Abstract
Based on fifth-order intrinsic aberration theory of plane-symmetric optical system with one-dimension source, the fifth-order intrinsic aberration and extrinsic aberration calculation method of soft x-ray multi-element orthogonal arrangement optical system with large aperture is studied. Firstly, the fifth-order intrinsic aberration calculation expressions of multi-element orthogonal arrangement optical system are given, and then, the fifth-order extrinsic aberration calculation method for this kind of optical systems are discussed and their corresponding expressions are derived; secondly, the fifth-order defocus aberration caused by the meridional field of source is analyzed in detail. Finally, applying the fifth-order aberration expressions and ray-tracing software Shadow to calculate the ray spot diagrams on the image plane of two design examples of soft x-ray multi-element orthogonal arrangement optical system with large aperture, respectively; and comparing these calculation results using two methods in the above, and they shows that the aberration expressions derived have a satisfactory calculation accuracy. The analytical analysis of aberration is helpful in the design and optimization of this kind of optical systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
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.
References
K. Veyrinas, N. Saquet, S. Marggi Poullain, M. Lebech, D. Dowek. Dissociative photoionization of NO across a shape resonance in the XUV range using circularly polarized synchrotron radiation. J. Chem. Phys. 151(17), 174305 (2019).
E. Fogelqvist, M. Kördel, V. Carannante, Laboratory cryo x-ray microscopy for 3D cell imaging. Sci. Rep. 7, 13433 (2017)
Q. Yuan, B. Deng, Y. Guan, K. Zhang, Y. Jiu, Novel developments and applications of nanoscale synchrotron radiation microscopy. Physics 48(4), 205–218 (2019)
L. Lu, D. Lin, Aberrations of plane-symmetric multi-element optical systems. Optik 121, 1198–1218 (2010)
H. Beutler, The Theory of the concave grating. J. Opt. Soc. Am. 35(5), 311–350 (1945)
H. Noda, T. Namioka, M. Seya, Geometrical theory of the grating. J. Opt. Soc. Am. 64(8), 1031–1036 (1974)
T. Namioka, M. Koike, D. Content, Geometric theory of the ellipsoidal grating. Appl. Opt. 33(31), 7261–7274 (1994)
S. Masui, T. Namioka, Geometric aberration theory of double-element optical systems. J. Opt. Soc. Am. A 16(9), 2253–2268 (1999)
K. Goto, T. Kurosaki, Canonical formulation for the geometric optics of concave gratings. J. Opt. Soc. Am. A 10(3), 452–465 (1993)
C. Palmer, W. Mckinney, Imaging equations for spectroscopic systems using Lie transformations: I. Theoretical foundations. Proc. of SPIE 3450, 55–66 (1998)
C. Palmer, B. Wheeler, W. Mckinney, Imaging equations for spectroscopic systems using Lie transformations: II. Multielement systems. Proc. of SPIE 3450, 67–77 (1998)
M.P. Chrisp, Aberrations of holographic toroidal grating systems. Appl. Opt. 22(10), 1508–1518 (1983)
F.Bridou, R. Mercier, A Raynal, JY. Clotaire, C. Colas, P. Fournet, M. Idir, G. Soullie, C. Remond, P. Troussel. Large field double Kirkpatrick-Baez microscope with nonperiodic multilayers for laser plasma imaging. Rev. Sci. Instrum. 73(11), 3789–3795 (2002).
P. Mercere, M. Idir, T. Moreno, G. Cauchon, Automatic alignment of a Kirkpatrick-Baez active optic by use of a soft-x-ray Hartmann wavefront sensor. Opt. Lett. 32(2), 199–201 (2006)
P. Kirkpatrick, V. Baez, Formation of optical images by X-ray. J. Opt. Soc. Am. A 38(9), 766–774 (1948)
Y. Cao, L. Lu, Aberrations of soft x-ray and vacuum ultraviolet optical system with orthogonal arrangement of elements. J. Opt. Soc. Am. A 34(3), 299–307 (2017)
C. Yu, L. Lu, Calculating MTF of Kirkpatrick-Baez system by wave aberration theory. J. Appl. Opt. 41(5), 904–910 (2020)
M. Sanchez del Rio, N. Canestrari, F. Jiang, F. Cerrina, SHADOW3: a new version of the synchrotron x-ray optics modeling package. J. Synchrotron Radiat. 18, 708–716 (2011)
Y. Cao, Z. Shen, Fifth-order intrinsic aberration calculation method for soft x-ray and vacuum ultraviolet optical systems. Appl. Opt. 60(11), 3242–3249 (2021)
Funding
National Nature Science Foundation of China (62205168); Young and Middle-Aged Teachers’ Educational Research Projects of Fujian Province of China (JAT220294); Natural Science Foundation of Fujian Province (2020J01916).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declares that there are no conflicts of interest related to this article.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Cao, Y., Yao, Y., Shen, Z. et al. Fifth-order intrinsic aberration and extrinsic aberration of soft x-ray multi-element orthogonal arrangement optical system with large aperture. J Opt (2024). https://doi.org/10.1007/s12596-024-01762-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12596-024-01762-9