Abstract

The process of Zernike mode detection with a Shack–Hartmann wavefront sensor is computationally extensive. A holographic modal wavefront sensor has therefore evolved to process the data optically by use of the concept of equal and opposite phase bias. Recently, a multiplexed computer-generated hologram (CGH) technique was developed in which the output is in the form of bright dots that specify the presence and strength of a specific Zernike mode. We propose a wavefront sensor using the concept of phase biasing in the latter technique such that the output is a pair of bright dots for each mode to be sensed. A normalized difference signal between the intensities of the two dots is proportional to the amplitude of the sensed Zernike mode. In our method the number of holograms to be multiplexed is decreased, thereby reducing the modal cross talk significantly. We validated the proposed method through simulation studies for several cases. The simulation results demonstrate simultaneous wavefront detection of lower-order Zernike modes with a resolution better than λ/50 for the wide measurement range of ±3.5λ with much reduced cross talk at high speed.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. M. Geary, Introduction to Wavefront Sensor, Tutorial Text TT-18 (SPIE Press, 1995).
    [CrossRef]
  2. F. Rigaut, B. L. Ellerbroek, and M. J. Northcot, “Comparison of curvature-based and Shack-Hartmann based adaptive optics for the Gemini telescope,” Appl. Opt. 36, 2856-2868(1997).
    [CrossRef] [PubMed]
  3. C. Canovas and E. N. Ribak, “Comparison of Hartmann analysis methods,” Appl. Opt. . 46, 1830-1835 (2007).
    [CrossRef] [PubMed]
  4. F. Ghebremichael, G. P. Andersen, and K. S. Gurley, “Holography-based wavefront sensing,” Appl. Opt. 47, A62-A69 (2008).
    [CrossRef] [PubMed]
  5. W. Jiang, X. Rao, Z. Yang, and N. Ling, “Applications of Hartmann-Shack wavefront sensors,” Proc. SPIE 6018, 60180N (2005).
    [CrossRef]
  6. M. A. Vorontsov and G. W. Carhart, “Adaptive phase distortion correction in strong speckle-modulation conditions,” Opt. Lett. 27, 2155-2157 (2002).
    [CrossRef]
  7. M. A. Vorontsov, V. V. Kolosov, and E. Polnau, “Target-in-the-loop wavefront sensing and control with a Collett-Wolf beacon: speckle average phase conjugation,” Appl. Opt. 48, A13-A29 (2009).
    [CrossRef]
  8. R. K. Tyson, Principle of Adaptive Optics (Academic, 1998).
  9. S. K. Mishra, D. Meena, D. Mohan, and A. K. Gupta, “FPGA based fast Shack Hartmann wavefront sensor for aircraft vision,” in Proceedings of the National Conference on Advances in Sensors for Aerospace Applications (Research Center Imarat, 2007).
  10. K. Chen, Z. Yang, H. Wang, and E. Li, “PSD-based Hartmann-Shack wavefront sensor,” Proc. SPIE 5639, 87-94 (2004).
    [CrossRef]
  11. J. Lin, J. Tang, and H. Chen, “High speed wavefront sensor based on PSDs,” Proc. SPIE 5639, 95-102 (2004).
    [CrossRef]
  12. M. A. A. Neil, M. J. Booth, and T. Wilson, “New modal wavefront sensor: a theoretical analysis,” J. Opt. Soc. Am. A 17, 1098-1107 (2000).
    [CrossRef]
  13. M. A. A. Neil, M. J. Booth, and T. Wilson, “Closed-loop aberration correction by use of a modal Zernike wavefront sensor,” Opt. Lett. 25, 1083-1085 (2000).
    [CrossRef]
  14. M. J. Booth, “Direct measurement of Zernike aberration modes with a modal wavefront sensor,” Proc. SPIE 5162, 79-90 (2003).
    [CrossRef]
  15. E. N. Ribak and S. M. Ebstein, “A fast modal wavefront sensor,” Opt. Express 9, 152-157 (2001).
    [CrossRef] [PubMed]
  16. M. A. Lauterbach, M. Ruckel, and W. Denk, “Light-efficient, quantum-limited interferometric wavefront estimation by virtual mode sensing,” Opt. Express 14, 3700-3714(2006).
    [CrossRef] [PubMed]
  17. A. D. Corbett, T. D. Wilkinson, J. J. Zhong, and L. Diaz-Santana, “Designing the holographic modal wavefront sensor for detection of static ocular aberrations,” J. Opt. Soc. Am. A 24, 1266-1275 (2007).
    [CrossRef]
  18. O. Glazer, E. N. Ribak, and L. Mirkin, “Adaptive optics implementation with a Fourier reconstructor,” Appl. Opt. 46, 574-580 (2007).
    [CrossRef] [PubMed]
  19. P. Dyrud and G. P. Andersen, “Fast holographic wavefront sensor,” Proc. SPIE 6215, 621501 (2006).
  20. V. A. Soifer, Methods for Computer Design of Diffractive Optical Elements (Wiley, 2002).
  21. R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
    [CrossRef]
  22. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207-211 (1976).
    [CrossRef]
  23. J. A. Davis, K. O. Valadez, and D. M. Cottrell, “Encoding amplitude and phase information onto a binary phase-only spatial light modulator,” Appl. Opt. 42, 2003-2008(2003).
    [CrossRef] [PubMed]

2009

2008

F. Ghebremichael, G. P. Andersen, and K. S. Gurley, “Holography-based wavefront sensing,” Appl. Opt. 47, A62-A69 (2008).
[CrossRef] [PubMed]

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
[CrossRef]

2007

2006

2005

W. Jiang, X. Rao, Z. Yang, and N. Ling, “Applications of Hartmann-Shack wavefront sensors,” Proc. SPIE 6018, 60180N (2005).
[CrossRef]

2004

K. Chen, Z. Yang, H. Wang, and E. Li, “PSD-based Hartmann-Shack wavefront sensor,” Proc. SPIE 5639, 87-94 (2004).
[CrossRef]

J. Lin, J. Tang, and H. Chen, “High speed wavefront sensor based on PSDs,” Proc. SPIE 5639, 95-102 (2004).
[CrossRef]

2003

2002

2001

2000

1997

1976

Andersen, G. P.

F. Ghebremichael, G. P. Andersen, and K. S. Gurley, “Holography-based wavefront sensing,” Appl. Opt. 47, A62-A69 (2008).
[CrossRef] [PubMed]

P. Dyrud and G. P. Andersen, “Fast holographic wavefront sensor,” Proc. SPIE 6215, 621501 (2006).

Bhatt, R.

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
[CrossRef]

Booth, M. J.

Canovas, C.

Carhart, G. W.

Chen, H.

J. Lin, J. Tang, and H. Chen, “High speed wavefront sensor based on PSDs,” Proc. SPIE 5639, 95-102 (2004).
[CrossRef]

Chen, K.

K. Chen, Z. Yang, H. Wang, and E. Li, “PSD-based Hartmann-Shack wavefront sensor,” Proc. SPIE 5639, 87-94 (2004).
[CrossRef]

Corbett, A. D.

Cottrell, D. M.

Davis, J. A.

Denk, W.

Diaz-Santana, L.

Dyrud, P.

P. Dyrud and G. P. Andersen, “Fast holographic wavefront sensor,” Proc. SPIE 6215, 621501 (2006).

Ebstein, S. M.

Ellerbroek, B. L.

Geary, J. M.

J. M. Geary, Introduction to Wavefront Sensor, Tutorial Text TT-18 (SPIE Press, 1995).
[CrossRef]

Ghebremichael, F.

Glazer, O.

Gupta, A. K.

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
[CrossRef]

S. K. Mishra, D. Meena, D. Mohan, and A. K. Gupta, “FPGA based fast Shack Hartmann wavefront sensor for aircraft vision,” in Proceedings of the National Conference on Advances in Sensors for Aerospace Applications (Research Center Imarat, 2007).

Gurley, K. S.

Jiang, W.

W. Jiang, X. Rao, Z. Yang, and N. Ling, “Applications of Hartmann-Shack wavefront sensors,” Proc. SPIE 6018, 60180N (2005).
[CrossRef]

Kolosov, V. V.

Lauterbach, M. A.

Li, E.

K. Chen, Z. Yang, H. Wang, and E. Li, “PSD-based Hartmann-Shack wavefront sensor,” Proc. SPIE 5639, 87-94 (2004).
[CrossRef]

Lin, J.

J. Lin, J. Tang, and H. Chen, “High speed wavefront sensor based on PSDs,” Proc. SPIE 5639, 95-102 (2004).
[CrossRef]

Ling, N.

W. Jiang, X. Rao, Z. Yang, and N. Ling, “Applications of Hartmann-Shack wavefront sensors,” Proc. SPIE 6018, 60180N (2005).
[CrossRef]

Meena, D.

S. K. Mishra, D. Meena, D. Mohan, and A. K. Gupta, “FPGA based fast Shack Hartmann wavefront sensor for aircraft vision,” in Proceedings of the National Conference on Advances in Sensors for Aerospace Applications (Research Center Imarat, 2007).

Mirkin, L.

Mishra, S. K.

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
[CrossRef]

S. K. Mishra, D. Meena, D. Mohan, and A. K. Gupta, “FPGA based fast Shack Hartmann wavefront sensor for aircraft vision,” in Proceedings of the National Conference on Advances in Sensors for Aerospace Applications (Research Center Imarat, 2007).

Mohan, D.

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
[CrossRef]

S. K. Mishra, D. Meena, D. Mohan, and A. K. Gupta, “FPGA based fast Shack Hartmann wavefront sensor for aircraft vision,” in Proceedings of the National Conference on Advances in Sensors for Aerospace Applications (Research Center Imarat, 2007).

Neil, M. A. A.

Noll, R. J.

Northcot, M. J.

Polnau, E.

Rao, X.

W. Jiang, X. Rao, Z. Yang, and N. Ling, “Applications of Hartmann-Shack wavefront sensors,” Proc. SPIE 6018, 60180N (2005).
[CrossRef]

Ribak, E. N.

Rigaut, F.

Ruckel, M.

Soifer, V. A.

V. A. Soifer, Methods for Computer Design of Diffractive Optical Elements (Wiley, 2002).

Tang, J.

J. Lin, J. Tang, and H. Chen, “High speed wavefront sensor based on PSDs,” Proc. SPIE 5639, 95-102 (2004).
[CrossRef]

Tyson, R. K.

R. K. Tyson, Principle of Adaptive Optics (Academic, 1998).

Valadez, K. O.

Vorontsov, M. A.

Wang, H.

K. Chen, Z. Yang, H. Wang, and E. Li, “PSD-based Hartmann-Shack wavefront sensor,” Proc. SPIE 5639, 87-94 (2004).
[CrossRef]

Wilkinson, T. D.

Wilson, T.

Yang, Z.

W. Jiang, X. Rao, Z. Yang, and N. Ling, “Applications of Hartmann-Shack wavefront sensors,” Proc. SPIE 6018, 60180N (2005).
[CrossRef]

K. Chen, Z. Yang, H. Wang, and E. Li, “PSD-based Hartmann-Shack wavefront sensor,” Proc. SPIE 5639, 87-94 (2004).
[CrossRef]

Zhong, J. J.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Express

Opt. Lasers Eng.

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
[CrossRef]

Opt. Lett.

Proc. SPIE

W. Jiang, X. Rao, Z. Yang, and N. Ling, “Applications of Hartmann-Shack wavefront sensors,” Proc. SPIE 6018, 60180N (2005).
[CrossRef]

M. J. Booth, “Direct measurement of Zernike aberration modes with a modal wavefront sensor,” Proc. SPIE 5162, 79-90 (2003).
[CrossRef]

K. Chen, Z. Yang, H. Wang, and E. Li, “PSD-based Hartmann-Shack wavefront sensor,” Proc. SPIE 5639, 87-94 (2004).
[CrossRef]

J. Lin, J. Tang, and H. Chen, “High speed wavefront sensor based on PSDs,” Proc. SPIE 5639, 95-102 (2004).
[CrossRef]

P. Dyrud and G. P. Andersen, “Fast holographic wavefront sensor,” Proc. SPIE 6215, 621501 (2006).

Other

V. A. Soifer, Methods for Computer Design of Diffractive Optical Elements (Wiley, 2002).

J. M. Geary, Introduction to Wavefront Sensor, Tutorial Text TT-18 (SPIE Press, 1995).
[CrossRef]

R. K. Tyson, Principle of Adaptive Optics (Academic, 1998).

S. K. Mishra, D. Meena, D. Mohan, and A. K. Gupta, “FPGA based fast Shack Hartmann wavefront sensor for aircraft vision,” in Proceedings of the National Conference on Advances in Sensors for Aerospace Applications (Research Center Imarat, 2007).

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

Optical implementation scheme of the MZWS.

Fig. 2
Fig. 2

Sensor response of single defocus mode detection with the CGH designed for the same mode.

Fig. 3
Fig. 3

Multiplexed CGH ( Z 4 Z 8 ) coded for mode strength ε = ± 2 and detection of spot for defocus with mode strength δ = 0.5 λ .

Fig. 4
Fig. 4

Multiplexed CGH ( Z 4 Z 8 ) coded for mode strength ε = ± 5 λ and detection of spot for defocus with mode strength δ = 0.5 λ .

Fig. 5
Fig. 5

Detection response curves for Zernike modes with a multiplexed CGH ( Z 4 Z 8 ) coded for mode strength ε = ± 5 λ when defocus is present and astigmatism and coma are absent in the test beam.

Fig. 6
Fig. 6

Detection response curves for Zernike modes with a multiplexed CGH ( Z 4 Z 8 ) coded for mode strength ε = ± 5 λ when astigmatism1 and coma1 are present only in the test beam.

Fig. 7
Fig. 7

Detection response curves for Zernike modes with a multiplexed CGH ( Z 4 Z 8 ) coded for mode strength ε = ± 5 λ when astigmatism1 and astigmatism2 are present only in the test beam.

Fig. 8
Fig. 8

Detection response curves for Zernike modes with a multiplexed CGH ( Z 4 Z 8 ) coded for mode strength ε = ± 5 λ when defocus, astigmatism, and coma are all present in the test beam.

Tables (1)

Tables Icon

Table 1 Illustration of Individual Zernike Modes for Designed CGHs for the Same Mode and Its Detection

Equations (7)

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

W ( r , θ ) = k a k Z k ,
ψ abr k = ψ plane exp ( i 2 π λ a k Z k ) ,
I k = [ ψ abr k + FT ( d p ) ] [ ψ abr k + FT ( d p ) ] * = | ψ abr k | 2 + | FT ( d p ) | 2 + ψ abr k [ FT ( d p ) ] * + [ ψ abr k ] * FT ( d p ) .
h k = [ ψ abr k ] * FT ( d p ) ,
H k = [ ψ abr + ε ] * FT ( d p 1 ) + [ ψ abr ε ] * FT ( d p 2 ) .
ψ test = ψ plane exp ( i 2 π λ j b j Z j ) .
I k = I 1 I 2 ,

Metrics