The First Steps in Vision:
Seeing Stars
Outline
What is light?
• Types of waves
• Dual nature of light: waves and particles
• Spectrum of electromagnetic radiation
• Intensity, wavelength, polarization, direction
• Range of light intensities
• Interactions between light and matter
Anatomy and function of the eye
• univariance principle
• eye cups
• pinhole eye
• lens eye
Optics of the eye
• accommodation
• refractive errors
• role of the pupil
To suppose that the eye, with all its inimitable contrivances for
adjusting the focus to different distances, for admitting different
amounts of light, and for the correction of spherical and chromatic
aberration, could have been formed by natural selection, seems, I
freely confess, absurd in the highest possible degree.
Charles Darwin
Additional reading
Richard Dawkins (1996). Climbing Mount Improbable. W.W. Norton &
Company. A wonderful text about how evolution works. Chapter 5 describes
the 40 different ways of designing light sensing organs that nature came up
with.
Types of waves
Longitudinal
Transverse
Wavelength, frequency, speed
λ
wavelength λ [m]
frequency f [Hz] (1/s, number of waves per second)
speed c [m/s]
λ∗f=c
speed of light: 300,000,000 m/s
speed of sound: 340 m/s
Big numbers and small numbers
pico-
10-12
nano-
10-9
micro-
10-6
milli-
10-3
-meter
wavelength of green light: 500 x 10-9 m
100
kilo-
103
mega-
106
giga-
109
tera-
1012
distance earth - moon
380 x 106 m
distance earth - sun
150 x 109 m
The spectrum of electromagnetic radiation
Light: A wave; a stream of photons, tiny particles that each
consist of one quantum of energy
Light intensities
Luminance
[ cd m-2 ]
photons
m-2 sr-1 s-1
photons per
receptor
paper in starlight
0.001
1013
0.01
paper in moon light
0.2
1015
1
computer monitor
65
1017
100
room light
350
1018
1,000
blue sky
2,500
1019
10,000
paper in sun light
40,000
1020
100,000
• our visual system has to cope with a HUGE range of intensities
• bright sunlight is about 10,000,000 times more intense than starlight
Interactions between
light and matter
Intensity
Wavelength
Polarisation
Direction
absorption &
reflection
scattering
(defraction)
refraction
absorption &
transmission
Cell response
Principle of
Univariance
(William Rushton, 1972)
Sensitivity
Number of photons absorbed
Direction
A photoreceptor's
response corresponds to
just a single variable:
the number of photons
absorbed
Sensitivity
Seeing direction
Direction
Sensitivity
Seeing direction
Direction
Eye cup
The eye cup makes
an array of
photoreceptors
sensitive to direction
Eye cups
bivalve mollusc
flatworm
limpet
polychaet worm
An eye cup cannot generate an image
Pinhole eye
The pinhole eye can
generate an image on
the retina
Pinhole eyes
marine snail
bivalve mollusc
Nautilus
abalone
Nautilus
Pinhole eye
The pinhole eye
can generate an
image on the retina
... however, lots of
valuable light is
wasted
Lens eye
The solution:
a collecting lens
Compound eye
Cross section of the vertebrate eye: the lens
Zonules
Analogies between eye and camera
Aperture: Iris/pupil. Regulates the amount of light coming
into the eye and affects depth of field
Focus: Lens changes shape to adjust focus
Film: Retina records the image
Accommodation in eye and camera
Pin hole eye
The pinhole eye can
generate an image on
the retina
... however, lots of
valuable light is
wasted
Lens eye
The solution:
a collecting lens
Accommodation
f
focal length: the distance between lens and image plane for a distant stimulus
Accommodation
f
focal length: the distance between lens and image plane for a distant stimulus
Cross section of the vertebrate eye: the zonules
Zonules
Accommodation
Lens, zonules and ciliary muscle
Distant
focus
Close
focus
Ciliary
muscle
relaxed
contracted
Zonules
tense
relaxed
Lens
flat
spherical
Accommodation
Accommodation
Accommodation
Near-point: the closest distance at which accommodation is still possible
Presbyopia: far-sightedness in elderly people
due to reduced flexibility of the lens
Refractive errors of the eye
Emmetropia
Myopia
“Short-sightedness”
Hyperopia
“Far-sightedness”
Refractive errors of the eye
Role of the pupil
Smaller aperture sharpens the image
and thus increases depth of field
Role of the pupil
Smaller aperture sharpens the image
and thus increases depth of field
Pin hole eye
The pinhole eye can
generate an image on
the retina
... however, lots of
valuable light is
wasted
What is the pupil for?
Reduce amount of incident light
(but only by a factor 10)
Reduces refractional problems
Increases depth of field
Fechner‘s law: S = c * log I
Brightness: Perceived intensity (sensation magnitude)
Brightness
3
2
1
0
1 10
100
Intensity
0 1
2
log(Int)
Fechner‘s law: S = c * log I
Brightness: Perceived intensity (sensation magnitude)
Brightness
3
2
1
0
1
10
100
1000
Intensity
0
1
2
3
log(Int)
Cell response
Log (Number of photons absorbed)
Outline
What is light?
• Types of waves
• Dual nature of light: waves and particles
• Spectrum of electromagnetic radiation
• Intensity, wavelength, polarization, direction
• Range of light intensities
• Interactions between light and matter
Anatomy and function of the eye
• univariance principle
• eye cups
• pinhole eye
• lens eye
Optics of the eye
• accommodation
• refractive errors
• role of the pupil