Abstract

Real-time correction of an optically aberrated wave front by use of a 10 × 10 ferroelectric liquid-crystal spatial light modulator as the correction device and a point-diffraction interferometer as the wave-front sensor is demonstrated. This type of interferometer requires no reference arm and so can be used, in theory, in an astronomical adaptive-optics system. We discuss some of the unusual features of the point-diffraction interferometer for wave-front sensing.

© 1998 Optical Society of America

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References

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  1. R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991).
  2. G. D. Love, N. Andrews, P. Birch, D. Buscher, P. Doel, C. Dunlop, J. Major, R. Myers, A. Purvis, R. Sharples, A. Vick, A. Zadrozny, S. R. Restaino, A. Glindemann, “Binary adaptive optics: atmospheric wave-front correction with a half-wave phase shifter,” Appl. Opt. 34, 6058–6066 (1995);addenda 35, 347–350 (1996).
  3. M. O. Freeman, T. A. Brown, D. M. Walba, “Quantized complex ferroelectric liquid crystal spatial light modulators,” Appl. Opt. 31, 3917–3929 (1992).
    [CrossRef] [PubMed]
  4. H. M. Kim, J. W. Jeong, M. H. Kang, S. I. Jeong, “Phase correction of a spatial light modulator displaying a binary phase-only filter,” Appl. Opt. 27, 4167–4168 (1988).
    [CrossRef] [PubMed]
  5. E. C. Tam, S. Wu, A. Tanone, F. T. S. Yu, D. A. Gregory, “Closed-loop binary phase correction of an LCTV using a point diffraction interferometer,” IEEE Photon. Technol. Lett. 2(2), 143–146 (1990).
    [CrossRef]
  6. S. E. Broomfield, M. A. Neil, E. G. Paige, I. D. Thomas, “Binary optical correction of a wavefront aberration using spatial light modulators,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 167–175 (1995).
    [CrossRef]
  7. R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. 14, Suppl. 14-1 (1975).
  8. G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Opt. 36, 1517–1524 (1997).
    [CrossRef] [PubMed]
  9. J. Wang, J. K. Markey, “Modal compensation of atmospheric turbulence phase distortion,” J. Opt. Soc. Am 68, 78–87 (1978).
    [CrossRef]

1997 (1)

1995 (1)

1992 (1)

1990 (1)

E. C. Tam, S. Wu, A. Tanone, F. T. S. Yu, D. A. Gregory, “Closed-loop binary phase correction of an LCTV using a point diffraction interferometer,” IEEE Photon. Technol. Lett. 2(2), 143–146 (1990).
[CrossRef]

1988 (1)

1978 (1)

J. Wang, J. K. Markey, “Modal compensation of atmospheric turbulence phase distortion,” J. Opt. Soc. Am 68, 78–87 (1978).
[CrossRef]

1975 (1)

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. 14, Suppl. 14-1 (1975).

Andrews, N.

Birch, P.

Broomfield, S. E.

S. E. Broomfield, M. A. Neil, E. G. Paige, I. D. Thomas, “Binary optical correction of a wavefront aberration using spatial light modulators,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 167–175 (1995).
[CrossRef]

Brown, T. A.

Buscher, D.

Doel, P.

Dunlop, C.

Freeman, M. O.

Glindemann, A.

Gregory, D. A.

E. C. Tam, S. Wu, A. Tanone, F. T. S. Yu, D. A. Gregory, “Closed-loop binary phase correction of an LCTV using a point diffraction interferometer,” IEEE Photon. Technol. Lett. 2(2), 143–146 (1990).
[CrossRef]

Jeong, J. W.

Jeong, S. I.

Kang, M. H.

Kim, H. M.

Love, G. D.

Major, J.

Markey, J. K.

J. Wang, J. K. Markey, “Modal compensation of atmospheric turbulence phase distortion,” J. Opt. Soc. Am 68, 78–87 (1978).
[CrossRef]

Myers, R.

Neil, M. A.

S. E. Broomfield, M. A. Neil, E. G. Paige, I. D. Thomas, “Binary optical correction of a wavefront aberration using spatial light modulators,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 167–175 (1995).
[CrossRef]

Paige, E. G.

S. E. Broomfield, M. A. Neil, E. G. Paige, I. D. Thomas, “Binary optical correction of a wavefront aberration using spatial light modulators,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 167–175 (1995).
[CrossRef]

Purvis, A.

Restaino, S. R.

Sharples, R.

Smartt, R. N.

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. 14, Suppl. 14-1 (1975).

Steel, W. H.

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. 14, Suppl. 14-1 (1975).

Tam, E. C.

E. C. Tam, S. Wu, A. Tanone, F. T. S. Yu, D. A. Gregory, “Closed-loop binary phase correction of an LCTV using a point diffraction interferometer,” IEEE Photon. Technol. Lett. 2(2), 143–146 (1990).
[CrossRef]

Tanone, A.

E. C. Tam, S. Wu, A. Tanone, F. T. S. Yu, D. A. Gregory, “Closed-loop binary phase correction of an LCTV using a point diffraction interferometer,” IEEE Photon. Technol. Lett. 2(2), 143–146 (1990).
[CrossRef]

Thomas, I. D.

S. E. Broomfield, M. A. Neil, E. G. Paige, I. D. Thomas, “Binary optical correction of a wavefront aberration using spatial light modulators,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 167–175 (1995).
[CrossRef]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991).

Vick, A.

Walba, D. M.

Wang, J.

J. Wang, J. K. Markey, “Modal compensation of atmospheric turbulence phase distortion,” J. Opt. Soc. Am 68, 78–87 (1978).
[CrossRef]

Wu, S.

E. C. Tam, S. Wu, A. Tanone, F. T. S. Yu, D. A. Gregory, “Closed-loop binary phase correction of an LCTV using a point diffraction interferometer,” IEEE Photon. Technol. Lett. 2(2), 143–146 (1990).
[CrossRef]

Yu, F. T. S.

E. C. Tam, S. Wu, A. Tanone, F. T. S. Yu, D. A. Gregory, “Closed-loop binary phase correction of an LCTV using a point diffraction interferometer,” IEEE Photon. Technol. Lett. 2(2), 143–146 (1990).
[CrossRef]

Zadrozny, A.

Appl. Opt. (4)

IEEE Photon. Technol. Lett. (1)

E. C. Tam, S. Wu, A. Tanone, F. T. S. Yu, D. A. Gregory, “Closed-loop binary phase correction of an LCTV using a point diffraction interferometer,” IEEE Photon. Technol. Lett. 2(2), 143–146 (1990).
[CrossRef]

J. Opt. Soc. Am (1)

J. Wang, J. K. Markey, “Modal compensation of atmospheric turbulence phase distortion,” J. Opt. Soc. Am 68, 78–87 (1978).
[CrossRef]

Jpn. J. Appl. Phys. (1)

R. N. Smartt, W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. 14, Suppl. 14-1 (1975).

Other (2)

R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991).

S. E. Broomfield, M. A. Neil, E. G. Paige, I. D. Thomas, “Binary optical correction of a wavefront aberration using spatial light modulators,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 167–175 (1995).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Alignment of the input and output polarizers with reference to the switching angle of the FLC, as needed to attain a phase shift of π when the retardance of the device is not π.

Fig. 2
Fig. 2

Detail of the PDI aperture. The incident light is focused onto the pinhole with a lens. The zeroth-order light passes through the pinhole, creating a reference beam for the higher orders to interfere with.

Fig. 3
Fig. 3

Computer simulations of the PDI showing the PDI interferogram and the PSF. (a) The initial aberration. (b)–(j) The correction attempts. (c), (e), (g), (i) The wave front’s simulated PSF’s. The horizontal axis represents the spatial frequency in arbitrary units. (d), (f), (h), (j) The corresponding simulated one-dimensional interferograms. The dotted lines represent the intensity threshold. FLC pixels below this line are flipped.

Fig. 4
Fig. 4

Experimental setup. L1–L5, lenses; BS, beam splitter; POL, polarizer; BE, beam expander and spatial filter; FLC, ferroelectric liquid-crystal SLM.

Fig. 5
Fig. 5

Experimentally measured PSF’s. (a) The unaberrated PSF with SR = 100% (by definition). (b) The PSF with an aberration induced by the Model Hex69 with SR = 5%. (c) The PSF corrected by the FLC with SR = 26%.

Fig. 6
Fig. 6

Intensity plots of Figs. 5(a)5(c). The left image is the unaberrated PSF; the middle image is the PSF with an aberration induced by the Model Hex69; the right image is the corrected PSF. Each image is self-normalized to show the features.

Equations (7)

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

W = exp - i Γ / 2 cos 2   θ + exp i Γ / 2 sin 2   θ exp - i Γ / 2 sin   θ   cos   θ - exp i Γ / 2 sin   θ   cos   θ exp - i Γ / 2 sin   θ   cos   θ - exp i Γ / 2 sin   θ   cos   θ exp - i Γ / 2 sin 2   θ + exp i Γ / 2 cos 2   θ .
V = 0 1 ,
P = 1 0 0 0 .
T = PWV
= exp - i Γ / 2 cos   θ   sin   θ - exp i Γ / 2 cos   θ   sin   θ 0
= - 0.572 exp ± i π / 2 0
I r ˆ = I 0 / 2 1 + γ   cos Δ ϕ r ˆ ,

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