Normalized quadrature four-frame phase shift algorithm based on crossed fringe patterns

Lei Tang; Dahai Li; Ruiyang Wang; Wuxiang Zhao; Jiangang Zhao

doi:10.1117/1.OE.58.3.035103

27 March 2019 Normalized quadrature four-frame phase shift algorithm based on crossed fringe patterns

Lei Tang, Dahai Li, Ruiyang Wang, Wuxiang Zhao, Jiangang Zhao

Author Affiliations +

Funded by: National Natural Science Foundation of China (NSFC), National Natural Science Foundation of China, National Key R&D Program of China, National Key Research and Development Program of China, National Key Research and Development Program, National Key RD Program of China, National Key Research and Development Plan, Equipment Research Program in Advance of China

Optical Engineering, Vol. 58, Issue 3, 035103 (March 2019). https://doi.org/10.1117/1.OE.58.3.035103

Abstract

In the phase measurement deflectometry, sinusoidal fringe patterns are separately projected on a specular test surface, and the distorted fringes reflected by the surface are recorded by a charge-coupled device (CCD) camera. The phase shift algorithm is used to find the position of the light source on the display corresponding to the pixel point on the CCD, thereby calculating the slope of each point on the element to be tested, and finally retrieving the surface shape of the test element by using the surface reconstruction algorithm. The phase information is usually obtained by traditional 16-step phase-shifting algorithm, which involves certain complicated and time-consuming procedures, for instance, fringe projection in the horizontal and vertical directions. Therefore, to avoid these procedures, a four-step phase shift algorithm based on crossed fringes is proposed. Based on Gram–Schmidt orthonormalization method, only four crossed fringe patterns are needed to determine the phase in both directions simultaneously. Both numerical simulation and experiment are conducted to verify the validity of the algorithm.

Citation Download Citation

Lei Tang, Dahai Li, Ruiyang Wang, Wuxiang Zhao, and Jiangang Zhao "Normalized quadrature four-frame phase shift algorithm based on crossed fringe patterns," Optical Engineering 58(3), 035103 (27 March 2019). https://doi.org/10.1117/1.OE.58.3.035103

Received: 29 October 2018; Accepted: 15 March 2019; Published: 27 March 2019

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