Quantities and Units in Radiometry

What are the quantities and units used in radiometry?

Radiometric units can be divided into two conceptual areas: those having to do with power or energy, and those that are geometric in nature. The first two are:

Energy is an SI derived unit, measured in joules (J). The recommended symbol for energy is Q. An acceptable alternate is W.

Power (a.k.a. radiant flux) is another SI derived unit. It is the derivative of energy with respect to time, dQ/dt, and the unit is the watt (W). The recommended symbol for power is F (the uppercase Greek letter phi). An acceptable alternate is P.

Energy is the integral over time of power, and is used for integrating detectors and pulsed sources. Power is used for non-integrating detectors and continuous sources. Even though we patronize the power utility, what we are actually buying is energy in watt-hours.

Now we become more specific and incorporate power with the geometric quantities area and solid angle

Irradiance (a.k.a. flux density) is another SI derived unit and is measured in W/m2. Irradiance is power per unit area incident from all directions in a hemisphere onto a surface that coincides with the base of that hemisphere. A similar quantity is radiant exitance, which is power per unit area leaving a surface into a hemisphere whose base is that surface. The symbol for irradiance is E and the symbol for radiant exitance is M. Irradiance (or radiant exitance) is the derivative of power with respect to area, dF /dA. The integral of irradiance or radiant exitance over area is power.

Radiant intensity is another SI derived unit and is measured in W/sr. Intensity is power per unit solid angle. The symbol is I. Intensity is the derivative of power with respect to solid angle, dF /dw . The integral of radiant intensity over solid angle is power.

Radiance is the last SI derived unit we need and is measured in W/m2-sr. Radiance is power per unit projected area per unit solid angle. The symbol is L. Radiance is the derivative of power with respect to solid angle and projected area, dF /dw dA cos(q) where q is the angle between the surface normal and the specified direction. The integral of radiance over area and solid angle is power.

A great deal of confusion concerns the use and misuse of the term intensity. Some folks use it for W/sr, some use it for W/m² and others use it for W/m²-sr. It is quite clearly defined in the SI system, in the definition of the base unit of luminous intensity, the candela. Some attempt to justify alternate uses by adding adjectives like field or optical (used for W/m²) or specific (used for W/m²-sr), but this practice only adds to the confusion. The underlying concept is (quantity per unit solid angle). For an extended discussion, I wrote a paper entitled "Getting Intense on Intensity" for Metrologia (official journal of the BIPM) and a letter to OSA's "Optics and Photonics News". A modified version is available on the web.

Photon quantities are also common. They are related to the radiometric quantities by the relationship Q_p = hc/l where Q_p is the energy of a photon at wavelength l , h is Planck's constant and c is the velocity of light. At a wavelength of 1 mm, there are approximately 5×10¹⁸ photons per second in a watt. Conversely, also at 1 mm, 1 photon has an energy of 2×10^–19 joules (watt-sec). Common units include sec^–1-m^–2-sr^–1 for photon radiance.