APPENDIX: Measuring Light
Where vision is concerned, light is generally
specified in photometric units, not in quanta
(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)
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)
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.
Just because something is twice as
intense does not mean it is twice as bright!!
Photometric Terminology
Luminous flux is emitted
in all directions from a
point source of light. A
lumen is equivalent to
4.07 x 10 15quanta/ second
at 555 nm.
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
iIluminance 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
r
A
q
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 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
q
r
B
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.
A steradian is "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."
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 10 15quanta/ second
at 555 nm.
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
iIluminance 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
q
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 10 15quanta/ second
at 555 nm.
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
iIluminance 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
q
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 1015quanta/ second
at 555 nm.
Luminous intensityis
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
iIluminanceis 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
q
Illuminance decreases with surface
r orientation relative
to the source
The Cosine Law of Illuminance.
Illuminanc e  (1/r 2 ) cos q
Eq. A.2
where r is the perpendicular distance from the source of
luminous intensity, I, to the surface and q 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 10 15quanta/ second
at 555 nm.
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
iIluminance 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
r
A
q
B
Luminous flux is emitted
in all directions from a
point source of light. A
lumen is equivalent to
4.07 x 1015quanta/ second
at 555 nm.
Luminous intensity is
luminous flux in a solid
angle. A candela is
defined as one lumen/
steradian.
iIluminanceis 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
q
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)
SOURCE
Luminance (cd/m2)
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 4
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 –6
Photopic
Mesopic
Scotopic
For Reference:
1 lumen/m2 = 0.0929 lumen/ft2 (e.g., foot candles)
1 cd/m2 = 3.1416 apostilbs
= 0.2919 foot-lamberts
= 0.3142 millilamberts
The troland (td), the 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.
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.
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
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
There are 60” in 1’ of arc