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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 40, Iss. 4 — Feb. 1, 2001
  • pp: 435–438

Curvature sensors, adaptive optics, and Neumann boundary conditions

Christ Ftaclas and Alex Kostinski  »View Author Affiliations


Applied Optics, Vol. 40, Issue 4, pp. 435-438 (2001)
http://dx.doi.org/10.1364/AO.40.000435


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Abstract

We consider the Neumann boundary-value problem for curvature adaptive optics systems. We show that, because curvature sensors average over extended regions of the wave front, inconsistent data for the solution of the Neumann problem result when the measurements are treated as local. Because this inconsistency is generally resolved passively in the adaptive mirror itself, it can be interpreted as an uncontrolled degree of freedom of the system. We offer several procedures for treating the data in a more consistent fashion.

© 2001 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

History
Original Manuscript: May 9, 2000
Revised Manuscript: October 23, 2000
Published: February 1, 2001

Citation
Christ Ftaclas and Alex Kostinski, "Curvature sensors, adaptive optics, and Neumann boundary conditions," Appl. Opt. 40, 435-438 (2001)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-4-435


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References

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  9. This is of course trivially true because, in general, the slopes sk are discontinuous, having been averaged over finite regions. In this case it is easy to see that this is resolved by the intrinsic stiffness of the mirror that prevents the formation of a slope or surface discontinuity, resulting in a smooth slope distribution. This illustrates the interplay of mechanical properties and boundary conditions in the determination of the final shape of curvature systems.
  10. G. Barton, “Peculiarities of the Neumann problem,” in Elements of Green’s Functions and Propagation, Oxford Science Publications (Clarendon, Oxford, UK, 1989), Sect. 6.1, p. 142.
  11. This can be seen most easily when Eq. (1) is integrated over R and by use of Gauss’s law.
  12. L. Salas, “Variable separation in curvature sensing: fast method for solving the irradiance transport equation in the context of optical telescopes,” Appl. Opt. 35, 1593–1596 (1996). [CrossRef] [PubMed]
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  14. F. Roddier, C. Roddier, “Wavefront reconstruction using iterative Fourier transforms,” Appl. Opt. 30, 1325–1327 (1991). [CrossRef] [PubMed]

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