I have learned that by Using Rayleigh Sommerfeld boundary condition, the inconsistency, which is present in the Fresnel-Kirchhoff Diffraction theory, can be removed. But the Fresnel-Kirchhoff Diffraction theory is valid when the the dimension of the aperture is large compared to the wavelength of the incoming wave. My question is that can we use the Rayleigh- Sommerfeld Diffraction theory for the case, where the dimension of the aperture is alomost or nearly equal to the wavelength? If possible, then would you please give me any reference.
The answer is yes. When the linear dimension of the aperture is almost nearly equal to the wavelength, then using Rayleigh-Sommerfeld diffraction formula one can get the answer. For detail discussion and derivation the following reference is given: 1) E. Marchand & E. Wolf, Consistent formulation of the Rayleigh-Kirchhoff diffraction theory , Journal of Optical society of America, Volume 56, Number 12., December, 1966.