Abstract

Individual photoreceptor waveguiding suggests that the entire retina can be considered as a composite fiber-optic element relating a retinal image to a corresponding waveguided image. In such a scheme, a visual sensation is produced only when the latter interacts with the pigments of the outer photoreceptor segments. Here the possible consequences of photoreceptor waveguiding on vision are studied with important implications for the pupil-apodization method commonly used to incorporate directional effects of the retina. In the absence of aberrations, it is found that the two approaches give identical predictions for an effective retinal image only when the pupil apodization is chosen twice as narrow as suggested by the traditional Stiles–Crawford effect. In addition, phase variations in the retinal field due to ocular aberrations can delicately alter a waveguided image, and this may provide plausible justification for an improved visual sensation as compared with what should be expected on the grounds of a retinal image only.

© 2007 Optical Society of America

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2006 (1)

G. Westheimer, "Specifying and controlling the optical image on the human retina," Prog. Retinal Res. 25, 19-42 (2006).
[CrossRef]

2005 (2)

2004 (2)

P. Artal, L. Chen, E. J. Fernández, B. Singer, S. Manzanera, and D. R. Williams, "Neural compensation for the eye's optical aberrations," J. Vision 4, 281-287 (2004).
[CrossRef]

B. Vohnsen, I. Iglesias, and P. Artal, "Directional imaging of the retinal cone mosaic," Opt. Lett. 29, 968-970 (2004).
[CrossRef] [PubMed]

2002 (4)

A. Roorda, F. Romero-Borja, W. J. Donnelly III, H. Queener, T. J. Hebert, and M. C. W. Campbell, "Adaptive optics scanning laser ophthalmoscopy," Opt. Express 10, 405-412 (2002).
[PubMed]

D. A. Atchinson and D. H. Scott, "Contrast sensitivity and the Stiles-Crawford effect," Vision Res. 42, 1559-1569 (2002).
[CrossRef]

Q. V. Hoang, R. A. Linsenmeier, C. K. Chung, and C. A. Curcio, "Photoreceptor inner segments in monkey and human retina: mitochondrial density, optics, and regional variation," Visual Neurosci. 19, 395-407 (2002).
[CrossRef]

D. A. Atchison, D. H. Scott, N. C. Strang, and P. Artal, "Influence of Stiles-Crawford apodization on visual acuity," J. Opt. Soc. Am. A 19, 1073-1083 (2002).
[CrossRef]

2001 (4)

H. S. Smallman, D. I. A. MacLeod, and P. Doyle, "Realignment of cones after cataract removal," Nature (London) 412, 604-605 (2001).
[CrossRef]

M. Kono, J. M. Enoch, E. Strada, P. Shih, R. Srinivasan, V. Lakshminarayanan, W. Susilasate, and A. Graham, "Stiles-Crawford effect of the first kind: assessment of photoreceptor alignments following dark patching," Vision Res. 41, 103-118 (2001).
[CrossRef] [PubMed]

M. J. McMahon and D. I. A. MacLeod, "Retinal contrast losses and visual resolution with obliquely incident light," J. Opt. Soc. Am. A 18, 2692-2703 (2001).
[CrossRef]

E. J. Fernández, I. Iglesias, and P. Artal, "Closed-loop adaptive optics in the human eye," Opt. Lett. 26, 746-748 (2001).
[CrossRef]

1999 (2)

S. Marcos, E. Moreno, and R. Navarro, "The depth-of-field of the human eye from objective and subjective measurements," Vision Res. 39, 2039-2049 (1999).
[CrossRef] [PubMed]

X. Zhang, M. Ye, A. Bradley, and L. Thibos, "Apodization by the Stiles-Crawford effect moderates the visual impact of retinal image defocus," J. Opt. Soc. Am. A 16, 812-820 (1999).
[CrossRef]

1998 (2)

1995 (1)

1989 (2)

1987 (1)

1985 (1)

1980 (1)

1976 (1)

1975 (1)

B. Drum, "Additivity of the Stiles-Crawford effect for a Fraunhofer image," Vision Res. 15, 291-298 (1975).
[CrossRef] [PubMed]

1974 (2)

1973 (1)

A. W. Snyder and C. Pask, "The Stiles-Crawford effect--explanation and consequences," Vision Res. 13, 1115-1137 (1973).
[CrossRef] [PubMed]

1971 (1)

A. M. Laties and J. M. Enoch, "An analysis of retinal receptor orientation," Invest. Ophthalmol. Visual Sci. 10, 69-77 (1971).

1968 (1)

W. L. Makous, "A transient Stiles-Crawford effect," Vision Res. 8, 1271-1284 (1968).
[CrossRef] [PubMed]

1967 (1)

D. G. Green, "Visual resolution when light enters the eye through different parts of the pupil," J. Physiol. (London) 190, 583-593 (1967).

1965 (2)

F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J. Physiol. (London) 181, 576-593 (1965).

H. Metcalf, "Stiles-Crawford apodization," J. Opt. Soc. Am. 55, 72-74 (1965).
[CrossRef]

1963 (1)

1961 (1)

J. M. Enoch, "Wave-guide modes in retinal receptors," Science 133, 1353-1354 (1961).
[CrossRef] [PubMed]

1958 (2)

1957 (1)

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

1946 (1)

1944 (1)

1933 (1)

W. S. Stiles and B. H. Crawford, "The luminous efficiency of rays entering the eye pupil at different points," Proc. R. Soc. London, Ser. B 112, 428-450 (1933).
[CrossRef]

Artal, P.

Atchinson, D. A.

D. A. Atchinson and D. H. Scott, "Contrast sensitivity and the Stiles-Crawford effect," Vision Res. 42, 1559-1569 (2002).
[CrossRef]

Atchison, D. A.

Bouman, M. A.

W. Wijngaard, M. A. Bouman, and F. Budding, "The Stiles-Crawford colour change," Vision Res. 14, 951-957 (1974).
[CrossRef] [PubMed]

Bradley, A.

Budding, F.

W. Wijngaard, M. A. Bouman, and F. Budding, "The Stiles-Crawford colour change," Vision Res. 14, 951-957 (1974).
[CrossRef] [PubMed]

Burns, S. A.

Campbell, F. W.

F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J. Physiol. (London) 181, 576-593 (1965).

F. W. Campbell, "A retinal acuity direction effect," J. Physiol. (London) 143, 25-26 (1958).

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

Campbell, M. C. W.

Carroll, J. P.

Chen, B.

B. Chen and W. Makous, "Light capture by human cones," J. Physiol. (London) 414, 89-109 (1989).

Chen, L.

P. Artal, L. Chen, E. J. Fernández, B. Singer, S. Manzanera, and D. R. Williams, "Neural compensation for the eye's optical aberrations," J. Vision 4, 281-287 (2004).
[CrossRef]

Chung, C. K.

Q. V. Hoang, R. A. Linsenmeier, C. K. Chung, and C. A. Curcio, "Photoreceptor inner segments in monkey and human retina: mitochondrial density, optics, and regional variation," Visual Neurosci. 19, 395-407 (2002).
[CrossRef]

Coletta, N. J.

Crawford, B. H.

W. S. Stiles and B. H. Crawford, "The luminous efficiency of rays entering the eye pupil at different points," Proc. R. Soc. London, Ser. B 112, 428-450 (1933).
[CrossRef]

Curcio, C. A.

Q. V. Hoang, R. A. Linsenmeier, C. K. Chung, and C. A. Curcio, "Photoreceptor inner segments in monkey and human retina: mitochondrial density, optics, and regional variation," Visual Neurosci. 19, 395-407 (2002).
[CrossRef]

Delori, F.

Donnelly, W. J.

Doyle, P.

H. S. Smallman, D. I. A. MacLeod, and P. Doyle, "Realignment of cones after cataract removal," Nature (London) 412, 604-605 (2001).
[CrossRef]

Drum, B.

B. Drum, "Additivity of the Stiles-Crawford effect for a Fraunhofer image," Vision Res. 15, 291-298 (1975).
[CrossRef] [PubMed]

Elsner, A. E.

Enoch, J. M.

M. Kono, J. M. Enoch, E. Strada, P. Shih, R. Srinivasan, V. Lakshminarayanan, W. Susilasate, and A. Graham, "Stiles-Crawford effect of the first kind: assessment of photoreceptor alignments following dark patching," Vision Res. 41, 103-118 (2001).
[CrossRef] [PubMed]

A. M. Laties and J. M. Enoch, "An analysis of retinal receptor orientation," Invest. Ophthalmol. Visual Sci. 10, 69-77 (1971).

J. M. Enoch, "Optical properties of the retinal receptors," J. Opt. Soc. Am. 53, 71-85 (1963).
[CrossRef]

J. M. Enoch, "Wave-guide modes in retinal receptors," Science 133, 1353-1354 (1961).
[CrossRef] [PubMed]

J. M. Enoch, "Summated response of the retina to light entering different parts of the pupil," J. Opt. Soc. Am. 48, 392-405 (1958).
[CrossRef] [PubMed]

Fernández, E. J.

P. Artal, L. Chen, E. J. Fernández, B. Singer, S. Manzanera, and D. R. Williams, "Neural compensation for the eye's optical aberrations," J. Vision 4, 281-287 (2004).
[CrossRef]

E. J. Fernández, I. Iglesias, and P. Artal, "Closed-loop adaptive optics in the human eye," Opt. Lett. 26, 746-748 (2001).
[CrossRef]

Graham, A.

M. Kono, J. M. Enoch, E. Strada, P. Shih, R. Srinivasan, V. Lakshminarayanan, W. Susilasate, and A. Graham, "Stiles-Crawford effect of the first kind: assessment of photoreceptor alignments following dark patching," Vision Res. 41, 103-118 (2001).
[CrossRef] [PubMed]

Green, D. G.

D. G. Green, "Visual resolution when light enters the eye through different parts of the pupil," J. Physiol. (London) 190, 583-593 (1967).

F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J. Physiol. (London) 181, 576-593 (1965).

Hebert, T. J.

Hoang, Q. V.

Q. V. Hoang, R. A. Linsenmeier, C. K. Chung, and C. A. Curcio, "Photoreceptor inner segments in monkey and human retina: mitochondrial density, optics, and regional variation," Visual Neurosci. 19, 395-407 (2002).
[CrossRef]

Iglesias, I.

Joblin, A.

Kono, M.

M. Kono, J. M. Enoch, E. Strada, P. Shih, R. Srinivasan, V. Lakshminarayanan, W. Susilasate, and A. Graham, "Stiles-Crawford effect of the first kind: assessment of photoreceptor alignments following dark patching," Vision Res. 41, 103-118 (2001).
[CrossRef] [PubMed]

Lakshminarayanan, V.

M. Kono, J. M. Enoch, E. Strada, P. Shih, R. Srinivasan, V. Lakshminarayanan, W. Susilasate, and A. Graham, "Stiles-Crawford effect of the first kind: assessment of photoreceptor alignments following dark patching," Vision Res. 41, 103-118 (2001).
[CrossRef] [PubMed]

Laties, A. M.

A. M. Laties and J. M. Enoch, "An analysis of retinal receptor orientation," Invest. Ophthalmol. Visual Sci. 10, 69-77 (1971).

Linsenmeier, R. A.

Q. V. Hoang, R. A. Linsenmeier, C. K. Chung, and C. A. Curcio, "Photoreceptor inner segments in monkey and human retina: mitochondrial density, optics, and regional variation," Visual Neurosci. 19, 395-407 (2002).
[CrossRef]

MacLeod, D. I. A.

H. S. Smallman, D. I. A. MacLeod, and P. Doyle, "Realignment of cones after cataract removal," Nature (London) 412, 604-605 (2001).
[CrossRef]

M. J. McMahon and D. I. A. MacLeod, "Retinal contrast losses and visual resolution with obliquely incident light," J. Opt. Soc. Am. A 18, 2692-2703 (2001).
[CrossRef]

Makous, W.

B. Chen and W. Makous, "Light capture by human cones," J. Physiol. (London) 414, 89-109 (1989).

Makous, W. L.

W. L. Makous, "A transient Stiles-Crawford effect," Vision Res. 8, 1271-1284 (1968).
[CrossRef] [PubMed]

Manzanera, S.

P. Artal, L. Chen, E. J. Fernández, B. Singer, S. Manzanera, and D. R. Williams, "Neural compensation for the eye's optical aberrations," J. Vision 4, 281-287 (2004).
[CrossRef]

Marcos, S.

S. Marcos, E. Moreno, and R. Navarro, "The depth-of-field of the human eye from objective and subjective measurements," Vision Res. 39, 2039-2049 (1999).
[CrossRef] [PubMed]

McMahon, M. J.

Metcalf, H.

Moon, P.

Moreno, E.

S. Marcos, E. Moreno, and R. Navarro, "The depth-of-field of the human eye from objective and subjective measurements," Vision Res. 39, 2039-2049 (1999).
[CrossRef] [PubMed]

Navarro, R.

S. Marcos, E. Moreno, and R. Navarro, "The depth-of-field of the human eye from objective and subjective measurements," Vision Res. 39, 2039-2049 (1999).
[CrossRef] [PubMed]

Noll, R. J.

O'Brien, B.

Palmer, D. A.

Pask, C.

C. Pask and A. Stacey, "Optical properties of retinal photoreceptors and the Campbell effect," Vision Res. 38, 953-961 (1998).
[CrossRef] [PubMed]

A. W. Snyder and C. Pask, "The Stiles-Crawford effect--explanation and consequences," Vision Res. 13, 1115-1137 (1973).
[CrossRef] [PubMed]

C. Pask and A. W. Snyder, "Theory of the Stiles-Crawford effect of the second kind," in Photoreceptor Optics, A.W.Snyder and R.Menzel, eds. (Springer-Verlag, 1975), pp. 152-156.

Queener, H.

Romero-Borja, F.

Roorda, A.

Scott, D. H.

D. A. Atchinson and D. H. Scott, "Contrast sensitivity and the Stiles-Crawford effect," Vision Res. 42, 1559-1569 (2002).
[CrossRef]

D. A. Atchison, D. H. Scott, N. C. Strang, and P. Artal, "Influence of Stiles-Crawford apodization on visual acuity," J. Opt. Soc. Am. A 19, 1073-1083 (2002).
[CrossRef]

Shih, P.

M. Kono, J. M. Enoch, E. Strada, P. Shih, R. Srinivasan, V. Lakshminarayanan, W. Susilasate, and A. Graham, "Stiles-Crawford effect of the first kind: assessment of photoreceptor alignments following dark patching," Vision Res. 41, 103-118 (2001).
[CrossRef] [PubMed]

Singer, B.

P. Artal, L. Chen, E. J. Fernández, B. Singer, S. Manzanera, and D. R. Williams, "Neural compensation for the eye's optical aberrations," J. Vision 4, 281-287 (2004).
[CrossRef]

Smallman, H. S.

H. S. Smallman, D. I. A. MacLeod, and P. Doyle, "Realignment of cones after cataract removal," Nature (London) 412, 604-605 (2001).
[CrossRef]

Smith, G.

Snyder, A. W.

A. W. Snyder and C. Pask, "The Stiles-Crawford effect--explanation and consequences," Vision Res. 13, 1115-1137 (1973).
[CrossRef] [PubMed]

C. Pask and A. W. Snyder, "Theory of the Stiles-Crawford effect of the second kind," in Photoreceptor Optics, A.W.Snyder and R.Menzel, eds. (Springer-Verlag, 1975), pp. 152-156.

Spencer, D. E.

Srinivasan, R.

M. Kono, J. M. Enoch, E. Strada, P. Shih, R. Srinivasan, V. Lakshminarayanan, W. Susilasate, and A. Graham, "Stiles-Crawford effect of the first kind: assessment of photoreceptor alignments following dark patching," Vision Res. 41, 103-118 (2001).
[CrossRef] [PubMed]

Stacey, A.

C. Pask and A. Stacey, "Optical properties of retinal photoreceptors and the Campbell effect," Vision Res. 38, 953-961 (1998).
[CrossRef] [PubMed]

Stiles, W. S.

W. S. Stiles and B. H. Crawford, "The luminous efficiency of rays entering the eye pupil at different points," Proc. R. Soc. London, Ser. B 112, 428-450 (1933).
[CrossRef]

Strada, E.

M. Kono, J. M. Enoch, E. Strada, P. Shih, R. Srinivasan, V. Lakshminarayanan, W. Susilasate, and A. Graham, "Stiles-Crawford effect of the first kind: assessment of photoreceptor alignments following dark patching," Vision Res. 41, 103-118 (2001).
[CrossRef] [PubMed]

Strang, N. C.

Susilasate, W.

M. Kono, J. M. Enoch, E. Strada, P. Shih, R. Srinivasan, V. Lakshminarayanan, W. Susilasate, and A. Graham, "Stiles-Crawford effect of the first kind: assessment of photoreceptor alignments following dark patching," Vision Res. 41, 103-118 (2001).
[CrossRef] [PubMed]

Thibos, L.

Vohnsen, B.

Westheimer, G.

G. Westheimer, "Specifying and controlling the optical image on the human retina," Prog. Retinal Res. 25, 19-42 (2006).
[CrossRef]

G. Westheimer, "The resolving power of the eye," Vision Res. 45, 945-947 (2005).
[CrossRef] [PubMed]

Wijngaard, W.

Williams, D. R.

P. Artal, L. Chen, E. J. Fernández, B. Singer, S. Manzanera, and D. R. Williams, "Neural compensation for the eye's optical aberrations," J. Vision 4, 281-287 (2004).
[CrossRef]

D. R. Williams and N. J. Coletta, "Cone spacing and the visual resolution limit," J. Opt. Soc. Am. A 4, 1514-1523 (1987).
[CrossRef] [PubMed]

Wu, S.

Ye, M.

Zhang, X.

Invest. Ophthalmol. Visual Sci. (1)

A. M. Laties and J. M. Enoch, "An analysis of retinal receptor orientation," Invest. Ophthalmol. Visual Sci. 10, 69-77 (1971).

J. Opt. Soc. Am. (8)

J. Opt. Soc. Am. A (9)

J. Physiol. (London) (4)

B. Chen and W. Makous, "Light capture by human cones," J. Physiol. (London) 414, 89-109 (1989).

F. W. Campbell, "A retinal acuity direction effect," J. Physiol. (London) 143, 25-26 (1958).

F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J. Physiol. (London) 181, 576-593 (1965).

D. G. Green, "Visual resolution when light enters the eye through different parts of the pupil," J. Physiol. (London) 190, 583-593 (1967).

J. Vision (1)

P. Artal, L. Chen, E. J. Fernández, B. Singer, S. Manzanera, and D. R. Williams, "Neural compensation for the eye's optical aberrations," J. Vision 4, 281-287 (2004).
[CrossRef]

Nature (London) (1)

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G. Westheimer, "Specifying and controlling the optical image on the human retina," Prog. Retinal Res. 25, 19-42 (2006).
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Figures (9)

Fig. 1
Fig. 1

Schematic of (a) retinal light-coupling configuration considered, (b) retinal image ψ r 2 , and (c) waveguided image [dashed curve at outer segments in (a)] produced via coupling of the retinal field to individual photoreceptor waveguide modes. The waveguided image represents a sampled (by the photoreceptors arranged approximately in a hexagonal pattern at the fovea) and inhomogenously weighted copy of the retinal image.

Fig. 2
Fig. 2

Waveguided power fraction T 01 ( u c , 0 ) (dotted curves) compared with (rescaled) retinal PSF I r ( u c , 0 ) (solid curves) in the absence of aberrations Φ WA 0 for pupil diameters D of 3, 5, and 7 mm . The mode width w 01 of the single-mode photoreceptor waveguide is 1.5 μ m .

Fig. 3
Fig. 3

Magnitude of retinal field ψ r ( u c , 0 ) and its phase (wrapped on π to π) for 3 and 5 mm pupil diameters. Defocus is 0 D (solid curve), 0.1 D (dashed curve), 0.2 D (dotted curve), and 0.3 D (dashed–dotted curve).

Fig. 4
Fig. 4

Power fraction T 01 ( u c , 0 ) (curve) of waveguided light compared with (rescaled) retinal intensity I r ( u c , 0 ) (markers) in the case of 0.1 D and 0.3 D defocus. Pupil size is (solid, ×) 3 mm , (dashed, +) 5 mm , and (dotted, 엯) 7 mm . The mode width w 01 of the single-mode photoreceptor waveguide is 1.0 μ m . Note that for 0.1 D defocus with a 7 mm pupil, the intensity distribution has been reduced by a factor of 4 to include off-axis oscillations within the scale of the plot.

Fig. 5
Fig. 5

Simulated modulation transfer function (MTF) for a 5 and 7 mm pupil for an amplitude apodization function G eye ( r ) = 10 ρ SCE r 2 . The curves are grouped according to the different amounts of defocus included and show the MTF for ρ SCE = 0 (solid curves), ρ SCE = 0.05 mm 2 (dashed curves), and ρ SCE = 0.10 mm 2 (dotted curves).

Fig. 6
Fig. 6

Influence of 0.1 D defocus (left) and 0.3 D defocus (right) on retinal I r ( u , v ) and waveguided P ( u , v ) images for a 7 mm pupil. The phase of the wavefront [wrapped from π (black) to π (white)] is shown at the top of the figure for the pupil plane and for the retina respectively. The waveguided power distributions have been obtained for a 1.0 and 1.5 μ m photoreceptor mode width, respectively. Image size is 64 × 64 μ m at the retina and 10.6 × 10.6 mm for the phase distributions at the pupil.

Fig. 7
Fig. 7

Influence of Zernike polynomial terms Z 6 = 0.5 μ m astigmatism (left) and Z 11 = 0.2 μ m spherical aberration (right) on retinal and waveguided images for a 7 mm pupil. In the case of spherical aberration, magnitude distributions have been shown instead of intensity and power distributions to enhance the visibility of the concentric rings. Other details are the same as in Fig. 6.

Fig. 8
Fig. 8

Influence of real-eye-like ocular aberrations with Zernike terms: Z 4 = 0.5 , Z 5 = 0.3 , Z 6 = 0.5 , Z 7 = 0.1 , Z 8 = 0.2 , Z 9 = 0.1 , Z 10 = 0.3 , and Z 11 = 0.1 μ m with all other terms identically zero (left), and the same with exclusion of defocus (right) for a 7 mm pupil. The root-mean-square wavefront aberration at the pupil is 0.866 μ m when all terms are included and 0.707 μ m when defocus is excluded. Other details are the same as in Fig. 6.

Fig. 9
Fig. 9

Comparison of retinal and waveguided images of two point sources emitting radiation coherently and in phase (left) and incoherently (right). Without aberrations, the first-order approximation of Section 4 leads to identical retinal and waveguided images (top). With aberrations (here defocus 0.1 D), the retinal images (middle) and waveguided images (bottom) differ. Sources are located at 6.1 m in front of the eye and angularly separated by 1.0 as corresponding to the line width in 20 20 visual tests. The pupil size is 5 mm , photoreceptor mode width is 1.5 μ m , and the image size is 32 × 32 μ m .

Equations (14)

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ψ r ( u , v ) = 2 n eye i π D λ f eye F n eye u λ f eye , n eye v λ f eye { P eye ( x , y ) exp [ i Φ WA ( x , y ) ] } ,
T = m ψ r ψ m * d u d v 2 ψ r 2 d u d v ψ m 2 d u d v ,
ψ r ( ρ ) = π D n eye 2 i λ f eye [ 2 J 1 ( π D n eye λ f eye ρ ) π D n eye λ f eye ρ ] ,
I r ( ρ ) = π 4 D 2 ( n eye λ f eye ) 2 [ 2 J 1 ( π D n eye λ f eye ρ ) π D n eye λ f eye ρ ] 2 .
ψ 01 ( ρ ) = 2 π w 01 2 exp [ ρ 2 w 01 2 ] ,
T 01 ( u c , 0 ) = ψ r ( u , v ) ψ 01 ( u u c , v ) d u d v 2 .
ψ r ( ρ ) = 4 π n eye i D λ f eye 0 D 2 r exp ( i Φ WA ) J 0 ( 2 π n eye λ f eye r ρ ) d r ,
T 01 ( u c , v c ) = F n eye u λ f eye , n eye v λ f eye { P eye exp ( i Φ WA ) } ψ 01 ( u , v ) 2 ,
I ̃ ( u c , v c ) = F n eye u λ f eye , n eye v λ f eye { G eye P eye exp ( i Φ WA ) } 2 = F n eye u λ f eye , n eye v λ f eye { P eye exp ( i Φ WA ) } F n eye u λ f eye , n eye v λ f eye { G eye } 2 .
T 01 ( u c , v c ) = F n eye u λ f eye , n eye v λ f eye { G eye 1 P eye exp ( i Φ WA ) } ψ 01 ( u , v ) 2 .
A A 0 + A u u c , v c ( u u c ) + A v u c , v c ( v v c ) = A 0 + A u ( u u c ) + A v ( v v c ) ,
ϕ ϕ 0 + ϕ u u c , v c ( u u c ) + ϕ v u c , v c ( v v c ) = ϕ 0 + ϕ u ( u u c ) + ϕ v ( v v c ) .
P 2 π η w 01 2 [ A 0 2 + ( w 01 2 2 ) 2 ( A u ϕ u + A v ϕ v ) 2 ] exp [ w 01 2 2 ( ϕ u 2 + ϕ v 2 ) ] ,
w = λ f eye π n eye ρ SCE log ( e ) .

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