The Illuminated Surface is used to simulate the emission of rays from a surface, under the assumption that the emitted rays are specularly reflected from an external radiation source. It is assumed that the entire selected surface has direct line of sight to the external radiation source; that is, shadowing due to other geometric entities is not taken into account.

If the Incident ray direction vector is a User defined direction or based on Solar position, the incident rays are treated as plane waves arriving from a distant source, and the intensity of the incident rays Ii is specified directly.

If the Incident ray direction vector is computed using a User defined point source, the principal radii of curvature of the incident wavefront are set equal to the distance from the source point to the initial ray position,

where q is the initial ray position, rsrc is the position vector of the point source, and r1 and r2 are the principal radii of curvature of the incident wavefront. In 2D, only one principal radius of curvature is defined. The incident ray intensity is derived from the total source power Psrc,

The principal radii of curvature of the reflected rays are then computed using the approach outlined in the Principal Radii of Curvature section. Because no thin films are present on the surface, the intensity of the reflected ray is equal to the intensity of the incident ray. The effect of specular reflection is to negate the third and fourth Stokes parameters of the ray.

To release rays with a perturbation from the initial directions because of the finite size of the radiation source, select Create light cones at release points or Sample from conical distribution option from the Corrections for finite source diameter in the settings window for the Illuminated Surface and Solar Radiation features.

Selecting Create light cones at release points causes a cone of rays to be released at each release point. Selecting Sample from conical distribution causes only a single ray to be released at each point, but each ray’s initial direction is sampled form a cone-shaped probability distribution function. The maximum angle between any incident ray and the specified incident ray direction is the user-defined maximum disk angle ψm (SI unit: rad).

The options described above are also available in the settings window for the Solar Radiation feature, in which they have the same effects on the initial direction of the solar radiation.

The default value of the maximum disk angle, or the maximum angle between the direction of the incident rays and the specified incident ray direction vector, is ψm = 4.65 mrad based on the following expressions (see for example Ref. 22):

When the finite size of the sun is taken into account, radiation from the center of the solar disk tends to be greater in intensity than radiation from the edges of the disk, a phenomenon known as limb darkening. Given the intensity I(0) of radiation along a line intersecting the center of the sun, the incident solar radiation from any other point on the sun is given by the expression

where fL is the limb darkening function and ψs is the angle between a line of sight to the center of the sun and a line from the center of the sun to another visible point on its surface. If Empirical power law is selected from the Limb darkening model list in the settings window for the Illuminated Surface or Solar Radiation feature, the solar radiation is assumed to follow a power law distribution using

The exponent α can vary from 0, for which all solar radiation is of uniform intensity, to 1, at which the intensity of solar radiation falls off linearly as a function of radial position on the visible solar disk. Based on Ref. 22 the exponent α is given as a function of the free-space wavelength λ0:

If Linear is selected from the Limb darkening model list, the distribution of solar intensity is obtained using

If User defined is selected from the Limb darkening model list, you need to define limb darkening function fL. It is by default 1. The None option in the Limb darkening model indicates a uniform intensity distribution where fL = 1.

It is also possible to include the effect of surface roughness when computing the incident ray direction vector at illuminated surfaces by selecting the Include surface roughness checkbox. The value of the Surface slope error σ is used as the standard deviation in a Rayleigh distribution of perturbation angles about the unperturbed ray direction vector, from which a user-defined number of rays are sampled. For more details see Surface Slope Error.