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Another, I hope final, explanation for annular rings on stars

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#1 freestar8n

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Posted 04 May 2021 - 09:16 PM

The topic of these occasionally seen tight rings around stars has come up several times.  Here is a Hubble example:
 
Sour1.png

There have been a few proposed explanations but nothing made sense to me, mainly because the rings hold intensity well and they don't die off quickly.  In the Airy pattern they die off very quickly - but these rings show even in linear images with no stretch.

 

The rings are also fairly narrow and they get tighter as you go out.

 

For me they are correlated with good guiding and good seeing - and very small stars.

 

I think they are a form of Tolansky fringes, described in this early paper and seen in Fabry Perot interferometry:

 

https://royalsociety.../rspa.1946.0043

https://en.wikipedia..._interferometer

 

What I think happens is the star image is formed mostly on a single pixel and the microlens reflection acts like a point source.  The sensor coverslip then acts like an etalon and allows the fringes to form.  The key thing is that the number of bounces within the window isn't increasing as you go away from the star - that is why the fringes remain bright.  Only the effective path length is increasing - not the number of bounces.  If the number of bounces increased as you go out - they would die off very quickly.

 

To view it properly you need to forget about the light coming from the star itself through the OTA and instead view the pixel itself as the local point source.  So you have a point source next to an etalon and you get fringes.

 

If you have less good guiding then the fringes from nearby pixels will overlap and blur out the pattern - so a key factor is that most of the light is concentrated on a single pixel so it acts like a point source.

 

And nothing to do with filters or bounces off elements in the OTA.  But it does depend on the AR coatings of the coverslip.  No connection to f/number except in ending up with a very small star spot mostly landing on one pixel.

 

Frank


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#2 freestar8n

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Posted 04 May 2021 - 10:16 PM

Ugh - the above led me in a way of thinking but it doesn't make sense either.  I think it is more subtle.

 

If the reflections off the glass are even as high as 0.04 the fringes would still be very faint - but these are strong.

 

Here is another take - and it does require light from the star.

 

There is still a point star spot on one pixel - but surrounding it is a halo caused by a filter that is fairly uniform around the star spot.

 

At the same time you have light from the point pixel making a *single* bounce off the coverslip.  The phase after that single bounce will depend on how far out from the star the bounce happens.

 

So that single bounce with a single reflection interferes with the faint halo/annulus around the star - and if both are about the same intensity there will be strong interference.  

 

So a key requirement is still a small star spot - but in addition you need the brightness of the glow around the star to match the brightness after a single bounce so they can interfere and make strong fringes.  And again the fringes stay strong because there is only one bounce involved.

 

I guess a lot of factors have to be right for this to happen - which is why it only happens in some Hubble and amateur images.

 

Frank



#3 freestar8n

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Posted 05 May 2021 - 02:40 AM

Here's a picture showing the geometry.  For the interference fringes to be visible the halo needs to be similar brightness to the light radiated by the star spot - and the path differences need to be within the coherence length of the light.  The coherence length is much greater with narrowband light - but as long as the path lengths end up very similar there could be fringes also with wideband light.

 

Frank

 

HaloInterferenceDrawing.png

 


Edited by freestar8n, 05 May 2021 - 03:27 PM.


#4 sharkmelley

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Posted 05 May 2021 - 03:51 AM

Have you done the calculations to work out the spacing of each fringe?  I think you'll find that the spacing between successive fringes varies much more than in your example Hubble image above. 

 

Mark



#5 freestar8n

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Posted 05 May 2021 - 04:05 AM

I'll check it out - but I'm pretty sure the mechanism involves interference between two light sources with varying optical path difference and similar irradiance - and the number of bounces is fixed.  That doesn't leave many options.

 

If the optical path in the halo is somewhat in step with the path from the point source it would cause the rings to have wider spacing than might be expected just from distances in the diagram.

 

The strange thing is that I can't find an explanation for this anywhere.  The Hubble site talks about a number of known artifacts around stars but they don't describe this specifically - even though it's a fairly prominent feature in some of the images.

 

I think it's because stars with that stuff around them wouldn't be useful for anything quantitative anyway.

 

Frank


Edited by freestar8n, 05 May 2021 - 04:06 AM.


#6 sharkmelley

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Posted 05 May 2021 - 04:09 AM

I manually calculated the fringes and this is the pattern I ended up with:

 

InterferenceFringes.jpg

 

Mark



#7 freestar8n

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Posted 05 May 2021 - 04:27 AM

That looks good to me - and the fading out radially in the images is a mixture of fading of the halo, along with loss of coherence between the two.

 

Frank



#8 sharkmelley

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Posted 05 May 2021 - 04:33 AM

I think the pattern I generated is significantly different to what we are seeing in that Hubble image - in terms of fringe spacing.

 

Mark



#9 freestar8n

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Posted 05 May 2021 - 04:50 AM

I don't see a scale in your image?  I was just going by the appearance of the pattern.

 

The increasing radius after the single bounce from the star spot has an opd dependent on the coverslip thickness.  And it interferes based on the OPD of the halo at that radius.

 

It's easy to calculate the changing OPD from the star spot as you go out if you know the thickness - but you need to find the difference between that OPD and the halo OPD at that point.

 

I think it's similar to a point diffraction interferometer setup:

 

https://en.wikipedia..._interferometer

 

You have an arriving wavefront and you generate a point source to interfere with it.  And that point source is slaved to the wavefront.

 

Frank



#10 sharkmelley

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Posted 05 May 2021 - 05:16 AM

The fringes in the example Hubble image are regularly spaced as far as I can see.  It will be interesting to see if this is reproduced by your explanation.

 

Mark



#11 freestar8n

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Posted 05 May 2021 - 05:42 AM

Oh - I always viewed these examples as getting narrower as you went out.  The rate of change may vary but that was my impression.  The outer ones are harder to measure.

 

They may be fairly evenly spaced but that's also ok if the OPD in the halo is increasing similarly to the OPD from the star spot.

 

Any other explanation I have seen involved either an Airy pattern where the peaks should die out very quickly, or multiple bounces where increasing reflection counts should die out very quickly.

 

This explanation centers on a single bounce in each path and subsequent differences in OPD leading to interference - within the region of a halo.  Halo too bright or too faint - no fringes.  OPD too big relative to coherence length - no fringes.  Star spot spanning several pixels - no fringes.

 

That is consistent with why they are somewhat rare and not directly associated with given equipment.

 

Frank



#12 sharkmelley

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Posted 05 May 2021 - 10:40 AM

You cannot achieve evenly spaced annular rings using your geometry.  The OPD (optical path difference) will be a quadratic in the radial distance from the centre of the star.  This will always lead to interference fringes like Newton's rings or Fabry-Perot fringes where the spacing becomes tighter as the radial distance increases.

 

Mark



#13 pfile

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Posted 05 May 2021 - 10:51 AM

fwiw i have seen this on some of my narrowband images taken with an AT6RC + tele-vue reducer + STT-8300M. with the seeing here it's hard to believe these bright stars illuminated only one pixel:

 

Screen Shot 2021-05-05 at 8.48.47 AM.png

 

not sure if it is the same phenomenon.

 

i can dig out the raw data if it is of interest.

 

rob

 



#14 sharkmelley

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Posted 05 May 2021 - 11:00 AM

I came up with an alternative explanation which involves a periodic modulation of the Airy rings caused by the central obstruction:

https://www.cloudyni...200/?p=10521229

 

Mark


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#15 RJF-Astro

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Posted 05 May 2021 - 11:47 AM

That thread Mark points out makes sense to me, with the secondary playing a big role. I have this too with my 6RC, see below. There are from two different 6RCs and 0.67x reducers. Camera is the same (ASI1600), the first is Ha narrowband and the second red filter.

 

The third image is made with a 130mm newton, also narrowband. It is harder to see, bu still there.

 

I have not seen this on my refractor images, with most of the rest being the same except the reducer/corrector.

 

20190622 NGC6888 3h.jpg

 

_20210417_M63_R_1h40_registered_DBE.jpg

 

20200120 Flaming star 5h.jpg



#16 CygnusBob

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Posted 05 May 2021 - 11:55 AM

freestar8n

 

If the focused star image is acting like a diffuse point source on the focal plane, how do we get an interference pattern?  You say the light is bouncing once off the top of the coverslip, but what other light path is interfering with the single light reflection?  You need to have multiple paths to create an interference pattern.

 

Bob



#17 freestar8n

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Posted 05 May 2021 - 03:29 PM

I came up with an alternative explanation which involves a periodic modulation of the Airy rings caused by the central obstruction:

https://www.cloudyni...200/?p=10521229

 

Mark

I'm afraid that never worked for me because Airy rings die out very quickly.  I image them all the time and it is hard to see beyond the first one even with sct and secondary obstruction.  The pattern here is very steady and has the look of interference fringes.

 

Frank



#18 freestar8n

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Posted 05 May 2021 - 03:38 PM

freestar8n

 

If the focused star image is acting like a diffuse point source on the focal plane, how do we get an interference pattern?  You say the light is bouncing once off the top of the coverslip, but what other light path is interfering with the single light reflection?  You need to have multiple paths to create an interference pattern.

 

Bob

There is no diffusion here at all, and there are indeed two sources that are coherent.  One is the spherical wave emitted from the lagging point of focus above, and the other is from the star spot itself.

 

I have modified the figure above to show these more clearly.  This is all basic optics with mirrors and spherical waves.  What matters for interference is the difference in optical path between the two waves.  The way I drew it originally did not show the spherical wave, but now I hope it's clear that the OPD from both sources is increasing as you go out from the star spot - so the difference in optical path will increase more slowly.  And it's the difference in optical path that causes the fringes.  The OPD need not be zero - it just needs to increase as you go out from the star spot.  Every change of one wavelength will cause a fringe.

 

If you unfold everything it is just the interference of light from two separate point sources spaced a bit apart.  Normally the one farther away would be fainter due to the greater distance the wave traveled, but that is nicely compensated here by the loss of light at the star spot.  The wave from above is the original starlight after two reflections, while the wave from the point source is a much smaller sphere - but it has loss of light at the star spot reflection in addition to the loss from the bounce off the coverslip.  I assume there is less reflectivity off the sensor but I guess that depends.

 

For simplicity I am not showing refraction in the glass so that would need to be included in any calculation of fringes.  But ultimately it's just the interference of light from two displaced and coherent point sources onto a screen.

 

Frank


Edited by freestar8n, 05 May 2021 - 03:54 PM.


#19 freestar8n

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Posted 05 May 2021 - 03:46 PM

fwiw i have seen this on some of my narrowband images taken with an AT6RC + tele-vue reducer + STT-8300M. with the seeing here it's hard to believe these bright stars illuminated only one pixel:

 

not sure if it is the same phenomenon.

 

i can dig out the raw data if it is of interest.

 

rob

I don't think it literally needs to be one pixel so that part in my explanation may not be correct or relevant.  But the surface of the sensor needs to reflect and return a spherical wave.  There may not need to be isolated microlenses or a single one acting as an emitter - but I do associate it with well focused images and small star spots.

Frank



#20 calypsob

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Posted 05 May 2021 - 03:56 PM

This Kind of looks like some diagrams I have seen of newtons rings

#21 freestar8n

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Posted 05 May 2021 - 04:01 PM

This Kind of looks like some diagrams I have seen of newtons rings

Yes it always had the look of some kind of interference pattern involving overlapping spherical waves.  They are fairly uniform brightness as you go out from the star spot.

 

It takes the right set of circumstances for the two waves to be similar brightness and for the spacing to be not too big or too small so the fringes show well and with good contrast.  And they are only visible within the halo itself - so that needs to be big enough - but not so big it is faint or the OPD is so big the waves aren't coherent anymore.

 

Frank



#22 sharkmelley

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Posted 05 May 2021 - 06:05 PM

I came up with an alternative explanation which involves a periodic modulation of the Airy rings caused by the central obstruction:

https://www.cloudyni...200/?p=10521229

 

 

I'm afraid that never worked for me because Airy rings die out very quickly.  I image them all the time and it is hard to see beyond the first one even with sct and secondary obstruction.  The pattern here is very steady and has the look of interference fringes.

 

Frank

 

Fair enough - I know I won't persuade you.  But for the benefit of others reading this, I won't let your comment go unchallenged.

 

The best (non-Hubble) example I've seen so far is this one:

 

GammaCygniRockstarbill.jpg

 

I can count 25 or more equally spaced rings.  It's a 15minute H-alpha exposure taken by CN contributor @rockstarbill with a AG Optical 10" iDK and ZWO ASI6200 camera.  The intensity of the rings certainly dies out very quickly (just as you would expect from Airy rings) but I've applied an extreme stretch to make them visible.

 

Anyone interested enough can look at the raw data  - the download link is provided in the original post of the thread I linked earlier:

https://www.cloudyni...in-the-asi6200/

 

Mark


Edited by sharkmelley, 05 May 2021 - 06:09 PM.

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#23 freestar8n

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Posted 05 May 2021 - 06:23 PM

Fair enough - I know I won't persuade you.  But for the benefit of others reading this, I won't let your comment go unchallenged.

 

The best (non-Hubble) example I've seen so far is this one:

 

attachicon.gifGammaCygniRockstarbill.jpg

 

I can count 25 equally spaced rings.  It's a 15minute H-alpha exposure taken by CN contributor @rockstarbill with a AG Optical 10" iDK and ZWO ASI6200 camera.  The intensity of the rings certainly dies out very quickly (just as you would expect from Airy rings) but I've applied an extreme stretch to make them visible.

 

Anyone interested enough can look at the raw data  - the link is provided in the original post of the thread I linked earlier:

https://www.cloudyni...in-the-asi6200/

 

Mark

I don't see anything that is contrary to what I'm describing - and the fact that you see 25 rings of fairly steady intensity completely rules out the Airy pattern.  I have seen your plots of Airy patterns but aren't you boosting the height with radius in your plots?  If you don't do any boosting you should see the rings die out quickly.

 

If your main point is that the rings appear to be uniform - that's perfectly fine in what I'm describing because how rapidly they get narrow will depend on the different radii of the spheres.

 

If you plot the Airy pattern out to 25 rings and look at the expected intensities of those rings - do you really think that is consistent with these images?  I have never seen any Airy pattern structure in a long exposure amateur image - though I can capture the first ring with lucky imaging.  Even if aliasing is somehow involved the ring structure is very fine and it would blur out - and aliasing would not boost an already very tiny signal to make it visible.

 

Frank



#24 sharkmelley

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Posted 05 May 2021 - 06:31 PM

I don't see anything that is contrary to what I'm describing - and the fact that you see 25 rings of fairly steady intensity completely rules out the Airy pattern.  I have seen your plots of Airy patterns but aren't you boosting the height with radius in your plots?  If you don't do any boosting you should see the rings die out quickly.

 

If your main point is that the rings appear to be uniform - that's perfectly fine in what I'm describing because how rapidly they get narrow will depend on the different radii of the spheres.

 

If you plot the Airy pattern out to 25 rings and look at the expected intensities of those rings - do you really think that is consistent with these images?  I have never seen any Airy pattern structure in a long exposure amateur image - though I can capture the first ring with lucky imaging.  Even if aliasing is somehow involved the ring structure is very fine and it would blur out - and aliasing would not boost an already very tiny signal to make it visible.

 

Frank

As I just said, the 25 rings in that image have an intensity that decays very rapidly - just like Airy rings do.  Download the raw data and look at it for yourself. 

 

Mine is a testable hypothesis with actual calculations to predict the resulting ring spacing.  If you feel you have an example that doesn't fit this hypothesis then make it available so we can examine it.  Maybe you are seeing a different effect but we cannot know without seeing the data.

 

Mark


Edited by sharkmelley, 05 May 2021 - 06:42 PM.


#25 freestar8n

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Posted 05 May 2021 - 07:03 PM

Here is the Airy pattern for 50pct obstruction:

 

Airy50pct.png

 

Here is a close up:

 

Airy50pctCloseUp.png

 

The rings die off quickly and don't appear regular.

 

Here is a simulation of the hubble image - with two gaps involved each 1mm thick:

 

HubbleSim.png

 

There is a central bright spot overlapping the star spot and after that are regular rings of about the same brightness.  The compress a bit in distance but I see that in the image also.  The spacings should be 0.52" or 73um with wavelength of 1.64 microns - if I measured them correctly.  I didn't try to exactly match the image - just using gaps of 1mm immediately gave a very good match with no free parameters.

 

The spacings and rate of compression are set by the two gaps involved - plus the wavelength.

 

Frank




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