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Grid Raytrace - calculation of actual Beam Width

Question

I have set up a Grid Raytrace with a rectangular grid boundary, with half-height x and y set = 10. I also selected a Rectangular Grid Pattern with 10 x-points and 10 y-points. I expected to get a 20x20 beam, but the Irradiance Map shows the beam to be 18x18. What is wrong?

Synopsis

Grid Raytrace - calculation of actual Beam Width

Symptoms

To determine the starting points of the rays for a Grid Raytrace, TracePro divides the rectangular grid boundary into an array of cells. In this case, with the X Half-Height of 10, and Number of X-Points =10, each cell has a width of 2. So the starting x-positions of the rays are as follows - X = -9,-7,-5,-3,-1,1,3,5,7,9. The rays emitted from X = -9 and +9 result in a beam width of 18.

Solution

A couple of useful equations can help determine the proper Grid Raytrace entries to achieve the desired Beam Width: B = actual Beam Width H = Half-Width or Half-Height selected for the Grid Raytrace boundary P = number of Points selected for the Grid Pattern To calculate the actual Beam Width resulting from the settings in the Grid Raytrace dialog: B = 2H-(2H/P) To calculate the necessary Half-Width entry required to produce the desired Beam Width: H = BP/[2(P-1)]