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How do I plot Radiance(x,z) as a function of X-Z polar angle from 0:2*Pi?

May 12, 2012 at 9:57 PM

As mentioned in the previous discussion, I would like to run a simulation in the x-z plane (all "Y" information in a single bin), where the goal is to capture 2D images of radiance pointing in different polar angles in the X-Z plane. I'm not sure that we have this angle directly available in our existing detectors.

In these results, you can see RadianceOfXAndYAndZAndThetaAndPhi, where each image represents a different theta, or polar angle off of the Uz=1 axis. The source is a collimated point source pointing downward, and you can see the forward-directed photons in the top left image. Theta goes (by definition) from 0 (Uz=1) to Pi (Uz=-1), and data is collected in a single phi bin.

Here's my challenge: I now want to tilt the direction of the source toward the positive x-direction. However, since theta is only defined to go from 0:Pi, I will not be able to capture the "backward" (negative-x-pointing) photons from Pi:2*Pi.

Is the solution (using existing detectors) to break up Phi into four quadrants, such that the negative-x-pointing" photons are in either -Pi<phi<-Pi/2 or Pi/2<phi<Pi and the positive-x-pointing ones are in -Pi/2<phi<0 and 0<phi<Pi/2? Presumably this would let me separate out angles the XZ plane that were negative vs positive x at a given theta.

May 12, 2012 at 10:47 PM

I'm not sure I completely understand your question. If theta spans [0,pi] and phi spans[-pi,pi], then all angles are covered within the unit sphere.  So any Direction Cosine that describes the angular orientation of the photon will be capture in some bin, none will be lost.

May 12, 2012 at 11:47 PM
Edited May 12, 2012 at 11:48 PM

I didn't mean to imply I was losing photons. When I said:

"I will not be able to capture the "backward" (negative-x-pointing) photons from Pi:2*Pi"

I should have said:

"I will not be able to discriminate the "backward" (negative-x-pointing) photons from Pi:2*Pi from the "forward" ones"

In any case, consider a 2D geometry in X-Z. Say we name the polar angle in that plane "alpha". I want to tally Radiance(X,Z,Alpha), where Alpha goes from 0:2*Pi.

I did what I proposed above, and the results are making intuitive sense, but I'd like to gain some more confidence in this mathematically.