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Light as a stimulus for vision
The physics of light:
–  Light is considered both as a propagating
electromagnetic wave and as a stream of individual
particles (photons). In Vision Science, both of these
aspects are important.
–  Light as rays help us trace the path of light through
optical systems.
–  Light as waves help us understand refraction,
diffraction and interference phenomena. Wave front
measurement is a common tool for describing the
optics of the eye.
–  Light as photons helps us understand the detection
of light by photoreceptors and its conversion to
electrical activity.
Radiant Energy (Electromagnetic)
Spectrum
Nanometer (10-9 m): most common units for wavelength
Electromagnetic spectrum
Solar Radiation Spectrum
UV c b a
Black Body Radiators
Spectral radiance of some artificial lights
The spectrum of a light source
depends on how energy is converted
to photons. Incandescence produces
a broad, continuous spectrum that
depends on temperature.
Fluorescence produces a peaked,
discontinuous spectrum that depends
on the chemicals being electrically
excited. Lasers produce extremely
narrow spectra.
Hot objects like a stove, an incandescent bulb, or the sun give off
light in a characteristic way. At 700° F they start to glow a dull red,
as they heat more they get bright red, then white, then bluish. The
surface of the sun is about 10,340° F (6000° K)
Black body spectra vs. Temp
Color appearance
Spectra of the sun and sky
Light directly from the sun (“noon
sunlight 5500K”) appears yellow
and peaks at around 500 nm
Light from the sky (“north sky light”)
appears blue, and peaks around
400 - 450 nm
Light falling on the ground (“noon
daylight 6500K”) is a mixture of
yellow sunlight and blue sky light.
At sunset, (“sunset sky + sunlight
<4000K”) the sky is reddish, and
peaks at around 650 nm.
These curves have all been adjusted
to intersect at 580 nm, for easier
comparison of the shapes.
Absorption of short wavelengths in the eye
Each curve here shows the spectrum of light as it
passes through the eye. The light hitting the
cornea is assumed to be a flat, white light
spectrum (“light at surface of cornea”)
Light that gets through the cornea is less blue,
because the cornea absorbs short wavelengths.
Light that gets through the lens is even more
filtered, especially the shortest wavelengths. The
lens removes light less than 400 nm.
Light that gets through the macular pigment is
further reduced in short wavelengths up to 500
nm.
The light that finally reaches the cones has
almost no UV in it and much less blue.
As the lens ages, it absorbs more blue light and
begins to look yellow. Artificial lenses implanted
after cataract surgery are clear, so patients notice
a sudden increase in blues. They still absorb UV,
though!
Absorption of light
by Rods and Cones
Rods are 100 times more sensitive
than cones in the middle of the
spectrum. Cones are a little more
sensitive for very long wavelengths
(deep red). Vision with rods is called
“scotopic” and with cones is called
“photopic”.
Photopic & scotopic spectral sensitivity
functions:
CIE 1951 scotopic luminous efficiency
CIE 1964 wide field (10°) photopic luminous
efficiency,
Normalized to peak photopic sensitivity on log
vertical scale;
Luminous Efficiency Functions
The same curves from the
previous figure are shown now
with a linear (not log) vertical
scale.
Rods
Cones
The cone curve is called Vλ (“Vee lambda”)
The rod curve is called V λ, (“Vee Prime lambda”.)
Retinal illuminance
T
Troland = cd/m2 x pupil
area mm2
-----Scotopic---
Radiometric units measure the total energy of light from a source, or falling
on a surface.
Photometric units are similar, but they are compensated by the human
spectral luminous efficiency curves Vλ or V λ. Photometric units predict
how visible a light should be to a human.
Sun s surface at noon 109
108
107
Tungsten filament 106
105
White paper in sunlight 104
103
102
Comfortable Reading 101
100
10-1
White paper in moonlight 10-2
10-3
White paper in starlight 10-4
10-5
Absolute Threshold 10-6
---photopic--------------
From Kaiser & Boynton Human Color
Vision (1996)
Radiometric and photometric units
Each curve is adjusted so it’s
peak is at 1, to show the
relative sensitivity to light.
The term “efficiency” is
referring to how likely it is that
a photon will be absorbed.
They let you predict the
relatively sensitivity of the eye
to lights of various wavelength.
These are standardized
curves, based on lots and lots
of people with normal vision.
Luminance of
everyday scenes
Our eyes are able to adjust
to a very large range of
luminance levels in the
environment, spanning more
than ten orders of magnitude
from dim to dazzling.
Units are approximate cd/m2
Adapted from Vision and Visual
Perception, C.H. Graham, Ed.
Candelas/m2, Trolands, and
Photons compared
Recall that the Troland is a photometric unit of retinal illumination, found by multiplying
luminance with pupil area (cd/m2 * pupil area). For a pupil diameter of 3.5 mm, a surface
with luminance of 1 cd/m2 will produce about 10 Trolands on the retina.
Recall that the area of a circle is π * r2
Pupil area in this example is π * (3.5/2)2 = 9.6 mm2 so 1 cd/m2 is 9.6 td.
A photon has a very very small amount of energy. In this table, Troland values are
compared with the number of photons hitting a small patch of the retina each second,
assuming a white piece of paper in white light.
Cone Threshold
0.1 td
106 photons/sec/deg2
Comfortable reading light
1,000 td
1010 photons/sec/deg2
100,000 td
1012
Bright Sunlight
photons/sec/deg2
From Kaiser & Boynton “Human Color Vision” 1996
Photons from the sun
Solar energy reaching the Earth s surface is about 1000
Watts per square meter on a sunny day. 1 Watt = 1 joule/sec.
Based on the previous calculation, the number of photons
falling on one square meter of Earth each second is about 10
22
Or 10,000,000,000,000,000,000,000
Or 10 thousand billion billion
The pupil is around 1 * 10-5 m2, so 1017 photons per second
enter your pupil from the sun when you look up at the sky.
Compare this to Niagara Falls: Each second, there are 5 x
1010 drops of water that pass over the falls. So the photons
entering your eye from the sun is like 2 million Niagaras!
Energy of one photon
The energy of a photon depends on its frequency. Higher frequency, shorter wavelength
photons have higher energy. Energy and frequency are related through Plank s constant:
E=h*ν
Where E is energy in joules
ν (Greek letter Nu ) is frequency in cycles / second (aka Hertz)
And h is Planck s constant = 6.626 × 10-34 joule - seconds.
Alternatively we can write
E = h * c / λ
Where c is the speed of light in a vacuum 3 x 108 meters / second
And λ (Greek letter lambda ) is the wavelength of light in meters
Example: What is the energy of one quantum of 500 nanometer light?
E = 6.626 x 10-34 * 3 x 108 / 500 x 10 -9 = about 4 x 10 -19 joules
For comparison, one joule is the energy required to lift an apple one meter. Just sitting there
you are generating 100 joules of heat every second.
How light interacts with a medium
How light interacts with the eye
Scattered light
forming haze
Light speed and wavelength
change with different media
The index of refraction n describes the ratio of light speed in vacuum
compared to a given medium, such as glass. The frequency of light and the
energy of the photons do not change as light passes from one medium to
another, but wavelength does.
Focused light
forming image
Courtesy of Dr. Ray Applegate
© RAA
Refraction at a surface
Refraction occurs when light is transmitted from one medium to
another with a different index. The change in direction depends
on factors such as index change and wavelength.
Diffraction of light at an aperture
A planar wavefront entering from the left
interacts with the pupil margin, producing a
diffraction pattern on the retina.
Diffraction occurs where
light hits the edges of an
aperture, such as the pupil
of the eye.
In this example, light
entering from the left is
diffracted, resulting in a
ripple interference pattern
at the imaging surface.
Diffraction limits the ability
of the eye to focus points
sharply, especially when
the pupil is small.
Diffraction of light at an aperture
The spread of a
focused point is
called the Airy disk.
In order to resolve
two points, they
must be separated
so that their peaks
are distinct.
Because diffraction
spreads out the
points, it limits our
ability to resolve
them.
Mie and Rayleigh scattering
Mie and Rayleigh scattering
Particles smaller than the wavelength of light scatter by
diffraction, in proportion to 1/λ4 (Rayleigh)
Larger particles scatter by reflection primarily (Mie).
Reflection at a surface
Reflection occurs when light passes from one index of refraction
to another. The amount reflected depends on factors such as the
index change, the angle of incidence, the wavelength, and the
polarization angle of the light.
Rayleigh scattering is strongly wavelength dependent (1/λ4) and
gives us the blue color of the sky.
Mie scattering is not strongly wavelength dependent and produces
the almost white glare around the sun when a lot of particulate
material is present in the air. It also gives us the white light from
mist and fog. Mie scattering in the eye produces haze from
cataracts and other particles clouding the ocular media. The
direction of scatter depends somewhat on the size of particles.
Absorption of photons
Once light reaches the photoreceptors of the eye, it is
absorbed by a particular molecule called a photopigment. The
energy of the photon causes the molecule to change shape
(isomerize) and this starts a cascade of activity that results in
electrical signals through the nervous system.
Two important characteristics of this photon absorption are:
1)  There is an inherent randomness to the process. When and
where a photon gets absorbed is a matter of probability,
following a Poisson statistical distribution.
2)  Once a photon is absorbed, the photoreceptor responds the
same way, regardless of the wavelength. This is the Principle
of Univariance.
Example of damage from laser exposure
A 15 year old bought a “laser pointer” through the internet. He stood in
front of a mirror and looked right into it. The laser was 50 X more
powerful than most laser pointers. NEJM september 9, 2010
Light exposure damage
Intense light exposure can damage the eye through three principle
mechanisms:
Thermal Damage: proteins in the eye are denatured by tissue heating,
especially in the retinal pigment epithelium (RPE) which absorbs light over a
broad spectrum.
Photochemical Damage: particular pigments, such as photoreceptor
photopigments, or lipofuscin in the RPE, are altered by absorbed light
resulting in damaging byproducts such as free radicals.
ThermoAcoustic Damage: extremely intense pulses of light can produce
vibrations that damage tissue.
As light intensity increases, usually either thermal or photochemical damage
will occur first. With very brief pulses of light, thermoacoustic damage might
be the first to occur. To determine safe levels, we make sure none of the
three will occur!
Maximum Permissible Exposures (MPEs)
MPEs refer to the highest intensity of light exposure
that is considered safe: that is, a level that is not
likely to cause damage to the eye.
MPEs are established through animal experiments
and through accidental damage in humans.
The MPE for a particular situation is 1/10th the
intensity of light that would produce damage in half
the cases.
MPE values are published by the American
National Standards Institute in their document ANSI
Z136.1-2007. Other organizations have similar
standards.
Calculating MPEs is not simple
Determining light exposure safety limits is complicated. It
depends on wavelength (nm), power (Watts), exposure time
(sec), area of retina exposed (mm2), pupil size (mm2), eye
motion (deg/sec).
We have to answer:
–  How much energy in Joules was delivered to one retinal location?
–  Does the wavelength(s) used produce thermal or photochemical
damage first?
–  If it is thermal damage, was the exposure long enough that some
of the heat could dissipate away?
A significant problem is that some eyes may be more
susceptible to damage than others, for example in retinal
disease.
Comparing direct vs. indirect view of a laser
Laser Classes and Safety
Lasers are sorted into Classes based on their potential to do damage.
(The old system used Roman numerals and A/B designations. The
classes shown here are the new system.)
Class 1 lasers do not exceed MPE level even for very long exposures.
Class 1M is a special case: they are safe as sold, but could be
hazardous if optics were used to focus the beam to a point.
Class 2 lasers are visible (400–700 nm) lasers that do not exceed MPE
level for exposure durations less than 0.25 sec. The assumption here is
that you will blink or look away (aversion reflex). Power is less than 1
mWatt. A Class 2M laser is safe unless optics are used to focus it down.
Class 3R lasers (firearm sights, laser pointers) have power less than 5
mWatt and generally won t do damage unless they are focused.
Class 3B lasers have power from 5 to 500 mWatt and will damage the
eye if viewed directly even with short exposures. Diffusely reflected light
from the spot they make is not hazardous.
Class 4 lasers have power over 500 mWatt, will burn the skin, start fires,
etc. Surgical lasers are in this category.
Effects of time and wavelength on
exposure damage
The damage calculations assume that all the laser light
goes into the eye. When you look at a laser dot on the
wall, only a very small fraction of the light goes into
your eye.
The screen scatters light from
laser dot in all directions
At a distance of 7 meters, the
light has spread out into a
hemisphere that is 308 square
meters in area
a 4 mm pupil has an area of .000025 square meters
so pupil gets just 1 part in 12,254,000 of the light!
From Delori et al. JOSA 2007
Apparent Brightness is not a measure of safety!
The curves show the
luminance of light at the
threshold for damage across
the visible spectrum. The
heavy curve is for 300
seconds continuous exposure,
the lighter curve is for 30
seconds exposure. The
vertical axis plots log Trolands,
a photometric unit. Damaging
light at 800 nm will appear
10,000 times less bright than
equally damaging light at 550
nm.
Notice that the curves are
different in the blue, but the
same in the red. In the blue,
damage is photochemical and
accumulates over longer time
periods.
The longer the flash lasts, the lower
the power must be to avoid damage.
The vertical axis here is
radiometric, showing power in
Watts entering the pupil for a
2 arc minute spot at 488 nm.
For brief flashes thermal
damage is more likely. Time
and damage threshold do not
trade off perfectly, because
heat can dissipate away if
exposures are long.
For very long exposures (e.g.
103 seconds) photochemical
damage becomes more likely.
MPE calculation for ophthalmic instruments
The sloping blue line
shows the MPE
calculated for
photochemical
damage across a
large range of
exposure times.
The horizontal lines
show the power
output of various
instruments. The
point where each
line intersects the
MPE shows the
maximum safe
exposure time for
that instrument.
Dong Chen 2016 Masters thesis: “Safety Evaluation of Light Levels in Ophthalmic Instruments and Devices.”
Photons fall randomly, like rain
Photons fall randomly, like rain
Photons fall randomly, like rain
Photons fall randomly, like rain
Photons fall randomly, like rain
Photons fall randomly, like rain
Photons fall randomly, like rain
Photons fall randomly, like rain
E
Visual angles in the eye
Absorption of light by optical
surfaces of the eye
Solar
spectrum
with Vλ