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When the Fresnel–Kirchhoff (FK) diffraction integral is evaluated exactly (instead of using the Fresnel approximation), the well-known mathematical inconsistency in the FK boundary conditions leads to unacceptable results for the intensity of Poisson's spot. The Rayleigh–Sommerfeld (RS) integral has no inconsistencies and leads to an accurate description. The case for RS is bolstered by the observation that it is equivalent to Fourier propagation.

Gaussian beam modes can be used for efficient computation of Fresnel diffraction patterns. Using results derived in a previous paper for the case of the uniformly illuminated circular aperture, an efficient method for calculating the patterns of a circular obstacle and zone plate is outlined, and three-dimensional diffraction pattern plots are presented. The approach is interesting for those teaching optics using the methodology of computational physics.

Gaussian beam modes, which are normally associated with laser cavities and quasi-optical propagation, can be used to solve some classic problems in Fresnel diffraction. A particular advantage of the technique is that, for the cases of the uniformly illuminated circular aperture, narrow slit and straight edge, it is possible to derive analytical recursive relationships for the mode amplitude coefficients, which allow for speedy computation of the diffraction patterns.

We comment on the nature of an unexpected real image obtained in Fresnel holography in terms of pinhole imaging.

The author presents a method of calculating the radial intensity distribution of the Fresnel diffraction pattern of a circular aperture. The method uses the concept of counting whole or partial Fresnel zones and has an accuracy of about five per cent of the maximum intensity, although it can be refined to improve this figure somewhat. The method can also be applied to calculations of the Fresnel diffraction patterns of more complicated apertures.

The author confirms the recent work of Southwell (1981) showing that the Fresnel approximation is valid for points within the geometrically defined beam even very close to the diffracting object. By providing a physical explanation for this fact, the paper goes on to derive qualitatively the shape of the entire region in which the Fresnel approximation is valid.