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A recently reported vision ray metrology technique [Opt. Express29,43480(2021)OPEXFF1094-408710.1364/OE.443550] measures geometric wavefronts with high precision. This paper introduces a method to convert these wavefront data into height information, focusing on the impact of back surface flatness and telecentricity errors on measurement accuracy. Systematic errors from these factors significantly affect height measurements. Using ray trace simulations, we estimate reconstruction errors with various plano-concave and plano-convex elements. We also developed a calibration technique to mitigate telecentricity errors, achieving submicron accuracy in surface reconstruction. This study provides practical insights into vision ray metrology systems, highlighting validity limits, emphasizing the importance of calibration for larger samples, and establishing system alignment tolerances. The reported technique for the conversion of geometric wavefronts to surface topography employs a direct non-iterative ray-tracing-free method. It is ideally suited for reference-free metrology with application to freeform optics manufacturing. 

A novel Vision ray metrology technique is reported that estimates the geometric wavefront of a measurement sample using the sample-induced deflection in the vision rays. Vision ray techniques are known in the vision community to provide image formation models even when conventional camera calibration techniques fail. This work extends the use of vision rays to the area of optical metrology. In contrast to phase measuring deflectometry, this work relies on differential measurements, and hence, the absolute position and orientation between target and camera do not need to be known. This optical configuration significantly reduces the complexity of the reconstruction algorithms. The proposed vision ray metrology system does not require mathematical optimization algorithms for calibration and reconstruction – the vision rays are obtained using a simple 3D fitting of a line. 

A super-sensitive phase measuring Deflectometry technique is presented to obtain effective fringe periods beyond the MTF limit. This allows decreasing significantly the random component of the uncertainty in the measured slope.