Camera calibration for anamorphic lenses with three-dimensional targets

Jinkai Zhang; Xue Wang; Mengmeng Ma; Fajia Li; Haining Liu; Huanyong Cui

doi:10.1364/AO.59.000324

Applied Optics
Vol. 59,
Issue 2,
pp. 324-332
(2020)
•https://doi.org/10.1364/AO.59.000324

Camera calibration for anamorphic lenses with three-dimensional targets

Jinkai Zhang, Xue Wang, Mengmeng Ma, Fajia Li, Haining Liu, and Huanyong Cui

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Jinkai Zhang, Xue Wang, Mengmeng Ma, Fajia Li, Haining Liu, and Huanyong Cui, "Camera calibration for anamorphic lenses with three-dimensional targets," Appl. Opt. 59, 324-332 (2020)

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Abstract

Anamorphic lenses, with different optical powers along the tangential plane and the sagittal plane, are calibrated in this paper. The imaging model for anamorphic lenses is introduced. Compared with the pinhole model, it has two more intrinsic parameters: the anamorphic distance and the anamorphic angle. The anamorphic lens has two optical centers: one is in the tangential plane and the other is in the sagittal plane. The distance between the two optical centers is the anamorphic distance. The anamorphic angle refers to the angle between the camera coordinates and the pixel coordinates in the CCD plane. Formulas determining the initial value of the anamorphic distance are provided. Two experiments are conducted for the anamorphic lens calibration. As a comparison, the anamorphic lens is calibrated using the anamorphic imaging model and the pinhole model, respectively. The calibration accuracy can be improved remarkably if the anamorphic imaging model is applied, and calibrated results for the anamorphic distance and the anamorphic angle are very stable for different positions of the calibration target, which shows the validity and effectiveness of the anamorphic imaging model for anamorphic lens calibration.

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$A_{s p}$	$f$ (mm)	$u_{0}$	$v_{0}$	$K_{1}$
0.5996	13.4058	1.0528E3	−551.1322	$7.1976 E - 3$
$K_{2}$	$T_{1}$	$T_{2}$	$t_{x}$ (mm)	$t_{y}$ (mm)
$- 1.7028 E - 5$	$- 1.4572 E - 2$	$- 2.6827 E - 3$	20.5017	146.3721
$t_{z}$ (mm)	$w_{a}$ (°)	$p_{a}$ (°)	$r_{a}$ (°)	$a d$ (mm)	$a a$ (°)
437.7134	−30.3465	−42.4741	21.7923	0	0

$A_{s p}$	$f$ (mm)	$u_{0}$	$v_{0}$	$K_{1}$
0.4869	15.2098	1.1133E3	1.1875E3	$- 5.2752 E - 4$
$K_{2}$	$T_{1}$	$T_{2}$	$t_{x}$ (mm)	$t_{y}$ (mm)
$2.6664 E - 4$	$- 9.8801 E - 4$	$2.7355 E - 4$	15.1166	−40.1338
$t_{z}$ (mm)	$w_{a}$ (°)	$p_{a}$ (°)	$r_{a}$ (°)	$a d$ (mm)	$a a$ (°)
402.6465	4.6968	−46.9674	−0.6902	97.0872	2.5809

$A_{s p}$	$f$ (mm)	$u_{0}$	$v_{0}$	$K_{1}$
0.5966	22.8921	1.2653E3	3.2242E3	$2.5910 E - 3$
$K_{2}$	$T_{1}$	$T_{2}$	$t_{x}$ (mm)	$t_{y}$ (mm)
$- 5.00 E - 6$	$6.40 E - 3$	$1.58 E - 3$	25.1679	−230.8778
$t_{z}$ (mm)	$w_{a}$ (°)	$p_{a}$ (°)	$r_{a}$ (°)	$a d$ (mm)	$a a$ (°)
548.6192	26.5244	−39.4806	−17.2949	0	0

$A_{s p}$	$f$ (mm)	$u_{0}$	$v_{0}$	$K_{1}$
0.5031	25.0251	1.2754E3	1.0175E3	$- 1.94 E - 5$
$K_{2}$	$T_{1}$	$T_{2}$	$t_{x}$ (mm)	$t_{y}$ (mm)
$5.73 E - 5$	$- 2.92 E - 5$	$2.65 E - 5$	22.1411	−47.3519
$t_{z}$ (mm)	$w_{a}$ (°)	$p_{a}$ (°)	$r_{a}$ (°)	$a d$ (mm)	$a a$ (°)
534.1193	1.6919	−43.5304	1.4300	95.9566	2.3906

$A_{s p}$	$f$ (mm)	$u_{0}$	$v_{0}$	$K_{1}$
0.5996	13.4058	1.0528E3	−551.1322	$7.1976 E - 3$
$K_{2}$	$T_{1}$	$T_{2}$	$t_{x}$ (mm)	$t_{y}$ (mm)
$- 1.7028 E - 5$	$- 1.4572 E - 2$	$- 2.6827 E - 3$	20.5017	146.3721
$t_{z}$ (mm)	$w_{a}$ (°)	$p_{a}$ (°)	$r_{a}$ (°)	$a d$ (mm)	$a a$ (°)
437.7134	−30.3465	−42.4741	21.7923	0	0

Abstract

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Tables (4)

Equations (25)

Applied Optics