Ray Power Assignment

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At Ray Creation

FRED offers a great deal of power and flexibility in the definition of sources; and with that flexibility comes the possibility of ambiguity and misunderstanding. Source definition confusion can be avoided with an understanding of the ray generation rules. The user can define the source in any order but when the user asks FRED to Create Rays, the ray generation recipe ALWAYS follows these five steps in strict order for each source.

1.		The requested number rays are positioned with each ray having unity power.
2.		The ray directions are set.
3.		Each ray’s flux is scaled according to the position apodization.
4.		Each ray’s flux is scaled according to the direction apodization.
5.		All of the rays are scaled to meet the total integrated power.

This last step can cause some confusion. For example, say that a plane wave is defined with an angle f to the normal of the surface containing the grid of rays. Then if the user selects a Lambertian direction apodization, the rays would be scaled by cos(f). However, the last step would rescale all the rays back to the total power requested by the user because the total power specification is the total integrated power of the rays and not the total power of the rays as directed along the grid surface normal.

During the Raytrace

During the raytracing process, rays encounter interfaces which have reflection, transmission and scatter properties and are split. FRED follows a specific recipe for allocating flux to the various ray components. Consider Figure (A) below in which a ray (green) is incident upon an interface which has both specular and scatter property assignments. Let F_inc be the flux of this incident ray. The specular properties of this interface are controlled by its coating assignment while its scatter properties are dictated by the particular scatter model(s) and at least one importance direction assignment. Assuming an Allow All Raytrace Control is utilized with absorbed rays, FRED generates a reflected ray shown here in red, a transmitted ray in blue, backscattered rays in gold and absorbed rays at the surface intersection point.

For the following discussion, we will assume that the surface is scattering into the full 2p steradian hemisphere so that the power contained in the scattered rays is equal to the total integrated scatter of all scatter models on the surface. The first step in flux allocation involves subtracting the scatter model TIS from the incident flux. The total flux assigned to the backscattered rays is then:

F_backscat = TIS * F_inc,

leaving the remainder to be allocated to the reflected, transmitted and absorbed rays. Thus, the reflected ray flux is:

F_refl = ( 1 - TIS ) * R * F_inc,

the transmitted ray flux is:

F_trans = ( 1-TIS ) * T * F_inc,

and the absorbed ray flux is:

F_abs = F_inc - F_backscat - F_refl - F_trans.

In an extension of this illustration, consider Figure (B) where both forward and backward scatter are involved. In this case, the TIS for both the backward scatter and forward scatter must be removed from the specular components. Thus, the backward scatter flux is:

F_backscat = TIS_backscat * F_inc,

and the forward scattered flux is:

F_frwdscat = TIS_fwdscat * F_inc.

The reflected ray then has flux:

F_refl = ( 1- TIS_backscat- TIS_fwdscat) * R * F_inc,

the transmitted ray has flux:

F_trans = ( 1 - TIS_backscat- TIS_fwdscat) * T * F_inc,

and the absorbed ray has flux:

F_abs = F_inc - F_backscat - F_fwdscat - F_refl - F_trans.

The underlying assumption is that the specular quantities are treated separately in terms of the coating specifications.

Scattering from Diffraction Gratings

The same basic recipe as above is followed when tracing diffraction gratings, in that the scattered rays are generated first, and specular rays afterwards. However it should be noted that in the case of gratings the TIS of the scatter function is distributed between the grating orders and weighted by the order efficiency.

E.g. for a reflective scattering grating with -1R, 0R and +1R orders, grating efficiencies of 2%, 10% and 2% respectively, and a scatter function with a TIS = 100%, then the full 100% of the incident power will be scattered around the three orders (i.e. around 3 specular directions), where the central 0th order will have 5x the power of the +/-1 outer orders.