A Tutorial on
Photometric Dimensions and Units
George Joblove
Prima Lumina Consulting
Hollywood, California
george [at] joblove.com
Dimensions and Units
Dimension: a measurable physical characteristic,
property, or quantity
– Examples: length, time, velocity
Unit: a defined standard magnitude of a dimension,
used for expressing measurements of that dimension
– Examples: meter, second, meter per second
SI: Système International d’Unités,
International System of Units
A Tutorial on Photometric Dimensions and Units
George Joblove
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SI (International System)
Seven “base quantities”
– length, mass, time,
electric current, thermodynamic temperature,
amount of substance, luminous intensity
Base units
– meter (m), kilogram (kg), second (s),
ampere (A), kelvin (K),
mole (mol), candela (cd)
A Tutorial on Photometric Dimensions and Units
George Joblove
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SI (International System)
Derived units
– Products of powers of the base units
• Examples:
– square meter (m2) (area)
– meter per second, m/s (velocity)
– Special defined names
• Examples:
– hertz (Hz) (frequency) = reciprocal second (s−1)
– newton (N) (force) = meter-kilogram per second squared (m kg s−2)
– volt (V) (electric potential difference) =
kilogram-meter squared per ampere per second cubed (m2 kg s−3 A−1)
A Tutorial on Photometric Dimensions and Units
George Joblove
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SI (International System)
Derived units (continued)
– Dimensionless units
• Defined as ratios of two quantities of the same dimension
• Examples:
– radian (rad) (plane angle)
• angle subtended at a circle’s center
by an arc on the circle equal in length to its radius
– steradian (sr) (solid angle)
• solid angle subtended at a sphere’s center
by an area of its surface equal to the square of its radius
A Tutorial on Photometric Dimensions and Units
George Joblove
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Radiometry and Photometry
Radiometry: The measurement of electromagnetic
radiation, of which visible light is one kind, or range of
wavelengths
Photometry: The measurement of visible light, as it is
perceived by the human visual system
– Radiation evaluated “according to its action upon
the CIE standard photometric observer”
(standardized spectral luminous efficiency function)
A Tutorial on Photometric Dimensions and Units
George Joblove
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Photometric Dimensions and Units
Base SI photometric quantity: luminous intensity
– Luminous flux (power) per unit solid angle
Base SI photometric unit: candela
– Formal definition:
• “The luminous intensity, in a given direction, of a source that
emits monochromatic radiation of frequency 540 × 1012 hertz
and that has a radiant intensity in that direction
of 1/683 watt per steradian”
Other photometric quantities measured in units derived
from the candela together with other SI units
such as the meter, second, and steradian
A Tutorial on Photometric Dimensions and Units
George Joblove
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Photometric Dimensions and Units
Six photometric dimensions to be discussed:
– Luminous energy
– Luminous power
– Luminous intensity
– Illuminance
– Luminance
– Luminous exposure
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminous energy
Amount of radiant energy, weighted by
human sensitivity across the spectrum
Unit: lumen-second (lm s)
– Luminous energy radiated by a source
with a luminous intensity of one candela
through a solid angle of one steradian
for one second
Unit derivations:
– candela-steradian-second (cd sr s)
– talbot (T) (not an SI unit)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminous energy
Amount of radiant energy, weighted by
human sensitivity across the spectrum
Unit: lumen-second (lm s)
Unit derivations:
– candela-steradian-second (cd sr s)
– talbot (T) (not an SI unit)
Proportional to: photons
Radiometric equivalent: radiant energy (joule)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminous energy
Example: 1000 lumens × 3600 seconds = 3.6 × 106 lm s
1 hour
1000 lumens
For light of frequency of 540 THz (wavelength 555 nm),
1 lumen-second (1 talbot) is:
(683 — 540 × 1012 — 6.626 × 10−34)−1 = 4.092 × 1015 photons
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminous power
Rate of flow of luminous energy (luminous flux)
– Luminous energy per unit time
Unit: candela-steradian (cd sr), or lumen (lm)
– Luminous flux radiated by a source
with a luminous intensity of one candela
through a solid angle of one steradian
Unit derivations:
– lumen-second per second (lm s / s)
– talbot per second (T/s) (not an SI unit)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminous power
Rate of flow of luminous energy (luminous flux)
– Luminous energy per unit time
Unit: candela-steradian (cd sr), or lumen (lm)
Unit derivations:
– lumen-second per second (lm s / s)
– talbot per second (T/s) (not an SI unit)
Proportional to: photons per second
Radiometric equivalent: radiant power or flux (watt)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminous intensity
Luminous power per unit solid angle
Unit: candela (cd)
Unit derivations:
– lumen per steradian (lm/sr)
– talbot per second per steradian (T/s/sr) (not an SI unit)
Proportional to: photons per second per unit solid angle
Radiometric equivalent: radiant intensity
(watt per steradian)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Illuminance
Luminous power per unit area
Unit: lumen per square meter (lm/m2), or lux (lx)
– Luminous flux radiated by
a source with a luminous intensity of one candela
through a solid angle of one steradian
that falls on one square meter of a surface
of a sphere whose center is at the source
Unit derivations:
– candela-steradian per square meter (cd sr/m2)
– talbot per second per square meter (T/s/m2) (not SI)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Illuminance
Luminous power per unit area
Unit: lumen per square meter (lm/m2), or lux (lx)
Unit derivations:
– candela-steradian per square meter (cd sr/m2)
– talbot per second per square meter (T/s/m2) (not SI)
Proportional to: photons per second per unit area
Radiometric equivalent: irradiance
(watt per square meter)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Illuminance
Two non-SI units of illuminance
– meter-candle = lux = lumen per square meter
• The illuminance of a surface one meter from
a source with a luminous intensity of one candela
– footcandle (fc) = lumen per square foot
• The illuminance of a surface one foot from
a source with a luminous intensity of one candela
• 1 footcandle = 1 lm/ft2 × (3.281 ft/m)2 = 10.76 lm/m2 = 10.76 lux
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminance
Luminous power radiating through a unit solid angle
per unit area
– Luminous intensity per unit area
Unit: candela per square meter (cd/m2)
– Luminous flux radiated by a surface with
a luminous intensity of one candela,
per square meter of surface
– Also called a “nit” (not an SI unit)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminance
Unit derivations:
– lumen per steradian per square meter (lm/sr/m2)
– talbot per second per steradian per square meter
(T/s/sr/m2) (not SI)
Proportional to:
photons per second
per unit solid angle per unit area
Radiometric equivalent: radiance
(watt per steradian per square meter)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminance
Relationship between incident illuminance (Ev)
and resulting reflected luminance (Lv)
(for a Lambertian surface):
Lv = Ev / π
– Examples:
• surface illuminated by π = 3.1416 lx
has a luminance of 1 cd/m2
• surface illuminated by 1 lx
has a luminance of 1/π = 0.3183 cd/m2
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminance
Obsolete and non-SI units of luminance
– Units defined in terms of luminance of
a Lambertian surface reflecting a specified illuminance
• lambert
– luminance of surface illuminated by 1 lm/cm2
• meterlambert = apostilb = blondel
– luminance of surface illuminated by 1 lm/m2
(meter-candle, or lux)
– 1 meterlambert = 1/π cd/m2
• footlambert (fL)
– luminance of surface illuminated by 1 lm/ft2
(footcandle)
A Tutorial on Photometric Dimensions and Units
Table of correspondences
Illuminance
1 lx = lm/m2
1 lm/cm2
1 fc = 1 lm/ft2
Reflected luminance
(Lambertian surface)
1/π cd/m2
= 1/π nit
= 1 meterlambert
= 1 apostilb
= 1 blondel
1 lambert
1 foot-lambert
George Joblove
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Luminance
More about the footlambert
– Relationship between the footlambert and nit
• 1 fL = [(ft/m)2 × 1/π] cd/m2 = 3.2812/π cd/m2
= 10.76/π cd/m2 = 3.426 cd/m2
• For example: 48 cd/m2 ≈ 14 fL
– Easy calculations with Lambertian luminance units
• For example (assuming unity-gain screen):
– Projector luminous power output to the screen (in lumens)
required to yield a desired luminance
= screen area (in square feet) × luminance (in footlamberts);
e.g., to achieve 14 fL on a 1000-ft2 screen requires 14,000 lumens
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminance
More about luminance and illuminance
– The luminance of a reflecting or emitting surface
is also equal to:
the illuminance it casts on another, receiving, surface,
divided by the solid angle subtended by
the source surface
– That is, the illuminance received
from a reflecting or emitting surface is equal to:
the luminance of that surface
multiplied by the solid angle it subtends
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminance
Example: Is a “supermoon” (moon at perigee) “brighter”?
– Its luminance is no different
• Distance from sun is unchanged,
thus so is its luminance
(the luminance of a surface
does not vary with viewing distance)
howeverO
– Its illuminance cast on Earth
is increased
• Since it is closer,
it subtends a greater solid angle
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminous exposure
Luminous energy per unit area
– Illuminance times time
Unit: lux-second (lx s)
– Luminous energy of a lumen incident on
a surface of one square meter
over a duration of one second
Unit derivations:
– lumen-second per square meter (lm s/m2)
– candela-steradian-second per square meter (cd sr s/m2)
– talbot per square meter (T/m2) (not an SI unit)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Luminous exposure
Luminous energy per unit area
Unit: lux-second (lx s)
Unit derivations:
– lumen-second per square meter (lm s/m2)
– candela-steradian-second per square meter (cd sr s/m2)
– talbot per square meter (T/m2) (not an SI unit)
Proportional to: photons per unit area
Radiometric equivalent: radiant exposure
(joule per square meter)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
26
Luminous exposure
Example: Film sensitometric curves
– Typical
tungsten-balanced
ISO-500 film stock:
• Recommended
exposure
of 18%-gray card:
.04 lux-seconds
(log .04 = −1.4)
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Example: How “bright” is the sun?
Depends on what is being measured
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Example: How “bright” is the sun?
Total luminous energy output each second
= 3.53 × 1028 lm s
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Example: How “bright” is the sun?
Total luminous energy output each second
= 3.53 × 1028 lm s
Total luminous power output
= luminous energy per second
= (3.53 × 1028 lm s) / s
= 3.53 × 1028 lm
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Example: How “bright” is the sun?
Total luminous power output
= luminous energy per second
= (3.53 × 1028 lm s) / s
= 3.53 × 1028 lm
Luminous intensity
= luminous power per unit solid angle
= (3.53 × 1028 lm) / (4π sr)
= 2.81 × 1027 cd
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
31
Example: How “bright” is the sun?
Total luminous power output
= luminous energy per second
= 3.53 × 1028 lm
Luminous intensity
= 2.81 × 1027 cd
Illuminance at surface
= total luminous flux / surface area
= total luminous flux / 4πr 2
= (3.53 × 1028 lm) / [4π — (6.96 × 108 m)2]
= (3.53 × 1028 lm) / (6.09 × 1018 m2)
= 5.80 × 109 lx
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Example: How “bright” is the sun?
Illuminance at surface
= total luminous flux / surface area
= 5.80 × 109 lx
Luminance of solar disk
= illuminance at surface / π
= (5.80 × 109 lx) / [π lx/(cd/m2)]
= 1.85 × 109 cd/m2
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Example: How “bright” is the sun?
Illuminance at surface
= total luminous flux / surface area
= 5.80 × 109 lx
Luminance of solar disk
= illuminance at surface / π
= 1.85 × 109 cd/m2
Illuminance at Earth (above atmosphere)
= illuminance at the sun’s surface / (d / r ) 2
= (5.80 × 109 lx) / [(1.5 × 1011 m) / (6.96 × 108 m)]2
= 1.2 × 105 lx
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Example: How “bright” is the sun?
Luminance of solar disk
= illuminance at surface / π
= 1.85 × 109 cd/m2
Illuminance at Earth (above atmosphere)
= luminance of solar disk × subtended solid angle
= luminance of solar disk × πr 2 / d 2
= (1.85 × 109 cd/m2) — [π — (6.96 × 108 m)2 / (1.5 × 1011 m)2] sr
= (1.85 × 109 cd/m2) — (6.8 × 10−5 sr)
= 1.2 × 105 cd sr/m2
= 1.2 × 105 lx
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
35
Example: How “bright” is the sun?
Luminance of solar disk
= illuminance at surface / π
= 1.85 × 109 cd/m2
Illuminance at Earth (above atmosphere)
= illuminance at the sun’s surface / (d / r ) 2
= luminance of solar disk × subtended solid angle
= 1.2 × 105 lx
Illuminance at Earth (attenuated by atmosphere, typical)
≈ 1.0 × 105 lx
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Example: How “bright” is the sun?
Illuminance at Earth (attenuated by atmosphere, typical)
≈ 1.0 × 105 lx
Luminance of white card (100% Lambertian reflector)
= illuminance / π
= (1.0 × 105 lx) / [π lx/(cd/m2)]
= 3.2 × 104 cd/m2
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
37
Example: How “bright” is the sun?
Illuminance at Earth (attenuated by atmosphere, typical)
≈ 1.0 × 105 lx
Luminance of white card (100% Lambertian reflector)
= illuminance / π
= 3.2 × 104 cd/m2
Luminance of 18%-gray card
= (3.2 × 104 — 0.18) cd/m2
= 5700 cd/m2
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
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Example: How “bright” is the sun?
Illuminance at Earth (attenuated by atmosphere, typical)
≈ 1.0 × 105 lx
Luminance of white card (100% Lambertian reflector)
= illuminance / π
= 3.2 × 104 cd/m2
Luminance of 18%-gray card
= (3.2 × 104 — 0.18) cd/m2
= 5700 cd/m2
Luminous exposure of photographic sensor (500T)
≈ 0.04 lx s
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
39
Example: How “bright” is the sun?
Total luminous energy output each second
Total luminous power output
Luminous intensity
Illuminance at surface
Luminance of solar disk
Illuminance at Earth (typical)
Luminance of white card
Luminance of 18%-gray card
Luminous exposure of film, ISO 500 (tungsten)
A Tutorial on Photometric Dimensions and Units
3.53 × 1028 lm s
3.53 × 1028 lm
2.81 × 1027 cd
5.80 × 109 lx
1.85 × 109 cd/m2
1.0 × 105 lx
3.2 × 104 cd/m2
5700 cd/m2
0.04 lx s
George Joblove
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Summary
Photometric dimensions and units
Dimension
Luminous energy
Luminous flux (power)
Luminous intensity
Illuminance
Luminance
Luminous exposure
A Tutorial on Photometric Dimensions and Units
Unit, unit derivation(s)
lm s = cd sr s = T
lm = cd sr = T/s
cd = lm/sr = T/s/sr
lx = lm/m2 = cd sr/m2 = T/s/m2
cd/m2 = lm/sr/m2 = T/s/sr/m2
lx s = lm s/m2 = cd sr s/m2 = T/m2
Radiometric equiv’t
J
W
W/sr
W/m2
W/sr/m2
J/m2
George Joblove
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Photometric Dimensions and Units
George Joblove
george [at] joblove.com
A Tutorial on Photometric Dimensions and Units
George Joblove
rev. c
42