Abstract

The extent to which holographic modal wavefront sensing can be applied to the detection of ocular aberrations was investigated. First, the idea of extending the dynamic range of the sensor by increasing the mask bias and the collection area of the pinhole detectors used in the sensor is reviewed. Errors in the detection of single-mode aberrations owing to reduced coherence from retinal scattering, photon, readout, and quantization noise are evaluated. A sensitivity-to-noise metric is introduced to evaluate sensor designs and is found to be maximized by using a pinhole detector radius of 8.6(fλNΔ) for every wave of mask bias (where f=transform lens focal length, λ=wavelength, and N and Δ are the number and size of the hologram pixels, respectively). The problem of detecting ocular aberrations composed of multiple modes required a generalization of the sensitivity measure to include all incident aberration modes. A “detect and correct” ocular aberration detection scheme was implemented that reduced the effects of cross talk and showed a maximum sensitivity-to-noise ratio of 40, which varied inversely with the size of the ocular aberration being detected.

© 2007 Optical Society of America

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References

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  1. H. Hofer, P. Artal, B. Singer, J. L. Aragón, and D. R. Williams, "Dynamics of the eye's wave aberration," J. Opt. Soc. Am. A 18, 497-506 (2001).
    [CrossRef]
  2. B. R. Brown and A. W. Lohmann, "Complex spatial filtering with binary masks," Appl. Opt. 5, 967-969 (1966).
    [CrossRef]
  3. T. D. Wilkinson and R. J. Mears, "Compact optical correlator using silicon backplane FLC SLMs for fingerprint recognition," Ferroelectrics 181, 47-52 (1996).
    [CrossRef]
  4. T. D. Wilkinson, D. C. O'Brien, and R. J. Mears, "Scale invariant binary phase-only matched filter using a ferroelectric liquid crystal spatial light modulator," Appl. Opt. 33, 4452-4453 (1993).
    [CrossRef]
  5. T. D. Wilkinson, Y. Petillot, R. J. Mears, and J. L. de Bougrenet de la Tocnaye, "Scale invariant optical correlators using ferroelectric liquid crystal spatial light modulators," Appl. Opt. 34, 1885-1890 (1995).
    [CrossRef] [PubMed]
  6. P. M. Blanchard, D. J. Fisher, S. C. Woods, and A. H. Greenaway, "Phase-diversity wave-front sensing with a distorted diffraction grating," Appl. Opt. 39, 6649-6655 (2000).
    [CrossRef]
  7. L. J. Otten, P. Soliz, I. McMakin, A. H. Greenaway, and P. M. Blanchard, "3-D cataract imaging system," in Proceedings of the 2nd International Workshop on Adaptive Optics for Industry and Medicine, G.D.Love, ed. (World Scientific, 1999), pp. 51-56.
  8. M. A. A. Neil, M. J. Booth, and T. Wilson, "New modal wave-front sensor: a theoretical analysis," J. Opt. Soc. Am. A 17, 1098-1107 (2000).
    [CrossRef]
  9. J. J. Zhong, D. Gil Leyva, A. D. Corbett, L. Diaz-Santana, and T. D. Wilkinson, "Mirror-mode sensing with a holographic modal wavefront sensor," Proc. SPIE 6018, 60181I (2005).
    [CrossRef]
  10. M. A. A. Neil, M. J. Booth, and T. Wilson, "Closed-loop aberration correction by use of a modal Zernike wave-front sensor," Opt. Lett. 25, 1083-1085 (2000).
    [CrossRef]
  11. M. J. Booth, M. A. A. Neil, and T. Wilson, "New modal wave-front sensor: application to adaptive confocal fluorescence microscopy and two-photon excitation fluorescence microscopy," J. Opt. Soc. Am. A 19, 2112-2120 (2002).
    [CrossRef]
  12. M. A. A. Neil, R. Juskaitis, M. J. Booth, T. Wilson, T. Tanaka, and S. Kawata, "Active aberration correction for the writing of three-dimensional optical memory devices," Appl. Opt. 41, 1374-1379 (2002).
    [CrossRef] [PubMed]
  13. M. J. Booth, "Direct measurement of Zernike aberration modes with a modal wavefront sensor," Proc. SPIE 5162, 79-90 (2003).
    [CrossRef]
  14. L. Diaz-Santana, G. Walker, and S. Bará, "Sampling geometries for ocular aberrometry: a model for evaluation of performance," Opt. Express 13, 8801-8818 (2005).
    [CrossRef] [PubMed]
  15. A. D. Corbett, D. G. Leyva, L. Diaz-Santana, T. D. Wilkinson, and J. J. Zhong, "Characterising a holographic modal phase mask for the detection of ocular aberrations," Proc. SPIE 6018, 601808 (2005).
    [CrossRef]
  16. American National Standards Institute "Ophthalmics--Methods for reporting optical aberrations of the eye," ANSI Z80, 28-2004 (ANSI, 2004), http://www.ansi.org/.
  17. P. Corke, "High-performance visual closed-loop robot control," Ph.D. thesis (University of Melbourne, 1994).
  18. S. Marcos, S. A. Burns, and J. C. He, "Model for cone directionality reflectometric measurements based on scattering," J. Opt. Soc. Am. A 15, 2012-2022 (1998).
    [CrossRef]
  19. F. Romero-Borja, K. Venkateswaran, A. Roorda, and T. Hebert, "Optical slicing of human retinal tissue in vivo with the adaptive optics scanning laser ophthalmoscope," Appl. Opt. 44, 4032-4040 (2005).
    [CrossRef] [PubMed]

2005 (4)

J. J. Zhong, D. Gil Leyva, A. D. Corbett, L. Diaz-Santana, and T. D. Wilkinson, "Mirror-mode sensing with a holographic modal wavefront sensor," Proc. SPIE 6018, 60181I (2005).
[CrossRef]

L. Diaz-Santana, G. Walker, and S. Bará, "Sampling geometries for ocular aberrometry: a model for evaluation of performance," Opt. Express 13, 8801-8818 (2005).
[CrossRef] [PubMed]

A. D. Corbett, D. G. Leyva, L. Diaz-Santana, T. D. Wilkinson, and J. J. Zhong, "Characterising a holographic modal phase mask for the detection of ocular aberrations," Proc. SPIE 6018, 601808 (2005).
[CrossRef]

F. Romero-Borja, K. Venkateswaran, A. Roorda, and T. Hebert, "Optical slicing of human retinal tissue in vivo with the adaptive optics scanning laser ophthalmoscope," Appl. Opt. 44, 4032-4040 (2005).
[CrossRef] [PubMed]

2003 (1)

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

2002 (2)

2001 (1)

2000 (3)

1998 (1)

1996 (1)

T. D. Wilkinson and R. J. Mears, "Compact optical correlator using silicon backplane FLC SLMs for fingerprint recognition," Ferroelectrics 181, 47-52 (1996).
[CrossRef]

1995 (1)

1993 (1)

1966 (1)

Aragón, J. L.

Artal, P.

Bará, S.

Blanchard, P. M.

P. M. Blanchard, D. J. Fisher, S. C. Woods, and A. H. Greenaway, "Phase-diversity wave-front sensing with a distorted diffraction grating," Appl. Opt. 39, 6649-6655 (2000).
[CrossRef]

L. J. Otten, P. Soliz, I. McMakin, A. H. Greenaway, and P. M. Blanchard, "3-D cataract imaging system," in Proceedings of the 2nd International Workshop on Adaptive Optics for Industry and Medicine, G.D.Love, ed. (World Scientific, 1999), pp. 51-56.

Booth, M. J.

Brown, B. R.

Burns, S. A.

Corbett, A. D.

A. D. Corbett, D. G. Leyva, L. Diaz-Santana, T. D. Wilkinson, and J. J. Zhong, "Characterising a holographic modal phase mask for the detection of ocular aberrations," Proc. SPIE 6018, 601808 (2005).
[CrossRef]

J. J. Zhong, D. Gil Leyva, A. D. Corbett, L. Diaz-Santana, and T. D. Wilkinson, "Mirror-mode sensing with a holographic modal wavefront sensor," Proc. SPIE 6018, 60181I (2005).
[CrossRef]

Corke, P.

P. Corke, "High-performance visual closed-loop robot control," Ph.D. thesis (University of Melbourne, 1994).

de Bougrenet de la Tocnaye, J. L.

Diaz-Santana, L.

J. J. Zhong, D. Gil Leyva, A. D. Corbett, L. Diaz-Santana, and T. D. Wilkinson, "Mirror-mode sensing with a holographic modal wavefront sensor," Proc. SPIE 6018, 60181I (2005).
[CrossRef]

A. D. Corbett, D. G. Leyva, L. Diaz-Santana, T. D. Wilkinson, and J. J. Zhong, "Characterising a holographic modal phase mask for the detection of ocular aberrations," Proc. SPIE 6018, 601808 (2005).
[CrossRef]

L. Diaz-Santana, G. Walker, and S. Bará, "Sampling geometries for ocular aberrometry: a model for evaluation of performance," Opt. Express 13, 8801-8818 (2005).
[CrossRef] [PubMed]

Fisher, D. J.

Gil Leyva, D.

J. J. Zhong, D. Gil Leyva, A. D. Corbett, L. Diaz-Santana, and T. D. Wilkinson, "Mirror-mode sensing with a holographic modal wavefront sensor," Proc. SPIE 6018, 60181I (2005).
[CrossRef]

Greenaway, A. H.

P. M. Blanchard, D. J. Fisher, S. C. Woods, and A. H. Greenaway, "Phase-diversity wave-front sensing with a distorted diffraction grating," Appl. Opt. 39, 6649-6655 (2000).
[CrossRef]

L. J. Otten, P. Soliz, I. McMakin, A. H. Greenaway, and P. M. Blanchard, "3-D cataract imaging system," in Proceedings of the 2nd International Workshop on Adaptive Optics for Industry and Medicine, G.D.Love, ed. (World Scientific, 1999), pp. 51-56.

He, J. C.

Hebert, T.

Hofer, H.

Juskaitis, R.

Kawata, S.

Leyva, D. G.

A. D. Corbett, D. G. Leyva, L. Diaz-Santana, T. D. Wilkinson, and J. J. Zhong, "Characterising a holographic modal phase mask for the detection of ocular aberrations," Proc. SPIE 6018, 601808 (2005).
[CrossRef]

Lohmann, A. W.

Marcos, S.

McMakin, I.

L. J. Otten, P. Soliz, I. McMakin, A. H. Greenaway, and P. M. Blanchard, "3-D cataract imaging system," in Proceedings of the 2nd International Workshop on Adaptive Optics for Industry and Medicine, G.D.Love, ed. (World Scientific, 1999), pp. 51-56.

Mears, R. J.

Neil, M. A. A.

O'Brien, D. C.

Otten, L. J.

L. J. Otten, P. Soliz, I. McMakin, A. H. Greenaway, and P. M. Blanchard, "3-D cataract imaging system," in Proceedings of the 2nd International Workshop on Adaptive Optics for Industry and Medicine, G.D.Love, ed. (World Scientific, 1999), pp. 51-56.

Petillot, Y.

Romero-Borja, F.

Roorda, A.

Singer, B.

Soliz, P.

L. J. Otten, P. Soliz, I. McMakin, A. H. Greenaway, and P. M. Blanchard, "3-D cataract imaging system," in Proceedings of the 2nd International Workshop on Adaptive Optics for Industry and Medicine, G.D.Love, ed. (World Scientific, 1999), pp. 51-56.

Tanaka, T.

Venkateswaran, K.

Walker, G.

Wilkinson, T. D.

A. D. Corbett, D. G. Leyva, L. Diaz-Santana, T. D. Wilkinson, and J. J. Zhong, "Characterising a holographic modal phase mask for the detection of ocular aberrations," Proc. SPIE 6018, 601808 (2005).
[CrossRef]

J. J. Zhong, D. Gil Leyva, A. D. Corbett, L. Diaz-Santana, and T. D. Wilkinson, "Mirror-mode sensing with a holographic modal wavefront sensor," Proc. SPIE 6018, 60181I (2005).
[CrossRef]

T. D. Wilkinson and R. J. Mears, "Compact optical correlator using silicon backplane FLC SLMs for fingerprint recognition," Ferroelectrics 181, 47-52 (1996).
[CrossRef]

T. D. Wilkinson, Y. Petillot, R. J. Mears, and J. L. de Bougrenet de la Tocnaye, "Scale invariant optical correlators using ferroelectric liquid crystal spatial light modulators," Appl. Opt. 34, 1885-1890 (1995).
[CrossRef] [PubMed]

T. D. Wilkinson, D. C. O'Brien, and R. J. Mears, "Scale invariant binary phase-only matched filter using a ferroelectric liquid crystal spatial light modulator," Appl. Opt. 33, 4452-4453 (1993).
[CrossRef]

Williams, D. R.

Wilson, T.

Woods, S. C.

Zhong, J. J.

J. J. Zhong, D. Gil Leyva, A. D. Corbett, L. Diaz-Santana, and T. D. Wilkinson, "Mirror-mode sensing with a holographic modal wavefront sensor," Proc. SPIE 6018, 60181I (2005).
[CrossRef]

A. D. Corbett, D. G. Leyva, L. Diaz-Santana, T. D. Wilkinson, and J. J. Zhong, "Characterising a holographic modal phase mask for the detection of ocular aberrations," Proc. SPIE 6018, 601808 (2005).
[CrossRef]

Appl. Opt. (6)

Ferroelectrics (1)

T. D. Wilkinson and R. J. Mears, "Compact optical correlator using silicon backplane FLC SLMs for fingerprint recognition," Ferroelectrics 181, 47-52 (1996).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (3)

J. J. Zhong, D. Gil Leyva, A. D. Corbett, L. Diaz-Santana, and T. D. Wilkinson, "Mirror-mode sensing with a holographic modal wavefront sensor," Proc. SPIE 6018, 60181I (2005).
[CrossRef]

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

A. D. Corbett, D. G. Leyva, L. Diaz-Santana, T. D. Wilkinson, and J. J. Zhong, "Characterising a holographic modal phase mask for the detection of ocular aberrations," Proc. SPIE 6018, 601808 (2005).
[CrossRef]

Other (3)

American National Standards Institute "Ophthalmics--Methods for reporting optical aberrations of the eye," ANSI Z80, 28-2004 (ANSI, 2004), http://www.ansi.org/.

P. Corke, "High-performance visual closed-loop robot control," Ph.D. thesis (University of Melbourne, 1994).

L. J. Otten, P. Soliz, I. McMakin, A. H. Greenaway, and P. M. Blanchard, "3-D cataract imaging system," in Proceedings of the 2nd International Workshop on Adaptive Optics for Industry and Medicine, G.D.Love, ed. (World Scientific, 1999), pp. 51-56.

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Figures (12)

Fig. 1
Fig. 1

Schematic representation of the effect of biasing (adapted from Ref. [8]).

Fig. 2
Fig. 2

Relation between the detector response curve of a sensor with mask bias b (solid curve) and the normal distribution of aberration mode coefficients with standard deviation σ pop (dashed curve).

Fig. 3
Fig. 3

Schematic diagram of the HMWFS system. From left to right, the modeled components include the ocular wavefront, the SLM, the transform lens of focal length f, and the detection of the replay field by a CCD camera.

Fig. 4
Fig. 4

Histograms showing population frequency against aberration size (in micrometers) in the City data set for Zernike modes increasing left–right and top–bottom from Z 1 , 1 to Z 4 , 4 .

Fig. 5
Fig. 5

Output curves for a Z 2 , 2 sensor with different values of dynamic range. It can be seen that the gradient of the response curves falls with increasing dynamic range.

Fig. 6
Fig. 6

Sensitivity matrices showing how the sensitivity of a mask with a bias mode given by the position along the y axis varies with an input aberration with a mode given by the position along the x axis. Shown above are matrices for sensors (top left–bottom right) 1, 2, 3, and 5 used in Ref. [14] with dynamic ranges of 0.12, 0.24, 0.52, and 1.24 waves, respectively. The maximum sensitivity values in each matrix are 0.31, 0.14, 0.12, and 0.1, respectively.

Fig. 7
Fig. 7

Demonstration of the relationship between the RMS error in the output signal, σ Δ W , to the RMS error in the input aberration coefficient, σ a , through the sensitivity, S.

Fig. 8
Fig. 8

Independent contributions to the RMS output signal error (vertical axis, in photons) for a range of mask biases (left axis, waves) and pinhole sizes (right axis, pixels) for a Zernike mode (2,2) mask bias. (a) Quantization noise, (b) readout noise, (c) photon noise (in log photons).

Fig. 9
Fig. 9

Top row: Mesh grids showing the variation in mode-averaged (a) sensitivity, (b) noise, and (c) SNR for different values of mask bias (left lower axis, waves) and pinhole size (right lower axis, pixels). (d) Pinhole size that, for each mask bias value, maximizes the sensitivity (dots, ± 2   pixels ), noise (stars, ± 0   pixels ), and SNR (circles, ± 3   pixels ). The last two panels show for each value of the mask bias the maximum values of (e) sensitivity and (f) SNR.

Fig. 10
Fig. 10

Variation in (a) the average output signal and (b) the output signal variance with the number of averaged frames. (c) Logarithmic representation of (b) showing the intercept with the baseline photon noise variability.

Fig. 11
Fig. 11

Results of total error calculation averaged across all subjects and modes: (a) sensitivity, (b) RMS aberration coefficient error, (c) SNR. (d) Variation in optimal value of the pinhole size with sensitivity (dots, ± 10   pixel ), RMS error (stars, ± 20   pixels ), and SNR (circles, ± 15   pixels ). Maximum values of the sensitivity (e) and SNR (f) with respect to pinhole size for different mask biases are also shown.

Fig. 12
Fig. 12

Demonstration of the variation in the optimum SNR against mask bias for different modes. These include Z 2 , 0 (dots), Z 2 , 2 (stars), Z 2 , 2 (circles), Z 3 , 1 (pluses), Z 3 , 3 (squares).

Tables (1)

Tables Icon

Table 1 City Data Set Mean Values and Standard Deviations of the Zernike Polynomial Coefficients for Mode Z 2 , 0 to Z 3 , 3

Equations (11)

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I 1 , 2 ( ν , ξ ) = I 0 2 8 π 3 F T [ exp ( j a Z k ( r , θ ) ± j b Z i ( r , θ ) ) ] 2 ,
S = ( I 1 I 2 ) a a = 0 ,
I 1 , 2 a a = 0 = I 0 4 π 3 Im { F T [ exp ( ± j b Z i ( r , θ ) ) ] × F T [ Z ̃ k exp ( j b Z i ( r , θ ) ) ] } ,
Z ̃ k ( r , θ ) = Z k ( r , θ + π ) .
I 1 , 2 a a = 0 = I 0 4 π 3 Re { DFT [ U ( r , θ ) ] × DFT 1 [ j Z ̃ k U * ( r , θ ) ] } ,
I 1 , 2 ( ν , ξ ) = I 0 8 π 3 FT [ exp ( j a Z k ( r , θ ) + i k j c l Z l ( r , θ ) ± j b Z i ( r , θ ) ) ] 2 ,
I 1 , 2 a a = 0 = I 0 4 π 3 Im { FT [ exp ( + l k j c l Z l ( r , θ ) ± j b Z i ( r , θ ) ) ] FT [ Z ̃ k exp ( + l k j c l Z l ( r , θ ) j b Z i ( r , θ ) ) ] } ,
I 1 , 2 a a = 0 pop = I 0 4 π 3 Im { FT [ exp ( + l k j c l Z l ( r , θ ) ± j b Z i ( r , θ ) ) ] FT [ Z ̃ k exp ( + l k j c l Z l ( r , θ ) j b Z i ( r , θ ) ) ] } pop ,
I 1 , 2 a a = 0 pop = I 0 4 π 3 Im { FT [ exp ( + l k j c l Z l ( r , θ ) pop ± j b Z i ( r , θ ) ) ] FT [ Z ̃ k exp ( + l k j c l Z l ( r , θ ) pop j b Z i ( r , θ ) ) ] } ,
c l pop = 0 l ,
I 1 , 2 a a = 0 = I 0 4 π 3 Im { FT [ exp ( ± j b Z i ( r , θ ) ) ] FT [ Z ̃ k exp ( j b Z i ( r , θ ) ) ] } ,

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