Abstract

A model based on the framework of fundal reflectance model III is developed for the lateral spreading of light that emerges from the human ocular fundus after scattering in the choriocapillaris and the choroidal stroma. Blood in these layers is modeled as a forward scatterer, and the Kubelka–Munk diffuse radiation environment used for the choroid in model III is replaced by an arrangement of embedded reflectors that gives the same remittance. An equation is derived for the point-spread function, and sample calculations illustrate the dependence of the spreading function on retinal site and wavelength and identify the characteristic influences of the long-wavelength edge of the 575-nm oxyhemoglobin absorption band and the choroidal melanin.

© 1994 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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1993

1992

1991

I. J. Hodgkinson, K. M. Chong, A. C. B. Molteno, “Characterization of the fundal reflectance of infants,” Optom. Vis. Sci. 68, 513–521 (1991).
[CrossRef] [PubMed]

I. J. Hodgkinson, K. M. Chong, A. C. B. Molteno, “Photo-refraction of the living eye: a model for linear knife edge photoscreening,” Appl. Opt. 30, 2263–2269 (1991).
[CrossRef] [PubMed]

1989

1987

1979

Artal, P.

Burns, S. A.

Chong, K. M.

I. J. Hodgkinson, K. M. Chong, A. C. B. Molteno, “Photo-refraction of the living eye: a model for linear knife edge photoscreening,” Appl. Opt. 30, 2263–2269 (1991).
[CrossRef] [PubMed]

I. J. Hodgkinson, K. M. Chong, A. C. B. Molteno, “Characterization of the fundal reflectance of infants,” Optom. Vis. Sci. 68, 513–521 (1991).
[CrossRef] [PubMed]

Delori, F. C.

Dwight, H. B.

H. B. Dwight, Tables of Integrals and Other Mathematical Data (Macmillan, New York, 1961).

Elsner, A. E.

Hodgkinson, I. J.

I. J. Hodgkinson, K. M. Chong, A. C. B. Molteno, “Photo-refraction of the living eye: a model for linear knife edge photoscreening,” Appl. Opt. 30, 2263–2269 (1991).
[CrossRef] [PubMed]

I. J. Hodgkinson, K. M. Chong, A. C. B. Molteno, “Characterization of the fundal reflectance of infants,” Optom. Vis. Sci. 68, 513–521 (1991).
[CrossRef] [PubMed]

Howland, B.

Howland, H. C.

Hughes, G. W.

Kortum, G.

G. Kortum, Reflectance Spectroscopy (Springer-Verlag, New York, 1969).
[CrossRef]

Molteno, A. C. B.

I. J. Hodgkinson, K. M. Chong, A. C. B. Molteno, “Characterization of the fundal reflectance of infants,” Optom. Vis. Sci. 68, 513–521 (1991).
[CrossRef] [PubMed]

I. J. Hodgkinson, K. M. Chong, A. C. B. Molteno, “Photo-refraction of the living eye: a model for linear knife edge photoscreening,” Appl. Opt. 30, 2263–2269 (1991).
[CrossRef] [PubMed]

Navarro, R.

Pflibsen, K. P.

Webb, R. H.

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Figures (9)

Fig. 1
Fig. 1

Apparatus for investigating the red-halo effect that is observed in the human eye when a white source is imaged on the retina. When the parallel layer of blood in the figure is a few tenths of a millimeter thick, the red halo occurs and contours the edges of the image of the slit, as in the case of the human fundus. However, when the thickness of the layer of blood is increased to a few centimeters so that the red light cannot penetrate into and return from the reflector, the red halo is not observed.

Fig. 2
Fig. 2

Multilayered structure used to represent the absorbing, reflecting, and scattering media in the human eye. When a narrow column of rays enters the eye and penetrates into the choriocapillaris and the choroidal stroma, blood scatters the light in the forward direction, and reflections at internal interfaces cause some of the light to return through the retina. The PSF is the flux density of the rays that return through a reference surface, here taken to be the inner limiting membrane, after adjustment for viewing from outside the eye.

Fig. 3
Fig. 3

Symbols, experimental values recorded for lateral spreading of 633-nm laser light after transmission through a 200-μm layer of human blood; curves, Lorentzian, Gaussian, and sech2 profiles considered for an empirical PSF.

Fig. 4
Fig. 4

Symbols, measured values of lateral spreading of light after transmission through layers of human blood; curves, fitted sech2 profiles.

Fig. 5
Fig. 5

Distribution of embedded reflectors in the choroidal stroma.

Fig. 6
Fig. 6

Heavy solid curves, reflection coefficients (total scatter RS) for light that has returned from within the choriocapillaris, from within the choroidal stroma, and after reflection at the sclera. The long-wavelength edge of the 575-nm oxyhemoglobin absorption band divides the reflectance curves into low- and high-value zones; dotted curves in bottom-right-hand corner, reflection coefficients for scattered light that has penetrated to and been reflected from the sclera; light solid curves, reflection coefficients RR for light that returns from the anterior reflector; dashed curve, form of the absorption coefficient Khb for blood. (N, nasal fundus; P, perifovea; F, fovea.)

Fig. 7
Fig. 7

PSF and LSF shapes typical of the low- and high-value zones separated by λ = 575 nm.

Fig. 8
Fig. 8

Peak value PS(0) of the PSF’s. N, nasal fundus; P, perifovea; F, fovea.

Fig. 9
Fig. 9

Standard deviation σS of the PSF’s. N, nasal fundus; P, perifovea; F, fovea.

Equations (51)

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σ PS = [ 0 P ( r ) r 3 d r / 0 P ( r ) r d r ] 1 / 2 ,
σ LS = [ 0 L ( x ) x 2 d x / 0 L ( x ) d x ] 1 / 2 .
D om , 420 = [ 0.5 , 0.5 , 0.5 ] D . U . ,
K om = 0.42 exp [ - 0.0117 ( λ - 450 ) ] .
D ms = [ 0.1 , 0.1 , 0.1 ] D . U . ,
T 1 = 10 ( - K om D om , 420 + D ms ) .
d 2 = [ 250 , 200 , 100 ] μ m .
D mp , 460 = [ 0.0 , 0.024 , 0.21 ] D . U . ,
K mp = 0.9 exp [ - 0.0024 ( λ - 456 ) 2 ] + 0.84 × exp [ - 0.0017 ( λ - 490 ) 2 ] ,
T 2 = 10 - K mp D mp , 460 .
R 3 = [ 0.037 , 0.029 , 0.023 ] ,
d 3 = [ 10 , 10 , 10 ] μ m .
D RPE , 500 = [ 0.35 , 0.5 , 0.6 ] D . U . ,
K me = ( λ / 500 ) - 3.4 .
T 3 = 10 - K me D RPE , 500 .
d 4 = [ 10 , 10 , 10 ] μ m .
K hb = 0.0161 exp [ - 0.028 ( λ - 450 ) ] + 0.0109 exp [ - 0.0021 ( λ - 540 ) 2 ] + 0.0112 exp [ - 0.0063 ( λ - 575 ) 2 ] ,
T 4 = 10 - K hb d 4 .
d 5 = [ 400 , 400 , 400 ] μ m
D me , 500 = [ 0.96 , 1.92 , 2.13 ] D . U . ,
D x = [ 0.17 , 0.09 , 0.10 ] D . U .
D 5 = K me D me , 500 + K hb d hb + D x .
T 5 = 10 - D 5 ,
S = 0.0006 μ m - 1 ,
d hb = [ 146 , 182 , 168 ] μ m .
R 6 = 0.5 exp [ - 0.00261 ( λ - 675 ) ] .
R 5 = [ 1 - R 6 ( a - b coth b S d 5 ) ] / ( a + b coth b S d 5 - R 6 ) ,
a = 1 + D 5 log e 10 / d 5 S ,
b = ( a 2 - 1 ) 1 / 2 .
R = R S + R R .
R S = T 1 2 T 2 2 ( 1 - R 3 ) T 3 2 T 4 2 R 5 ,
R R = T 1 2 T 2 2 R 3 .
P ( r ) = P S ( r ) + P R ( r ) .
P B ( r ) sech 2 ( 1.763 r / w B ) ,
w B = 0.25 z B + 5.8 × 10 - 11 z B 4.6 .
σ B = [ 9 × 1.202057 / ( 8 × 1.763 2 log e 2 ) ] 1 / 2 w B = 0.7923 w B .
P B ( r ) sech 2 ( 1.397 r / σ B ) ,
σ B = 0.2 z B + 4.6 × 10 - 11 z B 4.6 .
w LS w PS
σ LS [ 2 π 2 log e 2 / ( 27 × 1.202057 ) ] 1 / 2 σ P S = 0.6493 σ PS .
Δ r 1 + Δ r 2 T 5 2 / N + Δ r 3 T 5 4 / N + + Δ r N T 5 2 ( N - 1 ) / N + Δ r N + 1 T 5 2 = R 5 .
Δ r 1 = Δ r 2 = = Δ r N = Δ r ,
Δ r N + 1 = R 6 .
Δ r = ( 1 - T 5 2 / N ) ( R 5 - T 5 2 R 6 ) / ( 1 - T 5 2 ) .
z j = 2 d 4 + 2 ( j - 1 ) d hb / N ,
σ j = ( 0.2 z j + 4.6 × 10 - 11 z j 4.6 ) ( d 2 + d 3 + 2 d j ) / z j .
p j ( r ) = p j ( 0 ) sech 2 ( 1.397 r / σ j ) ,
p j ( 0 ) = 0.448 T 1 2 T 2 2 ( 1 - R 3 ) T 3 2 T 4 2 T 5 2 ( j - 1 ) / N Δ r j / σ j 2 ,
P S ( r ) = j = 1 N + 1 p j ( 0 ) sech 2 ( 1.397 r / σ j ) .
P S ( 0 ) = j = 1 N + 1 p j ( 0 ) ,
σ S = [ j = 1 N + 1 Δ r j T 5 2 ( j - 1 ) / N σ j 2 / R 5 ] 1 / 2 .

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