Determination of off-axis aberrations of imaging systems using on-axis measurements

Abstract

Imaging aberrations that have linear dependence on field angle are caused by pupil aberrations that can be described using the Abbe sine condition. This well-known relationship is frequently used to guide the design of optical imaging systems. For example, the aberration of coma is eliminated in the design of axisymmetric systems by controlling the pupil distortion, as defined by a standard implementation of the sine condition. An optical system with misalignments of surface irregularities will suffer pupil distortions that are quantified using a more generalized form of the sine condition. Such pupil aberrations create image aberrations that have linear dependence on field angle. While it is possible to infer the state of alignment by measuring multiple field points, it may be more straightforward to perform a single on-axis measurement of the sine condition violations. This paper summarizes the generalized sine condition and relationship between violations of this condition and aberrations with linear field dependence. An application is discussed for measuring sine condition violations of a 4-mirror system, which allows determination of the off-axis aberrations.