Spatial filtering techniques are used for enhancing the features of amplitude objects where part of the Fourier spectrum is either blocked or transmitted depending on the filtering scheme. Mostly these filters can be described as amplitude or binary filters. In the conventional 4f spatial filtering scheme, however, if the amplitude object is replaced with a phase object and the spatial filter with a phase filter, the phase filter only alters the phase of part of the Fourier spectrum. Such a processing scheme is nothing but phase contrast imaging which is widely used to observe phase objects.
Phase objects are transparent – they provide no contrast with their environment and alter only the phase of the wave. The optical thickness of such objects generally varies from point to point due to changes in either the refractive index or physical thickness or both. Since eye cannot detect the changes in phase variations, phase objects are invisible to the naked eye. However, if an additional phase difference is created between the undeviated (low spatial frequencies) and deviated (high spatial frequencies) light, then they interfere either constructively or destructively (depending on the amount of phase added) thereby converting the phase variation into amplitude contrast. Phase contrast imaging was developed in 1933 by Zernike [39
] to observe phase objects. He used a phase plate to create a π/2 phase difference between the undeviated light and the light diffracted by the object thereby transforming minute variations in phase of the object into corresponding changes in the image contrast. This principle is exploited in the phase contrast microscope which is widely used in teaching and research labs to view high-contrast images of transparent specimens, such as living cells (usually in culture), microorganisms, thin tissue slices, lithographic patterns, fibers, latex dispersions, glass fragments, and subcellular particles (including nuclei and other organelles).
Several alternative concepts for phase contrast imaging are demonstrated to avoid the complications with the usage of phase plate as a phase filter. It is difficult to place the phase plate at the exact location so that the required phase shift is induced between low and high spatial frequencies, and manufacturing the phase plate is also not trivial. Liu et al. used photorefractive crystals at the Fourier plane to introduce uniform phase shift to low spatial frequency components [40
]. A C-cut LiNbO3
:Fe crystal sheet served as the phase filter and good phase contrast images are obtained. Glückstad worked out both theoretical and experimental ways to improve imaging of phase objects [41
]. As an extension to Zernike phase contrast configu-ration, they showed that phase-only encoding utilizing full-range (0–2π) yields phase-only imaging with high energy efficiency.
The optically addressed spatial light modulator (OASLM) also serves as a nonlinear filter when placed at the Fourier plane and edge enhancement and phase contrast imaging are demonstrated [43
]. The required phase change is obtained through the dependence of the extraordinary index of refraction of OASLM on voltage. Similarly, Komorowska et al. used an OASLM made of a planar nematic liquid crystal layer sandwiched between a photoconducting polymer and a polyimide orienting layer and performed phase contrast imaging [44
]. The induced phase modulation is proportional to the intensity of the incident light on the OASLM.
Popescu et al. developed Fourier phase microscopy by combining phase contrast microscopy and phase shifting interferometry (PSI) to quantify the phase shifts induced by the phase objects [21
]. Fourier transform of the object is projected onto the surface of a reflective programmable phase modulator (PPM) and the phase of diffracted light is shifted into four increments of π/2 with respect to the average field (undeviated or dc), as in typical PSI measurements. After recording four interferograms, the phase shift associated with the object is evaluated qualitatively at each and every point of the field of view.
Nonlinear optical materials are also used as phase filters. Castillo et al. utilized the Kerr-type nonlinear property of bacteriorhodopsin film for self-induced Zernike-type filter and obtained phase contrast images [45
]. Sendhil et al. exploited the intensity dependent refractive index of zinc tetraphenyl porphyrin for phase contrast imaging [46
].In these methods, the zero order of the Fourier spectrum induces intensity dependent refractive index changes thereby modifying its phase. Since only the zero order induces a phase shift and not the higher orders, a phase filter is created and phase contrast imaging is performed.
Photothermal induced birefringence property of dye doped twisted nematic liquid crystals are exploited for self-adaptive all-optical Fourier phase contrast imaging of biological species [47
]. When the dye doped twisted nematic liquid crystal cell is placed at the back focal plane of a converging lens, high intensity low spatial frequencies induce local liquid crystal molecules into isotropic phase, whereas low intensity high spatial frequencies are not intense enough and molecules in this region remain in an anisotropic phase. Liquid crystal molecules in the anisotropic phase add certain amount of phase to the incident polarized light, whereas the molecules in the isotropic phase do not add any additional phase. Therefore, the high spatial frequencies acquire an additional π/2 phase as they transmit through the self-induced anisotropic phase of local liquid crystal molecules. The low spatial frequencies, however, transmit through the self-induced isotropic phase of liquid crystal molecules without acquiring any phase difference. This leads to a relative phase difference of π/2 between high and low spatial frequencies, primary criteria for phase contrast imaging, at the exit plane of liquid crystal cell.
illustrates images of paramecium. Paramecia are unicellular microorganisms belonging to the protoctist phylum Ciliophora. Members of this phylum (ciliates) are characterized by their cigar or slipper shape and external covering of continuously beating, hair-like cilia, and these fine structures in particular are not always easy to visualize with bright field microscopy unless the rest of the specimen is out of focus. The bright field image obtained with our system () shows the distinguishing specimen outline and oral groove of the paramecium but not much more. displays the Fourier phase contrast image where the outline of the Paramecium is identifiable, and the external fine hair-like structures called cilia can be seen at the posterior end (top of the image). The feeding structure, the oral groove and other internal structures are clearly visible.
Fourier phase contrast imaging of Paramecium. (a) Bright field image of live Paramecium. (b) Corresponding Fourier phase contrast image.
We also applied the Fourier phase contrast technique to view onion peel. Onion cells from the skin of an onion bulb are commonly used for early training comparisons between plants and animals. The thin layer of cells is so translucent that phase contrast or staining is needed for viewing. shows a bright field image of such a preparation of onion cells, the walls and nuclei are visible but that is greatly enhanced with the phase contrast image seen in .
(a) Bright field image and (b) Fourier phase contrast image of onion cells.