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- Understanding Sobol Sampling
Understanding Sobol Sampling
- By Mark Nicholson
- Published 10 November 2005
- Sources, Splitting and Scattering
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Signal to Noise Ratio

10,000,000 rays:
100,000,000 (one hundred million) rays per source:
and 1,000,000,000 rays (one billion rays!) per source
When there are very few rays (10,000) and many many rays (1 billion) the results of the random ray-trace and Sobol ray-trace are similar. Hence Sobol sampling is most useful in a "sweet-spot" region. The signal to noise ratio (SNR) of the random ray-trace is SQRT(N) where N is the average number of rays hitting a pixel. For the Sobol sampling scheme, the SNR goes linearly as N (see reference 1). This can be seen by taking a cross-section through the distribution with 1 billion rays per source:
Note however that Sobol sampling is not a "magic bullet". In this case, we know that the source irradiance is intended to be uniform. Our prior knowledge of the intended distribution allows us to claim that Sobol sampling is "better" in this case. However, in any Monte-Carlo simulation, there is ultimately no more accurate method that making many samples with a truly random number generator. For this reason, ZEMAX allows you to select either a Sobol sampling scheme, or to use ZEMAX's long-period random number generator, in the source tab of the object properties: