Page 210 - Algae Anatomy, Biochemistry, and Biotechnology

Working with Light 193

Spectral radiant flux density is measured in watts per square meter per nanometer
(W m 22 nm 21 ).

RADIANCE
Imagine a ray of light arriving at or leaving a point on a surface in a given direction. Radiance
is simply the amount of radiant flux contained in this ray (a cone of solid angle dv). If the ray
intersects a surface at an angle u with the normal to that surface, and the area of intersection
with the surface has an infinitesimal cross-sectional area dA, the cross-sectional area of the ray
is dAcos u. The radiance of this ray is:

2
d F
L ¼ (5:13)
dA dv cos u
22 21
Radiance is measured in watts per square meter per steradian (W m sr ).
Unlike radiant flux density, the definition of radiance does not distinguish between flux arriving
at or leaving a surface.
Another way of looking at radiance is to note that the radiant flux density at a point on a
surface due to a single ray of light arriving (or leaving) at an angle u to the normal to that
2
surface is dF/dA cos u. The radiance at that point for the same angle is then d F/(dA dv cos u),
or radiant flux density per unit solid angle.
The irradiance, E, at any distance from a uniform extended area source, is related to the radi-
ance, L, of the source by the following the relationship, which depends only on the subtended
central viewing angle, u, of the radiance detector:

u
2
E ¼ p L sin (5:14)
2
Radiance is independent of distance for an extended area source, because the sampled area
increases with distance, cancelling inverse square losses. The inverse square law defines the
relationship between the irradiance from a point source and distance (d). It states that the intensity
per unit area varies in inverse proportion to the square of the distance. In other words, if you
measure 16 W m 22 at 1 m, you will measure 4 W m 22 at 2 m, and can calculate the irradiance
at any other distance. An alternate form is often more convenient:

2
E 1 d ¼ E 2 d 2 2 (5:15)
1

SPECTRAL RADIANCE
Spectral radiance is the radiance per unit wavelength interval at wavelength l. It is defined as:

3
d F
L l ¼ (5:16)
dA dv cos u dl
and is measured in watts per square meter per steradian per nanometer (W m 22 sr 21 nm 21 ).

RADIANT INTENSITY
We can imagine a small point source of light that emits radiant flux in every direction. The amount
of radiant flux emitted in a given direction can be represented by a ray of light contained in an