# 5 Simulation test of different fwhmr50whisker measures:¶

I generated simulated PSF from both bivariate Gaussian profile and Moffat profile and then run the various fwhm/whisker/r50 measures. In the simulation, I generated 500 PSF stars for each profile and assume the stars art 16.5 mag for an 100 second exposure. My tentative summary based on these analysis are:

- For whisker, we may want to use the weighted moments, as it gives more robust results. There could be a bit off from the true value for moffat like profiles, but this offset is liear.
- We should use R50 instead of FWHM and the results from sextractor on R50 is pretty consistent. Or alternatively, we can use the weighed moments with a correction:
- fwhm_input = 0.955* fwhm_weighted -0.0898

- In general, the weighted moments (use 2 pix kernel weight) is more robust than the other methods.

The following are more details about the comparison results:

- For Gaussian PSFs:
- weighted moments gives very consistent whisker, adaptive moments and sextractor underestimate the whisker.
- sextractor sometimes gives very wrong whisker estimates
- most methods give consistent fwhm, except sech2 profile fitting.

- For Moffat PSFs: