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Radiometry

Radiometry is the science of detection and measurement of electromagnetic radiation. This is performed with the help of a radiometer. Central component of a radiometer is a photodetector. The signal of such devices is a function of the intensity of the incident radiation. In most cases the distribution in space or the received/emitted energy of the radiant energy is measured. In photochemistry, radiometry is used to measure the radiation, which is available for a reaction, in a photoreactor. This in turn is necessary for actinometry and the determination of the quantum yield of a photochemical reaction.

The quantity giving information of the energy of a portion of radiation per time is the radiant power P:

 radiometryeq1

For a radiant source it is the amount of energy Q per time t, which is emitted in every direction as electromagnetic radiation. This quantity wavelength dependent. Typical emission spectra of light sources are shown in section ??. According to the IUPAC recommendations[1], The wavelength dependency of a quantity is indicated by a subscripted λ. Considering the entire wavelength region requires integration within the respective wavelengths:

radiometryeq2

From the spectral radiant power Pλ it is also possible to determine the number of emitted photons. The energy by the PLANCK-EINSTEIN relation. With this, the spectral amount of photons emitted per period qn,p,λ can be calculated from: radiometryeq3

As shown in the following Equation, the total photon flux results from integration:

 radiometryeq4

It must be taken into account, that the number of photons per radiant energy is decreasing with lower wavelengths. Especially when considering photochemical reactions, where the number of photons often is relevant for the economy of the process. Hence, photon based quantities should be used instead of energy based quantities when possible and meaningful. Figure 1 shows the difference between energy and amount of photons as a function of the wavelength exemplary for a theoretical monochromatic light source with Pλ = 1W. Table 1 gives an overview of the most common photon based and energy based radiometric units.

 radiometry1

Figure 1: Photon flux of theoretical monochromatic light sources with a radiant power Pλ = 1W. Additionally the relative difference to the photon flux at 200nm is given.

Table 1: Energy and photon based radiometric units in comparison to each other.

 radiometryT1

 

The amount of photons irradiated to a surface can be defined as photon fluence rate En,p,o:

                                                                                               radiometryeq5

For point-shaped light sources it might be convenient to use the solid angle as reference quantity. On a sphere with 1m radius, a steradian covers a surface of 1m2 (see Figure 0.2). The solid angle of the entire sphere is 4π. Hence, the emitted radiant power (or photon flux) can be given per A unit solid angle Ω in a given direction:

radiometryeq6

                                                                                                 

radiometry2

Figure 2: Description of a steradian and the solid angle .

                                                                      

Although ideal point-shaped light sources do not exist, this approximation is correct, if the distance of the receiver towards the arc is 20 times greater than the arc. The use of a quantitiy based on the solid angle can be useful, since it does not change with the distance to the light source, only by the individually solid angle. Such a description can be beneficial for light sources which do not have an isotropic light emission.

 

  1. BRASLAVSKY, S. E.; BRAUN, A. M.; CASSANO, A. E.; EMELINE, A. V.; LITTER, M. I.; PALMISANO, L.; PARMON, V. N.; SERPONE, N.: Glossary of terms used in photocatalysis and radiation catalysis (IUPAC Recommendations 2011), 2011, 83, DOI:10.1351/PAC-REC-09-09-36.

 

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