Pixel size, binning, over/undersampling, etc. - Help please...!!

[geoflewis]

Hi everyone,

I'm fairly new to CCD imaging and will be using 2 very different imaging trains with the same CCD camera, a QSI583 which has the KAF8300 sensor with square pixels at 5.4µm.

The 2 imaging trains are:

• C14+Optec focal reducer yielding FL = 2575 (F7.25) (0.43 arc sec per pixel)
• TSAPO100Q 100mm (4") - FL = 580mm

I am trying to understand what binning I should use, if any, for both configurations, but especially when I'm using my C14.

I've been reading around the topic somewhat, but I haven't reached a clear understanding. What I think I understand is that to optimise performance the CCD camera's pixels should be approximately one third the FWHM of a star as produced by your telescope. Assuming seeing of say 3 arcsecs and using the formulae Star Size = (Seeing * Focal Length)/206.3 and Nyquist criteria = 3.3 I get the following:

Star Size = ((3*2574)/206.3) = 37.43 (NB FL = 355*7.25 = 2574)

Star Siize/Nyquist = 37.43/3.3 = 11.34 optimum pixel size

I have no idea where the 206.3 comes from, nor why I should use Nyquist = 3.3, but I trust the formulae and don't really need to know this. If my calculations are correct then as I suspected the C14 configuration with the QSI583 Kodax 8300 sensor is significantly oversampled. I'm therefore concluding that I should always bin when imaging with this configuration, but is that bin 2x2, 3x3, 4x4 or what please? e.g. does binning 2x2 give me an effective pixel size of 10.8µm, not so far off the calculated 11.3 optimum, or am I completely off track with my very limited understanding thus far?

Oh BTW I know that I'm pushing water uphill trying to image DSOs with the C14, which was purchased mainly for planetary work, but if possible I want to also use it for globulars, individual galaxies, PNs, etc., which I have already attempted shooting bin1, but think that binning 2x2 might be faster, with improved SNR and without losing resolution....

If anything the formulae suggests that TSAPO100Q looks to be undersampled with the KAF8300 sensor, so binning is not required, or desirable, but I'm interested in your feedback on this too please.

All advice will be very much appreciated.

Cheers, Geof

 

 

[vlaiv]

Well, there are a lot of information floating around on optimum resolution for long exposure imaging and I must say that none is quite "correct", all of it is approximation to some degree.

First of all, I've done some research and concluded that out of commonly encountered figures for optimum sampling, that being x2, x3, x3.3, only x2 has really any merit in theory, but that theory is also approximation in case of long exposure.

Let me explain a bit what is going on.

In long exposure imaging star size, and detail in general is blurred by 3 sources, that combine into one "blur function", usually called PSF - Point spread function (or what happens to the star, which is for all intents and purposes single point of light when astro imaging - how does it get spread into non point). First blur is Airy disk blur and it is inherent in optical instrument - related to aperture size and shape. Second blur source is seeing, which in long exposure astrophotography can be well approximated with Gaussian type PSF. Third source of blur is tracking / guiding error. In well behaved mount this also can be approximated with Gaussian PSF (by "well behaved" mount I here think of mount which guide / track error is random in both RA and DEC with same intensity - so no elongated stars either from bad PA or unguideable PE).

Now Airy disk PSF is a bit different from other two (those being Gaussian). It effectively cuts off completely higher frequencies in the image. There is no way (even theoretical) to recover that detail in the image that has been lost by Airy Disk PSF.

With Gaussian PSF, when looking at ideal Gaussian PSF, none of the higher frequencies are effectively cut off - they just get attenuated, higher the frequency - higher the attenuation. Fourier transform of Gaussian PSF is again Gaussian - and if you look at Gaussian curve - it tends to 0 as you move away from origin, but never quite reaches 0 - this means that higher and higher frequencies get attenuated more and more but are never cut off (or effectively multiplied by 0 to give 0 value).

Problem with this description is that both seeing and guide/tracking error are close to Gaussian but never quite the same (according to Central theorem, they tend to Gaussian profile for infinite exposure time).

So if you really want to get "maximum" possible information out of image - you should go for x2 (Nyquist for 2d sampling in regular rectangular grid) Airy disk size. Planetary imagers aim for this resolution when using lucky imaging. Even then, one must employ special techniques to retrieve high frequency signal that has been attenuated by Gaussian PSF of seeing and tracking error - such as Wavelet sharpening or Deconvolution.

Ok, so where does all of this bring us? If you are not going to do any "special" processing of your images, and plan to do "normal" processing work flow, I would say that you should aim for x2 - x3 expected FWHM of your stars - and that will depend on 3 factors - scope aperture size (greater the scope smaller the Airy disk), range of seeing values that you expect when imaging, and average guiding error of your setup.

From my own experience, I would say that for almost all amateur astronomers lower limit in long exposure for resolution is 1"/pixel. This would mean that you should at least bin x2 when working with C14, and even go x3 depending on your mount and seeing. And I don't think you are pushing things with C14 on DSO. Provided that you can handle that scope well for imaging (all technical problems like mirror shift, using appropriate field flattener / corrector, suitable mount) - with aperture of that size you will simply have great advantage over anyone with smaller scope for given target resolution - in terms of SNR for given imaging time.

You can even try and go for higher resolution with C14 and then try to process out detail by using Wavelet sharpening or Deconvolution - just to see where it gets you (do this on bright targets like planetaries because it is easier to achieve good SNR, and you need good SNR because all the noise gets amplified when you try to process out the detail).

For TSAPO100Q just leave it as is - don't bin it. 1.92"/pixel is decent resolution for "wide field imaging" (I like high resolution work, so anything that is more then 1 degree - for me is wide field ). You can even bin x2 with this scope if your target is for example narrow band nebula - where object of interest is more important than surrounding stars (stars will be small points - almost single pixels in case you decide to bin x2).

Hope this helps somewhat.

 

 

[geoflewis]

Hi Vlaiv, thank you for the full and detailed reply. The first part somewhat went over my head, but it is good to have the information as the more I delve into this topic the better I may understand it. The scopes are mounted on an AP1200 and with PHD2 I am getting guiding sub 0.5 arcsec, (sometimes 0.3'') so I am pretty confident on that aspect. The C14 is an old pre Edge version so even with the Optec FF/FR lens there is residual coma, but I can crop out the worst of that. I did some imaging at bin1 earlier this year with the below image of M95 an example of what that yielded, this being 5.5 hours of data all 10 min subs (15L, 6 each RGB).

More recently I've been reading that the camera is likely to be oversampled at Bin1 so whilst testing SGP for control of my observatory, I experimented with Bin2 on globular cluster M15, the below image being just 6x120sec on each RGB, so a mere 36mins total.

They are not the best of images, but clearly it is possible to get something usable with the C14.

Thanks for confirming that bin2 or even bin3 is likely to be the best way to continue with this configuration and that bin1 is good for the TSAPO.

Best regards, Geof

[ollypenrice]

I've rather given up on trying to work from theory and have gone back to my roots, which are based on experiment. So I simply recommend that you 'try it.' But, in doing so (especially with the C14), take note of the seeing on the night. There is no point in chasing fine resolution on a turbulent night. Shoot RGB instead and look for luminance when the seeing is stable. Try shooting in bin 2 and bin 1 and see what the effect on resolution really is when you downsize the bin1 to the scale of the bin2.

Olly

[geoflewis]

Thanks Olly,

That sounds like good advice and certainly trying different capture methods is what I’ve been doing, but I wondered if I was literally shooting in the dark (pun intended), so wanted some expert opinions/advice. It’s also good to know that I should hold off luminance unless seeing is good. I’ve certainly had some bad luminance sessions that I threw away and just processed the RGB; I think you’ve just explained what might have been the root cause of the problem - poor seeing..!!

Many thanks, Geof