Scalar diffraction theory is frequently considered inadequate for predicting diffraction efficiencies for grating applications where lambda/d>0.1. It has also been stated that scalar theory imposes energy upon the evanescent diffracted orders. These notions, as well as several other common misconceptions, are driven more by an unnecessary paraxial approximation in the traditional Fourier treatment of scalar diffraction theory than by the scalar limitation. By scaling the spatial variables by the wavelength, we have previously shown that diffracted radiance is shift invariant in direction cosine space. Thus simple Fourier techniques can now be used to predict a variety of wide-angle (nonparaxial) diffraction grating effects. These include (1) the redistribution of energy from the evanescent orders to the propagating ones, (2) the angular broadening (and apparent shifting) of wide-angle diffracted orders, and (3) nonparaxial diffraction efficiencies predicted with an accuracy usually thought to require rigorous electromagnetic theory.

Near-field diffraction patterns are merely aberrated Fraunhofer diffraction patterns. These aberrations, inherent to the diffraction process, provide insight and understanding into wide-angle diffraction phenomena. Nonparaxial patterns of diffracted orders produced by a laser beam passing through a grating and projected upon a plane screen exhibit severe distortion (W311). This distortion is an artifact of the configuration chosen to observe diffraction patterns. Grating behavior expressed in terms of the direction cosines of the propagation vectors of the incident and diffracted orders exhibits no distortion. Use of a simple direction cosine diagram provides an elegant way to deal with nonparaxial diffraction patterns, particularly when large obliquely incident beams produce conical diffraction.

The Fraunhofer criterion defines the location of the boundary between the Fresnel and the Fraunhofer diffraction regions and thus determines the location of that region commonly referred to as the far field. The Fraunhofer criterion is usually given as an axial distance much greater than some amount relative to the maximum dimension of the aperture. By recognizing that Fresnel diffraction patterns are merely defocused Fraunhofer diffraction patterns, we show that the Fraunhofer criterion can be written precisely in terms of an allowable tolerance on defocus. This new criterion provides insight that is useful to optical designers and engineers who routinely deal with such tolerances.