High-precision anamorphic lens calibration with 3D and 2D calibration targets

Xiaobo Chen; Xiaobo Chen; Xiaobo Chen; Jinkai Zhang; Jinkai Zhang

doi:10.1364/AO.456166

Applied Optics
Vol. 61,
Issue 20,
pp. 6062-6075
(2022)
•https://doi.org/10.1364/AO.456166

High-precision anamorphic lens calibration with 3D and 2D calibration targets

Xiaobo Chen and Jinkai Zhang

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Xiaobo Chen and Jinkai Zhang, "High-precision anamorphic lens calibration with 3D and 2D calibration targets," Appl. Opt. 61, 6062-6075 (2022)

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Abstract

This paper presents a high-precision camera calibration approach for anamorphic lenses. The distortion model for anamorphic lenses is substantially more sophisticated than the distortion model for spherical lenses for the adaption of cylindrical lenses in anamorphic lens attachments. Based on the anamorphic aberration theory and numerical experiments, a polynomial type distortion model is provided for anamorphic lenses, with which high-precision camera calibrations can be achieved using 3D calibration targets. 3D calibration targets are typically limited in size, unable to encompass the whole imaging field of anamorphic lenses. The calibration results using 3D calibration targets tend to be unstable with the increased number of distortion coefficients in the anamorphic distortion model. Thus, after the anamorphic lenses have been calibrated with 3D calibration targets, they are recalibrated with 2D calibration targets that may fill the anamorphic lenses’ field of view, resulting in more dependable and exact calibration results. Two anamorphic lenses are calibrated with high precision at the end the paper, which proves the effectiveness of the proposed method.

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Data availability

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 (28)

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Surface	R (mm)	d (mm)	Index	Abbe
0 Image	—	11.2723094	—	—
1 Spherical	7.85628034	2.0000000	1.620410	60.323649
2 Spherical	117.6742148	2.8061835	—	—
3 Stop	Infinity	0.9988091	—	—
4 Spherical	20.00020099	1.0000000	1.620040	36.366491
5 Spherical	20.0001223	2.1023880	—	—
6 Spherical	−68.60726395	2.0000000	1.620410	60.323649
7 Spherical	−18.21467055	5.0000000	—	—
8 Toroidal	Infinity	3.0000000	1.784700	25.720000
9 Toroidal	−109	25.8284009	—	—
10 Toroidal	−27	2.0000000	1.755000	52.340000
11 Toroidal	Infinity	40.0000000	—	—
12 Object	—	—	—	—

Factor1	Factor2	Factor3	Factor4
$4. {389 e}^{- 4}$	$6. {846 e}^{- 4}$	$2. {368 e}^{- 4}$	$1. {361 e}^{- 4}$
Factor5	Factor6	Factor7	Factor8
$1. {353 e}^{- 4}$	$9. {749 e}^{- 4}$	0	$1. {596 e}^{- 4}$
Factor9	Factor10	Factor11	Factor12
$3. {009 e}^{- 4}$	$1. {902 e}^{- 4}$	$1. {049 e}^{- 4}$	$4. {886 e}^{- 4}$
Factor13	Factor14	Factor15	Factor16
0	$5. {682 e}^{- 4}$	$2. {303 e}^{- 4}$	$1. {309 e}^{- 4}$

Config0	Config1	Config2
$6. {3826 e}^{- 4}$	$8. {0699 e}^{- 4}$	0.0010
Config3	Config4	Config5
0.0015	0.0015	0.0013
Config6	Config7	Config8
0.0014	$5. {3803 e}^{- 4}$	$4. {5921 e}^{- 4}$

	Model 0	Model 1	Model 2	Model 3
Std	0.2326	0.0640	0.0562	0.0378
Max	0.7506	0.2640	0.2492	0.1319

	Model 0	Model 1	Model 2	Model 3
$f_{x} (m m)$	10.2032	12.9408	13.5016	13.7238
$f_{y} (m m)$	22.5092	26.6494	26.4007	25.9250
$u_{0} (p i x e l)$	1242.4520	1276.7808	1266.16790	1335.7022
$v_{0} (p i x e l)$	1047.9633	1030.9145	1021.4235	936.1826
ad(mm)	254.9333	192.6859	106.4372	46.0475
aa(°)	$8. {5716 e}^{- 3}$	$- 2. {4752 e}^{- 3}$	$- 1. {9972 e}^{- 2}$	$- 2. {0472 e}^{- 2}$

Plane	Std B	Std A	Max B	Max A
Plane1	0.1933	0.04799	1.0338	0.1801
Plane2	0.1832	0.077089	0.9841	0.3072
Plane3	0.2890	0.06922	0.8762	0.2209
Plane4	0.1593	0.06194	0.8857	0.2495
Plane5	0.1503	0.05823	0.7105	0.2693
Plane6	0.1127	0.08503	0.3604	0.2810
Plane7	0.1339	0.05144	0.8151	0.1556
Plane8	0.1511	0.09327	0.6792	0.3041
Plane9	0.3210	0.05690	1.1629	0.1676
Plane10	0.1900	0.04567	0.9468	0.1511
Plane11	0.2066	0.06784	0.9199	0.2201
Plane12	0.1658	0.05333	0.7629	0.1531

	Model 0	Model 1	Model 2	Model 3
$f_{x} (m m)$	12.8771	13.1444	13.3559	13.3596
$f_{y} (m m)$	19.9042	26.36027	25.9299	25.9418
$u_{0} (p i x e l)$	1238.4662	1263.9099	1260.4367	1257.9755
$v_{0} (p i x e l)$	−1415.5107	994.7251	989.7439	995.5347
ad(mm)	74.6683	147.4047	93.8234	93.9019
aa(°)	−2.1362	$1. {1294 e}^{- 2}$	$- 8. {4232 e}^{- 3}$	$- 1. {1888 e}^{- 2}$

	Model 0	Model 1	Model 2	Model 3
$f_{x} (m m)$	14.9947	18.0076	18.4107	18.5084
$f_{y} (m m)$	32.2107	36.5073	35.9224	35.7389
$u_{0} (p i x e l)$	1226.7295	1313.7479	1274.9873	1352.4394
$v_{0} (p i x e l)$	1044.4164	970.2605	965.6540	910.3352
ad(mm)	287.9491	200.2221	110.7816	86.2408
aa(°)	$8. {051 e}^{- 3}$	$- 4. {519 e}^{- 3}$	$- 1. {8551 e}^{- 2}$	$- {.30302 e}^{- 2}$

	Model 0	Model 1	Model 2	Model 3
$f_{x} (m m)$	18.2704	18.3336	18.2602	18.2589
$f_{y} (m m)$	33.8679	35.6132	35.4381	35.4559
$u_{0} (p i x e l)$	1284.6110	1277.2319	1275.6168	1233.3338
$v_{0} (p i x e l)$	−951.5414	985.2653	970.5338	871.9745
ad(mm)	95.9774	98.6836	98.2102	99.6691
aa(°)	−0.3887	$- 2. {7857 e}^{- 3}$	$- 2. {24915 e}^{- 3}$	$- 1. {7292 e}^{- 2}$

Plane	Std B	Std A	Max B	Max A
Plane1	0.09207	0.08249	0.2570	0.2403
Plane2	0.08548	0.08317	0.2227	0.2424
Plane3	0.1710	0.07854	0.5363	0.3197
Plane4	0.09546	0.08800	0.2991	0.2868
Plane5	0.1651	0.08829	0.5827	0.2665
Plane6	0.09594	0.08656	0.2631	0.2585
Plane7	0.1054	0.07192	0.5632	0.2392
Plane8	0.1017	0.07358	0.4586	0.2187
Plane9	0.2079	0.07585	0.7187	0.2701
Plane10	0.08665	0.06926	0.4004	0.1920
Plane11	0.1381	0.07641	0.3745	0.2331
Plane12	0.1311	0.08404	0.6565	0.2299

	Model 0	Model 1	Model 2	Model 3
$f_{x} (m m)$	12.8777	13.0661	13.0615	13.0620
$f_{y} (m m)$	24.5035	26.0060	25.9287	25.9129
$u_{0} (p i x e l)$	1215.6429	1271.7852	1264.3020	1284.0033
$v_{0} (p i x e l)$	2546.0089	1025.1794	1033.3823	1088.9493
ad(mm)	152.6174	102.9910	101.3197	99.9714
aa(°)	−0.5135	−0.9203	−0.89102	−0.8927

	Model 0	Model 1	Model 2	Model 3
$f_{x} (m m)$	17.3720	17.9647	17.9643	17.9493
$f_{y} (m m)$	33.9844	35.8049	35.4878	35.5100
$u_{0} (p i x e l)$	1298.1951	1388.3642	1377.7694	1402.5486
$v_{0} (p i x e l)$	−810.2122	1006.1957	988.5124	1242.2363
ad(mm)	172.7220	110.0633	91.6966	93.7749
aa(°)	−1.3398	−0.8964	−0.8758	−0.8602

	Model 0	Model 1	Model 2	Model 3
Std	1.0498	0.2287	0.0827	0.0644
Max	4.3298	1.0108	0.4838	0.3071

	Model 0	Model 1	Model 2	Model 3
Std	0.1608	0.0675	0.0630	0.0593
Max	0.5607	0.2072	0.2121	0.1774

	Model 0	Model 1	Model 2	Model 3
Std	0.5939	0.1522	0.0881	0.0783
Max	2.3411	0.6607	0.3647	0.3197

	Model 0	Model 1	Model 2	Model 3
Std	0.9281	0.2803	0.1077	0.1052
Max	3.3233	1.3927	1.0227	1.0545

Abstract

Data availability

Cited By

Figures (13)

Tables (17)

Equations (28)

Applied Optics