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 the final optic surface. Here, we present our method and experimental results for measuring a 1 m inflatable reflector’s shape response to dynamic perturbations in a thermal vacuum chamber. Our method uses phase-measuring deflectometry to track shape change in response to pressure change, thermal gradient, and controlled puncture. We use an initial measurement as a virtual null reference, allowing us to compare 500 mm of measurable aperture of the concave f/2, 1-meter diameter inflatable optic. We built a custom deflectometer that attaches to the TVAC window to make full use of its clear aperture, with kinematic references behind the test article for calibration. Our method produces 500 × 500 pixel resolution 3D surface maps with a repeatability of 150 nm RMS within a cryogenic vacuum environment (T = 140 K, P = 0.11 Pa).
One of deflectometry’s cardinal strengths is its ability to measure highly dynamically sloped optics without needing physical null references. Accurate surface measurements using deflectometry, however, require precise calibration processes. In this Letter, we introduce an alignment technique using a computational fiducial to align a deflectometry system without additional hardware equipment (i.e., algorithmic innovation). Using the ray tracing program, we build relationships between the plane of the screen and detector and algorithmically generate a fiducial pattern for the deflectometry configuration. Since the fiducial pattern is based on ideal system geometry, misalignment of the unit under test with its target position causes a discrepancy between the actual image on the camera detector and the ideal fiducial image. We leverage G and C vector polynomials to quantify misalignment and estimate the alignment status through a reverse optimization method. Simulation and experimental results demonstrate that the proposed algorithm can align the 195 m m × 80 m m of a rectangular aperture freeform optic within 10 µm of peak-to-valley accuracy. The computational fiducial-based alignment algorithm is simple to apply and can be an essential procedure for conventional methods of deflectometry system alignment.
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