The Mueller pupils Reduction-Zernike polynomial decomposition and polarization design criteria for the astronomical telescope system

This study introduces a novel method for decomposing polarization aberrations. It uses two sets of reduction matrices to decompose the diattenuation and retardance Mueller matrix into five independent reduction coefficients. And then, it uses Zernike polynomials to decompose these coefficients at the exit pupil, thereby providing a method for quantitatively analyzing the polarization aberrations. This method also gives the constraint values of the Zernike term of polarization aberrations during astronomical telescope design. Finally, the effectiveness and correctness of the process are verified by simulation of the actual optical system, pointing out that the D₁, D₂, D₃, and R₅ terms need to be calibrated and optimized to ensure polarization accuracy. This method offers a valuable tool and theoretical guidance for the polarization design of high-precision optical systems.