Photometric measure
Luminance
is a
photometric
measure of the
luminous intensity
per
unit area
of
light
travelling in a given direction.
[1]
It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls within a given
solid angle
.
The procedure for conversion from spectral
radiance
to luminance is standardized by the
CIE
and
ISO
.
[2]
Brightness
is the
term
for the
subjective
impression of the
objective
luminance measurement standard (see
Objectivity (science) § Objectivity in measurement
for the importance of this contrast).
The
SI unit
for luminance is
candela per square metre
(cd/m
2
). A non-SI term for the same unit is the
nit
. The unit in the
Centimetre?gram?second system of units (CGS)
(which predated the SI system) is the
stilb
, which is equal to one candela per square centimetre or 10 kcd/m
2
.
Description
[
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]
Luminance is often used to characterize emission or reflection from flat,
diffuse
surfaces. Luminance levels indicate how much
luminous power
could be detected by the
human eye
looking at a particular surface from a particular
angle of view
. Luminance is thus an indicator of how
bright
the surface will appear. In this case, the solid angle of interest is the solid angle subtended by the eye's
pupil
.
Luminance is used in the video industry to characterize the brightness of displays. A typical computer display emits between
50 and 300 cd/m
2
. The sun has a luminance of about
1.6
×
10
9
cd/m
2
at noon.
[3]
Luminance is
invariant
in
geometric optics
.
[4]
This means that for an ideal optical system, the luminance at the output is the same as the input luminance.
For real, passive optical systems, the output luminance is
at most
equal to the input. As an example, if one uses a lens to form an image that is smaller than the source object, the luminous power is concentrated into a smaller area, meaning that the
illuminance
is higher at the image. The light at the image plane, however, fills a larger solid angle so the luminance comes out to be the same assuming there is no loss at the lens. The image can never be "brighter" than the source.
Health effects
[
edit
]
Retinal damage can occur when the eye is exposed to high luminance. Damage can occur because of local heating of the retina. Photochemical effects can also cause damage, especially at short wavelengths.
[5]
The IEC 60825 series gives guidance on safety relating to exposure of the eye to lasers, which are high luminance sources. The IEC 62471 series gives guidance for evaluating the photobiological safety of lamps and lamp systems including luminaires. Specifically it specifies the exposure limits, reference measurement technique and classification scheme for the evaluation and control of photobiological hazards from all electrically powered incoherent broadband sources of optical radiation, including LEDs but excluding lasers, in the wavelength range from
200 nm
through
3000 nm
. This standard was prepared as Standard CIE S 009:2002 by the International Commission on Illumination.
Luminance meter
[
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]
A
luminance meter
is a device used in
photometry
that can measure the luminance in a particular direction and with a particular
solid angle
. The simplest devices measure the luminance in a single direction while imaging luminance meters measure luminance in a way similar to the way a
digital camera
records color images.
[6]
Formulation
[
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]
The luminance of a specified point of a light source, in a specified direction, is defined by the
mixed partial derivative
where
- L
v
is the luminance (
cd
/
m
2
);
- d
2
Φ
v
is the
luminous flux
(
lm
) leaving the area
dΣ
in any direction contained inside the solid angle
dΩ
Σ
;
- dΣ
is an
infinitesimal
area (m
2
) of the source containing the specified point;
- dΩ
Σ
is an infinitesimal
solid angle
(
sr
) containing the specified direction; and
- θ
Σ
is the
angle
between the
normal
n
Σ
to the surface
dΣ
and the specified direction.
[7]
If light travels through a lossless medium, the luminance does not change along a given
light ray
. As the ray crosses an arbitrary surface
S
, the luminance is given by
where
- d
S
is the infinitesimal area of
S
seen from the source inside the solid angle
dΩ
Σ
;
- dΩ
S
is the infinitesimal solid angle
subtended
by
dΣ
as seen from
d
S
; and
- θ
S
is the angle between the normal
n
S
to
d
S
and the direction of the light.
More generally, the luminance along a light ray can be defined as
where
- d
G
is the
etendue
of an infinitesimally narrow beam containing the specified ray;
- dΦ
v
is the luminous flux carried by this beam; and
- n
is the
index of refraction
of the medium.
Relation to illuminance
[
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]
The luminance of a reflecting surface is related to the
illuminance
it receives:
where the integral covers all the directions of emission
Ω
Σ
,
In the case of a perfectly
diffuse reflector
(also called a
Lambertian reflector
), the luminance is isotropic, per
Lambert's cosine law
. Then the relationship is simply
Units
[
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]
A variety of units have been used for luminance, besides the candela per square metre.
Units of luminance
|
cd/m
2
(
SI
unit)
≡ nit
≡ lm/m
2
/sr
|
stilb
(sb)
(
CGS
unit)
≡ cd/cm
2
|
|
apostilb
(asb)
≡ blondel
|
bril
|
skot
(sk)
|
lambert
(L)
|
|
foot-lambert
(fL)
= 1 ⁄
π
cd/ft
2
|
1 cd/m
2
|
=
|
1
|
10
?4
|
π
? 3.142
|
10
7
π
? 3.142
×
10
7
|
10
3
π
? 3.142
×
10
3
|
10
?4
π
? 3.142
×
10
?4
|
0.3048
2
π
? 0.2919
|
1 sb
|
=
|
10
4
|
1
|
10
4
π
? 3.142
×
10
4
|
10
11
π
? 3.142
×
10
11
|
10
7
π
? 3.142
×
10
7
|
π
? 3.142
|
30.48
2
π
? 2919
|
1 asb
|
=
|
1 ⁄
π
? 0.3183
|
10
?4
⁄
π
? 3.183
×
10
?5
|
1
|
10
7
|
10
3
|
10
?4
|
0.3048
2
? 0.09290
|
1 bril
|
=
|
10
?7
⁄
π
? 3.183
×
10
?8
|
10
?11
⁄
π
? 3.183
×
10
?12
|
10
?7
|
1
|
10
?4
|
10
?11
|
0.3048
2
×
10
?7
? 9.290
×
10
?9
|
1 sk
|
=
|
10
?3
⁄
π
? 3.183
×
10
?4
|
10
?7
⁄
π
? 3.183
×
10
?8
|
10
?3
|
10
4
|
1
|
10
?7
|
0.3048
2
×
10
?3
? 9.290
×
10
?5
|
1 L
|
=
|
10
4
⁄
π
? 3183
|
1 ⁄
π
? 0.3183
|
10
4
|
10
11
|
10
7
|
1
|
0.3048
2
×
10
4
? 929.0
|
1 fL
|
=
|
1 ⁄ 0.3048
2
⁄
π
? 3.426
|
1 ⁄ 30.48
2
⁄
π
? 3.426
×
10
?4
|
1 ⁄ 0.3048
2
? 10.76
|
10
7
⁄ 0.3048
2
? 1.076
×
10
8
|
10
3
⁄ 0.3048
2
? 1.076
×
10
4
|
10
?4
⁄ 0.3048
2
? 1.076
×
10
?3
|
1
|
See also
[
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]
Table of SI light-related units
[
edit
]
- ^
The symbols in this column denote
dimensions
; "
L
", "
T
" and "
J
" are for length, time and luminous intensity respectively, not the symbols for the
units
litre, tesla and joule.
- ^
Standards organizations
recommend that photometric quantities be denoted with a subscript "v" (for "visual") to avoid confusion with radiometric or
photon
quantities. For example:
USA Standard Letter Symbols for Illuminating Engineering
USAS Z7.1-1967, Y10.18-1967
- ^
a
b
c
Alternative symbols sometimes seen:
W
for luminous energy,
P
or
F
for luminous flux, and
ρ
for luminous efficacy of a source.
References
[
edit
]
- ^
"luminance, 17-21-050"
.
CIE S 017:2020 ILV: International Lighting Vocabulary, 2nd edition
. CIE - International Commission on Illumination. 2020
. Retrieved
20 April
2023
.
- ^
ISO/CIE 23539:2023 CIE TC 2-93 Photometry ? The CIE system of physical photometry
. ISO/CIE. 2023.
doi
:
10.25039/IS0.CIE.23539.2023
.
- ^
"Luminance"
.
Lighting Design Glossary
. Retrieved
Apr 13,
2009
.
- ^
Dorband, Bernd; Gross, Herbert; Muller, Henriette (2012). Gross, Herbert (ed.).
Handbook of Optical Systems
. Vol. 5, Metrology of Optical Components and Systems.
Wiley
. p. 326.
ISBN
978-3-527-40381-3
.
- ^
IEC 60825-1:2014
Safety of laser products - Part 1: Equipment classification and requirements
(in English, French, and Spanish) (3rd ed.).
International Electrotechnical Commission
. 2014-05-15. p. 220.
-
TC 76
- Optical radiation safety and laser equipment
- ^
"e-ILV : Luminance meter"
. CIE. Archived from
the original
on 16 September 2017
. Retrieved
20 February
2013
.
- ^
Chaves, Julio (2015).
Introduction to Nonimaging Optics, Second Edition
.
CRC Press
. p. 679.
ISBN
978-1482206739
.
Archived
from the original on 2016-02-18.
External links
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]