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6 March 2013 A polynomial phase-shift algorithm for high precision three-dimensional profilometry
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The perspective effect is common in real optical systems using projected patterns for machine vision applications. In the past, the frequencies of these sinusoidal patterns are assumed to be uniform at different heights when reconstructing moving objects. Therefore, the error caused by a perspective projection system becomes pronounced in phase-measuring profilometry, especially for some high precision metrology applications such as measuring the surfaces of the semiconductor components at micrometer level. In this work, we investigate the perspective effect on phase-measuring profilometry when reconstructing the surfaces of moving objects. Using a polynomial to approximate the phase distribution under a perspective projection system, which we call a polynomial phase-measuring profilometry (P-PMP) model, we are able to generalize the phase-measuring profilometry model discussed in our previous work and solve the phase reconstruction problem effectively. Furthermore, we can characterize how the frequency of the projected pattern changes according to the height variations and how the phase of the projected pattern distributes in the measuring space. We also propose a polynomial phase-shift algorithm (P-PSA) to correct the phase-shift error due to perspective effect during phase reconstruction. Simulation experiments show that the proposed method can improve the reconstruction quality both visually and numerically.
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Fuqin Deng, Chang Liu, Wuifung Sze, Jiangwen Deng, Kenneth S. M. Fung, and Edmund Y. Lam "A polynomial phase-shift algorithm for high precision three-dimensional profilometry", Proc. SPIE 8661, Image Processing: Machine Vision Applications VI, 866102 (6 March 2013); doi: 10.1117/12.2001418;

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