Ambiguity function as a design tool for high focal depth

Abstract

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.

Key concepts for extending the depth of field with high resolution

“…Later on, we explored the use of the ambiguity function for shaping the OTF [29][30][31]. For the sake of completeness of our presentation, we discuss out-of-focus image formation when using a classical, 4-f, optical processor, as the one in Fig.…”

Helical apodizers for tunable hyper Gaussian masks

“…This novel approach was later applied for expanding the OTF vs. focus errors as a Taylor series expansion 11 . It was found that half of the terms (of the Taylor series) can be reduced to zero if the complex amplitude transmittance of the pupil aperture is a hermitian function.…”

A two incoherent sources resolution criterion in the phase space

“…In optics, the WDF has been introduced by Bastiaans 16 and the most common optical set up used to display it has been implemented by Bartelt, et al 17 for the 1-D and 2-D spatial functions. A hybrid processor for image processing has been proposed by Gonzalo, et al 18 Other applications in optics can be found in the analysis of complex amplitude pupil functions 19 and in the explanation of paraxial polychromatic optics 20 . In most of the WDF applications implicitly are involved the linear, paraxial and isoplanatic conditions, and the mathematical properties of this function can be found in the classical paper of Claasen and Mecklenbräuker 21 .…”