
Hi everyone,
I have been messing around a little with 1D 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 2D, 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 1D, I find that this is the same as the unnormalized 2D reflectance, and that it actually is lower for locations from
about 00.5mm, then peaks around 0.51mm, 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 unnormalized results correctly, it could be the "halo" that Arnold Kim described in his paper "Backscattering of beams by forwardpeaked scattering media", Optics Letters 29(1), p. 746, 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(x0)". Photons would be randomized in their input position along the x=0 axis, and reflectance collected in rectangular xbins extending from
y_min to y_max. Normalizing by the x bin lengths would get you
R(x).
With realworld Monte Carlo and finite yextent of the medium, it's often convenient to alternatively simulate this same reflectance by use of a point illumination, delta(y0)*delta(x0), but collecting this data in the same fashion
as above. This works fine assuming your medium is homogeneous along the ydirection, since the exiting yposition 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 "unnormalized"
R(rho), where each unnormalized bin was COUNTS_bin * [ Pi*(r2^2r1^2) ]. I would not expect this to be the same as
R(x),  R(x) should look like unnormalized R(x) differing by a constant factor. If you're using a point illumination, rho takes into account both x and yposition (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.

