Generalized Phase Contrast

Light intensity is easily quantified by using calibrated detectors that can directly exploit the energy flux from an incident light. Spatial intensity variations can be imaged using an array of such energy detectors, as in a camera, for instance. On the other hand, light phase is invisible to energy detectors and is usually detected indirectly by exploiting phase-dependent phenomena that affect intensity. For example, intercepting light with a lenslet array would generate an array of spots at the common focal plane of the lenslets and any phase perturbations could be deduced from observed changes in the configuration of the intensity spots. When using coherent illumination, a common method consists of introducing a reference beam and then analyzing the phase-dependent interference pattern to determine the phase perturbation. Working without the benefit of coherent laser sources, Gabor invented the first holograms capable of interferometri-cally recording phase information by adapting Zernike's phase contrast configuration, where the reference and the object beams propagate along a common path to ensure coherence [1]. Aside from coherence, common-path interferometry also surmounts typical experimental hurdles that tend to smear out the interference pattern with its relative tolerance to vibrations and fluctuations in the ambient conditions, which becomes a major problem when the reference beam travels along a different path.

The accuracy of the extracted phase information from the output of an interferometer is dependent on assumptions about the reference wave, and this is no different for a common-path interferometer. Thus it is vital to examine how a phase contrast method models the reference wave in order to understand its limitations. In this chapter, we examine the assumptions employed in Zernike's phase contrast method. Although sufficient for very thin phase objects like biological samples, its limited range of validity necessitates a generalized formulation to encompass a wider range and broaden the horizon for possible applications.