cs781 - Colour for Computer Graphics - Winter 2012

Course Notes

Lecture 3 - Photoreception

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Windows in the atmosphere
- opaque for wavelengths below 0.2 micron
- very transparent from 0.2 microns to 0.8 microns
- variable transparency from 0.8 microns to 8 microns
- very transparent from 8 microns to 12 microns
- opaque from 12 microns to 2 cm (20,000 microns)
- transparent from 2 cm to 15 m (radio, television, mobile phones)
- opaque for wavelengths longer than 15 m
Overview of colour matching

Interaction of Light and Matter

Light

particles: with energy and wavelength
- position goes without saying
waves: with energy and position
- wavelength goes without saying

Matter

From our point of view nothing more than a collection of states.

Two types of state, explained using the hydrogen atom -- one electron (negative charge) interacting electromagnetically with one proton (equal positive charge) through the electromagnetic force -- as an example.

The hydrogen atom is electrically neutral, but has charged components.
The hydrogen atome is chemically active, but the hydrogen molecule -- two separated protons sharing two electrons -- is not.

The two types of state:

Internal states: internal rearrangement of electron and proton
- These are discrete
Kinetic states: motion of the atom as a whole
- These are, for our purposes, continuous
- Kinetic energy is spread around very quickly
  - mean free path: 40 nanometres
  - mean time between collisions: 30 picoseconds

Most interactions of visible light with matter excite internal states;

in general, interactions of longer wavelengths excite kinetic states
in general, interactions of shorter wavelengths break molecules apart

Visual optics

The purpose is to focus an image on the retina.

Cornea

Most focussing occurs at the air/cornea boundary.

Lens

Muscular tissue stretches the lens to tune the focus.

Variability declines with age.

Pupil

Varies the amount of light entering the eye

the smaller the pupil the greater the depth of field
diameter varies from 3 mm to 8 mm: factor of 25 in light level

Controlling light level mattersNumbers are log_10 lux (= lumens /m^2)


Light level	Natural conditions	Photodetectors	Greek name
-5 to -2	Moonless night	Rods	Scotopic
-2 to -1	Night with moon	Rods & cones	Mesopic
-1 to +2	Between night & day	Rods & cones	Mesopic
+2 to +4	Dawn, overcast	Cones	Photoopic
+4 to +6	Sunny	Cones, bleaching	Photopic

Sclera

The bounding membrane of the eyeball.

white on the outside. Why?
black on the inside. Why?

Optical Quality

Good enough to get spatial detection down to the diffraction limit.

Declines with age.

Colour Quality

We measure colour at the cornea/air boundary. Why?

Cornea, lens, intra-ocular fluids all yellow with age.

Retina

Overall Layout

Blood vessels

Fovea

all cones
no blood vessels
foveal pit

Periphery

mixture of rods and cones
fewer cones the further out you get

Photoreception

Bacterial purple: ion pump

Rods and cones: G-coupled

Ganglion and other cells:

genetically like bacterial purple
but G-coupled

Stages of photoreception

In the dark Na+ ions pass through a cGMP-gated channel into the cell. Resting potential is -40 mV.
A photon releases retinal from a pigment protein in the cell membrane, deforming the pigment protein.
The deformed pigment protein binds to a G protein in the membrane.
The G protein activates about 100 transducin proteins in the cell interior.
Each transducin binds to a phosphodiesterase enzyme.
The enzyme then catalyses the hydrolysis of about 1000 cGMP.
Na+ gates close; the membrane potential decreases.
The decreased membrane potential closes Ca2+ gates.
The increased Ca2+ reduces the release of neurotransmitter to the bipolar cells

Rods

100 million in the human retina
80 million rhodopsin molecules per rod
big, fast
slow (30 minutes) to recover after saturation

Cones

10 million in the mouse retina
slow, small, near the diffraction limit
fast (30 seconds) to recover after saturation

Ganglion Cells and Others

only 700 in the mouse retina
seem to be responsible for the many other effects that light has
- maintaining circadian rhythm
- synthesizing melanin and vitamin D
- modulating pupil size

Quality of Photodetection

Absolute Thresholds

rods
- 6 photons at the cornea
- 2 photons absorbed
- a candle at 3-10 Km
cones
- 1000 times as high as rods
ganglion cells
- 100,000 times as high as rods
- 100 times as high as cones

Dynamic Range

Of individual photoreceptors: controversial, but the biggest estimates are below 1000.

Of the entire system. Numbers are log_10 (lux = lumens /m^2)


Light level	Natural conditions	Photodetectors	Greek name
-6 to -2	Moonless night	Rods Rod threshold: -6, 20 photons per second	Scotopic
-2 to 0	Night with moon	Rods & cones Cone threshold: -2, 20,000 photons per second	Mesopic
-1 to +2	Between night & day	Rods & cones Rod saturation: +2	Mesopic
+2 to +4	Dawn, overcast	Cones	Photoopic
+4 to +6	Sunny	Cones, bleaching	Photopic

For comparison

CRT screens: +1 to +3
LCD screens: +1.5 to +3.5
LCD projectors: +1 to +3
OLED screens: +1 to +4

Or another set of categories (minima)

reading +2.5
industrial work +3.5
surgery +4.5

The Principle on which the Computer Graphics Use of Colour is Based.

`If the photoreceptors provide the same signal to the brain, the perceptual systems of the brain will provide the same visual experience.'

This principle is reasonable ceteris paribus. Examining how reasonable it is in reality is one interest of this course.

This principle is made operational by the principle of univariance: `the signal provided by any photoreceptor depends only on the number of photons absorbed.'

There is a large amount of empirical evidence, explicit and implicit, for the truth of the principle of univariance.

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