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.
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.
Apodizers with relatively high transmittance over an annular region of the exit pupil can reduce the sensitivity to defocusing and to spherical aberration [Opt. Lett. 11, 487 (1986)]. Here, we analyze the imaging properties (pupil functions, point spread functions, optical transfer functions, and Strehl ratios) of the Bessel type of annular apodizers. We also show some computer-simulated images, obtained with and without this kind of annular apodizer.
Image formation at out-of-focus planes has been the subject of several recent papers that explore the following issues: the focal shift effect, automatic focusing, understanding the properties of 3-D wave fields, and increasing the depth of focus. A simple way to analyze defocused imagery is to employ the Strehl (irradiance) ratio, which is defined as the ratio between the on-axis irradiance of the defocused point spread function (PSF), and the on-axis irradiance of the diffraction-limited PSF. Here, we apply the Strehl (irradiance) ratio to design a spatial filter that increases the depth of focus. We explain how the Strehl ratio, in the form of McCutchen's theorem, can be used to design a spatial filter to increase the depth of focus. We present computer simulated images to show the increment in focal depth.
Apodizers designed to increase focal depth have been conveniently interpreted as the Fourier spectra of certain objects, which then exhibit high focal depth. These objects were employed to create self-images with high focal depth.1 Now we identify circular symmetrical objects that show low sensitivity to spherical aberration. Based on this interpretation, we propose zone plate profiles that will create self-images beyond the paraxial approximation.
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