Koehler source
asassa01
Qianqian Fang
hi Angelo,
you can use cfg.angleinvcdf in combination with an area source to control the launch angular distribution - for a uniform cone with an half-angle of pi/4, you can do this
this is similar to this built-in example
https://github.com/fangq/mcx/blob/v2025.10/mcxlab/examples/demo_mcxlab_launchangle.m#L26-L32
when cfg.angleinvcdf has odd number element, launch angles are linearly interpolated between each angle value in the vector, creating a continuous distribution
when cfg.angleinvcdf has even number of element, each angle element in the vector are sampled without interpolation.
Qianqian
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Qianqian Fang
hi Angelo,
there are two mechanism controlling the launch angles.
1. Mechanism 1: cfg.srcdir(4)
the 4th element of srcdir defines the focal length if the source is an area source (disk, planar, fourier, gaussian, pattern ...), positive focal length makes a converging beam, negative makes a diverging beam;
there are two special settings: if srcdir(4) = nan, the launch angles follows isotropic distribution; if srcdir(4)=-inf, it follows the Lambertian distribution (cosine); of course, if srcdir(4) = inf, it is a collimated beam just based on focal length
srcdir(4) only controls the launch angles for area sources, has no effect to point source (pencil, isotropic, cone, zgaussian).
Mechanism 1 is relatively simple, easy to use, but has limited control.
2. Mechanism 2: cfg.angleinvcdf
cfg.angleinvcdf asks users to manually specify the distribution of the launch angle (zenith angle relative to srcdir(1:3)) via a discretized inverse cumulative distribution function (CDF) of the zenith angle.
angleinvcdf applies to all source types, regardless it is an area or point source; when angleinvcdf is used, Mechanism 1 above is disabled.
angleinvcdf is a 1D vector [ a1, a2, a3, ...a_N ] contains normalized (0-1 value, 1 means Pi) monotonically increasing angles
when angleinvcdf is used to generate launch angles, mcx first produces a 0-1 uniformly distributed random variable U, and map it to the full vector indices [0, (N - 1)] and use it to lookup the value in angleinvcdf to determine the angle to be launched. there are two ways to map U to the angle values:
1. when N is an odd number, the launch angle is interpolated between the two adjacent angles on either side of U, producing continuous distributions;
for example, if angleinvcdf=[0.2, 0.5, 0.8], where N=3, if U=0.25, converting to the index axis, we get index = 0.25*(3-1) = 0.5, you can see index 0.5 means it is half-way between the first (idx=0) and the 2nd element (idx=1), so the launch angle is determined to be theta = (0.2*0.5)/2*pi = 0.35pi; if U=0.2, then, we have index=0.4, we need to interpolate the 1st/2nd element using a 6:4 ratio, i.e. theta = (0.6*0.2 + 0.4*0.5) * pi = 0.32*pi
based on this method, if your anginvcdf is produced by a linspace() of odd number length, your distribution stays exactly the same as long as the linspace length is an odd number.
2. when N is an even number, we just round-down the index and use it to get the angleinvcdf element as the angle. this produces an discrete angular distribution.
for example, if angleinvcdf = [0.2, 0.3, 0.4, 0.4], when mapping 0-1 distributed U to the index axis, we see that 50% of the chance the photon will launch at 0.4*pi, 25% of the chance will launch at 0.2*pi, and 25% of the chance will launch at 0.3*pi. again, this only determines the zenith angle theta; the azimuth angle phi is always a 0-2*pi uniformly distributed random angle. combing these two angles, angleinvcdf=[0.2,0.3,0.5,0.5] will produce 3 concentric cone-shaped light sheets, with the 0.4*pi cone taking 50% of the brightness, and the other two cones taking 1/4 of the total brightness.
regardless which mechanism you use, all the computed launch angles are zenith angles relative to the user specified source direction: srcdir(1:3). You can steer the beam by changing srcdir(1:3), and all the above settings will keep its beam profile but steered following srcdir.
let me know if this is clear.
Qianqian
Thanks so much! My bad, I missed to look at this part in the documentation of MCX!!So, if I want a "DISK" source with a given radius (the radius is set by srcparam1(1) (in grid unit)) and where each point in the disk emits in a uniform half cone (as in your example) with z axis, I must define cfg.srcdir=[0 0 1], right? (no 4th element). If I want the cone with a different axis, I should define a different cfg.srcdir accordingly, right? Also, in your example the number "5" controls the interpolation, and can be chosen as a different odd number?Thanks!!Angelo
Qianqian Fang
sorry, I have one correction and one clarification:
first, the below statements were actually incorrect.
1. when N is an odd number, the launch angle is interpolated
2. when N is an even number, we just round-down the index and use it to get the angleinvcdf element as the angle.
using even/odd length of angleinvcdf to decide interpolation or discrete angle was the first implementation, but shortly it was replaced by using cfg.srcdir(4) = 0 for interpolation, and 1 for discrete angle, added in this commit
https://github.com/fangq/mcx/commit/ca1bf2b9da826994d7d1be12f5aa6c4ec4aa1076
because Mechanism 1 was disabled when cfg.angleinvcdf is defined, so cfg.srcdir(4) was re-purposed to control interpolation - it is more intuitive compared to using odd/even length.
regardless which mechanism you use, all the computed launch angles are zenith angles relative to the user specified source direction: srcdir(1:3).
the above statement is not exactly correct. for most sources where the source-determined launch angle follows srcdir(1:3), the above statement is true.
however, some sources requires to compute a new direction at launch, including cone, zgaussian, isotropic, arcsine, and hyperboloid, line and slit (when launchsrc->param2.{x,y}>0).
for these sources, the angleinvcdf-determined zenith angle is actually applied on top of the randomly sampled source-induced launch directions.
for example, if you define cfg.angleinvcdf for a cone beam, the launch vector is first randomly sample the uniform cone based on the source, then, it further steer based on angleinvcdf. it is really a convolution of the two effects.
To view this discussion visit https://groups.google.com/d/msgid/mcx-users/ece1e871-e2b4-441d-af1f-9d707a1b7688%40neu.edu.