where vision is concerned, light is generally specified in photometric units, not in quanta of light...
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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)
Wavelength (nm)
400 450 500 550 600 650 700
RelativeLuminousEfficiency
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Photopic, VScotopic, V'
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)
Measure the threshold luminance at each wavelength.
Set the minimum threshold (maximum sensitivity) at 1.0 and compare all other sensitivities to that
Light adapteddark adapted
Figure A1- 1. The photopic (V) and scotopic (V’) curvesof 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.
Wavelength (nm)
400 450 500 550 600 650 700
RelativeLuminousEfficiency
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Photopic, VScotopic, V'
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)
PointSource
Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 105 quanta/ secondat 555 nm.
Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.
Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area
Iluminance is whatfalls on a surface. It ismeasured in lumens/unit area
rB
A
Fig. A.2Typo: Illuminance
1015
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 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.
PointSource
Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 105 quanta/ secondat 555 nm.
Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.
Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area
Iluminance is whatfalls on a surface. It ismeasured in lumens/unit area
rB
A
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 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.
PointSource
Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 105 quanta/ secondat 555 nm.
Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.
Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area
Iluminance is whatfalls on a surface. It ismeasured in lumens/unit area
rB
A
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.
Table A.1 Luminous intensity of various sources.
SOURCE Approximate luminous Intensity
(candelas)
Sun 10 27
Electric arc 10 3
40 W light bulb 10 2
Candle flame 10 0
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.
PointSource
Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 105 quanta/ secondat 555 nm.
Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.
Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area
Iluminance is whatfalls on a surface. It ismeasured in lumens/unit area
rB
A
Fig. A.2
Table A.2. Illuminance from various sources.
TARGET/SOURCE Illuminance
(lux)
On the earth from the sun at noon 10 5
On an eye chart from room lights 10 2.5
On walls of a typical room interior
from incident lighting 10 2
On the earth from a full moon 10 –1
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/4r2 Eq. A.1
This is the famous Inverse-square Law.
PointSource
Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 105 quanta/ secondat 555 nm.
Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.
Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area
Iluminance is whatfalls on a surface. It ismeasured in lumens/unit area
rB
A
I l l u m i n a n c e d e c r e a s e s w i t h s u r f a c e o r i e n t a t i o n r e l a t i v e
t o t h e s o u r c e
T h e C o s i n e L a w o f I l l u m i n a n c e .
cos )(1 /r eIlluminanc 2 E q . A . 2
w h e r e r i s t h e p e r p e n d i c u l a r d i s t a n c e f r o m t h e s o u r c e o f
l u m i n o u s i n t e n s i t y , I , t o t h e s u r f a c e a n d i s t h e a n g l e o f t i l t o f
t h e s u r f a c e .
PointSource
Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 105 quanta/ secondat 555 nm.
Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.
Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area
Iluminance is whatfalls on a surface. It ismeasured in lumens/unit area
rB
A
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).
PointSource
Luminous flux is emittedin all directions from apoint source of light. Alumen is equivalent to4.07 x 105 quanta/ secondat 555 nm.
Luminous intensity isluminous flux in a solidangle. A candela isdefined as one lumen/steradian.
Luminance is thelight that comes offa surface whetherreflected or emitted.It is measured incandelas/unit area
Iluminance is whatfalls on a surface. It ismeasured in lumens/unit area
rB
A
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
Learn at least 4 of these values; they will never change during your career and are handy to know
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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
1 lux =
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:
Sxtd L 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:
BBT /L)L(L Eq. A.4
where LB is the luminance of the ref erence 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”
0 200 400 600 800 1000
RelativeLuminance
0
20
40
60
80
100
0
20
40
60
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100
0
20
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100
Horizontal Position (arbitrary units)
0 200 400 600 800 1000
0
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A
B
C
D
The contrast of sine-wave gratings is measured differently
Fig. 6.6
Horizontal Position (arbitrary units)
0 90 180 270 360 450 540 630 720
Relative Luminance
0
20
40
60
80
Width of 1 cycle
B
ALmax of A
Lmax of B
Lmin of B
Lmin of A
Mean Luminance
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
T h e r e i s a s e c o n d d e f i n i t i o n o f c o n t r a s t u s e d f o r g r a t i n g s
( a l t e r n a t i n g l i g h t a n d d a r k b a r s ) c a l l e d “ M i c h e l s o n c o n t r a s t ”
T h i s i s d e f i n e d a s :
)L/(L)L(Lminmaxminmax
E q . A . 5
w h e r e L m a x i s t h e h i g h e s t l u m i n a n c e i n t h e g r a t i n g a n d L m i n
i s l o w e s t l u m i n a n c e i n t h e g r a t i n g . ( W e w i l l c o v e r t h i s l a t e r )
Specifying and Using Visual AngleStimulus size is often expressed in terms of visual angleFig. A.3
Specifying and Using Visual AngleStimulus size is often expressed in terms of visual angleFig. A.3
Specifying and Using Visual AngleStimulus 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