Abstract

Purpose: the method described here allows for automatic calculation of the fundus pulse from interferometric measurements. Method: a low intensity laser beam is coupled into the eye. Two strong reflections, one of the cornea and one of the retina, interfere on a high-speed complementary metal-oxide-semiconductor camera chip. After eye movement compensation, a speckle-free phase of the interferograms is calculated from a series of interference fringes. Then, the fundus pulsation is calculated from the phase shift between two consecutive interferograms. Problems: occurring speckle perturbs the fringe images, and therefore, classical geometrical movement compensation algorithms do not work with sufficient accuracy. The movement compensation algorithm needs to work without prior knowledge of the phase. Results: the proposed algorithms yield the fundus pulse from speckled interferograms, overcoming the above mentioned problems.

© 2011 Optical Society of America

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References

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  1. A. F. Fercher, “Invivo measurement of fundus pulsations by laser interferometry,” IEEE J. Quantum Electron. 20, 1469–1471(1984).
    [CrossRef]
  2. L. Schmetterer, F. Lexer, C. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711 (1995).
    [CrossRef]
  3. S. Dallinger, O. Findl, K. Strenn, H.-G. Eichler, M. Wolzt, and L. Schmetterer, “Age dependence of choroidal blood flow,” J. Am. Geriatr. Soc. 46, 484–487 (1998).
    [PubMed]
  4. A. Hommer, G. Fuchsjäger-Mayrl, H. Resch, C. Vass, G. Garhofer, and L. Schmetterer, “Estimation of ocular rigidity based on measurement of pulse amplitude using pneumotonometry and fundus pulse using laser interferometry in glaucoma,” Invest. Ophthalmol. Vis. Sci. 49, 4046–4050 (2008).
    [CrossRef] [PubMed]
  5. J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006).
  6. A. Malz, P. Boll, I. Eix, W. Stork, and K.-D. Müller-Glaser, “Research training group 1126: intelligent surgery,” Int. J. Comput. Assisted Radiol. Surg. 3, 138–144 (2008).
    [CrossRef]
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    [CrossRef]
  9. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. J. Zhong and J. Weng, “Phase retrieval of optical fringe patterns from the ridge of a wavelet transform,” Opt. Lett. 30, 2560–2562 (2005).
    [CrossRef] [PubMed]
  12. L. R. van den Doel, P. T. Nagy, L. J. van Vliet, and P. Neitzel, “Regularized phase tracker with isophase scanning strategy for analysis of dynamic interferograms of nonwetting droplets under excitation,” Appl. Opt. 44, 2695–2704 (2005).
    [CrossRef] [PubMed]
  13. J. L. Marroquin, M. Servin, and R. Rodriguez-Vera, “Adaptive quadrature filters and the recovery of phase from fringe pattern images,” J. Opt. Soc. Am. A 14, 1742–1753 (1997).
    [CrossRef]
  14. C. Quan, C. J. Tay, F. Yang, and X. He, “Phase extraction from a single fringe pattern based on guidance of an extreme map,” Appl. Opt. 44, 4814–4821 (2005).
    [CrossRef] [PubMed]
  15. E. Robin, V. Valle, and F. Brémand, “Phase demodulation method from a single fringe pattern based on correlation with a polynomial form,” Appl. Opt. 44, 7261–7269 (2005).
    [CrossRef] [PubMed]
  16. J. Meneses, T. Gharbi, and P. Humbert, “Phase-unwrapping algorithm for images with high noise content based on a local histogram,” Appl. Opt. 44, 1207–1215 (2005).
    [CrossRef] [PubMed]
  17. Q. Yu, K. Andresen, W. Osten, and W. P. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
    [CrossRef]
  18. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36, 4540–4548 (1997).
    [CrossRef] [PubMed]
  19. J. L. Marroquin, M. Servin, and R. R. Vera, “Adaptive quadrature filters for multiple phase-stepping images,” J. Opt. Soc. Am. A 14, 1742–1753 (1997).
    [CrossRef]
  20. M. Servin, J. L. Marroquin, and F. J. Cuevas, “Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms,” J. Opt. Soc. Am. A 18, 689–695 (2001).
    [CrossRef]
  21. M. Servin, J. A. Quiroga, and J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 925–934(2003).
    [CrossRef]
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    [CrossRef] [PubMed]

2009 (1)

2008 (2)

A. Hommer, G. Fuchsjäger-Mayrl, H. Resch, C. Vass, G. Garhofer, and L. Schmetterer, “Estimation of ocular rigidity based on measurement of pulse amplitude using pneumotonometry and fundus pulse using laser interferometry in glaucoma,” Invest. Ophthalmol. Vis. Sci. 49, 4046–4050 (2008).
[CrossRef] [PubMed]

A. Malz, P. Boll, I. Eix, W. Stork, and K.-D. Müller-Glaser, “Research training group 1126: intelligent surgery,” Int. J. Comput. Assisted Radiol. Surg. 3, 138–144 (2008).
[CrossRef]

2006 (1)

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006).

2005 (6)

2004 (1)

2003 (1)

2001 (1)

1998 (1)

S. Dallinger, O. Findl, K. Strenn, H.-G. Eichler, M. Wolzt, and L. Schmetterer, “Age dependence of choroidal blood flow,” J. Am. Geriatr. Soc. 46, 484–487 (1998).
[PubMed]

1997 (3)

1995 (1)

L. Schmetterer, F. Lexer, C. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711 (1995).
[CrossRef]

1994 (1)

Q. Yu, K. Andresen, W. Osten, and W. P. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
[CrossRef]

1984 (1)

A. F. Fercher, “Invivo measurement of fundus pulsations by laser interferometry,” IEEE J. Quantum Electron. 20, 1469–1471(1984).
[CrossRef]

1982 (1)

1978 (1)

A. W. Lohmann, “Optical information processing,” Lecture Notes, 2nd ed. (Physikalisches Institut der Universität Erlangen, 1978), pp. 22–25.

Andresen, K.

Q. Yu, K. Andresen, W. Osten, and W. P. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
[CrossRef]

Boll, P.

A. Malz, P. Boll, I. Eix, W. Stork, and K.-D. Müller-Glaser, “Research training group 1126: intelligent surgery,” Int. J. Comput. Assisted Radiol. Surg. 3, 138–144 (2008).
[CrossRef]

Brémand, F.

Chen, L.

Cuevas, F. J.

Dallinger, S.

S. Dallinger, O. Findl, K. Strenn, H.-G. Eichler, M. Wolzt, and L. Schmetterer, “Age dependence of choroidal blood flow,” J. Am. Geriatr. Soc. 46, 484–487 (1998).
[PubMed]

Eichler, H.-G.

S. Dallinger, O. Findl, K. Strenn, H.-G. Eichler, M. Wolzt, and L. Schmetterer, “Age dependence of choroidal blood flow,” J. Am. Geriatr. Soc. 46, 484–487 (1998).
[PubMed]

Eix, I.

A. Malz, P. Boll, I. Eix, W. Stork, and K.-D. Müller-Glaser, “Research training group 1126: intelligent surgery,” Int. J. Comput. Assisted Radiol. Surg. 3, 138–144 (2008).
[CrossRef]

Estrada, J. C.

Fercher, A. F.

L. Schmetterer, F. Lexer, C. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711 (1995).
[CrossRef]

A. F. Fercher, “Invivo measurement of fundus pulsations by laser interferometry,” IEEE J. Quantum Electron. 20, 1469–1471(1984).
[CrossRef]

Findl, O.

S. Dallinger, O. Findl, K. Strenn, H.-G. Eichler, M. Wolzt, and L. Schmetterer, “Age dependence of choroidal blood flow,” J. Am. Geriatr. Soc. 46, 484–487 (1998).
[PubMed]

Fuchsjäger-Mayrl, G.

A. Hommer, G. Fuchsjäger-Mayrl, H. Resch, C. Vass, G. Garhofer, and L. Schmetterer, “Estimation of ocular rigidity based on measurement of pulse amplitude using pneumotonometry and fundus pulse using laser interferometry in glaucoma,” Invest. Ophthalmol. Vis. Sci. 49, 4046–4050 (2008).
[CrossRef] [PubMed]

Garhofer, G.

A. Hommer, G. Fuchsjäger-Mayrl, H. Resch, C. Vass, G. Garhofer, and L. Schmetterer, “Estimation of ocular rigidity based on measurement of pulse amplitude using pneumotonometry and fundus pulse using laser interferometry in glaucoma,” Invest. Ophthalmol. Vis. Sci. 49, 4046–4050 (2008).
[CrossRef] [PubMed]

Gharbi, T.

Gomez-Pedrero, J. A.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006).

He, X.

Hommer, A.

A. Hommer, G. Fuchsjäger-Mayrl, H. Resch, C. Vass, G. Garhofer, and L. Schmetterer, “Estimation of ocular rigidity based on measurement of pulse amplitude using pneumotonometry and fundus pulse using laser interferometry in glaucoma,” Invest. Ophthalmol. Vis. Sci. 49, 4046–4050 (2008).
[CrossRef] [PubMed]

Humbert, P.

Ina, H.

Jueptner, W. P.

Q. Yu, K. Andresen, W. Osten, and W. P. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
[CrossRef]

Kemao, Q.

Kobayashi, S.

Lexer, F.

L. Schmetterer, F. Lexer, C. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711 (1995).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann, “Optical information processing,” Lecture Notes, 2nd ed. (Physikalisches Institut der Universität Erlangen, 1978), pp. 22–25.

Malz, A.

A. Malz, P. Boll, I. Eix, W. Stork, and K.-D. Müller-Glaser, “Research training group 1126: intelligent surgery,” Int. J. Comput. Assisted Radiol. Surg. 3, 138–144 (2008).
[CrossRef]

Marroquin, J. L.

Meneses, J.

Müller-Glaser, K.-D.

A. Malz, P. Boll, I. Eix, W. Stork, and K.-D. Müller-Glaser, “Research training group 1126: intelligent surgery,” Int. J. Comput. Assisted Radiol. Surg. 3, 138–144 (2008).
[CrossRef]

Nagy, P. T.

Neitzel, P.

Osten, W.

Q. Yu, K. Andresen, W. Osten, and W. P. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
[CrossRef]

Quan, C.

Quiroga, J. A.

Resch, H.

A. Hommer, G. Fuchsjäger-Mayrl, H. Resch, C. Vass, G. Garhofer, and L. Schmetterer, “Estimation of ocular rigidity based on measurement of pulse amplitude using pneumotonometry and fundus pulse using laser interferometry in glaucoma,” Invest. Ophthalmol. Vis. Sci. 49, 4046–4050 (2008).
[CrossRef] [PubMed]

Robin, E.

Rodriguez-Vera, R.

Sattmann, H.

L. Schmetterer, F. Lexer, C. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711 (1995).
[CrossRef]

Schmetterer, L.

A. Hommer, G. Fuchsjäger-Mayrl, H. Resch, C. Vass, G. Garhofer, and L. Schmetterer, “Estimation of ocular rigidity based on measurement of pulse amplitude using pneumotonometry and fundus pulse using laser interferometry in glaucoma,” Invest. Ophthalmol. Vis. Sci. 49, 4046–4050 (2008).
[CrossRef] [PubMed]

S. Dallinger, O. Findl, K. Strenn, H.-G. Eichler, M. Wolzt, and L. Schmetterer, “Age dependence of choroidal blood flow,” J. Am. Geriatr. Soc. 46, 484–487 (1998).
[PubMed]

L. Schmetterer, F. Lexer, C. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711 (1995).
[CrossRef]

Servin, M.

Stork, W.

A. Malz, P. Boll, I. Eix, W. Stork, and K.-D. Müller-Glaser, “Research training group 1126: intelligent surgery,” Int. J. Comput. Assisted Radiol. Surg. 3, 138–144 (2008).
[CrossRef]

Strenn, K.

S. Dallinger, O. Findl, K. Strenn, H.-G. Eichler, M. Wolzt, and L. Schmetterer, “Age dependence of choroidal blood flow,” J. Am. Geriatr. Soc. 46, 484–487 (1998).
[PubMed]

Takeda, M.

Tay, C. J.

Unfried, C.

L. Schmetterer, F. Lexer, C. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711 (1995).
[CrossRef]

Valle, V.

van den Doel, L. R.

van Vliet, L. J.

Vass, C.

A. Hommer, G. Fuchsjäger-Mayrl, H. Resch, C. Vass, G. Garhofer, and L. Schmetterer, “Estimation of ocular rigidity based on measurement of pulse amplitude using pneumotonometry and fundus pulse using laser interferometry in glaucoma,” Invest. Ophthalmol. Vis. Sci. 49, 4046–4050 (2008).
[CrossRef] [PubMed]

Vera, R. R.

Weng, J.

Wolzt, M.

S. Dallinger, O. Findl, K. Strenn, H.-G. Eichler, M. Wolzt, and L. Schmetterer, “Age dependence of choroidal blood flow,” J. Am. Geriatr. Soc. 46, 484–487 (1998).
[PubMed]

Yang, F.

Yu, Q.

Q. Yu, K. Andresen, W. Osten, and W. P. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
[CrossRef]

Zhong, J.

Appl. Opt. (8)

M. Servin, J. L. Marroquin, and F. J. Cuevas, “Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique,” Appl. Opt. 36, 4540–4548 (1997).
[CrossRef] [PubMed]

Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
[CrossRef] [PubMed]

J. Meneses, T. Gharbi, and P. Humbert, “Phase-unwrapping algorithm for images with high noise content based on a local histogram,” Appl. Opt. 44, 1207–1215 (2005).
[CrossRef] [PubMed]

C. Quan, C. J. Tay, and L. Chen, “Fringe-density estimation by continuous wavelet transform,” Appl. Opt. 44, 2359–2365(2005).
[CrossRef] [PubMed]

L. R. van den Doel, P. T. Nagy, L. J. van Vliet, and P. Neitzel, “Regularized phase tracker with isophase scanning strategy for analysis of dynamic interferograms of nonwetting droplets under excitation,” Appl. Opt. 44, 2695–2704 (2005).
[CrossRef] [PubMed]

C. Quan, C. J. Tay, F. Yang, and X. He, “Phase extraction from a single fringe pattern based on guidance of an extreme map,” Appl. Opt. 44, 4814–4821 (2005).
[CrossRef] [PubMed]

E. Robin, V. Valle, and F. Brémand, “Phase demodulation method from a single fringe pattern based on correlation with a polynomial form,” Appl. Opt. 44, 7261–7269 (2005).
[CrossRef] [PubMed]

J. A. Quiroga, M. Servin, J. C. Estrada, and J. A. Gomez-Pedrero, “Steerable spatial phase shifting applied to single-image closed-fringe interferograms,” Appl. Opt. 48, 2401–2409 (2009).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

A. F. Fercher, “Invivo measurement of fundus pulsations by laser interferometry,” IEEE J. Quantum Electron. 20, 1469–1471(1984).
[CrossRef]

Int. J. Comput. Assisted Radiol. Surg. (1)

A. Malz, P. Boll, I. Eix, W. Stork, and K.-D. Müller-Glaser, “Research training group 1126: intelligent surgery,” Int. J. Comput. Assisted Radiol. Surg. 3, 138–144 (2008).
[CrossRef]

Invest. Ophthalmol. Vis. Sci. (1)

A. Hommer, G. Fuchsjäger-Mayrl, H. Resch, C. Vass, G. Garhofer, and L. Schmetterer, “Estimation of ocular rigidity based on measurement of pulse amplitude using pneumotonometry and fundus pulse using laser interferometry in glaucoma,” Invest. Ophthalmol. Vis. Sci. 49, 4046–4050 (2008).
[CrossRef] [PubMed]

J. Am. Geriatr. Soc. (1)

S. Dallinger, O. Findl, K. Strenn, H.-G. Eichler, M. Wolzt, and L. Schmetterer, “Age dependence of choroidal blood flow,” J. Am. Geriatr. Soc. 46, 484–487 (1998).
[PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Eng. (2)

Q. Yu, K. Andresen, W. Osten, and W. P. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
[CrossRef]

L. Schmetterer, F. Lexer, C. Unfried, H. Sattmann, and A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711 (1995).
[CrossRef]

Opt. Lett. (1)

Other (2)

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2006).

A. W. Lohmann, “Optical information processing,” Lecture Notes, 2nd ed. (Physikalisches Institut der Universität Erlangen, 1978), pp. 22–25.

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Figures (12)

Fig. 1
Fig. 1

Fundus pulsation measurement setup.

Fig. 2
Fig. 2

Typical interference image, 144 × 144 pixel, intensity resolution 7   bit depending on sample rate and image size.

Fig. 3
Fig. 3

Phase differences, cut of approximately rotationally symmetric phase φ d ( x , y , t ) .

Fig. 4
Fig. 4

Fringe pattern containing nonclosed fringes due to speckle.

Fig. 5
Fig. 5

Simulated nonclosed fringes.

Fig. 6
Fig. 6

Simulated interference patterns for different values of phase offset φ o (upper row) and computed Schuster fringes moiré pattern with equal moiré phase (lower row).

Fig. 7
Fig. 7

(a) Phase (wrapped), (b) phase signal added with noise (variance 20), (c) estimated cosine, and (d) sine component for phase estimation gained by averaging 4000 samples.

Fig. 8
Fig. 8

Autocorrelation of the cosine of the parabolic phase φ s ( x , y ) .

Fig. 9
Fig. 9

Movement compensation along the x and y axis (unfiltered, zero mean).

Fig. 10
Fig. 10

(a) Cosine and (b) sine component for the estimated phase, (c) estimated phase (wrapped, before smoothing), and (d) corresponding estimated local modulation.

Fig. 11
Fig. 11

Estimated phase offset differences Δ φ o , k ( t ) .

Fig. 12
Fig. 12

Fundus pulse curve.

Equations (17)

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

I c ( x , y , t ) = c ( x , y ) · cos ( φ d ( x , y , t ) ) + ε ( x , y , t ) .
I k ( x , y ) = c k ( x , y ) · cos ( φ s ( x , y ) + φ k ) + ε k ( x , y ) k = 1 n .
I ¯ ( x , y ) = 1 m k = 1 m I k ( x , y ) 0.
COR k = x y I c ( x , y ) · I k ( x , y ) .
SET c + = { I k , COR k > 0 φ k π 4 < φ c < φ k + π 4 } .
SET c = { I k , COR k < 0 φ k π 4 < φ c π < φ k + π 4 } .
I ¯ c ( x , y ) = 1 n ( I k SET c + I k ( x , y ) I k SET c I k ( x , y ) ) .
I ¯ c ( x , y ) = c c ( x , y ) · cos ( φ s ( x , y ) + φ c ) .
I ¯ s ( x , y ) = c s ( x , y ) · cos ( φ s ( x , y ) + φ c ± π 2 ) = ± c s ( x , y ) · sin ( φ s ( x , y ) + φ c ) ,
SET c 0 = { I k , tr < COR k < tr φ k π 4 · r < φ c π 2 < φ k + π 4 · r ; φ k π 4 · r < φ c 3 π 2 < φ k + π 4 · r } .
tr = 1 m k = 1 m | COR k | .
CORS k = x y I s ( x , y ) · I k ( x , y ) | I k SET c 0 .
c c ( x , y ) c s ( x , y ) .
± ( φ s , est ( x , y ) + φ c ) 2 π = angle ( I ¯ c + i · I ¯ s ) .
CORT k ( x , y ) = F 1 { F { I k } · { cos ( φ s ( x , y ) ) } } + i · F 1 { F { I k } · { sin ( φ s ( x , y ) ) } } .
[ x , y ] = max x , y ( A k ( x , y ) · A k 1 ( x , y ) ) .
fp ( t ) = fp ( t Δ t ) + λ 2 · Δ φ o , k 2 π .

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