Abstract

This correspondence demonstrates a closed-form, linearized solution of the general N-element adaptive optics system in terms of the feedback parameters of the separate control loops. It is shown that the stability of the Nth-order loop is nearly identical with that of the separate (decoupled) loops.

© 1977 Optical Society of America

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  1. T. R. O'Meara, "Multidither principle in adaptive optics," J. Opt. Soc. Am. 67, 306–315 (1977) (preceding paper).
  2. R. H. Dicke, J. Opt. Soc. Am. 65, 1206 (1975).
  3. Roger W. Brockett, Finite Dimensional Linear Systems (Wiley, New York, 1970).
  4. V. Evelight, "A General Stability Analysis of Sinusoidal Perturbation Extrener Searching Adaptive Systems," Proceedings of the 1963 International Federation for Automatic Control, Basle, Switzerland, Vol. I (Butterworths, London, 1964), p. 472.
  5. R. Smyth and N. Nahi, "On the Stability and Design of Dither Adaptive Systems," in Proceedings of the 1963 International Federation for Automatic Control, Basle, Switzerland, Vol. II (Butterworths, London, 1964), p. 358.
  6. See Eq. (8) of Ref. 1.
  7. With some wave-front interferometers the reference is the entire phasor combination from all channels; for these cases N should be substituted for N-1 in the work that follows.
  8. It should be clearly understood that by the "phase-detector" box we are representing the phase-to-amplitude conversion process exhibited by (1). There may be no phase detector of the usual type in the control loop.

1977 (1)

Brockett, Roger W.

Roger W. Brockett, Finite Dimensional Linear Systems (Wiley, New York, 1970).

Dicke, R. H.

R. H. Dicke, J. Opt. Soc. Am. 65, 1206 (1975).

Evelight, V.

V. Evelight, "A General Stability Analysis of Sinusoidal Perturbation Extrener Searching Adaptive Systems," Proceedings of the 1963 International Federation for Automatic Control, Basle, Switzerland, Vol. I (Butterworths, London, 1964), p. 472.

Nahi, N.

R. Smyth and N. Nahi, "On the Stability and Design of Dither Adaptive Systems," in Proceedings of the 1963 International Federation for Automatic Control, Basle, Switzerland, Vol. II (Butterworths, London, 1964), p. 358.

O’Meara, T. R.

Smyth, R.

R. Smyth and N. Nahi, "On the Stability and Design of Dither Adaptive Systems," in Proceedings of the 1963 International Federation for Automatic Control, Basle, Switzerland, Vol. II (Butterworths, London, 1964), p. 358.

J. Opt. Soc. Am. (1)

Other (7)

R. H. Dicke, J. Opt. Soc. Am. 65, 1206 (1975).

Roger W. Brockett, Finite Dimensional Linear Systems (Wiley, New York, 1970).

V. Evelight, "A General Stability Analysis of Sinusoidal Perturbation Extrener Searching Adaptive Systems," Proceedings of the 1963 International Federation for Automatic Control, Basle, Switzerland, Vol. I (Butterworths, London, 1964), p. 472.

R. Smyth and N. Nahi, "On the Stability and Design of Dither Adaptive Systems," in Proceedings of the 1963 International Federation for Automatic Control, Basle, Switzerland, Vol. II (Butterworths, London, 1964), p. 358.

See Eq. (8) of Ref. 1.

With some wave-front interferometers the reference is the entire phasor combination from all channels; for these cases N should be substituted for N-1 in the work that follows.

It should be clearly understood that by the "phase-detector" box we are representing the phase-to-amplitude conversion process exhibited by (1). There may be no phase detector of the usual type in the control loop.

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