eight light and image

Oscillation Occurs when two forces are in opposition Causes energy to alternate between two forms Guitar string Motion stretches the string Which slows the motion And eventually reverses it But then the stretch reverses And so on … Commonly takes the form of a sine wave speed(t) = cos ωt stretch(t) = sin ωt ω is the frequency of the oscillation (how often it repeats) speed stretch time

Waves Waves are oscillations that move through space Frequency Rate of cycling Period (how far between cycles) Amplitude (intensity): Size of the oscillation w(x) = A sin(ωx)

Light as a wave Light is an oscillation between electric and magnetic fields Frequency/wavelength determines apparent color But color is perceptual property, not a physical one Amplitude determines apparent brightness magnetic field electric field time High frequency Short wavelength Low frequency Long wavelength

Radiance and irradiance Light typically reaches our eyes by bouncing off of surfaces Surface reflectance is very complicated There are two main models of reflectance Specular (shiny) surfaces bounce it directly off Lambertian (matte) bounce it evenly in all directions incident ray specular reflection (highlights) Lambertian reflection (matte/diffuse)

Lambertian reflection

When light hits a surface at an angle It gets spread out Making it dimmer Lambertian reflection Assuming light dims due to the angle of incident ray But not the angle of viewed ray So the intensity of the light coming out is dimmed by a factor of sin θ θ d θ d/sin θ beam spreads out by 1/sin θ

Light as a ray But in everyday life, light mostly acts like a ray Starts at a source Travels in a straight line Bounces off of things Hits your eye Light gets projected into an image Pinhole camera model Bigger focal lengths make bigger images Y Z y f Image plane object light ray Y = height of object Z = depth y = “height” of projection (note image is really upside down) f = focal length y/f = Y/Z y = fY/Z

The thin lens model A pinhole camera doesn’t allow much light through A lens allows many rays to focus to the same point Brighter image But only focuses a single depth The range of depths that are in focus is the depth of field The aperture of the lens controls how much light gets through Small apertures are like a pinhole  large depth of field Large apertures allow more light but less depth of field Image plane object light rays aperture lens

Chromatic aberration A lens actually focuses different wavelengths (colors) at slightly different depths In extreme cases, this leads to a colored blur around bright lights blue/violet artifacts

The human eye Lens and iris Photoreceptors Rods (b/w) Cones (color) Fovea Small (size of thumbnail at 3’) High resolution Color vision Macula, and periphery Low resolution, wide FOV Retinal processing Gain control Edge enhancement? Simple motion detection lens/iris rods cones retinal ganglion

Chromatic aberration in the eye The blue photoreceptors of the eye evolved first So the have lower resolution And nature didn’t try to fix the chromatic aberration of the eye So blue light is significantly out of focus on the retina  Blue backgrounds in PowerPoint are evil blue is poorly focused on the retina green is well focused on the retina

Photoreceptors Rods Found mostly in the macula and periphery Very sensitive to light But don’t detect color Cones Found in the fovea Less sensitive Color sensitive  Colors seem to fade in low light

Trichromacy Having different cones for every possible wavelength would be bad We just have three kinds of cones “Blue” cones: short wavelengths “Green” cones: intermediate wavelengths “Red” cones: long wavelengths However, their responses overlap The eye reduces all the wavelengths at a given pixel to just the total “amount” of “red”, “green”, and “blue”

Components of a color image

Images An image is really just an assignment of colors to each position in the plane So it’s a function from position to color