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.
This work presents a stable noise-robust numerical integration technique derived from a gradient representation of the Q-Forbes polynomials for surfaces with axial symmetry. This modal-integration technique uses an orthogonalization process through the Householder reflections to obtain a numerically orthogonal set for the surface slopes that is used to reconstruct the surface shape. It is shown that for typical Deflectometry measurements, the resulting random component of the uncertainty after numerical integration has a root mean square error well below 1nm.
Multi-wavelength phase unwrapping techniques have traditionally been used to unwrap the phase at the shortest measurement wavelength, where numerous techniques have been developed with distinct advantages for a given application. Nevertheless, multi-wavelength techniques are more than phase unwrapping approaches: super-sensitive multiwavelength interferometers have a lower uncertainty than conventional interferometers, multi-wavelength techniques can break the Nyquist limit and thereby relax the requirements on the measurement system, and multi-wavelength techniques have also unconventional applications as e.g. optical encryption. This work discusses different multi-wavelength techniques, derives new noise criteria with no approximations, and outlines important, but still little researched areas of multi-wavelength phase unwrapping techniques.
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