Modulation transfer function of a fish-eye lens based on the sixth-order wave aberration theory

Han Jia; Lijun Lu; Yiqing Cao

doi:10.1364/AO.57.000314

Applied Optics
Vol. 57,
Issue 2,
pp. 314-321
(2018)
•https://doi.org/10.1364/AO.57.000314

Modulation transfer function of a fish-eye lens based on the sixth-order wave aberration theory

Han Jia, Lijun Lu, and Yiqing Cao

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Han Jia, Lijun Lu, and Yiqing Cao, "Modulation transfer function of a fish-eye lens based on the sixth-order wave aberration theory," Appl. Opt. 57, 314-321 (2018)

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Abstract

A calculation program of the modulation transfer function (MTF) of a fish-eye lens is developed with the autocorrelation method, in which the sixth-order wave aberration theory of ultra-wide-angle optical systems is used to simulate the wave aberration distribution at the exit pupil of the optical systems. The autocorrelation integral is processed with the Gauss–Legendre integral, and the magnification chromatic aberration is discussed to calculate polychromatic MTF. The MTF calculation results of a given example are then compared with those previously obtained based on the fourth-order wave aberration theory of plane-symmetrical optical systems and with those from the Zemax program. The study shows that MTF based on the sixth-order wave aberration theory has satisfactory calculation accuracy even for a fish-eye lens with a large acceptance aperture. And the impacts of different types of aberrations on the MTF of a fish-eye lens are analyzed. Finally, we apply the self-adaptive and normalized real-coded genetic algorithm and the MTF developed in the paper to optimize the Nikon F/2.8 fish-eye lens; consequently, the optimized system shows better MTF performances than those of the original design.

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Equations (29)

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$k$	1, 2	3, 4	5, 6	7, 8	9, 10	11, 12	13, 14	15, 16	17, 18	19, 20
${(- 1)}^{k + 1} t_{20, k}$	0.9931	0.9640	0.9122	0.8391	0.7463	0.6361	0.5109	0.374	0.2278	0.0765
$w_{20, k}$	0.0176	0.0406	0.0627	0.0833	0.1019	0.1182	0.1317	0.1421	0.1492	0.1528

	$C_{i}$	$S_{i}$	$V_{i}$	$E_{i}$
C light	0.0766	275	0.526	1
D light	0.6983	152	0.709	1
F light	0.2251	100	0.939	1

Surface	Radius/mm	Spacing/mm	Index	Glass
1	143.47	7.00	1.51680	N-BK7
2	52.50	28.00	—	—
3	76.40	3.80	1.51680	N-BK7
4	31.521	21.80	—	—
5	150.00	3.00	1.51680	N-BK7
6	17.10	16.50	—	—
7	−60.00	7.00	1.62090	SK51
8	22.625	0.60	—	—
9	23.90	12.60	1.72825	SF10
10	78.988	29.60	—	—
11	278.333	3.00	1.64831	SF12
12	−185.420	0.10	—	—
13	52.030	7.00	1.52310	KF5
14	−28.50	2.00	1.77314	LAFN28
15	−77.00	13.00	—	—
STO	Infinite	2.00	—	—
17	45.00	6.00	1.51823	K3
18	−14.40	0.60	1.80610	LAH53
19	−34.50	0.10	—	—
20	−110.00	1.00	1.71736	SF1
21	35.00	3.50	1.51680	N-BK7
22	−27.763	41.890

Field angle	0°	10°	20°	30°	40°	50°	60°	70°	80°
Weight factor	1	1	1	5	5	5	10	10	10

Surface	1	2	3	4	5	6	7	8	9	10	11	12	13
Search Range (%)	$\pm 100$	$\pm 20$	$\pm 30$	$\pm 20$	$\pm 20$	$\pm 20$	$\pm 20$	$\pm 20$	$\pm 20$	$\pm 5$	$\pm 5$	$\pm 5$	$\pm 5$

Surface	Radius/mm		Spacing/mm		Index
Surface	Original	Optimized	Original	Optimized	Index
1	69.631	106.680	1.650	1.648	1.6405
2	15.002	16.347	10.260	10.259	—
3	123.323	103.550	1.600	1.596	1.6204
4	15.003	14.940	4.011	4.011	—
5	32.657	31.501	8.020	8.020	1.6259
6	−15.306	−14.804	8.890	8.889	1.7946
7	−39.042	−40.841	5.545	5.545	—
STO	Infinite	Infinite	5.500	5.500	—
8	−80.805	−90.513	1.140	1.140	1.5814
9	23.917	27.169	5.000	4.927	1.5182
10	−20.618	−20.849	0.089	0.089	—
11	46.798	47.000	5.510	5.510	1.5205
12	−19.203	−18.988	1.280	1.280	1.7847
13	−40.716	−41.049

Surface	Radius/mm		Spacing/mm		Index
Surface	Original	Optimized	Original	Optimized	Index
1	69.631	106.680	1.650	1.648	1.6405
2	15.002	16.347	10.260	10.259	—
3	123.323	103.550	1.600	1.596	1.6204
4	15.003	14.940	4.011	4.011	—
5	32.657	31.501	8.020	8.020	1.6259
6	−15.306	−14.804	8.890	8.889	1.7946
7	−39.042	−40.841	5.545	5.545	—
STO	Infinite	Infinite	5.500	5.500	—
8	−80.805	−90.513	1.140	1.140	1.5814
9	23.917	27.169	5.000	4.927	1.5182
10	−20.618	−20.849	0.089	0.089	—
11	46.798	47.000	5.510	5.510	1.5205
12	−19.203	−18.988	1.280	1.280	1.7847
13	−40.716	−41.049

Abstract

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Applied Optics