Arc seconds per pixel

[Simon Pepper]

Hi all,

I have been using the https://astronomy.tools/calculators/field_of_view/ site to choose my next scope (galaxy season) but I will use this with my current ASI294 MC pro I need to better understand the arc seconds per pixel and what this means to the final image and does it have any impact on that image if I want to get it blown up and printed? 

I like the look of the Edge HD series so I am thinking the 8 with my 294 this gives me a resolution of 0.47x0.47 and a dawes limit of 0.57 per pixel, but I have absolutely no idea what these numbers mean. I have seen on other posts saying the lower the numbers the better, but I am not sure if this is accurate. To throw another question out there as well I do plan on going mono at some point and I am keen on the 294MM. I have seen this has a feature where you can bin 1x1 (think default is 2x2) and this increases the MP to 47 which sounds interesting, but again how do all these figures go hand in hand?

Hopefully someone can assist.

 

Thanks

 

[vlaiv]

Very complex topic, but here is quick introduction.

Given your scope (optics and aperture size), mount and guiding accuracy and seeing conditions - you will achieve certain detail in the image. There is limit to how much detail you have because all of things listed - blur image to some extent and final blur in the image is governed by total blur when you combine all those things.

Good measure of that blur is FWHM of stars in the image.

You need certain sampling rate - or "/px resolution in order to record all the detail available. If you don't have enough resolution - which means "low" arc seconds per pixel (actual number is high - say 4"/px but we say low resolution) - this is condition called under sampling.

Nothing wrong with under sampling (in spite of what you may read) - and it is valid way to get wide field of view in your shot as there is only limited number of pixels on any camera - and you have to have low sampling rate to cover larger parts of the sky in single go (without making a mosaic).

If you use too much pixels to record the image - this condition is called over sampling - and it is bad. It is bad because light is spread over more pixels than you need - and each individual pixel gets less light and hence signal to noise ratio suffers - image is more noisy because of that. More noise and no additional detail - well, you get it - poor image.

There is also optimum sampling rate that sits in between of these two. That is most "zoomed" in image - while it still makes sense to zoom in (afterwards - higher zoom - just makes image look blurry with no detail).

In fact, this optimum resolution can't be precisely determined for long exposure imaging, but can for planetary imaging as for planetary imaging there is hard cut off that happens due to physics of light - there details are lost because of aperture of the scope.

In deep sky imaging - this happens sooner because there is also atmosphere and mount / guiding performance, however actual line where it happens is "fuzzy" - there is no clear line. I've done some calculations and set some conditions where it is sensible to draw the line and optimum sampling rate for DSO is at x1.6 (number was just rounded up because of fuzzy nature of this bound) FWHM of the star in arc seconds.

This means that if you manage to record stars that are 3" FWHM - you really need 3 / 1.6 = 1.875"/px.

Problem of course is that you can't know in advance how good your sky is going to be on particular night and what sort of FWHM you will manage to record.

But above approach can tell you if you are in principle over sampling (bad) or you are close to optimum sampling rate (good). It can also give us some rules of thumb in terms of what can be achieved by amateur setups. So breakdown is as follows:

4 or more "/px - very wide field resolutions, any decent mount will do and small scopes / lens will manage that (50-60mm aperture) - average sky conditions

3-4 "/px - wide field resolutions - mount can still be entry level one and scopes in class of 70-80mm - average sky conditions

2-3 "/px - medium to wide resolutions - here we are looking at Eq5 or higher class of mount and 80-100mm of aperture - average sky conditions

1.5 - 2 "/px - this is very good medium / general working resolution. Mounts like HEQ5 and scopes of 120-150mm are needed - better sky conditions

1.2-1.5 " /px is high resolution 150mm + needed, very good mount and guiding (tuned and modded HEQ5 / HEQ6 mounts) - very good sky conditions

1-1.2"/px is very high resolution - I'd say 8" + aperture needed, premium mount needed - exceptional sky needed.

higher than 1"/px - don't bother.

This does not mean that you can't image with 0.47"/px - it just means that you are wasting resolution - you'll get massive stars when viewed 1:1 or 100% zoom level and things at that scale won't be looking nice. It also means that you are spreading light around too much and that you can achieve better SNR if you change working resolution.

There are few ways in which you can change working resolution for a given camera:

- change scope for one with shorter focal length

- use focal length reducer

- use binning - whether hardware (only CCD sensors) or software (any type but in principle only used with CMOS as CCDs have hardware version) to increase effective pixel size

In the end 294 will have 2.3µm pixel when it is not binned. With such a small pixels - you'll have a problem finding large scope of suitable focal length (remember - small scopes don't have enough resolving power for high resolution work). Good thing about such small pixels is that you can pick your bin factor after to match actual resolution of the image.

With 2000mm FL and 2.3µm pixel size - you'll be 0.24"/px

If you bin that x4 you'll be 0.95"/px (which is too high in my view - but close enough to very high resolution limits in above "table"). Bin x5 or x6 and you get more sensible working resolutions.

Throw in focal reducer and things get even more interesting as you have more room to play with.

In the end - having sensor of 47MP - does not mean much as resolution is governed by sky, scope aperture and mount performance, however having large sensor with small pixels is a good thing as it lets you "dial in" your working resolution better (important thing is to have low read noise as well if you are going to bin in software - but most CMOS sensors have low read noise).

Hope this helps

 

[oldannie]

Glad you asked those questions Simon as the reply from Vlaiv is really helpful - so thanks for that.

 

Annie

[Simon Pepper]

Its funny when asking these questions I almost addressed it specifically to Vlaiv

@Vlaiv thanks for putting in the effort there its helped me and others I am sure who come across this. Just to clarify things if you could I am bortle 4 with good sky conditions and have a HEQ5 pro currently my guiding usually averages around 1 rms total error. So checking your scale ideally I need to be somewhere around the 1.5 mark? Looks like with a .7 reducer and binning 2x2 that gives 1.34 or 2.01 at 3x3. I guess what I am asking here is the combination I am looking at isnt going to be a disaster? By the sounds of it there are options available if I invest in a reducer and add in some binning? I did dust out an old slt 127 1500mm with the 294 and was pleasantly surprised at the result hence why I am looking into the Edge 8.

Also just to edit reading again you mention the 294 has 2.3µm is that a typo as I believe its 4.63 when not binned? Hopefully that will also help?

Thanks again!

 

 

Edited April 10, 2021 by Simon Pepper

[vlaiv]

5 minutes ago, Simon Pepper said:

Its funny when asking these questions I almost addressed it specifically to Vlaiv

@Vlaiv thanks for putting in the effort there its helped me and others I am sure who come across this. Just to clarify things if you could I am bortle 4 with good sky conditions and have a HEQ5 pro currently my guiding usually averages around 1 rms total error. So checking your scale ideally I need to be somewhere around the 1.5 mark? Looks like with a .7 reducer and binning 2x2 that gives 1.34 or 2.01 at 3x3. I guess what I am asking here is the combination I am looking at isnt going to be a disaster? By the sounds of it there are options available if I invest in a reducer and add in some binning? I did dust out an old slt 127 1500mm with the 294 and was pleasantly surprised at the result hence why I am looking into the Edge 8.

Also just to edit reading again you mention the 294 has 2.3µm is that a typo as I believe its 4.63 when not binned? Hopefully that will also help?

Thanks again!

 

 

Here is a bit more details.

Scope, atmosphere and mount guiding combine to give you resulting FWHM.

Each of those three can be approximated with gaussian of certain sigma.

There is simple relation between sigma and FWHM of gaussian and that is x2.355 I think, yes - here is exact expression from wiki:

In any case - airy disk of the scope can be approximated with gaussian, seeing is often given as FWHM of star profile - again can be viewed as gaussian and guide RMS is sigma of gaussian. Add those three things in quadrature and you'll get resulting FWHM of stars.

For example, if you use 8" scope and have 2" FWHM seeing and your mount has 1" RMS guide error total - your resulting FWHM will be 3.14" and corresponding sampling rate should be ~1.96"/px.

Same scope and same guiding error in 1.5" FWHM seeing (good seeing), will result in FWHM of 2.85" and sampling of 1.78"/px - so there is some improvement but not very good improvement. This is because 1" RMS is not very good result.

Rule of the thumb is that you need to guide at about half of sampling rate that you are aiming for. If you want to work below 2"/px - you need to guide below 1" RMS. For 1.5"/px - you need to guide at 0.6-0.7" RMS.

In above calculation 8" + 1.5" seeing and 0.7" RMS guiding results in 2.3" FWHM and 1.44"/px.

If you want to go below 1.5"/px - then make sure you can hit 0.5" RMS or less. This is realistically lower limit for Chinese mounts - even tuned and modded ones. You need premium mount to get below 0.5" RMS.

In any case - 0.7 reducer, proper binning and if you manage to get your mount to guide below 1" RMS - yes, then 1.5" is quite achievable (even if on particular night seeing does not play ball - and you have 1.8"/px data - you can still happily image at 1.5"/px - difference is not that obvious).

As far as I understand - 4.63µm pixel size is for stock ASI294 (both mc and mm) - unlocked version that is bin x2 by default. If you unlock bin 1 mode - then you split original 4.63µm pixel into 2x2 smaller pixels - each of which has ~2.31µm pixel size (I rounded that to 2.3µm).

[Simon Pepper]

Thanks Vlaiv great explanation as usual! 

Edited April 10, 2021 by Simon Pepper

[knobby]

Excellent thread 👍🏻

Just to add another variable ... Would you bin with camera software or after capture ?

I know for CCD definitely camera software but not too clear with CMOS.

[vlaiv]

6 minutes ago, knobby said:

Excellent thread 👍🏻

Just to add another variable ... Would you bin with camera software or after capture ?

I know for CCD definitely camera software but not too clear with CMOS.

Yes indeed, CCDs should be binned at hardware level as that gives you improvement in read noise.

With CMOS sensors, I'd say that it is better to do it after capture.

In principle - doing it in firmware (camera software) and after capture gives you the same result - most of the time, but there are several pros and cons for each approach.

- binning in firmware means less data captured as you cut to 1/4 (or more for higher bin sizes) data to be transferred over USB (or any other link type that connects the camera) and stored on your hard drive. It also means less data to process. This is pro to doing it in camera firmware / software

- binning after capture gives you sort of flexibility. You can decide what bin factor to use for that particular dataset. That is pro for binning after capture

- Sometimes binning in camera firmware can result in "data loss". Cameras that are for example 12 or 14 bit - you don't have to worry about that as binning will still give you 16bit data, but recent CMOS sensors started being 16bit ADC. If you add couple of 16bit numbers - you will exceed 16bit precision and if you download that data in 16bit format it will be a bit truncated. This does not happen with binning after capture as you can convert data to 32bit float before you start processing. That way you loose no precision.

- You might like to try some advanced stuff like fractional binning and similar - again, for that it is better to bin your data after in processing rather than at capture time.

In the end - it is tradeoff - would you like to do it to save storage space and achieve faster downloads (which are pretty fast with USB 3.0 as is), or would you like added flexibility of doing it after calibration.