The Photoreceptor Mosaic Aristophanis Pallikaris IVO, University of Crete Institute of Vision and Optics 10th Aegean Summer School
Overview Brief Anatomy Photoreceptors Categorization Visual Function Photoreceptor Mosaic Density Size Spatial Regularity Sampling Resolution Limits Conclusions & Discussion
Eye Anatomy (RPE) Cornea Retina Pupil Lens Fovea
Retinal Anatomy Pigmented cells Photoreceptors Horizontal, Amacrine, Bipolar Cells Ganglion cells PUPIL 2004, John Willey & Sons, Inc Huffman: PSYCHOLOGY IN ACTION, 7E
Photoreceptor s Characteristics Discs The photoreceptors consist of an outer segment, an inner segment, a cell body, and a synaptic terminal. Cones have conical shaped structure and the discs of the outer segment remain attached to the outer segment membrane. Rods have slim rod-shaped structure and the discs of the outer segment are free floating inside the outer segment disc. Outer Segment Inner Segment Synaptic Terminal CONE
Photoreceptor s Characteristics Discs Outer Segment Rods contain the visual pigment rhodopsin, are highly sensitive photoreceptors, and are used for vision under dark-dim conditions. Cones contain cone opsins, are used for color vision, and provide the highest acuity during high light levels. Inner Segment Synaptic Terminal CONE
Dark Adaptation of Photoreceptors Low Rods Logarithm of sensitivity Cones High 10 20 Time in Dark (min) McFarland et al 1960
Dark Adaptation of Photoreceptors Low Rods Logarithm of sensitivity Cones High 10 20 Time in Dark (min) McFarland et al 1960
Dark Adaptation of Photoreceptors Low Rods Logarithm of sensitivity Cones High 10 20 Time in Dark (min) McFarland et al 1960
Spectral Absorptance of Cone Opsins Normalized spectral absorptance 1.0 0.8 0.6 0.4 0.2 0.0 400 450 500 550 600 650 700 Wavelength (nm) Brown & Wald 1964,
Spectral Absorptance of Cone Opsins Normalized spectral absorptance Rods 1.0 0.8 0.6 0.4 0.2 0.0 400 450 500 550 600 650 700 Wavelength (nm) Brown & Wald 1964,
Spectral Absorptance of Cone Opsins Normalized spectral absorptance S-Cones Rods 1.0 0.8 0.6 0.4 0.2 0.0 400 450 500 550 600 650 700 Wavelength (nm) Brown & Wald 1964,
Spectral Absorptance of Cone Opsins Normalized spectral absorptance M-Cones S-Cones Rods 1.0 0.8 0.6 0.4 0.2 0.0 400 450 500 550 600 650 700 Wavelength (nm) Brown & Wald 1964,
Spectral Absorptance of Cone Opsins Normalized spectral absorptance 1.0 0.8 0.6 0.4 0.2 M-Cones S-Cones Rods L-Cones 0.0 400 450 500 550 600 650 700 Wavelength (nm) Brown & Wald 1964,
Spatial Density of Cones Spatial Density (cells/mm2) 160000 100000 20000 Cones are densely packed in the fovea and their density decreases abruptly with eccentricity. 5 million cones 25 20 15 10 5 0 5 10 15 20 Retinal Eccentricitiy (mm) After Osterberg 1935, as modified by Rodieck 1988, micrographs from Curcio 1990
Power Spectrum Yellot s ring 1/r r Triangular mosaic that is fairly regular r = 3/2 * center-to-center spacing
Power Spectrum Yellot s ring Average Radial Power Spectrum Spatial Frequency (cycles/degree)
High Resolution Retinal Images Heidi Hofer and Matt McMahon
Cone Mosaic in the Extrafoveal Retina Irregular Lattice Regularity degenerates with eccentricity approaching an asympotic amount of dissaray at 2-3 deg Packer et al 1996
Spatial Density of Rods Rods are absent from the center of the fovea, their density reaches a maximum at around 20 deg and decreases again toward the periphery. 200 million After Osterberg 1935, as modified by Rodieck 1988, micrographs from Curcio 1990
Rod Mosaic in the Extrafoveal Retina Packer et al 1996
Trichromatic Cone Mosaic in the Fovea AP
Trichromatic Cone Mosaic in the Fovea Average L:M = 2:1 Roorda & Wiliams, 1999, Hofer et al 2005
Waveguide Properties Refracted The individual photoreceptors behave as a classic fiber-optic element which capture the incident light and channel the electromagnetic to sites of visual absorption. n 2 n 1 >n 2 θ c θ 1 θ 2 Reflected n 3 n 2 n 1 >n 2, n 3 n 2
Cone Directionality -2 mm Registered sum of 8 images along 9 different positions -1 mm 1 eccentricity -2 mm -1 mm 0 mm 1 mm 2 mm 1 mm 2 mm 5 arcmin Pallikaris et al 2003
Cone Directionality Normalized Intensity 140 120 100 80 60 40 20 0-6 -4-2 0 2 4 6 Pupil Position (mm) Pallikaris et al 2003
Sampling Resolution The Sampling Theorem: Helmholtz (1911): When the widths of two luminous objects used in the test are vanishingly small as compared with the interval between them, they cannot be seen as separate unless there is an unstimulated retinal element between the retinal elements on which their images fall. In other words, the diameter of such an element must certainly be less than the interval between the two images. Goodman (1968): a band-limited signal that is sampled at regular intervals can be completely recovered from the sample values without aliasing if the highest frequency of the signal does not exceed 1/2S where S is the spacing between samples.
Sampling Resolution f1 fn 2f1 S, Sampling frequency = 1/S
Sampling Resolution f1 fn Sampled Output 2f1 S, Sampling frequency = 1/S
Sampling Resolution Reconstructed f1 fn Sampled Output 2f1 S, Sampling frequency = 1/S
Sampling Resolution Reconstructed f1 fn Sampled Output 2f1 S, Sampling frequency = 1/S fn=1/2s Nyquist Frequency (maximum resolvable frequency
Sampling Resolution Sampled and Reconstructed Sine Grating
Sampling in the Central Retina Primate Central Fovea (0.5 deg) Slide courtesy David R. Williams
Slide courtesy David R. Williams Nyquist Limit Sampling Frequency 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
Slide courtesy David R. Williams Nyquist Limit Sampling Frequency 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
Slide courtesy David R. Williams Nyquist Limit Sampling Frequency 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
Slide courtesy David R. Williams Nyquist Limit Sampling Frequency 0 10 20 30 40 50 60 70 80 90 100 110120 130 140 150 160
Sampling Limits by Laser Interferometry 1 deg Drawings of appearance of 110 c/deg Interference Fringes Williams et al. 1985
Cone Density and Resolution Visual Resolution 28.6/10 21.3/10 17.5/10 Cone Density (1000/mm 2 ) 1 ~ 10/10 Retinal Eccentricity (µm) Curcio et al., 1990
Distribution of Photoreceptors and Ganglion Cells Geisler and Banks, 1995
Sampling in the Peripheral Retina Ganglion Cell Receptive Field Ganglion Cells Bipolar, Amacrine Horizontal Cells Photoreceptors Fovea Peripheral Retina
Resolution Acuity Matches RGC Sampling Density Neural Resolution (cycles/deg) LNT acuity (Thibos 1987) Cones (Curcio 1990) Gagglion Cells (Curcio 1990) (Temporal field) Eccentricity from fovea (deg)
Sampling in the Peripheral Retina Contrast Sensitivity Spatial Frequency (cycles/deg) 20 deg eccentricity Williams et al 1996
Conclusions & Discussion There is a significant variation in the arrangement of the photoreceptors across the retina. There is a significant variation in the resolution limits related to the sampling properties of the photoreceptor mosaic across the retina. Modulation Tranfer The peripheral retinal image is subject to retinal undersampling, which will cause perceptual aliasing of spatial frequencies greater than the resolution limit of the central fovea.
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