Eq B.1

Radiant exitance sums emitted and reflected light. The former term emittance excludes reflected light.

Some thermal engineers use the term radiosity for radiant exitance. In computer graphics, radiosity refers to a specialized technique to compute illumination; it does not refer to any particular quantity.

In photography, the symbol I

is often used for irradiance or illuminance, instead of intensity. Beware that sound intensity is conceptually unlike light intensity: Sound intensity has dimensions of power per unit area, comparable to irradiance of light.

Palmer, James M. (1993), “Getting intense on intensity,” in Metrologia 30 (4): 371–372.

Radiometry and photometry involve light, in space. No surface is necessary! Light properties may be described at a real or imaginary surface; however, they are not properties of a surface. Absorptance (α), reflectance (ρ), and transmittance (τ) are intrinsic properties of surfaces, not properties of light.

In what follows, I use the usual physics convention of writing letter symbols in italics and units in Roman type.

Radiometry

Radiometry starts with energy (symbolized Q) at wavelengths between about 100 nm and 1 mm. Energy is expressed in units of joules [J]. A photon’s energy (Qp) is related to its wavelength (λ), here given in meters:

The rate of flow – or formally, the time-derivative – of radiant energy is power (P), also known as radiant flux (F, or preferably, Φ ), expressed in units of watts [W].

Radiant flux per unit area – that is, flux density – arriving at a point, throughout all directions in a hemisphere, is irradiance (E). Irradiance is expressed in units of watts per meter squared [W·m-2 or W/m2]. Solar irradiance (insolation) at noon is about 1 kW·m-2.

Radiant flux per unit area leaving a point, in all directions, is radiant exitance (M). Formally, this is the derivative of radiant flux with respect to area. Radiant exitance is expressed in units of watts per meter squared [W·m-2]. Radiant exitance from a nonemissive surface is simply its irradiance times its reflectance.

Radiant flux in a specified direction – formally, radiant flux per unit solid angle – is radiant intensity (I); its SI unit is watts per steradian [W·sr-1 or W/sr]. Intensity must be specified in a particular direction. Intensity is a property of a point-like source; it is independent of distance to the observer or measurement device. Intensity does not follow the inverse square law! Intensity has many other meanings in physics, with the most common being power per unit area, but the unambiguous term for that quantity is irradiance.

The late James M. Palmer pointed out that the term intensity is widely misused, for no good reason, because it is one of the seven base units of the SI system!

Normal

dω

θ

dA

Φ

[x, y, z]

Figure B.1 Geometry associated with the definition of radiance The quantity dA represents unit area; the quantity dω represents unit solid angle. Projected area falls off as cos θ.

Beware so-called intensity expressed in units other than watts per steradian, W·sr-1. Some authors in thermal engineering, and some authors in the computer graphics field of radiosity, use the term radiant intensity for what I call radiance, which I will now describe.

Radiant flux density in a specified direction is radiance (symbol L). Formally, radiance is radiant flux differentiated with respect to both solid angle and projected area; the geometry of this definition is depicted in Figure B.1. Radiance is expressed in units of watts per steradian per meter squared [W/sr/m2, or preferably, W·sr-1·m-2]. For a large, nonpoint source, radiance is independent of distance.

Confusingly, radiance is often called intensity in some domains, especially heat transfer, astrophysics, and astronomy. Also, what is today called radiance was once called radiometric brightness, or just brightness. The term brightness remains in use in astronomy, but it is deprecated for image and colour science.

Radiance can be considered to be the fundamental quantity of radiometry: All other radiometric quantities can be computed from it. You might find it intuitive to start with radiance, and then consider the following:

•Radiant intensity is radiance integrated across an area.

•Irradiance is radiance integrated through solid angle, that is, integrated across all directions in a hemisphere.

•Flux is irradiance integrated across area, or equivalently, radiant intensity integrated through solid angle.

All of these radiometric terms relate to a broad spectrum of wavelengths. Any of these terms may be limited to a narrow spectrum by prepending spectral to the term, subscripting the letter symbol with λ , and appending per nanometer (·nm-1) to the units.

Photometry

So far, I have discussed the physical quantities of radiometry. Photometry is entirely analogous, except that the spectral composition of each quantity is weighted by the spectral sensitivity of human vision, standardized as the luminous efficiency of the CIE Standard Observer (graphed in Figure 20.1 on page 205).

A lumen is produced by about 1.5 mW of monochromatic power at 555.5 nm. That wavelength,

a frequency of 540 THz, corresponds to the peak luminous efficiency of vision.

The quantity illuminance was formerly called illumination. However, use of illumination for this quantity is deprecated, owing to the more general meaning of the word as the act of illuminating, or the state of being illuminated.

The old footcandle and metercandle units for luminous exitance were misleading, because the old candle was a unit of intensity, not flux.

Nit isn’t an official SI unit but it is synonymous with cd·m-2. It has been used by the CIE since 1947 and is in common use today. Nit is derived from the Latin word nitere, “to shine.”

It is an error, sadly common among home theatre calibrators, to abbreviate candela per meter squared as candela. Candela is a different unit. To abbreviate cd·m-2, use nit [nt].

Radiometry and photometry are linked by the definition of the candela: One candela [cd] is the luminous intensity of a monochromatic 540 THz source having

a radiant intensity of 1⁄683 W·sr -1. Once this definition is established, the remaining photometric quantities and units parallel those of radiometry. The relationships are sketched in Figure B.2 opposite.

The photometric analog of radiant flux is luminous flux (Φ v ). To quote James Palmer, luminous flux is what you want when you buy a light bulb. Its brightness is lumens, the photometric analog of watts; its efficacy is measured in lumens per watt. One lumen appears equally bright regardless of its spectral composition.

Luminous flux per unit area – that is, luminous flux density – arriving at point is illuminance (Ev), having SI units of lux [lx]. One lux is defined as 1 lm·m-2. Illuminance is the photometric analog of irradiance; it is the quantity measured by an incident light meter. Luminous flux per unit area leaving a point is luminous exitance (Mv). One lux equals 1 lm·m-2, whether the light is coming or going; however, traditionalists often state luminous exitance in units of lm·m-2. Luminous exitance from a nonemissive surface is its illuminance times its reflectance.

Luminous flux in a particular, specified direction is luminous intensity (Iv ), expressed in units of lm·sr-1, or candela [cd]. The candela is the modern equivalent of the old candle (colloquially, candlepower). Intensity is independent of distance: A candle has a luminous intensity of about 1 cd, at any viewing distance.

The unit of luminous energy is the talbot [T]. A talbot is a lumen-second.

Luminous flux density in a particular direction is luminance (Lv). Formally, luminance is luminous flux differentiated with respect to both solid angle and projected area. Luminance is the photometric analog of radiance; it is expressed in units of cd·m-2, or colloqially, nit [nt]. Luminance is an important and useful measure, because it is invariant under transformation by a lens. Luminance of 1 cd·m-2 corresponds to roughly a million photons at 560 nm, per square degree, per second. Brightness is the perceptual correlate of luminance; however, brightness perception is very complex

illuminance, EV luminous exitance, MV lm·m-2 = lux [lx]