Stereo-phase rectification for metric profilometry with two calibrated cameras and one uncalibrated projector

Rigoberto Juarez-Salazar; Obed I. Rios-Orellana; Victor H. Diaz-Ramirez

doi:10.1364/AO.461168

Applied Optics
Vol. 61,
Issue 21,
pp. 6097-6109
(2022)
•https://doi.org/10.1364/AO.461168

Stereo-phase rectification for metric profilometry with two calibrated cameras and one uncalibrated projector

Rigoberto Juarez-Salazar, Obed I. Rios-Orellana, and Victor H. Diaz-Ramirez

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Rigoberto Juarez-Salazar, Obed I. Rios-Orellana, and Victor H. Diaz-Ramirez, "Stereo-phase rectification for metric profilometry with two calibrated cameras and one uncalibrated projector," Appl. Opt. 61, 6097-6109 (2022)

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Abstract

Fringe projection profilometry requires calibrating both cameras and projectors for metric measurements. Cameras are relatively simple to calibrate, but projectors require more sophisticated procedures. In this paper, a fringe projection profilometer with two calibrated cameras and one uncalibrated projector is developed for metric measurements. A phase rectification method, which is crucial for stereo matching, is designed by minimizing the perspective distortion. Also, a simple method for point matching using stereo rectified phase maps is proposed. The principles of metric profilometry using the proposed rectification method are introduced. The developed system is evaluated experimentally by the metric measurement of three-dimensional objects. The obtained results confirm a high accuracy of metric measurement and versatility in the design of fringe projection profilometers with uncalibrated projectors.

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No data were generated or analyzed in the presented research.

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	$k_{11}$	$k_{12}$	$k_{13}$	$k_{22}$	$k_{23}$
$K_{1}$	2.2390	0.0021	0.0477	2.2426	−0.0430
$K_{2}$	2.2431	0.0025	0.0480	2.2464	−0.0414
	$δ_{0}^{'}$	$δ_{1}^{'}$	$δ_{2}^{'}$	$δ_{3}^{'}$
$δ_{1}^{'}$	1	0	−0.0984	−0.0155
$δ_{2}^{'}$	1	0	−0.0930	−0.0145
	$γ$	$θ$	$ϕ$
$R_{1}$	2.9259	1.5017	1.6029
$R_{2}$	3.2503	1.5065	1.5931
	$t_{x}$	$t_{y}$	$t_{z}$
$t_{1}$	−96.3910	−87.6615	547.3791
$t_{2}$	55.5096	−85.9893	549.6456

	$a$	$b$	$c$	$d$	$e$	$f$	$ρ$	$ξ$	$ζ$
$Θ_{0}$	0.9920	0	0.0887	−26.4573	0	1.4815	1.0121	0	0
$Θ_{6}$	0.9917	−0.0019	0.0883	−26.4455	−0.0329	1.4837	0.9911	0.0213	−0.0049
	$g_{11}$	$g_{12}$	$g_{13}$	$g_{21}$	$g_{22}$	$g_{23}$	$g_{31}$	$g_{32}$	$g_{33}$
$G_{1}$	0.9918	−0.0020	0.0884	−0.0674	0.9860	0.0272	0.0884	0.0112	0.9920
$G_{2}$	1.0171	0.0013	−0.0571	−0.0214	0.9945	−0.0103	−0.0571	0.0113	1.0174

	$D$ [mm]	$x$ [mm]	$y$ [mm]	$z$ [mm]
S1	40.0271	−18.1452	42.2110	28.3747
S2	39.9904	−125.6507	−79.3758	56.5086
S3	40.0804	90.1862	−52.3494	84.9199

	Nominal	Deviation	Measured	Error
G1	0.2	$- 1 \times 10^{- 6}$	0.2008	$- 7.72 \times 10^{- 4}$
G2	0.4	$- 12 \times 10^{- 6}$	0.3999	$6.98 \times 10^{- 5}$
G3	0.6	$- 13 \times 10^{- 6}$	0.6009	$- 8.98 \times 10^{- 4}$
G4	0.8	$- 6 \times 10^{- 6}$	0.8002	$- 1.95 \times 10^{- 4}$
G5	1	$- 3 \times 10^{- 6}$	0.9988	$1.21 \times 10^{- 3}$

	$k_{11}$	$k_{12}$	$k_{13}$	$k_{22}$	$k_{23}$
$K_{1}$	2.2390	0.0021	0.0477	2.2426	−0.0430
$K_{2}$	2.2431	0.0025	0.0480	2.2464	−0.0414
	$δ_{0}^{'}$	$δ_{1}^{'}$	$δ_{2}^{'}$	$δ_{3}^{'}$
$δ_{1}^{'}$	1	0	−0.0984	−0.0155
$δ_{2}^{'}$	1	0	−0.0930	−0.0145
	$γ$	$θ$	$ϕ$
$R_{1}$	2.9259	1.5017	1.6029
$R_{2}$	3.2503	1.5065	1.5931
	$t_{x}$	$t_{y}$	$t_{z}$
$t_{1}$	−96.3910	−87.6615	547.3791
$t_{2}$	55.5096	−85.9893	549.6456

Rigoberto Juarez-Salazar	https://orcid.org/0000-0001-6917-7558
Victor H. Diaz-Ramirez	https://orcid.org/0000-0002-9331-1777

Abstract

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Equations (67)

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