Re: Resolution with Gaussian point spread function

spasmous2 wrote:
On Jun 24, 6:30 pm, Helpful person <rrl...@xxxxxxxxx> wrote:
On Jun 24, 5:23 pm, spasmous2 <spasm...@xxxxxxxxx> wrote:

If you have a Gaussian PSF, then how can you determine resolution
(resolvability) using the Raleigh criterion? As I understand the
Raleigh criterion says the maximum of one PSF must sit on top of the
minimum of the neighbor for them to be "just" resolved. This is OK for
a sinc-like PSF but what about a Gaussian PSF which doesn't even have
a minimum?
It's easy to do the mathematics yourself. Just add two Gaussian
functions separated by a distance that just shows a dip between the
two peaks.

By the way, how do you get a Gaussian point spread function?


Thanks for your suggestion - does this method have a name?

Actually the PSF not Gaussian - that was just a simplification to get
to my question about the Raleigh criterion. The types of PSF I am
working with are numerically generated to simulate the effects of
different filters on image resolution. But I don't really know a good
criterion for determining resolution - from the PSF I can obtain the
FWHM, the measure you mention above or basically anything numerically
calculable - I was hoping to use a "standard" metric. The Raleigh
broke down pretty quickly for obvious reasons and I was looking for
new ideas.


Rayleigh and Sparrow and so forth are useful for visual and photographic detection, because the human visual system is bad at distinguishing small intensity variations in featureless round blobs. With electronic detectors. there's really no good way to specify resolution in the sense Rayleigh used it--i.e., determining whether you have one star or two in that bright blob--without signal-to-noise considerations. If you really know your PSF, and your signal to noise ratio is really high, you can use curve fitting to extract the separation of two unresolved objects.

On the other hand, if what you want is to be able to 'see what's there' without having to fit an *a priori* underlying model, then something along the lines of Rayleigh (adapted for your circumstances) might be best.

Cheers,

Phil Hobbs

Cheers,

Phil Hobbs
.

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