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.
