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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 29, Iss. 31 — Nov. 1, 1990
  • pp: 4622–4628

Zonal model of an adaptive mirror

Kenneth E. Moore and George N. Lawrence  »View Author Affiliations


Applied Optics, Vol. 29, Issue 31, pp. 4622-4628 (1990)
http://dx.doi.org/10.1364/AO.29.004622


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Abstract

An approximate model of an adaptive optic element is presented which works well for components having many actuators. This zonal model is used to gain insight into the general behavior of systems that correct for high spatial frequency errors. The model is derived from the method of least squares, and considers the nonshift invariant properties of adaptive mirrors. It may be implemented with Fourier transform techniques and is, therefore, easy to program. The relationship between the zonal model and the simpler bandpass filter model of Harvey and Callahan is discussed.

© 1990 Optical Society of America

History
Original Manuscript: July 31, 1989
Published: November 1, 1990

Citation
Kenneth E. Moore and George N. Lawrence, "Zonal model of an adaptive mirror," Appl. Opt. 29, 4622-4628 (1990)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-29-31-4622


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References

  1. J. E. Pearson, R. H. Freeman, H. C. Reynolds, “Adaptive Optical Techniques for Wave-Front Correction,” in Applied Optics and Optical Engineering, Volume 7, R. R. Shannon, J. C. Wyant, Eds. (Academic, New York, 1979), pp. 245–340.
  2. R. E. Wagner, “Imagery Utilizing Multiple Focal Planes,” Ph.D. dissertation (University of Arizona, 1976).
  3. J. E. Harvey, G. M. Callahan, “Wavefront Error Compensation Capabilities of Multi-Actuator Deformable Mirrors,” Proc. Soc. Photo-Opt. Instrum. Eng. 141, 50 (1978).
  4. R. K. Tyson, D. M. Byrne, “The Effect of Wavefront Sensor Characteristics and Spatiotemporal Coupling on the Correcting Capability of a Deformable Mirror,” Proc. Soc. Photo-Opt. Instrum. Eng. 228, 21 (1980).
  5. R. K. Tyson, “Adaptive Optics Compensation of Thermal Distortion,” Proc. Soc. Photo-Opt. Instrum. Eng. 270, 142 (1981).
  6. R. K. Tyson, “Using the Deformable Mirror as a Spatial Filter: Application to Circular Beams,” Appl. Opt. 21, 787–793 (1982). [CrossRef] [PubMed]
  7. J. E. Pearson, S. Hansen, “Experimental Studies of a Deformable-Mirror Adaptive Optical System,” J. Opt. Soc. Am. 67, 325 (1977). [CrossRef]
  8. T. R. O’Meara, “The Multidither Principle in Adaptive Optics,” J. Opt. Soc. Am. 67, 306–333 (1977). [CrossRef]
  9. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).
  10. C. Lawson, R. Hansen, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, NJ, 1979).
  11. G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1985).
  12. J. E. Harvey, G. M. Callahan, “Transfer Function Characterization of Deformable Mirrors,” J. Opt. Soc. Am. 67, 1367–1367 (1977).
  13. J. E. Harvey, Hughes Danburg Optical Systems, private communication.

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