Mínimos cuadrados para la calibración en reconstrucción 3D mediante proyección de franjas

Authors

DOI:

https://doi.org/10.31349/RevMexFisE.20.010206

Keywords:

Profilometry, fringe analysis, 3D measurement, least squares

Abstract

In surface measurement systems using the phase shift technique with fringe projection, the calibration of the system is essential to determine the relation between obtained phase and real height of the object. In this work, we present a detailed mathematical analysis for the linear calibration model. Derivation of the least squares scheme which is required for data estimation, is developed intuitively by means of using the underlying theory in numerical analysis. The calibration method is applied to the surface of a 3D object obtaining remarkable results.

Author Biographies

Antonio Muñoz, University of Guadalajara

Researcher Full Professor, Engineering Department

Omar Aguilar Loreto, Universidad de Guadalajara

Research Full Professor, Engineering Department

Jorge L. Flores, University of Guadalajara

Researcher Full Professor, Electronic Engineering Department

References

L. C. Chen, and C.-C. Huang, Miniaturized 3D surface profilometer using digital fringe projection, Measurement Science and Technology, 16 (2005) 1061.

J. Gutiérrez-García et al., A novel application of the white light/fringe projection duo: Recovering high precision 3-D images from fossils for the digital preservation of morphology, Palaeontologa Electronica, 18 (2015) 1.

P. Hariharan, B. F. Oreb, and T. Eiju, Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm, Applied Optics, 26 (1987) 2504.

Y. Surrel, Phase stepping: a new self-calibrating algorithm, Applied Optics, 32 (1993) 3598.

G. Zhan. et al., High-speed FPGA-based phase measuring profilometry architecture, Optics Express, 25 (2017) 10553.

R. Juarez-Salazar et al., How do phase-shifting algorithms work?, European Journal of Physics 39 (2018) 065302.

C. Zuo et al., Phase shifting algorithms for fringe projection profilometry: A review, Optics and Lasers in Engineering, 109 (2018) 23.

Q. Hu et al., Calibration of a three-dimensional shape measurement system, Optical Engineering, 42 (2003) 487.

F. J. Cuevas et al., Multi-layer neural network applied to phase and depth recovery from fringe patterns, Optics Communications, 181 (2000) 239.

M. J. Baker, J. Xi, and J. F. Chicharo, Neural network digital fringe calibration technique for structured light profilometers, Applied Optics, 46 (2007) 1233.

S. Zhang and P. S. Huang, Novel method for structured light system calibration, Optical Engineering, 45 (2006) 1.

Y. Fu et al., Least-squares calibration method for fringe projection profilometry with some practical considerations, Optik, 124 (2013) 4041.

V. Suresh, J. Holton, and B. Li, Structured light system calibration with unidirectional fringe patterns, Optics and Lasers in Engineering, 106 (2018) 86.

H. Guo et al., Least-squares calibration method for fringe projection profilometry, Optical Engineering, 44 (2005) 033603.

J. P. Kofman, C. English, Comparison of linear and nonlinear calibration methods for phase-measuring profilometry, Optical Engineering 46 (2007) 043601.

P. J. Tavares, and M. A. Vaz, Linear calibration procedure for the phase-to-height relationship in phase measurement profilometry, Optics Communications, 274 (2007) 307.

J. H. Bruning et al., Digital wavefront measuring interferometer for testing optical surfaces and lenses, Appl. Opt. 13 (1974) 2693.

D. C. Ghiglia, and L. A. Romero, Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods, Journal of the Optical Society of America A, 11 (1994) 107.

Downloads

Published

2023-01-13

How to Cite

[1]
A. . Muñoz, O. Aguilar Loreto, and J. . L. Flores, “Mínimos cuadrados para la calibración en reconstrucción 3D mediante proyección de franjas”, Rev. Mex. Fis. E, vol. 20, no. 1 Jan-Jun, pp. 010206 1–, Jan. 2023.