Deflectometry for Astronomical Reflectors and Industrial Optics

Abstract

In the last decade, slope-measuring deflectometry has seen rapid progress in configuration design, hardware calibration, and computational processing. As a highly-reconfigurable, non-null technique, deflectometry fills many widening metrology gaps left by optical design trends in freeform industrial optics and astronomical reflectors. This study advances the accuracy of the art and the variety of measurable optical surfaces across three major topics. The first topic is the measurement of large inflatable membrane reflectors with phase-measuring deflectometry. The metrology of membrane structures, especially inflatable, curved, optical surfaces, remains challenging. Internal pressure, mechanical membrane properties, and circumferential boundary conditions imbue highly dynamic slopes to a varifocal optical surface. Beyond measurement in ambient, I present the method and experimental results for measuring a 1-meter inflatable reflector’s shape response to pressure change, thermal gradient, and controlled puncture across multiple refractive interfaces in thermal vacuum. The method produced 500 × 500 pixel resolution 3D surface maps with a repeatability of 150 nm RMS at T = 140 K and P = 0.11 Pa. In the second topic, I propose, implement, and analyze a novel on-axis deflectometry system that uses custom non-planar illumination source to measure convex axicons. Axicons are challenging to measure due to their characteristically steep, convex geometry. However, if an axicon is coaxially aligned with a camera and a surrounding cylindrical illumination source, high-resolution surface measurements can be obtained via the principle of deflectometry. Emitted from the temporally modulated source, light deflects at the conical surface and into the entrance pupil of a camera, illuminating the full axicon aperture. Deflectometry measurements of a 100° and 140° axicon showed holistic cone angle agreement within 0.035° against touch probe data and up to 7.93 micron root mean square difference from a best-fit cone. In the final topic, I propose and examine the influence of radiometric shift variance in deflectometry. In deflectometry, illumination variation across the detector is the consequence of two features: irradiance fall-off with target field angle from the camera optical axis, and the blur of extended source points at the detector because the camera is only conjugate to the test optic and not the source. I derive how the combined effect of these factors manifests as low-order shape error in long-wave infrared line-scanning deflectometry. Then, I provide a radiometrically-faithful suite of raytraced studies to obtain the surface error as a function of deflectometry system geometry. Empirical relationships generalized by this case study show that the classical centroiding algorithm underestimates surface power and overestimates astigmatism in final surface maps.