UNIVERSITY OF HONG KONG
Department of Electrical & Electronic Engineering
ELEC 3105 Building Services
“God made two great lights” (Genesis 1:16)
LUMINOUS FLUX
, luminous flux is the total quantity of light emitted per second by a
source. Unit is lumen. It can be defined as the energy radiated by a
light source per second, weighted against the spectral sensitivity of the
human eye.
It is sometimes denoted as F.
In lighting engineering, we are concerned with how much light, and so need
to calculate lux level, or illuminance, E
E

,
A
unit is lux (lumen per m2)
Typical example
Bicycle headlamp
Incandescent lamp
Compact fluorescent lamp
Tubular fluorescent lamp
High pressure sodium
Low pressure sodium
High pressure mercury
Metal Halide
Induction lamp
K.F. Chan (Mr.)
Argenta
3W
75W
30lm
900lm
SL
“TL”D
SON-T
SOX-E
HPL-N
HPI-T
QL
18W
58W
100W
130W
1000W
2000W
85W
900lm
5400lm
10,000lm
26,000lm
58,000lm
190,000lm
6,000lm
Page A1a1 of 8
Sept 2010
UNIVERSITY OF HONG KONG
Department of Electrical & Electronic Engineering
ELEC 3105 Building Services
Solid Angle
While the unit of angle on a 2-D plane is radian, the unit of solid angle in a 3-D
space is steradian. It is the three-dimensional angle enclosed by a conical
surface with the vertex of the cone at the centre of a sphere:
While an angle subtended by an “arc” of a circle is equivalent to the “width” of
that arc divided by the radius of the circle, solid angle subtended by a “surface”
of a sphere is equivalent to the “area” of that surface divided by the square of
the radius of the sphere. In other words:
surface area of the sec tion of sphere
Solid angle 
radius of the sphere 2
While a complete circle subtends the maximum possible angle of 2π, a
complete sphere subtends the maximum possible solid angle. As the surface
area of a sphere of radius R is 4R 2 , therefore, the solid angle of a complete
sphere is:
4R 2
 4
R2
K.F. Chan (Mr.)
Page A1a2 of 8
Sept 2010
UNIVERSITY OF HONG KONG
Department of Electrical & Electronic Engineering
ELEC 3105 Building Services
1) I, luminous intensity is the luminous flux in a certain direction, radiated
per unit solid angle.
Luminous intensity I 
luminous flux
solid angle
, unit is
lumens
 cd
steradian
The concept of luminous intensity is of tremendous importance in lighting
technology, because virtually no luminaire emits flux equally in all directions.
This is quite deliberately so because some directions are of far more use to the
lighting user, while some others have to be avoided (such as to prevent glare).
In the period from 1948 to 1979, the candela was defined as the luminous
intensity of 1/60 cm2 of a black body at the freezing point of platinum.
In 1979, candela was re-defined as:“the luminous intensity in a specific direction of a source emitting
monochromatic radiation of a frequency 540x1012Hz (approximately 555nm in
air), and of which the radiant intensity in that direction is 1/683 Watt per
steradian.”
(Speed of light in vacuum is 299,792,458m/s)
From the above definition, it can be seen that an “ideal” lamp can only output
683 lumen per Watt energy input. In reality, luminous efficacy ranges from
tens to just over hundred lumen/Watt only.
K.F. Chan (Mr.)
Page A1a3 of 8
Sept 2010
UNIVERSITY OF HONG KONG
Department of Electrical & Electronic Engineering
ELEC 3105 Building Services
Some examples:Bicycle headlamp without reflector,
in any direction
Bicycle headlamp with reflector,
center of beam
Incandescent reflector lamp
PAR38E spot 120 Watt, center of beam
Lighthouse, center of beam
2.5cd
250cd
10,000cd
200,000cd
Intensity of a light source is independent of viewing distance.
Manufacturers present intensity of luminaires in different directions in form of
polar curve. An example is shown here below:
K.F. Chan (Mr.)
Page A1a4 of 8
Sept 2010
UNIVERSITY OF HONG KONG
Department of Electrical & Electronic Engineering
ELEC 3105 Building Services
2) Luminance L 
luminous intensity
apparent area
, unit is cd/m2
Luminance is how “bright” we see an object. In reality we cannot see
flux or illuminance. We see variations in luminances. Luminance, in cd/m2,
is the most important quantity in lighting engineering, although luminous
flux, luminous intensity and illuminance are usually easier to comprehend,
measure and calculate.
Luminance
Illuminance
It should be noted that like luminous intensity, luminance is also
independent of viewing distance
Some typical values
Surface of the sun
Filament of a clear incandescent lamp
Bulb of an “Argenta” incandescent lamp
Fluorescent lamp
1.65 billion cd/m2
7 million cd/m2
200,000cd/m2
5,000 – 15,000 cd/m2
Surface of the full moon
Sun-lit beach
White paper (reflectance 0.8) under 400 lux
Grey paper (reflectance 0.4) under 400 lux
Black paper (reflectance 0.04) under 400 lux
Road surface under artificial lighting
T8 tube
T12 tube
55Watt compact fluorescent
2,500 cd/m2
15,000 cd/m2
100 cd/m2
50 cd/m2
5 cd/m2
0.5 – 2 cd/m2
11,000 cd/m2
7,000 cd/m2
35,000 cd/m2
K.F. Chan (Mr.)
Page A1a5 of 8
Sept 2010
UNIVERSITY OF HONG KONG
Department of Electrical & Electronic Engineering
ELEC 3105 Building Services
It is worth noting that the denominator in the definition of luminance is apparent
area, i.e. area of the surface that one sees.
K.F. Chan (Mr.)
Page A1a6 of 8
Sept 2010
UNIVERSITY OF HONG KONG
Department of Electrical & Electronic Engineering
ELEC 3105 Building Services
3) To make calculations easier, in lighting calculations, matt surfaces are
usually assumed to be perfectly diffusing surfaces.
(Perfectly diffusing surface is the opposite of specular surface.
Specular surface reflects light without diffusion in accordance with the
Snell’s Law of reflection, as in mirror.)
Matt surface, or perfectly diffusing surface, reflects light in which the
reflected light is diffused and there is no significant specular reflection, as
from a matt paint. Perfectly diffusing surface displays equal luminance
in ALL directions (not equal luminous intensity in all directions)
K.F. Chan (Mr.)
Page A1a7 of 8
Sept 2010
UNIVERSITY OF HONG KONG
Department of Electrical & Electronic Engineering
ELEC 3105 Building Services
Cosine diffuser
Consider a light-emitting surface of area S. The maximum intensity emitted
normal to the surface is Io. Its luminance when viewed normal to the surface is
Lo 
Io
S
When viewed at an angle of θ away from its normal, the apparent area
becomes Scosθ. Let the intensity at angle θ be I θ, so the luminance of the
surface when viewed at angle θ is L 
I
S cos 
However, luminance of a perfect diffuser is the same irrespective of viewing
direction, thus Lo = Lθ, or
Io
I

S S cos 
 I
 I o cos 
It is why a perfect diffuser is also called a cosine diffuser.
K.F. Chan (Mr.)
Page A1a8 of 8
Sept 2010