An analytic expression for the field dependence of three-order Zernike aberrations in decentered and/or tilted optical systems

The double Zernike polynomials can describe the aperture dependence and field dependence of non-coaxial optical system aberrations simultaneously, and characterize the complex optical aberrations, which are of great value in the optical system design and alignment. In this paper, the specific analytic forms of all third-order double Zernike aberrations in decentered and/or tilted optical systems are derived based on the nodal aberration theory. This paper realizes the orthogonalization of the third-order aberrations with different aperture dependence and field dependence. The calculation process of the third-order double Zernike aberrations is presented. The ray tracing of the Cassegrain telescope verifies the analytic derivation of the double Zernike aberrations.