Abstract

We employ an acousto-optic cell as a tunable-pitch wavefront sensor and study its performance. The index of refraction of two cross-standing waves forms, in the near field, an adjustable array of caustics. These caustics, similar to the lenslets used for Hartmann–Shack sensing, were measured to have an extended focal relief of 200 times their pitch. We discovered a strong interaction between the caustics and source speckle, so much so that we had to modulate the beam to reduce it. We measured ocular wavefronts at different frequencies and established the consistency and reliability of the reconstruction.

© 2008 Optical Society of America

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References

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  1. B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573-577(2001).
  2. A. Korpel, Acousto-Optics (CRC Press, 1997).
  3. E. N. Ribak, “Harnessing caustics for wavefront sensing,” Opt. Lett. 26, 1834-1836 (2001).
    [CrossRef]
  4. B. E. A. Saleh and M. C. Teich, Fundamental of Photonics (Wiley, 1991).
    [CrossRef]
  5. P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, “Analysis of the performance of the Hartmann-Shack sensor in the human eye,” J. Opt. Soc. Am. A 17, 1388-1398 (2000).
    [CrossRef]
  6. Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215, 285-288(2003).
    [CrossRef]
  7. I. Grulkowski and P. Kwiek, “Experimental study of light diffraction by standing ultrasonic wave with cylindrical symmetry,” Opt. Commun. 267, 14-19 (2006).
    [CrossRef]
  8. J.C.Dainty, ed., Laser Speckle and Related Phenomena (Springer, 1984).
  9. I. Freund and D. A. Kessler, “Singularities in speckled speckle,” Opt. Lett. 33, 479-481 (2008).
    [CrossRef] [PubMed]
  10. V. Albanis, E. N. Ribak, and Y. Carmon, “Reduction of speckles in retinal reflection,” Appl. Phys. Lett. 91, 054104(2007).
    [CrossRef]
  11. M. V. Berry and C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” in Progress in Optics E. Wolf, ed. (Elsevier, 1980), Vol. 18, pp. 257-346.
    [CrossRef]
  12. M. V. Berry, “Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces,” J. Phys. A 8, 566-584 (1975).
    [CrossRef]
  13. A. Talmi and E. N. Ribak, “Direct demodulation of Hartmann-Shack patterns,” J. Opt. Soc. Am. A 21, 632-639 (2004).
    [CrossRef]
  14. Y. Carmon and E. N. Ribak, “Fast Fourier demodulation,” Appl. Phys. Lett. 84, 4656-4657 (2004).
    [CrossRef]
  15. E. N. Ribak, “Separating atmospheric layers in adaptive optics,” Opt. Lett. 28, 613-615 (2003).
    [CrossRef] [PubMed]

2008 (1)

2007 (1)

V. Albanis, E. N. Ribak, and Y. Carmon, “Reduction of speckles in retinal reflection,” Appl. Phys. Lett. 91, 054104(2007).
[CrossRef]

2006 (1)

I. Grulkowski and P. Kwiek, “Experimental study of light diffraction by standing ultrasonic wave with cylindrical symmetry,” Opt. Commun. 267, 14-19 (2006).
[CrossRef]

2004 (2)

A. Talmi and E. N. Ribak, “Direct demodulation of Hartmann-Shack patterns,” J. Opt. Soc. Am. A 21, 632-639 (2004).
[CrossRef]

Y. Carmon and E. N. Ribak, “Fast Fourier demodulation,” Appl. Phys. Lett. 84, 4656-4657 (2004).
[CrossRef]

2003 (2)

E. N. Ribak, “Separating atmospheric layers in adaptive optics,” Opt. Lett. 28, 613-615 (2003).
[CrossRef] [PubMed]

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215, 285-288(2003).
[CrossRef]

2001 (2)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573-577(2001).

E. N. Ribak, “Harnessing caustics for wavefront sensing,” Opt. Lett. 26, 1834-1836 (2001).
[CrossRef]

2000 (1)

1975 (1)

M. V. Berry, “Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces,” J. Phys. A 8, 566-584 (1975).
[CrossRef]

Albanis, V.

V. Albanis, E. N. Ribak, and Y. Carmon, “Reduction of speckles in retinal reflection,” Appl. Phys. Lett. 91, 054104(2007).
[CrossRef]

Artal, P.

Berry, M. V.

M. V. Berry, “Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces,” J. Phys. A 8, 566-584 (1975).
[CrossRef]

M. V. Berry and C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” in Progress in Optics E. Wolf, ed. (Elsevier, 1980), Vol. 18, pp. 257-346.
[CrossRef]

Carmon, Y.

V. Albanis, E. N. Ribak, and Y. Carmon, “Reduction of speckles in retinal reflection,” Appl. Phys. Lett. 91, 054104(2007).
[CrossRef]

Y. Carmon and E. N. Ribak, “Fast Fourier demodulation,” Appl. Phys. Lett. 84, 4656-4657 (2004).
[CrossRef]

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215, 285-288(2003).
[CrossRef]

Freund, I.

Goelz, S.

Grulkowski, I.

I. Grulkowski and P. Kwiek, “Experimental study of light diffraction by standing ultrasonic wave with cylindrical symmetry,” Opt. Commun. 267, 14-19 (2006).
[CrossRef]

Kessler, D. A.

Korpel, A.

A. Korpel, Acousto-Optics (CRC Press, 1997).

Kwiek, P.

I. Grulkowski and P. Kwiek, “Experimental study of light diffraction by standing ultrasonic wave with cylindrical symmetry,” Opt. Commun. 267, 14-19 (2006).
[CrossRef]

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573-577(2001).

Prieto, P. M.

Ribak, E. N.

V. Albanis, E. N. Ribak, and Y. Carmon, “Reduction of speckles in retinal reflection,” Appl. Phys. Lett. 91, 054104(2007).
[CrossRef]

Y. Carmon and E. N. Ribak, “Fast Fourier demodulation,” Appl. Phys. Lett. 84, 4656-4657 (2004).
[CrossRef]

A. Talmi and E. N. Ribak, “Direct demodulation of Hartmann-Shack patterns,” J. Opt. Soc. Am. A 21, 632-639 (2004).
[CrossRef]

E. N. Ribak, “Separating atmospheric layers in adaptive optics,” Opt. Lett. 28, 613-615 (2003).
[CrossRef] [PubMed]

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215, 285-288(2003).
[CrossRef]

E. N. Ribak, “Harnessing caustics for wavefront sensing,” Opt. Lett. 26, 1834-1836 (2001).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamental of Photonics (Wiley, 1991).
[CrossRef]

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573-577(2001).

Talmi, A.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamental of Photonics (Wiley, 1991).
[CrossRef]

Upstill, C.

M. V. Berry and C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” in Progress in Optics E. Wolf, ed. (Elsevier, 1980), Vol. 18, pp. 257-346.
[CrossRef]

Vargas-Martín, F.

Appl. Phys. Lett. (2)

V. Albanis, E. N. Ribak, and Y. Carmon, “Reduction of speckles in retinal reflection,” Appl. Phys. Lett. 91, 054104(2007).
[CrossRef]

Y. Carmon and E. N. Ribak, “Fast Fourier demodulation,” Appl. Phys. Lett. 84, 4656-4657 (2004).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Phys. A (1)

M. V. Berry, “Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces,” J. Phys. A 8, 566-584 (1975).
[CrossRef]

J. Refract. Surg. (1)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, 573-577(2001).

Opt. Commun. (2)

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215, 285-288(2003).
[CrossRef]

I. Grulkowski and P. Kwiek, “Experimental study of light diffraction by standing ultrasonic wave with cylindrical symmetry,” Opt. Commun. 267, 14-19 (2006).
[CrossRef]

Opt. Lett. (3)

Other (4)

M. V. Berry and C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” in Progress in Optics E. Wolf, ed. (Elsevier, 1980), Vol. 18, pp. 257-346.
[CrossRef]

B. E. A. Saleh and M. C. Teich, Fundamental of Photonics (Wiley, 1991).
[CrossRef]

A. Korpel, Acousto-Optics (CRC Press, 1997).

J.C.Dainty, ed., Laser Speckle and Related Phenomena (Springer, 1984).

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Figures (4)

Fig. 1
Fig. 1

(a)–(d) Reference images, white light: the power indicated is root-mean-square output, excluding returned power, which can be significant at resonance. (d) is magnified to show details. (e), (f) best ocular images, showing laser speckle–caustic interaction.

Fig. 2
Fig. 2

(a) An oscillating laser beam is scattered off the retina and reimaged by the acoustic wave into an array of retinal images to be imaged again by the camera. (b) Propagation of the two ocular planes: retinal (R) and corneal (C).

Fig. 3
Fig. 3

Focal length versus acoustic pitch. Scatter in the results is due to the large depth of focus of the caustics. The line fit is to F [ mm ] = 0.21 Δ [ μm ] = 16 / f [ MHz ] .

Fig. 4
Fig. 4

Hartmanngrams of (a) subject and (b) reference; (c) reconstruction, AOC frequency 3.543 MHz ; (d) reconstruction of the same subject at 3.74 MHz ; (e), (f) reconstructions from two more subjects at 3.2 MHz .

Equations (4)

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u D ( x , y ) = k , l = 1 N u k , l ( x , y ) k , l A k , l × exp { i κ [ θ x k , l ( x k Δ ) + θ y k , l ( y l Δ ) ] } ,
H ( x , y ) s ( x , y ) * k , l A k , l δ [ x ( k Δ + F θ x k , l ) , y ( l Δ + F θ y k , l ) ] .
Λ ( f ) = 2 π / K ( f ) = c ( H 2 O ) / f 2 Δ ( f ) .
n ( x , y , t ) = n 0 Δ n [ cos ( ω t K x ) + cos ( ω t K y ) ] .

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