Design of single element gradient-index collimator

Duncan T. Moore

doi:10.1364/JOSA.67.001137

Journal of the Optical Society of America
Vol. 67,
Issue 9,
pp. 1137-1143
(1977)
•https://doi.org/10.1364/JOSA.67.001137

Design of single element gradient-index collimator

Duncan T. Moore

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Duncan T. Moore, "Design of single element gradient-index collimator," J. Opt. Soc. Am. 67, 1137-1143 (1977)

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Abstract

Gradient-index materials will provide new valuable degrees of freedom for the lens designer. The gradient-index single element lens is studied in terms of its third-order aberration coefficients, ray-trace analysis, and wave-front error.

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Focal length = 20. 0 cm
Diameter of lens = 5.0 cm
Tangent of field angle = 0. 02
Object at infinity
Curvature of surface 1 = 0. 078 496 cm⁻¹
Thickness of lens = 1. 0 cm
Curvature of surface 2 = 0. 001 673 cm⁻¹
Index of refraction polynomial
N = 1. 65 − 0. 030294 x
Third-order aberrations	Totals

Spherical aberration	0. 000000
Coma	0. 000000
Astigmatism	−0. 000488
Petzval curvature	−0. 000304
Distortion	0. 000000

Ordinary surface contribution	Inhomogeneous surface contribution	Inhomogeneous transfer contribution	Total contribution
Spherical aberration
−0. 012 024	0. 029 144	−0. 000 280	0. 018 840
−0. 010 824	−0. 000 008	0. 000 000	−0. 018 840
−0. 028 848	0. 029 136	−0. 000 280	−0. 000 000
Coma
−0. 001 840	0. 000 000	0. 000 048	−0. 001 792
0. 001 792	−0. 000 000	0. 000 000	0. 001 792
−0. 000 048	−0. 000 000	0. 000 048	0. 000 000
Astigmatism
−0. 000 184	0. 000 000	−0. 000 008	−0. 000 192
−0. 000 296	−0. 000 000	−0. 000 000	−0. 000 296
−0. 000 488	−0. 000 000	−0. 000 008	−0. 000 488
Petzval curvature
−0. 000 312	None	0. 000 000	−0. 000 312
0. 000 008	None	0. 000 000	0. 000 008
−0. 000 304	None	0. 000 000	−0. 000 304
Distortion
−0. 000 048	0. 000 000	0. 000 000	−0. 000 048
0. 000 048	−0. 000 000	0. 000 000	0. 000 048
−0. 000 000	−0. 000 000	0. 000 000	−0. 000 000

Parameter	Deviation of parameter for peak wave-front error of
Parameter	Nominal value	λ/20	λ/4
Tilt of gradient	0. 0	±0. 0003 radians	±0. 0008 radians
N₀₁	−0. 030 294	±0. 0008	±0. 0002
N₀₂	0. 0	±0. 0015	±0. 006
N₀₃	0. 0	±0. 005	±0. 025

Curve	N₀₀		N₀₁		Back focal length
A	1. 520 600	(0. 5145 μm)	−.033 444	(0. 5145 μm)	19. 395 479 cm
B	1. 515 120	(0. 6328 μm)	−.033 444	(0. 5145 μm)	19. 609 329 cm
C	1. 515 120	(0. 6328 μm)	−.030 000	(0. 6328 μm)	19. 580 535 cm

Ordinary surface contribution	Inhomogeneous surface contribution	Inhomogeneous transfer contribution	Total surface contribution
Spherical aberration
−0. 03042	−0. 58980	2.06827	1. 44805
−0. 359 90	−1. 088 19	0. 000 00	−1. 448 09
−0. 39032	−1. 67799	2.06827	−0. 00004
Coma
−0. 030 42	0. 000 00	0. 388 74	0. 358 32
0. 037 44	−0. 395 76	0. 000 00	−0. 358 33
0. 007 01	−0. 395 76	0. 388 74	−0. 000 00
Astigmatism
−0. 030 42	0. 000 00	0. 178 23	0. 147 81
−0. 003 89	−0. 143 93	0. 000 00	−0. 147 83
−0. 034 32	−0. 143 93	0. 178 23	−0. 000 02
Petzval curvature
−0. 04630	None	0. 06684	0. 02053
−0. 08137	None	0. 000 00	−0. 08137
0. 127 67	None	0. 066 84	−0. 060 84
Distortion
−0. 076 72	0. 000 00	0. 083 82	0. 007 10
0. 008 87	−0. 052 35	0. 000 00	−0. 043 48
−0. 06785	0. 05235	0. 08382	−0. 03538

Focal length = 10 cm
Diameter of lens = 2.0 cm
Tangent of field angle = 0. 30
Object at infinity
Curvature of surface 1 = 0. 172 063 cm⁻¹
Thickness of lens = 1. 0 cm
Curvature of surface 2 = −0. 010 393 cm⁻¹
Index of refraction polynomial
N = 1. 55 +0. 000261 ξ² + 0. 000030 ξ³
Third-order aberrations	Total

Spherical aberration	−0. 00000
Coma	0. 00000
Astigmatism	−0. 04269
Petzval curvature of field	−0. 02913
Distortion	−0. 00646

Ordinary surface contribution	Inhomogeneous surface contribution	Inhomogeneous transfer contribution	Total surface contribution
Spherical aberration
−0. 005 83	0. 000 00	0. 009 25	0. 003 42
−0. 003 43	0. 000 00	0. 000 00	−0. 003 43
−0. 009 26	0. 000 00	0. 009 25	−0. 000 01
Coma
−0. 010 17	0. 000 00	0. 000 89	−0. 009 27
0. 009 27	0. 000 00	0. 000 00	−0. 009 27
−0. 000 89	0. 000 00	0. 000 89	−0. 000 00
Astigmatism
−0. 017 73	0. 000 00	0. 000 12	−0. 017 61
−0. 025 08	0. 000 00	0. 000 00	−0. 025 08
−0. 042 81	0. 000 00	0. 000 12	−0. 042 69
Petzval curvature
−0. 027 47	None	0. 000 00	−0. 027 47
−0. 001 66	None	0. 000 00	−0. 001 66
−0. 029 13	None	0. 000 00	−0. 029 13
Distortion
−0. 078 81	0. 000 00	0. 000 02	−0. 078 79
0. 072 33	0. 000 00	0. 000 00	0. 072 33
−0. 006 48	0. 000 00	0. 000 02	−0. 006 46

Abstract

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Figures (13)

Tables (9)

Equations (3)

Journal of the Optical Society of America