CCD Imager

With your sampling at 0.9 arc sec/pixel, even given Nyquist at 2x sampling, you would not achieve resolution better than 1.8 arc secs. That is quite a lot worse than 1.4 arc secs and would be visually noticeable. I think you have answered your own question with your belief that higher S/N is more gratifying. To me the two most important factors are BOTH S/N and resolution, I treat them with equal respect.

Vlaiv As a follow up on downsizing the image 2x, using the original unprocessed data, the FWHM increased from 1.4 arc secs to 1.6 arc secs. So evidence I wasnt over-sampled with 3x sampling. Adrian

Vlaiv, it is impossible to interpret a JPEG image and also one that is processed. I did a quick clone of the TIFF imaged, resample then increased magnification to match. My result is below. But really I need to go back to original data and make the comparison with resampling. I must add that the original will be much more amenable to deconvolution algorithms like Blur XTerminator.

Indeed and is applied to astro images, but there are differences in its application

I have read Wiki, many other articles and also watched presenters discuss Nyquist. Most make reference to continuous electrical signal. The problem with your proposal is that FWHM varies wildly. It is better to know the best FWHM with an over-sampled system and use that. Should FWHM be higher, you can always bin/resize to suit. Under sampling equals loss of resolution And as most astro imagers suffer from less than perfect mount tracking/guiding/focusing, there is an acceptance that resultant FWHM values are the best they can achieve. However, if the "real seeing" is known, it brings home how their equipment is compromising FWHM. Having near perfect optics, a mount that doesnt require guiding and better autofocus hardware and algorithms, would suit greater over sampling. In other words your proper sampling frequency completely changes. Sorry, not your theory, just what you were advocating.

Nyquist formulated the theory based on telegram electrical signals that have a CONTINUOUS sinusoidal waveform. It has since been adapted to other signal forms including measuring stars. But there are significant differences, not least that you are measuring round signal with square pixels. In simplistic terms, it has been translated that you need 2x sampling to reproduce signal and can I stress this is AT LEAST 2x sampling, the more, the more likely it is to be accurate. Because of the 3D nature and wasted area of square pixels, the consensus in the knowledgeable astro community is that 3x sampling is necessary. I see this in practise and this very M51 image that I have uploaded. Given a sampling rate of 0.47 arc secs, I should be able to resolve 1.4 arc secs, but according to your theory I could resolve 0.94 and when you perform a stellar line graph, its plainly obvious there are insufficient points. Just from eyeballing, I believe the 1.1 measurement is false, purely because it is under sampled.

Here is the processed luminance image taken over 2 nights and shown at 100% full resolution, but please bare in mind a JPEG will reduce its quality, the average FWHM was 1.4 arc secs. I would like to point out the beauty of over-sampling, it gives deconvolution something to get its teeth into. Ive uploaded the luminance only so that you eye is directed to resolution, colour images in this respect are distracting Hopefully now, I have satisfied Olly's curiosity. Adrian

and here is the linear unstretched data, but to perform an analysis you need the raw FITS data. This is purely to give a visual interpretation that Olly was asking for

Never play with a JPEG and stretched data!

I dont like comparing an electrical sine wave to a Gaussian plot of a star, apples and oranges Lets remember that Nyquist 2x sampling was specifically related to continuous electrical signals, a stellar plot is a snapshot and presents a gaussian profile. The Nyquist theorem was adapted to be used for applying to stellar images, measuring circular stars with square pixels has its issues and explains why you need greater sampling. I cant agree with you that a stellar profile is not 3D. Thirty years ago, this was discussed ad nauseum on Compuserve and agreed by many mathematicians and astrophysicists.

Here is the single sub image taken through a blue filter. Stars in the center measure around 1.1 arc secs and periphery around 1.2 arc secs. BUT, a line plot thru stars gives insufficient points to adequately measure, i.e. under-sampled

It was a single sub simply because the seeing was its best for that night, other subs had higher FWHM measurements. As mentioned, the final image which was taken over a couple of nights had a FWHM of 1.4, so if you apply the Nyquist sampling theorem, I need a scale of less than 0.5 arc sec/pixel to take advantage of that excellent seeing, anything more and I am missing out.

A stellar profile has three axes - x-axis (right ascension), y-axis (declination), and intensity. Brighter stars have higher intensities. We shouldn’t compare with a sine wave, a completely different signal, an optical system forms an image of a point source as a Gaussian curve. Let me dig out the image in question and show you a line plot of said image, It is on CN, but I need to find it again for here

That doesnt fit with image analysis experience, when a line plot was drawn through a star, it is obvious there are insufficient points for meaningful measurement. Do go and have a look at the CM discussion

Lol Olly apologies about the spelling, I forgot you were a teacher! The image in question is a single sub and the final image had a FWHM of 1.4 arc secs. I don't think you would be enamoured with a single sub? Adrian

You are misinterpreting, it is the stellar profile that you are measuring and is 3D - x, y and intensity

There was a discussion on CN about am image I took with 1.2 arc sec FWHM. The debate centered on insufficient pixels to properly sample in addition to insufficient aperture! I used the SW Esprit 150. However, I have regularly captured images around the 1.5 arc sec FWHM

In fact the precise calculation from memory is more like 3.2x

Because the Nyquest theorem was applicable to continuous audio signal and astronomical measurements are 3D and pixels are rectangular not circular

You havent heard of Nyquest sampling? I have used a sampling rate of 0.47 arc sec/pixel and been under sampled.

Continuing my theme of faint stuff, I started imaging this at the beginning of July and over several nights, accumulated 20 hours of LRGB data. Taken with a SW Esprit 150 and ASI 6200, all unguided. Adrian

I dont know how Meteoblue calculates their FWHM, I tried to find a reference to it, but alas nothing. However, they may not be far off. Nearly 30 years ago, I performed seeing analysis on the majority of clear nights over one year, using an SBIG STV, utilising the DIMM method. Seeing was mostly sub 2.0 arc secs and often less than 1.5, occasionally less than 1.0 This is the raw base seeing, but you then have to add the effects of optical quality, focus, guiding etc that blurs the FWHM, so users usually end up with a much higher FWHM. Over the many years since I measured raw FWHM, I have been working to reduce additional blurring components, Should you manage to own a high quality triplet refractor and a mount that tracks to less than 0.5 arc sec, your resultant images will have a much better FWHM. Most astro Imagers aim for a sampling of 1.0 arc sec/pixel, a good compromise for the majority of users Adrian

Anything over 0.5 arc sec is under-sampled! Seriously, UK skies offer around 1.5 to 2.5 arc secs FWHM and you need to sample at a rate of 3x for optimal sampling. Not only that, if seeing is better than your optical resolution, you have missed out and if you end up over sampling, you can bin in post to suit your taste. And lastly, deconvolution algorithms just love an over sampled image, give Blur XTerminator a decent chance! Adrian

Great image Peter. Isnt it nice to compare with old photos and see how far we have come. I bet if you re-processed the right hand image with todays techniques, you'll improve it no end, not that it is shabby to begin with. Adrian