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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 67, Iss. 3 — Mar. 1, 1977
  • pp: 318–325

Theory of multidither adaptive optical systems operating with zonal control of deformable mirrors

T. R. O’Meara  »View Author Affiliations


JOSA, Vol. 67, Issue 3, pp. 318-325 (1977)
http://dx.doi.org/10.1364/JOSA.67.000318


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Abstract

A theory is developed for multidither adaptive optical systems that employ N discrete actuators driving a deformable control and dither mirror with the same shape of influence function. The major emphasis is on mirrors with a Gaussian influence function. It is shown, as a special case, that single-actuator displacements or errors of such systems yield error signals that can be described in closed form, via sine integral functions of the actuator displacement. Closed-form expressions for both the first- and second-harmonic content in the dither signal outputs are developed. Expressions for servo cross coupling (from adjacent actuator deformations) are developed and it is shown how the coupling is typically larger than the mechanical (actuator center) coupling. Effective modulation index comparisons are established between Gaussian and piston mirrors, for piston and Gaussian phasing error components. It is shown how a potential secondary maxima lock-up condition (the 2nπ problem) can occur when operating hill-climbing adaptive optical systems with deformable mirrors. In some cases a major loss in system Strehl ratio may result.

© 1977 Optical Society of America

Citation
T. R. O’Meara, "Theory of multidither adaptive optical systems operating with zonal control of deformable mirrors," J. Opt. Soc. Am. 67, 318-325 (1977)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-67-3-318


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References

  1. T. R. O'Meara, "The multidither principle in adaptive optics," J. Opt. Soc. Am. 67, 306–315 (1977) (this issue).
  2. W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O'Meara, J. A. Sanguinet, and W. P. Brown, Jr., Appl. Opt. 13, 291 (1974).
  3. J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, Appl. Opt. 13, 611 (1976).
  4. J. E. Pearson and S. Hansen, "Experimental studies of a deformable-mirror adaptive optical system," J. Opt. Soc. Am. 67, 325–333 (1977) (following paper).
  5. J. E. Pearson et al., "High Power Closed Loop, Adaptive System (HICLAS) Study," Contract N60921-76-C-0008, June 1976, available from DDC or HSWC.
  6. Exact in the sense that a near central actuator on a very large mirror is assumed.
  7. Dave Kocher, Lincoln Laboratory (private communication).
  8. Servo ambiguities analogous to the 2Nπ states of interest here can also occur for "modal" systems like Zernike polynomial control.
  9. This conclusion was independently reached by Dave Kocher of Lincoln Laboratory, who also showed that the relative width and center-center alignment of dither mirror and corrector mirror influence functions is important for the 2Nπ problem.

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