How many photons are enough?

[Alex]

I wanted to ask what is generally used as the stopping criteria? I previous posted that I was using larger domains 10cm^3 and those larger domains have to run for a bit longer than normal so what is considered a good solution? I would assume once all of the voxels in the domain have some kinda of measurement i.e. fluence/energy density is not -inf.

[Qianqian Fang]

On 3/25/19 11:37 AM, Alex wrote:

I wanted to ask what is generally used as the stopping criteria? I previous posted that I was using larger domains 10cm^3 and those larger domains have to run for a bit longer than normal so what is considered a good solution? I would assume once all of the voxels in the domain have some kinda of measurement i.e. fluence/energy density is not -inf.

hi Alex

I remember seeing a paper on either BOE or JBO, discussing the stopping criteria for MC photon simulations. However, I remember when I read it, it did not really match my expectations.

In my experience, the stopping criteria should be determined by the SNR in the ROI that one is interested in. There is no need to ensure all voxels to receive enough photons, which is often a time-consuming requirement, but instead, you just need to make sure the ROI received enough photons. For example, if you do fNIRS simulations, you only need to make sure your detectors (max 4cm away from the src) receive enough photons, as well as gray-matter region beneath src/det have good SNR. There is no need to wait until the entire head/brain to get sufficient photons everywhere because it will take way too long.

However, to compute SNR, you need to run multiple simulations with different seeds - from which you can calculate the means and stds of each voxel, and compute SNR. The SNR is pretty much linearly proportional to #photons. See Figure 4 in our recently published MC denoising paper https://doi.org/10.1117/1.JBO.23.12.121618 . Every 10-fold photons give you 10dB SNR everywhere, but SNR is spatially dependent because it has shot-noise.

So, what I suggest to do is to first run a relatively small number of photons (so that you have just enough photon to drive a trustworthy SNR in the ROI), and run 10-20 repetitions with different random seeds. Then from the output fluence maps, compute the averaged SNR in the ROI; in the meantime, set a threshold for your desirable SNR, from that, you can estimate how many more photons you need to run (again, increase by 10-fold gives you 10dB extra SNR).

of course, our recent works on MC denoising can offset this - the ANLM filter in the above paper can add 5.5dB (equivalent to 3.5x more photons). My student/postdoc is working on CNN based denoiser which gives more benefit (presented in Photonics West'19). 

let me know if this makes sense to you. feel free to jump in if anyone has different thoughts.

Qianqian

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[Alex]

Thank you Fang,

I'll take a look at that paper and if everything makes sense I'll look at integrated that into my simulations to make it more robust. My specific simulations are with photoacoustics so I would like to have some signal from deeper regions of various phantoms. I'll also check out the ANLM filter and get back to you here if I have any questions.

When you suggest running a small number of photons to get a trustworthy SNR what would define a trustworthy SNR? Something that doesn't change too much between different seeds?

Thanks for the suggestions!