Figure 1. Radiance (R) of source is the Power (P) emitted from the source emitting Area (A) and propagated in the Solid Angle (Ω).
Figure 2. Steradian [sr] is a unit for measuring solid angles (Ω) defined by the solid angle that projects on the surface of a sphere, with a radius of r, having an area of A = r2 (Ω = A/r2 = r2/r2 = 1 [sr]).
Irradiance is the radiometry term for the power per unit area of electromagnetic radiation incident on a surface. The SI unit for irradiance is watts per square meter [W/m2], or milliwatts per square millimeter [mW/mm2]. (Irradiance is sometimes called intensity, but this usage leads to confusion with another standard, but infrequently used, radiometry unit —Radiant Intensity — which is measured in watts per steradian.)
If a point radiation source emits radiation uniformly in all directions and there is no absorption, then the irradiance drops off in proportion to the distance squared from the source, since the total power is constant and it is spread over an area that increases with the distance squared from the radiation source. To compare the irradiance of different sources, one must take into account the distance from the source. A 50cm distance is often used for such measurements.
Irradiance is a useful measure for applications where power must be delivered to large areas. For example, illuminating a classroom or a football field is primarily a question of delivering a certain number of watts per square meter. This can be achieved by using a single high power source. However, since irradiance does not depend on solid angle, multiple sources can be combined, illuminating the walls or the field from different angles.
The irradiance of a source is not the most useful measure when designing an efficient optical coupling system that collects radiation from a source, and then delivers the radiation into an optical instrument. Such optical instruments will have a limited entrance aperture and a limited acceptance solid angle. In such cases it is the radiance of the source (its ‘brightness’) that is most useful.
Radiant flux is radiant energy per unit time, also called radiant power [W, mW or μW]. Radiant flux is often used to describe the radiation power output of a radiation source, or the radiation power received by an optical instrument. Examples of radiant flux are: the radiation power passing through a pinhole; the radiation power emerging from the optical fiber of a fiber-coupled laser; the radiation power received by a power detector.
The units of Radiant Flux do not include area or solid angle, and are therefore not helpful in determining whether a particular light source with a particular radiant flux will be useful in delivering its power to an optical instrument. In our earlier example, the 60W fluorescent tube emits a greater radiant flux (power) than the 35W Xe arc-lamp. But, with an appropriate focusing optic, the arc lamp will deliver a higher radiant flux to the 200μm diameter optical fiber. A Laser-Driven Light Source, such as Energetiq’s EQ-99, may have a lower radiant flux emitted than the 35W arc-lamp, but its higher radiance allows it to deliver even higher radiant flux to the 200μm diameter optical fiber than the 35W arc-lamp.
The three terms discussed above are quantities used to characterize radiation within a certain wavelength band, (UV, VIS and/or IR). It is also common to consider those values for unit wavelength (per nm) in the spectrum. For radiation power per unit of wavelength, spectral radiant flux is used with SI units of watts per meter [W/m], or more commonly milliwatts per nanometer [mW/nm]. For radiation incident on a surface, the term spectral irradiance is used, and has the SI unit of [W/m3], or more commonly units of [mW/mm2-nm]. For radiation power within in a unit solid angle from a unit emitting area and unit wavelength, the term is spectral radiance, most commonly with units of [mW/mm2-nm-sr].
Spectral radiance is a key measure when selecting a source for an application. In general, most radiation sources exhibit variations in spectral radiance across their spectrum of emission. In Figure 3, the spectral radiance is shown for a 30W deuterium lamp (D2), a 75W high-brightness Xe arc-lamp, and for two versions of Energetiq’s Laser-Driven Light Source, the EQ-99 and the EQ-1500.
Figure 3: Spectral radiance of EQ-99X LDLS, EQ-77 LDLS, EQ-400, LDLS, 75W short-arc Xe Lamp,
Tungsten Lamp and D2 lamp.
For our earlier example of illuminating a 200μm optical fiber, let us assume that we wish to compare the four light sources in Figure 3 at delivering 200nm wavelength radiation into the fiber. Since the key parameter is the spectral radiance of the sources at 200nm, we can see from Figure 3 that the Xe lamp’s spectral radiance is about one order of magnitude higher (‘brighter’) than the D2 lamp and the LDLS sources are a further order of magnitude higher than the Xe lamp. With the same focusing optic used to couple the light from each source into the 200μm fiber, the radiant flux delivered into the fiber would similarly vary by the same orders of magnitude.
In the design of optical instruments, scientists and engineers choosing light sources will be exposed to a variety of source specifications and radiometric terms. It is important to understand the nature of the specifications and to couch them in radiometric terms that will enable appropriate design decisions. In general, for typical optical instrument applications, such as spectroscopy and imaging, it is the radiance and spectral radiance of the light source that most needs to be understood. For an instrument with limiting apertures and solid angles, it is the radiance of the source that determines how much radiation passes through the instrument. By carefully matching the instrument with a source of appropriate radiance, an optimum system can be designed.