The solar spectrum

White light usually has a broad spectrum extending over the entire visible range. An instructive model for white light is sunlight. The sun’s optical spectrum is shown in Fig. 18.1, including the spectrum at sea level with the sun at zenith, incident above the earth’s atmosphere, and at sunset and sunrise (Jackson, 1975). The spectrum of sunlight extends over the entire visible region. However, the sun’s spectrum depends on the time of day, season, altitude, weather, and other factors.

Exact replication of the solar spectrum for white-light illumination sources would not yield an efficient source due to the large infrared (IR) and ultraviolet (UV) components of the solar spectrum. Thus, “mother nature” does not serve as a good example for an efficient white source. Even if the IR and UV components of the spectrum were to be eliminated, the solar spectrum still would not be optimum, due to the high intensity at the visible-IR and visible-UV boundaries.


18.1 The planckian spectrum It is desirable to define an independent standard for white light. The planckian black-body radiation spectrum is used as one such standard. The black-body spectrum is characterized by only one parameter, the temperature of the body. The black-body spectrum was first derived by Max Planck (1900) and is given by

t (A) 2hc 2

.i w -



f hc 1 1 ]


v A kT J

The planckian spectrum is shown for different black-body temperatures in Fig. 18.2. The maximum intensity of radiation emanating from a black body of temperature T occurs at a specific wavelength which is given by Wien’s law



2880 K T

At “low” black-body temperatures, e. g. 3 000 K, the radiation occurs mostly in the infrared. As the temperature increases, the maximum of the radiation shifts into the visible wavelength range.

The location of the black-body radiation in the (x, y) chromaticity diagram (called planckian locus) is shown in Fig. 18.3. As the temperature of the black body increases, the chromaticity location moves from the red wavelength range towards the center of the diagram. Typical black - body temperatures in the white region of the chromaticity diagram range between 2 500 and 10 000 K. Also shown in Fig. 18.3 are the locations of several illuminants standardized by the CIE. These standard illuminants include Illuminants A, B, C, D65, and E. The planckian locus and the locations of the black-body temperatures in the (u', v’) uniform chromaticity diagram are shown in Fig. 18.4. The (x, y) and in (u' , v' ) chromaticity coordinates of the planckian radiator are tabulated in Appendix 18.1.

In both the (x, y) and the (u, v ) chromaticity diagrams, the planckian locus starts out in the red, then moves through the orange and yellow, to finally the white region. This sequence of colors is reminiscent of the colors of a real object (e. g. a piece of metal) heated to high

Fig. 18.4. CIE 1976 (u v') uniform chromaticity diagram calculated using the CIE 1931 2° standard observer and planckian lo­cus.

«'-chromaticity coordinate

temperatures, indicating that real objects closely follow the chromaticity of Planck’s idealized black bodies.

Комментарии закрыты.