Spectral radiation density

As a function of frequency, the spectral radiation density is given by... 

Cu, oo describes the influence of the radiation source, (dfJy/dl) is the spectral radiation density for the background intensity, B0 is the radiant density for an analytical line at the concentration c = 1 and A7L is the physical width of the analysis line. The second term (Ai) describes the influence of the spectral apparatus. 

The integral of the temperature gradient of the spectral power density from wavelength Xl to X2, is readily calculable using the Planck radiation law (5). Constant emissivity is assumed for equation 3. 

This is Planck s famous radiation law, which predicts a spectral energy density, p , of the thermal radiation that is fully consistent with the experiments. Figure 2.1 shows the spectral distribution of the energy density p for two different temperatures. As deduced from Equation (2.2), the thermal radiation (also called blackbody radiation) from different bodies at a given temperature shows the same spectral shape. In expression (2.2), represents the energy per unit time per unit area per frequency interval emitted from a blackbody at temperature T. Upon integration over all frequencies, the total energy flux (in units of W m ) - that is, Atot = /o°° Pv Av - yields... 

In dealing with problems of solar radiation, as opposed to blackbody radiation, the effect of the solid angle in which the radiation is confined has been examined (2-4) by considering the volume density of photons to be reduced. Landsberg(6) considers dilute radiation in the sense that the spectral distribution is retained but the radiation density is reduced. This leads to defining the temperature of a spectral component as... 

The radiation of the primary source (a) is lead through the absorption volume (f) and subsequently into the monochromator (h). As a rule the radiation densities are measured with a photomultiplier (i) and the measured values are processed electronically. Usually a Czerny-Turner or an Ebert monochromator with a low focal length (0.3-0.4 m) and a moderate spectral bandpass (normally not below 0.1 nm) is used. 

On the other hand, the work done on the oscillator per second by a radiation field with the spectral energy density is... 

In equation 6.23, s is measured along a chosen direction for photon transport in space (H). The spectral specific intensity must not be confused with radiation density fluxes. They are equal only for unidirectional irradiation, a case very distant from the general one. Radiation may be arriving at one point inside a photochemical reactor from all directions in space. For a photochemical reaction to occur, this radiation must be absorbed by an elementary reacting volume (a material point in space) thus, pencils of radiation coming from all directions must cross the whole elementary surface that bounds such an element of volume. Consequently, the important photochemical property is the spectral incident radiation (or spectral spherical irradiance) given by... 

Contrary to radiation sources with broad emission continua used in conventional spectroscopy, tunable lasers offer radiation sources in the spectral range from the UV to the IR with extremely narrow bandwidths and with spectral power densities that may exceed those of incoherent light sources by many orders of magnitude (Vol. 1, Sects. 5.7, 5.8). 

The average spectral energy density in a blackbody cavity radiator, ct) is given in eqn [1],... 

This chapter deals with basic considerations about absorption and emission of electromagnetic waves interacting with matter. Especially emphasized are those aspects that are important for the spectroscopy of gaseous media. The discussion starts with thermal radiation fields and the concept of cavity modes in order to elucidate differences and connections between spontaneous and induced emission and absorption. This leads to the definition of the Einstein coefficients and their mutual relations. The next section explains some definitions used in photometry such as radiation power, intensity, and spectral power density. 

In a stationary field the total absorption rate NiBnpi ), which gives the number of photons absorbed per unit volume per second, has to equal the total emission rate N2B2ip(v) -j- N2A21 (otherwise the spectral energy density p(v) of the radiation field would change). This gives (Fig. 2.4)... 

In Sect. 2.2 we derived Planck s law (2.13) for the spectral energy density p v) of the thermal radiation field. Since both (2.13,2.20) must be valid for an arbitrary temperature T and all frequencies v, comparison of the constant coefficients yields the relations... 

For a spherical isotropic radiation source of radius R (e.g., a star) with a spectral energy density pv, the spectral radiance Ly(v) is independent of 9 and can be expressed by... 

The spectral distribution of the radiant flux from a source is called its emission spectrum. The thermal radiation discussed in Sect. 2.2 has a continuous spectral distribution described by its spectral energy density (2.13). Discrete emission spectra, where the radiant flux has distinct maxima at certain frequencies Vik, are generated by transitions of atoms or molecules between two bound states, a higher energy state Ek and a lower state Ei, with the relation... 

Assume the isotropic emission of a pulsed flashlamp with spectral bandwidth Ak = 100 nm around k = 400 nm amounts to 100-W peak power out of a volume of 1 cm. Calculate the spectral power density p(v) and the spectral intensity I(v) through a spherical surface 2 cm away from the center of the emitting sphere. How many photons per mode are contained in the radiation field ... 

A sodium atom is placed in a cavity with walls at the temperature T, producing a thermal radiation field with spectral energy density p v). At what temperature T are the spontaneous and induced transition probabilities equal... 

According to (2.15) and (3.69), the power absorbed per unit volume on the transition 1) 2) by atoms with the population densities A i, N2 in a radiation field with a broad spectral profile and spectral energy density p is... 

The function of the optical resonator is the selective feedback of radiation emitted from the excited molecules of the active medium. Above a certain pump threshold this feedback converts the laser amplifier into a laser oscillator. When the resonator is able to store the EM energy of induced emission within a few resonator modes, the spectral energy density p(v) may become very large. This enhances the induced emission into these modes since, according to (2.22), the induced emission rate already exceeds the spontaneous rate for p(v) > hv. In Sect. 5.1.3 we shall see that this concentration of induced emission into a small number of modes can be achieved with open resonators, which act as spatially selective and frequency-selective optical filters. 

In Sect. 2.1 it was shown that in a closed cavity a radiation field exists with a spectral energy density p(v) that is determined by the temperature T of the cavity walls and by the eigenfrequencies of the cavity modes. In the optical... 

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