FIGURE 1 Water absorption spectrum between 200 nm and 200 μm.
Source: Data from Ref. (7).
In solid‐state semiconductor materials, absorption of a photon can cause an electron to transition from a low‐energy state (the valence band), in which it is localized in a chemical bond, to a higher energy state (the conduction band), in which it is free to move throughout the material. The vacancy left in the valence band, called a “hole,” behaves as if it were a positive charge. In the presence of an electric field, electrons in the conduction band and holes in the valence band flow as electrical current, which can be measured. Semiconductors are widely used for the detection of optical radiation.
The thermal, photochemical, and/or electrical changes resulting from the absorption of optical radiation may lead to observable effects such as a biological response or a detector signal. The strength of a specific response of a system to radiation as a function of wavelength is called the action spectrum or the spectral response function.
2.3 Radiometric and Photometric Terms and Units
A number of specialized terms and units are used to describe temporal and spatial aspects of energy transfer in the form of optical radiation (8). Radiometric units are based on the measures of energy or power without predefined spectral weighting. The Système Internationale (SI) unit of energy is joule (J). Power is the temporal rate of energy transfer. The SI unit of power is watt (W) (1 W = 1 J s−1). Photometric units are measures of visible radiation in which the power at each wavelength is weighted by the photopic luminous efficiency at that wavelength. The photopic luminous efficiency is a standard spectral response function defined by the CIE in 1924 to represent the relative response of the light‐adapted human eye to different wavelengths of visible light. The photopic luminous efficiency curve is illustrated in Figure 2. The photometric equivalent of the radiant power is the luminous flux, measured in SI units of lumens (lms). For monochromatic radiation at 555 nm, which is the maximum of the photopic response function, 1 W of radiant power is equivalent to 683 lm of luminous flux. At other wavelengths, 1 W is equivalent to 683 lm multiplied by the photopic luminous efficiency at that wavelength.
FIGURE 2 Photopic luminous efficiency function, representing the relative sensitivity of the human eye to different wavelengths of light.
2.3.1 Measures of Source Output
The terms radiant energy Q and radiant power Φ refer, respectively, to the total energy output and the time rate of energy emission of a source. Radiant power is also called radiant flux. The photometric analogues to radiant energy and radiant flux are luminous energy, measured in lumen‐seconds, and luminous flux, measured in lumens.
Radiant intensity I is the radiant flux per unit solid angle emitted by a point source. Solid angle may be pictured as a cone with its vertex at the point source. Solid angle is represented by the symbol Ω. The unit of solid angle is the steradian (sr), which is defined as a solid angle, having its vertex at the center of sphere, that cuts out an area on the surface of the sphere equal to the square of the radius of the sphere. Because the surface area of a sphere of radius r is 4πr2, there are a total of 4π steradians in a sphere. Radiant intensity is measured in watts per steradian. Luminous intensity, the photometric analogue of radiant intensity, is measured in the SI unit candela (cd), which is equal to 1 lm sr−1.
Radiance L is the radiant flux per unit solid angle per unit projected area emitted by an area source. Radiance is measured in watts per steradian per square meter. Luminance, the photometric analogue of radiance, is measured in candelas per square meter. The radiance or luminance of a Lambertian (perfectly diffusing) source is independent of the direction of emission.
Radiant exitance M is the radiant flux per unit area emitted by an area source. It may be noted that radiant exitance is the integral over a hemisphere of the radiance of an area source (9), which for a flat Lambertian source is
(5)
where the solid angle is expressed in terms of an integral over the spherical coordinates θ and φ (the elevation angle and the azimuthal angle, respectively, in radians) and the factor cos θ accounts for the projection of a differential area of the source on any differential element of the hemisphere. The photometric analogue of radiant exitance is the luminous exitance, measured in lumens per square meter. Emittance is an older term for exitance.
The radiometric and photometric terms relating to source output are summarized in Table 1 (part (a)). The radiometric terms and their defining relationships are illustrated in Figure 3.
2.3.2 Measures of Radiation at a Receiving Surface
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 |
| |