The optical transfer functions for variable focus error are contained as a single picture representation in the ambiguity function that is associated with the pupil function. This picture representation is shown to be useful for designing pupil functions that increase the depth of focus. We specify a criterion for an optical transfer function with low sensitivity defocus in terms of a nonlinear differential equation for the point spread function. Based on this approach, we design and compare five new spatial filters for achieving high focal depth.

The Strehl ratio, in the form of McCutchen's theorem, is employed to design a spatial filter that increases the depth of focus. Computer-simulated images show the increment in focal depth.

We show that a zone plate with a prespecified number of foci, which are separated axially by Rayleigh's limit of resolution, can create an arbitrarily high focal depth when used as an apodizer over an otherwise clear aperture. We discuss the resolution and light gathering power of this method.

A model of the human eye has been developed, including scattering from cataracts inside the nucleus of the lens. The cataracts are modeled as spherical particles with refractive index different from that of the surrounding lens medium. Scattering from the retina is also included in the simulations. Variations of scattering particle diameter, number of particles, and wavelength of the illuminating light are investigated. It is shown that particle size is the most important parameter affecting the scattered light, and that the scattering from the retina can mask the effect of the scattering particles, for some range of the parameters.

A new approach for obtaining line-spread functions (LSF's), which vary slowly in out-of-focus planes, is described. Based on this approach, we report a LSF that shows relatively less sensitivity to focus errors than that shown by both the diffraction-limited LSF and a LSF previously reported.