency around \(20{-}40\%\) in the blue–green spectral region that drops down to \(<{\mathrm{1}}\%\) moving to the red region. This is a good condition, especially in MPE mode, because it is desirable to reject as much as possible wavelengths above \({\mathrm{680}}\,{\mathrm{nm}}\) that are mainly used for excitation. Another advantage is that the large size of the sensitive area of photomultiplier tubes allows efficient collection of signals in the nondescanned mode within a dynamic range of the order of \(\mathrm{10^{8}}\). Avalanche photodiodes are excellent in terms of sensitivity exhibiting quantum efficiency close to \(70{-}80\%\) in the visible spectral range. Unfortunately, they are high in cost and the small active photosensitive area, \(<{\mathrm{1}}\,{\mathrm{mm}}\) size, could introduce drawbacks in the detection scheme and requires special descanning optics [21.191]. CCD cameras are used in video rate multifocal imaging [21.148, 21.192]. However, once the best quality image possible has been obtained, image restoration algorithms can be applied to enhance the features of interest to the biological researcher and to improve the quality of data to be used for three-dimensional modeling, such as those used for single-photon optical sectioning microscopy, available at http://www.powermicroscope.com [21.128, 21.130, 21.131, 21.193, 21.194, 21.195, 21.196, 21.197, 21.33].

Laser sources, as often happens in optical microscopy, represent an important resource, especially in fluorescence microscopy [21.100, 21.198]. For nonresonant TPE, owing to the comparatively low TPE cross-sections of fluorophores, high-photon flux densities are required, \(> {\mathrm{10^{24}}}\) photons \(\mathrm{cm^{-2}{\,}s^{-1}}\) [21.45]. Using radiation in the spectral range of \(600{-}1100\)nm for TPE, excitation intensities in the MW–GW \(\mathrm{cm^{-2}}\) range are required. This high energy can be obtained by the combined use of focusing lens objectives and CW [21.199, 21.200] or pulsed [21.1] laser radiation of \({\mathrm{50}}\,{\mathrm{mW}}\) mean power or less [21.148, 21.150]. TPE microscopes have been realized using CW, femtosecond, and picosecond laser sources [21.10, 21.11, 21.147, 21.84]. Since the original successful experiments in TPE microscopy, advances have been made in the technological field of ultrashort pulsed lasers. Today, laser sources suitable for TPE can be described as turnkey compact systems [21.147, 21.201, 21.202].

Figure 21.10 shows an ultrafast Ti:sapphire laser source. The emission range between \(\mathrm{700}\) and \({\mathrm{1050}}\,{\mathrm{nm}}\) of the Ti:sapphire laser allows a large number of commonly used fluorescent molecules to be excited. Other laser sources used for TPE are Cr-LiSAF, pulse-compressed Nd-YLF in the femtosecond regime, and mode-locked Nd-YAG and picosecond Ti-sapphire lasers in the picosecond regime [21.198, 21.202]. Most of the laser sources used for TPE operate in a mode-locking mode. This endows the laser with the ability to generate a train of very short pulses by modulating the gain or excitation of a laser at a frequency with a period equal to the round-trip time of a photon within the laser cavity [21.100, 21.201] (Fig. 21.11). The resulting pulse width is in the \(50{-}150\,{\mathrm{fs}}\) regime. The parameters that are more relevant in the selection of the laser source are average power, pulse width and repetition rate, and wavelength also according to (21.15). The most popular features for an infrared pulsed laser are \({\mathrm{700}}\,{\mathrm{mW}}\) to \({\mathrm{1}}\,{\mathrm{W}}\) average power, \(80{-}100\,{\mathrm{MHz}}\) repetition rate, and \(100{-}150\,{\mathrm{fs}}\) pulse width.

Fig. 21.10

Typical laser sources in use for TPE microscopy

Fig. 21.11

Laser emission time scale for TPE excitation: a short pulse at high photon density is released for approximately \({\mathrm{100}}\,{\mathrm{fs}}\); this laser shot is able to prime fluorescence without damaging the sample so fluorescence occurs in the next few nanoseconds. The laser is silent for \({\mathrm{10}}\,{\mathrm{ns}}\) and then delivers a new high-density photon pulse. This modality allows TPE to be experienced at tolerable time-averaged power

At present, the use of short pulses and small duty cycles are mandatory to allow image acquisition in a reasonable time while using power levels that are biologically tolerable [21.133, 21.171, 21.203, 21.204, 21.205, 21.206, 21.45, 21.66, 21.67]. To minimize pulse width dispersion problems König [21.45] suggested working with pulses around \(150{-}200\,{\mathrm{nm}}\), and this constitutes a very good compromise both for pulse stretching and sample viability. It should always be remembered that a shorter pulse broadens more than a longer one. Pulse width measurement is a very delicate issue. In fact, because it is not very easy to measure it at the focal volume within the sample, little can be said definitely about it [21.199, 21.207, 21.208]. Although users do not perform measurement of the pulse width at the sample when they use two-photon microscopy, which would require a specific procedure that, even if not too complex for a researcher in the field, could be irksome for the majority of users, it is a reasonable approximation to assume that at the focal volume, \(1.5{-}2\) times temporal pulse broadening occurs using high-quality optics [21.148, 21.208]. As an example, for a measured laser pulse width of about \({\mathrm{100}}\,{\mathrm{fs}}\), an estimate at the sample is about \(150{-}180\,{\mathrm{fs}}\) under favorable experimental conditions, sample characteristics included. Sample properties are mentioned, because for thick samples the role played by thickness, also in terms of pulse width broadening, is not so obvious [21.156, 21.209, 21.210, 21.211].

21.6 Comparison of Confocal and Two-Photon Excitation Microscopy

Confocal microscopy, in the authors' opinion, constitutes one of the most significant advances in optical microscopy within the past decades and has become a powerful investigative tool for the molecular, cellular, and developmental biologist, the materials scientist, the biophysicist, and the electronic engineer. It is entirely compatible with the range of classical light microscopic techniques, and, at least in scanned beam instruments, can be applied to the same specimens on the same optical microscope stage. Its peculiar advantages result in its ability to generate multidimensional (\(x\)\(y\)\(z\)\(t\)) images by noninvasive optical sectioning with a virtual absence of out-of-focus blur, its capacity for multiparametric imaging of multiply labeled samples, and its property of investigating at microscopic resolution large objects as a result of the rejection of scattered light. So far, the advent of confocal microscopy in the mid-1980s has favored the rapid spreading of two and multiphoton excitation microscopy, since Denk's report at the beginning of the 1990s, bringing dramatic changes in designing experiments that utilize fluorescent molecules and, more specifically, in fluorescence 3-D optical microscopy.

While confocal microscopy is moving to spectral and fast-scanning architectures in terms of acquisition, it is mainly two-photon microscopy that occupies the scene of advances in fluorescence optical microscopy. TPE microscopy, with its intrinsic three-dimensional resolution, the absence of background fluorescence, and the attractive possibility of exciting UV excitable fluorescent molecules, thus increasing sample penetration, constitutes significant progress in science. In fact, in a TPE scheme two \({\mathrm{720}}\,{\mathrm{nm}}\) photons combine to produce the very same fluorescence conventionally primed at \(\approx{\mathrm{360}}\,{\mathrm{nm}}\), to be utilized in a classical confocal microscope using conventional excitation of fluorescent molecules. The excitation of the fluorescent molecules bound to the specific components of the biological systems being studied mainly takes place (\({\mathrm{80}}\%\)) in an excitation volume of the order of magnitude of \({\mathrm{0.1}}\,{\mathrm{fl}}\). This results in an intrinsic 3-D optical sectioning effect. What is invaluable for cell imaging and, in particular, for live-cell imaging, is the fact that weak endogenous one-photon absorption and highly localized spatial confinement of the TPE process dramatically reduce phototoxicity stress. To summarize the unique characteristics and advantages of TPE we recall the following properties:
  1. 1.

    Spatially confined fluorescence excitation in the focal plane of the specimen can be considered the key feature of TPE microscopy. It is one of the advantages over confocal microscopy, where fluorescence emission occurs across the entire thickness of the sample being excited by the scanning laser beam. A strong implication is that there is no photon signal from sources out of the geometric position of the optical focus within the sample. Therefore, the SNR increases, photo degradation effects decrease, and optical sectioning is immediately available without the need for pinhole or deconvolution algorithms. In addition, very efficient acquisition schemes can be implemented, such as the nondescanned one operating at an excellent signal-to-noise ratio.

     
  2. 2.

    The use of near-infrared/IR wavelengths permits examination of thick specimens in depth. This is due to the fact that, apart from some cases such as pigmented samples and portions of the absorption spectral window of water, cells and tissues absorb poorly in the near-IR/IR region. Cellular damage is globally minimized, thus allowing cell viability to be prolonged with long-term 3-D sessions. Moreover, scattering is reduced and deeper targets can be reached with fewer problems than in one-photon excitation. The depth of penetration can be up to \({\mathrm{0.5}}\,{\mathrm{mm}}\). In addition, whereas in one-photon excitation, the emission wavelength is comparatively close to the excitation one (about \(50{-}200\,{\mathrm{nm}}\) longer), in TPE the fluorescence emission occurs at a substantially shorter wavelength and at a larger spectral distance than in one-photon excitation. Thus, separation of the excitation light and the emitted light can be easily performed.

     

Continuing research in this field is focused on very intriguing problems (http://www.focusonmicroscopy.org offers a complete scenario of the evolution of three-dimensional microscopy in early 2000s), such as local heating from absorption of IR light by water at high laser power [21.212] and photothermal effects on fluorescent molecules [21.145], phototoxicity from long-wavelength IR excitation and short wavelength fluorescence emission [21.144, 21.171, 21.205, 21.213, 21.45], photoactivation and photocycling of visible fluorescent proteins [21.214, 21.79, 21.82], development of new fluorochromes better suited for TPE and multiphoton excitation [21.159, 21.160], and the investigation of the cross-sections of uncharacterized molecules [21.215, 21.216].

One of the major benefits in setting up an MPE microscope is the flexibility in choosing the measurement modality favored by the simplification of the optical design. In fact, a TPE microscope offers a greater variety of measurement options without changing any optics or hardware. This means that during the very same experiments real multimodal information can be obtained from the specimen being studied [21.217, 21.55], see Fig. 21.12a-da–d. Moreover, the usefulness of the TPE scheme for spectroscopic and lifetime studies [21.175, 21.218, 21.61, 21.65, 21.69], for optical data storage and microfabrication [21.219, 21.220], and for single-molecule detection [21.140, 21.191, 21.71, 21.75, 21.76] has been well documented. Other very interesting applications involve the study of impurities affecting the growth of protein crystals [21.221], TPE imaging in the field of plant biology [21.222], and measurements in living systems [21.138, 21.214, 21.223, 21.224, 21.225]. Here, the combination of MPE and second-harmonic generation offers the opportunity to investigate the morphometric properties on the basis of the microstructure of blood cells [21.226]. Another promising field is the investigation of complex formation where the TPE properties will improve the information that is accessible [21.62]. Another, more indirect usage that provides a look at the sample with nanometer resolution is the excitation of an evanescent wave at a metal surface [21.227]. For microscopic purposes, the evanescent wave needs to be localized at a nanoparticle or a fine metal tip [21.228, 21.229]. The MPE microscope can also be used as an active device, with increasing applications related to nanosurgery [21.45], selective uncaging of caged compounds [21.230], and photodynamic therapy [21.140, 21.231]. Recently, TPE microscopy, even if in an evanescent-field-induced configuration, was extended to large-area structures of the order of square centimeters [21.232]. This has application in the realization of biosensing platforms, such as genomic and proteomic microarrays based upon large planar waveguides. It is easy to perceive that the range of applicability of MPE microscopes is rapidly increasing in the biomedical, biotechnological, and biophysical sciences and is expanding to clinical applications [21.11, 21.29, 21.84].

Fig. 21.12a-d

Multiple excitation of three fluorescent dyes using \({\mathrm{740}}\,{\mathrm{nm}}\) under a TPE regime. The conventional excitation would have required the utilization of \(\mathrm{360}\) or \(\mathrm{405}\), \(\mathrm{488}\), and \({\mathrm{543}}\,{\mathrm{nm}}\), laser lines. The final image (d) is realized by merging the three subsets. (This image was acquired by students of the Biotechnology School during the course of Advanced Microscopy Techniques activated at the University of Genoa, academic year 2005. Advisors: Grazia Tagliafierro and Alberto Diaspro)

21.7 Super-Resolved Imaging of Biological Systems

The field of fluorescence light microscopy offers an incredibly wide and still growing variety of new imaging capabilities with a special focus on biology [21.233, 21.234, 21.235, 21.236, 21.237, 21.238]. It is self-evident that fluorescence light microscopy is unique for cellular and molecular biology in providing the chance to get direct insight into living cells at subcellular and molecular spatial resolution [21.239]. Developments in microscope architectures, light sensors, and image processing, and image formation models coupled with the specificity given by fluorescent labels allow us to paint in an incredible way what is going on in biological cells. Advantages were already clear some decades ago [21.112], and today we can indicate a precise roadmap in the domain of super-resolved fluorescence microscopy or optical nanoscopy  [21.233, 21.234, 21.237, 21.240, 21.241, 21.242, 21.243, 21.244, 21.245, 21.246].

The optical microscopy scenario reported in Fig. 21.13 is in continuing evolution and technologically rich. From the point of view of a researcher neither expert in microscopy nor in optics, it can be difficult to match the most appropriate imaging techniques to biological, medical, biomedical, or biophysical questions. At the very same time, when the potential impact of a certain optical approach is understood, new cutting-edge questions can be posed. However, one point is immediately evident from the optical microscopy framework shown in Fig. 21.13. Today, it is more obvious than it was in the past that we are dealing with two major approaches to form images under the microscope, namely: the optical approach and the probe approach [21.247, 21.248]. Pushing the spatial resolution limit by means of the optical approach is very intriguing and has allowed us to get interesting results that, at the end, were limited by the use of optical lenses and visible light. The turning point came by exploiting the properties of the probes being used and moving to switching and/or nonlinear approaches offering the potentiality of unlimited spatial resolution [21.248]. Since the advent of the term super-resolution due to Giuliano Toraldo di Francia, it has been clear that one cannot violate the physical law of diffraction [21.249, 21.250]:

Two-point resolution is impossible unless the observer has a priori an infinite amount of information about the object.

Fig. 21.13

Optical microscopy scenario. Adapted after [21.58]

In a recent paper about the development of the theory of microscope resolution, Colin Sheppard [21.251] analyzes the different approaches starting from some considerations regarding the resolution limit proposed by Abbe in 1893 [21.252]. The proposal was originally developed in terms of Fourier optics  [21.253]. A test object, made by a flat substrate with a ruling of groups of lines, was used to demonstrate that the diffraction of light took place through an angle that increases as the test object features are decreased in terms of spacing. This implies that light is able to contribute to the microscope image formation only:

If the angle of diffraction is small enough to pass through the aperture stop located in the back focal plane of the lens.

As commented by Sheppard, Fripp, who translated Abbe's paper into English [21.254], utilizes the word limit in Abbe's sentence:

The physical limit of resolution, on the other hand, depends wholly on angular aperture, and is proportional to the sine of half the angular aperture

to imply a definite and sudden transition from being resolved to not being resolved [21.251].
Now, it is established and used, at least as a first approximation, that the diffraction limit dominates lateral \((x,y)\) and axial \((z)\) resolution to values of
$$\begin{aligned}\displaystyle\Updelta x,\Updelta y&\displaystyle\approx\frac{\lambda}{2n\sin\alpha}\;,\\ \displaystyle\Updelta z&\displaystyle\approx\frac{2\lambda}{(n\sin\alpha)^{2}}\;,\end{aligned}$$
with \(\lambda\), \(\alpha\), and \(n\) denoting the wavelength, the semi-aperture angle of the objective, and the refractive index of the medium, respectively. The quantity \(n\sin\alpha\) is referred as numerical aperture and usually abbreviated as NA. Switching from spatial to frequency coordinates, this limitation is reflected in a cut-off frequency of the transmission channel realized by means of the optical microscope, Fig. 21.14a,b.
Fig. 21.14a,b

Intensity distribution changes versus spatial frequency behavior of an image formation system with a cut-off frequency. After [21.236]

So far, when Giuliano Toraldo di Francia addressed the topic of super-resolution there was nothing about any possible violation of the physical laws. He referred to the possible additional information that can be used to further extend the cut-off frequency of the microscope, seen as a communication channel where the term frequency is related to a spatial frequency and its cut-off value to the inverse of the spatial resolution limit [21.236]. This element is crucial for performing an optimal and effective sampling during the image formation processing within the Shannon and Nyquist formulations [21.255, 21.256, 21.257, 21.258]. Among the attempts to extend the cut-off frequency confocal and two-photon laser scanning microscopy are worthy of note. Laser beam scanning introduces, point by point, the additional knowledge of the position of the probe in the image formation process. The use of fluorescence, under linear and nonlinear modality of excitation, allows us to operate under favorable SNR conditions—dark background and bright signal—coupled to a biochemical affinity of the fluorescent probe for the specific biological compartment under examination. This is the key point for making fluorescence microscopy an indispensable tool in cell biology; it is uniquely specific with regard to the objects to be mapped and visualized, it is largely non-invasive, it can probe the three-dimensional layers of the specimen at ambient conditions, and it enables spectroscopic diagnosis with high (bio)chemical sensitivity [21.239]. In modern super-resolution methods, the knowledge about the emitters' position is incremented with the further ability of controlling fluorescent states. It is the ability to control the states of fluorescent molecules (for instance, dark–bright, different wavelengths' emission) that produces an advantage comparable to the ones available by introducing known objects or filters or by controlling the position of an illumination beam as in beam scanning microscopy or nanoscopy [21.259, 21.260, 21.261]. The practical spatial resolution, the Abbe limit , is set around \({\mathrm{200}}\,{\mathrm{nm}}\) for visible light. This wall has been smashed by a large variety of super-resolution techniques coupled with an improved ability to perform 4-D (\(x\)\(y\)\(z\)\(t\)) imaging within the possibilities offered by image scanning ( ) [21.262], confocal laser scanning ( ) [21.36], two-photon excitation ( ) [21.11], and light sheet (LS ) [21.263] microscopy (M). Such technical revolutions have been amplified by the advances in the utilization of fluorescence in optical microscopy. Fluorescence microscopy has become an indispensable tool in cell biology because of its unique advantages: it is a largely noninvasive technique, it can probe the deeper layers of a specimen at ambient conditions and enables spectroscopic diagnosis with chemical sensitivity [21.264]. Figure 21.15 shows a classical image reporting the intensity of different labels associated to DNA, (blue), mitochondria (red), and cytoskeleton (green). For many years, researchers mainly considered as a mappable property the one related to fluorescence intensity. Today, thanks to important developments that started at the end of the 1980s in terms of detection of photon-based signals, the information available through fluorescence labeling is driven by changes in intensity, fluorescence lifetime, polarization, photobleaching rate, spectral changes, and blinking [21.238, 21.239, 21.265, 21.266]. The advent of green fluorescent proteins ( ) led to a further revolution [21.164, 21.267, 21.268, 21.269]; this was also one of the keys of success towards super-resolved fluorescence microscopy [21.270] when photoactivatable and photoswitchable visible fluorescent proteins appeared both under conventional and two-photon photoactivation [21.17, 21.271, 21.272, 21.82]. Fluorescent-label-free methods are also growing, offering new perspectives and taking advantage of the possibility of recording not only the intensity of the emitted fluorescence [21.273]. The trend is for a smart balancing of some tradeoff starting from the utilization of low photon doses for excitation towards an optimized collection. The recently developed MinFlux method is a clear example of such a trend [21.275]. However, a balance has to be found between minimizing phototoxicity and photobleaching [21.276] and signal-to-noise ratio, spatial, and temporal resolution optimization.

Fig. 21.15

Selective labeling of cell compartments and related multicolor emission, namely: DNA (blue), mitochondria (red), and cytoskeleton (green)

Referring once again to the optical microscopy framework offered by Fig. 21.13, one can envision a new kind of optical microscope capable of collecting data simultaneously through different image formation modalities. Image formation modalities can be easily mixed, just like liquids, and spatial and temporal resolution can be tuned, just like a radio station. In other words, a liquid tunable microscope [21.277]. The realization of such a multiscale microscope allowing several contrast options in the image formation process can lead to a new paradigm for the image formation process within a liquid approach, LIQUITOPY ® [21.278].

21.7.1 Resolution Criteria

Since we are dealing with spatial resolution as the main focus related to optical microscopy developments, a comment about resolution criteria is needed. The comment is related to the ways we use for reporting the spatial resolution of a specific optical microscopy setup.

In order to decipher what an image tells us, we need to know quantitatively the value of the spatial resolution achieved. This value, most of the time, is evaluated with methods like the following. Modeling or analytical formulation with the aim of taking into account any optical aberrations/distortions, noise, and sample conditions is hard to derive [21.279]. One should consider the image formation process as a linear and space-invariant transformation having as Dirac's function impulse response the point spread function ( ) of the system [21.256, 21.261, 21.280]. Within such a linear and space invariant model, the knowledge of the point spread function, i. e., Dirac's impulse response of the system, completely characterizes the imaging system. More recently, the use of a calibration sample like DNA origami  [21.281, 21.282] allows us, in most of the super-resolved techniques, to take into account both optical aberrations/distortions and sample conditions related to the photophysical properties of the fluorescent probe being used. The line profile of subresolved-sized structures is used even if it does not match with the definition of spatial resolution as the minimum distance between two point structures that can be resolved. Figure 21.16a-c summarizes such popular solutions. A quantitative way to get a value of the spatial resolution accessible by an image formed by the optical microscope is related to an analysis referred as Fourier-ring-correlation ( ) [21.283, 21.284, 21.285]. FRC allows us to estimate the effective spatial resolution of an imaging system without any a-priori information, such as an analytical model, taking into account all optical conditions (aberrations, distortions, and misalignments), noise conditions, and sample conditions. It is applied directly on the formed image of the sample under study by the optical microscope being used. It needs two identical but statistically independent images of the same sample and a careful analysis of the noise. Figure 21.17a-c shows how to get a quantitative value of the cut-off frequency following a simple procedure:
  1. 1.

    Two identical and statistical independent images are collected.

     
  2. 2.

    The two-dimensional Fourier transform is calculated.

     
  3. 3.

    Correlation analysis is used for evaluating \(\text{FRC}(q)\).

     
  4. 4.

    The plot of \(\text{FRC}(q)\) allows the cut-off frequency to be evaluated by intercepting the noise threshold line.

     
The inversion of the resulting value produces the value of the effective spatial resolution attainable by the image formation system being used, including all the actors, from optics to sample characteristics.
Fig. 21.16a-c

Methods to determine spatial resolution achievable after the image formation process. (a) Linear and space-invariant model of the image formation process; (b) DNA-origami fluorescent ruler with a designed distance of \({\mathrm{71}}\,{\mathrm{nm}}\) between two lines made by 12 Atto \({\mathrm{647}}\,{\mathrm{N}}\) molecules each (left) and formed super-resolution image (right), modified from [21.274]; (c) point-like subdiffraction fluorescent beads imaged by two super resolution approaches and plot of the line intensity distribution

Fig. 21.17a-c

FRC steps, from left to right: record a couple of statistically independent images of the very same object, apply 2-D Fourier transformation, evaluate and plot \(FRC(q)\), \(q\) being the spatial frequency coordinate. The intersection with noise average value provides the cut-off frequency

In order to obtain two identical images under the condition of independent noise realizations some practical approaches can be carried out, namely [21.285]:
  1. 1.

    Frame-based acquisition. Two consecutive measurements are performed and a drift correction applied.

     
  2. 2.

    Line-based acquisition. Every line is raster scanned twice, and the two different images are formed by considering even and odd lines.

     
  3. 3.

    Pixel-based acquisition. The pixel dwell-time of every pixel is split into two temporal windows with the same duration to obtain two independent images at the end of a single scan.

     
It is worth noting that in the case of time-dependent phenomena, such as diffusion, it is possible to isolate fake spatial frequencies. This aspect mainly applies to case 1. In general, the FRC approach is a robust and effective way to determine the frequency content of the collected dataset used to form an image.

21.7.2 Super-Resolution Methods

The most immediate question considered when mentioning super-resolution related to the image formation process of the optical microscope concerns the possibility of distinguishing objects that, due to the instrumental physical limitations, could not be recognized as separate objects under a certain data acquisition and reconstruction scheme. In optical microscopy, there are architectural solutions that allow one to form images beyond the diffraction limit, like confocal laser scanning microscopy, for example, Fig. 21.18. Physical laws are not violated. Simply, the reconstructed image takes advantage of additional information. In the case of confocal laser scanning, the additional set of information used for image reconstruction is contributed by the knowledge of the location of the scanned point, point by point. A formal mathematical treatment of the fundamental principles behind super-resolution is to be found in a brilliant paper by Colin Sheppard, along with a classification of different schemes and the analysis of the definitions for the localization of a wave [21.286]. Figure 21.19 sketches the current tunability. Despite the fact that some approaches offer unlimited spatial resolution, we limit the tuning to \({\mathrm{25}}\,{\mathrm{nm}}\). This reflects the fact that within the optical microscopy framework, the most important application is related to imaging of living cells at room temperature. Since the Royal Swedish Academy of Sciences awarded Eric Betzig, Stefan W. Hell, and William E. Moerner the Nobel Prize in Chemistry 2014 for the development of super-resolved fluorescence microscopy, we will mainly refer to the related approaches known as coordinate-stochastic and coordinate-targeted super-resolved fluorescence microscopy  [21.248, 21.287, 21.288, 21.289, 21.290]. The former is a parallelized or wide-field approach (PALM, STORM, GSDIM), and the latter is a point scanning approach (STED, RESOLFT) [21.244]. Figure 21.20 sketches the related solutions. Structured illumination microscopy (SIM ) [21.291] and ExM [21.292] will be briefly discussed.

Fig. 21.18

(a) Sharpening of the point spread function, widefield versus confocal. (b) Image of two fluorescent beads closer than the diffraction limit under widefield versus confocal

Fig. 21.19

Spatial resolution is tunable according to the scientific question

Fig. 21.20

Effect of the application of super-resolved fluorescence microscopy. In the first row, fluorescent molecules are organized at distances closer than the diffraction limit. Green and blue circular spots represent the excitation (green) and photoactivation (blue) beams for implementing the single molecule localization process depicted in the mid row that allows forming the final image on the right frame by frame. In the top row, we also have a red donut beam, which coupled to the excitation (green) beam, allows achieving STED imaging. In both cases, the pattern is revealed, and emitters can be counted

Coordinate Stochastic Super-Resolved Fluorescence Microscopy

This method is also referred as the single-molecule localization method [21.293]. Single-molecule imaging of a sparse distribution of fluorescent molecules represents a starting point for increasing the ability to recognize and handle the main actors of this family of super-resolved methods [21.76]. Localization-based techniques, exploiting photoactivation, photoconversion, or ground-state depletion of fluorescent molecules, allow super-resolution imaging of biological samples. A major role is played by single-molecule localization, which provides direct information at the molecular scale. Several variants belong to this family of super-resolution techniques. Among the most important are photoactivation localization microscopy ( ) [21.294], fluorescence photoactivation localization microscopy ( ) [21.295], stochastic optical reconstruction microscopy ( ) [21.296], point accumulation for imaging in nanoscale topography ( ) [21.297], and individual molecule localization selective plane illumination microscopy ( ) [21.298]. The knowledge of a single emitter as a unique source of photons, apart from background, allows to one localize it with nanometric precision. More specifically, the localization precision, typically ranging from \(5{-}30\,{\mathrm{nm}}\), is driven by following relationship [21.299]
$$\sigma^{2}_{x,y}\approx\dfrac{s^{2}+\frac{a^{2}}{12}}{N}+f(b,N^{2})\;,$$
where \(s\) and \(a\) are related to the point spread function and the pixel size technicalities, respectively, of the imaging system, \(N\) is the number of photons collected, and \(b\) is the background noise. Under some general conditions, the function \(f\) can be approximated by [21.294]
$$f(b,N^{2})\approx\frac{4\sqrt{\pi}}{aN^{2}}s^{3}b^{2}\;.$$
This relation shows that the uncertainty falls as the inverse of the number of photons for the background noise and as \(N^{-1/2}\) for the photon counting noise. Here, it is self-evident that the role of the background increases with the thickness of the specimen being imaged.
The effective resolution in FPALM is affected by the molecular density and also by the distance between contiguous molecules. For this reason, the overall resolution of the system should take into account both the localization precision and the molecules sparseness. The spatial resolution can be estimated considering
$$d=\sqrt{\sigma_{x,y}^{2}+r_{\text{NN}}^{2}}\;,$$
where \(r_{\text{NN}}\) represent the nearest-neighbor distance between the molecules, and \(\sigma_{x,y}\) is the localization precision. Therefore, the maximization of the number of photons collected for each molecule is a crucial aspect in FPALM imaging, and it allows the localization precision to \(b\) increased.
Furthermore, for practical imaging of large scattering biological samples, several factors are limiting the resolution, mainly related to scattering and aberration effects. To consider additional errors induced in the localization process that can contribute to a decreased effective localization precision, the precision can be redefined by considering also the standard deviation \(\sigma_{\text{inst}}\) of the instabilities of the system [21.299]
$$\sigma^{2}_{\text{eff}}=\sqrt{2\sigma^{2}_{x,y}+\sigma^{2}_{\text{inst}}}\;,$$
where the factor 2 takes into account, for example, the excess noise introduced by electron multiplying process of the (electron multiplying charge coupled device).

Figure 21.21a,b shows an example of spatial resolution improvement in the \(x\)\(y\) plane. A super-resolution ability can also be obtained along the \(z\)-axis by exploiting, for example, an induced astigmatism in the optical system. In the presence of astigmatism, the round shape given by the signature of single molecules in the focal region is distorted towards an elliptical shape. The extension and the preferential elongation of the axes of the single-molecule signature provide information about the position of the emitter along the illumination axis. A calibration of the system allows us to get a precise position along the \(z\)-axis as implemented by [21.296, 21.298].

Fig. 21.21a,b

Image of cytoskeletal structures (microtubules labeled with Alexa 647) in HeLa cells. (a) 3-D storm image of microtubules. (b) Corresponding widefield image. Localization precision: lateral \({\mathrm{20}}\,{\mathrm{nm}}\), axial \({\mathrm{65}}\,{\mathrm{nm}}\)

However, a precise localization is coupling the increased spatial resolution at the molecular scale with a quantitative evaluation of protein distribution in biological systems. On the one hand, the possibility to image single molecules at a high temporal resolution rate allows us to follow the trajectories of individual molecules by single-particle tracking-photoactivation localization microscopy ( ) [21.300, 21.301] and to estimate mobility and interactions of proteins (single-molecule tracking) . On the other hand, to address specific biological problems efforts have been focused on the development of innovative quantitative approaches, based on single-molecule detection, capable of estimating protein copy numbers at the cellular level precisely. The most used quantitative approaches for single-molecule localization, ranging from molecular counting approaches such as step-wise photobleaching [21.302], local density estimation, and clustering analysis [21.299], have been demonstrated to be suitable tools to address specific biological questions [21.303, 21.304, 21.305]. The most common methods for analysis of single-molecule localization datasets, capable of identifying clusters and associate molecules belonging to the same cluster, are pair correlation and the Ripley function . These functions provide a trend based on the intensity and the length scale for clustering within each dataset. However, both synthetic dyes and fluorescent proteins exhibit multiple localized events from each single fluorophore, thus leading to an overestimation of the real molecule number (due to the blinking phenomenon that induces multiple counts by the localization algorithm for each molecule). Furthermore, when immunofluorescence labeling techniques are used, the uncontrollable stoichiometry increases the overcounting phenomenon, thus making an accurate estimation even more challenging. Within this context, correct quantitative analysis and accurate molecular counting first require a precise control over the number of targeted fluorescent molecules. Therefore, a suitable calibration method is needed to address the challenges of molecular counting using super-resolution. To overcome this limitation, solutions based on DNA nanostructures [21.306, 21.307, 21.308] allow one to account for the labeling density and for the fluorophore photophysics, and they represent an optimal calibration standard for the characterization of the response in terms of the number of localizations/molecule. In particular, a 12-helix DNA origami chassis [21.309] has been demonstrated to be a suitable tool for protein copy number estimation using STORM [21.282]. Figure 21.22a-e shows the quantification of nucleoporins NUP 133 by quantitative super-resolution based on DNA origami calibration [21.282].

Fig. 21.22a-e

Quantification of nucleoporins NUP 133 by quantitative super-resolution based on DNA origami calibration. (a) Sketch of the DNA origami structure (12 helix) used as calibration standard for quantitative super-resolution. STORM imaging (b) and cluster analysis (c) of DNA origami functionalized with organic fluorophores (Alexa647 and TAMRA) and proteins. (d) STORM image of NUP133 immunostained by photoswitchable dyes Alexa405-Alexa647 in siRNA resistant NUP133-GFP expressing U20S cells. Cluster analysis (e) of super-resolution images combined with DNA origami calibration provides a quantitative estimation of the NUP133-GFP copy number and the number of clusters/nuclear pore (inset), modified after [21.282]

In practice, this represents a valuable tool to calibrate and train the response at the single molecule level, thus providing a versatile way to characterize the response from a given number of fluorophores or proteins located at known positions at specific distances. DNA origami with biotinylated handles can be immobilized on the glass surface and can be used to characterize the photophysical behavior of a single dye or protein in terms of:
  • \(N\) number of localizations/molecule

  • Fluorescence intensity

  • Blinking rate

  • Distances among proteins attached at specific handles.

Such features allow precise molecular quantification in super-resolution microscopy, and can be considered as the starting point to develop a suitable approach to quantify protein numbers organized in clusters or clutches within cellular compartments of interest. The precise knowledge of the localization events for a controlled number of molecules permits estimation of the number of proteins organized in clusters in a given sample. The calibration sample provides a calibration function \(f_{n}\), and the localizations distribution \(g(x)\) extracted from clusters in a sample of interest can be described mathematically as a linear combination of calibration functions
$$g(x)=\sum^{\mathrm{N}}_{n=1}\alpha_{n}\,f_{n}(x)\;.$$
The improved performances in terms of SNR and imaging speed provided by the new generation of CCD cameras ( (complementary metal oxide semiconductor) and EMCCDs) have made these techniques more and more popular and allow the application of super-resolution imaging techniques based on single-molecule localization to a wide range of biological contexts.

The ability to quantify proteins is essential to elucidate cellular mechanisms related to the number and concentration of molecules within specific cellular compartments. Quantitative single-molecule techniques have found application in the neuroscience context, towards the elucidation of the subunit stoichiometry defining receptor-neurotransmitter interactions [21.304] or quantifying the copy number of scaffold proteins [21.303, 21.310]. In particular, cluster analysis has been successfully applied to show that scaffold proteins within synapses are organized in nanodomains [21.310, 21.311] as well as to show that presynaptic proteins closely align with concentrated postsynaptic proteins, through the presence of transsynaptic molecular nanocolumns [21.312].

Furthermore, quantitative single-molecule approaches have recently attracted growing interest, and they have also been successfully applied to study nuclear structures and the nucleosomes organized in chromatin high-order structures [21.305, 21.313].

Since the natural interactions among molecules are cell-to-cell, it is interesting to face the problem of getting a precise localization in thick cell aggregates such as tumor spheroids.

In order to reduce the background signals, a solution can be to move to a different scheme of illumination like the one implemented in selected-plane-of-illumination microscopy [21.298]. Figure 21.23 shows a possible setup that allows single-molecule localization within a light sheet architecture, thus reducing the influence of the fluorescence background. Figure 21.24a-c shows some optically cut planes at different depths within a spheroid and one of the frames mapping the position of single fluorescent molecules at the nm scale. Such an approach has been named individual molecule localization-selective-plane-illumination microscopy ( ). We demonstrate 3-D super-resolution live-cell imaging through thick specimens (\(50{-}150\,{\mathrm{\upmu{}m}}\)) by coupling far-field individual molecule localization with selective-plane-illumination microscopy ( ).

Fig. 21.23

IML-SPIM architecture coupling the PALM and SPIM approaches. Top: a color sketch of the positioning of the SPIM detection unit (right) compared with conventional ballistic detection (left). Inset: the cubic sample holder with the selective plane of illumination. From [21.298]

Fig. 21.24a-c

The orthogonal positioning of the illumination and detection objectives allows us to reduce background signals. In this case, the optical sectioning in a thick sample is facilitated (a). Within each plane of illumination (b), single-molecule localization detection is achieved (c). From [21.298]

The improved SNR of selective-plane-illumination allows nanometric localization of single molecules in thick specimens without activating or exciting molecules outside the focal plane. We report 3-D super-resolution imaging of cellular spheroids.

The IML-SPIM approach can also be implemented under a two-photon photoactivation regime that is particularly suitable to maintain a homogenous thickness in the light sheet under increased scattering usually affecting thick samples [21.314], Fig. 21.25a,b.

Fig. 21.25a,b

Comparison of (a) UV-VIS photoactivation and (b) IR two-photon photoactivation under increased scattering conditions

Coordinate-Targeted Super-Resolved Fluorescence Microscopy

Stimulated emission depletion ( ) microscopy [21.315, 21.316] is a super-resolution technique that uses the fundamental process of stimulated emission to engineer a PSF of arbitrarily small size and circumvent the diffraction barrier limitation [21.245, 21.317]. This is the preferred method in the realm of coordinate-targeted super-resolved fluorescence microscopy methods. In the STED microscope, a diffraction-limited excitation volume is made to overlap with a doughnut-shaped STED beam that is typically red-shifted with respect to the fluorophore's emission peak. The two most relevant technical features of the STED beam are:
  1. 1.

    The STED beam wavelength should be set in a spectral region with a low probability of excitation, as far as possible from the red tail of the absorbtion spectrum of the fluorescent molecule being used.

     
  2. 2.

    The intensity distribution of the STED beam, typically a doughnut shape, has to drop to zero at least in the center of the beam.

     
So, since the doughnut shape has to feature a zero intensity point in the center of the beam with an intensity profile driven by the diffraction-limited point spread function of the focusing lens coupled to the power of the STED beam, the STED beam depletes the molecular fluorescent state everywhere within the diffraction-limited excitation volume, by means of stimulated emission, except at the center and its neighborhood, where the probability is very poor due to the cross-section at the STED beam wavelengths. The use of the fundamental process of stimulated emission makes STED microscopy compatible, at least in principle, with all fluorescent probes. Figure 21.26 shows the excitation-emission-depletion scheme.
Fig. 21.26

Following the blue excitation within the absorption spectrum region of the fluorescent molecule, green fluorescent emission can be perturbed by imposing a third red beam forcing stimulated—not collected—emission

It appears evident that in STED microscopy the increase of spatial resolution is directly related to the extent of the depletion, i. e., the fraction of excited fluorophores that undergo stimulated emission. The probability of stimulated emission depends on the power of the depletion beam and on many other factors related to the fluorophore (e. g., emission spectrum, orientational distribution, and rotational behavior of the dye molecules) and to the characteristics of the inhibition light (e. g., wavelength, temporal structure, and polarization). These factors are generally quantified through a constant \(I_{\mathrm{s}}\) named saturation intensity. Saturation is towards zero, in terms of fluorescence, and it refers to the \({\mathrm{50}}\%\) forced depopulation of the excited state. Considering the fluorescence emission behavior \(F\), one has
$$F=\mathrm{e}^{-\text{ln}\,2\left(\frac{I_{\text{STED}}}{I_{\mathrm{s}}}\right)}\;.$$
Now, in order to establish a relationship between spatial resolution and STED power, we can assume that the diffraction-limited point spread function is described by a Gaussian function with waist \(w\)
$$h_{\text{CONF}}(r)=\mathrm{e}^{-\frac{2r^{2}}{w^{2}}}\;,$$
and the STED beam profile in the proximity of the center can be approximated by a parabola
$$I_{\text{STED}}(r)=I_{\text{STED}}\frac{r^{2}}{w^{2}}\;,$$
where \(I_{\text{STED}}\) is the value at \(r=w\). We can describe the effective STED point spread function \(h_{\text{STED}}\) as
$$\begin{aligned}\displaystyle h_{\text{STED}}&\displaystyle=\mathrm{e}^{-\frac{2r^{2}}{w^{2}}}\mathrm{e}^{-\text{ln}\,2\left(\frac{I_{\text{STED}}(r)}{I_{\mathrm{S}}}\right)}\\ \displaystyle&\displaystyle=\mathrm{e}^{-\frac{2r^{2}}{w^{2}}}\mathrm{e}^{-\text{ln}\,2\left(\frac{I_{\text{STED}}r^{2}}{w^{2}I_{\mathrm{s}}}\right)}=\mathrm{e}^{-\frac{2r^{2}}{w^{2}_{\text{eff}}}}\;,\end{aligned}$$
where
$$\begin{aligned}\displaystyle\frac{1}{w^{2}_{\text{eff}}}&\displaystyle=\frac{1}{w^{2}}\left(1+c\frac{I_{\text{STED}}}{I_{\mathrm{s}}}\right)\\ \displaystyle\text{with }c&\displaystyle=\frac{\text{ln}2}{2}\;.\end{aligned}$$
Thus, the effective PSF of a STED microscope can be approximated with a Gaussian function whose effective waist \(w_{\text{eff}}\) is reduced by a factor that depends on the STED power as \(\propto 1/(1+cI_{\text{STED}}/I_{\mathrm{s}})^{1/2}\).

A key point in STED implementation is the fact that in some cases, the power of the STED beam cannot be increased to the level required for getting a certain resolution. One does not want to take the risk of inducing photobleaching or other undesired photophysical effects on the sample. For some reasons the STED beam intensity has to be limited. In a classical configuration, this implies that spatial resolution is also limited. However, this limitation can be overcome by considering in a spectroscopic way what is going on when the STED beam is introduced into the image formation process. Figure 21.27 sketches the consequence of the depletion considering the analogy with the use of differently shaped brushes by a pointillist painter. It links the sharpening of the point spread function to the local perturbation induced by the STED beam on the pool of excited fluorescent molecules. When the STED beam has a limited power, the effect is that the probability of forcing excited molecules to the ground state by stimulated emission is decreased. The immediate consequence is that, within the geometry defined by the depletion beam, fluorescence is still allowed. Now, the question is: what is the difference between the fluorescence emitted from the central part of the excited regions, where the STED beam intensity is designed to be zero or very close to zero, and from the peripheral regions where the depletion beam intensity grows to its maximum value? [21.318]. In the peripheral regions, the second beam gives another chance for the excited molecules to go to the ground state, and this is reflected in a shorter fluorescence lifetime with respect to the unperturbed regions with the original fluorescent molecule lifetime, Fig. 21.28. The most relevant result is given by the fact that, by reducing the STED power, spatial resolution can be kept in the super-resolved domain by considering the time of arrival of photons.

Fig. 21.27

Considering the scanning process as a pointillist-like image formation, following perturbation of the fluorescence process primed by the blue brush tip one has at disposal a sharper brush (green) to form a more detailed image

Fig. 21.28

The difference between fluorescence coming from an unperturbed region—the center of the donut beam—or from perturbed regions located at the periphery of the depletion beam is self-evident by analyzing fluorescent lifetimes

Now, an interesting STED implementation employs pulsed excitation and a continuous-wave ( ) depletion beam. In this case, the effect of stimulated emission causes a decrease of the excited-state fluorescence lifetime \(\tau\) of the fluorophore. In fact, the stimulated emission process represents an additional decay pathway from the excited singlet state. In this case, we can redefine the saturation intensity as the STED intensity at which the lifetime \(\tau\) is reduced by half of its unperturbed value \(\tau_{0}\) such that
$$\frac{1}{\tau}=\frac{1}{\tau_{0}}\left(1+\frac{I_{\text{STED}}}{I_{\mathrm{s}}}\right).$$
We can then rewrite the confocal spatio-temporal point spread function as
$$h_{\text{CONF}}(r,t)=\mathrm{e}^{-\frac{2r^{2}}{w^{2}}}\mathrm{e}^{-\frac{t}{\tau_{0}}}\;,$$
and the effective STED spatiotemporal point spread function as
$$h_{\text{STED}}(r,t)=\mathrm{e}^{-\frac{2r^{2}}{w^{2}}}\mathrm{e}^{-\frac{t}{\tau_{0}}\left[1+\left(\frac{I_{\text{STED}}r^{2}}{w^{2}I_{\mathrm{s}}}\right)\right]}=\mathrm{e}^{-\frac{2r^{2}}{w^{2}_{\text{eff}}}}\mathrm{e}^{-\frac{t}{\tau(r)}}\;.$$
The last equation shows that, in a CW-STED microscope, the STED beam induces a gradient of fluorescence lifetimes between the center and periphery of the PSF, \(1/\tau(r)=1/\tau_{0}(1+k_{\mathrm{s}}r^{2}/w^{2})\). The value of \(k_{\mathrm{s}}=I_{\text{STED}}/I_{\mathrm{s}}\) quantifies the relative variation of decay rate values within the PSF of the CW-STED microscope. This gradient can be exploited to tune the spatial resolution by STED strategies such as gated-STED [21.319, 21.320, 21.321] and STED-SPLIT [21.322, 21.323].

The STED concept can be generalized to any systems where light can switch the molecule between two states [21.245, 21.317, 21.324, 21.325, 21.326]. The idea applies to techniques like ground-state depletion ( ) [21.327] and RESOLFT [21.328, 21.329, 21.330, 21.331]. Both these methods rely on dark and bright states, but light emission is not a limiting factor; in nanolithography, for instance, the states involved are polymerizing and non-polymerizing ones [21.332, 21.333]. Another very interesting variant is based on a pump–probe process, where a pump perturbation of charge carrier density in a sample and the consequent change in transmission of the probe are the key elements for the super-resolution [21.334, 21.335, 21.336].

It should be evident that a typical STED nanoscope is quite similar to a beam scanning microscope. It requires, at least, two co-aligned laser beams. The former for the excitation and the latter for the depletion of fluorescence, Fig. 21.29. The spatial profile of the STED beam has been discussed before, Fig. 21.27. In order to achieve an annular pattern along the lateral plane, the most commonly used approach is the introduction of a vortex phase plate  [21.337, 21.338]. A bottle profile made by an axial phase plate is used to improve the spatial resolution along the propagation axis [21.316]. In general, a balance of the power of the two STED beam profiles is realized in order to adjust the overall 3-D resolution on demand [21.339]. Fluorescence microscopy is multicolored from the beginning. This means that one cannot avoid implementing such a feature in this case also. Single-color STED made by a pair of co-aligned beams could already be considered a good achievement. However, by taking advantage of the spatial resolution along the axial direction using a confocal or two-photon excitation approach, multicolor STED imaging is feasible in a balance between the photophysical properties of the fluorescent molecules and the spatial resolution needed. As an example, considering a nanoscope equipped with one STED beam, two-color STED nanoscopy can be achieved by coupling a further excitation beam. An appropriate fluorophore has to be selected in order to have different excitation spectra with similar emission behavior, enabling the exploitation of the same depletion beam for both fluorophores [21.317, 21.340].

Fig. 21.29

Simplified setup of a STED microscope architecture

Another approach to towards two-color STED is given by the possibility of combining different excitation and depletion beams. Fluorophores have to be chosen as having with optimal performances for each pair of beams [21.341, 21.342, 21.343]. Figure 21.30 shows a multicolor STED example. A convenient and promising method is one that uses a family of newly developed large-Stokes-shift dyes, such as Abberior STAR 470SX (Abberior GmbH, Gottingen, Germany) or ATTO 490LS (Atto-Tech GmbH, Siegen, Germany). In this case, one can get two or three-color STED without excessive loss of spatial resolution. Now, the first effective STED setup was realized by using synchronized trains of pulses for excitation and depletion [21.316]. This guarantees a sufficiently high flux of stimulating photons within the short (\(1{-}5\,{\mathrm{ns}}\)) excited-state lifetime of the fluorophores to quench fluorophores in the focal periphery. Technically, in this configuration, a depletion pulse immediately follows the excitation pulse. In general, the excitation pulse should be much shorter than the STED one, while the depletion pulse should be longer than the vibrational relaxation time (\(> {\mathrm{50}}\,{\mathrm{ps}}\)) and shorter than the fluorescence lifetime of the fluorophore (\(<{\mathrm{250}}\,{\mathrm{ps}}\)) [21.344]. However, longer pulses can also guarantee the resolution advantage facilitating the STED implementation [21.338].

Fig. 21.30

Image of a HeLa cell under STED and confocal microscopy. Labeling: NUP153 with Abberior 440SX (red-hot) and tubulin with Oregon Green 488 (green-fire blue). The image was collected sequentially by two hybrid detectors in the spectral range \(465{-}505\) and \(520{-}580\,{\mathrm{nm}}\), respectively. Excitation was \(\mathrm{458}\) and \({\mathrm{514}}\,{\mathrm{nm}}\), respectively. The STED wavelength was \({\mathrm{592}}\,{\mathrm{nm}}\) for both the fluorophores. HCX PL APO CS \({\mathrm{100}}\times\) \({\mathrm{1.4}}\,{\mathrm{NA}}\) oil objective (Leica Microsystems, Mannheim, Germany) was used. The scanning speed was \({\mathrm{1000}}\,{\mathrm{Hz}}\) for \(\mathrm{2048}\) pixels per line with a 64-lines average. The microscope used was a Leica TCS SP5 gated STED-CW (Leica Microsystems, Mannheim, Germany)

More recently, CW lasers came into use and offered interesting solutions [21.345]. CW-stimulated emission depletion ( ) has a reduced complexity and costs and increased the versatility of the system. In fact, CW lasers provide almost any wavelengths in the visible and near-infrared region. However, since the peak intensity supplied by a STED beam running in CW is lower than that of a pulsed beam, the resolution performance of a CW-STED system lags behind that of a pulsed STED system. A solution to this problem is obtained by combining CW-STED microscopy with a time-gated detection scheme according to the previous observations: the so-called gated continuous wave-stimulated emission depletion ( ) implementation [21.318, 21.322]. Practically, all fluorescent molecules are excited at the very same time through a pulsed laser, and the time-gated detection allows us to discard early fluorescence photons, arriving at a time \(<T_{\mathrm{g}}\), which are said to be time gated. As a result, the ability to remove fluorophores outside the center of the STED beam for a given STED laser power is substantially improved, Fig. 21.31. In terms of point-by-point imaging, the longer the time delay \(T_{\mathrm{g}}\) between the excitation and the fluorescence collection, the better is it ensured that fluorescence is recorded mainly from fluorophores located in the doughnut-center where the STED beam intensity is zero, so that the effective spatial resolution is higher. Unfortunately the reduction of the effective collection volume is accompanied by a reduction of the overall signal which forms the image [21.346]. Thereby, the SNR and the signal-to-background ratio ( ) reduction impose an upper limit on the choice of the time delay \(T_{\mathrm{g}}\). Different hardware and software-based approaches have been implemented to raise this upper limit. In particular, different lock-in and synchronous detection schemes have been combined with gCW-STED to remove uncorrelated background sources, like the anti-Stokes fluorescence emission potentially induced by the STED beam itself [21.347].

Fig. 21.31

STED imaging resolution as function of beam power depletion and time-gated windows

Furthermore, ad hoc deconvolution algorithms, capable of reassigning the early photons instead of simply rejecting them have been implemented and have demonstrated a significant improvement of the SNR with respect to the raw-gated STED images [21.348]. For this reason, the SPLIT-STED approach introduced above becomes relevant, Fig. 21.32. Photons are classified in terms of arrival time, and the related distance from the center of the STED beam is used, along with uncorrelated original background signal, to get an improved result with respect to the application of a mere gated-STED solution. Figure 21.33 shows an example comparing G-STED and SPLIT-STED. Any STED configuration can be also implemented under a two-photon excitation (2PE) regime, which is particularly suitable for thick specimens [21.274]. Despite its reliance on a nonlinear, quadratic dependence of the excitation power, 2PE is diffraction limited in terms of spatial resolution [21.274]. Two-photon excitation fluorescence microscopy has been combined with STED [21.349, 21.350], allowing super-resolution imaging of a mouse brain [21.351]. 2PE adopts a pulsed ultrafast Ti:sapphire laser source for the excitation beam; thus when combined with a pulsed STED beam, it needs expensive and sophisticated instrumentation capable of synchronizing the two lasers. The best-balanced approach is the use of CW lasers for depletion. This solution does not require any synchronization and guarantees good resolution that could be directly improved by time-gated detection [21.352]. A novel pulsed 2PE-STED implementation has been demonstrated [21.353]. Such an approach utilizes the very same wavelength for 2PE and STED. The main requirement is a fluorophore that can be excited and depleted at exactly the same wavelength, e. g., ATTO647n (Atto-Tech GmbH, Siegen, Germany). Since we are in the two-photon excitation framework, the excitation beam line is delivered using a \({\mathrm{100}}\,{\mathrm{fs}}\) pulse width, while the depletion beam operates at \({\mathrm{200}}\,{\mathrm{ps}}\) in order to avoid 2PE. Such a single wavelength ( ) 2PE-STED approach has the advantage that no other lasers are necessary for STED; it is a pulsed implementation and is easy to realize, but the excitation wavelength may not be the optimal for the fluorophore, hence reducing the SNR.

Fig. 21.32

Fluorescence decay reflecting lifetime changes as function of the distance of the center of the illumination/depletion beam

Fig. 21.33

Comparison between STED and SPLIT STED referred to a confocal image. Background evaluation allows us to improve the contrast in the final SPLIT-STED image

It is possible that the intensities used with the STED beam can induce some photostress on the fluorophore or on the sample [21.242, 21.354]. The reason for the high intensity level requirement, as anticipated before, lies in the probability of the depletion process in the picosecond temporal window. SPLIT-STED is an effective and tangible solution to reduce the STED beam intensity while keeping the resolution advantage. However, another way of shrinking the observation region is to induce photoswitching in photoswitchable fluorophores using the STED-beam shape geometry. In this case, the ability to control fluorescent light-driven states is also part of a more general concept, named RESOLFT, which is an abbreviation of reversible saturable optical fluorescence transitions  [21.329].

RESOLFT enables comparatively fast and continuous imaging of sensitive, nanosized features in thick samples like living brain tissue, as brilliantly demonstrated by Testa et al [21.331]. Such an approach uses low-intensity illumination to switch photochromic fluorescent proteins reversibly between two fluorescent states, i. e., fluorescent versus nonfluorescent or green-emitted versus red-emitted wavelengths, allowing an increase of resolution in all dimensions. Dendritic spines located \(10{-}50\,{\mathrm{mm}}\) deep inside living organotypic hippocampal brain slices were recorded for hours without signs of degradation. The imaging speed can be increased by using fast-switching fluorescent protein. The main points about this approach are related to the different temporal window of the process with respect to depletion and with the possible influence of the environment in inducing changes of the photophysical properties of the fluorescent molecules being used. It is mandatory to take special care with the sample preparation when using such a low STED-beam intensity approach. A new form of green fluorescent protein has allowed super-resolution imaging to be performed faster on living cells with low radiation doses [21.355].

A further key point when dealing with STED is given by the extremely relevant opportunity to employ super-resolved fluorescence solutions for the study of molecular dynamics in living cells. Within this goal, FCS [21.356, 21.357] represents an established technique to recover single-molecule diffusion and binding properties in cells. Moreover, scanning microscopy imaging was applied to add a spatial dimension to the classic FCS modality: spatiotemporal fluorescence correlation spectroscopy ( ) provides details about the routes that are followed by the diffusing particles or molecules in the specimen [21.358, 21.359]. STED nanoscopy has been recently been combined with all these FCS techniques, i. e., STED-FCS [21.360], raster imaging correlation spectroscopy ( ) STED [21.361, 21.362] and cross-pair correlation spectroscopy ( (pair correlation function)) STED [21.363]. By coupling the STED-FCS method to two analytical approaches, the recent separation of photons by lifetime tuning ( ) [21.323] and the fluorescence lifetime correlation spectroscopy ( ), diffusion in three dimensions at different sub-diffraction scales can be probed simultaneously. In this way, measurement of the diffusion of green fluorescent proteins at spatial scales tunable from the diffraction size down to \(\approx{\mathrm{80}}\,{\mathrm{nm}}\) in the cytoplasm of living cells [21.364] has been achieved.

Structured Illumination Microscopy

Super-resolved SIM ( ) was conceived by Mats Gustafsson [21.365], who implemented the concepts indicated by Lukosz [21.366] and Toraldo di Francia [21.249]. The additional knowledge carried by a patterned illumination and by its interaction with an unknown sample allows the spatial resolution to be enhanced. Two patterns are mixed to generate moiré fringes . The approach is comparatively simple since it consists in measuring the spatial frequencies produced by the interaction of the known illumination patterns with the spatial frequencies of the real sample and solving for the underlying spatial frequencies present in the sample. Figure 21.34 sketches the process. The relevance of such an elegant and effective approach lies in the fact that it can be applied to three-dimensional living samples prepared for conventional fluorescence microscopy. It thus allows multiple fluorescence imaging, optical sectioning, and live-cell imaging [21.291, 21.368]. Considering the fluorescence microscopy case, one has a diffraction-limited excitation patterns as multiplied by the emission PSF, point-by-point in the sample. This leads to the extension in frequency space. The known excitation pattern carries on its shoulders the latent spatial frequencies in the sample. The excitation pattern is made as sharp as possible within the diffraction limitations and a balance with sample characteristics. To reconstruct the image originated by such a structured illumination strategy along the \(x\)\(y\)\(z\) axes with equivalent resolution, the excitation pattern is rotated and phase shifted. Different solutions are implemented in terms of the number of rotations, phase shifts, data treatments, and image reconstruction algorithms [21.367]. It is worth noting that data treatment strategies in SIM were introduced early on and discussed by Benedetti and colleagues [21.369], who took inspiration from the pioneering work of Petráǒ [21.370] and was in tune with the work done by Heintzmann and Cremer [21.371]. For example, the illumination pattern generated by projecting a movable pinhole mask into the sample for each pattern position can be used in a wide-field fluorescence microscope setup to form a super-resolved image [21.372].

Fig. 21.34

(a) Frequency spectrum distribution of the PSF and of the sample (b) (arrows indicate the infinite extent of the spectrum). (c) Shifted frequency components of the object collected by the imaging system for a fringe pattern projected in different orientations. (d) The region mapped by the circles extends the frequency spectrum of the object after processing/assembling \(r\) different orientations of the projected fringe pattern. Reprinted with permission from [21.367]. The Optical Society

However, within the structured illumination layout, for the fluorescent molecules that respond nonlinearly to the illumination intensity, the use of sinusoidal illumination can lead to an emission that has contributions from the harmonics of the illuminated light frequency, which are uniquely distinct from those of linear SIM, which only delivers contributions from the first-harmonic of the incident light. Starting with linear SIM, one is still limited by the use of lenses in the expansion of the collectable frequencies from the sample. The introduction of any nonlinearities endows the system with almost unlimited spatial resolution potential [21.371, 21.373, 21.374]. The structured-illumination approach is spread over different optical microscopy modalities [21.235, 21.236, 21.367]. Among variations on the theme of SIM setups, the use of sensitive cameras [21.375] and of multiphoton excitation [21.376] can improve the performances at specimen depths \(> {\mathrm{100}}\,{\mathrm{\upmu{}m}}\).

Plasmon-assisted excitation has also benefited from structured illumination, leading towards lateral resolution improvements [21.377].

Expansion Microscopy

ExM is a novel method that, upon a specific sample treatment, allows super-resolved fluorescence imaging with conventional microscopes [21.378, 21.379]. It has been demonstrated that by synthesizing a swellable polymer network within a specimen, it can be physically expanded, resulting in physical magnification that can be imaged by means of an optical microscope. Figure 21.35 shows a cartoon of the process of the sample preparation for implementing the expansion microscopy approach. Sample preparation consists in soaking the biological cells in a polymer, inducing the polymerization to form a dense meshwork throughout the cell that crosslinks the fluorophores. After digestion of cellular protein and rehydration of the sample the image formation process can take place. The effect of swelling of the polymer gel leads to an \(N\)-fold isotropic stretching of the sample. The separation between objects that otherwise could not be appreciated now becomes visible. The utilization of such an approach is growing in the scientific community [21.292]. Recently, interesting variations have coupled ExM with STED nanoscopy [21.380, 21.381]. Despite the loss of the advantage of using a conventional microscope, there is the benefit of reducing the mechanical stretching of the specimen. Figure 21.36 shows an example comparing confocal, expansion, and expansion-STED microscopy [21.380, 21.382].

Fig. 21.35

Steps of the ExM sample preparation. Fluorescent labels in the sample are cross-linked with a polymer. Digestion preserves the fluorescent molecules linked to the polymer. The resulting sample, after gelification and digestion, is expanded following gel–water interaction. In the expanded sample, molecules that were closer than the diffraction limit appear physically separated and can be imaged by a conventional optical microscope

Fig. 21.36

The sample, imaged by confocal microscopy, is \(2\times\) expanded (top left) and compared with the original one (mid center). Despite the modest expansion, one can obtain a further improvement in resolution by imaging using super-resolution microscopy (bottom right), STED in this case, for the first time

21.8 Conclusions

The modern scenario of super-resolution methods is growing steadily. This fact generates ongoing developments in science and technology. Fluorescence and other mechanisms of contrast are continually evolving and improving. Scientific questions can be tackled from different perspectives, taking advantage of multimodal and multiscale microscopy approaches. Coupling with scanning probe methods, like atomic force microscopy, can produce brand new experiments at the nanoscale [21.383, 21.384, 21.385, 21.386]. However, it is possible that correlation or integration of different images generated by different mechanisms of contrast is somehow biased by our expectations. The possibility of integrating different light–matter interactions to form images in optical microscopy is the starting point for the design and realization of LIQUITOPY®, a liquid tunable microscope . This could represent a new paradigm in data collection and image formation with a potentially high impact in biophysics. Liquid takes inspiration from the philosophical and sociological speculation by Zygmunt Bauman [21.387] and tunable from the fact that, today, we have at our disposal methods that allow us to tune the microscope across a large, almost unlimited, range of spatial and temporal resolutions, as demonstrated here. It is liquid because it aims to overlap in an efficient and optimized way different mechanisms of contrast, and it is tunable because it offers a real-time tunability regarding spatial and temporal resolution, like a radio tuned to the preferred radio station. It is smart because it can adapt the current configuration to the scientific question, and it is open to additional light–matter interaction modules. The integration with label-free approaches, and more specifically with Mueller matrix microscopy [21.128, 21.388, 21.389], is one of the key points for its development from the point of view of available mechanisms of contrast. The perspective related to label-free approaches is growing, since at the nanoscale the dimension of the labels matters. Three different main directions can be explored within the LIQUITOPY® framework, namely:
  1. 1.

    Intrinsic fluorescence of biological macromolecules within the super-resolved fluorescence microscopy scenario considering interchangeable encoding and decoding of space and time at the nanoscale, from lifetime to correlation spectroscopy and from pump–probe to single-molecule behavior.

     
  2. 2.

    Label-free unlimited super-resolved microscopy in transmission exploiting the saturation of the absorption states of the molecules under investigation within a pump-probe temporal window, nonlinear interactions including multiphoton excitation and high-order harmonic generation.

     
  3. 3.

    Label-free microscopy based on Mueller and Jones matrix signatures from angular scattering processes and exploiting differential polarization interactions and refractive index mismatches in the VIS-IR regions.

     
Aspects related to the different SNR and variable spatial/temporal resolutions can be technically solved and mathematically analyzed. What is relevant it is that they bring unique multimodal capabilities when collected all together. Figure 21.37 sketches a possible configuration [21.277, 21.278]. So far, LIQUITOPY® means that a brand new image can be produced by the microscope itself, this image being made by a mix of \(C_{1},\dots,C_{n}\), properly re-scaled if acquired at different resolution or pixel size. This is the liquid image, because for each point of the image, there is a decision made by the microscope to put at that certain pixel a specific contrast that comes from \(C_{1},\dots,C_{n}\) available in real time. Machine and deep learning approaches in microscopy [21.390, 21.391, 21.392, 21.393] are a natural partner for the LIQUITOPY® image formation scheme. The authors would like to coin for such an approach the term multimessenger microscopy ( ) considering the different messages from the sample that the multiscale and multimodal methods can collect to form images and to decipher fundamental questions in cellular and molecular biology in a super-resolution scenario [21.246].
Fig. 21.37

Possible architecture for a multimessenger microscope within the LIQUITOPY® concept . SPAD single photon avalanche diode, complementary metal–oxide semiconductor

Notes

Acknowledgements

The first Italian TPE architecture realized at LAMBS was supported by INFM grants. LAMBS-MicroScoBio is currently funded by IFOM (Istituto FIRC di Oncologia Molecolare, FIRC Institute of Molecular Oncology, Milano). This chapter is dedicated to the memory of Osamu Nakamura, who passed away January 23, 2005 at Handai Hospital.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dept. of NanophysicsItalian Institute of TechnologyGenoaItaly
  2. 2.Dept. of NanoscopyItalian Institute of TechnologyGenoaItaly
  3. 3.Nikon Imaging CenterItalian Institute of TechnologyGenoaItaly
  4. 4.Dept. of PhysicsUniversity of GenoaGenoaItaly

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