Fourier Opacity Map volumetric shadow.

I implemented volumetric shadow of particle system in UE3.
There were several options for this effect. The most feasible 3 were like below.

1. per pixel deep shadow map(need CS, UE3 didnt have CS back then)
2. FOM
3. Simple thickness map

I tried #2 first. the result was quite good with some resource. But finally I chose simple thickness map technique because of the severe ringing effect of some particles with high opacity! ringing effect is seen in spherical harmonics too. because frouier and SH use wave like basis functions.

Today, I found that UE4 is using FOM for volumetric self shadow. and document is warning about ringing effect.

why did they choose FOM? maybe they must have found solution for ringing effect.
I will look into source code later.