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Odd behavior at short separations in 1-D

Jun 13, 2012 at 6:20 PM

Hi everyone,

  I have been messing around a little with 1-D Monte Carlo Distributions, and I noticed some odd things at detector locations very near the source (<0.5mm).  I find that when plotting R of rho in 2-D, and normalizing to detector area, that the reflectance decreases monotonically away from the origin as expected.  However, when I just look at the X location of the photon in 1-D, I find that this is the same as the un-normalized 2-D reflectance, and that it actually is lower for locations from about 0-0.5mm, then peaks around 0.5-1mm, and decreases from there.  I am linking to plots which show this.  This behavior is making some of my results come out quite odd.  Have any of you noticed anything like this?

http://i.imgur.com/7T9FU.png

Tyler

Developer
Jun 14, 2012 at 12:10 AM

Hi Tyler,

If I understand your un-normalized results correctly, it could be the "halo" that Arnold Kim described in his paper "Backscattering of beams by forward-peaked scattering media", Optics Letters 29(1), p. 74-6, 2004.  Does the peak move to the right when the anisotropy coefficient g is increased?

Carole

Coordinator
Jun 14, 2012 at 12:22 AM

Hi Tyler,

Thanks for posting the question.

Let's clarify "1D" distributions first. I assume you mean to capture "the reflectance, R(x), resulting from a line illumination, 1(y)*delta(x-0)". Photons would be randomized in their input position along the x=0 axis, and reflectance collected in rectangular x-bins extending from y_min to y_max. Normalizing by the x bin lengths would get you R(x).

With real-world Monte Carlo and finite y-extent of the medium, it's often convenient to alternatively simulate this same reflectance by use of a point illumination, delta(y-0)*delta(x-0), but collecting this data in the same fashion as above. This works fine assuming your medium is homogeneous along the y-direction, since the exiting y-position of the photons does not impact the tally of the "1D" R(x) result.

Now, what I understand your question/concern is about this R(x) appearing the same as and "un-normalized" R(rho), where each un-normalized bin was COUNTS_bin * [ Pi*(r2^2-r1^2) ]. I would not expect this to be the same as R(x), - R(x) should look like un-normalized R(x) differing by a constant factor. If you're using a point illumination, rho takes into account both x- and y-position (sqrt(x*x+y*y)), whereas a true R(x) would only take into account x, so rho on average will always be GREATER than x, and possibly be the reason your estimate is not monotonically decreasing with x. Does this jive?

Coordinator
Jun 14, 2012 at 12:32 AM

Carole, that's cool - didn't know about the halo. But it looks like if this was a halo effect with Tyler's optical properties, it would show up in the correct R(rho) green curve. Plotting R(rho) with our online tool, it looks like the default OP's (mua=0.01/mm, mus'= 1.0/mm, g=0.8) put the halo peaking at about 15 microns. I think this is a separate issue having to do with 2D tallies in a 1D estimator.