Laboratory Geometric Calibration Method for Multi-band Fisheye Lens Camera

Equipment	Parameter name	Parameter
Lens	Focal length	4 mm
	Field of view	210°
	Maximum aperture	F2.8
	Minimum aperture	F16
	Lens structure	6 groups， 7 elements
Camera	Image resolution	2 048 pixels×2 048 pixels
	Pixel size	5.5 μm×5.5 μm
	Dynamic range	10 bit
Filter	Central wavelength	440 nm， 500 nm， 676 nm， 880 nm， 940 nm
Filter	Bandwidth	10 nm

Table 2. Fisheye lens fitting data for each band

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Table 2. Fisheye lens fitting data for each band

Model	Band/nm	f	R-square
Stereographic projection	440	0.397 6	0.805 1
	500	0.396 8	0.805 1
	676	0.397 8	0.805 1
	880	0.398 8	0.805 1
	940	0.399 5	0.805 1
Equidistance projection	440	3.772 6	0.999 8
	500	3.765 2	0.999 8
	676	3.774 0	0.999 8
	880	3.783 8	0.999 8
	940	3.790 2	0.999 8
Equisolid angle projection	440	3.999 8	0.999 9
	500	3.992 1	0.999 9
	676	4.001 4	0.999 9
	880	4.011 7	0.999 9
	940	4.018 5	0.999 9
Orthogonal projection	440	4.750 6	0.995 9
	500	4.741 4	0.995 9
	676	4.752 5	0.995 9
	880	4.764 7	0.995 9
	940	4.772 8	0.995 9

Table 3. Calibration coefficients for each band

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Table 3. Calibration coefficients for each band

Band/nm	f	a₁	a₂	a₃	a₄	a₅	u₀	v₀
440	3.999 9	-0.089 8	0.003 7	0.101 7	-0.000 5	-0.022 2	1 070.502 9	1 019.791 2
500	3.992 1	-0.089 1	0.003 4	0.100 8	-0.000 4	-0.022 0	1 071.254 8	1 019.065 9
676	4.001 4	-0.089 2	0.003 3	0.100 9	-0.000 2	-0.022 0	1 069.270 3	1 015.395 9
880	4.011 8	-0.089 6	0.003 9	0.101 1	-0.000 8	-0.022 0	1 072.556 1	1 017.718 4
940	4.018 6	-0.089 8	0.003 2	0.102 0	-0.000 2	-0.022 4	1 071.649 2	1 018.534 8

Table 4. Cost function iteration process
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Table 4. Cost function iteration process
Iterations θ/rad e/mm
1 0.917 7 1.549 2×10^-2
2 0.921 9 5.926 8×10^-6
3 0.921 9 8.739 6×10^-13

Table 5. 940 nm principal point coordinate
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Table 5. 940 nm principal point coordinate
Azimuth angle/（°） u₀ v₀
0 1 070.48 1 017.23
30 1 069.51 1 019.94
45 1 070.22 1 020.28
60 1 071.08 1 020.28
90 1 072.58 1 019.87
120 1 073.09 1 018.14
135 1 073.09 1 017.47
150 1 073.04 1 016.76

Table 6. Geometric calibration result verification

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Table 6. Geometric calibration result verification

Band/ nm	Data	Time	Calculated zenith/（°）	Calculated azimuth/（°）	Actual zenith/（°）	Actual azimuth/（°）	Zenith difference/（°）	Azimuth difference/（°）
440	11.2	14∶25∶07	58.80	224.30	59.25	223.84	-0.45	0.46
		15∶19∶03	67.78	235.45	68.12	234.90	-0.34	0.55
		16∶08∶21	76.54	243.44	76.84	242.93	-0.30	0.51
	11.3	9∶11∶33	60.90	133.83	60.98	134.20	-0.08	-0.37
		10∶03∶16	54.00	146.01	53.93	146.54	0.07	-0.53
		11∶33∶32	47.24	173.17	47.27	173.75	-0.03	-0.58
		12∶25∶22	47.55	189.91	47.67	190.47	-0.12	-0.56
		13∶01∶17	49.64	201.28	49.79	201.69	-0.15	-0.41
500	11.2	14∶26∶08	58.67	224.07	59.10	223.62	-0.43	0.45
		15∶21∶33	67.59	235.29	67.94	234.72	-0.35	0.57
		16∶09∶08	76.38	243.27	76.66	242.77	-0.28	0.50
	11.3	9∶12∶09	61.10	133.52	61.14	133.99	-0.04	-0.47
		10∶04∶08	54.01	145.81	54.05	146.28	-0.04	-0.47
		11∶35∶15	47.28	172.83	47.29	173.43	-0.01	-0.60
		12∶26∶13	47.50	189.61	47.63	190.15	-0.13	-0.54
		13∶02∶47	49.67	201.08	49.71	201.39	-0.04	-0.31
676	11.2	14∶27∶13	58.67	224.22	58.95	223.39	-0.28	0.83
		15∶22∶31	67.37	235.18	67.60	234.36	-0.23	0.82
		16∶10∶09	76.27	243.38	76.47	242.62	-0.20	0.76
	11.3	9∶13∶12	60.90	133.56	61.29	133.78	-0.39	-0.22
		10∶05∶04	53.87	145.67	54.16	146.02	-0.29	-0.35
		11∶36∶09	47.18	172.61	47.34	172.77	-0.16	-0.16
		12∶27∶09	47.31	189.70	47.60	189.83	-0.29	-0.13
		13∶03∶31	49.45	200.88	49.64	201.09	-0.19	-0.21
880	11.2	14∶28∶09	59.31	224.70	59.54	224.29	-0.23	0.41
		15∶23∶38	68.26	235.80	68.47	235.26	-0.21	0.54
		16∶11∶27	77.09	243.69	77.22	243.23	-0.13	0.46
	11.3	9∶15∶00	60.64	134.44	60.68	134.63	-0.04	-0.19
		10∶07∶34	53.72	146.99	53.58	147.32	0.14	-0.33
		11∶37∶27	47.27	174.10	47.22	174.41	0.05	-0.31
		12∶28∶43	47.89	190.81	47.75	191.11	0.14	-0.30
		13∶04∶32	49.94	201.79	49.95	202.28	-0.01	-0.49
940	11.2	14∶29∶06	59.03	224.54	59.39	224.06	-0.36	0.48
		15∶24∶37	67.99	235.73	68.29	235.08	-0.30	0.65
		16∶12∶19	76.60	243.72	77.03	243.08	-0.43	0.64
	11.3	9∶15∶45	60.65	134.13	60.68	134.63	-0.03	-0.50
		10∶08∶21	53.66	146.62	53.70	147.06	-0.04	-0.44
		11∶38∶34	47.16	173.61	47.25	174.08	-0.09	-0.47
		12∶29∶47	47.57	190.38	47.71	190.79	-0.14	-0.41
		13∶05∶18	49.70	201.58	49.87	201.99	-0.17	-0.41

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Caixia WANG, Hongyao CHEN, Xiaolong SI, Xin LI, Jiawei LI, Liming ZHANG, Shiwei BAO. Laboratory Geometric Calibration Method for Multi-band Fisheye Lens Camera[J]. Acta Photonica Sinica, 2024, 53(8): 0811001

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