## Apodization for maximum Strehl ratio and specified Rayleigh limit of resolution

JOSA, Vol. 67, Issue 8, pp. 1027-1030 (1977)

http://dx.doi.org/10.1364/JOSA.67.001027

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### Abstract

Earlier authors have considered the apodization problem of determining the pupil function that has the maximum Strehl ratio in the class of all pupil functions that have the same Rayleigh limit of resolution, specified in advance. They did not, however, verify that the solution they offered for this problem actually has the desired, rather than a smaller, Rayleigh limit. We shall supply this verification when the specified Rayleigh limit does not exced 139% of the Rayleigh limit for the classical Airy-type objective. For larger values of the specified Rayleigh limit, the offered solution does indeed have a smaller Rayleigh limit and is accordingly not a solution to the apodization problem. We show in this case that there is no solution, but that the Strehl ratio computed for the offered solution is a least upper bound that can be approached (but not attained) arbitrarily closely by using a suitably chosen complex-valued pupil function.

© 1977 Optical Society of America

**Citation**

J. Ernest Wilkins, Jr., "Apodization for maximum Strehl ratio and specified Rayleigh limit of resolution," J. Opt. Soc. Am. **67**, 1027-1030 (1977)

http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-67-8-1027

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### References

- R. K. Luneburg, Mathematical Theory of Optics (University of California, Berkeley, 1964), pp. 349–351.
- R. Barakat, "Solution of the Luneberg apodization problems," J. Opt. Soc. Am. 52, 264–275 (1962).
- J. E. Wilkins, "Luneberg apodization problems," J. Opt. Soc. Am. 53, 420–424 (1963).
- P. Jacquinot and B. Roizen-Dossier, "Apodization," in Progress in Optics, Vol. III, edited by E., Wolf (North-Holland, Amsterdam, 1964), Chap. 2.
- H. Osterberg and J. E Wilkins, "The resolving power of a coated objective," J. Opt. Soc. Am. 39, 553–557 (1949).
- P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p, 436.
- O. Szász, "Inequalities concerning ultraspherical polynomials and Bessel functions," Proc. Am. Math. Soc. 1, 256–267 (1950).

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