How can full-spectrum light sources be compared?

To develop a method of comparing full-spectrum light sources, full-spectrum lighting must first be defined. Full-spectrum light sources are often claimed to mimic daylight, so it makes sense that full-spectrum light sources should be defined in terms of daylight. The problem with this approach it that there is no single spectral power distribution (SPD) associated with natural daylight, since the spectrum of daylight varies constantly. In Figure 4, note that the relative spectral radiant power distributions derived have a common value of 100 at the wavelength of 560 nm (CIE, 1964). Moreover, a daylight SPD is not particularly smooth and uniform depending upon atmospheric composition, particularly the amount of water vapor.

Figure 4. Relative radiant power distribution of 10 different phases of daylight.

The infinite variety and variance of natural daylight spectra makes it impossible to evaluate quantitatively an electric light source in terms of its ability to emulate natural daylight. Choosing a particular reference spectrum for daylight for comparison would not only be completely arbitrary, it would also undermine a basic marketing argument for manufacturers of full-spectrum light sources. Since daylight is a naturally varying light source, a light source that emulates one particular daylight spectrum is, by definition, unnatural. Nevertheless, all electric full-spectrum light sources have fixed SPDs, so it would be useful to define a reference light source to which all can be compared.

In selecting an ideal light source as a reference, an equal energy spectrum becomes the logical choice for two main reasons. First, the SPD of an equal energy spectrum is, indeed, "full" across the entire visible spectrum and, second, an equal energy spectrum is neutral with regard to any prejudicial associations, positive or negative, with "natural" light sources. Moreover, there are several electric and natural light sources that have SPDs approximating an equal energy spectrum, so choosing an equal energy spectrum as the reference full-spectrum source is not entirely abstract or irrelevant.

Formally then, the proposed reference full-spectrum light source is an ideal light source with equal energy across the visible region of the spectrum, from 380 to 730 nm, inclusive. A new metric, called full-spectrum index (FSI), based on this proposed reference, can be calculated from a light source's SPD to determine how much that SPD differs from an equal energy spectrum. FSI is based on the sums of the squared deviations (SOS) between the cumulative SPDs of the test light source and the reference equal energy source. So that spikes or dips in the SPD are weighted equally no matter where along the spectrum they occur, the SOS is calculated 351 times (one for each 1 nm increment between 380 and 730, inclusive) and the values are averaged. For each of these calculations, the starting point is incremented by 1 nm and when the end of the spectrum range is reached, it is wrapped back around to the beginning (i.e., 380 follows 730). As noted in personal communication with the authors by Dr. Duane Miller of APL Engineered Materials, Inc., this averaging procedure ensures that FSI values are independent of the starting point for the calculation. The lower the FSI value the more "full" the spectrum, with zero being an equal energy spectrum. Table 1 includes typical FSI ranges for several types of commercially available light sources.

The lower limit of the FSI reference spectrum range (380 nm) was chosen because it is the shortest wavelength tabulated in the abridged International Commission on Illumination (CIE) color matching functions, and because invisible UV radiation should be excluded as part of the definition of full-spectrum light sources (see "Is ultraviolet radiation production important?"). The upper limit (730 nm) and the lower limit (380 nm) both have the same x-bar value of 0.0014. The upper limit, 730 nm, minimizes the influence of invisible infrared radiation on the FSI calculations while still including the important contributions of long-wavelength radiation on color perception. As an important note, choosing a slightly different spectral range for the reference full-spectrum light source, shorter or longer, does not significantly alter the relative FSI values for the commercially available light sources shown in Table 1. Figure 5 presents the spectra of several popular light sources together with their cumulative SPDs. These figures illustrate the concept behind FSI, namely, the more the cumulative SPD resembles the flat slope of a cumulative equal energy spectrum, the closer the light source is to having a "full" spectrum.

Based on an arbitrary cutoff of FSI = 2.0, the following light sources can be categorized as full-spectrum: natural daylight from 4000K to 11000K, xenon lamps, some fluorescent T12 lamps marketed as full-spectrum, some T12 fluorescent lamps not marketed as full-spectrum, and some ceramic metal halide lamps. At the time this report was written, the following T12 lamps marketed as full-spectrum met the FSI = 2.0 cutoff: Duro-Test Daylight 65, Duro-Test Vita-Lite 5500K, Lumiram Lumichrome 1XC, and Verilux VLX fluorescent lamps.

Figure 5. Relative cumulative SPDs for two phases of daylight and several electric light sources.
The cumulative SPD for an equal energy spectrum is shown (blue) with the cumulative SPD of the example light source (green). The FSI values in these figures are for specific lamp SPDs and are not necessarily the same as the representative values in Table 1.