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Design method of soft X-ray and vacuum ultraviolet optical system based on plane-symmetric aberration theory


Soft X-ray and vacuum ultraviolet optical system has the imaging performance of plane-symmetric optical system, this paper propose a design method of this kind of optical systems based on the third-order aberration theory of plane-symmetric optical system. First, applying the aberration expressions to calculate all kinds of wave aberrations of every optical element of optical system and building the wave aberration equilibrium equations, and we propose to apply self-adaptive variation probability genetic optimization algorithm to solve them to obtain the initial structure parameters. Second, the evaluation function of imaging performance of optical system is studied and the corresponding expression is given, and then we use the same algorithm discussed in the above for solve the function. Finally, the design method discussed in this paper is applied to design a soft X-ray and vacuum ultraviolet optical system consisting of double elements and its imaging results before and after the optimization are compared and analyzed; and it will verify the effectiveness of the proposed method in this paper. The results show that the design method provides an effective measure for design soft X-ray and vacuum ultraviolet optical system and has a strong practical value.

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  1. Veyrinas, K., Saquet, N., Poullain, S.M., Lebech, M., Houver, J., Lucchese, R., Dowek, D.: Dissociative photoionization of NO across a shape resonance in the XUV range using circularly polarized synchrotron radiation. J. Chem. Phys. 151, 174305 (2019)

    ADS  Article  Google Scholar 

  2. Fogelqvist, E., Kördel, M., Carannante, V.: Laboratory cryo X-ray microscopy for 3D cell imaging. Sci. Rep. 7, 13433 (2017)

    ADS  Article  Google Scholar 

  3. Yuan, Q.X., Deng, B., Guan, Y., Zhang, K., Liu, Y.J.: Novel developments and applications of nanoscale synchrotron radiation microscopy. Physics 48, 205–218 (2019)

    Google Scholar 

  4. Cao, Y., Lu, L.: Aberrations of soft X-ray and vacuum ultraviolet optical system with orthogonal arrangement of elements. J. Opt. Soc. Am. A 34, 299–307 (2017)

    ADS  Article  Google Scholar 

  5. Lu, L.: Aberration theory of plane-symmetric grating systems. J. Synchrotron Radiat. 15, 399–410 (2008)

    Article  Google Scholar 

  6. Beutler, H.: The theory of the concave grating. J. Opt. Soc. Am. 35, 311–350 (1945)

    ADS  MathSciNet  Article  Google Scholar 

  7. Masui, S., Namioka, T.: Geometric aberration theory of double-element optical systems. J. Opt. Soc. Am. A 16, 2253–2268 (1999)

    ADS  MathSciNet  Article  Google Scholar 

  8. Goto, K., Kurosaki, T.: Canonical formulation for the geometric optics of concave gratings. J. Opt. Soc. Am. A 10, 452–465 (1993)

    ADS  Article  Google Scholar 

  9. Chrisp, M.: Aberrations of holographic toroidal grating systems. Appl. Opt. 22, 1508–1518 (1983)

    ADS  Article  Google Scholar 

  10. Lu, L., Lin, D.: Aberrations of plane-symmetric multi-element optical systems. Optik 121, 1198–1218 (2010)

    ADS  Article  Google Scholar 

  11. Cao, Y.Q., Shen, Z.J., Xie, H.H.: Third-order aberration of soft X-ray optical systems with orthogonal and coplanar arrangement of the main planes of elements. J. Synchrotron Radiat. 27, 1477–1484 (2020)

    Article  Google Scholar 

  12. Cao, Y.Q., Shen, Z.J.: Method of calculating the aberrations of soft X-ray and vacuum ultraviolet optical systems. J. Synchrotron Radiat. 26, 1558–1564 (2020)

    Article  Google Scholar 

  13. Lu, L.J., Zhu, G.Q.: Extension of aberration theory of grating systems from one- to two-dimension extended source. Optik 123, 157–166 (2012)

    ADS  Article  Google Scholar 

  14. Zhu, C.H., Zhou, P., Zhu, J.P., You, D., An, S.Y.: Stripe binary encoding method using genetic algorithms to optimize kernel parameters of error diffusion. Acta Opt. Sin. 41, 2110002 (2021)

    Article  Google Scholar 

  15. Sanchez del Rio, M., Canestrari, N., Jiang, F., Cerrina, F.: SHADOW3: a new version of the synchrotron X-ray optics modeling package. J. Synchrotron Radiat. 18, 708–716 (2011)

    Article  Google Scholar 

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The authors would like to thank Prof. Lijun Lu from Shanghai University for helpful discussions and useful comments.


This research was supported by the Project of Natural Science Foundation of Fujian Province of China (2020J01916), the Science and Technology Planning Project of Putian City of China (2020GP004), the Introduction of Talent Research Start-up Fee Project of Putian University of China (2019010).

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Cao, Y. Design method of soft X-ray and vacuum ultraviolet optical system based on plane-symmetric aberration theory. Opt Rev 29, 207–214 (2022).

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  • Optical design
  • Soft X-ray and vacuum ultraviolet
  • Plane-symmetric
  • Evaluation function
  • Optimum design