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We propose a method for designing apodizers that increase the depth of focus and reduce the influence of spherical aberration. These two properties are explicitly manifested in computer-generated pictures and values of the Strehl ratio for variable spherical aberration.

We present a family of asymmetric phase masks that extends the depth of field of an optical system. To verify our proposal, we compute several modulation transfer functions with focus errors, and we report numerical simulations of the images that can be achieved by use of our proposed procedure.

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.

We explore the use of phase profiles with fractional power for tailoring modulation transfer functions with high focal depth at high pupil apertures. We present numerical simulations of the images that can be obtained with certain fractional-power profiles.

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.