Table 1. Open in new tab Real and...

Real	f	ϖ	θ_S	θ	θ_E	θ_S/d
#1	0.0875	0	0.0871	0.0616	0.9807	0.1876
	0.0865	0.0006	0.0871	0.0610	0.9829
#2	0.6401	0.3307	0.0189	5.2981	0.8911	0.1459
	0.6386	0.3300	0.0189	5.2988	0.8912
#3	0.1806	0.6614	0.0661	5.7952	1.1218	0.1379
	0.1796	0.6621	0.0661	5.7944	1.1226
#4	0.0451	0.9921	0.0807	4.8440	1.1944	0.1459
	0.0447	0.9896	0.0806	4.8461	1.1982
#5	0.7232	1.3228	0.0111	0.2680	0.8120	0.1280
	0.7222	1.3228	0.0111	0.2680	0.8123
#6	0.3474	1.6535	0.0066	2.3762	1.0143	0.0206
	0.3474	1.6535	0.0066	2.3762	1.0143
#7	0.6606	1.9842	0.0204	4.4255	0.8348	0.1799
	0.6585	1.9845	0.0204	4.4249	0.8346
#8	0.3839	2.3149	0.0808	4.5837	1.1208	0.2490
	0.3786	2.3189	0.0805	4.5805	1.1228
#9	0.6273	2.6456	0.0161	1.4092	1.1957	0.0886
	0.6267	2.6459	0.0161	1.4092	1.1958
#10	0.0216	2.9762	0.0841	1.6905	0.8268	0.2428
	0.0201	2.9770	0.0841	1.6905	0.8561
#11	0.9106	3.3069	0.0032	4.2288	1.1758	0.0866
	0.9104	0.1653	0.0032	4.2290	1.1758
#12	0.8006	3.6376	0.0132	3.0002	0.8073	0.2216
	0.7985	0.4965	0.0132	2.9984	0.8071

Real	f	ϖ	θ_S	θ	θ_E	θ_S/d
#1	0.0875	0	0.0871	0.0616	0.9807	0.1876
	0.0865	0.0006	0.0871	0.0610	0.9829
#2	0.6401	0.3307	0.0189	5.2981	0.8911	0.1459
	0.6386	0.3300	0.0189	5.2988	0.8912
#3	0.1806	0.6614	0.0661	5.7952	1.1218	0.1379
	0.1796	0.6621	0.0661	5.7944	1.1226
#4	0.0451	0.9921	0.0807	4.8440	1.1944	0.1459
	0.0447	0.9896	0.0806	4.8461	1.1982
#5	0.7232	1.3228	0.0111	0.2680	0.8120	0.1280
	0.7222	1.3228	0.0111	0.2680	0.8123
#6	0.3474	1.6535	0.0066	2.3762	1.0143	0.0206
	0.3474	1.6535	0.0066	2.3762	1.0143
#7	0.6606	1.9842	0.0204	4.4255	0.8348	0.1799
	0.6585	1.9845	0.0204	4.4249	0.8346
#8	0.3839	2.3149	0.0808	4.5837	1.1208	0.2490
	0.3786	2.3189	0.0805	4.5805	1.1228
#9	0.6273	2.6456	0.0161	1.4092	1.1957	0.0886
	0.6267	2.6459	0.0161	1.4092	1.1958
#10	0.0216	2.9762	0.0841	1.6905	0.8268	0.2428
	0.0201	2.9770	0.0841	1.6905	0.8561
#11	0.9106	3.3069	0.0032	4.2288	1.1758	0.0866
	0.9104	0.1653	0.0032	4.2290	1.1758
#12	0.8006	3.6376	0.0132	3.0002	0.8073	0.2216
	0.7985	0.4965	0.0132	2.9984	0.8071

Table 1.

Real and first-order lens parameters for the 12 SIE models represented, respectively, in Fig. 5. For each lens model denoted by #i, we have reported the real model parameters (first line) and the retrieved first order ones (second line).

Real	f	ϖ	θ_S	θ	θ_E	θ_S/d
first order
#1	0.0875	0	0.0871	0.0616	0.9807	0.1876
	0.0865	0.0006	0.0871	0.0610	0.9829
#2	0.6401	0.3307	0.0189	5.2981	0.8911	0.1459
	0.6386	0.3300	0.0189	5.2988	0.8912
#3	0.1806	0.6614	0.0661	5.7952	1.1218	0.1379
	0.1796	0.6621	0.0661	5.7944	1.1226
#4	0.0451	0.9921	0.0807	4.8440	1.1944	0.1459
	0.0447	0.9896	0.0806	4.8461	1.1982
#5	0.7232	1.3228	0.0111	0.2680	0.8120	0.1280
	0.7222	1.3228	0.0111	0.2680	0.8123
#6	0.3474	1.6535	0.0066	2.3762	1.0143	0.0206
	0.3474	1.6535	0.0066	2.3762	1.0143
#7	0.6606	1.9842	0.0204	4.4255	0.8348	0.1799
	0.6585	1.9845	0.0204	4.4249	0.8346
#8	0.3839	2.3149	0.0808	4.5837	1.1208	0.2490
	0.3786	2.3189	0.0805	4.5805	1.1228
#9	0.6273	2.6456	0.0161	1.4092	1.1957	0.0886
	0.6267	2.6459	0.0161	1.4092	1.1958
#10	0.0216	2.9762	0.0841	1.6905	0.8268	0.2428
	0.0201	2.9770	0.0841	1.6905	0.8561
#11	0.9106	3.3069	0.0032	4.2288	1.1758	0.0866
	0.9104	0.1653	0.0032	4.2290	1.1758
#12	0.8006	3.6376	0.0132	3.0002	0.8073	0.2216
	0.7985	0.4965	0.0132	2.9984	0.8071

Real	f	ϖ	θ_S	θ	θ_E	θ_S/d
first order
#1	0.0875	0	0.0871	0.0616	0.9807	0.1876
	0.0865	0.0006	0.0871	0.0610	0.9829
#2	0.6401	0.3307	0.0189	5.2981	0.8911	0.1459
	0.6386	0.3300	0.0189	5.2988	0.8912
#3	0.1806	0.6614	0.0661	5.7952	1.1218	0.1379
	0.1796	0.6621	0.0661	5.7944	1.1226
#4	0.0451	0.9921	0.0807	4.8440	1.1944	0.1459
	0.0447	0.9896	0.0806	4.8461	1.1982
#5	0.7232	1.3228	0.0111	0.2680	0.8120	0.1280
	0.7222	1.3228	0.0111	0.2680	0.8123
#6	0.3474	1.6535	0.0066	2.3762	1.0143	0.0206
	0.3474	1.6535	0.0066	2.3762	1.0143
#7	0.6606	1.9842	0.0204	4.4255	0.8348	0.1799
	0.6585	1.9845	0.0204	4.4249	0.8346
#8	0.3839	2.3149	0.0808	4.5837	1.1208	0.2490
	0.3786	2.3189	0.0805	4.5805	1.1228
#9	0.6273	2.6456	0.0161	1.4092	1.1957	0.0886
	0.6267	2.6459	0.0161	1.4092	1.1958
#10	0.0216	2.9762	0.0841	1.6905	0.8268	0.2428
	0.0201	2.9770	0.0841	1.6905	0.8561
#11	0.9106	3.3069	0.0032	4.2288	1.1758	0.0866
	0.9104	0.1653	0.0032	4.2290	1.1758
#12	0.8006	3.6376	0.0132	3.0002	0.8073	0.2216
	0.7985	0.4965	0.0132	2.9984	0.8071

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