Simultaneous interferometric optical-figure characterizations for two optical elements in series: Proposal for a non-Newtonian numerical integration scheme

Abstract

The article proposes a scheme to break a Catch-22 loop in an optical-figure–wavefront measurement. For instance, to measure the tilt-independent optical figure of a nominal optical flat at cryogenic temperatures, one requires a cryogenic Dewar-window system for a Fizeau interferometer mainframe outside the Dewar to see through. The problem is: how to calibrate the window system in situ using the yet-to-be-calibrated nominal optical flat, and vice versa, in only one cryogenic cooldown? The proposal includes: (a) interferometric phase-map measurements with the test piece slightly offset in different transverse directions, and (b) an unconventional numerical integration scheme, starting with one-dimensional bidirectional integrations, to synthesize the two-dimensional wavefront distortion function. The numerical scheme helps minimize the nonuniformity in noise-power distribution that results from integrating phase-map data, and thus the associated uncorrelated random noise. The numerical integration scheme represents a non-Newtonian concept specifically for noise-carrying experimental data. The algorithm that determines the algorithm for the domain-shape-specific integration scheme is described in detail.