Abstract

An adjustable, high sensitivity, wide dynamic range two channel wave-front sensor based on moiré deflectometry has been constructed for measuring distortions of light wave-front transmitted through the atmosphere. In this approach, a slightly divergent laser beam is passed through the turbulent ground level atmosphere and then a beam-splitter divides it into two beams. The beams pass through a pair of moiré deflectometers which are installed parallel and close together. From deviations in the moiré fringes we calculate the two orthogonal components of angle of arrival at each location across the wave-front. The deviations have been deduced in successive frames which allows evolution of the wave-front shape to be determined. The dynamic range and sensitivity of detection are adjustable by merely changing the separation of the gratings and the angle between the rulings of the gratings in both of channels. The spatial resolution of the method is also adjustable by means of bright, dark, and virtual traces for given moiré fringes without paying a toll in the measurement precision.

© 2010 Optical Society of America

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References

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  1. M. Lombardo, and G. Lombardo, “New methods and techniques for sensing the wave aberrations of human eyes,” Clin. Exp. Optom. 92, 176–186 (2009).
    [CrossRef] [PubMed]
  2. F. Roddier, Adaptive optics in astronomy (Cambridge University Press, Cambridge, United Kingdom, 1999).
    [CrossRef]
  3. R. V. Shack, and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).
  4. B. C. Platt, and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
    [PubMed]
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    [CrossRef] [PubMed]
  6. G. W. R. Leibbrandt, G. Harbers, and P. J. Kunst, “Wavefront analysis with high accuracy by use of a doublegrating lateral shearing interferometer,” Appl. Opt. 35, 6151–6161 (1996).
    [CrossRef] [PubMed]
  7. R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).
  8. R. Ragazzoni, and J. Farinato, “Sensitivity of a pyramidic wave front sensor in closed loop adaptive optics,” Astron. Astrophys. 350, L23–L26 (1999).
  9. R. Legarda-Saenz, “Robust wavefront estimation using multiple directional derivatives in moiré deflectometry,” Opt. Lasers Eng. 45, 915–921 (2007).
    [CrossRef]
  10. J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
    [CrossRef]
  11. N. H. Salama, D. Patrignani, L. D. Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
    [CrossRef]
  12. Ch. Siegel, F. Loewenthal, and L. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
    [CrossRef]
  13. R. Sekine, T. Shibuya, K. Ukai, S. Komatsu, M. Hattori, T. Mihashi, N. Nakazawa, and Y. Hirohara, “Measurement of wavefront aberration of human eye using Talbot image of two-dimensional grating,” Opt. Rev. 13, 207–211 (2006).
    [CrossRef]
  14. M. Rottenkolber, and H. Podbielska, “Measuring ophthalmologic surfaces by means of moir’e deflectometry,” Opt. Eng. 35, 1124–1133 (1996).
    [CrossRef]
  15. S. Rasouli, and M. T. Tavassoly, “Application of moiré technique to the measurement of the atmospheric turbulence parameters related to the angle of arrival fluctuations,” Opt. Lett. 31, 3276–3278 (2006).
    [CrossRef] [PubMed]
  16. S. Rasouli, and M. T. Tavassoly, “Moiré technique improves the measurement of atmospheric turbulence parameters,” SPIE Newsroom DOI 10.1117/2.1200702.0569, (2007), http://spie.org/documents/Newsroom/Imported/0569/0569-2007-02-20.pdf.
  17. S. Rasouli, and M. T. Tavassoly, “Application of the moiré deflectometry on divergent laser beam to the measurement of the angle of arrival fluctuations and the refractive index structure constant in the turbulent atmosphere,” Opt. Lett. 33, 980–982 (2008).
    [CrossRef] [PubMed]
  18. S. Rasouli, “Use of a moir’e deflectometer on a telescope for atmospheric turbulence measurements,” Opt. Lett. 35, 1470–1472 (2010).
    [CrossRef]
  19. S. Rasouli, and M. T. Tavassoly, “Measurement of the refractive-index structure constant, C2 n, and its profile in the ground level atmosphere by moir’e technique,” in Optics in Atmospheric Propagation and Adaptive Systems IX, A. Kohnle and K. Stein, ed., Proc. SPIE 6364, 63640G–1–11 (2006).
    [CrossRef]
  20. S. Rasouli, K. Madanipour, and M. T. Tavassoly, “Measurement of modulation transfer function of the atmosphere in the surface layer by moir’e technique,” in Optics in Atmospheric Propagation and Adaptive Systems IX, A. Kohnle, and K. Stein, ed., Proc. SPIE 6364, 63640K–1–10 (2006).
  21. S. Rasouli, and N. Anamparambu, Ramaprakash, H. K. Das, C. V. Rajarshi, Y. Rajabi, and M. Dashti, “Two channel wavefront sensor arrangement employing moir’e deflectometry,” in Optics in Atmospheric Propagation and Adaptive Systems XII, A. Kohnle, K. Stein, and J. D. Gonglewski, ed., Proc. SPIE 7476, 74760K–1–9 (2009).
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2010 (1)

2009 (1)

M. Lombardo, and G. Lombardo, “New methods and techniques for sensing the wave aberrations of human eyes,” Clin. Exp. Optom. 92, 176–186 (2009).
[CrossRef] [PubMed]

2008 (1)

2007 (1)

R. Legarda-Saenz, “Robust wavefront estimation using multiple directional derivatives in moiré deflectometry,” Opt. Lasers Eng. 45, 915–921 (2007).
[CrossRef]

2006 (2)

R. Sekine, T. Shibuya, K. Ukai, S. Komatsu, M. Hattori, T. Mihashi, N. Nakazawa, and Y. Hirohara, “Measurement of wavefront aberration of human eye using Talbot image of two-dimensional grating,” Opt. Rev. 13, 207–211 (2006).
[CrossRef]

S. Rasouli, and M. T. Tavassoly, “Application of moiré technique to the measurement of the atmospheric turbulence parameters related to the angle of arrival fluctuations,” Opt. Lett. 31, 3276–3278 (2006).
[CrossRef] [PubMed]

2001 (2)

Ch. Siegel, F. Loewenthal, and L. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

B. C. Platt, and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

1999 (3)

J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
[CrossRef]

N. H. Salama, D. Patrignani, L. D. Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

R. Ragazzoni, and J. Farinato, “Sensitivity of a pyramidic wave front sensor in closed loop adaptive optics,” Astron. Astrophys. 350, L23–L26 (1999).

1996 (2)

M. Rottenkolber, and H. Podbielska, “Measuring ophthalmologic surfaces by means of moir’e deflectometry,” Opt. Eng. 35, 1124–1133 (1996).
[CrossRef]

G. W. R. Leibbrandt, G. Harbers, and P. J. Kunst, “Wavefront analysis with high accuracy by use of a doublegrating lateral shearing interferometer,” Appl. Opt. 35, 6151–6161 (1996).
[CrossRef] [PubMed]

1988 (1)

1982 (1)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).

1980 (2)

1979 (1)

1977 (1)

1971 (1)

R. V. Shack, and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Balmer, L. E.

Ch. Siegel, F. Loewenthal, and L. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Bernabeu, E.

J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
[CrossRef]

Crespo, D.

J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
[CrossRef]

Farinato, J.

R. Ragazzoni, and J. Farinato, “Sensitivity of a pyramidic wave front sensor in closed loop adaptive optics,” Astron. Astrophys. 350, L23–L26 (1999).

Fried, D. L.

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).

Harbers, G.

Hattori, M.

R. Sekine, T. Shibuya, K. Ukai, S. Komatsu, M. Hattori, T. Mihashi, N. Nakazawa, and Y. Hirohara, “Measurement of wavefront aberration of human eye using Talbot image of two-dimensional grating,” Opt. Rev. 13, 207–211 (2006).
[CrossRef]

Herrmann, J.

Hirohara, Y.

R. Sekine, T. Shibuya, K. Ukai, S. Komatsu, M. Hattori, T. Mihashi, N. Nakazawa, and Y. Hirohara, “Measurement of wavefront aberration of human eye using Talbot image of two-dimensional grating,” Opt. Rev. 13, 207–211 (2006).
[CrossRef]

Hunt, B. R.

Komatsu, S.

R. Sekine, T. Shibuya, K. Ukai, S. Komatsu, M. Hattori, T. Mihashi, N. Nakazawa, and Y. Hirohara, “Measurement of wavefront aberration of human eye using Talbot image of two-dimensional grating,” Opt. Rev. 13, 207–211 (2006).
[CrossRef]

Kunst, P. J.

Legarda-Saenz, R.

R. Legarda-Saenz, “Robust wavefront estimation using multiple directional derivatives in moiré deflectometry,” Opt. Lasers Eng. 45, 915–921 (2007).
[CrossRef]

Leibbrandt, G. W. R.

Loewenthal, F.

Ch. Siegel, F. Loewenthal, and L. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Lombardo, G.

M. Lombardo, and G. Lombardo, “New methods and techniques for sensing the wave aberrations of human eyes,” Clin. Exp. Optom. 92, 176–186 (2009).
[CrossRef] [PubMed]

Lombardo, M.

M. Lombardo, and G. Lombardo, “New methods and techniques for sensing the wave aberrations of human eyes,” Clin. Exp. Optom. 92, 176–186 (2009).
[CrossRef] [PubMed]

Mihashi, T.

R. Sekine, T. Shibuya, K. Ukai, S. Komatsu, M. Hattori, T. Mihashi, N. Nakazawa, and Y. Hirohara, “Measurement of wavefront aberration of human eye using Talbot image of two-dimensional grating,” Opt. Rev. 13, 207–211 (2006).
[CrossRef]

Nakazawa, N.

R. Sekine, T. Shibuya, K. Ukai, S. Komatsu, M. Hattori, T. Mihashi, N. Nakazawa, and Y. Hirohara, “Measurement of wavefront aberration of human eye using Talbot image of two-dimensional grating,” Opt. Rev. 13, 207–211 (2006).
[CrossRef]

Pasquale, L. D.

N. H. Salama, D. Patrignani, L. D. Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

Patrignani, D.

N. H. Salama, D. Patrignani, L. D. Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

Platt, B. C.

B. C. Platt, and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

R. V. Shack, and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Podbielska, H.

M. Rottenkolber, and H. Podbielska, “Measuring ophthalmologic surfaces by means of moir’e deflectometry,” Opt. Eng. 35, 1124–1133 (1996).
[CrossRef]

Quiroga, J. A.

J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
[CrossRef]

Ragazzoni, R.

R. Ragazzoni, and J. Farinato, “Sensitivity of a pyramidic wave front sensor in closed loop adaptive optics,” Astron. Astrophys. 350, L23–L26 (1999).

Rasouli, S.

Roddier, E.

Rottenkolber, M.

M. Rottenkolber, and H. Podbielska, “Measuring ophthalmologic surfaces by means of moir’e deflectometry,” Opt. Eng. 35, 1124–1133 (1996).
[CrossRef]

Salama, N. H.

N. H. Salama, D. Patrignani, L. D. Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

Sekine, R.

R. Sekine, T. Shibuya, K. Ukai, S. Komatsu, M. Hattori, T. Mihashi, N. Nakazawa, and Y. Hirohara, “Measurement of wavefront aberration of human eye using Talbot image of two-dimensional grating,” Opt. Rev. 13, 207–211 (2006).
[CrossRef]

Shack, R.

B. C. Platt, and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

Shack, R. V.

R. V. Shack, and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Shibuya, T.

R. Sekine, T. Shibuya, K. Ukai, S. Komatsu, M. Hattori, T. Mihashi, N. Nakazawa, and Y. Hirohara, “Measurement of wavefront aberration of human eye using Talbot image of two-dimensional grating,” Opt. Rev. 13, 207–211 (2006).
[CrossRef]

Sicre, E. E.

N. H. Salama, D. Patrignani, L. D. Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

Siegel, Ch.

Ch. Siegel, F. Loewenthal, and L. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Southwell, W. H.

Tavassoly, M. T.

Ukai, K.

R. Sekine, T. Shibuya, K. Ukai, S. Komatsu, M. Hattori, T. Mihashi, N. Nakazawa, and Y. Hirohara, “Measurement of wavefront aberration of human eye using Talbot image of two-dimensional grating,” Opt. Rev. 13, 207–211 (2006).
[CrossRef]

Appl. Opt. (2)

Astron. Astrophys. (1)

R. Ragazzoni, and J. Farinato, “Sensitivity of a pyramidic wave front sensor in closed loop adaptive optics,” Astron. Astrophys. 350, L23–L26 (1999).

Clin. Exp. Optom. (1)

M. Lombardo, and G. Lombardo, “New methods and techniques for sensing the wave aberrations of human eyes,” Clin. Exp. Optom. 92, 176–186 (2009).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (5)

J. Refract. Surg. (1)

B. C. Platt, and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

Opt. Commun. (1)

Ch. Siegel, F. Loewenthal, and L. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Opt. Eng. (3)

J. A. Quiroga, D. Crespo, and E. Bernabeu, “Fourier transform method for automatic processing of moiré deflectograms,” Opt. Eng. 38, 974–982 (1999).
[CrossRef]

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 829–832 (1982).

M. Rottenkolber, and H. Podbielska, “Measuring ophthalmologic surfaces by means of moir’e deflectometry,” Opt. Eng. 35, 1124–1133 (1996).
[CrossRef]

Opt. Laser Technol. (1)

N. H. Salama, D. Patrignani, L. D. Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

Opt. Lasers Eng. (1)

R. Legarda-Saenz, “Robust wavefront estimation using multiple directional derivatives in moiré deflectometry,” Opt. Lasers Eng. 45, 915–921 (2007).
[CrossRef]

Opt. Lett. (3)

Opt. Rev. (1)

R. Sekine, T. Shibuya, K. Ukai, S. Komatsu, M. Hattori, T. Mihashi, N. Nakazawa, and Y. Hirohara, “Measurement of wavefront aberration of human eye using Talbot image of two-dimensional grating,” Opt. Rev. 13, 207–211 (2006).
[CrossRef]

Other (5)

S. Rasouli, and M. T. Tavassoly, “Measurement of the refractive-index structure constant, C2 n, and its profile in the ground level atmosphere by moir’e technique,” in Optics in Atmospheric Propagation and Adaptive Systems IX, A. Kohnle and K. Stein, ed., Proc. SPIE 6364, 63640G–1–11 (2006).
[CrossRef]

S. Rasouli, K. Madanipour, and M. T. Tavassoly, “Measurement of modulation transfer function of the atmosphere in the surface layer by moir’e technique,” in Optics in Atmospheric Propagation and Adaptive Systems IX, A. Kohnle, and K. Stein, ed., Proc. SPIE 6364, 63640K–1–10 (2006).

S. Rasouli, and N. Anamparambu, Ramaprakash, H. K. Das, C. V. Rajarshi, Y. Rajabi, and M. Dashti, “Two channel wavefront sensor arrangement employing moir’e deflectometry,” in Optics in Atmospheric Propagation and Adaptive Systems XII, A. Kohnle, K. Stein, and J. D. Gonglewski, ed., Proc. SPIE 7476, 74760K–1–9 (2009).

F. Roddier, Adaptive optics in astronomy (Cambridge University Press, Cambridge, United Kingdom, 1999).
[CrossRef]

S. Rasouli, and M. T. Tavassoly, “Moiré technique improves the measurement of atmospheric turbulence parameters,” SPIE Newsroom DOI 10.1117/2.1200702.0569, (2007), http://spie.org/documents/Newsroom/Imported/0569/0569-2007-02-20.pdf.

Supplementary Material (3)

» Media 1: MPG (4217 KB)     
» Media 2: MPG (12298 KB)     
» Media 3: MPG (3418 KB)     

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. DF, A, BS, M, Zk, D, PL stand for the neutral density filter, square aperture, beam splitter, mirror, Talbot distance, diffuser, and projecting lens, respectively. G1, G2, G3 and G4 stand for the gratings.

Fig. 2
Fig. 2

A typical recorded frame consists of two sets of orthogonal moiré patterns.

Fig. 3
Fig. 3

(Color online) (a) and (d) typical moiré fringes in the horizontal and vertical directions, (b) and (e) the corresponding low-frequency illumination of the patterns. The corresponding bright and dark moiré fringes traces and the first order virtual traces are shown in (c) and (f). All the recorded frames, the corresponding low-frequency illumination and traces can be observed in the background “movie” ( Media 1 MPEG, 4.2 MB).

Fig. 4
Fig. 4

Displacement vectors of intersection points of all the traces. A larger shift is visualized by a larger length of the arrow. The “movie” ( Media 2) shows the corresponding patterns for all of the successive recorded frames (MPEG, 12.2 MB).

Fig. 5
Fig. 5

Moiré fringes in the horizontal and vertical directions and the reconstructed wave-front, surface plot, corresponding to the distortions induced by atmospheric turbulence. The corresponding “movie” ( Media 3) for all of the successive recorded frames can be observed in the background (MPEG, 3.4 MB).

Equations (5)

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

δ x m ( x , y ) = d m d δ y ( x , y ) ,
α y ( x , y ) = δ y ( x , y ) Z k = 1 Z k d d m δ x m ( x , y ) .
α x ( x , y ) = δ x ( x , y ) Z k = 1 Z k d d m δ y m ( x , y ) ,
[ α x ( x , y ) , α y ( x , y ) ] = d z k [ δ y m ( x , y ) d m , δ x m ( x , y ) d m ] .
[ U ( x , y ) x , U ( x , y ) y ] = d Z k [ δ y m ( x , y ) d m , δ x m ( x , y ) d m ] .

Metrics