Kinds of noise

[Guest]

I've been reading about stacking and how it improves signal to noise ratio. The book talks about how noise originates and seems to be mostly in the sensor and electronics around it. But I wondered if it includes atmospheric noise which causes an image of a star to jiggle about slightly.  I've noticed that when I take a sequence of pictures of a star field that as the preview pops up I can see that they move very slightly from one frame to the next. This is not tracking error because the star stays in the same place over a period of time. I put this down to fluctuations in the atmosphere. The same thing which causes stars to twinkle. Or for example when I look at the moon or planet there is always a slight shimmer. 

So the question is - does stacking reduce the noise caused by atmospheric shimmer?

Cheers

Steve

 

[CraigT82]

It's not really noise as it's real signal. In long exposures stacking doesnt get rid of it as the star's image will be smeared on every long exposure. However other post processing techniques can reduce the smearing effect to make the stars more pint point. 

However if you're taking lots of very short exposures of a star and the seeing is causing the star to shift by a few pixels from frame to frame, then stacking software could align the star to a fixed point before stacking the frames. 

[vlaiv]

As explained - not noise. It is probably not atmosphere either.

That will depend on your sampling resolution and seeing values. To me this sounds like periodic error more than anything. This will move stars frame to frame but overall keep Field of view in same place (or maybe very small drift from first to last sub).

 

[Guest]

I'm still not sure. If I'm observing visually and I look at the moon it's quite clearly shimmering due to atmospheric movement. Or a better example is jupiter.  If you look at it with your eye it's not clear. Occasionally you'll get a couple of seconds when its clearer but still not very clear.  You can see it changing rapidly over time as you watch. It's not just poor optics. Isn't that atmospheric distortion? When you take a video of it with say 1000 frames and stack them then it comes out clear as anything, there are plenty of examples on this forum. So when you are stacking those frames aren't you reducing the 'noise' caused by atmospheric movement?

[vlaiv]

3 minutes ago, woodblock said:

When you take a video of it with say 1000 frames and stack them then it comes out clear as anything, there are plenty of examples on this forum. So when you are stacking those frames aren't you reducing the 'noise' caused by atmospheric movement?

When you stack say 1000 frames of moving Jupiter - you get relatively blurry mess.

Then comes magic of wavelet sharpening or deconvolution that exploits high signal to noise ratio of such stack and you are able to do something called frequency restoration. Without it, you'll still have blurry thing. With it, you'll get image better than is possible with naked eye (or rather with eyepiece).

This is because optics of telescope blurs the image somewhat and frequency restoration is able to sharpen up even that. Complicated topic.

In any case - you are now referring to seeing, but that seeing is on scales less than dozen of milliseconds (shimmers are rather fast). I'm guessing that your exposures are at least couple of seconds long if not longer. Seeing averages in that time. Really poor seeing needs a bit more - like 8-10 seconds to average out, but it does. If your exposures are in seconds range or longer - you are seeing periodic error and not atmospheric seeing.

And it is not the noise. Noise is related to uncertainty of pixel value - regardless where that pixel "falls". Distortion by seeing (or rather just one component of distortion - namely tilt) moves pixel out of it's position and you can compensate that by calculating average pixel position (not value) out of many frames. That is what planetary stacking software does - it "returns" pixel into proper place by distorting back every frame. However, tilt is only one component of aberrations that seeing brings. If your exposure is not fast enough to freeze the tilt part of seeing - you'll get motion blur. Other aberrations from seeing just manifest as regular blur and since it is random - it just blurs more or less (when you view it) - there are even moments when image is relatively clear. Point of lucky imaging is to capture these "clear" moments - without too much blur, or when only tilt is present.

It is quite a bit complex topic. We can discuss it in length if you are interested.

Noise is uncertainty in pixel value - average many same pixels (just make sure you place them in the right spot - both planetary and deep sky stacking software does that, just differently) and you reduce noise.

[CraigT82]

To illustrate vlaiv's first point in his post above, here is a sample of lunar video showing the shimmering effect you've noticed.  The exposures for this video were only a couple of milliseconds.

The next image is 1000 frames stacked: Still blurry but with much better signal to noise ratio.

The final image is the sharpened version of the stacked image (the frequency restoration)

[Guest]

I think you are right about Periodic Error causing stars to jump around from image to image.

In Craig's video of the moon you can see that the image is shifting around due to movements in the atmosphere either inside or outside the telescope.  Is that effect removed because the frames were aligned before stacking or is it the stacking itself or maybe it's a bit of both.

If you were to sharpen a single frame of the video how would it compare with the stacked and sharpened picture?

 

 

 

[CraigT82]

Yes the movement between individual frames is accounted for during the alignment phase of the stacking procedure. The key for this is that the exposures are short enough to limit the blurring caused by the movement on any individual frame.

The overall objective of the stacking is to increase the signal to noise ratio as you know, and this is what allows for aggressive sharpening without image breakdown.

Below is a single raw frame, and a sharpened version of the same frame.  Note how noisy the sharpened version is.

 

[ollypenrice]

Poor seeing, AKA atmospheric distortion, has never given me any visually apparent stellar movement on the chip. Its frequency is too high so that even a one second sub has largely blurred it out. I do use longer subs to focus, typically 3 seconds, in order to blur the seeing effects out fully and give stable full width half max values. Bad seeing shows itself this way - poor and unstable FWHM values. I think Vlaiv's suggestion of a PE issue is more convincing.

Olly

Edited April 29, 2020 by ollypenrice
Typo

[Guest]

Thanks everyone,  Sorry to keep going on.

When you look at Craig's video of the moon it is clearly moving about, Suppose that's not the moon but a starfield. In that case if you did exposures of say 30 seconds all the stars would be blurred on each sub. From what you're saying, stacking does nothing at all to alleviate that blurring in the stacked image.

One last question.  Is sharpening just a cosmetic thing to make the pictures look better or is it actually allowing you to see more detail? Also does sharpening apply to both starfields and deep sky as well as planetary and lunar images?

 

[vlaiv]

In deep sky imaging (long exposure), yes, seeing blurs each star into sort of gaussian profile. Seeing is measured by that - FWHM of star profile in long exposure (usually just 2 second exposure is enough to characterize seeing in terms of FWHM).

One of important parts of DSO imaging is to choose proper sampling rate to record all the detail there is in the image - and that depends on seeing, scope aperture and tracking / guiding precision combined. If your sampling rate is good - image will not look blurred. If you over sample - it will look blurred when viewed on 100% zoom.

Frequency restoration is real thing - it shows real details. There is upper limit to how much detail can be restored and it depends on aperture of telescope used. You may have seen graphs like this one:

Left is profile of the star that is blurred by optics alone - so called Airy function. Right is graph that shows attenuation (in this particular case - one obstructed - red line, and one clear gray line, aperture). This graph represents attenuation by frequency / detail. You can see that vertical axis is numbered 0-1. Line represents how much of a value particular frequency keeps. At some point - line reaches 0. This means that all frequencies above that one are effectively killed off - set to 0. You can't restore something that has been set to 0. You can restore something that has been attenuated to 20% of its value - just divide it with 0.2 and you'll get original value. But if you try to divide with 0 - you'll get infinity, so it is impossible to restore those frequencies above certain threshold frequency - and that depends on aperture size.

Atmosphere acts in similar way to aperture - except it is random. We can approximate impact of atmosphere by Gaussian type blur (or sometimes Moffat in some cases). Gaussian type blur - never reaches 0, not even at infinitely high frequencies. However, this is only approximation and we always have upper limit imposed by telescope aperture.

You might notice something here - we are "boosting" particular frequencies by dividing with number smaller than 1. This is the same as multiplying by number larger than one - or just simply getting particular frequency values to be larger. That is essence of frequency restoration - like when you have audio equalizer and you amplify some frequency range. Maybe even better comparison for this would be - you increase volume.

Increasing volume is fine if you have nice music, but if you have noisy music - increasing volume will increase noise as well.

This is why SNR part is important - when you sharpen image - you increase certain frequency components and you in the process increase noise on those frequencies. If you want that noise not to be visible in the final image - you need to have good enough SNR so that boosted noise is still small.

This is possible in planetary imaging because planets are relatively strong sources and we stack thousands of subs - which means we further increase SNR by factors of 30-50 and sometimes even more (imagine stacking 10000 subs in good seeing - that will boost snr by factor of x100).

In DSO imaging we stack hundred of subs, and single sub is noisy, so overall SNR is not great. In fact, we don't have much SNR to spare and are happy if SNR is good enough to render image properly. For this reason, sharpening is seldom used in DSO images - and only in brightest parts where SNR is good.

 

[Guest]

Thanks Vlaiv, sorry to be so dumb. When you refer to frequency I assume you're not talking about cycles per second (hz).  Is this to do with resolution (dots per mm) or something like that.

[vlaiv]

1 hour ago, woodblock said:

Thanks Vlaiv, sorry to be so dumb. When you refer to frequency I assume you're not talking about cycles per second (hz).  Is this to do with resolution (dots per mm) or something like that.

It has to do with 2d signal that represents image.

Any signal can be decomposed into sum of sine/cosine waves - Fourier analysis. With sound, we are talking about cycles per second. With image we are talking about cycles per unit length - spatial frequency.

It is related to resolution of the image but not in simple sense - high frequency = small detail, low frequency = large detail. There is such relationship to a small degree, but frequencies represent contrast more than actual detail / features.

This image can be used to understand:

In order to form a pulse train shape function - you need infinite frequencies (because it has very sharp edges - vertical ones), but if you limit yourself to finite frequencies, depending on how "fine grained" you want to be - you can either have just plain sine wave - edges will be very smooth and contrast will be gradually varying, or you can add more frequencies (middle ones) - and you will get green line - closer to what we want but still smooth, or add even more higher frequencies and get blue line - again closer approximation and sharper detail.

Now imagine that above pulse train is actually pixel intensities in an image - like checkerboard pattern or something like that. Using only low frequencies will make it smooth - and image will look blurred. Add high frequencies back and you'll get "sharper edges" - or image will be sharper.

 

[Guest]

Thanks Vlaiv, I've got that.  I think the 't' in your equation is not time. I think it represents a distance or position on the image.

Steve

 

[vlaiv]

19 minutes ago, woodblock said:

Thanks Vlaiv, I've got that.  I think the 't' in your equation is not time. I think it represents a distance or position on the image.

Steve

 

That is correct - I just used above image for illustration of Fourier transform of signal.

[ollypenrice]

5 hours ago, woodblock said:

Thanks everyone,  Sorry to keep going on.

When you look at Craig's video of the moon it is clearly moving about, Suppose that's not the moon but a starfield. In that case if you did exposures of say 30 seconds all the stars would be blurred on each sub. From what you're saying, stacking does nothing at all to alleviate that blurring in the stacked image.

One last question.  Is sharpening just a cosmetic thing to make the pictures look better or is it actually allowing you to see more detail? Also does sharpening apply to both starfields and deep sky as well as planetary and lunar images?

 

This would be perfectly true if you ever imaged a starfield at the resolution of a lunar-planetary imager and with comparably short sub-exposure times - but you don't. It's a combination of very high image resolution and very short exposure time which makes the movement visible. Various 'steps' in the movement are frozen. Longer exposure and lower resolution will blur out this level of movement. That's why nobody can capture M31 with the detail found in a Damian Peach Jupiter image.

One last question. Sharpening algorithms take various forms but they are derived from the data so they are more than cosmetic until they are overdone, at which point they create and even 'sharpen' artifacts. I can't speak for other people but I think most of us in deep sky imaging will avoid sharpening stars but will sharpen galactic details and, perhaps paradoxically, gassy structures in nebulae. (Why not sharpen stars? Because their visibility at all in our pictures is little more than an artifact. A perfect imaging rig of amateur resolution would make them all land on just a single pixel. In the final image they would hardly be visible at all. Optical laws mean that, in fact, they spread onto many pixels and imaging reality follows the star chart convention of brighter stars looking bigger. We stick with that.

We can have some confidence in our sharpening algorithms when they extract new details which are in accord with those of far higher resolution instruments like the Hubble and when they also agree with independent capture and processing results from other amateurs. In general they do this.

Olly

Edit. Thinking again about sudden shifts in stellar position I would suspect that play in the focuser or camera adapters (or even the chip) would be prime candidates.

Edited April 29, 2020 by ollypenrice