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

Justo Arines

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 4𝑓 system. I provide theoretical and experimental evidence. The experimental setup consisted of two 4𝑓 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 4𝑓 system are related independently of the magnification of the 4𝑓 system by the following equation: 𝑏𝑖=(−1)𝑛𝑎𝑖, with 𝑛 being the order of the radial Zernike polynomial.