Abstract
Single molecule detection (SMD) has become an important technique in recent years for studying dynamic processes such as chemical reactions and molecular motions at a fundamental level. Historically these processes are usually studied using methods based on ensemble averaging of a sample of molecules, however frequently the mean properties so found are insufficient. Studies on single molecules are thus advantageous as information, such as statistical distributions of particular quantities, is not lost by averaging. It should however be noted that even single molecule studies yield results that are temporally averaged over the course of the finite measurement time.
A physicist is just an atom’s way of looking at itself. Niels Bohr
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- 1.
The convention whereby an upper case letter denotes a random process and/or variable, whilst the lower case equivalent denotes a particular outcome is again used throughout this chapter.
- 2.
The independence of each \(Z_j\) can be shown to follow from the assumed independence of \(\tau _j\) regardless of the independence of \(\gamma _j\) [15].
- 3.
Although arguably a Fisher information analysis, as has been extensively utilised in this text, is possible using the derived PDFs, this is omitted here since consideration of the variance is adequate in highlighting the key points.
- 4.
Strictly speaking the integration should be performed over the Gaussian reference sphere, however for a low numerical aperture lens the inter-component mixing caused by bending of rays of light is negligible and it is hence satisfactory to integrate over the back focal plane. The form of the image field of an electric dipole using two high numerical aperture lenses was considered earlier in Sect. 6.4.2.1 in which it was found the field on axis takes the form \(\mathbf{ E} _2 \propto (K_0^A p_x,K_0^A p_y, K_0^B p_z)\),
where \(K_0^A\) and \(K_0^B\) are constants and \(K_0^B/K_0^A \ll 1\). This arrangement will be neglected in this chapter however due to its practical difficulties.
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Foreman, M.R. (2012). Single Molecule Studies. In: Informational Limits in Optical Polarimetry and Vectorial Imaging. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28528-8_8
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