Hand-eye calibration for an unfocused light-field camera

Jie Wang; Siwen Ye; Shengxian Shi; T. H. New

doi:10.1364/JOSAA.469703

Journal of the Optical Society of America A
Vol. 39,
Issue 11,
pp. 1946-1957
(2022)
•https://doi.org/10.1364/JOSAA.469703

Hand-eye calibration for an unfocused light-field camera

Jie Wang, Siwen Ye, Shengxian Shi, and T. H. New

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Jie Wang, Siwen Ye, Shengxian Shi, and T. H. New, "Hand-eye calibration for an unfocused light-field camera," J. Opt. Soc. Am. A 39, 1946-1957 (2022)

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Abstract

A calibration framework is established for an unfocused light-field camera and a robotic arm. With Gaussian optics and light-field imaging principles, the mapping relationship between a point light source and its corresponding plenoptic disc feature is established, and the intrinsic and extrinsic parameters of the unfocused light-field camera are calculated through nonlinear optimization. Transformation matrices for eye-to-hand and eye-in-hand configurations are subsequently solved and are validated by applying them to an industrial light-field camera-robotic arm system. With the proposed calibration method, 3D reconstruction for calibration board in different poses is demonstrated and calibration uncertainty is discussed in detail.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (31)

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Symbol	Meaning of the Symbol
$S_{i}$	Distance between image focal plane and main lens
$S_{o}$	Distance between object focal plane and main lens
$f_{l}$	Focal length of lenslet
$p_{l}$	Lenslet pitch
$p_{p}$	Pixel pitch
$p_{m}$	Effective size of main lens
$f_{m}$	Focal length of main lens
$M$	Magnification of main lens
PMR	Ratio of $p_{l}$ to $p_{p}$
$l_{c i}$	Center of the $i^{t h}$ lenslet on the MLA plane
$l_{p i}$	Center of the $i^{t h}$ lenslet aperture projection on the sensor plane
$p_{c i}$	Center of the white dot beneath the $i^{t h}$ lenslet
$O_{c}$	Optical center of unfocused light-field camera
$O_{l}$	Intersection point of $O_{c} Z_{c}$ and the MLA plane
$O_{p}$	Projection point of $O_{l}$ on the sensor plane
$D_{l}$	Diameter of plenoptic disc feature (on the MLA plane)
$C_{l}$	Center of plenoptic disc feature (on the MLA plane)
$D_{p}$	Diameter of plenoptic disc feature (on the sensor plane)
$C_{p}$	Center of plenoptic disc feature (on the sensor plane)

	Eye-to-Hand		Eye-in-Hand
Intrinsic Parameters	Initial Value	Optimized Value	Initial Value	Optimized Value
$T_{1}$	$- 2.5663 \times 10^{4}$	$- 2.5663 \times 10^{4}$	$- 2.9550 \times 10^{4}$	$- 2.9550 \times 10^{4}$
$T_{2}$	$1.7420 \times 10^{7}$	$1.7420 \times 10^{7}$	$2.0450 \times 10^{7}$	$2.0450 \times 10^{7}$
$f$	$2.4479 \times 10^{5}$	$2.4004 \times 10^{5}$	$2.4131 \times 10^{5}$	$2.3598 \times 10^{5}$

Symbol	Meaning of the Symbol
$S_{i}$	Distance between image focal plane and main lens
$S_{o}$	Distance between object focal plane and main lens
$f_{l}$	Focal length of lenslet
$p_{l}$	Lenslet pitch
$p_{p}$	Pixel pitch
$p_{m}$	Effective size of main lens
$f_{m}$	Focal length of main lens
$M$	Magnification of main lens
PMR	Ratio of $p_{l}$ to $p_{p}$
$l_{c i}$	Center of the $i^{t h}$ lenslet on the MLA plane
$l_{p i}$	Center of the $i^{t h}$ lenslet aperture projection on the sensor plane
$p_{c i}$	Center of the white dot beneath the $i^{t h}$ lenslet
$O_{c}$	Optical center of unfocused light-field camera
$O_{l}$	Intersection point of $O_{c} Z_{c}$ and the MLA plane
$O_{p}$	Projection point of $O_{l}$ on the sensor plane
$D_{l}$	Diameter of plenoptic disc feature (on the MLA plane)
$C_{l}$	Center of plenoptic disc feature (on the MLA plane)
$D_{p}$	Diameter of plenoptic disc feature (on the sensor plane)
$C_{p}$	Center of plenoptic disc feature (on the sensor plane)

	Eye-to-Hand		Eye-in-Hand
Intrinsic Parameters	Initial Value	Optimized Value	Initial Value	Optimized Value
$T_{1}$	$- 2.5663 \times 10^{4}$	$- 2.5663 \times 10^{4}$	$- 2.9550 \times 10^{4}$	$- 2.9550 \times 10^{4}$
$T_{2}$	$1.7420 \times 10^{7}$	$1.7420 \times 10^{7}$	$2.0450 \times 10^{7}$	$2.0450 \times 10^{7}$
$f$	$2.4479 \times 10^{5}$	$2.4004 \times 10^{5}$	$2.4131 \times 10^{5}$	$2.3598 \times 10^{5}$

Abstract

Data availability

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Equations (31)

Journal of the Optical Society of America A