Alberto Cordero-Dávila

For annular (circular and elliptical) and hexagonal exit pupils with any optical path differences (described by Zernike Polynomials), it was proven [Appl. Opt. 61, 1876 (2022) [CrossRef] ; Appl. Opt. 61, C20 (2022) [CrossRef] ] that the border of any spot diagram is composed of the caustic surface and/or marginal rays. In this paper, the previous results are extended to segmented (by hexagons or trapezoids) exit pupils.

Abstract This work presents a dynamical analysis of a tool rotating freely due to the action of glass rotating at a constant angular velocity is presented. Preston [J. Soc. Glass Tech. XI, 214 (1927) ] analyzed tool movement neglecting the tool thickness, and only one torque component was obtained along the tool’s normal direction. From this analysis, Preston concluded that angular velocities for tool and glass must be equal, even when this is not true experimentally.

Abstract 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 (${Z_{\textit{DF}}}$) 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.