Defocus transfer function for circularly symmetric pupils

Abstract

We present a two-dimensional function that graphically illustrates the effects of defocus on the optical transfer function (OTF) associated with a circularly symmetric pupil function. We call it the defocus transfer function (DTF). The function is similar in application to the ambiguity function, which can be used to display the OTF associated with a defocused rectangularly separable pupil function. The properties of the DTF make it useful for analyzing optical systems with circularly symmetric pupils when one is interested in the OTF as a function of defocus. In addition to presenting these properties, we give examples of the DTF for systems with clear, bifocal, and annular pupil functions.

The optimal axial interval in estimating depth from defocus

“…(16) is zero, is related to local extrema of the defocus transfer function. Unmonotonic transfer functions are theoretically predicted in [5,10,20] and measured in [8]. Thus our analysis provides guidelines for determining the optimal intervals and frequencies in a broad range of defocus PSF's.…”

Computational approach for depth from defocus

“…The blurring effect can be thought of as a convolution between the perfectly focused image and a blurring function called point spread function ͑PSF͒. In vision literature various models have been proposed to approximate the blurring function 10,23,24 but in practice the two-dimensional Gaussian 1,9,25 has been widely employed to approximate the PSF when paraxial geometric optics are used and diffraction effects are negligible.…”

Computational aspects of the through-focus characteristics of the human eye

“…Such attempts have been made with the introduction of the defocus transfer function [21][22][23] and the extended Nijboer-Zernike (ENZ) approach [24,25]. Although both methodologies are attractive for man-made optical systems, they have substantial limitations when it comes to utilizing them to study the eye's optical system because the defocus transfer function is limited to circularly symmetric aberrations while the ENZ approach is valid only for the even terms of Zernike polynomial expansion.…”