Abstract

We describe a binary approach to adaptive wave-front correction, especially suitable for narrow band applications, which would be simpler than conventional adaptive technology. Appropriate parts of the aberrant wave front are phase retarded by half a wavelength to ensure that none of the image-forming rays add together destructively. Simulations for monochromatic light show that the residual wave-front errors, in the absence of other errors, would result in Strehl ratios of ~40% with diffraction-limited widths at visible wavelengths. We simulate the imaging performance of such a system and describe a possible implementation that uses a ferroelectric liquid-crystal spatial light modulator.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Love, R. Myers, A. Purvis, R. Sharples, “A new approach to adaptive wavefront correction using a liquid crystal half-wave phase shifter,” in ICO-16 Conference on Active and Adaptive Optics, (European Southern Observatory, Garching bei München, 1993), pp. 295–300.
  2. V. N. Mahajan, Aberration Theory Made Simple, SPIE Tutorial Text 6 (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1991).
    [CrossRef]
  3. A. Glindemann, “Improved performance of adaptive optics in the visible,” J. Opt. Soc. Am. A 11, 1370–1375 (1994).
    [CrossRef]
  4. R. G. Lane, A. Glindemann, J. C. Dainty, “Simulations of a Kolmogorov phase screen,” Waves in Random Media 2, 209–224 (1992).
    [CrossRef]
  5. R. H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605–615 (1975).
    [CrossRef]
  6. J. R. P. Angel, “Ground based imaging of extrasolar planets,” Nature 368, 203–207 (1994).
    [CrossRef]
  7. J. R. P. Angel, “Optimization of wavefront sensors for the highest accuracy and sensitivity,” in Adaptive Optics for Astronomy, D. Alloin, J. M. Mariotti, eds. NATO Series C (Kluwer, Dordrecht, The Netherlands, 1994).
  8. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–392.
    [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), p. 468.
  10. G. Love, J. Major, A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19, 1170–1172 (1994).
    [CrossRef] [PubMed]
  11. S. R. Restaino, E. L. Gates, R. Dymale, G. C. Loos, “Use of electro-optical devices for path-length compensation,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200, 494–500 (1994).
  12. G. D. Love, S. R. Restaino, G. C. Loos, A. Purvis, “Wavefront control using a 64 × 64 pixel liquid crystal array,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2201, 1068–1072 (1994).
  13. G. D. Love, R. Bhandari, “Optical properties of a QHQ ferroelectric liquid crystal phase modulator,” Opt. Commun. 110, 475–478 (1994).
    [CrossRef]
  14. Chisso Corporation, Makuhari Head Office, WBG Marive West 24F, 2–6 Nakese Mihama, Chiba, Japan.
  15. M. A. A. Neil, “Improved transmission in a 2-level, phase-only spatial light modulator,” Electron. Lett. 30, 445–446 (1994).
    [CrossRef]
  16. Displaytech, Inc., 2200 Central Avenue, Boulder, Colo. 80301.
  17. K. M. Johnson, D. J. McKnight, I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 29, 699–714 (1993).
    [CrossRef]
  18. Boulder Nonlinear Systems, 1898 South Flatiron Court, Boulder, Colo. 80301.
  19. CRL Smectic Technology, Dawley Road, Hayes, UB3 1HH, UK.
  20. G. Moddel, “Ferroelectric liquid crystal spatial light modulators,” in Spatial Light Modulator Technology, U. Efron, ed. (Dekker, New York, 1995), pp. 287–359.
  21. A. D. Fisher, C. Warde, “Technique for real-time high-resolution adaptive phase compensation,” Opt. Lett 8, 353–355 (1983).
    [CrossRef] [PubMed]
  22. I. Thomas, “Programmable correction for optical aberrations using a phase-only spatial light modulator,” M.S. thesis (Department of Engineering Science, University of Oxford, Oxford, UK1993).

1994 (5)

J. R. P. Angel, “Ground based imaging of extrasolar planets,” Nature 368, 203–207 (1994).
[CrossRef]

G. D. Love, R. Bhandari, “Optical properties of a QHQ ferroelectric liquid crystal phase modulator,” Opt. Commun. 110, 475–478 (1994).
[CrossRef]

M. A. A. Neil, “Improved transmission in a 2-level, phase-only spatial light modulator,” Electron. Lett. 30, 445–446 (1994).
[CrossRef]

A. Glindemann, “Improved performance of adaptive optics in the visible,” J. Opt. Soc. Am. A 11, 1370–1375 (1994).
[CrossRef]

G. Love, J. Major, A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19, 1170–1172 (1994).
[CrossRef] [PubMed]

1993 (1)

K. M. Johnson, D. J. McKnight, I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 29, 699–714 (1993).
[CrossRef]

1992 (1)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulations of a Kolmogorov phase screen,” Waves in Random Media 2, 209–224 (1992).
[CrossRef]

1983 (1)

A. D. Fisher, C. Warde, “Technique for real-time high-resolution adaptive phase compensation,” Opt. Lett 8, 353–355 (1983).
[CrossRef] [PubMed]

1975 (1)

R. H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605–615 (1975).
[CrossRef]

Angel, J. R. P.

J. R. P. Angel, “Ground based imaging of extrasolar planets,” Nature 368, 203–207 (1994).
[CrossRef]

J. R. P. Angel, “Optimization of wavefront sensors for the highest accuracy and sensitivity,” in Adaptive Optics for Astronomy, D. Alloin, J. M. Mariotti, eds. NATO Series C (Kluwer, Dordrecht, The Netherlands, 1994).

Bhandari, R.

G. D. Love, R. Bhandari, “Optical properties of a QHQ ferroelectric liquid crystal phase modulator,” Opt. Commun. 110, 475–478 (1994).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), p. 468.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–392.
[CrossRef]

Dainty, J. C.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulations of a Kolmogorov phase screen,” Waves in Random Media 2, 209–224 (1992).
[CrossRef]

Dicke, R. H.

R. H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605–615 (1975).
[CrossRef]

Dymale, R.

S. R. Restaino, E. L. Gates, R. Dymale, G. C. Loos, “Use of electro-optical devices for path-length compensation,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200, 494–500 (1994).

Fisher, A. D.

A. D. Fisher, C. Warde, “Technique for real-time high-resolution adaptive phase compensation,” Opt. Lett 8, 353–355 (1983).
[CrossRef] [PubMed]

Gates, E. L.

S. R. Restaino, E. L. Gates, R. Dymale, G. C. Loos, “Use of electro-optical devices for path-length compensation,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200, 494–500 (1994).

Glindemann, A.

A. Glindemann, “Improved performance of adaptive optics in the visible,” J. Opt. Soc. Am. A 11, 1370–1375 (1994).
[CrossRef]

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulations of a Kolmogorov phase screen,” Waves in Random Media 2, 209–224 (1992).
[CrossRef]

Johnson, K. M.

K. M. Johnson, D. J. McKnight, I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 29, 699–714 (1993).
[CrossRef]

Lane, R. G.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulations of a Kolmogorov phase screen,” Waves in Random Media 2, 209–224 (1992).
[CrossRef]

Loos, G. C.

G. D. Love, S. R. Restaino, G. C. Loos, A. Purvis, “Wavefront control using a 64 × 64 pixel liquid crystal array,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2201, 1068–1072 (1994).

S. R. Restaino, E. L. Gates, R. Dymale, G. C. Loos, “Use of electro-optical devices for path-length compensation,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200, 494–500 (1994).

Love, G.

G. Love, J. Major, A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19, 1170–1172 (1994).
[CrossRef] [PubMed]

G. Love, R. Myers, A. Purvis, R. Sharples, “A new approach to adaptive wavefront correction using a liquid crystal half-wave phase shifter,” in ICO-16 Conference on Active and Adaptive Optics, (European Southern Observatory, Garching bei München, 1993), pp. 295–300.

Love, G. D.

G. D. Love, R. Bhandari, “Optical properties of a QHQ ferroelectric liquid crystal phase modulator,” Opt. Commun. 110, 475–478 (1994).
[CrossRef]

G. D. Love, S. R. Restaino, G. C. Loos, A. Purvis, “Wavefront control using a 64 × 64 pixel liquid crystal array,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2201, 1068–1072 (1994).

Mahajan, V. N.

V. N. Mahajan, Aberration Theory Made Simple, SPIE Tutorial Text 6 (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1991).
[CrossRef]

Major, J.

McKnight, D. J.

K. M. Johnson, D. J. McKnight, I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 29, 699–714 (1993).
[CrossRef]

Moddel, G.

G. Moddel, “Ferroelectric liquid crystal spatial light modulators,” in Spatial Light Modulator Technology, U. Efron, ed. (Dekker, New York, 1995), pp. 287–359.

Myers, R.

G. Love, R. Myers, A. Purvis, R. Sharples, “A new approach to adaptive wavefront correction using a liquid crystal half-wave phase shifter,” in ICO-16 Conference on Active and Adaptive Optics, (European Southern Observatory, Garching bei München, 1993), pp. 295–300.

Neil, M. A. A.

M. A. A. Neil, “Improved transmission in a 2-level, phase-only spatial light modulator,” Electron. Lett. 30, 445–446 (1994).
[CrossRef]

Purvis, A.

G. Love, J. Major, A. Purvis, “Liquid-crystal prisms for tip-tilt adaptive optics,” Opt. Lett. 19, 1170–1172 (1994).
[CrossRef] [PubMed]

G. Love, R. Myers, A. Purvis, R. Sharples, “A new approach to adaptive wavefront correction using a liquid crystal half-wave phase shifter,” in ICO-16 Conference on Active and Adaptive Optics, (European Southern Observatory, Garching bei München, 1993), pp. 295–300.

G. D. Love, S. R. Restaino, G. C. Loos, A. Purvis, “Wavefront control using a 64 × 64 pixel liquid crystal array,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2201, 1068–1072 (1994).

Restaino, S. R.

S. R. Restaino, E. L. Gates, R. Dymale, G. C. Loos, “Use of electro-optical devices for path-length compensation,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200, 494–500 (1994).

G. D. Love, S. R. Restaino, G. C. Loos, A. Purvis, “Wavefront control using a 64 × 64 pixel liquid crystal array,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2201, 1068–1072 (1994).

Sharples, R.

G. Love, R. Myers, A. Purvis, R. Sharples, “A new approach to adaptive wavefront correction using a liquid crystal half-wave phase shifter,” in ICO-16 Conference on Active and Adaptive Optics, (European Southern Observatory, Garching bei München, 1993), pp. 295–300.

Thomas, I.

I. Thomas, “Programmable correction for optical aberrations using a phase-only spatial light modulator,” M.S. thesis (Department of Engineering Science, University of Oxford, Oxford, UK1993).

Underwood, I.

K. M. Johnson, D. J. McKnight, I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 29, 699–714 (1993).
[CrossRef]

Warde, C.

A. D. Fisher, C. Warde, “Technique for real-time high-resolution adaptive phase compensation,” Opt. Lett 8, 353–355 (1983).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), p. 468.

Astrophys. J. (1)

R. H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605–615 (1975).
[CrossRef]

Electron. Lett. (1)

M. A. A. Neil, “Improved transmission in a 2-level, phase-only spatial light modulator,” Electron. Lett. 30, 445–446 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. M. Johnson, D. J. McKnight, I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 29, 699–714 (1993).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nature (1)

J. R. P. Angel, “Ground based imaging of extrasolar planets,” Nature 368, 203–207 (1994).
[CrossRef]

Opt. Commun. (1)

G. D. Love, R. Bhandari, “Optical properties of a QHQ ferroelectric liquid crystal phase modulator,” Opt. Commun. 110, 475–478 (1994).
[CrossRef]

Opt. Lett (1)

A. D. Fisher, C. Warde, “Technique for real-time high-resolution adaptive phase compensation,” Opt. Lett 8, 353–355 (1983).
[CrossRef] [PubMed]

Opt. Lett. (1)

Waves in Random Media (1)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulations of a Kolmogorov phase screen,” Waves in Random Media 2, 209–224 (1992).
[CrossRef]

Other (13)

I. Thomas, “Programmable correction for optical aberrations using a phase-only spatial light modulator,” M.S. thesis (Department of Engineering Science, University of Oxford, Oxford, UK1993).

Displaytech, Inc., 2200 Central Avenue, Boulder, Colo. 80301.

J. R. P. Angel, “Optimization of wavefront sensors for the highest accuracy and sensitivity,” in Adaptive Optics for Astronomy, D. Alloin, J. M. Mariotti, eds. NATO Series C (Kluwer, Dordrecht, The Netherlands, 1994).

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf ed. (North-Holland, Amsterdam, 1988), Vol. 26, pp. 349–392.
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989), p. 468.

G. Love, R. Myers, A. Purvis, R. Sharples, “A new approach to adaptive wavefront correction using a liquid crystal half-wave phase shifter,” in ICO-16 Conference on Active and Adaptive Optics, (European Southern Observatory, Garching bei München, 1993), pp. 295–300.

V. N. Mahajan, Aberration Theory Made Simple, SPIE Tutorial Text 6 (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1991).
[CrossRef]

Chisso Corporation, Makuhari Head Office, WBG Marive West 24F, 2–6 Nakese Mihama, Chiba, Japan.

S. R. Restaino, E. L. Gates, R. Dymale, G. C. Loos, “Use of electro-optical devices for path-length compensation,” in Amplitude and Intensity Spatial Interferometry II, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2200, 494–500 (1994).

G. D. Love, S. R. Restaino, G. C. Loos, A. Purvis, “Wavefront control using a 64 × 64 pixel liquid crystal array,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2201, 1068–1072 (1994).

Boulder Nonlinear Systems, 1898 South Flatiron Court, Boulder, Colo. 80301.

CRL Smectic Technology, Dawley Road, Hayes, UB3 1HH, UK.

G. Moddel, “Ferroelectric liquid crystal spatial light modulators,” in Spatial Light Modulator Technology, U. Efron, ed. (Dekker, New York, 1995), pp. 287–359.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Phasor diagram demonstrating a half-wave corrected imaging system: (a) Phasors produced by a diffraction-limited system. (b) Phasors from an atmospherically aberrant wave front with no correction. (c) Phasors from an atmospherically aberrant wave front with half-wave correction, calculated by adding π to each of the phasors in (b) whose argument is greater than π. (d) Enlargement of (b).

Fig. 2
Fig. 2

Simulated long-exposure PSF’s with (a) no correction and (b) half-wave correction. The results were calculated assuming monochromatic light and no errors, apart from a fitting error resulting from a correction array of size 32 × 32 pixels. Strehl ratios were (a) 0.35%, (b) 21.6%. D = 4 m, r0 = 18 cm, and λ = 550 nm.

Fig. 3
Fig. 3

Cross-sections of Fig. 2(a) and 2(b) plotted on a logarithmic vertical scale, and also showing a larger range on the horizontal axis, indicating where the uncorrected light is distributed.

Fig. 4
Fig. 4

Simulation of the wavelength dependence of half-wave correction. The design wavelength is 550 nm. Each curve shows a different number of correction elements. We calculated the wavelength dependence by scaling the phase with wavelength. (a) results for an uncorrected incident beam. (b) tip–tilt-corrected incident beam.

Fig. 5
Fig. 5

Simulation of half-wave imaging by convolving a USAF resolution chart with an appropriate PSF. The image is 256 × 256 pixels in size and is plotted at the Nyquist limit. (a) Diffraction-limited USAF image. (b) Seeing-limited simulated image, D = 4 m, r0 = 18 cm and λ = 550 nm. (c) Half-wave corrected simulated image, with light of the design wavelength (550 nm). The results were calculated assuming no errors and a correction screen of size 256 × 256 pixels. (d) Same as (c) but with a correction screen of 32 × 32 pixels. (e) Same as (d) but with 500-nm wavelength light (no global tip–tilt correction).

Fig. 6
Fig. 6

Comparison of half-wave correction versus analog (conventional) correction after wave-front sensing with a simulated photon-starved Smartt interferometer. The correction screen is of size 32 × 32 pixels. The half-wave corrections are calculated with a single interferogram, and the analog correction is calculated with three-bucket interferometry. (a) unit fringe visibility and no readout noise. (b) fringe visibility 0.75 and 5 photons readout noise per correction element.

Fig. 7
Fig. 7

Simulation of the wavelength dependence of quarter-wave correction. The design wavelength is 550 nm. Each curve shows a different number of correction elements. We calculated the wavelength dependence by scaling the phase with wavelength. (a) results for an uncorrected incident beam. (b) tip–tilt-corrected incident beam.

Fig. 8
Fig. 8

Simulation of quarter-wave imaging, by convolving a USAF resolution chart with an appropriate PSF. The image is of size 256 × 256 pixels and is plotted at the Nyquist limit. No errors are included.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

S = [ 1 N i = 1 N cos ( ϕ i ) ] 2 + [ 1 N i = 1 N sin ( ϕ i ) ] 2 ,
S = { 1 π 0 1 0 2 π exp [ i ϕ ( r ) ] r d r d θ } 2 ,
S = [ ϕ min ϕ max N ( ϕ ) exp ( i ϕ ) d ϕ ] 2 ,
S = [ ϕ min ϕ max exp ( i ϕ ) d ϕ ] 2 ,
S = sinc 2 ( Δ ϕ 2 ) ,
I ( r ) = I 0 2 [ 1 + γ cos ϕ ( r ) ] ,
I k ( r ) = I 0 2 { 1 + γ cos [ ϕ ( r ) + θ k ] } ,
ϕ ( r ) = atan 2 [ I 3 ( r ) I 2 ( r ) I 1 ( r ) I 2 ( r ) ] ,
N i = N D 2 Δ λ 10 0 . 4 m ,
N det = Q N i int τ n pix ,

Metrics