20 replies to this topic

[whwang]

In the last couple of new moons, I collected some exposures on M46 and M47.  This is the result:

 

 

Some hint of Galactic cirrus reflection (aka IFN) can be seen, but the image isn't really deep enough for me to aggressively pull them out. The second shell of the PN NGC2438 is also marginally visible.  The target is kind of low from my location and also low on my priority list. So I probably won't have a chance to get an image that's really deep enough for these faint stuffs.  But anyway, for the clusters, I think the depth is quite adequate.

 

The image contains 68 5-minute exposures from a TAK TOA150, TOA 645 flattener, and Pentax 645z.  For integration in PI, I tried the regular integration with debayerization, 1x Bayer drizzle integration, and 2x Bayer drizzle integration.  The results look very similar, nearly indistinguishable.  Given that the drizzle integration takes significantly longer time, I would say it's not quite worthwhile to run drizzle at all, for this set of exposures.

 

Note: The above conclusion only applies to this set of images. The stellar FWHM is about 2.5 pixels, so they are not undersampled. This naturally leads to the result that drizzle doesn't help much. Here I am definitely not making a general comment.  If the images are under-sampled, the conclusion should be different.

 

Then I tried running BXT, and things become very different. The combination of 2x Bayer drizzle and BXT dramatically improves the effective resolution. Many close visual binaries that are unresolved in the non-BXT images and the BXT results of non-drizzle and 1x drizzle images become clearly resolved in the BXT + 2x drizzle combination. Here is the comparisons I made:

 

even higher resolution version

 

In case you are curious, the BXT parameters are all identical for three cases. The star sharpen parameters are all 0.25 and the star halo parameters are all -0.25.  I suppose these are not very aggressive.  However, since one of the three has a different pixel scale, I cannot tell whether identical parameters imply identical strength of deconvolution.  (Furthermore, what's the definition of "identical strengths" when the image scales are different?)  There is no guarantee that the comparison is fair, but I think this is beyond the scope of discussion here.

 

To guide you, I circled a few close visual binaries or pairs of binaries that can best showcase the effects of BXT + 2x drizzle. The yellow and green circles contain pairs of binary stars of comparable brightness. The red, purple, and cyan circles contain binaries with large brightness contrasts.

 

You can see that in the non-BXT images, they all look more or less similar, drizzle or not.  Some of them become resolved once BXT is applied to the non-drizzle and 1x drizzle versions, but not all of them are resolved. They all become clearly resolved only in the BXT + 2x drizzle image.  In the non-BXT versions, many of them just show hint of elongation.  You probably wouldn't even guess they are binaries or there is a faint companion next to a moderately bright star in some of the cases here.  And yet BXT clearly resolved them when combined with 2x drizzle.

 

Now, the question is are they real?  Are they really close binaries?  Or BXT just created companion stars that do not really exist?  This is not easy to answer, as there do not exist high resolution modern images of this area in the public domain.  This area is in the south, near the Galactic plane.  So extragalactic surveys like the Sloan and DES do not cover this area.  The DSS covered this area, but the resolution and the point-source limiting magnitude of photographic plate are just too far behind today's digital sensor.  So I can't use DSS to verify these faint binaries either.  This area is right in the middle between M46 and M47.  So it is covered by many wide-field amateur images, but their resolution is typically not good enough to match the resolution of BXT + 2x drizzle here. There are higher resolution amateur images of M46 and M47 individually, but they do not cover the mid point between the two clusters.  The difficult of finding an adequate public image here probably also means that BXT does not know the ground truth during its training, although this is not guaranteed and only Russ knows.

 

Because I couldn't find a public image to verify the binaries, I ended up with asking for 10 minutes on a 1-m telescope in Taiwan to image this area to serve as the ground truth. Here is the 1-m telescope image:

 

 

This is a 5-min exposure with R filter. This is raw data. No calibration and no processing were applied. You can see that BXT is right in all the cases. It doesn't create something that does not exist in the 1-m telescope image.

 

The conclusion is that even if drizzle itself does not help to increase resolution (because of the pixel sampling rate), it can help once BXT comes into the equation. And at least within the scope of this test, BXT nicely recovers details that just barely showed up in the original images, and it does not create something that does not exist.

 

I think this gives me a much higher confidence about BXT.  This also urges me to get a new computer, to drizzle the images where I used to think drizzle is useless.

 

Cheers,

Wei-Hao

Edited by whwang, 21 January 2024 - 03:42 AM.

[arbit]

Very useful.

 

These findings are completely in line with Russel Croman's advice to drizzle before BXT to recover resolution. See https://www.rc-astro...er-combination/

 

The underlying theory is explained in more detail with an interactive web app at https://www.rc-astro.com/mtf-analyzer/

 

I also used drizzle rarely, as apart from star shapes at high magnification, there didn't seem much visible benefit over a simple 2x up sample. But the impact of BXT is significantly different and drizzle is standard now for me with the under sampled images.

[whwang]

Yes, I saw Russ's drizzle page before.  When I first saw it, I just thought the finer pixel allows stronger sub-pixel sharpening.  The example image there does not contain many stars, and no nearly-unresolved binaries.  So while I kept that in mind, I wasn't terribly convinced until I run this test by myself.

[smiller]

Excellent and thorough test, thanks for sharing the results.  

 

I will admit that to my eye these are very small differences, comparable to taking an image on two different nights with one night having just very slightly better seeing, given the huge differences I get night to night.  

 

But we astrophotographers are optimizers and will take every advantage we can get so you definitely demonstrated an advantage here.

 

You say your FWHM was 2.5 arcsec, was this measured by PI?   This may help define the threshold before you expect a benefit.

[whwang]

Ah, perhaps I wasn't clear enough.  2.5 is pixels.  It's measured with PI's FWHMEccentricity script.  It's larger than the Nyquist criterion: FWHM > 2 pixels.  So it is not under-sampled.

 

That being said, in this case, 1 pixel happens to be roughly 1".  So it's not wrong saying that FWHM is about 2.5 arcsec.

Edited by whwang, 21 January 2024 - 10:34 AM.

[R Botero]

Wei-Hao

 

An interesting test (and beautiful image of the two clusters).  Do you have a copy of the crops as png/tiff image?  It would be interesting to plate-solve it and then compare with GAIA3 data from Aladin to check on the centroids of the double stars you detected.

 

Roberto

[andysea]

Great validation, thank you for doing this experiment. Did you by any chance measure the S/N ratio in all three images?

[whwang]

 Do you have a copy of the crops as png/tiff image?  It would be interesting to plate-solve it and then compare with GAIA3 data from Aladin to check on the centroids of the double stars you detected.

Thank you for the suggestions.  I checked one of them (the one in the red circle). Its position is consistent with GAIA EDR3. I also plate-solved both the BXT image and the 1-m telescope image. All the small stars in the BXT image agree with that in the 1-m telescope image.

 

Great validation, thank you for doing this experiment. Did you by any chance measure the S/N ratio in all three images?

Unfortunately not.  I am not sure how to properly measure S/N in such highly altered (deconvolved) images.  That being said, Russ mentioned somewhere that AI4 conserves fluxes and presented some numbers.  I think it is possible to run a more thorough test on this. 

[Gschnettler]

Hello. What a fabulous picture! I used to think that open cluster images didn’t make for great photographs but now I am warming up to them. I’m doing the Astronomical League’s Messier Imaging program which of course includes a lot of open clusters. I can now aspire to results like you’ve obtained.

Quick question: I don’t drizzle when I’m not under sampled because I thought it wouldn’t help. But now it seems like does. I’ve read that in order to drizzle you need to be dithering every frame. Does that rule hold true in a situation like the one above (I.e. did you dither between each exposure)?

[whwang]

Yes, I dither every frame. For a mono sensor and 2x drizzle, I think you will need an absolute minimum of four dither positions. 16 dither positions and more will be much safer. And you need to multiply these numbers by 4 if you plan to do 2x drizzle with an OSC sensor. So you need a lot of dither positions, which essentially imply dithering every exposure.

[andysea]

I think that measuring the standard deviation of the same background area in all three images would provide a sufficient approximation of the noise levels in the tree images, no?

[whwang]

I think that measuring the standard deviation of the same background area in all three images would provide a sufficient approximation of the noise levels in the tree images, no?

Yes and no.  There are many ways to quantify noise in images, and depending on the purpose, some are more relevant while others are not.

 

Let me understand what you want to achieve here.  Are you interested in comparing the noise level of the three non-BXT images, in order to see the effects of the two types of drizzling?  Or are you interesting in comparing what BXT does to the background noise?  

[andysea]

I was just curious about the loss in S/N ratio which is intrinsic to drizzling 2x. The S/N should be worse in quadrature so 4x. Typically that is the price to pay for increased resolution. 

[whwang]

That's what many amateur astrophotographers want to believe, but personally I never think that's the right way to look at things.

 

When we talk about signal and noise, we need to first define the area where signal and noise is measured.  Such an area can hardly be individual pixels.  If we do measure noise in individual pixels (for example, circle a bunch of pixels and measure their standard deviation), then yes, drizzled image can have higher noise.  However, noise in individual pixels have no real meanings.

 

The smallest meaningful area one can possibly define is the size of a point source.  The meaning of point-spread-function is that any structure smaller than that should not exist.  So it makes no sense talking about signal and noise in areas smaller than the PSF.  If the PSF FWHM is 2.5 pixel in the undrizzled image, then it should be 5.0 pixel in the drizzled image.  If we measure S/N in a 2.5-pixel area in the undrizzled image, we should measure S/N in a 5-pixel area in the drizzled image to achieve fair comparison.  Of course, if the images are under-sampled to start with, there is a possibility that the PSF FWHM in the 2x drizzled image is smaller than 2x the PSF FWHM in the undrizzled image.  This means there is a real resolution gain, and this actually can lead to increased S/N in point-like objects in the drizzled image.

 

Back to the real-world example here, the simplest way to look at this is to find the faintest star that you can convince yourself to be real, instead of being noise.  This is essentially to find the star over which the "limiting magnitude" is defined.  An image with fainter limiting magnitude should have higher S/N on small objects.  Can you find a faint star that exists in some of the three images while not (i.e., embedded by noise) in the others?  If so, the image that shows such a critically faint star is deeper, and thus has higher S/N.  Among the three images, I can't convince myself that any of them is deeper than the others.  The quality of faint stars in all three images are comparable, or even almost indistinguishable.

 

Finally, if one really believes numbers, these are what I got:

     

image1  0.615  1.62e-4 

image2  0.653  8.57e-5

image3  0.431  8.94e-5

 

image1 is the undrizzled image.  image2 is the 1x Bayer drizzled image.  image3 is the 2x Bayer drizzled image.  (all before BXT.) The first numbers (from 0.6 to 0.4) are noise measured with the noise evaluation script of PI.  The second numbers (1.6e-4 to 9e-5) are my own measurements using the "sky" function in the NASA IDL Astronomy Library plus some simple clipping to better exclude stars in the noise measurements.  I can't explain any of the numbers.  None of them make any sense to me.  I think all I can say is, since all three images have comparable limiting magnitudes, they have similar S/N.

[Juno18]

I am with you 100%!

 

I found the same thing just recently imaging open clusters and focusing (no pun) on the stars. 

I am using an Explore Scientific ED102 essential series scope reduced to 571mm (image scale 1.35). Drizzling 2x and BXT produced amazing resolution on the tiny binary star systems.

I will drizzle 2x from now on despite the extra time and disk space.

 

A short snip of my results.

Both images drizzled (1x and 2x) and BXT.

 

 

https://drive.google...iew?usp=sharing

 

 

Thanks for sharing and confirming!

Edited by Juno18, 22 January 2024 - 08:55 AM.

[andysea]

Excellent thank you! Given that there is no penalty in SN Ratio, this opens up a lot of possibilities. I was just about to buy the extender for my Epsilon 180 but given your results I can just drizzle 2x and then retrieve resolution by using BXT.

[whwang]

Hi Andy,

 

I see. 

 

It's a complicated question.  If the common wisdom (which I don't agree with) is that 2x drizzle has a 2x penalty on S/N, then a 2x extender also has a 2x penalty on S/N.  So the 1.5x Epsilon extender should have the same S/N penalty as 1.5x drizzle (if there is such a thing).  From this point of view, indeed the extender has a less steep cost on S/N, as the minimum drizzle allowed by most software is 2x, while the extender is 1.5x.  (But again, I don't agree with all these.)

 

In terms of sharpness, I feel you will still get better results with the extender.  According to TAK's charts and claims, it will give you sharper stars (smaller FWHM in arcsec) in addition to the increased pixel scale.  If you want to push the sharpness to your seeing limit, that's still something worth considering.  On the other hand, if you want to maintain the wide field the original Epsilon has while getting higher resolution, drizzle plus BXT is a good way to go.  Maybe you can try this first and see if you like it.

 

Good luck, and let us know what you get!

 

Cheers,

Wei-Hao

[freestar8n]

Hi Andy,

 

I see. 

 

It's a complicated question.  If the common wisdom (which I don't agree with) is that 2x drizzle has a 2x penalty on S/N, then a 2x extender also has a 2x penalty on S/N.  So the 1.5x Epsilon extender should have the same S/N penalty as 1.5x drizzle (if there is such a thing).  From this point of view, indeed the extender has a less steep cost on S/N, as the minimum drizzle allowed by most software is 2x, while the extender is 1.5x.  (But again, I don't agree with all these.)

 

In terms of sharpness, I feel you will still get better results with the extender.  According to TAK's charts and claims, it will give you sharper stars (smaller FWHM in arcsec) in addition to the increased pixel scale.  If you want to push the sharpness to your seeing limit, that's still something worth considering.  On the other hand, if you want to maintain the wide field the original Epsilon has while getting higher resolution, drizzle plus BXT is a good way to go.  Maybe you can try this first and see if you like it.

 

Good luck, and let us know what you get!

 

Cheers,

Wei-Hao

Aggregate measures of SNR may not be affected by sampling - but the appearance of a scene at the pixel level certainly is - and when it comes to sharpening and drizzling presumably you want to let the viewer inspect the scene at a fine level where such factors come into play.

 

So - sure - if you drizzle into an image with smaller pixels you will lose SNR on a per pixel level, and a close up view of the scene will appear more noisy.

 

Similarly if you wanted to make a plot of the intensity representing a gap between two objects - if you drizzle and sample more finely - the detail in that line should increase, but the SNR in each measurement along the pixels will decrease.

 

As for using putative double stars to test for artifacts in the sharpening process - as long as you have a reasonable estimate of the local PSF there is no limit to how finely you can split a double star.  Some claim it is somehow limited by optics and MTF - but there is no limit.  All there is is a reduced confidence in the answer to "Is this a single or double star?"  When the stars are cleanly split there is high confidence, and when they are just touching and appear slightly oblong relative to the putative PSF, the answer will be more error prone.  So it's good to see examples where stars that appear double are accurately detected as such - but there is no hard limit how far it can go.  The likelihood of calling something double when it isn't simply increases as they get closer.  The error is always present at some level.

 

The only way you can be sure that what you are showing represents what you captured is not to apply sharpening.

 

Frank

[whwang]

The apparently higher noise at pixel level (even if there is such a thing) is nothing. The finer pixel scale from drizzle means that you can apply a more aggressive noise reduction and easily make the noise go away to a level comparable to undrizzled version. A good noise reduction routine (like NXT, or other methods combined with proper masking) can wipe out such a superficial noise while not affecting details above the noise level. So I am never bothered by such “noise.”

Edited by whwang, 22 January 2024 - 07:54 PM.

[freestar8n]

The apparently higher noise at pixel level (even if there is such a thing) is nothing. The finer pixel scale from drizzle means that you can apply a more aggressive noise reduction and easily make the noise go away to a level comparable to undrizzled version. A good noise reduction routine (like NXT, or other methods combined with proper masking) can wipe out such a superficial noise while not affecting details above the noise level. So I am never bothered by such “noise.”

??  A pixel has signal and it has noise.  The ratio is the SNR of that pixel.  An image consists of pixels and you look at them and see the signal and the noise.  There is a ton of professional literature on noise in images that focuses on pixel level noise, while at the same time there are astronomical applications that focus on aggregate measures such as a star's SNR.  But both are valid - and when it comes to a human inspecting an image at the pixel level - it's the pixel noise that is seen when you look up close - and the noise and signal are well defined.

 

Smoothing and binning are ways to reduce pixel level noise, but you also lose resolution.  You can do a form of outlier rejection that would remove outliers you consider invalid - but if you are using a software tool that claims to figure out what is noise and what is signal and thereby fix the noisy areas - that is purely an aesthetic fix equivalent to an artist painting over the areas that don't look good.  When it comes to masking and aesthetic "denoising" you depart from being able to talk about noise and signal in a well defined way.

 

Frank

[whwang]

Hi Frank,

Obviously we have very different understanding of S/N and noise reduction. I couldn’t convince you and you couldn’t convince me either. If I were 10 years younger, I probably would spend 100x more time to argue with you, but I am not young any more. So let’s stop here. Others can judge based on the arguments we both provided and based on pictures.