Abstract

A new system for the recording of high-resolution images of the cone mosaic in the living human fovea has been developed. The experimental method is inspired by stellar speckle interferometry, used in astronomy to resolve binary stars. Series of short-exposure images of small areas of the fovea are registered under coherent illumination. These images show speckle patterns that have some correlation with the topography of the cone mosaic and retain high-resolution information. Such correlation is better revealed in the power spectrum (square modulus of the Fourier transform). The signal-to-noise ratio is increased, without loss of high frequencies, by averaging the power spectra of a number of such speckle patterns. The average power spectra show, in most of the cases, an elliptical ring (or hexagon), whose mean radius corresponds to the characteristic spatial frequency of the cone mosaic (or the inverse of the mean row-to-row cone spacing) at a given retinal location. Good results are obtained in the five normal observers tested, at various retinal eccentricities, up to 1 visual degree, including the center of the fovea for two eyes. We find a decrease in the spatial frequency of the mosaic with the eccentricity and an important intersubject variability, in agreement with anatomical studies.

© 1996 Optical Society of America

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  2. C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
    [CrossRef]
  3. N. D. Drasdo, C. W. Fowler, “Non-linear projection of a retinal image in a wide-angle schematic eye,” Br. J. Ophthalmol. 58, 709–714 (1974).
    [CrossRef] [PubMed]
  4. D. R. Williams, “Topography of the foveal cone mosaic in the living human eye,” Vision Res. 28, 433–454 (1988).
    [CrossRef] [PubMed]
  5. W. S. Jagger, “Visibility of photoreceptors in the intact living cane toad eye,” Vision Res. 25, 729–731 (1985).
    [CrossRef] [PubMed]
  6. M. F. Land, W. A. Snyder, “Cone mosaic observed directly through the natural pupil of live vertebrate,” Vision Res. 25, 1519–1523 (1985).
    [CrossRef]
  7. P. Artal, R. Navarro, “High-resolution imaging of the living human fovea: measurement of the intercenter cone distance by speckle interferometry,” Opt. Lett. 14, 1098–1100 (1989).
    [CrossRef] [PubMed]
  8. J. C. Dainty, ed. Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1984), Chap. 7, pp. 255–320.
  9. J. C. Dainty, “Diffraction-limited imaging of stellar objects using telescopes of low optical quality,” Opt. Commun. 5, 129–134 (1972).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. D. R. Williams, D. Miller, G. M. Morris, “Images of the cone mosaic in the living human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1995), pp. 98–101.
  14. M. R. Atkinson, A. Roorda, M. C. W. Campbell, “Imaging of individual photoreceptors beyond the incoherent resolution limit,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, S188 (1995).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1995 (3)

M. R. Atkinson, A. Roorda, M. C. W. Campbell, “Imaging of individual photoreceptors beyond the incoherent resolution limit,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, S188 (1995).

R. Navarro, M. A. Losada, “Phase transfer and point-spread function of the human eye determined by a new asymmetric double-pass method,” J. Opt. Soc. Am. 11, 2385–2392 (1995).
[CrossRef]

S. A. Burns, S. Wu, F. Delori, A. E. Elsner, “Direct measurement of the human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1995).
[CrossRef]

1994 (2)

1993 (2)

1992 (2)

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[CrossRef]

P. Artal, R. Navarro, “Simultaneous measurement of two point-spread functions at different locations across the human fovea,” Appl. Opt. 31, 3646–3656 (1992).
[CrossRef] [PubMed]

1990 (1)

T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence,” J. Opt. Soc. Am. 7, 348–355 (1990).
[CrossRef]

1989 (2)

P. Artal, R. Navarro, “High-resolution imaging of the living human fovea: measurement of the intercenter cone distance by speckle interferometry,” Opt. Lett. 14, 1098–1100 (1989).
[CrossRef] [PubMed]

A. W. Dreher, J. F. Bille, R. N. Weinreb, “Active optical depth resolution improvement of the laser tomographic scanner,” Appl. Opt. 4, 804–808 (1989).
[CrossRef]

1988 (1)

D. R. Williams, “Topography of the foveal cone mosaic in the living human eye,” Vision Res. 28, 433–454 (1988).
[CrossRef] [PubMed]

1985 (2)

W. S. Jagger, “Visibility of photoreceptors in the intact living cane toad eye,” Vision Res. 25, 729–731 (1985).
[CrossRef] [PubMed]

M. F. Land, W. A. Snyder, “Cone mosaic observed directly through the natural pupil of live vertebrate,” Vision Res. 25, 1519–1523 (1985).
[CrossRef]

1982 (1)

J. J. Yellot, “Spectral analysis of spatial sampling of photoreceptors: topological disorder prevents aliasing,” Vision Res. 22, 1205–1210 (1982).
[CrossRef]

1974 (1)

N. D. Drasdo, C. W. Fowler, “Non-linear projection of a retinal image in a wide-angle schematic eye,” Br. J. Ophthalmol. 58, 709–714 (1974).
[CrossRef] [PubMed]

1972 (1)

J. C. Dainty, “Diffraction-limited imaging of stellar objects using telescopes of low optical quality,” Opt. Commun. 5, 129–134 (1972).

1957 (1)

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157–164 (1957).
[CrossRef]

1935 (1)

G. Osterberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophthalmol. Suppl. 6, 1–97 (1935).

Applegate, R. A.

Artal, P.

Atkinson, M. R.

M. R. Atkinson, A. Roorda, M. C. W. Campbell, “Imaging of individual photoreceptors beyond the incoherent resolution limit,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, S188 (1995).

Bille, J. F.

A. W. Dreher, J. F. Bille, R. N. Weinreb, “Active optical depth resolution improvement of the laser tomographic scanner,” Appl. Opt. 4, 804–808 (1989).
[CrossRef]

Brainard, D. H.

Burns, S. A.

Campbell, F. W.

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157–164 (1957).
[CrossRef]

Campbell, M. C. W.

M. R. Atkinson, A. Roorda, M. C. W. Campbell, “Imaging of individual photoreceptors beyond the incoherent resolution limit,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, S188 (1995).

Curcio, C. A.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[CrossRef]

Dainty, J. C.

T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence,” J. Opt. Soc. Am. 7, 348–355 (1990).
[CrossRef]

J. C. Dainty, “Diffraction-limited imaging of stellar objects using telescopes of low optical quality,” Opt. Commun. 5, 129–134 (1972).

Delori, F.

Drasdo, N. D.

N. D. Drasdo, C. W. Fowler, “Non-linear projection of a retinal image in a wide-angle schematic eye,” Br. J. Ophthalmol. 58, 709–714 (1974).
[CrossRef] [PubMed]

Dreher, A. W.

A. W. Dreher, J. F. Bille, R. N. Weinreb, “Active optical depth resolution improvement of the laser tomographic scanner,” Appl. Opt. 4, 804–808 (1989).
[CrossRef]

Elsner, A. E.

Fowler, C. W.

N. D. Drasdo, C. W. Fowler, “Non-linear projection of a retinal image in a wide-angle schematic eye,” Br. J. Ophthalmol. 58, 709–714 (1974).
[CrossRef] [PubMed]

Hendrickson, A. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[CrossRef]

Jagger, W. S.

W. S. Jagger, “Visibility of photoreceptors in the intact living cane toad eye,” Vision Res. 25, 729–731 (1985).
[CrossRef] [PubMed]

Kalina, R. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[CrossRef]

Lakshminarayanan, V.

Land, M. F.

M. F. Land, W. A. Snyder, “Cone mosaic observed directly through the natural pupil of live vertebrate,” Vision Res. 25, 1519–1523 (1985).
[CrossRef]

Losada, M. A.

R. Navarro, M. A. Losada, “Phase transfer and point-spread function of the human eye determined by a new asymmetric double-pass method,” J. Opt. Soc. Am. 11, 2385–2392 (1995).
[CrossRef]

Marcos, S.

S. Marcos, R. Navarro, P. Artal, “Foveal cone mosaic imaged in vivoby an objective high-resolution imaging technique,” in Lasers in Ophthalmology III, R. Birngruber, A. S. Fircher, eds. Proc. SPIE2632, 48–55 (1995).
[CrossRef]

Mavroidis, T.

T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence,” J. Opt. Soc. Am. 7, 348–355 (1990).
[CrossRef]

McMahon, M. J.

Miller, D.

D. R. Williams, D. Miller, G. M. Morris, “Images of the cone mosaic in the living human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1995), pp. 98–101.

Morris, G. M.

D. R. Williams, D. Miller, G. M. Morris, “Images of the cone mosaic in the living human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1995), pp. 98–101.

Navarro, R.

Northcott, M. J.

T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence,” J. Opt. Soc. Am. 7, 348–355 (1990).
[CrossRef]

Osterberg, G.

G. Osterberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophthalmol. Suppl. 6, 1–97 (1935).

Roorda, A.

M. R. Atkinson, A. Roorda, M. C. W. Campbell, “Imaging of individual photoreceptors beyond the incoherent resolution limit,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, S188 (1995).

Rynders, M. C.

M. C. Rynders, “The Stiles–Crawford effect and an experimental determination of its impact on vision,” Ph.D. dissertation (Indiana University, Bloomington, Ind., 1994).

Sliney, D.

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

Sloan, K. R.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[CrossRef]

Snyder, W. A.

M. F. Land, W. A. Snyder, “Cone mosaic observed directly through the natural pupil of live vertebrate,” Vision Res. 25, 1519–1523 (1985).
[CrossRef]

Tabernero, A.

A. Tabernero, “Representación de imágenes mediante funciones de Gabor. Modelado del sistema visual y análisis de texturas,” Ph.D. dissertation (Universidad Complutense de Madrid, Madrid, 1992).

Weinreb, R. N.

A. W. Dreher, J. F. Bille, R. N. Weinreb, “Active optical depth resolution improvement of the laser tomographic scanner,” Appl. Opt. 4, 804–808 (1989).
[CrossRef]

Williams, D. R.

D. R. Williams, D. H. Brainard, M. J. McMahon, R. Navarro, “Double-pass and interferometric measures of the optical quality of the eye,” J. Opt. Soc. Am. A 11, 3123–3135 (1994).
[CrossRef]

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[CrossRef] [PubMed]

D. R. Williams, “Topography of the foveal cone mosaic in the living human eye,” Vision Res. 28, 433–454 (1988).
[CrossRef] [PubMed]

D. R. Williams, D. Miller, G. M. Morris, “Images of the cone mosaic in the living human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1995), pp. 98–101.

Wolbarsht, M.

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

Wu, S.

Yellot, J. J.

J. J. Yellot, “Spectral analysis of spatial sampling of photoreceptors: topological disorder prevents aliasing,” Vision Res. 22, 1205–1210 (1982).
[CrossRef]

Acta Ophthalmol. Suppl. (1)

G. Osterberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophthalmol. Suppl. 6, 1–97 (1935).

Appl. Opt. (2)

P. Artal, R. Navarro, “Simultaneous measurement of two point-spread functions at different locations across the human fovea,” Appl. Opt. 31, 3646–3656 (1992).
[CrossRef] [PubMed]

A. W. Dreher, J. F. Bille, R. N. Weinreb, “Active optical depth resolution improvement of the laser tomographic scanner,” Appl. Opt. 4, 804–808 (1989).
[CrossRef]

Br. J. Ophthalmol. (1)

N. D. Drasdo, C. W. Fowler, “Non-linear projection of a retinal image in a wide-angle schematic eye,” Br. J. Ophthalmol. 58, 709–714 (1974).
[CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci. Suppl. (1)

M. R. Atkinson, A. Roorda, M. C. W. Campbell, “Imaging of individual photoreceptors beyond the incoherent resolution limit,” Invest. Ophthalmol. Vis. Sci. Suppl. 35, S188 (1995).

J. Comp. Neurol. (1)

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[CrossRef]

J. Opt. Soc. Am. (2)

T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence,” J. Opt. Soc. Am. 7, 348–355 (1990).
[CrossRef]

R. Navarro, M. A. Losada, “Phase transfer and point-spread function of the human eye determined by a new asymmetric double-pass method,” J. Opt. Soc. Am. 11, 2385–2392 (1995).
[CrossRef]

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

Opt. Acta (1)

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157–164 (1957).
[CrossRef]

Opt. Commun. (1)

J. C. Dainty, “Diffraction-limited imaging of stellar objects using telescopes of low optical quality,” Opt. Commun. 5, 129–134 (1972).

Opt. Lett. (1)

Vision Res. (4)

D. R. Williams, “Topography of the foveal cone mosaic in the living human eye,” Vision Res. 28, 433–454 (1988).
[CrossRef] [PubMed]

W. S. Jagger, “Visibility of photoreceptors in the intact living cane toad eye,” Vision Res. 25, 729–731 (1985).
[CrossRef] [PubMed]

M. F. Land, W. A. Snyder, “Cone mosaic observed directly through the natural pupil of live vertebrate,” Vision Res. 25, 1519–1523 (1985).
[CrossRef]

J. J. Yellot, “Spectral analysis of spatial sampling of photoreceptors: topological disorder prevents aliasing,” Vision Res. 22, 1205–1210 (1982).
[CrossRef]

Other (6)

D. R. Williams, D. Miller, G. M. Morris, “Images of the cone mosaic in the living human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1995), pp. 98–101.

S. Marcos, R. Navarro, P. Artal, “Foveal cone mosaic imaged in vivoby an objective high-resolution imaging technique,” in Lasers in Ophthalmology III, R. Birngruber, A. S. Fircher, eds. Proc. SPIE2632, 48–55 (1995).
[CrossRef]

J. C. Dainty, ed. Laser Speckle and Related Phenomena (Springer-Verlag, Berlin, 1984), Chap. 7, pp. 255–320.

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

A. Tabernero, “Representación de imágenes mediante funciones de Gabor. Modelado del sistema visual y análisis de texturas,” Ph.D. dissertation (Universidad Complutense de Madrid, Madrid, 1992).

M. C. Rynders, “The Stiles–Crawford effect and an experimental determination of its impact on vision,” Ph.D. dissertation (Indiana University, Bloomington, Ind., 1994).

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Figures (8)

Fig. 1
Fig. 1

Experimental setup. ND, neutral density filters; ES, electronic shutter; L1, L2, lenses (focal length = 60 mm); O, pinhole (diameter = 200 mm); BS, pellicle beam splitter; L3, L4, lenses (focal length = 120 mm); FS, field stop; AP, artificial pupil; L5, L6, lenses (focal length = 500 mm); CCD, high-resolution CCD camera; GF, green filter; AFT, accommodation-fixation target; LT, light trap; IR CCD, infrared CCD camera for monitoring the pupil size. The shaded areas indicate the ray path toward the eye. The ray tracing from the accommodation target has been partially omitted to avoid the overlapping with the beam reflected back from the eye.

Fig. 2
Fig. 2

(a) Series of 12 short-exposure images, corresponding to subject MA, at 0.5 deg of retinal eccentricity, inferior. The images marked with an asterisk at the upper-right corner were selected as the best speckle patterns, and the four remaining ones were rejected, according to the reasons explained in the text. (b) Power spectra of each of the images shown in (a). They are represented in a logarithmic scale, and the central peak has been removed.

Fig. 3
Fig. 3

(a) Two-dimensional average power spectra, for subject MA for 0.25, 0.5, and 1 deg of retinal eccentricities, processed as described in the text. (b) One-dimensional representations of the average power spectra shown in (a): sections along the minor (long-dashed curves) and major (short-dashed curves) axes of the elliptical ring, and radial profile when it is significant (solid curves).

Fig. 4
Fig. 4

Two-dimensional average power spectra, processed as described in the text, for three subjects: RN (left), SM (middle), and PA (left), and two different retinal eccentricities: 0.5 deg (top) and 1 deg (bottom).

Fig. 5
Fig. 5

Spatial frequency of the cone mosaic (mean radius of the rings in the average power spectra) as a function of the retinal eccentricity for various subjects. The length of the bars, plotted only for subject MA, indicate the range of spatial frequencies covered between the principal half-axes of elliptical rings. The solid curve represents a fit of the average histological data.

Fig. 6
Fig. 6

Short-exposure images for different pupil diameters: 2 mm (left), 5 mm (middle), and 8 mm (right), corresponding to observer MR at a retinal eccentricity of 1 deg. The speckle grains become smaller with increasing pupil size.

Fig. 7
Fig. 7

Resolution (cutoff spatial frequency of the average power spectra) as a function of pupil diameter for three subjects. The solid line represents the resolution of a diffraction-limited system at a wavelength of 543 nm as a function of the apparent pupil diameter. The curves also represent the resolution of a diffraction-limited system but for the effective pupil size, taking into account the Stiles–Crawford effect. Long-dashed curve, ρ = 0.02; short-dashed curve, ρ = 0.075.

Fig. 8
Fig. 8

Comparison between the range of spatial frequencies of the cone mosaic obtained by Williams et al.13 and from the measurements that we present here.

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