Abstract

Requirements for adaptive optics and compensating imaging systems lead to wave front reconstruction problems which we formulate as generalized least-squares problems. For a given array of phase-difference measurements, we construct explicit and exact solutions for the least-squares wave front error. Of particular interest are solutions with minimum norm. Two different discretizations for the gradient are used and the reasons for the different results are given.

© 1980 Optical Society of America

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  1. H. Margenau and G. M. Murphy, Inc., The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1956), Chap. 6.
  2. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961), Chap. 15.
  3. R. H. Hudgin, "Wave-front reconstruction for compensated imaging," J. Opt. Soc. Am. 67, 374–378 (1977).
  4. D. L. Fried, "Least-squares fitting a wave-front distortion estimate to an array of phase-difference measurements," J. Opt. Soc. Am. 67, 370–375 (1977).
  5. A. Ben-Israel and N. E. Greville, Generalized Inverses: Theory and Applications (Wiley, New York, 1974), Chaps. 3 and 5.
  6. C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and its Applications (Wiley, New York, 1971), Chap. 11.
  7. C. L. Lawson and R. J. Hanson, Solving Least Squaes Problems (Prentice Hall, Englewood Cliffs, New Jersey, 1974), Chap. 25.
  8. International Mathematical & Statistical Libraries, Inc., Sixth Floor GNB Building, 7500 Bellaire, Houston, Texas 77036.
  9. N. Balabanian and T. A. Bickart, Electrical Network Theory (Wiley, New York, 1969).
  10. W. H. Kim and H. E. Meadows, Jr., Modern Network Analysis (Wiley, New York, 1971), Chap. 3.

1977 (2)

R. H. Hudgin, "Wave-front reconstruction for compensated imaging," J. Opt. Soc. Am. 67, 374–378 (1977).

D. L. Fried, "Least-squares fitting a wave-front distortion estimate to an array of phase-difference measurements," J. Opt. Soc. Am. 67, 370–375 (1977).

Balabanian, N.

N. Balabanian and T. A. Bickart, Electrical Network Theory (Wiley, New York, 1969).

Ben-Israel, A.

A. Ben-Israel and N. E. Greville, Generalized Inverses: Theory and Applications (Wiley, New York, 1974), Chaps. 3 and 5.

Bickart, T. A.

N. Balabanian and T. A. Bickart, Electrical Network Theory (Wiley, New York, 1969).

Fried, D. L.

Greville, N. E.

A. Ben-Israel and N. E. Greville, Generalized Inverses: Theory and Applications (Wiley, New York, 1974), Chaps. 3 and 5.

Hanson, R. J.

C. L. Lawson and R. J. Hanson, Solving Least Squaes Problems (Prentice Hall, Englewood Cliffs, New Jersey, 1974), Chap. 25.

Hudgin, R. H.

R. H. Hudgin, "Wave-front reconstruction for compensated imaging," J. Opt. Soc. Am. 67, 374–378 (1977).

Kim, W. H.

W. H. Kim and H. E. Meadows, Jr., Modern Network Analysis (Wiley, New York, 1971), Chap. 3.

Korn, G. A.

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961), Chap. 15.

Korn, T. M.

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961), Chap. 15.

Lawson, C. L.

C. L. Lawson and R. J. Hanson, Solving Least Squaes Problems (Prentice Hall, Englewood Cliffs, New Jersey, 1974), Chap. 25.

Margenau, H.

H. Margenau and G. M. Murphy, Inc., The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1956), Chap. 6.

Meadows, Jr., H. E.

W. H. Kim and H. E. Meadows, Jr., Modern Network Analysis (Wiley, New York, 1971), Chap. 3.

Mitra, S. K.

C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and its Applications (Wiley, New York, 1971), Chap. 11.

Murphy, G. M.

H. Margenau and G. M. Murphy, Inc., The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1956), Chap. 6.

Rao, C. R.

C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and its Applications (Wiley, New York, 1971), Chap. 11.

J. Opt. Soc. Am. (2)

R. H. Hudgin, "Wave-front reconstruction for compensated imaging," J. Opt. Soc. Am. 67, 374–378 (1977).

D. L. Fried, "Least-squares fitting a wave-front distortion estimate to an array of phase-difference measurements," J. Opt. Soc. Am. 67, 370–375 (1977).

Other (8)

A. Ben-Israel and N. E. Greville, Generalized Inverses: Theory and Applications (Wiley, New York, 1974), Chaps. 3 and 5.

C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and its Applications (Wiley, New York, 1971), Chap. 11.

C. L. Lawson and R. J. Hanson, Solving Least Squaes Problems (Prentice Hall, Englewood Cliffs, New Jersey, 1974), Chap. 25.

International Mathematical & Statistical Libraries, Inc., Sixth Floor GNB Building, 7500 Bellaire, Houston, Texas 77036.

N. Balabanian and T. A. Bickart, Electrical Network Theory (Wiley, New York, 1969).

W. H. Kim and H. E. Meadows, Jr., Modern Network Analysis (Wiley, New York, 1971), Chap. 3.

H. Margenau and G. M. Murphy, Inc., The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1956), Chap. 6.

G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1961), Chap. 15.

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