Use of Pupil Mapping for Measurement of Linearly Field-dependent Aberrations

Abstract

Rather than measuring aberrations at several locations across the field to quantify the alignment of an optical system, we show how a simple measurement of the pupil mapping can be used to measure the off-axis performance of the system. This method uses the Abbe sine condition to relate the mapping between the entrance and the exit pupils, where the violations of the generalized sine condition are used to determine the pupil mapping error. From this pupil mapping, the linearly field-dependent aberrations can be calculated. One of the advantages to this method is that all of the test equipment can be aligned to the center of the field while making measurements of the off-axis performance, which reduces the uncertainty of the measurement. This advantage is particularly evident with systems or sub-systems that have large inherent aberrations where off-axis alignment tolerances are very tight. Additionally, in the Sine Condition Test (SCTest), the test equipment can be designed to compensate for the native Siedel coma in the system. This makes it more straightforward to measure the linearly field dependence of the aberrations. By reducing or removing coma, the measurement uncertainty is further reduced. This work begins by explaining the background of the Abbe sine condition, derivation of the pupil mapping error, and an overview of linearly field-dependent astigmatism that arises from misalignment. Next, the general method of implementation is discussed, and expanded further by exploring the two different source options: a point source with a grating or a flat-panel display. Experimental results from proof of concept systems are shown for both cases. Next, this dissertation explains how the SCTest can be implemented on more complex systems. Last, this dissertation shows how the linear aberrations, along with constant field-dependent aberrations, can be used to align a system. Here, the application of the alignment version of the SCTest on a three mirror anastigmat (TMA) is discussed. Using simulation, this dissertation then investigates the behavior of the alignment SCTest for various levels of mirror misalignment, mirror fabrication errors, and misalignment of the test equipment. All of these tests show that the alignment SCTest can successfully align an optical system.