Abstract

The Shack-Hartmann wave-front sensor offers many theoretical advantages over other methods for measuring aberrations of the eye; therefore it is essential that its accuracy be thoroughly tested. We assessed the accuracy of a Shack–Hartmann sensor by directly comparing its measured wave-front aberration function with that obtained by the Smirnov psychophysical method for the same eyes. Wave-front profiles measured by the two methods agreed closely in terms of shape and magnitude with rms differences of ∼λ/2 and ∼λ/6 (5.6-mm pupil) for two eyes. Primary spherical aberration was dominant in these profiles, and, in one subject, secondary coma was opposite in sign to primary coma, thereby canceling its effect. Discovery of an unusual, subtle wave-front anomaly in one individual further demonstrated the accuracy and sensitivity of the Shack–Hartmann wave-front sensor for measuring the optical quality of the human eye.

© 1998 Optical Society of America

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References

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  21. R. B. Mandell, “The enigma of the corneal contour,” Contact Lens Assoc. Ophthalmol. J. 18, 267–273 (1992).
  22. R. Mandell, “Apparent pupil displacement in videokeratography,” Contact Lens Assoc. Ophthalmol. J. 20, 123–7 (1994).
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    [CrossRef]
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    [CrossRef]

1997 (4)

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

L. Thibos, “The new visual optics,” Optom. Vision Sci. 74, 465–466 (1997).
[CrossRef]

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

L. N. Thibos, Y. Ming, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–565 (1997).
[CrossRef]

1996 (1)

R. Woods, A. Bradley, D. Atchison, “Monocular diplopia caused by ocular aberrations and hyperopic defocus,” Vision Res. 36, 3597–3606 (1996).
[CrossRef] [PubMed]

1995 (3)

G. Walsh, M. Cox, “A new computerized video-aberroscope for the determination of the aberration of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1995).
[CrossRef] [PubMed]

D. Atchison, M. Collins, C. Wildsoet, J. Christensen, M. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

1994 (3)

1992 (2)

1991 (1)

W. Charman, “Wave front aberration of the eye: a review,” Optom. Vision Sci. 68, 574–583 (1991).
[CrossRef]

1990 (2)

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

P. Simonet, M. Campbell, “The transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1990).
[CrossRef]

1986 (1)

G. J. van Blokland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef] [PubMed]

1984 (1)

1977 (1)

1961 (1)

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961).

1894 (1)

M. Tscherning, “Die monochromatischen aberrationen des menschlichen auges,” Z. Psychol. Physiol. Sinnesorg. 6, 456–471 (1894).

Atchison, D.

R. Woods, A. Bradley, D. Atchison, “Monocular diplopia caused by ocular aberrations and hyperopic defocus,” Vision Res. 36, 3597–3606 (1996).
[CrossRef] [PubMed]

D. Atchison, M. Collins, C. Wildsoet, J. Christensen, M. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Becklund, O.

C. Williams, O. Becklund, Introduction to the Optical Transfer Function (Wiley, New York, 1989).

Bille, J. F.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

Bradley, A.

L. N. Thibos, Y. Ming, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–565 (1997).
[CrossRef]

R. Woods, A. Bradley, D. Atchison, “Monocular diplopia caused by ocular aberrations and hyperopic defocus,” Vision Res. 36, 3597–3606 (1996).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Brainard, D. H.

Campbell, M.

P. Simonet, M. Campbell, “The transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1990).
[CrossRef]

Charman, W.

W. Charman, “Wave front aberration of the eye: a review,” Optom. Vision Sci. 68, 574–583 (1991).
[CrossRef]

Charman, W. N.

Christensen, J.

D. Atchison, M. Collins, C. Wildsoet, J. Christensen, M. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Collins, M.

D. Atchison, M. Collins, C. Wildsoet, J. Christensen, M. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Cox, M.

G. Walsh, M. Cox, “A new computerized video-aberroscope for the determination of the aberration of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1995).
[CrossRef] [PubMed]

Delori, F. C.

J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

Goelz, S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed., S. W. Director, ed. (McGraw-Hill, New York, 1996).

Gorrand, J. M.

J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

Grimm, B.

Howarth, P. A.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Howland, B.

Howland, H. C.

Liang, J.

Mandell, R.

R. Mandell, “Apparent pupil displacement in videokeratography,” Contact Lens Assoc. Ophthalmol. J. 20, 123–7 (1994).

Mandell, R. B.

R. B. Mandell, “The enigma of the corneal contour,” Contact Lens Assoc. Ophthalmol. J. 18, 267–273 (1992).

McMahon, M. J.

Miller, D. T.

Ming, Y.

L. N. Thibos, Y. Ming, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–565 (1997).
[CrossRef]

Murray Penney, C.

Navarro, R.

Simonet, P.

P. Simonet, M. Campbell, “The transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1990).
[CrossRef]

Sliney, D.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1981).

Smirnov, M. S.

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961).

Still, D. L.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Thibos, L.

L. Thibos, “The new visual optics,” Optom. Vision Sci. 74, 465–466 (1997).
[CrossRef]

Thibos, L. N.

L. N. Thibos, Y. Ming, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–565 (1997).
[CrossRef]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Thompson, K.

Tscherning, M.

M. Tscherning, “Die monochromatischen aberrationen des menschlichen auges,” Z. Psychol. Physiol. Sinnesorg. 6, 456–471 (1894).

van Blokland, G. J.

G. J. van Blokland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef] [PubMed]

van Norren, D.

G. J. van Blokland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef] [PubMed]

Walsh, G.

G. Walsh, M. Cox, “A new computerized video-aberroscope for the determination of the aberration of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1995).
[CrossRef] [PubMed]

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]

Waterworth, M.

D. Atchison, M. Collins, C. Wildsoet, J. Christensen, M. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Webb, R.

Wildsoet, C.

D. Atchison, M. Collins, C. Wildsoet, J. Christensen, M. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Williams, C.

C. Williams, O. Becklund, Introduction to the Optical Transfer Function (Wiley, New York, 1989).

Williams, D. R.

Wolbarsht, M.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1981).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

Woods, R.

R. Woods, A. Bradley, D. Atchison, “Monocular diplopia caused by ocular aberrations and hyperopic defocus,” Vision Res. 36, 3597–3606 (1996).
[CrossRef] [PubMed]

Zhang, X.

L. N. Thibos, Y. Ming, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–565 (1997).
[CrossRef]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biofizika (1)

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biofizika 6, 687–703 (1961).

Contact Lens Assoc. Ophthalmol. J. (2)

R. B. Mandell, “The enigma of the corneal contour,” Contact Lens Assoc. Ophthalmol. J. 18, 267–273 (1992).

R. Mandell, “Apparent pupil displacement in videokeratography,” Contact Lens Assoc. Ophthalmol. J. 20, 123–7 (1994).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

Ophthalmic Physiol. Opt. (1)

G. Walsh, M. Cox, “A new computerized video-aberroscope for the determination of the aberration of the human eye,” Ophthalmic Physiol. Opt. 15, 403–408 (1995).
[CrossRef] [PubMed]

Optom. Vision Sci. (3)

L. Thibos, “The new visual optics,” Optom. Vision Sci. 74, 465–466 (1997).
[CrossRef]

L. N. Thibos, Y. Ming, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–565 (1997).
[CrossRef]

W. Charman, “Wave front aberration of the eye: a review,” Optom. Vision Sci. 68, 574–583 (1991).
[CrossRef]

Vision Res. (6)

P. Simonet, M. Campbell, “The transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1990).
[CrossRef]

D. Atchison, M. Collins, C. Wildsoet, J. Christensen, M. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

G. J. van Blokland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef] [PubMed]

J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[CrossRef] [PubMed]

R. Woods, A. Bradley, D. Atchison, “Monocular diplopia caused by ocular aberrations and hyperopic defocus,” Vision Res. 36, 3597–3606 (1996).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Z. Psychol. Physiol. Sinnesorg. (1)

M. Tscherning, “Die monochromatischen aberrationen des menschlichen auges,” Z. Psychol. Physiol. Sinnesorg. 6, 456–471 (1894).

Other (4)

C. Williams, O. Becklund, Introduction to the Optical Transfer Function (Wiley, New York, 1989).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed., S. W. Director, ed. (McGraw-Hill, New York, 1996).

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1981).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980).

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Figures (7)

Fig. 1
Fig. 1

Principle of wave-front sensing in the S-H (top) and Smirnov psychophysical (bottom) apparatuses (Δy, displacement of point image from reference position; f, focal length of lenslet; Δs, displacement of point object from reference axis; and d, object distance). In the S-H apparatus a point source is placed on the fovea, and light is reflected out of the eye. The optical system relays an image of the eye’s entrance pupil (EP) to the plane of an array of microlenslets that, in effect, samples the emerging beam in the EP. For purposes of illustrating the principle, the lenslet array is shown inside the eye in the plane of the EP, though the optical sampling of the EP actually occurs outside the eye. In a theoretical aberration-free eye a bundle of rays is isolated by a lenslet, and rays converge to point y0 on the CCD. For an aberrated eye the image is displaced from reference point y0 by an amount Δy and by the ray deviation angle θ=Δy/f. In the Smirnov method rays from a distant axial point object are isolated by a pinhole near the eye, and, in the aberration-free case, these rays converge on the fovea. In the aberrated eye the subject must displace the object by an amount Δs to center its image on the fovea. Here the ray deviation angle θ=Δs/d. Both methods measure the same angle θ, which is the ray aberration at the isolated pupil location. Since rays are orthogonal to wave fronts, θ also represents the slope of the wave front W in object space, from which W may be derived by integration.

Fig. 2
Fig. 2

S-H wave-front sensor layout. A laser beam passes through neutral-density filters ND, an electronic shutter, spatial filter (SF), lenses L1–L3, lens Rx, and the eye’s optics to form a point of light on the fovea. The subject observes a fixation target during measurement. Light reflected off the retina passes out of the eye, through lenses Rx, L4, and L5 so that an image of the pupil is formed in the plane of the microlenslet array, and each lenslet forms an image of the retinal spot on the CCD. A confocal aperture, A2, prevents corneal reflections from reaching the camera while transmitting light from the retina. Digital images are stored on a computer and are analyzed to reconstruct the eye’s wave-front aberration function.

Fig. 3
Fig. 3

Psychophysical apparatus based on Smirnov’s principle. The subject observes a fixed annular target through his entire pupil while polarized light from a LED enters the pupil only through a small (0.6-mm) pinhole aperture drilled in a cross-polarized filter that is positioned in front of the eye. The pinhole is used to isolate predetermined locations within the pupil, and for each position the subject adjusts the LED until it appears centered in the annulus, making it conjugate to the fovea. The positions of the LED and pinhole allow computation of the wave-front slope for the pupil location isolated by the pinhole, as described in Fig. 1.

Fig. 4
Fig. 4

Two-dimensional wave-front aberration data from the S-H wave-front sensor. Data for subject LT are shown in the left-hand column [(a)–(c)]. The right-hand column [(d)–(f)] shows data for subject DH. Examples of raw data images are shown in the first row [(a),(d)]. The middle row shows mean (n=5) wave-front aberration maps (b) for LT with 1-λ contour intervals and (e) for DH with 0.3-λ intervals. The rectangular overlay in (b) delineates the region that contains a subtle wave-front anomaly described in detail in the text and graphed in Fig. 7 below. Corresponding standard error maps are shown (c) for LT with 0.25-λ contour intervals and (f) for DH with 0.1-λ intervals. Pupil diameters were 5.6 mm.

Fig. 5
Fig. 5

Direct comparison of wave-front aberration profiles measured by the S-H sensor (solid curve, circles) and by the Smirnov apparatus (dashed curve, squares) for subjects LT (top) and DH (bottom). Prism and defocus were removed, leaving only higher-order aberrations for the comparison. The wave-front aberration in wavelengths (λ=632.8 nm) across the 5.6-mm-diameter pupils shows close agreement between the two methods in terms of shape and magnitude. The greatest difference between the two techniques is noted in the nasal portion of LT’s pupil.

Fig. 6
Fig. 6

Relative contribution of primary coma (squares), primary spherical aberration (filled circles), secondary coma (open circles), and secondary spherical aberration (diamonds) to the total wave-front aberration profile (solid curve) for subjects LT (top) and DH (bottom). For LT, primary spherical aberration alone closely approximates the total aberration function. Combined primary and secondary coma make a minimal contribution to the total aberrations, since they have similar magnitude but opposite signs and cancel each other out. A small amount of positive secondary spherical aberration is also present. For DH, primary spherical aberration also dominates, while primary and secondary coma are negligible. A small amount of negative secondary spherical aberration partially negates the large positive primary spherical aberration in the peripheral pupil.

Fig. 7
Fig. 7

During psychophysical measurements of subject LT’s wave-front aberration function, he observed that, as the pinhole moved horizontally across the nasal half of his pupil, a fixed LED appeared to move in a looplike trajectory. This unusual aberration was verified in both the psychophysical (dashed curve) and the S-H (solid curve) measurements and is represented by a plot of the x and y wave-front slopes measured at successive points across the pupil. Numbers near selected symbols indicate the horizontal distance (in mm) of each sample point from the pupil center. Negative values indicate the temporal half-pupil; positive, the nasal. Labels for the S-H data are underlined. Though slightly shifted from each other, both curves show the same looplike reversal in the same part of the pupil where the pattern was noted subjectively. Additionally, miniscule and abrupt changes in wave-front slopes occur at corresponding pupil locations in both traces.

Tables (3)

Tables Icon

Table 1 Summary Data for Two Subjects Whose Right Eyes Were Measured with the S-H Wave-Front Sensor and the Smirnov Psychophysical Method

Tables Icon

Table 2 Parameters Describing Spherical Test Wave Frontsa Used for Calibration of the S-H Wave-Front Sensor and Measurement Errors

Tables Icon

Table 3 Mean Coefficients Used in Eqs. (1) and (2) and Other Parameters Describing Fifth-Order Polynomial Fits to the S-H Wave-Front Slope Dataa

Equations (2)

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θ=dW/du=B0+B1u+B2u2+B3u3+B4u4+B5u5,
W(u)=B2u3/3+B3u4/4+B4u5/5+B5u6/6.

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