Abstract

An adaptive system having 70,400 wave-front control channels has been experimentally analyzed. Wave-front control is based on the diffractive-feedback principle and requires neither a reference wave nor direct wave-front measurements. The key system elements are a liquid-crystal television used as a phase modulator, a CCD camera, and an optoelectronic feedback loop. Experiments demonstrated efficient suppression of wave-front distortions belonging to a bandpass spectral domain. Results demonstrate the system’s potential as a secondary high-resolution adaptive feedback system for adaptive optics applications.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  2. B. Y. Zeldovich, N. V. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical ciences (Springer-Verlag, Berlin, 1985);C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, J. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34, 2081–2088 (1995).
    [CrossRef] [PubMed]
  3. D. M. Pepper, C. J. Gaeta, P. V. Mitchell, “Real-time holography, innovative adaptive optics, and compensated optical processors using spatial light modulators,” in Spatial Light Modulator Technology: Materials, Devices, and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), pp. 585–654.
  4. R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, 1991); M. C. Roggemann, B. M. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).
  5. A. D. Fisher, C. Warde, “Technique for real-time high-resolution adaptive-phase compensation,” Opt. Lett. 8, 353–355 (1983).
    [CrossRef] [PubMed]
  6. M. A. Vorontsov, V. A. Katulin, A. F. Naumov, “Wavefront control by an optical-feedback interferometer,” Opt. Commun. 71, 35–38 (1989);M. A. Vorontsov, M. E. Kirakosyan, A. V. Larichev, “Correction of phase distortion in a nonlinear interferometer with an optical feedback loop,” Sov. J. Quantum Electron. 21, 105–108 (1991).
    [CrossRef]
  7. T. H. Barnes, T. Eiju, K. Matsuda, “High resolution adaptive optics using an interference phase loop,” Opt. Commun. 132, 494–502 (1996).
    [CrossRef]
  8. W. J. Firth, M. A. Vorontsov, “Adaptive phase distortion suppression in a nonlinear system with feedback mirror,” J. Mod. Opt. 40, 1841–1846 (1993).
    [CrossRef]
  9. E. V. Degtiarev, M. A. Vorontsov, “Spatial filtering in nonlinear two-dimensional feedback systems: phase-distortion suppression,” J. Opt. Soc. Am. B 12, 1238–1248 (1995).
    [CrossRef]
  10. V. P. Sivokon, M. A. Vorontsov, “High-resolution adaptive phase distortion suppression based solely on intensity information,” J. Opt. Soc. Am. A 15, 234–247 (1998).
    [CrossRef]
  11. R. Dou, M. K. Giles, “Phase measurement and compensation of a wavefront using a twisted nematic liquid-crystal television,” Appl. Opt. 35, 3647–3652 (1996).
    [CrossRef] [PubMed]
  12. R. Dou, M. K. Giles, “Closed-loop adaptive-optics system with a liquid-crystal television as a phase retarder,” Opt. Lett. 20, 1583–1585 (1995).
    [CrossRef] [PubMed]
  13. R. Dou, M. A. Vorontsov, V. P. Sivokon, M. K. Giles, “Iterative technique for high-resolution phase distortion compensation in adaptive interferometers,” Opt. Eng. 36, 3327–3335 (1997).
    [CrossRef]
  14. S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128×128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 55–59 (1995), and http://www.bnonlinear.com .
  15. M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997);M. C. Wu, “Micromachining for optical and opto-electronic systems,” Proc. IEEE 85, 1833 (1997).
    [CrossRef]
  16. A. G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996);C. A. Mead, “Neuromorphic electronic systems,” Proc. IEEE 78, 1629 (1990).
    [CrossRef]

1998 (1)

1997 (2)

R. Dou, M. A. Vorontsov, V. P. Sivokon, M. K. Giles, “Iterative technique for high-resolution phase distortion compensation in adaptive interferometers,” Opt. Eng. 36, 3327–3335 (1997).
[CrossRef]

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997);M. C. Wu, “Micromachining for optical and opto-electronic systems,” Proc. IEEE 85, 1833 (1997).
[CrossRef]

1996 (3)

A. G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996);C. A. Mead, “Neuromorphic electronic systems,” Proc. IEEE 78, 1629 (1990).
[CrossRef]

T. H. Barnes, T. Eiju, K. Matsuda, “High resolution adaptive optics using an interference phase loop,” Opt. Commun. 132, 494–502 (1996).
[CrossRef]

R. Dou, M. K. Giles, “Phase measurement and compensation of a wavefront using a twisted nematic liquid-crystal television,” Appl. Opt. 35, 3647–3652 (1996).
[CrossRef] [PubMed]

1995 (2)

1993 (1)

W. J. Firth, M. A. Vorontsov, “Adaptive phase distortion suppression in a nonlinear system with feedback mirror,” J. Mod. Opt. 40, 1841–1846 (1993).
[CrossRef]

1989 (1)

M. A. Vorontsov, V. A. Katulin, A. F. Naumov, “Wavefront control by an optical-feedback interferometer,” Opt. Commun. 71, 35–38 (1989);M. A. Vorontsov, M. E. Kirakosyan, A. V. Larichev, “Correction of phase distortion in a nonlinear interferometer with an optical feedback loop,” Sov. J. Quantum Electron. 21, 105–108 (1991).
[CrossRef]

1983 (1)

Andreou, A. G.

A. G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996);C. A. Mead, “Neuromorphic electronic systems,” Proc. IEEE 78, 1629 (1990).
[CrossRef]

Barnes, T. H.

T. H. Barnes, T. Eiju, K. Matsuda, “High resolution adaptive optics using an interference phase loop,” Opt. Commun. 132, 494–502 (1996).
[CrossRef]

Boahen, K. A.

A. G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996);C. A. Mead, “Neuromorphic electronic systems,” Proc. IEEE 78, 1629 (1990).
[CrossRef]

Bright, V. M.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997);M. C. Wu, “Micromachining for optical and opto-electronic systems,” Proc. IEEE 85, 1833 (1997).
[CrossRef]

Comtois, J. H.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997);M. C. Wu, “Micromachining for optical and opto-electronic systems,” Proc. IEEE 85, 1833 (1997).
[CrossRef]

Cowan, W. D.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997);M. C. Wu, “Micromachining for optical and opto-electronic systems,” Proc. IEEE 85, 1833 (1997).
[CrossRef]

Degtiarev, E. V.

Dou, R.

Eiju, T.

T. H. Barnes, T. Eiju, K. Matsuda, “High resolution adaptive optics using an interference phase loop,” Opt. Commun. 132, 494–502 (1996).
[CrossRef]

Firth, W. J.

W. J. Firth, M. A. Vorontsov, “Adaptive phase distortion suppression in a nonlinear system with feedback mirror,” J. Mod. Opt. 40, 1841–1846 (1993).
[CrossRef]

Fisher, A. D.

Gaeta, C. J.

D. M. Pepper, C. J. Gaeta, P. V. Mitchell, “Real-time holography, innovative adaptive optics, and compensated optical processors using spatial light modulators,” in Spatial Light Modulator Technology: Materials, Devices, and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), pp. 585–654.

Giles, M. K.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hick, S. R.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997);M. C. Wu, “Micromachining for optical and opto-electronic systems,” Proc. IEEE 85, 1833 (1997).
[CrossRef]

Katulin, V. A.

M. A. Vorontsov, V. A. Katulin, A. F. Naumov, “Wavefront control by an optical-feedback interferometer,” Opt. Commun. 71, 35–38 (1989);M. A. Vorontsov, M. E. Kirakosyan, A. V. Larichev, “Correction of phase distortion in a nonlinear interferometer with an optical feedback loop,” Sov. J. Quantum Electron. 21, 105–108 (1991).
[CrossRef]

Matsuda, K.

T. H. Barnes, T. Eiju, K. Matsuda, “High resolution adaptive optics using an interference phase loop,” Opt. Commun. 132, 494–502 (1996).
[CrossRef]

McKnight, D.

S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128×128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 55–59 (1995), and http://www.bnonlinear.com .

Mitchell, P. V.

D. M. Pepper, C. J. Gaeta, P. V. Mitchell, “Real-time holography, innovative adaptive optics, and compensated optical processors using spatial light modulators,” in Spatial Light Modulator Technology: Materials, Devices, and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), pp. 585–654.

Naumov, A. F.

M. A. Vorontsov, V. A. Katulin, A. F. Naumov, “Wavefront control by an optical-feedback interferometer,” Opt. Commun. 71, 35–38 (1989);M. A. Vorontsov, M. E. Kirakosyan, A. V. Larichev, “Correction of phase distortion in a nonlinear interferometer with an optical feedback loop,” Sov. J. Quantum Electron. 21, 105–108 (1991).
[CrossRef]

Pepper, D. M.

D. M. Pepper, C. J. Gaeta, P. V. Mitchell, “Real-time holography, innovative adaptive optics, and compensated optical processors using spatial light modulators,” in Spatial Light Modulator Technology: Materials, Devices, and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), pp. 585–654.

Pilipetsky, N. V.

B. Y. Zeldovich, N. V. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical ciences (Springer-Verlag, Berlin, 1985);C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, J. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34, 2081–2088 (1995).
[CrossRef] [PubMed]

Roberts, P. C.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997);M. C. Wu, “Micromachining for optical and opto-electronic systems,” Proc. IEEE 85, 1833 (1997).
[CrossRef]

Roggeman, M. C.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997);M. C. Wu, “Micromachining for optical and opto-electronic systems,” Proc. IEEE 85, 1833 (1997).
[CrossRef]

Serati, R.

S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128×128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 55–59 (1995), and http://www.bnonlinear.com .

Serati, S.

S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128×128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 55–59 (1995), and http://www.bnonlinear.com .

Sharp, G.

S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128×128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 55–59 (1995), and http://www.bnonlinear.com .

Shkunov, V. V.

B. Y. Zeldovich, N. V. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical ciences (Springer-Verlag, Berlin, 1985);C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, J. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34, 2081–2088 (1995).
[CrossRef] [PubMed]

Sivokon, V. P.

V. P. Sivokon, M. A. Vorontsov, “High-resolution adaptive phase distortion suppression based solely on intensity information,” J. Opt. Soc. Am. A 15, 234–247 (1998).
[CrossRef]

R. Dou, M. A. Vorontsov, V. P. Sivokon, M. K. Giles, “Iterative technique for high-resolution phase distortion compensation in adaptive interferometers,” Opt. Eng. 36, 3327–3335 (1997).
[CrossRef]

Stookley, J.

S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128×128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 55–59 (1995), and http://www.bnonlinear.com .

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, 1991); M. C. Roggemann, B. M. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Vorontsov, M. A.

V. P. Sivokon, M. A. Vorontsov, “High-resolution adaptive phase distortion suppression based solely on intensity information,” J. Opt. Soc. Am. A 15, 234–247 (1998).
[CrossRef]

R. Dou, M. A. Vorontsov, V. P. Sivokon, M. K. Giles, “Iterative technique for high-resolution phase distortion compensation in adaptive interferometers,” Opt. Eng. 36, 3327–3335 (1997).
[CrossRef]

E. V. Degtiarev, M. A. Vorontsov, “Spatial filtering in nonlinear two-dimensional feedback systems: phase-distortion suppression,” J. Opt. Soc. Am. B 12, 1238–1248 (1995).
[CrossRef]

W. J. Firth, M. A. Vorontsov, “Adaptive phase distortion suppression in a nonlinear system with feedback mirror,” J. Mod. Opt. 40, 1841–1846 (1993).
[CrossRef]

M. A. Vorontsov, V. A. Katulin, A. F. Naumov, “Wavefront control by an optical-feedback interferometer,” Opt. Commun. 71, 35–38 (1989);M. A. Vorontsov, M. E. Kirakosyan, A. V. Larichev, “Correction of phase distortion in a nonlinear interferometer with an optical feedback loop,” Sov. J. Quantum Electron. 21, 105–108 (1991).
[CrossRef]

Warde, C.

Welsh, B. M.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997);M. C. Wu, “Micromachining for optical and opto-electronic systems,” Proc. IEEE 85, 1833 (1997).
[CrossRef]

Zeldovich, B. Y.

B. Y. Zeldovich, N. V. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical ciences (Springer-Verlag, Berlin, 1985);C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, J. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34, 2081–2088 (1995).
[CrossRef] [PubMed]

Analog Integr. Circuits Signal Process. (1)

A. G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996);C. A. Mead, “Neuromorphic electronic systems,” Proc. IEEE 78, 1629 (1990).
[CrossRef]

Appl. Opt. (1)

J. Mod. Opt. (1)

W. J. Firth, M. A. Vorontsov, “Adaptive phase distortion suppression in a nonlinear system with feedback mirror,” J. Mod. Opt. 40, 1841–1846 (1993).
[CrossRef]

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

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

Opt. Commun. (2)

M. A. Vorontsov, V. A. Katulin, A. F. Naumov, “Wavefront control by an optical-feedback interferometer,” Opt. Commun. 71, 35–38 (1989);M. A. Vorontsov, M. E. Kirakosyan, A. V. Larichev, “Correction of phase distortion in a nonlinear interferometer with an optical feedback loop,” Sov. J. Quantum Electron. 21, 105–108 (1991).
[CrossRef]

T. H. Barnes, T. Eiju, K. Matsuda, “High resolution adaptive optics using an interference phase loop,” Opt. Commun. 132, 494–502 (1996).
[CrossRef]

Opt. Eng. (2)

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. 36, 1326–1338 (1997);M. C. Wu, “Micromachining for optical and opto-electronic systems,” Proc. IEEE 85, 1833 (1997).
[CrossRef]

R. Dou, M. A. Vorontsov, V. P. Sivokon, M. K. Giles, “Iterative technique for high-resolution phase distortion compensation in adaptive interferometers,” Opt. Eng. 36, 3327–3335 (1997).
[CrossRef]

Opt. Lett. (2)

Other (5)

S. Serati, G. Sharp, R. Serati, D. McKnight, J. Stookley, “128×128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 55–59 (1995), and http://www.bnonlinear.com .

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

B. Y. Zeldovich, N. V. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical ciences (Springer-Verlag, Berlin, 1985);C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, J. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34, 2081–2088 (1995).
[CrossRef] [PubMed]

D. M. Pepper, C. J. Gaeta, P. V. Mitchell, “Real-time holography, innovative adaptive optics, and compensated optical processors using spatial light modulators,” in Spatial Light Modulator Technology: Materials, Devices, and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), pp. 585–654.

R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, 1991); M. C. Roggemann, B. M. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).

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 (6)

Fig. 1
Fig. 1

Schematic of the adaptive system used in the experiments. The focal lengths corresponding to lenses L1, L2, and L3 are f1=1000 mm, f2=125 mm, and f3=350 mm.

Fig. 2
Fig. 2

Phase-modulation characteristic of the LCTV.

Fig. 3
Fig. 3

Experimental results of phase distortion compensation in a system with optical filtering: diffractive intensity registered by the CCD camera (a) without adaptation (b) after the first iteration, (c) after the first three iterations; (d) is the controlling gray-scale pattern corresponding to (c).

Fig. 4
Fig. 4

Compenstion of phase distortions by using a control algorithm with spatially modulated gain and digital filtering: (a) and (b) are diffractive intensity patterns [(a) without adaptation and (b) after five iterations], (c) is the controlling gray-scale pattern corresponding to (b), and (d) shows spatial spectra corresponding to distorted (top) and corrected (bottom) output waves. Wave-front correction was based on iterative procedure (4), (5), and (7) with α=0.4, K=-4, and L=4 mm.

Fig. 5
Fig. 5

Adaptive compensation of phase distortions introduced into the input beam by using (a), (b) Plexiglas plate and (c), (d) both the Plexiglas plate and the HEX127 phase modulator; (a) and (c) are the diffractive intensity patterns without adaptation, and (b) and (d) are those with adaptation. Wave-front correction was based on iterative procedure (6) with α=0.3, K=-4, and L=4 mm.

Fig. 6
Fig. 6

Spatiotemporal instabilities (diffractive intensity patterns) in the adaptive system: (a) traveling waves originating from wave-front tilts on the order of 5λ, (b) traveling shock waves observed at the boundaries of the large-scale phase distortion area (heated Plexiglas plate), (c) square pattern, (d) hexagonal pattern. Wave-front control was based on iterative procedure (6) for (a) and (b) and (4) and (5) for (c) and (d); α=0.3 and K=-8 for (a), α=0.8 and K=-10 for (b), and α=0.3 and K=-1 for (c) and (d). Patterns (c) and (d) were obtained for the Gaussian spatial filter with characteristic bandwidths qcut=1.2q1 for (c) and qcut=1.5q1 for (d). In all cases L=4 mm.

Tables (1)

Tables Icon

Table 1 Diffractive-Feedback System Phase Distortion Compensation Efficiency

Equations (14)

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

τ du(r, t)dt+u=KwFB(r, t),
wFB(r, t)=h(r-r)F[Id(r, t), Iin(r)]d2r.
wFB(r, t)=h(r-r)Id(r, t)d2r.
ui, j(n+1)=(1-α)ui,j(n)+Kwi, j(n),
wi, j(n)=Ii, j(n)*hi, j(i=1,, Nx,j=1,,Ny),
vi, j(n+1)=ui, j(n+1)-u¯(n+1)+const.
ui, j(n+1)=(1-α)ui, j(n)+KI˜i, j(n),
vi, j(n+1)=ui, j(n+1)-u¯(n+1)+const
(i=1,, Nx,j=1,, Ny),
Ki, j=K[2-Ii, jref /max(Ii, jref)],
T(q)=Ψ(q)Φ(q)=11-2K sin(q2Lλ/4π)(0<q<q1),
sin(LλqA,B2/4π)=1/(2|K|),
qA=[π-1 arcsin(0.5|K|-1)]1/2q1,
qB=q1-qA.

Metrics