The Theory of Using an Intensity-Correcting Algorithm to Overcome Quantization Error for Phase Measuring Profilometry

Abstract:

In the image process, intensity differs from its true value because the quantization process restricts image pixels to lie on an integer grid, and phase quantization error is introduced. In this paper, we propose a theory of using an intensity-correcting to overcome phase quantization error. According to the distribution of the intensity error in some pixels, the mathematical model of the intensity error is reconstructed to correct intensity values and reduce phase quantization error. Using specific example deduct the intensity-correction algorithm. At last, we compare the uncorrected quantization error and the quantization error after correction, and prove that the principle of this algorithm is right.

• Periodical: Advanced Materials Research (Volumes 718-720)
• Pages: 1170-1174
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.718-720.1170
• Online since: July 2013
• Authors: Qiu Ju Zhang, Yong Chang Wang, Kai Liu
• Keywords: Intensity Correcting, Intensity Quantization, Phase Error, Phase Measuring Profilometry

References

[1] V. SRINIVASAN, H. LIU, M. HALIOUA. Automated Phase-Measuring Profilometry of 3D Diffuse Objects. Applied Optics, vol. 23, no. 18, pp.3105-3108, 1984.

DOI: 10.1364/ao.23.003105

[2] R. ANCHINI, G.D. LEO, C. LIGUORI, A. PAOLILLO. A New Calibration Procedure for 3D Shape Measurement System Based on Phase-Shifting Projected Fringe Profilometry. IEEE Trans. Instrumentation and Measurement, vol. 58, no. 5, pp.1291-1298, May 2009.

DOI: 10.1109/tim.2009.2012952

[3] H. LIU, W. SU, K. REICHARD, AND S. YIN. Calibration-Based Phase-Shifting Projected Fringe Profilometry for Accurate Absolute 3D Surface Profile Measurement. Optics Comm., vol. 216, nos. 1-3,pp.65-80, 2003.

DOI: 10.1016/s0030-4018(02)02290-3

[4] P.J. TAVARES AND M.A. VAZ. Linear Calibration Procedure for the Phase-to-Height Relationship in Phase Measurement Profilometry. Optics Comm., vol. 274, no. 2, pp.307-314, 2007.

DOI: 10.1016/j.optcom.2007.02.038

[5] Eryi Hu, Yuan Hu, Haifeng Fang. A novel phase-recovering algorithm for the intensity quantization error in the digital grating phase-shifting profilometry. Optik, vol. 122, no. 2011, pp.2227-2229, 2011.

DOI: 10.1016/j.ijleo.2011.02.014

[6] Oleksandr A. Skydan, Francis Lilley, Michael J. Lalor, and David R. Burton. Quantization error of CCD cameras and their influence on phase calculation in fringe pattern analysis. Optical Society of Amerian, vol. 42, nos.26, pp.5302-5307, 2003.

DOI: 10.1364/ao.42.005302

[7] Bing Zhao and Yves Surrel. Effect of quantization error on the computed phase-shifting measurements. Optical Society of America, vol. 36, nos.10, pp.2070-2075, 1997.

DOI: 10.1364/ao.36.002070

[8] Bing Zhao. Effect of Intensity-correlated Error due to Quantization and Noise on Phase-shifting Method. Optics and Lasers in Engineering 28, pp.199-211, 1997.

DOI: 10.1016/s0143-8166(96)00059-0

[9] WU Xiaobo, AN Wendou and YANG Gang. The analysis of the error in image measuring system and the way to improve the measurement precision. Optics and Precision on Engineering, vol. 5, no. 5, pp.133-141, 1997.

[10] CHEN Wen-xin and LI Yong. Study of the influence of quantization on PMP measuring accuracy. Laser Journal, vol. 29, no. 2, pp.34-35, 2008.

[11] ZHAO Bing, GUO Bin, FANG Ruhua and Yves Surrel. Effect of Intensity-correlated Error due to Quantization and Noise on Phase-shifting Method. Acta Optica Sinica, vol. 16, no. 12, pp.1767-1772, 1996.