Fifth-order intrinsic aberration calculation method for soft x-ray and vacuum ultraviolet optical systems

Yiqing Cao; Yiqing Cao; Zhijuan Shen

doi:10.1364/AO.422375

Applied Optics
Vol. 60,
Issue 11,
pp. 3242-3249
(2021)
•https://doi.org/10.1364/AO.422375

Fifth-order intrinsic aberration calculation method for soft x-ray and vacuum ultraviolet optical systems

Yiqing Cao and Zhijuan Shen

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Yiqing Cao and Zhijuan Shen, "Fifth-order intrinsic aberration calculation method for soft x-ray and vacuum ultraviolet optical systems," Appl. Opt. 60, 3242-3249 (2021)

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Abstract

In this paper, we propose the fifth-order intrinsic aberration calculation method for soft x-ray and vacuum ultraviolet optical systems. First, the sixth-order intrinsic wave aberrations with the aperture-ray coordinates on the optical surface are derived based on the wave aberration method, and then applying the sixth-order mapping relationship of aperture-ray coordinates between the optical surface and the reference exit wavefront, the expressions with those on the reference exit wavefront can be obtained. Second, we derived the calculation expression for the fifth-order intrinsic aberration on the image plane. Finally, the fifth-order intrinsic aberration calculation expressions of the soft x-ray and vacuum ultraviolet optical system derived in this paper are applied to calculate the aberration distribution on the image plane of two design examples of this kind of optical system, and the calculation results are compared with the ray-tracing ones with Shadow software to validate the aberration expressions. The study shows that the accuracy of the aberration expressions is satisfactory.

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Supplementary Material (1)

Name	Description
Supplement 1	This supplemental document gives the relationship between the wave aberration coefficient expressions with aperture-ray coordinates on the reference exit wavefront and the ones on the optical surface.

Data Availability

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 (70)

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$N_{100} = 1 / Γ$	$N_{200} = n_{20} / 2$
$N_{300} = n_{30} / 2$	$N_{400} = n_{40} / 8$
$N_{500} = n_{50} / 8$	$N_{600} = n_{60} / 16$
$N_{020} = n_{02} / 2$	$N_{120} = n_{12} / 2$
$N_{220} = n_{22} / 4$	$N_{320} = n_{32} / 4$
$N_{420} = n_{42} / 16$	$N_{040} = n_{04} / 8$
$N_{140} = n_{14} / 8$	$N_{240} = n_{24} / 16$
$N_{060} = n_{06} / 16$	$N_{011} = n_{02} l_{s}$
$N_{111} = n_{12} l_{s}$	$N_{211} = n_{22} l_{s} / 2$
$N_{311} = n_{32} l_{s} / 2$	$N_{411} = n_{42} l_{s} / 8$
$N_{031} = n_{04} l_{s} / 2$	$N_{131} = n_{14} l_{s} / 2$
$N_{231} = n_{24} l_{s} / 4$	$N_{051} = 3 n_{06} l_{s} / 8$
$N_{102} = x_{c} n_{20} + n_{12} l_{s}^{2} / 2$	$N_{202} = 3 x_{c} n_{30} / 2 + n_{22} l_{s}^{2} / 4$
$N_{302} = x_{c} n_{40} / 2 + n_{32} l_{s}^{2} / 4$	$N_{402} = 5 x_{c} n_{50} / 8 + n_{42} l_{s}^{2} / 16$
$N_{022} = x_{c} n_{12} / 2 + 3 n_{04} l_{s}^{2} / 4$	$N_{122} = x_{c} n_{22} / 2 + 3 n_{14} l_{s}^{2} / 4$
$N_{222} = 3 x_{c} n_{32} / 4 + 3 n_{24} l_{s}^{2} / 8$	$N_{042} = x_{c} n_{14} / 8 + 15 n_{06} l_{s}^{2} / 16$
$N_{013} = x_{c} n_{12} l_{s} + n_{04} l_{s}^{3} / 2$	$N_{113} = x_{c} n_{22} l_{s} + n_{14} l_{s}^{3} / 2$
$N_{213} = 3 x_{c} n_{32} l_{s} / 2 + n_{24} l_{s}^{3} / 4$	$N_{033} = x_{c} n_{14} l_{s} / 2 + 5 n_{06} l_{s}^{3} / 4$
$\begin{array}{l} N_{104} = 3 x_{c}^{2} n_{30} / 2 + x_{c} n_{22} l_{s}^{2} / 2 \\ + n_{14} l_{s}^{4} / 8 \end{array}$	$\begin{array}{l} N_{204} = 3 x_{c}^{2} n_{40} / 4 + 3 x_{c} n_{32} l_{s}^{2} / 4 \\ + n_{24} l_{s}^{4} / 16 \end{array}$
$\begin{array}{ll} N_{024} = x_{c}^{2} n_{22} / 4 + 3 x_{c} n_{14} l_{s}^{2} / 4 \\ + 15 n_{06} l_{s}^{4} / 16 \end{array}$	$\begin{array}{l} N_{015} = x_{c}^{2} n_{22} l_{s} / 2 + x_{c} n_{14} l_{s}^{3} / 2 \\ + 3 n_{06} l_{s}^{5} / 8 \end{array}$

	$r_{m 1} (r_{s 1})$	$α_{1}$	$β_{1}$	$R_{1}$	$ρ_{1}$	$r_{m 1}^{'}$	$r_{s 1}^{'}$
System I	2000	86°	−86°	19114	–	1000	−2029.6
System II	2000	86°	−86°	19114	93	1000	1000

$N_{100} = 1 / Γ$	$N_{200} = n_{20} / 2$
$N_{300} = n_{30} / 2$	$N_{400} = n_{40} / 8$
$N_{500} = n_{50} / 8$	$N_{600} = n_{60} / 16$
$N_{020} = n_{02} / 2$	$N_{120} = n_{12} / 2$
$N_{220} = n_{22} / 4$	$N_{320} = n_{32} / 4$
$N_{420} = n_{42} / 16$	$N_{040} = n_{04} / 8$
$N_{140} = n_{14} / 8$	$N_{240} = n_{24} / 16$
$N_{060} = n_{06} / 16$	$N_{011} = n_{02} l_{s}$
$N_{111} = n_{12} l_{s}$	$N_{211} = n_{22} l_{s} / 2$
$N_{311} = n_{32} l_{s} / 2$	$N_{411} = n_{42} l_{s} / 8$
$N_{031} = n_{04} l_{s} / 2$	$N_{131} = n_{14} l_{s} / 2$
$N_{231} = n_{24} l_{s} / 4$	$N_{051} = 3 n_{06} l_{s} / 8$
$N_{102} = x_{c} n_{20} + n_{12} l_{s}^{2} / 2$	$N_{202} = 3 x_{c} n_{30} / 2 + n_{22} l_{s}^{2} / 4$
$N_{302} = x_{c} n_{40} / 2 + n_{32} l_{s}^{2} / 4$	$N_{402} = 5 x_{c} n_{50} / 8 + n_{42} l_{s}^{2} / 16$
$N_{022} = x_{c} n_{12} / 2 + 3 n_{04} l_{s}^{2} / 4$	$N_{122} = x_{c} n_{22} / 2 + 3 n_{14} l_{s}^{2} / 4$
$N_{222} = 3 x_{c} n_{32} / 4 + 3 n_{24} l_{s}^{2} / 8$	$N_{042} = x_{c} n_{14} / 8 + 15 n_{06} l_{s}^{2} / 16$
$N_{013} = x_{c} n_{12} l_{s} + n_{04} l_{s}^{3} / 2$	$N_{113} = x_{c} n_{22} l_{s} + n_{14} l_{s}^{3} / 2$
$N_{213} = 3 x_{c} n_{32} l_{s} / 2 + n_{24} l_{s}^{3} / 4$	$N_{033} = x_{c} n_{14} l_{s} / 2 + 5 n_{06} l_{s}^{3} / 4$
$\begin{array}{l} N_{104} = 3 x_{c}^{2} n_{30} / 2 + x_{c} n_{22} l_{s}^{2} / 2 \\ + n_{14} l_{s}^{4} / 8 \end{array}$	$\begin{array}{l} N_{204} = 3 x_{c}^{2} n_{40} / 4 + 3 x_{c} n_{32} l_{s}^{2} / 4 \\ + n_{24} l_{s}^{4} / 16 \end{array}$
$\begin{array}{ll} N_{024} = x_{c}^{2} n_{22} / 4 + 3 x_{c} n_{14} l_{s}^{2} / 4 \\ + 15 n_{06} l_{s}^{4} / 16 \end{array}$	$\begin{array}{l} N_{015} = x_{c}^{2} n_{22} l_{s} / 2 + x_{c} n_{14} l_{s}^{3} / 2 \\ + 3 n_{06} l_{s}^{5} / 8 \end{array}$

	$r_{m 1} (r_{s 1})$	$α_{1}$	$β_{1}$	$R_{1}$	$ρ_{1}$	$r_{m 1}^{'}$	$r_{s 1}^{'}$
System I	2000	86°	−86°	19114	–	1000	−2029.6
System II	2000	86°	−86°	19114	93	1000	1000

Abstract

Supplementary Material (1)

Data Availability

Cited By

Figures (4)

Tables (3)

Equations (70)

Applied Optics