RESUMEN
An exact equation to relate the optical path differences (OPD) with its transversal aberration components (TAC) is determined. The OPD-TAC equation reproduces the Rayces formula and introduces the coefficient for the longitudinal aberration. The defocus orthonormal Zernike polynomial (Z DF) is not a solution for the OPD-TAC equation since the obtained longitudinal defocus depends on the ray height on the exit pupil, meaning that it cannot be interpreted as a defocus. In order to find an exact expression for OPD defocus, first, a general relationship between the wavefront shape and its OPD is established. Second, an exact formula for the defocus OPD is established. Finally, it is proved that only the exact defocus OPD is an exact solution of the exact OPD-TAC equation.
RESUMEN
In a previous paper [Appl. Opt. 61, C20 (2022)] it was proven that for a circular exit pupil and any optical path differences, the border of any spot diagram is integrated by the caustic surface and/or marginal rays. In this paper, the previous results are extended to annular (circular an elliptical) as well as hexagonal (single and segmented) exit pupils. Several examples of wavefronts affected by linear combinations of orthonormal Zernike aberrations are shown.
RESUMEN
In this paper, it is proven that for any optical system with a circular exit pupil and wavefronts affected by any aberrations, the borders of all leaving rays are caustic surfaces and/or marginal rays. Several examples are shown for wavefronts affected by linear combinations of Zernike aberrations.