Measurement of Spectral Irradiance
Spectral irradiance at a point on a surface is defined by the equation:
Where dΦ(λ) is the radiant power in a wavelength interval dλ, incident on an element of a surface (from the hemipshere above that surface), by the area dA of that element and by the wavelength interval dλ.
Since irradiance accounts for illumination from the hemisphere above the surface one must consider the effect of off-axis contributions: as the incidence angle is taken away from the normal to the surface, so the irradiance produced by that source reduces by the cosine of the incidence angle.
In measuring spectral irradiance, therefore, the input optic should have a response which weights the angular components by the cosine of that angle.
In measuring irradiance, the measurement optic, typically a diffuser or an integrating sphere, should have a cosine angular response to correctly account for off-axis contributions: at a given angle from the surface normal, the projected area on the surface is increased by the cosine of the said angle, resulting in reduced irradiance.
Of note too is the application of the inverse square law. Given a source emitting equally in all directions, it can be seen that the irradiance varies inversely proportional to the distance from the source squared, the product of the two being the radiant intensity of the source.
The inverse square law is frequently used in computing the irradiance of the source at another distance or in goniophotometers where the reported parameter (luminous intensity) is derived from the product of illuminance and measurement distance squared.