I found a gaussian pyramid implementation in a MOPS paper (feature detection). They use sampling rate $s=2$ and $\sigma=1$ - i.e. to generate a new level of the pyramid, the current level is smoothed with Gaussian blur of that sigma and then subsampled. The same parameters are used to build each new level.
However, I need to use smaller sampling rates, e.g. $s=1.5$, to get more pyramid levels (non-integer sampling rates would be achieved by interpolation).
How to choose appropriate sigma, knowing the sampling rate?
My first guess is to use $\sigma=\sqrt{s/2}$, since the variance of the gaussian filter is half the sampling rate (radius) and sigma (standard deviation) is square root of that quantity. But I am not sure if that's correct.
In another words: Given a sampling rate, I need to pick gaussian blur sigma preventing aliasing.