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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 10 — Apr. 1, 2010
  • pp: 1964–1971

Generalized method for calculating astigmatism of the unit-magnification multipass system

Kexin Chen, Huaidong Yang, Liqun Sun, and Guofan Jin  »View Author Affiliations

Applied Optics, Vol. 49, Issue 10, pp. 1964-1971 (2010)

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A generalized method to accurately calculate astigmatism of the unit-magnification multipass system (UMS) is proposed. A practical coaxial optical transmission model is developed for the UMS. Astigmatism analysis is then made convenient by a 4 by 4 general transfer matrix. Astigmatism correction is significantly promoted, and hence further improvement in imaging quality can be expected. Good agreement between numerical simulations and Zemax ray tracing results verifies the effectiveness of this method. The resulted RMS spot size of this method is only 25% to 64% of other previous methods based on the golden section search for minimum astigmatism in real design cases. This method is helpful for the optical design of the UMS.

© 2010 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2730) Geometric optics : Matrix methods in paraxial optics
(080.2740) Geometric optics : Geometric optical design
(220.1000) Optical design and fabrication : Aberration compensation
(220.1010) Optical design and fabrication : Aberrations (global)

Original Manuscript: January 8, 2010
Revised Manuscript: March 9, 2010
Manuscript Accepted: March 9, 2010
Published: March 29, 2010

Kexin Chen, Huaidong Yang, Liqun Sun, and Guofan Jin, "Generalized method for calculating astigmatism of the unit-magnification multipass system," Appl. Opt. 49, 1964-1971 (2010)

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  1. C. Robert, “Simple, stable, and compact multiple-reflection optical cell for very long optical paths,” Appl. Opt. 46, 5408-5418 (2007). [CrossRef]
  2. J. Silver, “Simple dense-pattern optical multipass cells,” Appl. Opt. 44, 6545-6556 (2005). [CrossRef]
  3. R. P. Blickensderfer, G. E. Ewing, and R. Leonard, “A long path, low temperature cell,” Appl. Opt. 7, 2214-2217 (1968). [CrossRef]
  4. J. U. White, “Very long optical paths in air,” J. Opt. Soc. Am. 66, 411-416 (1976). [CrossRef]
  5. T. H. Edwards, “Multiple-traverse absorption cell design,” J. Opt. Soc. Am. 51, 98-102 (1961). [CrossRef]
  6. A. L. Vitushkin and L. F. Vitushkin, “Design of a multipass optical cell based on the use of shifted corner cubes and right-angle prisms,” Appl. Opt. 37, 162-165 (1998). [CrossRef]
  7. D. Horn and G. C. Pimentel, “2.5 km Low-temperature multiple-reflection cell,” Appl. Opt. 10, 1892-1898 (1971). [CrossRef]
  8. J.-F. Doussin, R. Dominique, and C. Patrick, “Multiple-pass cell for very-long-path infrared spectrometry,” Appl. Opt. 38, 4145-4150 (1999). [CrossRef]
  9. J. T. K. McCubbin and R. P. Grosso, “White-type multiple-pass absorption cell of simple construction,” Appl. Opt. 2, 764-765(1963). [CrossRef]
  10. H. M. Pickett, G. M. Bradley, and H. L. Strauss, “White type multiple pass absorption cell,” Appl. Opt. 9, 2397-2398 (1970). [CrossRef]
  11. S. M. Chernin, “Promising version of the three-objective multipass matrix system,” Opt. Express 10, 104-107 (2002).
  12. S. M. Chernin and E. G. Barskaya, “Optical multipass matrix systems,” Appl. Opt. 30, 51-58 (1991). [CrossRef]
  13. S. M. Chernin, S. B. Mikhailov, and E. G. Barskaya, “Aberrations of a multipass matrix system,” Appl. Opt. 31, 765-769(1992). [CrossRef]
  14. Y. G. Barskaya, “Aberrations of a multipass cell,” Opt. Technol. 38, 278-280 (1971).
  15. T. R. Reesor, “The astigmatism of a multiple path absorption cell,” J. Opt. Soc. Am. 41, 1059-1060 (1951). [CrossRef]
  16. W. H. Kohn, “Astigmatism and White cells: theoretical considerations on the construction of an anastigmatic White cell,” Appl. Opt. 31, 6757-6764 (1992). [CrossRef]
  17. D. C. Tobin, L. L. Strow, W. J. Lafferty, and W. B. Olson, “Experimental investigation of the self- and N2-broadened continuum within the N2 band of water vapor,” Appl. Opt. 35, 4724-4734 (1996). [CrossRef]
  18. H. J. Bernstein and G. Herzberg, “Rotation-vibration spectra of diatomic and simple polyatomic molecules with long absorbing paths,” J. Chem. Phys. 16, 30-39 (1948). [CrossRef]
  19. C. Kexin, Y. Huaidong, S. Liqun, and J. Guofan, “Astigmatism analysis by matrix methods in White cells,” Proc. SPIE 7156, 71560G (2008),
  20. X. Liu and K.-H. Brenner, “Minimal optical decomposition of ray transfer matrices,” Appl. Opt. 47, E88-E98 (2008). [CrossRef]
  21. H. H. Arsenault and B. Macukow, “Factorization of the transfer matrix for symmetrical optical systems,” J. Opt. Soc. Am. 73, 1350-1359 (1983). [CrossRef]
  22. B. Macukow and H. H. Arsenault, “Matrix decompositions for nonsymmetrical optical systems,” J. Opt. Soc. Am. 73, 1360-1366 (1983). [CrossRef]
  23. B. Macukow and H. H. Arsenault, “Extension of the matrix theory for nonsymmetrical optical system,” J. Opt. (Paris) 15, 145-151 (1984). [CrossRef]
  24. G. V. Reklaitis, A. Ravindran, and K. M. Ragsdell, Engineering Optimization: Methods and Applications (Wiley, 1983), pp. 43-47.

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