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What should be done to the measured Zernike coefficients when conjugating the pupil and wavefront sensor planes with a 4f system: discussion

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Abstract

The aim of this paper is to describe and demonstrate what should be done to the measured Zernike coefficients when conjugating the pupil and wavefront sensor planes with a ${4}f$ system. I provide theoretical and experimental evidence. The experimental setup consisted of two ${4}f$ systems of magnifications 1 and 1/3 with their corresponding wavefront sensors at their ends. Spherical and cylindrical trial lenses were measured. In addition, I measured a phase plate with high-order aberrations. I show that the Zernike coefficients of the wavefront expansion at two planes conjugated by a ${4}f$ system are related independently of the magnification of the ${4}f$ system by the following equation: ${b_i} = {(- 1)^{n}}{a_i}$, with $n$ being the order of the radial Zernike polynomial.

© 2021 Optical Society of America

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