Technical Reference

FIGURE 7.15 - A portion of the ASTM E-490-00 Solar Spectrum, from wavelength 0 to 4 μm.

Table

To make a Table Spectral Type surface property, you add wavelengths to the table using the Add button in the Data Points section of the Surface Source Property Editor. As you add new wavelengths, new rows will appear in the table, so that you can enter a different emissivity value for each wavelength. When the property is applied to a Surface Source using the Apply Properties dialog box, wavelengths entered there are used to linearly interpolate between the wavelengths in the property. Applied wavelengths that are outside the wavelengths in the property will have emissivity equal to zero.

Angular Types

Lambertian

A Lambertian Angular Type surface source property has the emissivity profile

E(θ) = cosθ

where θ is the angle between the surface normal and the emission direction. The only entries required are the half angle and emission. The Lambertian pattern is truncated by a cone with the half angle you enter. The Lambertian pattern is important because an ideal blackbody source emits in a Lambertian pattern, and many real incandescent, or thermal, surface sources emit in a very nearly Lambertian pattern.

Surface Source Properties

Uniform

A Uniform Angular Type surface source property does not vary with angle. The only entries required are the half angle and emission value. The pattern is truncated by a cone with the half angle you enter.

Gaussian

To make a Gaussian Angular Type surface property, you specify x and y 1/e2 halfwidth angles, in degrees. The spectral emissivity has the shape

where θx and θy are angles from the surface normal in the local x-z and y-z

planes. When you apply a Gaussian Angle Surface Source Property to a surface source, you must specify an Up Vector to orient the emission pattern. The Up Vector specifies the local y axis, and the local z axis is along the surface normal. The local x axis completes a right-handed coordinate system. An example Gaussian Angle distribution with half-width = 30 (along one axis) is shown in Figure 7.16.

FIGURE 7.16 - Gaussian Angular Type with 1/e2 angle = 30 degrees. The red lines show the half-width angle with emissivity value of 1/e2 = 0.1353.

Solar

The Solar Angle type models the variation of the sun’s brightness with angle. The “disk” of the sun is dimmer at the edge (limb darkening). Tha data for this angular dependence is taken from Astrophysical Quantities, by C.W. Allen, The Athone Press, University of London, Second Edition (1955). The limb darkening depends on wavelength as well.