JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 59, NUMBER 2 FEBRUARY 1969

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FIG. 1. Iλ is shown as a function of λ for the photoluminescence of HgGa2S4 as reported by. L. Krausbauer, R. Nitsche, and P. Wild, Physica 31, 113 (1965). (Fig. 4). Maxima: 6910 A (1.79 eV) and 7200 A (1.72 eV).

I t is obvious that if an infinitesimal bandwidth dE is kept constant over the spectrum, dv and dσ will also be constant but d\ will vary. Since E, v, and σ differ only by constant factors, we need only consider one of these three variables; we select E. If we choose a bandwidth dE, we define the spectral radiant power by the derivative

lE=dP/dE (the emitted power dP in the photon-energy interval dE). If, on the other hand, we choose a bandwidth d\ we define another quantity of spectral radiant power,

I\=dP/d\ (the emitted power dP in the wavelength interval dλ).

I\ is the quantity which is usually tabulated for blackbody radiation and therefore Iλ is traditionally dominant in the repre­sentation of the emission of light sources. When the spectral dis­tribution of a light source is measured, the calibration of the equipment is usually derived from a blackbody, e.g., via a tung­sten-ribbon lamp or an absorption radiometer.

Methods of Representing Emission, Excitation, and Photoconductivity Spectra

E. EJDER Department of Solid State Physics, Lund Institute oƒ Technology,

Lund, Sweden (Received 4 September 1968)

INDEX HEADINGS: Wavelength; Spectra; Spectroradiometry; Photoconduc­tivity; Sources.

THE spectral distribution of a light source can be graphically represented in different ways. We can choose a number of

quantities as independent variables, e.g., wavelength, quantum energy, or frequency.1-7 When choosing units of radiant power, we also have different possibilities. The aim of this paper is to point out that the way of representing data is of great importance for the physical interpretation of the spectral distribution. When com­paring the power emitted in different parts of the spectrum, it is necessary to measure the power within a stated spectral band be­cause no power can be associated with a discrete wavelength (λ), frequency {v), wavenuraber (σ), or photon energy (E). The band­width should of course be kept constant throughout the spectrum, but the problem is to select the variable in terms of which the bandwidth should be measured. This choice is decisive for the form of the emission curve and the conclusions drawn from it.

Terminology and notation. We have:

Thus:

224 L E T T E R S T O T H E E D I T O R Vol. 59

Two more quantities must be introduced, Jλ = dN /dλ (the number of photons dN emitted per unit time,

in the wavelength interval dλ), and JE=dN /dE (the number of emitted photons dN per unit time

in the photon-energy interval dE). The relations between Iλ, I E , JΛ, and JE can be written in terms of Iλ,

Examples of the consequences of different representations. As an instructive example of the consequences of different choices of representations, it is suitable to consider blackbody radiation. The Planck radiation law. can be expressed in terms of the different variables:

FIG. 2. The curves in Fig. 1 have been converted to ∫E as a function of E. Maxima: 1.71 eV (7260 A) and 1.67 eV (7410 A). Observe that the relative positions of the peaks have changed because short wavelength corresponds to high photon energy.

These expressions give maxima as follows:

The values of \T are taken from Boerdijki (1953). 3000 K has been chosen here to make the results applicable to a tungsten lamp.

Examples for an emission spectrum are shown in Figs. 1 and 2. In Fig. 1, the relative power per unit wavelength interval is plotted as a function of wavelength. These curves have been converted in Fig. 2 to the relative number of photons per unit time per unit photon-energy interval and plotted on a photon-energy scale. The differences are not negligible and the conversion must influence the conclusions drawn from the spectral distribution.

Choice of representation for correct physical interpretation. When spectral distributions are to be shown in a diagram, there are many possible combinations of measures of radiant flux and spec­trum variables. However, the choice is limited by the requirement that we want a representation in which the power radiated within a certain spectral band is proportional to the area under the curve within the spectral band. If the number of photons is considered, for example, this means that the number of photons per unit time interval should be proportional to the area under the curve. A correct-area representation of this kind is obtained, e.g., if I\ is plotted on a λ scale; then

interval. In a correct emission spectrum we have the relative number of photons per unit time per unit photon-energy interval (JE) plotted on a photon-energy (E) scale. Thus, we have a representation in which the area under the curve within a certain photon-energy interval is proportional to the number of photons emitted per unit time within the band; conclusions from the spectrum can be directly represented in an energy-level diagram. After that we can, of course, draw a nonlinear wavelength scale, just for orientation, in the same diagram. Often a better idea of an emission is conveyed if it is also expressed in terms of wavelength.

So far, only emission spectra have been discussed. Correspond­ing situations can arise in other cases. When an excitation spec­trum is recorded, a lamp with some known spectral distribution is used and so appropriate corrections must be made to the measured excitation spectrum. The correction should be made to constant number of photons per unit time per unit photon-energy interval in the excitation light, over the spectral region in question. The excitation spectrum can then be explained by an energy-level diagram.

The same situation arises in photoconductivity measurements. 1 A. H. Boerdijlc, Philips Research Reports 8, 291 (1953). 2 R. N. Bracewell, Nature 174, 563 (1954). 3 M. Eppley and A. R. ICaroli, J. Opt. Soc. Am. 43, 957 (1953). 4 L. Foitzik, Experim. Techn. d. Phys. 1, 209 (1953). 5 M. M. Gurevich, Usp. Fiz. Nauk 78, 463 (1962) [Sov. Phys.—Usp. 5.

908 (1963)]. 6 W. D. Ross. J. Opt. Soc. Am. 44, 770 (1954). 7 I. Wundermann, Appl. Opt. 7, 25 (1968).

The same situation arises if IE is plotted on an E scale. However, if Iλ is plotted on an E scale, equal areas under the curve will correspond to different radiated powers in different parts of the spectrum,

Similar relations hold for Jλ and JE. In studies of illumination, interest is usually in the distribution

of power through the spectrum. But in studies of solid-state physics, the reason for drawing an emission spectrum is usually that we want to know the positions of energy levels or bands. An energy-level diagram is drawn in a linear E scale (or v or σ scale), and hence a linear E scale (υ,σ) must also be used for the emission spectrum. The interesting quantity is not the power radiated but the number of photons emitted per unit time per unit energy