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Is Nyquist good for camera adaptation in video astronomy?

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#1 Jan_Fremerey

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Posted 05 February 2023 - 05:26 AM

Due to atmospheric seeing astro images typically jiggle around on camera chips over distances much larger than a single pixel separation. In video astronomy, therefore, single frames are broken up into small segments. These are subsequently aligned and stacked on an output grid at their most frequent positions for optimum enhancement of image detail. The original camera grid structure gets widely lost due to incoherent placement and stacking.

 

So the Nyquist criterion will make sense for selection of the output rather than the camera grid. It appears reasonable to set the output grid fine enough to register the “Rayleigh-dip“ with illumination profile “0o0“ of a double star image. This condition will be given with an output grid of 2/3 the separation according to what Nyquist recommends for the camara grid in case of undistorted optical signal transmission, i.e. without seeing, alignment and stacking.

 

We have checked the above reasoning by comparing the Jupiter image of a 10“ f/5 mirror collected by a 3.75 µm pitch camera (Point Grey Chameleon) with corresponding images derived from simulated lower resolution cameras. Simulated pixel sizes were virtually enlarged for comparison by 2x and 3x linear reduction (soft binning) and subsequent re-enlarging of the original high-resolution output image. As can be seen from the following GIF animation, image quality starts to significantly degrade at optical apertures only below about f/D = 2*p/µm where p denotes the camera pixel pitch in µm.

 

Jupiter_2010_Zwischenverkleinerungen.gif

 

By reference to Nyquist many experts in the field of amateur astronomy still recommend f/D > 3.5*p/µm for minimum adaptation of high resolution astro cameras.

 

In view of our above results a 2,4 µm pitch camera can now be placed right at the primary focus plane of a typical f/5 Newton telescope without Barlow enhancement for full resolution imaging. Inserting a 2x Barlow magnifyer would require 4x longer exposure times, and provide 4x less video frame rate and FOV area, see [1][2].

 

CS Jan


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#2 BQ Octantis

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Posted 05 February 2023 - 06:10 AM

Applying the Rayleigh (or even Dawes) criterion as the detail limit for an extended object is specious. The resolution limit set by the PSF is only relevant to a pair of point sources of equal brightness well below saturation.

 

For extended objects such as planetary disks, the image has details (in Nyquist language, an information rate) well below the PSF set by the convolution of the MTF and ESF of the optic.

 

See Edmund:

 

https://www.edmundop...nsfer-function/

 

and Sacek:

 

https://www.telescop...n.htm#mentioned

 

Once you establish the information rate of the system applied to the details of the target, you can apply the Nyquist criterion for sampling.

 

Suggest moving this topic to the Planetary Imaging Forum for more rigorous treatment.

 

Cheers,

 

BQ


Edited by BQ Octantis, 05 February 2023 - 07:03 AM.

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#3 Jan_Fremerey

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Posted 05 February 2023 - 09:24 AM

For extended objects such as planetary disks, the image has details (in Nyquist language, an information rate) well below the PSF set by the convolution of the MTF and ESF of the optic.

Thank you for your early reply and for providing links to theoretical background. Please note that I'm just trying to explain my high-resolution imaging results that apparently don't comply with established theories.

 

Thanks also for your suggestion to move this topic to the planetary imaging forum. I understand that my favourite high-resolution lunar and deep sky imaging [2] is explicitely excluded there.

 

CS Jan



#4 BQ Octantis

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Posted 05 February 2023 - 10:28 AM

The current rule-of-thumb for "ideal" sampling for planetary and lunar is f/D = 5*p/µm. But you can always undersample—indeed, drizzle stacking allows you to recover some of the detail lost to undersampling. So you might even be able to image at 1.37*p/µm and recover the detail you would have had if you imaged at 2.0*p/µm (which the simulation does not account for). And with a large enough aperture there's no need to bother with Nyquist—for example, the Hubble uses 0.8*p/µm for planetary.


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#5 Jan_Fremerey

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Posted 05 February 2023 - 12:23 PM

The current rule-of-thumb for "ideal" sampling for planetary and lunar is f/D = 5*p/µm.

How is this rule of thumb justified? I agree that drizzle stacking allows some significant gain in image recovery. In the present case, however, I didn't make use of, so I'm not able, in fact, to recover from 1,37. Yet my intermediate reduction test apparently shows that the above rule is far from reality even without drizzle stacking.


Edited by Jan_Fremerey, 05 February 2023 - 12:33 PM.


#6 BQ Octantis

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Posted 05 February 2023 - 01:02 PM

I first came across the recommended sampling range in Lodriguss's documentation for planetary capture with a DSLR. He also references the 3.5*p/µm as a bare minimum, but without justification.

 

Separately, the Planetary Forum vigorously defends the 5*p/µm rule with a loose mathematical proof that similarly fudges the Nyquist criterion—but still uses the PSF as the basis of the detail limit.

 

For my part, I measured the performance limits of my Mak 180 in exquisite seeing on Jupiter against a Hubble image that was taken two days later. The detail limit appeared to be closer to the MTF than the PSF (see the Edmunds link for the mathematics). But the appropriate sampling limit ultimately depends on the target brightness and detail contrast.

 

BQ



#7 Tulloch

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Posted 05 February 2023 - 04:13 PM

I've found the "5x rule" works pretty well most of the time.

 

In exceptional seeing you can push this to 7x, Niall MacNeill has a great video on YouTube where he discusses his sampling ratio (from about the 17:30 mark of this video) of 6.9x the focal ratio.

https://www.youtube....h?v=07g76_W0iO8

 

Andrew


Edited by Tulloch, 05 February 2023 - 04:13 PM.


#8 Jan_Fremerey

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Posted 05 February 2023 - 04:42 PM

(1) He also references the 3.5*p/µm as a bare minimum, but without justification.

(2) Separately, the Planetary Forum vigorously defends the 5*p/µm rule with a loose mathematical proof that similarly fudges the Nyquist criterion

(3) For my part, I measured the performance limits of my Mak 180 ...

In the first two cases I assume that theoretical treatment does not consider the effect of seeing, aligning and stacking which is the basis of my above theoretical considerations.

 

In my practical investigation as visualized in above GIF animation we see that 2,9*p/µm is not better than 2,0*p/µm. So I don't see any reason why anything > 2,9 should make a significant difference.



#9 BQ Octantis

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Posted 05 February 2023 - 04:54 PM

Actually, the 5-7 rule does account for seeing. Both Lodriguss and the Planetary Forum recommend 5*p/µm for average seeing and 7*p/µm for exceptional seeing.

 

If you're happy with your results at 2*p/µm, it comes with all the benefits you already mention, plus a wider field (so more moons). But I would highly recommend actual tests vice resampling simulations before you chuck your Barlow…

 

BQ


Edited by BQ Octantis, 05 February 2023 - 05:25 PM.


#10 Jan_Fremerey

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Posted 05 February 2023 - 05:12 PM

I've found the "5x rule" works pretty well most of the time.

In exceptional seeing you can push this to 7x ...

Thanks Andrew for your recommended figures with reference to practical experience, and for linking to the video that I just watched from 17:30. Please note that my above results have as well been obtained on the basis of real imaging with no difference between 2,0 and 2.9*p/µm. Why should I expect any significant improvement from 5x or 7x ?

 

CS Jan
 



#11 Jan_Fremerey

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Posted 05 February 2023 - 05:29 PM

I would highly recommend actual tests vice resampling simulations before you throw away your Barlow…

With my ASI178MM camera right at the f/5 primary focus of my 10" mirror I don't use Barlows any longer ...
 

CS Jan



#12 Tulloch

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Posted 05 February 2023 - 05:42 PM

Thanks Andrew for your recommended figures with reference to practical experience, and for linking to the video that I just watched from 17:30. Please note that my above results have as well been obtained on the basis of real imaging with no difference between 2,0 and 2.9*p/µm. Why should I expect any significant improvement from 5x or 7x ?

With 2 pix/um, you are sampling at about 1 pixel for each FWHM, sampling at a higher rate would get you a better view of the transition. 

 

You appear to have simulated a result at a lower focal ratio and stated that it's no better than at the higher one. However, it would have been more interesting to have take another image using a 3x barlow at the same/similar time (to get you close to the "5x rule" value) and compared those two. 

 

Of course, you are free to sample at whatever focal ratio you choose to, I haven't seen enough proof from your theoretical images to change the way I'm currently imaging.

 

Andrew


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#13 Jan_Fremerey

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Posted 05 February 2023 - 07:18 PM

I haven't seen enough proof from your theoretical images to change the way I'm currently imaging.

Hi Andrew,

 

the above images are in no way theoretical. They are just resampled from a real 2.9*p/µm original to 2.05 and 1.37 by real 2x and 3x linear reduction (soft binning) and subsequent interpolating remagnification by 2 and 3, respectively. Thereby, 75% of original image information has been thrown away in case of 2x intermediate reduction and 89% in case of 3x.

 

I won't urge anyone to image at 2,0*p/µm. I rather want to make clear that in vido astronomy, contrary to prevailing opinion, high resolution image quality does not really degrade down to that limit. You will find several examples (Moon, M3, Mars) on top of my website that were taken with 10" aperture and 2.4 µm camera pitch at 1.27 m focal length, i.e. with camera resolution of 0.39 arcsecs per pixel.

 

CS Jan

 

 



#14 BQ Octantis

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Posted 05 February 2023 - 08:51 PM

So is this a test of the quality of interpolation to recover detail lost to downsampling at 100% display scale…so not relevant to the imaging process at all? Shouldn't we also assess multiple interpolation and sharpening methods?

 

In exquisite seeing, I've often zoomed into my Jupiter and Mars animations to 1.5-2x sampling scale for a better look at what's going on…and I image those at ~9-10*p/µm!

 

Try it yourself…click on the full size PNG link and use your browser to zoom in to 200% scale.

 

GIF Preview @ ~30% scale

post-273658-0-14127600-1598621465.gif

Animated PNG @ 100% scale

 

Then zoom out to the minimum (30%). That is 2.5-3*p/µm. You can't interpolate your way from there back to 200%.

 

BQ


Edited by BQ Octantis, 05 February 2023 - 09:05 PM.


#15 Jan_Fremerey

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Posted 06 February 2023 - 03:51 AM

Try it yourself…click on the full size PNG link ...

Single frames of your 100% GIF animation are of very poor quality, so it does't make sense to do any processing on that basis.
 

 



#16 BQ Octantis

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Posted 06 February 2023 - 05:43 PM

Single frames of your 100% GIF animation are of very poor quality, so it does't make sense to do any processing on that basis.

The link to the 24-bit APNG is below the GIF.



#17 Jan_Fremerey

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Posted 06 February 2023 - 07:12 PM

The link to the 24-bit APNG is below the GIF.

This is a single frame taken from your 100% GIF with and without intermediate reduction to 20%:

 

BQ_Jupiter_02x5_58vdvy77.gif

 

CS Jan



#18 Jan_Fremerey

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Posted 07 February 2023 - 04:45 AM

... this is a single frame extracted from your 30% GIF after 4x magnification:

 

BQ_Jupiter_30_frame_2_dSinc400.jpg

 

When imaging at down to f/D = 2*p/µm you would largely benefit from reduced shutter times for lower seeing blur and much more frames per second to stack for better signal-to-noise ratio.

 

CS Jan


Edited by Jan_Fremerey, 07 February 2023 - 04:57 AM.


#19 BQ Octantis

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Posted 07 February 2023 - 04:49 PM

The 100% scale is an Animated Portable Network Graphic (APNG) file format. It does not have the 256-color gamut limitation of a CompuServe animated Graphics Interchange Format (GIF).

 

In your first example, you can clearly see the detail lost on the text, but the fine detail that is lost on the planet is masked by the GIF gamut deficiency. I don't know what you mean to show in the second example, but the deficiency of upscaling the GIF format is obvious.

 

I shoot with a DSLR. Shutter speed is fixed at 33ms at ~10 fps. I have found that the depth-of-field I get at ~9*p/µm provides very obvious peak focus that is much more forgiving than at lower magnifications. Jupiter has sufficient SNR for this, as do Mars, Venus, and the Moon. Saturn and further out do not—indeed, I shoot them at prime.

 

Cheers,

 

BQ



#20 Jan_Fremerey

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Posted 07 February 2023 - 07:14 PM

In your first example, you can clearly see the detail lost on the text, but the fine detail that is lost on the planet is masked by the GIF gamut deficiency.

In fact, I extracted the first image from your 100% APNG, just erroneously referred to as "GIF". If extracted frames don't work properly, perhaps we should better start from a single high-quality image. Otherwise, I don't really see less planet detail after resizing the downscaled APNG frame.

 

CS Jan



#21 BQ Octantis

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Posted 07 February 2023 - 09:45 PM

What downsample → upsampling algorithm are you testing? I have many options in Siril, Photoshop, RawTherapee, and Gimp (probably with slightly different implementations):

 

  • Nearest Neighbor
  • Bilinear
  • Bicubic
  • Pixel Area Relation
  • Lanczos-4
  • NoHalo
  • LoHalo

 

But as before, testing resampling algorithms is not the same as testing different image sampling configurations.

 

BQ



#22 BQ Octantis

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Posted 07 February 2023 - 09:56 PM

Check out this comparison of several more exotic methods of upscaling:

 

https://legacy.image...mpling_examples



#23 Jan_Fremerey

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Posted 08 February 2023 - 04:12 AM

What downsample → upsampling algorithm are you testing?

But as before, testing resampling algorithms is not the same as testing different image sampling configurations.

I'm using Fitswork with linear downscaling and dSinc for resampling. Please note hat I am not "testing" algorithms but rather try to demonstrate an outstanding benefit of video astronomy: the effective extinction of camera grids by destructive drizzle stacking, in fact, allows processing of output images on finer than camera grids, and Nyquist will apply to the output rather than to the camera grid. The downscaling/resampling procedure is just for identifying the practical limit of that grid refinement, i.e. where image detail significantly starts to degrade.

 

CS Jan



#24 Jan_Fremerey

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Posted 09 February 2023 - 07:08 AM

But as before, testing resampling algorithms is not the same as testing different image sampling configurations.

If you don not trust my retro-processing of the above 2010 Jupiter image, here is a new one from yesterday for better understanding:

 

Mars_230208_pf43ybm5.gif

 

The image this time was really taken at f/D = 2.05*p/µm with Mars image as "seen" by the 2.4 µm camera grid as well as by the 1.6 µm grid generated by the "Drizzle 1.5x" procedure in AutoStakkert! v3. Final processing is done on the basis of 4x upscaling the drizzle frame by interpolating dSinc algorithm in Fitswork. The final image size corresponds to direct camera adaptation at f/D = 12.3*p/µm.

 

CS Jan



#25 BQ Octantis

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Posted 09 February 2023 - 07:18 AM

I'm sorry, Jan, but I'm no longer understanding what you are trying to say.

 

Nyquist is a sampling rate requirement to not lose information to aliasing. Applied to imaging, it is most relevant to prevention of the color moiré pattern caused by undersampled interpolation of the Bayer array in a one-shot RGB camera.

 

https://www.imatest....quist-aliasing/

 

 

The RGB Bayer array has half the resolution of the sensor specification—i.e., each input Bayer BGGR cell occupies 4 output pixels. The deBayered output is therefore interpolated (using any of several algorithms) to fill in the holes for each color to achieve the output resolution. Drizzle is an interpolation method that uses the natural dithering of the image by the atmosphere to fill in the holes in the Bayer pattern for each color. Drizzle can also be used to upscale.

 

Nyquist is irrelevant to the detail on an extended object because there is no fixed detail limit on an extended object.

 

 

But Nyquist sufficiency was the very title of your post. But against "video" astronomy.

 

Your argument seemed to be

 

I posit that the f/D ≥ 3.5*p/µm sampling rule-of-thumb is invalid. I believe that the rule should be ≥2.0*p/µm.

 

Your proof is then with simulations. You downsample your image with linear interpolation, and then compare an unscaled output with a downsampled image upscaled to the same size—which introduced the scaling artifacts of blur, halo, tonal drift, moiré, and jaggies. But your blink comparison seemed to support your argument that the difference is imperceptible.

 

You conclude with a description of drizzle as "destructive", and then refer to Nyquist being relevant to the final image and not the camera grid. And your last demonstration compares drizzle on a grayscale sensor with dSinc upscaling.

 

And I have not seen any video yet.

 

So I'm puzzled as to your line of reasoning—and even what you are trying to convey.

 

So I'm not sure how to respond.

 

BQ




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