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Irradiance E is defined as the radiant flux incident per unit area of receiving surface and is measured in watts per square meters. Radiant exposure H is the energy incident per unit area of receiving surface. When spectrally weighted by a photobiologic spectral response function, radiant exposure can be considered the biologically effective dose for that response. The photometric analogue of irradiance is the illuminance, measured in lux (lx), where 1 lx is equal to 1 lm m⁻². The photometric analogue of radiant exposure is the light exposure, measured in lux‐seconds.

TABLE 1 Radiometric and photometric terms and units.

Radiometric term	Radiometric units	Photometric term	Photometric units	Symbol	Defining relationship
(a) Measures of radiation emitted at source
Radiant energy	J	Luminous energy, quantity of light	lm s (talbot)	Q	—
Radiant power, radiant flux	W	Luminous flux	lm	Φ
Radiant intensity	W sr−1	Luminous intensity	cd	I
Radiance	W m−2 sr−1	Luminance	cd m−2	L
Radiant exitance	W m−2	Luminous exitance	lm m−2	M
(b) Measures of radiation received at surface
Irradiance	W m−2	Illuminance	lx	E
Radiant exposure	J m−2	Light exposure	lx s	H

t, time; Ω, solid angle at source; A_s, area of source; θ, angle relative to source normal; A_r, area of receiving surface; J, joule; lm, lumen; s, second; W, watt; sr, steradian; cd, candela; m, meter; lx, lux.

FIGURE 3 Illustration of radiometric terms and their defining variables. dΩ, differential solid angle at source; dA, differential area cut off by dΩ on surface of sphere of radius r; dΦ, differential radiant flux; dA_s, differential area of source; θ, angle relative to source normal.

The radiometric and photometric terms relating to radiation received on a surface are summarized in Table 1 (part (b)).

The irradiance at a distance r from a point source that is emitting a total radiant flux Φ isotropically can be calculated as

(6)

This relationship is known as the inverse square law. The inverse square law is not valid within close distances of an area source. However, when the distance from an area source is more than five times greater than the longest dimension of the source, the irradiance does become proportional to the inverse square of the distance from the source (10). Under these circumstances, given a Lambertian source of area A_s, the radiant flux dΦ received at a differential receiving area dA_r is

(7)

where θ is the angle between the line of sight and the perpendicular to the radiating surface, and θ_r is the angle between the line of sight and the perpendicular to the receiving surface. The solid angle subtended by the differential receiving area is , where the factor cos θ_r takes account of the fact that the receiving area will subtend a smaller solid angle, and so capture less radiant flux, if it is not oriented perpendicular to the line of sight. The irradiance is then

(8)

which is Lambert's cosine law combined with the cosine response of the receiving surface.