ten

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 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)

Lambertian reflection

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”

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