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# Spot size, resolution and image scale?

9 replies to this topic

### #1 tjugo

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Posted 30 November 2012 - 12:20 PM

Hi,

I understand what is spot size and theoretical resolution of an optical system. However I don't understand the practical consequences of the spot size in the images.

Let's say that I have 2 instruments with the following specs:

10 inch newtonian with corrector that produces 10um spot size. The theoretical resolution of this instrument is 0.5 arcsec.

5 inch newtonian with corrector that produces 5um spot size. The theoretical resolution is 1 arcsec.

And lets say that I have a camera that has 5um square pixels.

Let's also say that we have perfect seeing (less than 0.5 arcsec)

If I use the camera with both systems, which system will have the greatest resolution?

Could someone shade some light on this? Is it correct to assume that spotsize is the practical resolution of the optical system? What about image scale?

Thanks,

Jose

### #2 Rick J

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Posted 30 November 2012 - 04:47 PM

Without knowing focal length the question can't be answered.

Assuming equal quality (both are performing to theory limit (assuming the same theory is used for both)) of the systems the 5" has one forth the focal length of the 10" and thus the 10" has twice the resolution even though twice the spot size. Just what theory predicts.

The main purpose of spot size diagrams is to show how well a system corrects the outer part of the field of view for curvature, coma, astigmatism etc. The less it expands as you move out from the center the better unless you give up way too much in the center. Most of today's correctors don't have a problem here though some are a bit better than others in this regard for DSO work.

Most correction systems greatly reduce the spot size and thus increase resolution toward the edges but to do so enlarge spot size in the center slightly giving up a bit of resolution in the center. Thus use a corrector for DSO work. There seeing makes the slight loss in the center meaningless but the correction greatly improves the overall image. Remove the corrector for best on axis planetary imaging however where you can freeze seeing with rapid exposures and achieve the maximum resolution the scope can provide in the center of its field.

Rick

### #3 Alph

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Posted 30 November 2012 - 07:26 PM

Proverbial apples and oranges. Resolution and spot sizes are not really related. Resolution is defined/determined mainly by light diffraction. Spot diagrams are part of geometrical optics which knows nothing about light diffraction and resolution.

The size of 80% encircled energy is a better measure of actual telescope resolution.

### #4 tjugo

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Posted 30 November 2012 - 08:39 PM

I need to do more reading...

Cheers,

Jose

### #5 Hilmi

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Posted 30 November 2012 - 11:56 PM

I don't claim to understand all this voodoo, but I read in a book somewhere that if you are under-sampling, as in your CCD's image scale in combination with your optics is lower than the resolution of the optics, you can recover some more detail through deconvolution. So to my limited understanding, if you have two optical systems which in combination with your camera provide the same image scale, but with one system, the telescope is actually able to resolve details to a far higher resolution, but is restricted by your pixel size, when you deconvolve the images coming out of that scope, you can actually squeeze out more details from the picture. This is assuming that you have good SNR to start with so that the deconvolve process actually works as designed.

I repeat, that I'm no expert and I am repeating what I read the same way a parrot repeats words it memorizes, therefore, take what I said with a grain of salt

### #6 Rick J

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Posted 01 December 2012 - 12:31 AM

They are measuring two different things. Spot size is a linear measurement. One made with a ruler. It says the star on your CCD at this spot in the field will be so many microns across. By itself it is meaningless, same as Solo's comment about making the Kessel run in 12 parsecs. That too was a linear measurement saying nothing about speed without also knowing the time involved. All star ships make the run in 12 parsecs. All optical systems can have a 10 micron pixel (make that spot size) if the appropriate focal reducer or expander (Barlow) is used.

With a spot size alone that's just a distance not a measurement of resolution as that depends on the magnification used to obtain that spot. Double the focal length the spot is doubled in size. Also a single spot tells you only the size at one spot in the field.

Resolution is an angular measurement. Draw an angle on a piece of paper. Go out say 10mm and measure the distance between the two lines, now measure the distance at 20mm. It will be twice the 10mm distance but the angle hasn't changed -- but its linear measurement has changed. That is independent of magnification and thus focal length. Though it is even more meaningless. Not only could it vary across the field it is dependent on many other factors. For instance I can easily resolve Cassini's division at 0.8" in my 60mm refractor even though Rayleigh's limit for that scope is 138/60= 2.3", three times greater! Being a high contrast linear feature it is seen when far smaller than "theory" would indicate.

In short a spot diagram showing spot size across a field of view tells you how resolution will degrade as you approach the edge of the field of view. But will not tell you what that resolution is. Knowing the focal length will give one measure of this nebulous thing called resolution. Though it likely won't be the same answer as one of the resolution formulae give.

Of course your tracking, guiding and atmospheric conditions have a big say in this as well.

Rick

### #7 Barry E.

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Posted 01 December 2012 - 10:23 PM

Can I interject with a follow-up question?

Let's say I have a single telescope and a single camera:

Scope: 203mm aperture, 1000mm focal length (f/4.9)
Camera: 5.4 um pixels

I want to image galaxies, which are small targets, and get the most detail possible. I have two options:

1. Image at f/4.9 and crop the image to contain only the galaxy

2. Use my 2x PowerMate, which changes the optical system:
Focal length: 1989mm, f/10
Aperture (unchanged): 203mm

This halves my field of view, basically "zooming in" on the galaxy so that it takes up more of the CCD chip.

However, the diffraction spot size also doubles:

Diffraction Spot Size:
Without 2x: 6.34 um
With 2x: 12.7um

Did I really gain anything by using the 2x? I'm thinking "no".

### #8 microstar

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Posted 01 December 2012 - 11:11 PM

I'm interested in Barry's question as well, as I've puzzled over the advantage of using my 2x PowerMate as well (pretty much the same setup as Barry).

And perhaps I'd add a third option: image at f/5 and collect enough lum frames to do a 2x drizzle on a sub-section of the frame (I use DeepSkyStacker for this) to get the FOV of the f/10 setup with the PowerMate. Any advantage?
...Keith

### #9 Rick J

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Posted 02 December 2012 - 02:17 AM

Barry,
In normal seeing you'd be right. Pixel size should be such that typical seeing is 2.5 to 3 times that of the pixel's resolution. Your pixel is 1.1" which works well in seeing of 2.5" or worse. That's my situation. I can image with a 0.5" pixel (similar to your 2x pixel) but only one or two nights a year does that help and even then it is minor except for two nights in 7 years when it did help as I'd expect.

When you halve the pixel it gets one forth the photons so you need 4x the exposure to get sky limited subs. That's 40 minutes for me in my skies rather than 10 for 1" pixels. That means the mount has to track with twice the accuracy for 4 times as long. If that hurdle is cleared you then have shot noise. While a single 40 minute 0.5" pixel sub has about the same total noise as 4 ten minute ones at 1" per pixel it has twice the resolution of shot noise (but likely far less than twice the resolution of the object - often the same in fact). This makes shot noise more objectionable unless you reduce the image back to 1" where it would be the same. So you would want more total exposure time to reduce the shot noise to a less objectionable level. How much more depends on final image resolution.

Drizzle is useful when taking wide angle shots with a short focal length scope such that the seeing is better than the system can resolve. Often the case with say a 500mm scope with a STL-11000 camera with a 3.7" resolution in 2.5" skies. With a reasonably sampled image for DSO work it doesn't add anything more than simple dithering would if done in non unitary moves. So if the dither is 1.8 pixels rather than 2, dither does the job of drizzle in deep sky imaging as well as reducing noise when done with a sigma type stack.

For planetary work the Barlow is very useful. I like to run at f/25 (0.2" pixel) with my 14" when doing planetary imaging as it gives the software a lot more to work with but then I'm freezing seeing and using only the best of thousands of frames. A very different situation than DSO imaging.

Rick

### #10 microstar

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Posted 02 December 2012 - 12:16 PM

Thanks for the great explanation Rick. I sometimes wonder if I'm ever going to actually understand what I'm doing!
...Keith

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