Fourier analysis of phase contrast microscopy of nanometric surfaces

The application of phase contrast microscopy is investigated by the derivation of analytical relationships between surface profiles and the light intensity produced. This analysis is based upon ideal conditions. In order to investigate the behaviour under realistic conditions, a computer simulation program has been devised. This program is based on the Fresnel approximation of the Kirchhoff-Fresnel diffraction integral. The approximation is implemented using a Fourier transform equivalent. Various optical and surface parameters can be varied. The program also produces image blur as produced by nonideal lenses. The results obtained are (i) Zernike spot size effects, and (ii) surface amplitude effects. In the first case a spot that is too small introduces an artificial curvature in the surface profile, so it is safer to apply a relatively large spot. This only affects the low-frequency components of the surface, which are not considered to be part of the surface finish. In the second case surface amplitudes of up to 20 nm can be reasonably reconstructed by a simple formula. Larger amplitudes will need some iterative methods for profile reconstruction due to nonlinear distortions.