Abstract

A comparison and validation study of Laser Ray Tracing (LRT) and Hartmann–Shack wave-front-sensor (to be referred to as H–S) methods was carried out on both artificial and human eyes. The aim of this work was double. First, we wanted to verify experimentally the equivalence of single- and double-pass measurements for both H–S and LRT. This interest is due to the impossibility of making single-pass measurements in human eyes. In addition, we wanted to validate the LRT technique by comparing it with the H–S wave-front sensor, currently used in many physiological optics laboratories. Comparison of the different methods and configurations carried out in the artificial eye yielded basically the same results in all cases, which means a reciprocal validation of both LRT and H–S, in either single- or double-pass configurations. Other aspects, such as robustness against speckle noise or the influence of the size of the entrance (H–S) or exit (LRT) pupil were studied as well. As a global reference, the point-spread function (PSF) of the artificial eye was recorded directly on a CCD camera and compared with simulated PSF’s computed from the experimental aberration data. We also applied these two methods to real eyes (double pass), finding again a close match between the resulting aberration coefficients and also between the standard errors for two normal subjects. However, for one myopic eye with an especially low optical quality (RMS wave-front error >2 μm) and asymmetric aberrations, the array of spots recorded with the H–S sensor was highly distorted and too difficult to analyze.

© 2000 Optical Society of America

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References

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  1. J. Liang, D. R. Williams, D. Miller, “Supernormal vision and high resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
    [CrossRef]
  2. L. Zhu, P. C. Sun, D.-U. Bartsch, W. R. Freeman, Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
    [CrossRef]
  3. R. Navarro, E. Moreno-Barriuso, S. Bará, T. Mancebo, “Phase plates for wave-aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000).
    [CrossRef]
  4. T. Young, “On the mechanisms of the eye,” Philos. Trans. R. Soc. London 19, 23–88 (1801).
    [CrossRef]
  5. A. Ivanoff, Les aberrations de l’oeil. Leur role dans l’accommodation (Éditions de la revue d’Optique Théorique et Instrumentale, Paris, 1953).
  6. M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961); Biophysics 6, 776–795 (1962) (English translation).
  7. H. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. A 67, 1508–1518 (1977).
    [CrossRef]
  8. J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
    [CrossRef]
  9. F. Berny, “Étude de la formation des images rétiniennes et détermination de l’aberration de sphéricité de l’oeil humain,” Vision Res. 9, 977–990 (1969).
    [CrossRef] [PubMed]
  10. G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
    [CrossRef] [PubMed]
  11. J. Liang, B. Grimm, S. Golez, J. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
    [CrossRef]
  12. R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
    [CrossRef]
  13. I. Iglesias, E. Berrio, P. Artal, “Estimates of the ocular wave aberration from pairs of double-pass retinal images,” J. Opt. Soc. Am. A 15, 2466–2476 (1998).
    [CrossRef]
  14. J. Liang, D. R. Willians, “Aberrations and retinal image quality of the normal human eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997).
    [CrossRef]
  15. R. Navarro, E. Moreno, C. Dorronsoro, “Monochromatic aberrations and point-spread functions of the human eyeacross the visual field,” J. Opt. Soc. Am. A 15, 2522–2529 (1998).
    [CrossRef]
  16. T. Salmon, L. Thibos, A. Bradley, “Comparison of the eye’s wave-front aberration measured psychophysically and with the Shack–Hartmann wave-front sensor,” J. Opt. Soc. Am. A 15, 2457–2465 (1998).
    [CrossRef]
  17. L. Thibos, X. Hong, “Comparison of monochromatic aberrations of the human eye measured with the Howland crossed-cylinder aberroscope and the Shack–Hartmann aberrometer,” presented at the OSA Annual Meeting, September 26–October 1, 1999, Santa Clara, Calif.
  18. R. Navarro, E. Moreno-Barriuso, “Laser ray-tracing versus Hartmann–Shack sensor for measuring aberrations in the eye,” presented at the OSA Annual Meeting, October 4–9, 1998, Baltimore, Md.
  19. R. Navarro, E. Moreno-Barriuso, “Laser ray-tracing method for optical testing,” Opt. Lett. 24, 1–3 (1999).
    [CrossRef]
  20. J. G. Sivak, R. O. Kreuzer, “Spherical aberration of the crystalline lens,” Vision Res. 23, 59–70 (1983).
    [CrossRef] [PubMed]
  21. P. Artal, R. Navarro, S. Marcos, D. R. Williams, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995).
    [CrossRef]
  22. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).
  23. J. M. Geary, Introduction to Wavefront Sensors (SPIE Optical Engineering Press, Bellingham, Wash., 1995).
  24. M. W. Campbell, H. Haman, P. Simonet, I. Brunette, “Dependence of optical image quality on refractive error: eyes after excimer laser photorefractive keratectomy (prk) versus controls,” Invest. Ophthalmol. Visual Sci. 40 (Suppl.), 7 (1999).
  25. Hopkins, M. J. Yzuel, “The computation of diffraction patterns in the presence of aberrations,” Opt. Acta 17, 157–182 (1970).
    [CrossRef]
  26. H. J. Hofer, J. Porter, D. R. Williams, “Dynamic measurement of the wave aberration of the human eye,” Invest. Ophthalmol. Visual Sci. 39 (Suppl.), 203 (1998).
  27. S. Marcos, R. Navarro, P. Artal, “Coherent imaging of the cone mosaic in the living human eye,” J. Opt. Soc. Am. A 13, 897–905 (1996).
    [CrossRef]
  28. S. Marcos, R. Navarro, “Imaging the foveal cones in vivo through ocular speckle interferometry theory and numerical simulations,” J. Opt. Soc. Am. A 13, 2329–2340 (1996).
    [CrossRef]
  29. D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources, 1st ed. (Plenum, New York, 1980).
  30. S. A. Burns, S. Marcos, J. McLellan, R. H. Webb, “Role of sampling pattern and size on measuring aberrations of the eye,” presented at the OSA Annual Meeting, September 26–October 1, 1999, Santa Clara, Calif.

2000 (1)

1999 (3)

R. Navarro, E. Moreno-Barriuso, “Laser ray-tracing method for optical testing,” Opt. Lett. 24, 1–3 (1999).
[CrossRef]

L. Zhu, P. C. Sun, D.-U. Bartsch, W. R. Freeman, Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
[CrossRef]

M. W. Campbell, H. Haman, P. Simonet, I. Brunette, “Dependence of optical image quality on refractive error: eyes after excimer laser photorefractive keratectomy (prk) versus controls,” Invest. Ophthalmol. Visual Sci. 40 (Suppl.), 7 (1999).

1998 (5)

1997 (3)

1996 (2)

1995 (1)

1994 (1)

1984 (1)

1983 (1)

J. G. Sivak, R. O. Kreuzer, “Spherical aberration of the crystalline lens,” Vision Res. 23, 59–70 (1983).
[CrossRef] [PubMed]

1977 (1)

H. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. A 67, 1508–1518 (1977).
[CrossRef]

1970 (1)

Hopkins, M. J. Yzuel, “The computation of diffraction patterns in the presence of aberrations,” Opt. Acta 17, 157–182 (1970).
[CrossRef]

1969 (1)

F. Berny, “Étude de la formation des images rétiniennes et détermination de l’aberration de sphéricité de l’oeil humain,” Vision Res. 9, 977–990 (1969).
[CrossRef] [PubMed]

1961 (1)

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961); Biophysics 6, 776–795 (1962) (English translation).

1801 (1)

T. Young, “On the mechanisms of the eye,” Philos. Trans. R. Soc. London 19, 23–88 (1801).
[CrossRef]

Artal, P.

Bará, S.

Bartsch, D.-U.

Berny, F.

F. Berny, “Étude de la formation des images rétiniennes et détermination de l’aberration de sphéricité de l’oeil humain,” Vision Res. 9, 977–990 (1969).
[CrossRef] [PubMed]

Berrio, E.

Bille, J.

Bradley, A.

Brunette, I.

M. W. Campbell, H. Haman, P. Simonet, I. Brunette, “Dependence of optical image quality on refractive error: eyes after excimer laser photorefractive keratectomy (prk) versus controls,” Invest. Ophthalmol. Visual Sci. 40 (Suppl.), 7 (1999).

Burns, S. A.

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

S. A. Burns, S. Marcos, J. McLellan, R. H. Webb, “Role of sampling pattern and size on measuring aberrations of the eye,” presented at the OSA Annual Meeting, September 26–October 1, 1999, Santa Clara, Calif.

Campbell, M. W.

M. W. Campbell, H. Haman, P. Simonet, I. Brunette, “Dependence of optical image quality on refractive error: eyes after excimer laser photorefractive keratectomy (prk) versus controls,” Invest. Ophthalmol. Visual Sci. 40 (Suppl.), 7 (1999).

Charman, W. N.

Dorronsoro, C.

Fainman, Y.

Freeman, W. R.

Geary, J. M.

J. M. Geary, Introduction to Wavefront Sensors (SPIE Optical Engineering Press, Bellingham, Wash., 1995).

Golez, S.

Grimm, B.

Haman, H.

M. W. Campbell, H. Haman, P. Simonet, I. Brunette, “Dependence of optical image quality on refractive error: eyes after excimer laser photorefractive keratectomy (prk) versus controls,” Invest. Ophthalmol. Visual Sci. 40 (Suppl.), 7 (1999).

He, J. C.

Hofer, H. J.

H. J. Hofer, J. Porter, D. R. Williams, “Dynamic measurement of the wave aberration of the human eye,” Invest. Ophthalmol. Visual Sci. 39 (Suppl.), 203 (1998).

Hong, X.

L. Thibos, X. Hong, “Comparison of monochromatic aberrations of the human eye measured with the Howland crossed-cylinder aberroscope and the Shack–Hartmann aberrometer,” presented at the OSA Annual Meeting, September 26–October 1, 1999, Santa Clara, Calif.

Hopkins,

Hopkins, M. J. Yzuel, “The computation of diffraction patterns in the presence of aberrations,” Opt. Acta 17, 157–182 (1970).
[CrossRef]

Howland, B.

H. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. A 67, 1508–1518 (1977).
[CrossRef]

Howland, H.

H. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. A 67, 1508–1518 (1977).
[CrossRef]

Howland, H. C.

Iglesias, I.

Ivanoff, A.

A. Ivanoff, Les aberrations de l’oeil. Leur role dans l’accommodation (Éditions de la revue d’Optique Théorique et Instrumentale, Paris, 1953).

Kreuzer, R. O.

J. G. Sivak, R. O. Kreuzer, “Spherical aberration of the crystalline lens,” Vision Res. 23, 59–70 (1983).
[CrossRef] [PubMed]

Liang, J.

Losada, M. A.

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

Mancebo, T.

Marcos, S.

McLellan, J.

S. A. Burns, S. Marcos, J. McLellan, R. H. Webb, “Role of sampling pattern and size on measuring aberrations of the eye,” presented at the OSA Annual Meeting, September 26–October 1, 1999, Santa Clara, Calif.

Miller, D.

Moreno, E.

Moreno-Barriuso, E.

R. Navarro, E. Moreno-Barriuso, S. Bará, T. Mancebo, “Phase plates for wave-aberration compensation in the human eye,” Opt. Lett. 25, 236–238 (2000).
[CrossRef]

R. Navarro, E. Moreno-Barriuso, “Laser ray-tracing method for optical testing,” Opt. Lett. 24, 1–3 (1999).
[CrossRef]

R. Navarro, E. Moreno-Barriuso, “Laser ray-tracing versus Hartmann–Shack sensor for measuring aberrations in the eye,” presented at the OSA Annual Meeting, October 4–9, 1998, Baltimore, Md.

Navarro, R.

Porter, J.

H. J. Hofer, J. Porter, D. R. Williams, “Dynamic measurement of the wave aberration of the human eye,” Invest. Ophthalmol. Visual Sci. 39 (Suppl.), 203 (1998).

Salmon, T.

Simonet, P.

M. W. Campbell, H. Haman, P. Simonet, I. Brunette, “Dependence of optical image quality on refractive error: eyes after excimer laser photorefractive keratectomy (prk) versus controls,” Invest. Ophthalmol. Visual Sci. 40 (Suppl.), 7 (1999).

Sivak, J. G.

J. G. Sivak, R. O. Kreuzer, “Spherical aberration of the crystalline lens,” Vision Res. 23, 59–70 (1983).
[CrossRef] [PubMed]

Sliney, D.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources, 1st ed. (Plenum, New York, 1980).

Smirnov, M. S.

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961); Biophysics 6, 776–795 (1962) (English translation).

Sun, P. C.

Thibos, L.

T. Salmon, L. Thibos, A. Bradley, “Comparison of the eye’s wave-front aberration measured psychophysically and with the Shack–Hartmann wave-front sensor,” J. Opt. Soc. Am. A 15, 2457–2465 (1998).
[CrossRef]

L. Thibos, X. Hong, “Comparison of monochromatic aberrations of the human eye measured with the Howland crossed-cylinder aberroscope and the Shack–Hartmann aberrometer,” presented at the OSA Annual Meeting, September 26–October 1, 1999, Santa Clara, Calif.

Walsh, G.

Webb, R. H.

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

S. A. Burns, S. Marcos, J. McLellan, R. H. Webb, “Role of sampling pattern and size on measuring aberrations of the eye,” presented at the OSA Annual Meeting, September 26–October 1, 1999, Santa Clara, Calif.

Williams, D. R.

Willians, D. R.

Wolbarsht, M.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources, 1st ed. (Plenum, New York, 1980).

Young, T.

T. Young, “On the mechanisms of the eye,” Philos. Trans. R. Soc. London 19, 23–88 (1801).
[CrossRef]

Yzuel, M. J.

Hopkins, M. J. Yzuel, “The computation of diffraction patterns in the presence of aberrations,” Opt. Acta 17, 157–182 (1970).
[CrossRef]

Zhu, L.

Appl. Opt. (1)

Biofizika (1)

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961); Biophysics 6, 776–795 (1962) (English translation).

Invest. Ophthalmol. Visual Sci. (2)

M. W. Campbell, H. Haman, P. Simonet, I. Brunette, “Dependence of optical image quality on refractive error: eyes after excimer laser photorefractive keratectomy (prk) versus controls,” Invest. Ophthalmol. Visual Sci. 40 (Suppl.), 7 (1999).

H. J. Hofer, J. Porter, D. R. Williams, “Dynamic measurement of the wave aberration of the human eye,” Invest. Ophthalmol. Visual Sci. 39 (Suppl.), 203 (1998).

J. Opt. Soc. Am. A (12)

S. Marcos, R. Navarro, P. Artal, “Coherent imaging of the cone mosaic in the living human eye,” J. Opt. Soc. Am. A 13, 897–905 (1996).
[CrossRef]

S. Marcos, R. Navarro, “Imaging the foveal cones in vivo through ocular speckle interferometry theory and numerical simulations,” J. Opt. Soc. Am. A 13, 2329–2340 (1996).
[CrossRef]

P. Artal, R. Navarro, S. Marcos, D. R. Williams, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995).
[CrossRef]

J. Liang, D. R. Williams, D. Miller, “Supernormal vision and high resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[CrossRef]

H. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. A 67, 1508–1518 (1977).
[CrossRef]

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration of the eye by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

I. Iglesias, E. Berrio, P. Artal, “Estimates of the ocular wave aberration from pairs of double-pass retinal images,” J. Opt. Soc. Am. A 15, 2466–2476 (1998).
[CrossRef]

J. Liang, D. R. Willians, “Aberrations and retinal image quality of the normal human eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997).
[CrossRef]

R. Navarro, E. Moreno, C. Dorronsoro, “Monochromatic aberrations and point-spread functions of the human eyeacross the visual field,” J. Opt. Soc. Am. A 15, 2522–2529 (1998).
[CrossRef]

T. Salmon, L. Thibos, A. Bradley, “Comparison of the eye’s wave-front aberration measured psychophysically and with the Shack–Hartmann wave-front sensor,” J. Opt. Soc. Am. A 15, 2457–2465 (1998).
[CrossRef]

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

J. Liang, B. Grimm, S. Golez, J. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
[CrossRef]

Opt. Acta (1)

Hopkins, M. J. Yzuel, “The computation of diffraction patterns in the presence of aberrations,” Opt. Acta 17, 157–182 (1970).
[CrossRef]

Opt. Lett. (2)

Optom. Vision Sci. (1)

R. Navarro, M. A. Losada, “Aberrations and relative efficiency of light pencils in the living human eye,” Optom. Vision Sci. 74, 540–547 (1997).
[CrossRef]

Philos. Trans. R. Soc. London (1)

T. Young, “On the mechanisms of the eye,” Philos. Trans. R. Soc. London 19, 23–88 (1801).
[CrossRef]

Vision Res. (2)

F. Berny, “Étude de la formation des images rétiniennes et détermination de l’aberration de sphéricité de l’oeil humain,” Vision Res. 9, 977–990 (1969).
[CrossRef] [PubMed]

J. G. Sivak, R. O. Kreuzer, “Spherical aberration of the crystalline lens,” Vision Res. 23, 59–70 (1983).
[CrossRef] [PubMed]

Other (7)

L. Thibos, X. Hong, “Comparison of monochromatic aberrations of the human eye measured with the Howland crossed-cylinder aberroscope and the Shack–Hartmann aberrometer,” presented at the OSA Annual Meeting, September 26–October 1, 1999, Santa Clara, Calif.

R. Navarro, E. Moreno-Barriuso, “Laser ray-tracing versus Hartmann–Shack sensor for measuring aberrations in the eye,” presented at the OSA Annual Meeting, October 4–9, 1998, Baltimore, Md.

A. Ivanoff, Les aberrations de l’oeil. Leur role dans l’accommodation (Éditions de la revue d’Optique Théorique et Instrumentale, Paris, 1953).

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

J. M. Geary, Introduction to Wavefront Sensors (SPIE Optical Engineering Press, Bellingham, Wash., 1995).

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources, 1st ed. (Plenum, New York, 1980).

S. A. Burns, S. Marcos, J. McLellan, R. H. Webb, “Role of sampling pattern and size on measuring aberrations of the eye,” presented at the OSA Annual Meeting, September 26–October 1, 1999, Santa Clara, Calif.

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Figures (10)

Fig. 1
Fig. 1

Schematic diagrams of the experimental setups. The light source is a TEM00 polarized red He–Ne laser. The artificial eye is composed of a high-quality lens plus a removable aberrating plate. In all cases the experimental spots are recorded with a cooled digital CCD camera (square pixels, 9-μm size). (a) Single-pass H–S sensor: The pinhole of a spatial filter acts as point object placed at the focal plane of the artificial eye. Lenses L1 and L2 (f=148 mm) project the pupil (1:1 magnification) onto the microlens array. The spots formed by the microlens array are imaged onto the CCD by means of lens L3 (f=200 mm) and the CCD objective (f=105 mm). (b) Single-pass LRT (version I): The scanner, placed at the artificial eye’s focal plane, delivers a divergent bundle of rays. Each spot is sequentially imaged onto the CCD by the objective (f=55 mm). (c) Single-pass LRT (version II): A set of rays (parallel after passing through the collimator) is delivered onto the artificial eye. Each individual spot is recorded onto the naked CCD (no objective), located at the focal plane. (d) Dual double-pass setup: For LRT the microlens array and L3 are removed. The scanner and the collimator produce a set of parallel rays. Each ray, after being reflected off the rotating diffuser (artificial retina), goes through the eye’s pupil and is imaged onto the CCD. The pupil stop, conjugate to the eye’s pupil, limits the width of the beam. This stop is removed for H–S measurements, and the scanner is set to zero-deflection angle. The unexpanded beam goes through the center of the artificial eye and is reflected off the rotating diffuser. The second pass (image recording) is the same as in (a).

Fig. 2
Fig. 2

Effect of speckle noise in double-pass recordings: left column, coherent recordings; right column, incoherent recordings. Upper panels, H–S; lower panels, LRT.

Fig. 3
Fig. 3

Double-pass H–S recordings in the artificial eye, obtained with different entrance pupil diameters of 0.7 mm, 3 mm, and 6 mm. Blur increases with pupil size.

Fig. 4
Fig. 4

Zernike coefficients (in micrometers) of the artificial eye obtained with five different conditions. Error bars represent the variability (standard error) obtained in four measurements.

Fig. 5
Fig. 5

Contour plots of the wave aberration obtained for H–S and LRT in single- and double-pass configurations (the single-pass LRT plot corresponds to version II). The step between adjacent contour lines is 0.5 μm. Tilts and defocus (Z4) have not been included, to enhance the asymmetrical and higher-order features of the wave aberration.

Fig. 6
Fig. 6

Average Zernike coefficients (in micrometers) of the artificial eye. Symbols represent the average of the five types of measurements, and error bars represent the variability (standard error) among all conditions.

Fig. 7
Fig. 7

PSF of the artificial eye recorded directly on the CCD (center) compared with simulations computed from aberration data: H–S (upper panels), LRT (lower panels), in single- (left panels) and double-pass (right panels) configurations. The horizontal size of the PSF is approximately 1° of field.

Fig. 8
Fig. 8

Contour plots of the wave aberration for subjects EM and RN, obtained with H–S and LRT. Tilt terms were not considered, and for RN neither was defocus (Z4). The step between adjacent contour lines is 0.5 μm.

Fig. 9
Fig. 9

H–S recording for subject SM, who presents low optical quality and strong asymmetrical aberrations.

Fig. 10
Fig. 10

Invariance against changes in the pupil sampling pattern for subject RN. The Zernike coefficients obtained with LRT and different sampling patterns (square and hexagonal) and step sizes (0.6 and 1 mm), show basically the same values.

Equations (6)

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Δx(ξi,ηi)=X(ξi,ηi)-X0(ξi,ηi)f;
Δy(ξi,ηi)=Y(ξi,ηi)-Y0(ξi,ηi)f.
Δx=1Rp W(ξ¯,η¯)ξ¯;Δy=1Rp W(ξ¯,η¯)η¯.
W(ξ¯,η¯)k=135ZkPk(ξ¯,η¯),
I(x, y)=FTT(ξ¯,η¯)exp-i2πλ W(ξ¯,η¯)2,
D=d(f+d/2)(f-d/2).

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