Fifth-order Aberration Coefficients for Plane-symmetric Optical Systems

Based on the the third-order aberration theory of plane-symmetric optical systems, this paper studies the effect on aberrations of the second-order accuracy of aperture-ray coordinates and the extrinsic aberrations of this kind of optical system; their calculation expressions are derived. The resultant aberration expressions are then applied to calculate the aberrations of two design examples of soft X-ray and vacuum ultraviolet (XUV) optical systems; images are compared with ray-tracing results using SHADOW software to validate the aberration expressions. The study shows that the accuracy of the aberration expressions is satisfactory.

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COSY 5.0 — The fifth order code for corpuscular optical systems

Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment ◽

10.1016/0168-9002(87)90920-x ◽

1987 ◽

Vol 258 (3) ◽

pp. 402-406 ◽

Cited By ~ 39

Author(s):

M. Berz ◽

H.C. Hoffmann ◽

H. Wollnik

Keyword(s):

Optical Systems ◽

Fifth Order

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Aberrations of plane-symmetric multi-element optical systems

Optik ◽

10.1016/j.ijleo.2009.01.016 ◽

2010 ◽

Vol 121 (13) ◽

pp. 1198-1218 ◽

Cited By ~ 7

Author(s):

Li-Jun Lu ◽

Dong-Liang Lin

Keyword(s):

Optical Systems ◽

Plane Symmetric

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The geometrical aberrations of general electron optical systems II. The primary (third order) aberrations of orthogonal systems, and the secondary (fifth order) aberrations of round systems

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1965.0014 ◽

1965 ◽

Vol 257 (1086) ◽

pp. 523-552 ◽

Cited By ~ 15

Keyword(s):

Second Order ◽

Order Perturbation ◽

Optical Systems ◽

Characteristic Functions ◽

Electron Optics ◽

Third Order ◽

Variation Of Parameters ◽

General Kind ◽

Fifth Order ◽

Orthogonal Systems

The theory of characteristic functions, developed by Sturrock for electron optics, is used to calculate the primary aberrations of rectilinear orthogonal systems of the most general kind. In the second part, the secondary aberrations of round systems are calculated with the aid of Sturrock’s second-order perturbation characteristic functions. A proof of the equivalence of the aberration formulae obtained by Melkich, using the variation of parameters method, and those obtained below is offered in an appendix.

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Third-order aberration of soft X-ray optical systems with orthogonal and coplanar arrangement of the main planes of elements

Journal of Synchrotron Radiation ◽

10.1107/s1600577520010474 ◽

2020 ◽

Vol 27 (6) ◽

pp. 1477-1484

Author(s):

Yiqing Cao ◽

Zhijuan Shen ◽

Haihe Xie

Keyword(s):

Optical System ◽

Optical Systems ◽

Analysis Method ◽

Third Order ◽

Optical Elements ◽

Analytical Analysis ◽

X Ray ◽

Plane Symmetric ◽

Design And Optimization ◽

Aberration Theory

A third-order aberration analytical analysis method of soft X-ray optical systems with orthogonal and coplanar arrangement of the main planes of elements is proposed. Firstly, the transfer equations of the aperture ray and the principle ray are derived; then, based on the third-order aberration theory with the aperture-ray coordinates on the reference exit wavefront of a plane-symmetric optical system, the aberration expressions contributed by the wave aberration and defocus of this kind of optical system are studied in detail. Finally, the derived aberration calculation expressions are applied to calculate the aberration of two design examples of such types of optical systems; the images are compared with ray-tracing results obtained using the Shadow software to validate the aberration expressions. The study shows that the accuracy of the aberration expressions is satisfactory. The analytical analysis method of aberration is helpful in the design and optimization of the soft X-ray optical systems with orthogonal and coplanar arrangement of the main planes of optical elements.

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