Validity of the Kirchhoff approximation for diffraction by weak phase objects

Abstract

The angular spectra of the diffraction fields of small and weak phase objects calculated by scalar Kirchhoff and Rayleigh-Sommerfield diffraction theories with adapted Kirchhoff boundary conditions are compared with the angular spectrum evaluated by Wolf [Optics Comm. 1 (1969) 153] derived in close analogy to the first Born approximation. Contour plots show the deviations from the theories depending on phase object thickness and spatial frequency. The phase objects should have a finite thickness d of approximately λ to minimize the deviations caused by the first Rayleigh-Sommerfeld diffraction theory, a result in contradiction to calculations of Evans [Optics Comm. 2 (1970) 317]. On the other hand a vanishing thickness is required in the second Rayleigh-Sommerfeld diffraction theory. The results agree with experiments carried out with electromagnetic cm-waves.