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Applied Optics

Applied Optics


  • Vol. 33, Iss. 10 — Apr. 1, 1994
  • pp: 2048–2056

Merit function for the design of grating instruments

Masato Koike and Takeshi Namioka  »View Author Affiliations

Applied Optics, Vol. 33, Issue 10, pp. 2048-2056 (1994)

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A merit function that is closely correlated with the rms spread of an infinite number of ray-traced spots by means of analytic spot-diagram formulas is critically evaluated in comparison with exact ray tracing. The analytic spot-diagram formulas are found to generate spot diagrams that are almost indistinguishable from ray-traced ones. The rms spread of ray-traced spots about the mean shows varying degrees of statistical dispersion depending on the number of rays traced, and it approaches the value given by the merit function as the number of rays is increased. All the results clearly show that the merit function behaves as defined and provides enough accuracy and a sufficiently short computing time for the design of highly sophisticated grating instruments.

© 1994 Optical Society of America

Original Manuscript: March 15, 1993
Published: April 1, 1994

Masato Koike and Takeshi Namioka, "Merit function for the design of grating instruments," Appl. Opt. 33, 2048-2056 (1994)

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  1. T. Namioka, “Theory of the concave grating. III. Seya-Namioka monochromator,” J. Opt. Soc. Am. 49, 951–961 (1959). [CrossRef]
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  17. In Ref. 13 the merit function Φ is defined by Φ = ΣwiΣ(δy + fδz)2 instead of Φ = ΣwiΣ[(δy)2 + f(δz)2]. As δy and δz include signs, δy + fδz does not have any physical significance.
  18. W. Meyer-Ilse, M. Koike, R. Beguiristain, J. Maser, D. Attwood, “X-Ray Microscopy Resource Center at the Advanced Light Source,” in Soft X-Ray Microscopy, C. J. Jacobsen, J. E. Trebes, Proc. Soc. Photo-Opt. Instrum. Eng.1741, 112–115 (1992).

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