High-order optical aberration coefficients: extension to finite objects and to telecentricity in object space

Florian Bociort; Torben B. Andersen; Leo H. J. F. Beckmann

doi:10.1364/AO.47.005691

Applied Optics
Vol. 47,
Issue 30,
pp. 5691-5700
(2008)
•https://doi.org/10.1364/AO.47.005691

High-order optical aberration coefficients: extension to finite objects and to telecentricity in object space

Florian Bociort, Torben B. Andersen, and Leo H. J. F. Beckmann

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Florian Bociort, Torben B. Andersen, and Leo H. J. F. Beckmann, "High-order optical aberration coefficients: extension to finite objects and to telecentricity in object space," Appl. Opt. 47, 5691-5700 (2008)

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Abstract

We extend the method for the automatic computation of high-order optical aberration coefficients to include (1) a finite object distance and (2) an infinite entrance pupil position (telecentricity in object space). We present coefficients of the power series expansion of the transverse aberration vector with respect to the normalized aperture and field coordinates. Aberration coefficients of very high order (e.g., 21) can be computed easily and—as shown by comparisons with trigonometric ray tracing—reliably.

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$σ 1$	Spherical aberration	bS2	bS2	$σ 1$
$σ 2$	Coma	$- bT 2$	bT2	$- σ 2$
$σ 3$	Astigmatism	$(bT 4) / 2$	bS3	$σ 3 + σ 4$
$σ 4$	Petzval blur	$bS 3 - (bT 4) / 2$	bT3	$- σ 5$
$σ 5$	Distortion	$- bT 3$	bS4	$- 2 (σ 2)$
			bT4	$2 (σ 3)$
$μ 1$	Spherical aberration	bS5	bS5	$μ 1$
$μ 2$		$- bT 5 - (bS 7) / 2$	bT5	$- μ 2 + μ 3$
$μ 3$	Coma	$- (bS 7) / 2$	bS6	$μ 5$
$μ 4$		$bT 7 + bS 6$	bT6	$- μ 7 + μ 8$
$μ 5$	Sagittal oblique spherical aberration	bS6	bS7	$- 2 (μ 3)$
$μ 6$		bS10	bT7	$μ 4 - μ 5$
$μ 7$		$- bT 6 - (bT 10) / 2 - (bS 9) / 2$	bS8	$μ 11$
$μ 8$		$- (bT 10) / 2 - (bS 9) / 2$	bT8	$- μ 12$
$μ 9$	Sagittal elliptical coma	$- (bS 9) / 2$	bS9	$- 2 (μ 9)$
$μ 10$		$bS 8 + bT 9$	bT9	$μ 10 - μ 11$
$μ 11$		bS8	bS10	$μ 6$
$μ 12$	Distortion	$- bT 8$	bT10	$- 2 (μ 8) + 2 (μ 9)$

Andersen		Buchdahl		Andersen					Buchdahl
n	i	j	k			#	n	i	j	k			#
1	1	0	0	bS2	$- Ap$	0	1	1	0	0	bT2	_Ap	6
1	0	1	0	bS3	$- Cp$	2	1	0	1	0	bT3	_Cp	8
1	0	0	1	bS4	Bp	1	1	0	0	1	bT4	$-_Bp$	7
2	2	0	0	bS5	$- S 1 p$	12	2	2	0	0	bT5	_S1p	13
2	1	1	0	bS6	$- S 3 p$	16	2	1	1	0	bT6	_S3p	17
2	1	0	1	bS7	S2p	14	2	1	0	1	bT7	$-_S 2 p$	15
2	0	2	0	bS8	$- S 6 p$	22	2	0	2	0	bT8	_S6p	23
2	0	1	1	bS9	S5p	20	2	0	1	1	bT9	$-_S 5 p$	21
2	0	0	2	bS10	$- S 4 p$	18	2	0	0	2	bT10	_S4p	19

1	0000	15	3111	29	4112	43	5221
2	1100	16	3102	30	4103	44	5212
3	1010	17	3030	31	4040	45	5203
4	1001	18	3021	32	4031	46	5140
5	2200	19	3012	33	4022	47	5131
6	2110	20	3003	34	4013	48	5122
7	2101	21	4400	35	4004	49	5113
8	2020	22	4310	36	5500	50	5104
9	2011	23	4301	37	5410	51	5050
10	2002	24	4220	38	5401	52	5041
11	3300	25	4211	39	5320	53	5032
12	3210	26	4202	40	5311	54	5023
13	3201	27	4130	41	5302	55	5014
14	3120	28	4121	42	5230	56	5005

Surface	Radius	Material	Thickness
1	66.08498	$Ca F_{2}$	6.000
2	$- 23.4200$	air	1.310
3	$- 21.3870$	$S i O_{2}$	2.500
4	35.3540	air	0.750
5	30.3290	$Ca F_{2}$	5.000
6	$- 69.2760$	air	88.5696 ( $= back focus$ )

Surface	Radius	Material	Thickness
1	75.6400	$S i O_{2}$	5.0000
2	$- 7009.000$	air	1.1265
3	$- 157.226$	$S i O_{2}$	3.0000
4	$- 643.710$	air	50.0000
5	99.8980	$S i O_{2}$	3.0000
6	58.5390	air	1.7538
7	128.2330	$S i O_{2}$	5.0000
8	$- 485.9800$	air	1.0000
9	111.3950	$S i O_{2}$	5.0000
10	201.2100	air	131.8090 ( $= back focus$ )

Order	x	y	Coefficients^b
3	$- 0.00197126169$	$- 0.00223978796$	5
5	0.00080325260	0.00052371064	11
7	0.00095543567	0.00069236162	21
9	0.00060327298	0.00035099301	36
11	0.00032401533	0.00007734528	57
13	0.00016591477	$- 0.00007799678$	85
15	0.00008616475	$- 0.00015642772$	121
17	0.00004795658	$- 0.00019401841$	166
19	0.00003011176	$- 0.00021157918$	221
21	0.00002188745	$- 0.00021967461$	287
Ray tracing	0.00001498059	$- 0.00022647769$

Order	x	y	Coefficients
3	$- 0.00091005727$	$- 0.00067646028$	5
5	$- 0.00014218731$	0.00011823761	11
7	$- 0.00003880366$	0.00022135621	21
9	$- 0.00002649336$	0.00023401047	36
11	$- 0.00002514060$	0.00023543557	57
13	$- 0.00002500005$	0.00023558595	85
15	$- 0.00002498592$	0.00023560122	121
17	$- 0.00002498452$	0.00023560275	166
19	$- 0.00002498438$	0.00023560290	221
21	$- 0.00002498437$	0.00023560292	287
Ray tracing	$- 0.00002498437$	0.00023560292

Order	x	y	Coefficients
3	$- 0.00000829745$	$- 0.00002446818$	5
5	0.00001715466	0.00001119838	11
7	0.00000616644	0.00001691790	21
9	0.00000215993	0.00000884134	36
11	$- 0.00000369338$	$- 0.00000264818$	57
13	$- 0.0000720344$	$- 0.00000914265$	85
15	$- 0.00000843942$	$- 0.00001155229$	121
17	$- 0.00000861676$	$- 0.00001211195$	166
19	$- 0.00000848592$	$- 0.00001208246$	221
21	$- 0.00000833213$	$- 0.00001194423$	287
Ray tracing	$- 0.00000808856$	$- 0.00001167454$

Abstract

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Tables (8)

Equations (30)

Applied Optics