Calculation of the wave aberration of an axial bundle&#x00A0;of rays

Jiří Novák; Antonín Mikš

doi:10.1364/JOSAA.497492

Journal of the Optical Society of America A
Vol. 41,
Issue 1,
pp. 54-58
(2024)
•https://doi.org/10.1364/JOSAA.497492

Calculation of the wave aberration of an axial bundle of rays

Jiří Novák and Antonín Mikš

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Jiří Novák and Antonín Mikš, "Calculation of the wave aberration of an axial bundle of rays," J. Opt. Soc. Am. A 41, 54-58 (2024)

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Abstract

A differential equation is derived for the calculation of the wave aberration of an axial bundle of rays affected by spherical aberration. The solution of the derived equation is analyzed, and the influence of the radius of the reference sphere on the value of the wave aberration is presented. The approximate formula for wave aberration is obtained, which allows the splitting of the wave aberration into a part relative to an infinitely distant reference sphere and a part showing the dependence of the wave aberration on the radius of the reference sphere. Furthermore, the case of third-order and fifth-order spherical aberration is investigated, and the formulas for the calculation of the Strehl definition for the case of small aberrations are derived. The accuracy of the approximated formulas for the wave aberration is analyzed in an example.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (28)

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$u$	$A_{2} / 1000$	$A_{4} / 1000$	$u^{'}$	$Δ s^{'}$	$W_{A} / λ$	$W / λ$	$W^{\infty} / λ$	$δ W_{R} / λ$
−1.0000	−1.6237	5.0630	1.1179	−0.6173	0.1079	0.1079	0.1076	0.0003
−2.0000	−1.6236	5.0022	2.2386	−2.4657	1.7416	1.7414	1.7262	0.0152
−3.0000	−1.6235	4.9002	3.3652	−5.5357	8.9523	8.9483	8.7744	0.1739
−4.0000	−1.6230	4.7556	4.5007	−9.8139	28.9181	28.8779	27.8973	0.9806
−5.0000	−1.6220	4.5660	5.6488	−15.2862	72.6730	72.4278	68.6665	3.7613
−6.0000	−1.6202	4.3268	6.8132	−21.9448	156.3384	155.2513	143.9287	11.3226

$a$	$A_{2} / 1000$	$A_{4} / 1000$	${S D}_{1}$	${S D}_{e}$	${S D}_{s u m}$	$Δ s^{'}$	$W^{\infty} / λ$	$δ W_{R} / λ$
1.0000	−1.6236	5.0022	1.0000	1.0000	1.0000	−0.0468	0.0006	0.0000
2.0000	−1.6236	5.0022	0.9997	0.9997	0.9997	−0.1870	0.0099	0.0000
3.0000	−1.6236	5.0022	0.9913	0.9913	0.9913	−0.4206	0.0499	0.0001
4.0000	−1.6236	5.0022	0.9163	0.9158	0.9154	−0.7473	0.1578	0.0004
5.0000	−1.6236	5.0022	0.5943	0.5831	0.5806	−1.1667	0.3850	0.0016
6.0000	−1.6236	5.0022	0.1070	0.1011	0.1000	−1.6784	0.7979	0.0048

$u$	$A_{2} / 1000$	$A_{4} / 1000$	$u^{'}$	$Δ s^{'}$	$W_{A} / λ$	$W / λ$	$W^{\infty} / λ$	$δ W_{R} / λ$
−1.0000	−1.6237	5.0630	1.1179	−0.6173	0.1079	0.1079	0.1076	0.0003
−2.0000	−1.6236	5.0022	2.2386	−2.4657	1.7416	1.7414	1.7262	0.0152
−3.0000	−1.6235	4.9002	3.3652	−5.5357	8.9523	8.9483	8.7744	0.1739
−4.0000	−1.6230	4.7556	4.5007	−9.8139	28.9181	28.8779	27.8973	0.9806
−5.0000	−1.6220	4.5660	5.6488	−15.2862	72.6730	72.4278	68.6665	3.7613
−6.0000	−1.6202	4.3268	6.8132	−21.9448	156.3384	155.2513	143.9287	11.3226

$a$	$A_{2} / 1000$	$A_{4} / 1000$	${S D}_{1}$	${S D}_{e}$	${S D}_{s u m}$	$Δ s^{'}$	$W^{\infty} / λ$	$δ W_{R} / λ$
1.0000	−1.6236	5.0022	1.0000	1.0000	1.0000	−0.0468	0.0006	0.0000
2.0000	−1.6236	5.0022	0.9997	0.9997	0.9997	−0.1870	0.0099	0.0000
3.0000	−1.6236	5.0022	0.9913	0.9913	0.9913	−0.4206	0.0499	0.0001
4.0000	−1.6236	5.0022	0.9163	0.9158	0.9154	−0.7473	0.1578	0.0004
5.0000	−1.6236	5.0022	0.5943	0.5831	0.5806	−1.1667	0.3850	0.0016
6.0000	−1.6236	5.0022	0.1070	0.1011	0.1000	−1.6784	0.7979	0.0048

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Journal of the Optical Society of America A