Abstract

A novel approach for the remote alignment of segmented mirrors is presented. In comparison with conventional methods in which near-field measurements (in the form of displacements between neighboring segments or phase across the mirror) are used in a feedback control system, the far-field optimization method utilizes only attributes of the point-spread function. A figure of merit based on the far-field intensity is used to configure iteratively the segmented mirror to alignment. Following computer simulations, we conduct successful laboratory experiments to validate the far-field optimization concept. The potential utility of far-field optimization to the alignment of other adaptive optical systems and to dynamic wave-front control is briefly discussed.

© 1992 Optical Society of America

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References

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  1. R. W. Sinnot, “The Keck telescope’s giant eye,” Sky & Telescope 80, 15–22 (1990).
  2. D. S. Acton, “Real-time solar imaging with a 19-segment active mirror system: a study of the standard atmospheric turbulence model,” Ph.D. dissertation (Texas Tech University, Lubbock, Tex., 1990).
  3. D. S. Acton, R. C. Smithson, “Results from the Lockheed solar adaptive optics system,” in Proceedings of the Tenth Sacramento Peak Summer Workshop on High Spatial Resolution Solar Observations, O. von der Luhe, ed. (National Solar Observatory, Sunspot, N.M., 1989), pp. 71–80.
  4. J. D. Downie, J. W. Goodman, “Optimal wavefront control for adaptive segmented mirrors,” Appl. Opt. 24, 5326–5332 (1989).
    [CrossRef]
  5. G. A. Chanan, J. E. Nelson, T. S. Mast, “Segment alignment for the Keck telescope primary mirror,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.628, 466–473 (1986).
    [CrossRef]
  6. R. V. Digumarthi, N. C. Mehta, “Mathematical optimization method for wavefront control,” Tech. Rep. F229027 (Lockheed Missile and Space Company, Sunnyvale, Calif., 1990).
  7. R. A. Muller, A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974).
    [CrossRef]
  8. A. Buffington, F. S. Crawford, R. A. Muller, A. J. Schwemin, R. G. Smits, “Correction of atmospheric distortion with an image-sharpening telescope,” J. Opt. Soc. Am. 67, 298–303 (1977).
    [CrossRef]
  9. A. Buffington, F. S. Crawford, R. A. Muller, C. D. Orth, “First observatory results with an image-sharpening telescope,” J. Opt. Soc. Am. 67, 304–305 (1977).
    [CrossRef]
  10. T. R. O’Meara, “The multidither principle in adaptive optics,” J. Opt. Soc. Am. 67, 306–315 (1977).
    [CrossRef]
  11. E. Ribak, J. Adler, S. G. Lipson, “Telescope phasing by simulated annealing,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 183–189 (1990).
  12. J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
  13. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.
  14. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1435 (1965).
    [CrossRef]
  15. E. K. Hege, J. M. Beckers, P. A. Strittmatter, D. W. McCarthy, “Multiple mirror telescope as a phased array telescope,” Appl. Opt. 24, 2565–2576 (1985).
    [CrossRef] [PubMed]
  16. C. R. De Hainaut, D. K. Marker, D. C. Duneman, R. C. Dymale, J. P. Blea, “Wide field of view phased array telescope,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 402–411 (1990).

1990 (1)

R. W. Sinnot, “The Keck telescope’s giant eye,” Sky & Telescope 80, 15–22 (1990).

1989 (1)

J. D. Downie, J. W. Goodman, “Optimal wavefront control for adaptive segmented mirrors,” Appl. Opt. 24, 5326–5332 (1989).
[CrossRef]

1985 (1)

1977 (3)

1974 (1)

1965 (2)

D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1435 (1965).
[CrossRef]

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

Acton, D. S.

D. S. Acton, “Real-time solar imaging with a 19-segment active mirror system: a study of the standard atmospheric turbulence model,” Ph.D. dissertation (Texas Tech University, Lubbock, Tex., 1990).

D. S. Acton, R. C. Smithson, “Results from the Lockheed solar adaptive optics system,” in Proceedings of the Tenth Sacramento Peak Summer Workshop on High Spatial Resolution Solar Observations, O. von der Luhe, ed. (National Solar Observatory, Sunspot, N.M., 1989), pp. 71–80.

Adler, J.

E. Ribak, J. Adler, S. G. Lipson, “Telescope phasing by simulated annealing,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 183–189 (1990).

Beckers, J. M.

Blea, J. P.

C. R. De Hainaut, D. K. Marker, D. C. Duneman, R. C. Dymale, J. P. Blea, “Wide field of view phased array telescope,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 402–411 (1990).

Buffington, A.

Chanan, G. A.

G. A. Chanan, J. E. Nelson, T. S. Mast, “Segment alignment for the Keck telescope primary mirror,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.628, 466–473 (1986).
[CrossRef]

Crawford, F. S.

De Hainaut, C. R.

C. R. De Hainaut, D. K. Marker, D. C. Duneman, R. C. Dymale, J. P. Blea, “Wide field of view phased array telescope,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 402–411 (1990).

Digumarthi, R. V.

R. V. Digumarthi, N. C. Mehta, “Mathematical optimization method for wavefront control,” Tech. Rep. F229027 (Lockheed Missile and Space Company, Sunnyvale, Calif., 1990).

Downie, J. D.

J. D. Downie, J. W. Goodman, “Optimal wavefront control for adaptive segmented mirrors,” Appl. Opt. 24, 5326–5332 (1989).
[CrossRef]

Duneman, D. C.

C. R. De Hainaut, D. K. Marker, D. C. Duneman, R. C. Dymale, J. P. Blea, “Wide field of view phased array telescope,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 402–411 (1990).

Dymale, R. C.

C. R. De Hainaut, D. K. Marker, D. C. Duneman, R. C. Dymale, J. P. Blea, “Wide field of view phased array telescope,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 402–411 (1990).

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.

Fried, D. L.

Goodman, J. W.

J. D. Downie, J. W. Goodman, “Optimal wavefront control for adaptive segmented mirrors,” Appl. Opt. 24, 5326–5332 (1989).
[CrossRef]

Hege, E. K.

Lipson, S. G.

E. Ribak, J. Adler, S. G. Lipson, “Telescope phasing by simulated annealing,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 183–189 (1990).

Marker, D. K.

C. R. De Hainaut, D. K. Marker, D. C. Duneman, R. C. Dymale, J. P. Blea, “Wide field of view phased array telescope,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 402–411 (1990).

Mast, T. S.

G. A. Chanan, J. E. Nelson, T. S. Mast, “Segment alignment for the Keck telescope primary mirror,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.628, 466–473 (1986).
[CrossRef]

McCarthy, D. W.

Mead, R.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

Mehta, N. C.

R. V. Digumarthi, N. C. Mehta, “Mathematical optimization method for wavefront control,” Tech. Rep. F229027 (Lockheed Missile and Space Company, Sunnyvale, Calif., 1990).

Muller, R. A.

Nelder, J. A.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

Nelson, J. E.

G. A. Chanan, J. E. Nelson, T. S. Mast, “Segment alignment for the Keck telescope primary mirror,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.628, 466–473 (1986).
[CrossRef]

O’Meara, T. R.

Orth, C. D.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.

Ribak, E.

E. Ribak, J. Adler, S. G. Lipson, “Telescope phasing by simulated annealing,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 183–189 (1990).

Schwemin, A. J.

Sinnot, R. W.

R. W. Sinnot, “The Keck telescope’s giant eye,” Sky & Telescope 80, 15–22 (1990).

Smithson, R. C.

D. S. Acton, R. C. Smithson, “Results from the Lockheed solar adaptive optics system,” in Proceedings of the Tenth Sacramento Peak Summer Workshop on High Spatial Resolution Solar Observations, O. von der Luhe, ed. (National Solar Observatory, Sunspot, N.M., 1989), pp. 71–80.

Smits, R. G.

Strittmatter, P. A.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.

Vettering, W.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.

Appl. Opt. (2)

J. D. Downie, J. W. Goodman, “Optimal wavefront control for adaptive segmented mirrors,” Appl. Opt. 24, 5326–5332 (1989).
[CrossRef]

E. K. Hege, J. M. Beckers, P. A. Strittmatter, D. W. McCarthy, “Multiple mirror telescope as a phased array telescope,” Appl. Opt. 24, 2565–2576 (1985).
[CrossRef] [PubMed]

Comput. J. (1)

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).

J. Opt. Soc. Am. (5)

Sky & Telescope (1)

R. W. Sinnot, “The Keck telescope’s giant eye,” Sky & Telescope 80, 15–22 (1990).

Other (7)

D. S. Acton, “Real-time solar imaging with a 19-segment active mirror system: a study of the standard atmospheric turbulence model,” Ph.D. dissertation (Texas Tech University, Lubbock, Tex., 1990).

D. S. Acton, R. C. Smithson, “Results from the Lockheed solar adaptive optics system,” in Proceedings of the Tenth Sacramento Peak Summer Workshop on High Spatial Resolution Solar Observations, O. von der Luhe, ed. (National Solar Observatory, Sunspot, N.M., 1989), pp. 71–80.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), p. 289.

C. R. De Hainaut, D. K. Marker, D. C. Duneman, R. C. Dymale, J. P. Blea, “Wide field of view phased array telescope,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 402–411 (1990).

G. A. Chanan, J. E. Nelson, T. S. Mast, “Segment alignment for the Keck telescope primary mirror,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.628, 466–473 (1986).
[CrossRef]

R. V. Digumarthi, N. C. Mehta, “Mathematical optimization method for wavefront control,” Tech. Rep. F229027 (Lockheed Missile and Space Company, Sunnyvale, Calif., 1990).

E. Ribak, J. Adler, S. G. Lipson, “Telescope phasing by simulated annealing,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 183–189 (1990).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the adaptive optical system under consideration. A monochromatic plane wave impinges on the segmented mirror, and the reflected wave front, which is aberrated in general, is imaged onto a far-field. Far-field measurements are then used to control iteratively the segmented mirror to alignment.

Fig. 2
Fig. 2

Block diagram of the FFO simulation testbed. For each mirror configuration, the near-field phase is combined with an amplitude mask, the wave front is propagated to the far field, and a FOM is calculated from the point-spread function. Starting with a set of initial conditions, the simplex algorithm specifies a new mirror configuration that yields a new FOM. The iterative procedure continues until the simplex algorithm reaches convergence or for a fixed number of iterations.

Fig. 3
Fig. 3

Representative misaligned segmented mirror with random piston and tilts on each segment: (a) Mirror surface in micrometers. Near-field phase error is ~ 0.68 wave rms for an operating wavelength of 6328 Å. (b) Corresponding far-field intensity pattern is characterized by a Strehl ratio of ~ 5% and an encircled energy of ~ 10%.

Fig. 4
Fig. 4

Segmented mirror after FFO (733 iterations): (a) Mirror surface in micrometers. Near-field phase error is ~ 0.051 wave rms. (b) Point-spread function with a Strehl ratio grater than 92% and an encircled energy of ~ 94%.

Fig. 5
Fig. 5

Simplex onvergence (most recent FOM versus number of iteration). A change in the FOM from energy in a bucket to the Strehl ratio occurs at iteration 513. Two nudges of the simplex object occur at iterations 414 and 635. Initial conditions are shown to the left of the vertical line at iteration 0.

Fig. 6
Fig. 6

Image plane attributes and residual phase error during FFO. Initial conditions are shown to the left of the vertical dashed line at iteration 0. The Strehl ratio improves from less than 7% to more than 92% and the encircled energy improves from 9–25% to ~ 94% (the corresponding diffraction-limited values are 100% and 98.6% for the simulation parameters used here). The near-field residual phase error reduces from 0.65–0.9 wave rms to ~ 0.051 wave rms.

Fig. 7
Fig. 7

Segmented mirror surface (in micrometers) after FFO optimization (1873 iterations), in contrast to Fig. 3(a). The simulation included three nudges of the simplex, a change of the FOM, and another three nudges of the simplex. The residual phase error is ~ 0.015 wave rms.

Fig. 8
Fig. 8

Schematic of the optical layout for the laboratory experiments. A collimated He–Ne laser beam is reflected off the segmented mirror and is imaged onto a photocell in the far field. The simplex algorithm uses only the photocell output to drive iteratively the segmented mirror to alignment. A diagnostic Mach–Zender interferometer is used to monitor the mirror surface in real time during the test.

Fig. 9
Fig. 9

Success of FFO in alignment of the 19-segment mirror. (a) Interferogram of mirror surface initially. Misaligned fringes on neighboring pairs of mirror segments are indicative of random piston and tilts on mirror segments. (b) Interferogram of mirror surface after FFO. Nearly vertical fringes across the mirror demonstrate an aligned mirror.

Tables (2)

Tables Icon

Table 1 FFO with Misaligned Initial States

Tables Icon

Table 2 Simplex Convergence Speed

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