Multiple-beam interference microscopy

Abstract
Many objects examined under the microscope influence the phase but not the amplitude of the incident light, and the image is of such poor contrast that much structural detail is lost. Multiple-beam interference, two-beam interference and phase-contrast microscopy all present means of overcoming this difficulty. The diffraction theory of multiple-beam interference microscopy, which has hitherto been neglected, is here developed by regarding the object under study as a phase grating; a comparison is then made with the two other forms of microscopy. In phase-contrast microscopy (Zernike 1935 a, b, 1942) the effective phase and amplitude of the zero-order beam are suitably changed by an absorbing phase plate situated in the rear focal plane of the objective or in an equivalent plane. Two-beam interference microscopy, such as is encountered in modified Michelson interferometers, closely resembles phase-contrast microscopy, because a coherent wave is superimposed upon the diffracted waves from the object, thereby effectively altering both the phase and amplitude of the zero-order beam (Berti 1948, 1951). With multiple-beam interference microscopy (Tolansky 1948), however, the phase and amplitude of each diffracted beam are changed to an extent determined by the phase and amplitude of all the other diffracted beams. This relationship prevents one from modifying a given beam without influencing all the others. When the interferometer is viewed in reflexion these modified diffracted waves are superimposed upon a coherent background, so that, when the interferometer reflectivity is low, the arrangement produces effectively two-beam interference. As the lateral structure of the object becomes finer, the image formed by multiple-beam interference becomes a less faithful portrayal of the object structure; the extent of this infidelity is enhanced as the reflectivity, gap and wedge angle of the interferometer are increased. The advantage of multiple-beam interference is the high accuracy with which phase differences within the object can be measured.

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