Computational vector fiducial for deflectometry system alignment

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 195mm×80mm 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.