Abstract

Analyses of the Zernike phase-contrast method in many standard texts^1,2 lead to a palpably wrong result. A common conclusion is as follows: For a phase object, whose amplitude transmittance is of the form expiϕ(x,y), the image irradiance goes as 1 + 2ϕ(x,y). Consider the case of a step phase object with amplitude transmittance 1 for x ᐸ 0 and expiα for x ᐳ 0. The standard analysis predicts a different image irradiance in the two areas. However, absolute phase is not manifested in an image, so an image is insensitive to an overall phase shift undergone by light in traversing the object. Thus the image of a broad clear area must be constant regardless of the thickness of the area. Therefore, the image of a phase step object must be identical in both regions, sufficiently far from the discontinuity. The error in the standard analysis is related to the commonly accepted notion that for a periodic object, as the period becomes large compared with the width of the lens response function, the form of each image unit is like that of a nonperiodic object. With the Zernike method, however, this is not the case.

© 1987 Optical Society of America