Chapter 2: Radiometry and Photometry

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Chapter 2 Radiometry and Photometry Schwartz,
chapter 4.
1. Electromagnetic energy and light 2. Wavelength/
frequency/photon energy 3. Source
Spectra 4. Geometry of radiation
(radianssteradians) 5. Ocular hazards (UV,
lasers) 6. Quantifying radiation and
light(power, flux, intensity, irradiance,
radiance, exitance) 7. Spectral Sensitivity
(visual others) 8. Luminance/Illuminance 9. Inve
rse square law, cosine law, Reflectance 10. Retina
l Illuminance (Trolands) 11. Reflectors http//ww
w.visionscience.com/vsInformation.html
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1. Electromagnetic energy and light
TV
FM
Gamma
Radar
X-rays
UV
Infra Red
V
1m
1mm
1mm
1nm

Wavelength (l)
Physical
1026
108
1014
1020
Frequency (n c/sec)
Visual
Visible range 380-740 nm
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Appearance of the spectrum from 400 to 700 nm.
400 nm
500nm
600nm
700nm
violet blue green yellow orange red
Color names associated with monochromatic stimuli
History First demonstrated that polychromatic
light is composed of many different wavelengths
each having a different color by Issac Newton
(1704) from his experiments using prisms to
disperse light.
Rainbow
But seen by almost everyoneRainbow is caused by
prismatic dispersion of sunlight dispersed as it
enters a rain drop, totally internally reflected,
and dispersion on the way out.
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2.Wavelength/frequency Photon energy
In a vacuum
lc/n
Ephot hn hc/l
l lambda wavelength C velocity of light in
a vacuum u nu frequency (cycles/sec)
hPlanks Constant (6.626 x 10-34 Js) e.g. for
one photon of 500nm light E(j) (6.626 x 10-34
Js)(600x1012) 3.7 x 10-21 Joules/photon
e.g. C3 x 108 m/sec (a constant) thus for a l
of 500nm, 0.5 microns, or 5 x 10-7 m, the
frequency u(3 x 108 m/s)/(5 x 10-7 m) c/s
0.6 x 1015 600 x 1012 600 TeraHz
phot Etotal/ Ephot
e.g. for one Joule of 500nm light phot
1/(3.7x10-21J/phot) 0.27x1021 photons 270
billion billion billion a lot!
In a refractive material
lc/(nn)
nrefractive index
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3. Source Spectra We plot the amount of
radiance as a function of wavelength. Here are
three examples.
1.0
0.8
Fluorescent light
Incandescent light bulb
0.6
Radiance
UV light
0.4
0.2
0.0
300
500
700
900
1100
Wavelength (nm)
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Radiometry Demonstration
Class Demo

• Examine the radiance spectra of light sources
• Incandescent bulb
• Fluorescent bulb
• Burton Lamp to irradiate (excite) fluorescein
• Emission spectrum of fluorescein
• BIO
• Narrow band source (laser)

Draw each spectrum on the graph below. Label
each, and point out the optometrically important
features of each.
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Plot radiance spectra on the graph below
Radiance
400 nm
700nm
500nm
600nm
800nm
900nm
1000nm
Wavelength (nanometers)
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Why is the overhead projector spectrum different
to that of the light bulb?
Radiance Spectra
Light Bulb
1.0
0.9
0.8
0.7
0.6
0.5
Normalized Radiance
0.4
Overhead projector
0.3
0.2
0.1
0.0
300
500
700
900
1100
wavelength (nm)
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Three different whites they all look white, but
are physically very different. This indicates
our visual system is very poor at resolving even
large differences in light spectra (see color
vision section).
Radiance Spectra
Fluorescent bulb
Incandescent bulb
1.0
0.9
0.8
0.7
TV/computer monitor
0.6
0.5
Normalized Radiance
0.4
0.3
0.2
0.1
0.0
300
500
700
900
1100
wavelength (nm)
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4. Geometry of radiation (radianssteradians)
Tutorial Radians (Two dimensional Circle)
Angle subtended by length of circumference of one
radius 1 radian. Thus 2p radians 360 degrees
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Extend 2-D radians to a three dimensional Sphere
Solid angle subtended by surface area of r2 1
steradian Thus 4p steradians in sphere
r
q
A
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Example calculation
Australia Area 7.6 million square
kilometers. Earth radius 6370 km Solid
angle (sr.) area/r2 7.6 x 106/(40.5 x
106) 0.19 sr Bonus 3 points calculate the
solid angle subtended at the center of the earth
by your country.
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Typical light source
Cross-section of sphere with origin at light
source and containing the eyes pupil
distanceradius
q
Aarea of pupil
Point source radiates in all directions forming a
sphere of radiation
eye
q
Proportion of light entering eye 1.
(angles) q/4p (A/d2)/ 4p 2. (areas) A/4pr2
solid angle subtended by pupil at light source
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Laser
Aarea of pupil
eye
Proportion of light entering eye 100
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5. Ocular hazards (UV, lasers)
Example 1 You are sitting watching IU beat
Purdue (again!) and wondering how much of the
light reflecting off the basketball is actually
entering your eye. Is it 1, 0.001, etc.? You
have great seats at an IU basketball game, 10
meters from the ball, and your pupil diameter is
4 mm. Pupil area p x 0.0022 0.0000126
m2 Sphere area 4 p x 102 1256
m2 Proportion of sphere covered by
pupil0.0000126 m2 / 1256 m2 1 x 10-8 Notice
that this proportion is produced by dividing two
areas, and thus the square meters cancel and the
final result is unitless, just a ratio
(proportion). The point of this calculation is
to emphasize how little light from a distance
source actually enters the eye. How bright
(hazardous) would the basket-ball be if ALL of
its light entered your eye? In this example the
ball would be 100 million times brighter.
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Example 2 Compare retinal irradiance from a
very bright light bulb (e.g. 400 Watts) that
emits 100,000 times more radiation than a dim
laser (4 milliwatts). The light bulb, just like
the basket ball in the previous example, radiates
in all directions but the laser radiates in only
one direction. Consider the light bulb and laser
located 10 meters from you and the laser beam is
narrow enough such that all of it can enter your
eye. Will more radiation enter your eye from the
laser of the light bulb? From the previous
example, we already know that at 10 meters, only
1 x 10-8 of the light emitted from the bulb will
enter a 4mm diameter pupil. That is (1 x 10-8) x
(400 x 103) milliwatts or 4 x 10-3 milliwatts
will enter the eye. That is, 0.004 milliwatts
will enter the eye from the 400 watt bulb, but
all 4 milliwatts from the laser can enter the
eye. That is although the laser output was only
1/100,000th that of the 400 watt bulb, 4/0.004 or
1000 times more light can enter your eye. Now
you know why lasers can be so dangerous! In
addition to the dangers produced by the fact that
100 of the laser light can enter the eye, all of
it will likely be imaged onto a single small
retinal area. Thus if the laser wavelength
coincides with the wavelengths at which the eyes
optics are transparent, the retina is at risk .
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Laser and UV hazard
Wavelengths that are transmitted through the
optics are dangerous to the retina (e.g.
400-1300nm), those that are not transmitted are
absorbed by the optics and they transfer their
energy (Ehn) to the material that absorbs the
photons. Excimer lasers (193 nm) are used for
corneal photoablation because the cornea absorbs
100 of this wavelength (Tzero)
UV
193nm
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6. Quantifying radiation and light (power, flux,
intensity, irradiance, radiance, exitance)
Typically quantify rate of light energy (flux)
not the total amount (e.g. Joules per second
Watts). (Analogous to describing water flow rates
in rivers, e.g. 106 gallons per minute)
Definitions 1. Radiant Power (Flux)
Energy/second. Units Joules/second
Watts 2. Radiant Intensity power per solid
angle leaving a point source. Units
Watts/steradian 3. Irradiance power arriving
at unit area of surface Units Watts/m2 4.
Radiance power leaving surface per solid angle
per unit area of surface Units Watts/(sr m2)
A
A
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7. Spectral Sensitivity (visual
others) Effectiveness of photons
Human Vision
Night Vision Goggles
For Typical Human
At 555nm, where Vl1, 1 Watt of radiant power
produces 680 lumens
Light 680 x S Rl X Vl
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Measuring Spectral Sensitivity of Human Vision
Three possible methods
1. Absolute threshold for each l how much
radiance is just detectable at each
wavelength? 2. Brightness as a function of l
Heterochromatic brightness matching How bright
is a fixed radiance at each wavelength?) 3. Flicke
r Photometry vs. l How much radiance at each
wavelength is required to cancel flicker?

3 seems the least intuitive, but is the method
used.
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1. Absolute threshold for each l
Radiance
Wavelength
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2. Brightness as a function of l
(heterochromatic brightness matching)
Wavelength
Use series of different wavelengths, each having
the same radiance. How bright are they? Adjust
the radiance of constant spectrum light (white in
this example) until it has the same brightness as
each individual wavelength. The brighter colors
will be matched with a higher radiance
white. The challenge is to say what gray level
is equally bright to a rad or green or ble. We
call this heterochromatic brightness matching,
and it is very difficult to do.
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Heterochromatic Flicker Photometry Measure
Radiometric Intensity necessary to minimize
flicker with standard wavelength
Spectral Sensitivity (Vl)
1.0
1.0
Radiance (standard)/Radiance (l)
555nm
l
We now normalize the data to the peak (555nm)
l
standard
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8. Luminance/Illuminance
From Schwartz, ch. 4
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Sample Luminances and Illuminances Approximate
Illuminance levels (lux) Earth surface in
direct sun 100,000 Earth on cloudy
day 10,000 Earth at night, w/ full
moon 0.1 Earth moonless clear night
sky 0.001 VA chart (recommended)
300 Luminance Levels (cd/m2) Sun 2,000
million Sky on sunny day 10,000 Clouds 100
- 1000 VA chart (recommended) 85
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9. Inverse square law, cosine law
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Geometric Proof of Inverse Square Law
A
A

4A
At 2x the distance, the same light that passes
through area A is distributed over 4 times A,
thus, for each unit area, the illuminance
decreased by 1/4 1/22
A
A
A
d
d
EI/d2
Point Source
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Cosine Law, modification of inverse square law.
Orthogonal surface
Tilted surface
Light source
q
As surface tilts, it is illuminated by a smaller
section of the beam, thus its illuminance
(lumens/m2) decreases. E (I x cosq)/d2
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Relationship between Illuminance and Luminance
Reflectance Luminous Exitance/Illuminance
Luminance L (lumens/(sr. x m2) L (cd/ m2)
Illuminance E (lumens/m2) E (lux)
R
For a cosine reflector Luminance (E x R)/p
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Notice the luminance output (lumens) of two
standard household bulbs, one incandescent and
one fluorescent is similar but the power
consumption (watts) is very different.
Fluorescent
Why does the incandescent bulb need 75 Watts of
power to generate 1125 lumens?
Incandescent
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• Efficiency of light source
• lumens/watt (light output per unit of power
  input)
• Compare two household bulbs
• 75 Watt incandescent bulb lumens
• Efficiency lumens/watt
• 25 Watt Fluorescent bulb lumens
• Efficiency lumens/watt

How much illuminance is provided by such a
bulb?Recall Illuminance(lum/m2) Intensity/d2
(Inverse square law) Intensity (lum/sr)
total light output/4p Therefore 75W bulb at
1meter Illuminance total lumens/(4p x d2)
lum/ m2
________ lux
What is required lux for VA chart? Will a 75 Watt
bulb at 1 meter generate sufficient illuminance?
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Lumens/Watt
Efficiency of Light Sources (how much light
output (lumens) for a given power input (watts)?
Gas mantel 1-2 Incandescent bulbs 40 Watt
11.4 60 Watt 14.5 100 Watt 17 Fluorescent
Light 50-80 High Pressure Sodium 100-140 Sunligh
t 200 Max Possible Monochromatic 555 nm 680
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10. Retinal Illuminance (Trolands)
Paradox Inverse Square law shows that as get
closer to source, surface illuminance increases,
BUT objects DO NOT appear brighter as we get
closer. Why?
As approach light source, corneal illuminance
follows the inverse square rule, e.g. half the
distance, 4x the corneal illuminance. However,
at half the distance, the object subtends 2x the
visual angle and the retinal image will be 2x
bigger. Thus it will have an area 4x bigger.
That is, 4x as much light will be in the retinal
image, but it will be spread out over 4x the
retinal area, and thus retinal illuminance
(lumens/mm2) will remain unchanged as will
brightness.
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What factors determine retinal illuminance?
1. Object luminance (how much light arrives at
eye) 2. Pupil area (how much gets into eye) 3.
Eye size/image magnification (how light is
spread out on retina) retinal illuminance in
lumens per m2 is lower in larger eyes.
We typically have no direct measure of eye size
and image magnification, thus the usual
definition of retinal illuminance only
incorporates 1 2. Retinal Illum. (Trolands)
Object lum. (cd/m2) X pupil Area (mm2)
Example Object luminance 100 cd/m2 Pupil
diameter 4mm thus pupil area p x 22 12.5
mm2 Retinal Illuminance 100 x 12.5 1250
Trolands
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Complication for ErLo x Ap
The simple equation assumes that light entering
all parts of the pupil is equally effective at
stimulating vision. Double the area, double the
retinal illuminance. This assumption is
incorrect. Stiles Crawford Effect (SCE), appears
like an apodizing filter in pupil, but actually
due to fiber optic characteristics of
photoreceptors (see V663 notes). Thus doubling
pupil area by dilation does not double amount of
light (slightly less than double)
Apodizing filter (transmits more in center than
at edge)
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• Reflectors
• Three general types
• Diffuse, Matte, or Cosine Reflectors
• Specula reflectors, or mirrors
• Hybrid surfaces glossy, metallic, aluminized

Class Demo
Highly reflective white surfaces are easy and
cheap to produce, but we use the hybrid
aluminized reflectors in clinic which overall
reflect less light. However, they reflect light
directionally, somewhat similar to a mirror.
Thus, if positioned such that the angles of
incidence the patients viewing angle, the
letter chart will have higher illuminance.
White screen
E
20-30 degrees
AB
luminance
q
Aluminized screen
q
angle
eye
light