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APPENDIX: Measuring Light
Where vision is concerned, light is generally
specified in photometric units, not in quanta of
light (photons) and energy
Radiometry is the measure of radiant energy in the
electromagnetic spectrum
Photometry is the measure of the luminous effect of
radiant energy
For radiant energy to be “luminous”, it must be absorbed by
the photoreceptors and be effective for vision.
Photometry measures the luminous effect of radiant energy.
Commission Internationale de l’Eclairage (CIE)
Measure the threshold luminance at each wavelength.
Relative
Luminous
Efficiency
1.0
Set the minimum threshold (maximum sensitivity) at
1.0 and compare all other sensitivities to that
0.9
Scotopic, V'
0.8
dark adapted
Photopic, V
Light adapted
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
400
450
500
550
600
650
700
Wavelength (nm)
Fig. A-1. The photopic (V) and scotopic (V’) curves of relative
luminosity as standardized by the Commission Internationale de
l’Eclairage (CIE). Modified from Wright (1958)
Relative
Luminous
Efficiency
1.0
0.9
Scotopic, V'
Photopic, V
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
400
450
500
550
600
650
700
Wavelength (nm)
Figure A1- 1. The photopic (V) and scotopic (V’) curves
of relative spectral luminosity as standardized by the CIE.
“m“ is the same as nanometers. Modified from Wright
(1958).
V is the relative luminous efficiency of radiant energy:
the luminous efficiency relative to the maximum at 555
nm.
The scotopic (rod mediated) luminous efficiency function,
V (V lambda prime), is similar in shape to the photopic
curve but has a maximum (1.0) at a shorter wavelength,
507 nm.
Luminous efficiency is not brightness.
It is a threshold measure
It can be used to set stimuli of different
wavelengths to the same amount above
threshold (e.g., 1 log unit above threshold)
Fig. A.2
Luminous flux is emitted
in all directions from a
point source of light. A
lumen is equivalent to
4.07 x 105 quanta/ second
at 555 nm.
Typo: Illuminance
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
Iluminance is what
falls on a surface. It is
measured in lumens/
unit area
A
1015
Luminance is the
light that comes off
a surface whether
reflected or emitted.
It is measured in
candelas/unit area
Point
Source
r

B
Photometric terminology
The output of a point source is called luminous flux and the unit of measure is
the lumen.
At a wavelength of 555 nm, one lumen is equal to approximately 4.07 x 10 15
quanta per second emitted from the point source. In energy terms, this is 1.46 x
104 ergs or 1/685th of a watt.
Luminous flux is emitted
in all directions from a
point source of light. A
lumen is equivalent to
4.07 x 105 quanta/ second
at 555 nm.
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
Iluminance is what
falls on a surface. It is
measured in lumens/
unit area
Luminance is the
light that comes off
a surface whether
reflected or emitted.
It is measured in
candelas/unit area
Point
Source
A

r
Luminous intensity is luminous flux per unit solid angle.
If one lumen is emitted per steradian then, by definition, the luminous intensity
is equal to one candela.
B
One steradian is defined as the solid angle
subtended at the center of a sphere of radius r
by a portion of the surface of the sphere having an area r2.
Photometric terminology
The output of a point source is called luminous flux and the unit of
measure is the lumen.
At a wavelength of 555 nm, one lumen is equal to approximately 4.07
x 1015 quanta per second emitted from the point source. In energy
terms, this is 1.46 x 104 ergs or 1/685th of a watt.
Luminous flux is emitted
in all directions from a
point source of light. A
lumen is equivalent to
4.07 x 105 quanta/ second
at 555 nm.
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
Iluminance is what
falls on a surface. It is
measured in lumens/
unit area
Luminance is the
light that comes off
a surface whether
reflected or emitted.
It is measured in
candelas/unit area
Point
Source
A

r
Luminous intensity is luminous flux per unit solid angle.
If one lumen is emitted per steradian then, by definition,
the luminous intensity is equal to one candela.
B
Table A.1 Luminous intensity of various sources.
SOURCE
Approximate luminous Intensity
(candelas)
Sun
Electric arc
40 W light bulb
Candle flame
10
27
10
10
10
3
2
0
Fig. A.2
Luminous flux is emitted
in all directions from a
point source of light. A
lumen is equivalent to
4.07 x 105 quanta/ second
at 555 nm.
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
Iluminance is what
falls on a surface. It is
measured in lumens/
unit area
Luminance is the
light that comes off
a surface whether
reflected or emitted.
It is measured in
candelas/unit area
Point
Source
A

r
B
Illuminance is a photometric measure of the density of light
falling on a surface. It is expressed in lumens per unit area.
One lumen per m2 is a lux. One lumen per ft2 is a foot candle,
which is equal to approximately 10.8 lux.
Table A.2. Illuminance from various sources.
TARGET/SOURCE
Illuminance
(lux)
On the earth from the sun at noon
On an eye chart from room lights
On walls of a typical room interior
10
10
5
2.5
10
2
from incident lighting
On the earth from a full moon
10
–1
Luminous flux is emitted
in all directions from a
point source of light. A
lumen is equivalent to
4.07 x 105 quanta/ second
at 555 nm.
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
Iluminance is what
falls on a surface. It is
measured in lumens/
unit area
Luminance is the
light that comes off
a surface whether
reflected or emitted.
It is measured in
candelas/unit area
Point
Source
A

r
Illuminance decreases in proportion to the square of the distance
from the light source
If F is the total luminous flux (in lumens) emitted by a point source at the
center of a sphere of radius r, then the illuminance (in lux) on the surface
of the sphere is given by:
Illuminance = F/4r2
Eq. A.1
This is the famous Inverse-square Law.
B
Luminous flux is emitted
in all directions from a
point source of light. A
lumen is equivalent to
4.07 x 105 quanta/ second
at 555 nm.
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
Iluminance is what
falls on a surface. It is
measured in lumens/
unit area
Luminance is the
light that comes off
a surface whether
reflected or emitted.
It is measured in
candelas/unit area
Point
Source
A

Illuminance decreases with surface
r orientation relative
to the source
The Cosine Law of Illuminance.
Illuminanc e  (1/r 2 ) cos 
Eq. A.2
where r is the perpendicular distance from the source of
luminous intensity, I, to the surface and  is the angle of tilt of
the surface.
B
Luminous flux is emitted
in all directions from a
point source of light. A
lumen is equivalent to
4.07 x 105 quanta/ second
at 555 nm.
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
Iluminance is what
falls on a surface. It is
measured in lumens/
unit area
Luminance is the
light that comes off
a surface whether
reflected or emitted.
It is measured in
candelas/unit area
Point
Source
A

r
Luminance is a photometric measure of the light emitted from
a surface.
The luminous intensity of the reflected or emitted light is
expressed in candelas per unit area of the emitting surface,
usually as candelas per square meter (cd/ m2).
B
Table A.3. Luminance of various sources. Modified from
Riggs (1965), Boynton, (1966) and Bartley (1951)
2
SOURCE
Luminance (cd/m )
Surface of sun at noon (clear day)
10 9
Tungsten filament
10 6
Upper limit of visual tolerance
10
4.7
White paper in sunlight (clear day)
10 4
Candle flame
10
Clear blue sky
10 3.8
Surface of moon (clear night)
10 3.3
Upper limit for rods (approximate)
10 2
White page in good reading light
10 1.7
Cone threshold (approximate)
10 –2
White paper in moonlight (clear night)
10 –2
White paper in starlight (clear night)
10 –4
Absolute threshold
10
*
4
*
*
–6
*
Learn at least 4 of
these values; they will
never change during
your career and are
handy to know
For Reference:
2
2
1 lux = 1 lumen/m = 0.0929 lumen/ft (e.g., foot candles)
1 cd/m2 = 3.1416 apostilbs
= 0.2919 foot-lamberts
= 0.3142 millilamberts
The troland (td), a unit of retinal illuminance, is defined as L, the
luminance of a surface (in the direction of viewing) multiplied by
the area of the eye pupil, S. Thus:
td  L x S
Eq. A.3
A stimulus with a luminance of 1 cd/m2 viewed through a pupil
with an area of 1 mm2 (1.13 mm diameter) provides 1 troland of
retinal illuminance.
Useful to create identical illuminance around the world
Reflectance is not a photometric term. Reflectance is the
ratio of the amount of light reflected from a surface divided by
the light incident on the surface.
Contrast is not a photometric term. Contrast is an expression of luminous
difference between two surfaces . The standard quantitative definition of contrast
for a target on a background is:
(LT - L B ) /L B
Eq. A.4
where L B is the luminance of the reference surface and L T is the luminance of the
second surface. If L T > LB then the contrast is positive; otherwise it is negative.
This is sometimes called “Weber Contrast ”
The contrast of sine-wave gratings is measured differently
Fig. 6.6
Relative
Luminance
A
100
80
60
40
20
B
0
100
80
60
40
20
C
0
100
80
60
40
20
D
0
100
80
60
40
20
0
0
200
400
600
800
1000
0
200
400
Horizontal Position (arbitrary units)
600
800
1000
Sine-wave gratings are measured in terms of their
spatial frequency defined as the number of cycles per
degree of visual angle
Fig. 6.7
Relative
Luminance
Width of 1 cycle
Lmax of A
80
A
60
Lmax of B
B
40
Mean Luminance
Lmin of B
20
Lmin of A
0
0
90
180
270
360
450
540
Horizontal Position (arbitrary units)
630
720
There is a second definition of contrast used for gratings
(alternating light and dark bars) called “Michelson contrast”
This is defined as:
(L - L ) /(L  L ) Eq. A.5
max
min
max
min
where Lmax is the highest luminance in the grating and Lmin
is lowest luminance in the grating. (We will cover this later)
Specifying and Using Visual Angle
Fig. A.3
Stimulus size is often expressed in terms of visual angle
Specifying and Using Visual Angle
Fig. A.3
Stimulus size is often expressed in terms of visual angle
Specifying and Using Visual Angle
Stimulus size is often expressed in terms of visual angle
Two advantages:
1)
Provides a measure of the stimulus size on the retina
2)
That allows investigators in other labs to duplicate the
stimulus size (without needing to duplicate the equipment)
Objects A and B are the
same size, but subtend
different angles on the
retina because they are
at different distances
from the cornea; when
an object moves closer,
it subtends a larger
retinal angle
Object C subtends the
same angle as object A,
so A and C would be
indistinguishable based
on retinal size and
position alone
Can calculate the visual angles subtended by
the visual stimuli:
Visual angles are expressed in degrees, minutes or seconds
of arc
Large stimuli subtend visual angles expressed in degrees ()
(e.g., a 10 spot)
There are 360 in a circle
Smaller stimuli are described in minutes (’) of arc
There are 60’ in 1 of arc
Still smaller stimuli are expressed in second (”) of arc (also
called “arc sec”)
There are 60” in 1’ of arc