ten light and image. oscillation occurs when two forces are in opposition causes energy to alternate...
Post on 22-Dec-2015
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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 ωtstretch(t) = sin ωt
ω is the frequency of the oscillation (how often it repeats)
speed
stre
tch
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
elec
tric
fie
ld
time
High frequencyShort wavelength
Low frequencyLong wavelength
Radiance and irradiance
incident ray
incident ray
specular reflection(highlights)
Lambertian reflection(matte/diffuse)
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
Zyf
Image plane object
light ray
Y = height of objectZ = depthy = “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 lightbut 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 peripheryLow resolution, wide FOV
Retinal processing Gain control Edge enhancement? Simple motion detection
lens/irisrods
conesretinal
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
blueis
poorlyfocused
onthe
retina
greenis
wellfocused
onthe
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”