Finding the Width of a Point Spread Function (PSF)
One simple way is to identify zeros in the Frequency Domain.
This was one of the legitimate method for Blind Deconvolution few decades ago.


Draw the connection between the zeros in frequency domain of the Convolution Kernel to the parameter $ w $.
Learn the zeros in frequency domain of the given image.
Find the $ w $ which explains most of the zeros of the image.


It's pretty simple and for a parameterized family of PSF's can be quite efficient.