Numerical Results Concerning the Transfer Functions and Total Illuminance for Optimum Balanced Fifth-Order Spherical Aberration

Richard Barakat

doi:10.1364/JOSA.54.000038

Journal of the Optical Society of America
Vol. 54,
Issue 1,
pp. 38-44
(1964)
•https://doi.org/10.1364/JOSA.54.000038

Numerical Results Concerning the Transfer Functions and Total Illuminance for Optimum Balanced Fifth-Order Spherical Aberration

Richard Barakat

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Richard Barakat, "Numerical Results Concerning the Transfer Functions and Total Illuminance for Optimum Balanced Fifth-Order Spherical Aberration," J. Opt. Soc. Am. 54, 38-44 (1964)

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Abstract

Numerical values of the transfer function and total illuminance (encircled energy) are presented for optimum balanced fifth-order spherical aberration.

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W₆	SC
0	1.000
1.0	0.986
2.0	0.945
3.0	0.893
4.0	0.796
5.0	0.698
6.0	0.593

ω	SC=0.9	SC=0.8	SC=0.7	SC=0.6
0	1.0	1.0	1.0	1.0
0.1	0.89674	0.86807	0.83374	0.79532
0.2	0.79669	0.74195	0.67692	0.60492
0.3	0.70953	0.63822	0.55446	0.46324
0.4	0.63782	0.56152	0.47357	0.38015
0.5	0.58297	0.51254	0.43233	0.34840
0.6	0.53754	0.47790	0.40988	0.33858
0.7	0.49281	0.44283	0.38463	0.32193
0.8	0.44627	0.40458	0.35537	0.30142
0.9	0.39882	0.36517	0.32623	0.28444
1.0	0.34993	0.32183	0.28997	0.25657
1.1	0.29917	0.27286	0.24244	0.20983
1.2	0.24909	0.22356	0.19337	0.16017
1.3	0.20385	0.18144	0.15489	0.12566
1.4	0.16544	0.14916	0.12985	0.10856
1.5	0.13133	0.12200	0.11088	0.09852
1.6	0.09618	0.09063	0.08420	0.07730
1.7	0.05931	0.05321	0.04629	0.03906
1.8	0.02907	0.02351	0.01739	0.01131
1.9	0.01078	0.00904	0.00707	0.00504
2.0	0	0	0	0

W₂	1.2	1.4	1.6	1.8	2.0	2.2	2.4	2.6

V₀
0	0	0	0	0	0	0	0	0
0.5	0.0115	0.0295	0.0464	0.0533	0.0474	0.0329	0.0176	0.0069
1.0	0.0419	0.1075	0.1691	0.1943	0.1727	0.1201	0.0643	0.0252
1.5	0.0830	0.2090	0.3272	0.3755	0.3337	0.2325	0.1248	0.0492
2.0	0.1281	0.3073	0.4749	0.5430	0.4830	0.3381	0.1833	0.0736
2.5	0.1773	0.3872	0.5817	0.6598	0.5885	0.4167	0.2311	0.0966
3.0	0.2363	0.4486	0.6417	0.7180	0.6442	0.4664	0.2696	0.1206
3.5	0.3096	0.5010	0.6693	0.7343	0.6663	0.5005	0.3080	0.1512
4.0	0.3943	0.5529	0.6848	0.7353	0.6798	0.5368	0.3564	0.1931
4.5	0.4784	0.6047	0.7020	0.7416	0.7030	0.5865	0.4195	0.2482
5.0	0.5466	0.6491	0.7227	0.7592	0.7401	0.6492	0.4943	0.3145
5.5	0.5891	0.6783	0.7415	0.7824	0.7831	0.7152	0.5723	0.3873
6.0	0.6087	0.6918	0.7535	0.8024	0.8201	0.7725	0.6443	0.4614
6.5	0.6185	0.6982	0.7607	0.8147	0.8436	0.8134	0.7039	0.5320
7.0	0.6348	0.7105	0.7702	0.8219	0.8538	0.8372	0.7493	0.5961
7.5	0.6670	0.7374	0.7889	0.8298	0.8563	0.8482	0.7821	0.6516
8.0	0.7129	0.7783	0.9190	0.8425	0.8574	0.8526	0.8052	0.6977
8.5	0.7617	0.8238	0.8518	0.8591	0.8603	0.8547	0.8214	0.7347
9.0	0.8016	0.8617	0.8812	0.8755	0.8651	0.8566	0.8326	0.7636
9.5	0.8270	0.8851	0.9000	0.8873	0.8697	0.8585	0.8403	0.7864
10.0	0.8410	0.8947	0.9075	0.8933	0.8732	0.8601	0.8456	0.8047
10.5	0.8515	0.8976	0.9086	0.8957	0.8760	0.8616	0.8493	0.8192
11.0	0.8652	0.9012	0.9095	0.8981	0.8792	0.8635	0.8518	0.8301
11.5	0.8834	0.9093	0.9137	0.9026	0.8838	0.8661	0.8536	0.8372
12.0	0.9023	0.9203	0.9211	0.9094	0.8898	0.8697	0.8550	0.8411

W₂	1.8	2.0	2.2	2.4	2.6	2.8	3.0	3.2

V₀
0	0	0	0	0	0	0	0	0
0.5	0.0097	0.0262	0.0417	0.0482	0.0434	0.0312	0.0180	0.0084
1.0	0.0356	0.0955	0.1520	0.1757	0.1582	0.1138	0.0658	0.0307
1.5	0.0708	0.1858	0.2941	0.3395	0.3057	0.2200	0.1275	0.0596
2.0	0.1103	0.2737	0.4269	0.4908	0.4421	0.3192	0.1859	0.0876
2.5	0.1554	0.3459	0.5231	0.5962	0.5376	0.3913	0.2310	0.1105
3.0	0.2116	0.4025	0.5775	0.6483	0.5868	0.4342	0.2633	0.1300
3.5	0.2825	0.4517	0.6028	0.6626	0.6050	0.4610	0.2922	0.1521
4.0	0.3639	0.5002	0.6170	0.6635	0.6159	0.4899	0.3299	0.1842
4.5	0.4429	0.5470	0.6321	0.6698	0.6377	0.5339	0.3840	0.2312
5.0	0.5042	0.5849	0.6497	0.6875	0.6750	0.5943	0.4544	0.2936
5.5	0.5391	0.6076	0.6653	0.7112	0.7203	0.6625	0.5336	0.3672
6.0	0.5520	0.6164	0.6756	0.7327	0.7616	0.7254	0.6109	0.4449
6.5	0.5578	0.6217	0.6837	0.7479	0.7903	0.7731	0.6769	0.5194
7.0	0.5739	0.6371	0.6973	0.7592	0.8051	0.8022	0.7268	0.5849
7.5	0.6096	0.6714	0.7231	0.7721	0.8110	0.8159	0.7607	0.6387
8.0	0.6620	0.7224	0.7613	0.7903	0.8143	0.8202	0.7819	0.6810
8.5	0.7183	0.7786	0.8048	0.8127	0.8189	0.8210	0.7950	0.7140
9.0	0.7648	0.8259	0.8430	0.8346	0.8252	0.8216	0.8037	0.7407
9.5	0.7948	0.8557	0.8682	0.8510	0.8315	0.8228	0.8102	0.7632
10.0	0.8111	0.8684	0.8794	0.8599	0.8362	0.8241	0.8151	0.7823
10.5	0.8223	0.8719	0.8816	0.8637	0.8394	0.8251	0.8183	0.7974
11.0	0.9363	0.8750	0.8823	0.8663	0.8426	0.8262	0.8197	0.8077
11.5	0.8553	0.8829	0.8866	0.8715	0.8476	0.8283	0.8201	0.8131
12.0	0.8757	0.8948	0.8952	0.8800	0.8554	0.8325	0.8207	0.8150

W₂	2.4	2.6	2.8	3.0	3.2	3.4	3.6	3.8

V₀
0	0	0	0	0	0	0	0	0
0.5	0.0079	0.0224	0.0362	0.0423	0.0388	0.0291	0.0183	0.0101
1.0	0.0289	0.0816	0.1318	0.1541	0.1416	0.1062	0.0669	0.0367
1.5	0.0576	0.1588	0.2551	0.2977	0.2734	0.2052	0.1293	0.0711
2.0	0.0909	0.2343	0.3704	0.4303	0.3950	0.2969	0.1875	0.1031
2.5	0.1307	0.2971	0.4541	0.5224	0.4794	0.3620	0.2301	0.1269
3.0	0.1823	0.3476	0.5018	0.5676	0.5214	0.3980	0.2566	0.1429
3.5	0.2485	0.3924	0.5244	0.5797	0.5354	0.4175	0.2769	0.1579
4.0	0.3241	0.4364	0.5372	0.5804	0.5436	0.4391	0.3046	0.1813
4.5	0.3959	0.4776	0.5504	0.5869	0.5634	0.4768	0.3500	0.2209
5.0	0.4494	0.5092	0.5653	0.6043	0.5999	0.5338	0.4135	0.2791
5.5	0.4773	0.5261	0.5783	0.6282	0.6463	0.6023	0.4939	0.3520
6.0	0.4851	0.5315	0.5875	0.6511	0.6908	0.6689	0.5740	0.4312
6.5	0.4888	0.5368	0.5971	0.6694	0.7242	0.7219	0.6439	0.5067
7.0	0.5061	0.5562	0.6152	0.6853	0.7442	0.7560	0.6964	0.5709
7.5	0.5461	0.5978	0.6481	0.7039	0.7564	0.7726	0.7303	0.6209
8.0	0.6048	0.6583	0.6953	0.7285	0.7616	0.7781	0.7495	0.6579
8.5	0.6681	0.7246	0.7483	0.7575	0.7692	0.7788	0.7598	0.6861
9.0	0.7210	0.7809	0.7952	0.7854	0.7781	0.7790	0.7664	0.7100
9.5	0.7556	0.8172	0.8271	0.8066	0.7863	0.7799	0.7719	0.7319
10.0	0.7742	0.8334	0.8422	0.8185	0.7921	0.7810	0.7767	0.7517
10.5	0.7860	0.8377	0.8458	0.8234	0.7955	0.7815	0.7799	0.7678
11.0	0.7997	0.8403	0.8464	0.8263	0.7986	0.7821	0.7811	0.7784
11.5	0.8185	0.8477	0.8509	0.8322	0.8043	0.7845	0.7813	0.7835
12.0	0.8393	0.8600	0.8609	0.8432	0.8147	0.7905	0.7825	0.7848

W₂	2.8	3.0	3.2	3.4	3.6	3.8	4.0	4.2

V₀
0	0	0	0	0	0	0	0	0
0.5	0.0001	0.0060	0.0182	0.0302	0.0359	0.0340	0.0268	0.0185
1.0	0.0006	0.0220	0.0665	0.1099	0.1309	0.1237	0.0978	0.0675
1.5	0.0030	0.0442	0.1295	0.2127	0.2528	0.2388	0.1888	0.1304
2.0	0.0121	0.0708	0.1915	0.3090	0.3653	0.3447	0.2725	0.1882
2.5	0.0354	0.1044	0.2440	0.3792	0.4432	0.4174	0.3305	0.2286
3.0	0.0797	0.1502	0.2874	0.4196	0.4812	0.4523	0.3601	0.2504
3.5	0.1452	0.2098	0.3271	0.4393	0.4910	0.4624	0.3731	0.2635
4.0	0.2230	0.2776	0.3660	0.4509	0.4918	0.4679	0.3880	0.2826
4.5	0.2967	0.3410	0.4014	0.4625	0.4983	0.4854	0.4196	0.3200
5.0	0.3506	0.3864	0.4270	0.4751	0.5153	0.5201	0.4722	0.3797
5.5	0.3780	0.4080	0.4392	0.4859	0.5389	0.5663	0.5392	0.4559
6.0	0.3851	0.4123	0.4423	0.4946	0.5628	0.6126	0.6072	0.5362
6.5	0.3875	0.4156	0.4485	0.5061	0.5840	0.6497	0.6636	0.6072
7.0	0.4011	0.4350	0.4720	0.5286	0.6046	0.6746	0.7014	0.6602
7.5	0.4334	0.4793	0.5202	0.5681	0.6292	0.6902	0.7210	0.6929
8.0	0.4802	0.5435	0.5888	0.6234	0.6605	0.7019	0.7281	0.7097
8.5	0.5300	0.6129	0.6638	0.6849	0.6962	0.7135	0.7296	0.7174
9.0	0.5721	0.6713	0.7282	0.7399	0.7301	0.7254	0.7301	0.7221
9.5	0.6028	0.7101	0.7706	0.7780	0.7556	0.7356	0.7311	0.7268
10.0	0.6270	0.7310	0.7903	0.7968	0.7700	0.7421	0.7319	0.7317
10.5	0.6525	0.7432	0.7956	0.8018	0.7757	0.7453	0.7321	0.7353
11.0	0.6841	0.7561	0.7977	0.8025	0.7788	0.7482	0.7328	0.7373
11.5	0.7197	0.7740	0.8044	0.8072	0.7857	0.7552	0.7363	0.7387
12.0	0.7522	0.7942	0.8169	0.8188	0.7996	0.7690	0.7454	0.7418

Abstract

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Figures (16)

Tables (6)

Equations (10)

Journal of the Optical Society of America