Page 215 - Algae

198 Algae: Anatomy, Biochemistry, and Biotechnology

Typical Values for Illuminance (in lux)

Sunlight 100,000
Skylight 10,000
Overcast daylight 1,000
Moonlight 0.1
Starlight 0.01

LUMINANCE
Luminance is a photometrically weighted radiance. In terms of visual perception, we perceive lumi-
nance. It is an approximate measure of how “bright” a surface appears when we view it from a given
direction. Luminance used to be called “photometric brightness.” Luminance is measured in
lumens per square meter per steradian (lm m 22 sr 21 ).

LAMBERTIAN SURFACES
A Lambertian surface is referred to as a perfectly diffusing surface, which adheres to Lambert’s
cosine law. This law states that the reflected or transmitted luminous intensity in any direction
from an element of a Lambertian surface varies as the cosine of the angle between that direction
and the normal of the surface. The intensity I u of each ray leaving the surface at an angle u from
the ray in a direction perpendicular to the surface (I n ) is given by:

I u ¼ I n cos u (5:22)

Therefore, even if the luminous intensity decreases with a factor cos(u) from the normal, the
projected surface decreases with the same factor; as a consequence, the radiance (luminance) of
a Lambertian surface is the same regardless of the viewing angle and is given by:

dI n cos u dI n
L ¼ ¼ (5:23)
dA cos u dA
It is worthwhile to note that in a Lambertian surface the ratio between the radiant exitance and
the radiance is p and not 2p:

M
¼ p (5:24)
L

This equation can be easily derived. Suppose we place an infinitesimal Lambertian emitter dA
on the inside surface of an imaginary sphere S. The inverse square law [Equation (5.15)] provides
the irradiance E at any point P on the inside surface of the sphere. However, d ¼ D cos u, where D
is the diameter of the sphere. Thus:

I u
E ¼ (5:25)
2
D cos u
and from Lambert’s cosine law [Equation (5.22)], we have:
I n
E ¼ (5:26)
D 2
which simply says that the irradiance (radiant flux density) of any point P on the inside surface of S
is a constant.