Astronomy tools ccd suitability

[vlaiv]

Seems that many people rely on this tool and given that its hosted / maintained by @FLO

I think it would be wise to revisit validity of the information presented by it.

I've been several times involved in discussions where people refer to above tool and either accept very flawed advice offered by the tool, or question otherwise sound setup as it is not in the "green zone" according to the tool.

There are also several statements made on that page that are simply false and should be corrected.

 

[malc-c]

LOL - just entered my camera and scope details and selected poor seeing...

Quote

The ideal pixel size for Poor Seeing (4-5" FWHM) seeing is: 1.33 - 2.5" / pixel.

This combination leads to slight over-sampling. Will require a good mount and careful guiding

Were we not discussing this in another thread 😉

[vlaiv]

Yes and things like this as well:

It further says that 2.2"/px with 80mm leads to "significant undersampling"

Or this part from "theory explanation":

Quote

The theory

In the 1920s Harold Nyquist developed a theorem for digital sampling of analog signals. Nyquist’s formula suggests the sampling rate should be double the frequency of the analog signal. So, if OK seeing is between 2-4” FWHM then the sampling rate, according to Nyquist, should be 1-2”.

There is some debate around using this for modern CCD sensors because they use square pixels, and we want to image round stars. Using typical seeing at 4” FWHM, Nyquist’s formula would suggest each pixel has 2” resolution which would mean a star could fall on just one pixel, or it might illuminate a 2x2 array, so be captured as a square.

and so on ...

 

[Pitch Black Skies]

8 hours ago, vlaiv said:

Seems that many people rely on this tool and given that its hosted / maintained by @FLO

I think it would be wise to revisit validity of the information presented by it.

I've been several times involved in discussions where people refer to above tool and either accept very flawed advice offered by the tool, or question otherwise sound setup as it is not in the "green zone" according to the tool.

There are also several statements made on that page that are simply false and should be corrected.

 

I used the tool to help choose my current camera.

What are the false statements and flawed advice that needs to be corrected?

I'm just a newcomer so would like to be more aware for going forward.

Thanks

Edited January 31, 2022 by Pitch Black Skies

[FLO]

Astronomy Tools and Clear Outside are both overdue an update (the pandemic distracted us) and you are both welcome to offer advice and make suggestions.

Contact Astronomy Tools

Contact Clear Outside

Grant will likely do or oversee the updates so if you contact us please be constructive - he has no time for snarky 🙂 

Steve 

[vlaiv]

Just now, FLO said:

Astronomy Tools and Clear Outside are both overdue an update (the pandemic distracted us) and you are both welcome to offer advice and make suggestions.

Contact Astronomy Tools

Contact Clear Outside

Grant will likely do or oversee the updates so if you do contact us please be constructive - he has no time for snarky 🙂 

Steve 

Is it ok if I do it here? I already posted several times what I find to be substandard / wrong, but I would like it to be open to a discussion so people can have their input on the matter?

[FLO]

1 minute ago, vlaiv said:

Is it ok if I do it here?

Yes, of course. 

1 minute ago, vlaiv said:

I already posted several times what I find to be substandard / wrong, but I would like it to be open to a discussion so people can have their input on the matter?

Have you ever contacted us regarding your concerns? 

Steve 

[vlaiv]

14 minutes ago, FLO said:

Yes, of course. 

Have you ever contacted us regarding your concerns? 

Steve 

Actually no. That is probably mistake on my part.

I just assumed that some of staff members are reading topics on here and that they would pick up on that chatter. I'm also not familiar with level of communication between moderators and staff at FLO - I also assumed that if any of moderators picked up on that - they would let you know.

Since no change was happening, I decided to start this thread (and mention FLO - so it would get the attention and we could all participate in this).

 

[Mr Spock]

As a Mod, don't look at me - all this technical stuff is like voodoo  I have no clue what you are saying.

On a more serious note, there are many members on here with huge amounts of knowledge. Some sort of collaborative effort could produce a very competent guide. Everyone has different areas of expertise and together could be quite effective.

[FLO]

18 hours ago, vlaiv said:

Actually no. That is probably mistake on my part.

If you had contacted us you would have found us receptive and grateful. 

Before we pick it apart let's remember how Astronomy Tools came into the world: In 2014 Grant offered to build a set of tools for our colleagues working on FLO's Helpdesk. We wanted them to have easy access to reliable information, rather than using various separate online tools. The project also enabled us to develop and improve some of those tools. When built we decided to make 'Astronomy Tools' publicly available so everyone could use it. Free of charge. 

Regarding the Astronomy Tools CCD Suitability Calculator: In 2014 (nearly eight years ago!) the guidance available to us was more basic than it is today. Much of the information included was based on lookup tables provided by leading camera manufacturers. The explanatory text was largely written for us by a prominent astrophotographer. I won't mention his name because he is a respected forum member and it isn't his fault we haven't updated his text with the new thinking and information available today.

When launched, Astronomy Tools was heavily scrutinised both on and off SGL then edited until it properly represented the best knowledge and information available at that time. But telescopes, cameras and best practices have evolved. Of course it needs updating. We should have done it sooner but it never seemed to rise far enough up the todo list. Today we are a larger company with more resources and the pandemic is easing so I am confident we soon will. When we do, it will continue to be available free of charge. 

HTH, 

Steve 

[vlaiv]

In any case, let's start at the beginning - I'll make series of short posts - outlining what is flawed and then we can think of the way to make it better.

This one will address errors on theoretical side. I'll try to cite sources for further verification on claims that I make.

Quote

A telescope focuses a star as a round point of light. Assuming high quality optics, the diameter of the point of light is determined by the telescope’s focal length (longer focal lengths result in larger star diameters) and the sky's ‘seeing’ conditions (atmospheric dispersion spreads the point of light, making it larger). Short focal length telescopes and ideal seeing conditions provide the smallest stars, longer focal lengths and less favourable skies produce larger stars.

This is not entirely false, but here is what I would use instead:

"Star point actually depends on several variables - seeing conditions, telescope aperture and hence airy disk / spot diagram and mount tracking performance. These all add up together to produce PSF in final image."

Even if telescope is high optical quality - it does not mean that it will be diffraction limited. That is often not the case - even with top line products if field flatteners / coma correctors are used. There are always tradeoffs - and if we correct for serious aberrations across the field - we can introduce minor aberrations even on axis.

This should be taken into account - if we assume diffraction limited performance of the telescope - it should be noted that it is "best case" scenario and that actual PSF in the image might be larger.

Quote

The challenge

For a star to retain it's round shape when viewed on your screen or photograph it’s diameter must cover a sufficient number of pixels. Too few and the image will be 'under-sampled’, the stars will appear blocky and angular'. For a smoother more natural look more pixels are required, but not too many because if you use more pixels than are necessary to achieve round stars the image is 'over-sampled’. Over-sampled images look rather nice because the stars are round with smooth edges but if you have more pixels than are necessary why not use a reducer to reduce the telescope’s effective focal length, which makes the image brighter and enables you to fit more sky on your sensor. In affect, over-sampling reduces field of view.

Star won't be appear blocky or angular if it is under sampled. This is myth and is consequence of interpolation / resampling algorithm used.

To demonstrate this effect - I'll use single pixel - representing very under sampled star. I'll upsample it considerably using different resampling methods:

this is single pixel - enlarged x20 so it can be clearly seen.

First one is enlarged using Nearest Neighbor interpolation method. Second is enlarged using Linear interpolation, third one using Cubic interpolation and so on. There are many interpolation algorithms used. All produce different result.

We often think of pixel being that first image - like a little square - but it is not. Mathematically, pixel is dimensionless point - it is just value at coordinate. As such, when we reconstruct image from it (or collection of them) - we need to do interpolation of some sorts - choice of this interpolation will give different resulting images. One will create "blocky" looking pixel, but others will produce "diamond" shape, or circular shape - or even shapes that start to resemble airy pattern (and for the same reason as airy pattern is created).

Moral of this part:

- undersampling is not bad and will not lead to blocky stars if we handle our data properly

- over sampling look as nice as properly sampled images when scaled up using one of these advanced interpolation algorithms

- Over sampling does not reduce field of view. Focal length and size of sensor do that.

Over sampling is much more sinister than this - it is very bad because it costs us signal to noise ratio - or in another words - it slows down our setup. Forget F/ratio and all that. Take F/4 setup and make it over sample and it will be sloooow.

Quote

The theory

In the 1920s Harold Nyquist developed a theorem for digital sampling of analog signals. Nyquist’s formula suggests the sampling rate should be double the frequency of the analog signal. So, if OK seeing is between 2-4” FWHM then the sampling rate, according to Nyquist, should be 1-2”.

There is some debate around using this for modern CCD sensors because they use square pixels, and we want to image round stars. Using typical seeing at 4” FWHM, Nyquist’s formula would suggest each pixel has 2” resolution which would mean a star could fall on just one pixel, or it might illuminate a 2x2 array, so be captured as a square.

There are several things wrong with this.  First, Nyquist theorem is proven mathematical theorem so there is really no doubt about what it says or is it correct or not.

It states following: For band limited signal, if we want to capture / reconstruct completely and faithfully (exact match) - we need to (point) sample it at frequency that is at least twice the highest frequency component of the signal.

FWHM should not be equated with highest frequency component of band limited signal. Saying that 2-4" FWHM requires 1-2"/px sampling is wrong as FWHM does not represent highest frequency component of the signal.

FWHM of 4" with sampling of 2"/px - does not mean that star will either fall on single pixel nor on 2x2 pixels.

Here is 1D Gaussian profile with plotted FWHM. I added "pixels" in two different rows / offsets - one representing centered pixel on star and other representing star centered between two pixels. You can clearly see that star profile will cover 6 or more pixels in either case as it extends considerably beyond FWHM "belt".

Quote

The solution

It is better then to image with a resolution 1/3 of the analog signal, doing this will ensure a star will always fall on multiple pixels so remain circular.

Our calculator, at typical seeing of 2-4”, uses the Nyquist formula of 1/2 and the 1/3 to stop stars becoming square so the optimal range is between 0.67” and 2”. (0.67 = 2 / 3, 2 = 4 / 2).

In summary, we are using Nyquist as a starting point, with a slight tweak, because we are typically sampling very small, circular, stars.

Not sure what 1/3 of analog signal means - but if it refers to using 1/3 of period of maximum frequency as sampling period (using 3x max frequency as sampling frequency) - that is over sampling, using x2 is enough.

We have seen that stars won't become squares because of under sampling.

Correct sampling is done at x2 max frequency. Problem is - determining that frequency and understanding Fourier transform of signal of the image produced by telescope in presence of both guiding errors and atmospheric seeing.

 

[vlaiv]

9 minutes ago, FLO said:

If you had contacted us you would have found us receptive and grateful. 

I'm sure of it.

If I come too strong in some of my comments about this - that is just because I feel strongly about this topic.

Given that the FLO is rightfully seen as very credible and trustworthy by so many people that do business with FLO - you can see how sensitive / high impact this can be.

 

[Clarkey]

I'm not going to argue with Vlaiv on any technical aspects - with my brains it would be foolish at best😁

However, in defence of the astronomy tools website, as a non-expert I have found it a useful source of information. Yes, I take the guidance with some scepticism, but it is still useful for me. Not least the field of view is useful for comparing scopes and cameras.

In terms of CCD suitability, work out the pixel scale and make your own judgement. After all, it is only a guide.

[vlaiv]

5 minutes ago, Clarkey said:

I'm not going to argue with Vlaiv on any technical aspects - with my brains it would be foolish at best😁

However, in defence of the astronomy tools website, as a non-expert I have found it a useful source of information. Yes, I take the guidance with some scepticism, but it is still useful for me. Not least the field of view is useful for comparing scopes and cameras.

In terms of CCD suitability, work out the pixel scale and make your own judgement. After all, it is only a guide.

It can be more than that - it can be valuable resource as is envisioned - it just needs few corrections and different interpretations of results.

For someone that wants easy advice to match two pieces of equipment - like scope and camera - it can do wonders.

Imagine you come and say - I want this scope and that camera, is it good combination?

And it says - yes, it is good combination given average seeing but only if you bin your data in such and such way and you have mount that is capable of such and such performance.

I'd add couple more things like illuminated and corrected field versus sensor size.

I'm sure that most people with experience do this "manually" when choosing potential combination - why not offer it as a tool that does the same view few clicks

[vlaiv]

Here is what I would recommend to be changed:

1. replace seeing with expected star FWHM calculation based on mount, seeing and telescope aperture (assuming diffraction limited optics)

2. given expected star FWHM - use FWHM / 1.6 as optimum sampling frequency.

(I can expand on both above points).

If telescope focal length + pixel size is below optimum frequency give warning and offer binning that will place it above optimum sampling frequency.

If not - say that it is ok, under sampling is not bad and that there is potential for a bit more detail if not under sampling - maybe categorize it as wide field setup - but don't put negative note to it.

So under sampling - ok, over sampling BAD - but can be corrected with binning the data.

[Catanonia]

15 minutes ago, vlaiv said:

It can be more than that - it can be valuable resource as is envisioned - it just needs few corrections and different interpretations of results.

For someone that wants easy advice to match two pieces of equipment - like scope and camera - it can do wonders.

Imagine you come and say - I want this scope and that camera, is it good combination?

And it says - yes, it is good combination given average seeing but only if you bin your data in such and such way and you have mount that is capable of such and such performance.

I'd add couple more things like illuminated and corrected field versus sensor size.

I'm sure that most people with experience do this "manually" when choosing potential combination - why not offer it as a tool that does the same view few clicks

Vlaiv,

No doubting your expertise in this subject and I would not even try to dispute any of it.

BUT

is there a danger that if your recommendations are applied to the site, it becomes "too" complicated for the newbie / average human and therefore effectively worthless ?

The site is supposed to be a top level guide for those that don't understand the science as you may understand it 

All I would say, is reading the original descriptions on the site, it makes sense to my small brain but reading your descriptions hurt my head.

I would only say, what ever is decided upon, dumb it down to simple language for us simpler folk

 

 

[vlaiv]

Now for a bit of mathematical stuff.

Part 1.

How to calculate expected FWHM depending on seeing FWHM, mount guide RMS and telescope aperture?

We will assume diffraction limited telescope and will assume all three component are Gaussian shape (we will use Gaussian approximation to Airy pattern).

Step 1 - convert all to RMS / sigma

- mount guide RMS stays the same - it is already sigma / standard deviation

- seeing FWHM is divided with 2.355 to get corresponding sigma (that is relationship between FWHM and sigma for Gaussian curve)

https://en.wikipedia.org/wiki/Full_width_at_half_maximum

- for telescope airy disk we use 0.42 * lambda / diameter as sigma - instead of expression for airy disk radius that is 1.22 * lambda / diameter. This expression is in radians - need to be converted to arc seconds.

for reference check this for example: https://www.researchgate.net/publication/304247659_Realisation_of_a_Digitally_Scanned_Laser_Light_Sheet_Fluorescent_Microscope_with_Determination_of_the_System_Resolution

1.22 / 2.9 = 0.42

Step 2:

Once we have all three sigma figures - we take square root of sum of their squares to be resulting sigma.

(convolution of a gaussian by gaussian is a gaussian and their sigmas related like that again see this: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.583.3007&rep=rep1&type=pdf

)

Once we have final sigma - we divide it with 2.355 and get final FWHM expected in the image.

Edited January 31, 2022 by vlaiv
One image too many

[vlaiv]

9 minutes ago, Catanonia said:

All I would say, is reading the original descriptions on the site, it makes sense to my small brain but reading your descriptions hurt my head.

I would only say, what ever is decided upon, dumb it down to simple language for us simpler folk

Sure - I don't think actual interface needs to change - it will remain the same - except results and recommendations.

[vlaiv]

I'll probably leave FWHM/1.6 = sampling rate bit for tomorrow as I'm a bit tired now, but I wanted to show how much different results can one get depending on method used.

Let's say I'm a beginner with a limited budget and I wanted to get into astrophotograhy. I've seen people use say 70mm F/6 refractor and AziGti mount and modern CMOS camera like ASI183.

I live where good seeing is not that uncommon. What will existing tool say about this combination:

It tells me that I'm mostly in the "Green" that I'm slightly under sampled at 1.15"/px and that this reduces influence of guiding errors and improves my SNR.

Let's now calculate things in a new model.

First the mount - from AzGTI we can expect 1.5" total RMS guide error on average (it has 0.625"/ step stepper resolution - 2073600 total steps for 360*60*60 = 1296000 arc seconds per revolution)

Let's take both 1" and 2" seeing and see what will difference be between them

1" FWHM = 1 / 2.355 = ~0.42463" sigma

2" FWHM = 2 / 2.355 = ~0.85" sigma

And finally let's calculate corresponding sigma for 72mm aperture (at 550nm wavelength - mid spectrum is fine approximation).

0.42 * 0.55µm / 72000µm (we convert all to micrometers)

= ~0.0000032 radians and that is 0.0000032 * 180 / pi * 60 * 60 arc seconds or ~0.662" sigma

Total sigma will be:

sqrt( 1.5 * 15 + 0.42463*0.42463 + 0.662*0.662) = sqrt(2.25 + 0.1803106369 + 0.438244) = 1.693681 sigma = 1.693681 * 2.355 FWHM = ~4" FWHM (for 1" seeing)

sqrt( 1.5 * 15 + 0.85*0.85 + 0.662*0.662) = sqrt(2.25+0.7225+0.438244) = ~1.84682 sigma = 1.84682 * 2.355 FWHM = ~4.35" FWHM (for 2" seeing)

4" FWHM requires sampling of 2.5"/px

4.35" FWHM requires sampling of 2.72"/px

With 1.15" we will be more than double over sampling in reality! Even if we bin our data x2 - we will still be over sampled with 2.3"/px in 1"-2" FWHM seeing.

 

[Martin Meredith]

Real world data point: I recently bought a small pixel camera (ASI 290MM) which coupled with my 800mm FL scope puts me in the slightly oversampled range, but I'm mainly using it binned 2x2, which places me in the middle i.e. critically-sampled. For many years I've used a large pixel Lodestar with the same scope, and astronomy.tools places that slightly in the undersampled region.

My practical experience so far (~100 DSOs observed with the new cam in various seeing conditions) is that astronomy.tools is spot on. In fact, I would go in the opposite direction to what I understand is your proposal and state that the 800mm/8.4um pixel combination is actually rather badly undersampled at times. There is really no comparison in terms of star shapes. It's been a bit of an eye-opener actually.

Martin

 

[vlaiv]

9 minutes ago, Martin Meredith said:

Real world data point: I recently bought a small pixel camera (ASI 290MM) which coupled with my 800mm FL scope puts me in the slightly oversampled range, but I'm mainly using it binned 2x2, which places me in the middle i.e. critically-sampled. For many years I've used a large pixel Lodestar with the same scope, and astronomy.tools places that slightly in the undersampled region.

My practical experience so far (~100 DSOs observed with the new cam in various seeing conditions) is that astronomy.tools is spot on. In fact, I would go in the opposite direction to what I understand is your proposal and state that the 800mm/8.4um pixel combination is actually rather badly undersampled at times. There is really no comparison in terms of star shapes. It's been a bit of an eye-opener actually.

Martin

 

That is very interesting assertion.

How do you know you are badly under sampled?

[Martin Meredith]

I can see beautiful stellar discs everywhere for the first time in 8 years. Is that a good enough reason?

 

 

[vlaiv]

Just now, Martin Meredith said:

I can see beautiful stellar discs everywhere for the first time in 8 years. Is that a good enough reason?

 

 

Beautiful stellar disc is not measure of optimum sampling.

Optimum sampling means that you can fully reconstruct underlying function.

Can you provide one hugely under sampled image so we can actually see those poor stellar discs vs beautiful stellar discs you now see?

 

[Martin Meredith]

And this was a good example for the Lodestar (left)

[Martin Meredith]

This is a more typical example (Lodestar on the right this time):