Conjugate phase plate use in analysis of the frequency response of imaging systems designed for extended depth of field

Abstract

We unveil a relationship between generating a point spread function with a pair of conjugate phase elements and visualizing the modulation transfer function (MTF) of a single phase element for a variable focus error, at a tunable spatial frequency. We show that the defocused MTF of a pair of conjugate phase elements can be expressed as the modulus of the second order ambiguity function of a single phase element. Finally, we propose a tunable wavefront coding technique with a pair of quartic (4th power) conjugate phase elements.

Key concepts for extending the depth of field with high resolution

“…Our following discussion extends the results reported in references [38][39][40][41][42][43]. If one neglects the size of the mask, one element (of the AlvarezLohmann pair) has the following complex amplitude transmittance ( ) ( ) (14) In Eq.…”

“…(14) By applying this result, one can propose the use of a mask that has phase variations to the four-power. This mask generates a cubic phase mask, with controllable optical path difference [37][38][39][40]. In mathematical terms, the complex amplitude transmittance of a single element is…”

Noncoherent imagery: a novel approach

“…Due to this interconnectivity, new optical devices have been proposed for extending the depth of field, while preserving the full pupil aperture [1]- [10]. These new devices are able to generate modulation transfers functions (MTFs) with the following two features.…”

Tunable sinusoidal Phase Gratings and sinusoidal Phase Zone Plates

“…These developments can be related to the efforts addressed to control fully (not only for extending) field depth; without modifying the size pupil aperture at [6,7].…”