Biophotonics_Concepts_to_Applications

Solution: From Eq. (4.1) the irradiance is

E¼

Power

Area

¼

1W

pðÞ 2 : 5  10 ^3 m^2

¼ 5 : 09  104 W=m^2

¼ 5 : 09  103 mW/cm^2

4.1.3 Radiant Intensity

Radiant intensity, or simplyintensityI, is the power per unit solid angleΩand is
measured in watts per steradian (W/sr). Because intensity is the derivative of power
with respect to solid angleΩ(that is, dP/dΩ), then that the integral of the intensity
over the solid angle is power. The angular intensity distribution is illustrated
comparatively in Fig.4.3for a lambertian source and a highly directional laser
diode in which the output beams have rotational symmetry. The power delivered at
an angleθmeasured relative to a normal to the emitting surface can be approxi-
mated by the expression

I(hÞ¼I 0 cosg^1 h ð 4 : 2 Þ

Here I 0 is the intensity normal to the source surface and g≥1. For example
g = 1 for an isotropic source (emits the same intensity in all directions)
g = 2 for a lambertian source (the intensity varies as coshbecause the projected
area of the emitting surface varies as coshwith viewing direction)
g≥30 for a lensed LED lamp or a laser diode (for example, g = 181 in Fig.4.3).

Lambertian source

Highly directional laser diode

Observation an

gle

Fig. 4.3 Intensity patterns
for a lambertian source and
the lateral output of a highly
directional laser diode. Both
sources have I 0 normalized to
unity

4.1 Radiometry 95