Six-pointed stars in JWST images

Why disturbing?

What's wrong with the diffraction spikes from the JWST?

Also, there should be 8, as I recall (although the horizontal ones are pretty dim, compared to the vertical and "X" shaped ones).

It is a characteristic feature of the hexagonal aperture symmetry and there is a minor cross line resulting from the support structure too. So it is actually a six pointed star with two short spikes across. ie

\ / \ / \ | / ______\|/_______ /|\ / | \ / \ / \

Point spread function of any aperture is the Fourier transform of its shape filed with 1's. It is a consequence of using a mirror of finite extent. You can't get rid of the diffraction pattern without inventing measurements for the spatial frequencies that you don't have (or severely compromising resolution).

It is actually quite a difficult inverse problem to remove diffraction artefacts and the raw images are much better for scientific purposes. On a good day with a trailing wind something like Maximum Entropy will get you 3x superresolution on the brightest point sources and some noise suppression. But it is also inclined to add ripples into any nebulae since the positivity contraint doesn't work well there like it does against the blackness of space.

Some images are much tougher than others to deconvolve reliably.

I don't find them offensive YMMV. It *is* what the telescope actually saw!

Whilst deconvolution will do it so that you get a prettier coffee book picture and depending on the method used you end up with either resolution that depends on local signal to noise and/or missing faint detail in the regions where the brighter spikes used to be.

JWST PSF stands out because of the unusual symmetry of its mirror.

The six pointed star is also a feature of some ground based telescopes with round mirrors and a 3 way centre diagonal support. They have less total power in each of the diffraction spikes as a result. The first biggish scope I used was of this sort. i didn't much like it back then preferring the more normal eight pointed stars of other big scopes. ie.

| | \ | / ______\|/______ /|\ / | \ | |

Some even have weird curved supports that behave a bit like an apodising filter.

Most big scopes these days have brutal straight 4 way central mirror support (or none if they are catadioptric and have a front optical surface with a silvered mirror spot on axis.

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I find them objectionable because they often obscure (oblude?) nearby detail. These days, it should be relatively easy to Fourier-transform the image, apply some window function to remove the hexagon pattern of the mirrors and the shadows of the secondary mirror supports, and then transform it back again.

Jeroen Belleman

That wouldn't work without losing a hell of a lot of resolution though. It is the *missing* spatial frequency data that is damaging the image quality. The de-facto window function already applied by the physics of a finite aperture is the autocorrelation of the aperture shape.

Because of the various straight sides it isn't that far off being a triangle with a peak in the middle and linear decline to zero at the diameter of the mirror along the direction you choose.

You can't filter away the fact that you don't have any data for some missing spatial frequencies that you were not able to measure because of the finite extent of the mirror and its supports.

You have to invent them to make the diffraction spikes go away. That can be done but it isn't unambiguous or simple and introduces new artefacts that can get in the way of interpretation.

Linear methods like Weiner filters exist that work fairly well but the non-linear ones which are more computationally expensive do better because they naturally include the heuristic knowledge that the sky is everywhere positive brightness and can use the empty sky being black to rule out impossible scenarios from their reconstructed image. This isn't a too bad introduction to what is possible at about the right level (with some algebra and more importantly sample pictures).

Any fast linear method invariably produces negative ringing around the point sources which is way more distracting than diffraction spikes.

First you have to decide what question you want to answer and then do the image processing that best facilitates solving your problem. It is invariably better to start from the raw data for astrophysics.