Lecture The Human Visual System The Human Visual System Retina Optic Nerve Optic Chiasm Lateral Geniculate Nucleus (LGN) Visual Cortex The Human Eye The Human Retina Lens rods cones Cornea Fovea Optic Nerve Pupil Vitreous Humor Iris Optic Disc bipolar horizontal Ocular Muscle Retina ganglion amacrine light
Cross-section of Human Retina Outer Retinal Photoreceptors rods OS ON L Receptor Models INL cone GCL Inner µm X Light Rods - Cones - Retinal Photoreceptors Low illumination levels (Scotopic vision). Highly sensitive (respond to a single photon). million rods in each eye. No rods in fovea. High illumination levels (Photopic vision) Less sensitive than rods. 5 million cones in each eye. Only cones in fovea (aprox. 5,). Density decreases with distance from fovea. Calculating the viewing angle of a single cone in the fovea: θ 7mm -6 2.5 x -4 tan(θ) = -2 =.47 x.7 x θ 2.5µ Receptors per square mm 8 x 4 rods cones 4 6 2-6 -4-2 2 4 6 Degrees of Visual Angle Distribution of rod and cone photoreceptors θ =.84 deg ~ =.5 ' (arcmin) Cones - 2.3 µ width 2.5 µ inter-cone distance.5 field of view
Cone Mosaic Retinal Photoreceptors Cones - High illumination levels (Photopic vision) Less sensitive than rods. 5 million cones in each eye. Only cones in fovea (aprox. 5,). Density decreases with distance from fovea. 3 cone types differing in their spectral sensitivity: L, M, and S cones. µm Cone Mosaic at Fovea Cone Spectral Sensitivity Cone Mosaic in periphery Rods Cones Relative sensitivity.75.5.25 L M S 4 5 6 7 Wavelength (nm) Cone Receptor Mosaic (Roorda and Williams, 999) S cone Sampling Mosaic Foveal Periphery L-cones M-cones S-cones rods S - Cones L/M - Cones
Human Image Formation Image Formation - Optics What is the quality of the optics of the human eye? scene film Put a piece of film in front of an object. source: Yung-Yu Chuang Image Formation - Optics Image Formation - Optics Shrinking the aperture pinhole camera scene barrier film Add a barrier to block off most of the rays. It reduces blurring The pinhole is known as the aperture The image is inverted Why not create the aperture as small as possible? Less light gets through Diffraction effect source: Yung-Yu Chuang
Image Formation - Optics Shrinking the aperture Image Formation - Optics Adding a Lens scene film Image Formation - Optics Adding a Lens Lens Design: Snell s Law scene lens film n sin( φ) = n'sin( φ') circle of confusion
Lensmaker s Equation Optical power and object distance object image d s d i d s d i = f d s = source dist d = image dist i f = focal length Encoding Characteristics - Line spread Line spread defines the optical quality of the eye Light Scattered From From The Retina Is Used To Estimate Optical Quality (e.g., Campbell and Gubisch) Double Pass Method
Measurements of light reflected from the retina (Linespread) at various pupil diameters Campell and Gubisch 966 Image formation satisfies : Homogeneity: 2a a a/2 monitor image Intensity of light reflected from the eye 6.6 5.8 4.9 3.8 3. 2.4 2..5. Additivity: b b/2 2b a a a a b b b b retinal image monitor image retinal image Visual Angle (minutes of arc) Image formation is a linear system Image Formation is a Linear System Image formation is a Shift Invariant linear system in a System f out f(a) = b A shifted input produces a shifted output: A system is Linear if it satisfies superposition: a a monitor image homogeneity f(ka) = kf(a) = kb additivity f(a a 2 ) = f(a ) f(a 2 ) = b b 2 b b retinal image A finite dimensional linear system can be written as a matrix equation: b = Ra where R is the system matrix.
Relative Intensity Modeling Image Formation (Westheimer)..8.6.4.2 Relative Intensity The Human Linespread Function..8.6.4.2. -4-2 2 4 Visual angle (arc mins). Scene: -4-2 2 4 Visual angle (arc mins) The Human Modulation Transfer Function. Retinal Image: Scale factor.5. 2 3 4 5 6 Spatial Frequency (cpd) The Pointspread Function The pointspread function is a generalization of the linespread function. Astigmatism Measures the Assymmetry and Orientation of the Pointspread Function Retinal Image Monitor Image
Visual Acuity Cones at fovea are 2.5µ apart corresponding to.5 (arc min). Typical acuity targets: Visual Acuity Do to linespread, movement of stimulus by less than receptor width causes change in receptor response: stimuli receptor positions Vernier Acuity Landolt C Resolution acuity Grating acuity Snellen Letter Expected acuity is size of cone or visual angle of cone. receptors light stimulus Actual acuity ~ 5 (arc seconds) = Hyperacuity Relative visual acuity..8.6.4.2. Nasal Blind spot -4-2 2 4 Visual angle Fovea Temporal..8.6.4.2. Scotopic reseptor responses Acuity is affected by retinal position and illumination: Photopic -4-3 -2-2 3 4 Log illumination (trolands) Visual Acuity Test Electromagnetic Radiation - Spectrum K 5 B 4 X 3 M 2 P A 5 S Ultraviolet Short- Gamma X rays Infrared Radar FM TV wave AM AC electricity -2-8 -4 4 8 Wavelength in meters (m) Visible light 4 nm 5 nm 6 nm 7 nm Wavelength in nanometers (nm= -9 m)
Spectral Power Distribution Examples of Spectral power Distributions The Spectral Power Distribution (SPD) of a light is a function f(l) which defines the energy at each wavelength..5.5 4 5 6 7 Blue Skylight 4 5 6 7 Tungsten bulb Relative Power.5 4 5 6 7 Wavelength (λ).5 4 5 6 7 Red monitor phosphor.5 4 5 6 7 Monochromatic light Multispectral Images Chromatic Aberration Different wavelengths bending at lens, focus at different distances.. 4 nm 5 nm 6 nm 7 nm Power of Lens (diopters). -. -2. * Wald and Griffin (947) Bedford and Wyszecki (957) Thibos et al. (992) 4 5 6 7-3. 4 5 6 7 Wavelength (nm)
Chromatic Aberration Chromatic Aberration Measures Differences in Optical Focus Across Wavelength A B C D E F G A B C D E F G A B C D E F G A B C D E F G A B C D E F G Chromatic Modulation Transfer Function Blue vs Green Modulation Transfer Function Chromatic Aberration affects the MTF Attenuation Factor.8.6.4.2 2 3 Spatial Frequency Sampling rate of Blue vs Green is in accord with Nyquist Theorem
Chromatic Linespread Function Cat Eye Some Animals Have Non-Circular Pupils Spatial position (deg) Wavelength (nm)