Aberrations of soft x-ray and vacuum ultraviolet optical systems with orthogonal arrangement of elements

Yiqing Cao; Lijun Lu

doi:10.1364/JOSAA.34.000299

Aberrations of soft x-ray and vacuum ultraviolet optical systems with orthogonal arrangement of elements

Yiqing Cao and Lijun Lu

Journal of the Optical Society of America A
Vol. 34,
Issue 3,
pp. 299-307
(2017)
•https://doi.org/10.1364/JOSAA.34.000299

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Yiqing Cao and Lijun Lu, "Aberrations of soft x-ray and vacuum ultraviolet optical systems with orthogonal arrangement of elements," J. Opt. Soc. Am. A 34, 299-307 (2017)

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Related Topics
Table of Contents Category
- X-ray Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Aberrations (global) (080.1010)
- Geometric optical design (080.2740)
- Synchrotron radiation (340.6720)
- X-ray microscopy (340.7460)

About this Article
History
- Original Manuscript: October 17, 2016
- Revised Manuscript: January 6, 2017
- Manuscript Accepted: January 9, 2017
- Published: February 2, 2017

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Abstract

The wave aberration of plane-symmetric optical systems is expressed with the aperture-ray coordinates on the reference exit wavefront in the paper; the defocus aberration caused by the meridional field of source is analyzed in detail. Based on the expressions of the wave aberration and the defocus, the aberrations of the soft x-ray and ultraviolet (XUV) optical systems with an orthogonal arrangement of elements are studied as a whole. The resultant aberration expressions are used to calculate the aberrations of two design examples; the images are compared to the ray-tracing results with Shadow to validate the aberration expressions. The study shows that the accuracy of the aberration expressions is satisfactory. The analytical analysis of aberrations is helpful in the design and optimization of the XUV optical systems with an orthogonal arrangement of elements.

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Supplementary Material (1)

Name	Description
» Code 1	Input files for Shadow for Kirkpatrick-Baez optics and the varied line spacing monochromator.

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${\bar{d}}_{i j k h}$	Expression	${\bar{h}}_{i j k h}$	Expression
${\bar{d}}_{1100}$	$2 A B^{2} r_{0}^{'} {\tilde{w}}_{120 (1)}$	${\bar{h}}_{0200}$	$3 A^{3} r_{0}^{'} {\tilde{w}}_{300 (1)}$
${\bar{d}}_{0030}$	$B r_{0}^{'} {\tilde{w}}_{013 (1)}$	${\bar{h}}_{2000}$	$A B^{2} r_{0}^{'} {\tilde{w}}_{120 (1)}$
${\bar{d}}_{1020}$	$2 B^{2} r_{0}^{'} {\tilde{w}}_{022 (1)}$	${\bar{h}}_{0020}$	$A r_{0}^{'} {\tilde{w}}_{102 (1)}$
${\bar{d}}_{0110}$	$A B r_{0}^{'} {\tilde{w}}_{111 (1)}$	${\bar{h}}_{0120}$	$2 A^{2} r_{0}^{'} {\tilde{w}}_{202 (1)}$
${\bar{d}}_{2010}$	$3 B^{3} r_{0}^{'} {\tilde{w}}_{031 (1)}$	${\bar{h}}_{1010}$	$A B r_{0}^{'} {\tilde{w}}_{111 (1)}$
${\bar{d}}_{0210}$	$A^{2} B r_{0}^{'} {\tilde{w}}_{211 (1)}$	${\bar{h}}_{1110}$	$2 A^{2} B r_{0}^{'} {\tilde{w}}_{211 (1)}$
${\bar{d}}_{2000}$	$3 r_{0}^{'} {\tilde{w}}_{300 (2)}$	${\bar{h}}_{1100}$	$2 r_{0}^{'} {\tilde{w}}_{120 (2)}$
${\bar{d}}_{0200}$	$r_{0}^{'} {\tilde{w}}_{120 (2)}$	${\bar{h}}_{0003}$	$C^{3} r_{0}^{'} {\tilde{w}}_{013 (2)}$
${\bar{d}}_{0002}$	$C^{2} r_{0}^{'} {\tilde{w}}_{102 (2)}$	${\bar{h}}_{0102}$	$2 C^{2} r_{0}^{'} {\tilde{w}}_{022 (2)}$
${\bar{d}}_{1002}$	$2 C^{2} r_{0}^{'} {\tilde{w}}_{202 (2)}$	${\bar{h}}_{1001}$	$C r_{0}^{'} {\tilde{w}}_{111 (2)}$
${\bar{d}}_{0101}$	$C r_{0}^{'} {\tilde{w}}_{111 (2)}$	${\bar{h}}_{0201}$	$3 C r_{0}^{'} {\tilde{w}}_{031 (2)}$
${\bar{d}}_{1101}$	$2 C r_{0}^{'} {\tilde{w}}_{211 (2)}$	${\bar{h}}_{2001}$	$C r_{0}^{'} {\tilde{w}}_{211 (2)}$
${\bar{d}}_{3000}$	$4 r_{0}^{'} (B^{4} {\tilde{w}}_{040 (1)} + {\tilde{w}}_{400 (2)})$	${\bar{h}}_{0300}$	$4 r_{0}^{'} (A^{4} {\tilde{w}}_{400 (1)} + {\tilde{w}}_{040 (2)})$
${\bar{d}}_{1200}$	$2 r_{0}^{'} (A^{2} B^{2} {\tilde{w}}_{220 (1)} + {\tilde{w}}_{220 (2)})$	${\bar{h}}_{2100}$	$2 r_{0}^{'} (A^{2} B^{2} {\tilde{w}}_{220 (1)} + {\tilde{w}}_{220 (2)})$

Parameter	Value
$m$	−1
$λ$	21.2 nm
$σ$	$1 / 1800 {mm}^{- 1}$
$b_{2}$	$6.63 \times 10^{- 4} {mm}^{- 1}$
$b_{3}$	$3.37 \times 10^{- 7} {mm}^{- 2}$
$b_{4}$	$- 2.62 \times 10^{- 10} {mm}^{- 3}$

Parameter	System I	System II
$R_{1}$	9700 mm	20000 mm
$ρ_{1}$		489.4 mm
$R_{2}$	9700 mm	$\infty$
$α_{1}$	88.948°	81°
$β_{1}$	−88.948°	−81°
$α_{2}$	−88.857°	−74.03°
$β_{2}$	88.857°	88.05°
$r_{m 1} (r_{s 1})$	100 mm	3128.7 mm
$d$	10 mm	170 mm
$r_{0}^{'}$	800 mm	2934.7 mm

	${\tilde{r}}_{m 2}^{'}$	${\tilde{r}}_{s 2}^{'}$	${\tilde{r}}_{m 2}^{' *}$	${\tilde{r}}_{s 2}^{' *}$	$r_{m 2}^{'}$	$r_{s 2}^{'}$	$\| {\tilde{r}}_{m 2}^{'} - {\tilde{r}}_{m 2}^{' *} \| / {\tilde{r}}_{m 2}^{'}$	$\| {\tilde{r}}_{s 2}^{'} - {\tilde{r}}_{s 2}^{' *} \| / {\tilde{r}}_{s 2}^{'}$
System I	1171.9	1369.3	1140.8	1285.1	801	800.2	2.65%	6.15%
System II	1898.6	3007.4	2202.8	3007.3	2934.7	2958.7	16.02%	$3.33 \times 10^{- 5}$

${\bar{d}}_{i j k h}$	Expression	${\bar{h}}_{i j k h}$	Expression
${\bar{d}}_{1100}$	$2 A B^{2} r_{0}^{'} {\tilde{w}}_{120 (1)}$	${\bar{h}}_{0200}$	$3 A^{3} r_{0}^{'} {\tilde{w}}_{300 (1)}$
${\bar{d}}_{0030}$	$B r_{0}^{'} {\tilde{w}}_{013 (1)}$	${\bar{h}}_{2000}$	$A B^{2} r_{0}^{'} {\tilde{w}}_{120 (1)}$
${\bar{d}}_{1020}$	$2 B^{2} r_{0}^{'} {\tilde{w}}_{022 (1)}$	${\bar{h}}_{0020}$	$A r_{0}^{'} {\tilde{w}}_{102 (1)}$
${\bar{d}}_{0110}$	$A B r_{0}^{'} {\tilde{w}}_{111 (1)}$	${\bar{h}}_{0120}$	$2 A^{2} r_{0}^{'} {\tilde{w}}_{202 (1)}$
${\bar{d}}_{2010}$	$3 B^{3} r_{0}^{'} {\tilde{w}}_{031 (1)}$	${\bar{h}}_{1010}$	$A B r_{0}^{'} {\tilde{w}}_{111 (1)}$
${\bar{d}}_{0210}$	$A^{2} B r_{0}^{'} {\tilde{w}}_{211 (1)}$	${\bar{h}}_{1110}$	$2 A^{2} B r_{0}^{'} {\tilde{w}}_{211 (1)}$
${\bar{d}}_{2000}$	$3 r_{0}^{'} {\tilde{w}}_{300 (2)}$	${\bar{h}}_{1100}$	$2 r_{0}^{'} {\tilde{w}}_{120 (2)}$
${\bar{d}}_{0200}$	$r_{0}^{'} {\tilde{w}}_{120 (2)}$	${\bar{h}}_{0003}$	$C^{3} r_{0}^{'} {\tilde{w}}_{013 (2)}$
${\bar{d}}_{0002}$	$C^{2} r_{0}^{'} {\tilde{w}}_{102 (2)}$	${\bar{h}}_{0102}$	$2 C^{2} r_{0}^{'} {\tilde{w}}_{022 (2)}$
${\bar{d}}_{1002}$	$2 C^{2} r_{0}^{'} {\tilde{w}}_{202 (2)}$	${\bar{h}}_{1001}$	$C r_{0}^{'} {\tilde{w}}_{111 (2)}$
${\bar{d}}_{0101}$	$C r_{0}^{'} {\tilde{w}}_{111 (2)}$	${\bar{h}}_{0201}$	$3 C r_{0}^{'} {\tilde{w}}_{031 (2)}$
${\bar{d}}_{1101}$	$2 C r_{0}^{'} {\tilde{w}}_{211 (2)}$	${\bar{h}}_{2001}$	$C r_{0}^{'} {\tilde{w}}_{211 (2)}$
${\bar{d}}_{3000}$	$4 r_{0}^{'} (B^{4} {\tilde{w}}_{040 (1)} + {\tilde{w}}_{400 (2)})$	${\bar{h}}_{0300}$	$4 r_{0}^{'} (A^{4} {\tilde{w}}_{400 (1)} + {\tilde{w}}_{040 (2)})$
${\bar{d}}_{1200}$	$2 r_{0}^{'} (A^{2} B^{2} {\tilde{w}}_{220 (1)} + {\tilde{w}}_{220 (2)})$	${\bar{h}}_{2100}$	$2 r_{0}^{'} (A^{2} B^{2} {\tilde{w}}_{220 (1)} + {\tilde{w}}_{220 (2)})$

Abstract

References

Supplementary Material (1)

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Figures (6)

Tables (4)

Equations (66)

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