Undersampling - Oversampling

Dave at al,

A quick and dirty search yielded two references to my comment about 3.3x oversampling (or greater). More specifically, we have:

"The Nyquist theorem suggests that in order to efficiently record this information and convert it into digital format, our system should be sampling the image more aggressively, by operating at an image scale of about 1/3 times the seeing, or in this example 1/3 x 3.5", or 1.17"/pixel. (Actually, it should be 1/3.3 times the seeing, but who's counting)."

Source: www.starrywonders.com/ccdcameraconsiderations.html

"Firstly unlike sound where it is oversampled 2.2X (CDs) and that is acceptable, Stan Moore contends that oversampling with light needs to be 3.3X. Now that is an educated theory but it does seem to work out."

Source: www.iceinspace.com.au/forum/showthread.php?t=46100 (half-way down the page)

Anthony.

Anthony - they're interesting references.

It seems that there is differing advice. I couldn't find any peer reviewed articles or other "scientific" papers although I didn't search too hard...

Here's a take on sampling from Apogee:

www.ccd.com/ccd113.html

This is where I took my info from in order to decide on the correct CCD for my typical seeing. Finger Lakes also agreed that the CCD/OTA combo was the best for my typical conditions.

You're sure blessed with the seeing you get and clearly, your sampling rate works given the images you take. So it seems the 1/3rd rule is sound.

Dave

This is my current understanding - and I don't assert it to be definitive in anyway - its just my take on the subject.

Nyquist theory is quite clear and sampling is bang on 2x max fequencey of the signal of interest. But I'm not sure that it can be applied to pixels in the same way as one can apply it to sound.

In most applications (not CCDs) there is one sensor and a continuosly varying signal. Between any two arbitrary points (no matter how close you choose) there is always another intermediate value. Nyquist sampling theory works very well here and the youtube post earlier demonstrates this nicely.

If we had one sensor scanning a projected image then Nyquist works out of the box. However, a CCD there are many discrete sensors and all signal is not shared across all sensors over time. So what we are seeking is what is the smallest pixel size that, given the smallest number of them, can reconstruct an idealised point spread. It will still look boxy but we can know the underlying form. To make it not boxy (for pretty pictures - not needed for science) we have to oversample - either at capture time - or postcapture (which we can do becuase we have enough information because we got our scale right - and we can interpolate to make it smooth).

Now the question which I have not seen comment on anywhere - why use the height and width of a pixel - surely we want the resolution across the diagonal as well and this introduces a factor of root 2 to our calculations for sqaure pixels?

Mark

Mark, err, yes... :blush: Sorry, over the head there - I'm no physicist or mathematician....

So are you saying that the most appropriate sampling rate is 2 times? Or 3? Or even 3.3?

This is a great discussion by the way - I only ever defaulted to listening to people who seemed to know what they were talking about. I recall never getting a satisfactory scientific explanation of one sampling rate over another for CCD's.

I could try and throw it out to another forum I subscribe to (CCDTech).

Apologies Dave - and to anyone else that read my previous diatribe. It wasn't very helpful and causes more confusion than enlightenment.

I have to say that this has been a very good thread.

If one wanted to leave with a bullet point guidline - I think I shall be using - for myself - and unless/until I am better informed:

max pixel dimension = Typical FWHM due to seeing / 2.8

this is the same as

Pixel diagonal = = Typical FWHM due to seeing / 2

(and for "typical seeing" I'd substitute something of the form of best reasonable expectation - however you want to define that)

The 2.8 is derived by using pythagoras to adjust from measuring pixel width or height against FHWM so that we are measuring pixel diagonal across FWHM and using nyquist critical smapling of 2x. This is maybe where the 3x comes from that is sometimes cited (that 2.8 rounded up). I have no idea why 3.3 should raise its head. If pixels aren't square then maths becomes a little more complicated.

Any sensor bigger than that would lead to undersampling and one looses unrecoverable information from an expensive setup.

If one finds a CCD that suits the pocket and pixel size is no greater than the above size (but can be smaller) then it can be considered to match - oversampling is okay. However there may be costs if one is grossly oversampling in that as sensor size gets smaller this is likely to affect sensitivity and/or full well depth. But I'd need to research that more.

I buy Anthony's advice - I really think oversampling is okay unless you go excessivly or are paying a premium for it.

Also one needs to factor in if one is going to a barlow etc and factor that in.

I think for science (photometry, astrometry) oversampling gets you nothing. However, oversampling makes for less pixelated (boxy) images hence is a beneift for pretty pictures without having to resample / interpolate.

If I find anything that nicely and definitively expresses this in a solid and clear way I will followup.

Again apologies for previous post - there was method in my madness but I don't think it helped man nor beast.


Mark

Hi Mark....I wrote this before you added your last post. I had to wait on internet to return before being able to get back in. The initial question was not intended to spark a very technical discussion - the fact that it did is good but perhaps not all readers are interested to the same depth. However - I got out of the discussion what I needed and am thankful for the insight into deeper aspects of the subject. What follows is what I wrote in light of your last post.....and like I said I may be way off the mark (no pun intended), but it is how it all appears to the 'uneducated'...............

This has indeed got very interesting but I think also it has drifted away from the core issue. I am no scientist but I can understand the sampling required on wave forms, whether it be sound or light waves. However, to my ‘layman’s’ way of looking at this we are not actually talking about sampling of wave forms when we talk about sample rates for CCDs.
I may be way off track – but when I initially asked about sample rates for CCD imaging (because I learned that the CCD should be 'paired' to the scope) I was looking at it like this.......if we do not have enough pixels for the area captured – closer examination will reveal coarse shapes and not fine points. As someone put it......imagine zooming in very high on the letter C as displayed on your computer. (Easily done through ‘paint’ or other simple programme). You will see that the edges of the ‘C’ are not in fact curved but a series of squared pixels forming an image that just appears curved at less zoom.
I imagine that if we have too many pixels then we will lose sharp edges to the items imaged on the CCD. So obviously the size and amount of pixels that show the image best lies somewhere between having too many and having too few. Thus there must be an ideal – this I believe is what ‘sampling’ for a CCD is all about – and not related to wave forms/frequencies.
Is it not a fact that we work out how many arcseconds are covered per pixel? Thus we are simply talking area. If we try to show too much sky per pixel we are undersampling – too little then we are oversampling. It has been made very clear that the oversampling can be adjusted after the fact.......and I think that is what I really needed to know initially......I will be safe enough buying either of the CCD cameras that caught my eye and begged me to ask the question re sampling in the first place.

Brendan.