Basic Quantities in Illumination
Basic Quantities in Illumination
Basic Quantities in Illumination
Solid Angle
A A
B l
B
θ θ θ =l/r
r (radians)
O O
2π radians in
a full circle
r ω=a/r2 (steradians)
ω
ω 4π steradians in
a full sphere
Basic Quantities in Illumination 3
Ω = ω cos ϕ
ϕ
Ω = π sin2 θ
Photometric Quantities
1.0
Luminous Efficiency
0.8
0.6
0.4
0.2
0.0
350 400 450 500 550 600 650 700 750 800
wavelength (nm)
Notes on notation:
• The photopic quantities of flux, irradiance,
intensity, and radiance are called luminous flux,
illuminance, luminous intensity, and
luminance, respectively.
• These quantities are sometimes notated with a
subscript “v” (for visual), as Φv, Ev, Iv, and Lv. But
often the subscript is omitted since the meaning is
usually clear from the context, and it could be
confused with the subscript notation often
reserved for integrable quantities.
• The designations Φ, E, I, and L are common but
not universally standard. Another set of symbols
sometimes used is P, H, J, and N, respectively, for
radiometric quantities; Pλ, H λ, J λ, and N λ for
spectral quantities; and F, E, I, and B for the
corresponding photometric quantities.
• Solid angle and projected solid angle are not
always distinguished by ω and Ω, respectively.
Basic Quantities in Illumination 7
SPECTRAL
Radio-
metric Spectral Photopic
Power Power/
wavelength Luminous flux
Flux interval
Watts (W) Watts/nm Lumens (lm)
Illuminance
Irradiance Spectral
Flux/ irradiance lm/m2
S or
area
P W/m2 W/m2·nm lux
A (Luminous)
T (Radiant) Spectral intensity
I Flux/ intensity intensity
A solid lm/sr
L angle or
W/sr W/sr·nm candela (cd)
Radiance Spectral Luminance
radiance
Flux/ lm/m2·sr
area· or
solid cd/m2
angle or
W/m2·sr W/m2·sr·nm nit
The table above shows the four spatial quantities and the
three spectral categories that are discussed in the
preceding pages. These create 12 distinct cells that cover
the vast majority of specifications for illumination
systems.
With two exceptions, both used mainly in the United
States, work in illumination is almost always done in SI
units. The two exceptions (both deprecated) are:
Illuminance
1 footcandle (lm/ft2) = 10.764 lux (lm/m2)
Luminance
1 footlambert (candela/πft2) = 3.426 nit (candela/m2)
8 Illumination
1.0
Luminous Efficiency
0.8
0.6
0.4
0.2
0.0
350 400 450 500 550 600 650 700 750 800
wavelength (nm)
Luminous Efficacy
Luminous Efficacy
(photopic)
700
Luminous Efficacy (lm/W)
600
500
400
300
200
100
0
350 400 450 500 550 600 650 700 750 800
wavelength (nm)