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# Determining resolution with a camera

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### #1 Stargazer3236

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Posted 04 January 2019 - 08:16 PM

I would like to know, how do I calculate resolution using say a 90mm Mak-Cass and a Celestron Neximage 5 camera for imaging the planets and using a 5X barlow for increased image size? What kind of planetary resolution can I expect? 5 arc seconds? More or less?

Camera Pixel size is 2.2um x 2.2um and resolution 2592 x 1944 (5 Mega-pixels)

Edited by Stargazer3236, 04 January 2019 - 08:17 PM.

### #2 RedLionNJ

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Posted 04 January 2019 - 08:48 PM

There are two different measurements coming into play, here. The LARGER of the two is going to be your limit.

Based on the aperture, you can expect (let's assume great seeing) somewhere around 0.75 arcsec or thereabouts

In order to achieve optimum image brightness for that resolution, I believe you need to be operating at somewhere around f/11 (probably even shorter than the Mak-Cass's native f-ratio).

If we assume the Mak-Cass has the popular f/14 focal ratio (approx), adding the 5x Barlow is going to put the effective focal ratio at around f/70. The image formed at this focal ratio is going to have nearly 7 times the desired diameter (with no additional information present) and the same incident light is going to have to cover nearly fifty times the area. So the resulting image will be 50 times fainter (but with no additional information).

Taking Mars as a more concrete example - if Mars is now 8 arcsec across, you could reasonably expect it to cover 10 or 11 pixels at f/11.  By imaging at f/70 , that same Mars would be covering a diameter of around 70 pixels. Bu there would still be the same amount of incident light, so it would be substantially dimmer, as it now covers nearly 50 times as many pixels.

Resolving fine planetary detail is all about seeing, excellent focus and aperture. You need all three.

### #3 gregj888

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Posted 08 January 2019 - 02:56 AM

If you want pixel scale and angle, you can do a drift calibration.  Easiest way is to download Speckle tool box (Yahoo speckle interferometry group).

Dawes limit gives a good approximation of resolution.

The airy disk is a function of the f/#, resolution (information in the airy disk)is a function of wavelength and aperture.

IMHO, if your main scope is above f/10, I doubt the 5x Barlow helps much and if you need one at all a 2x would be plenty.. per RedLion.

### #4 ToxMan

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Posted 08 January 2019 - 11:46 AM

For "wide field" planetary imaging, I used a 90mm Mak-Cass, at f13, native. This was sometime ago, when Jupiter was culminating much higher in the sky, and I could get decent images with average conditions. Some, I was able to make into an animation.

Here is an Astrobin link to one of the animations: http://www.astrobin....page=2&nc=&nce=

Consider ditching the barlow. And, give "wide field" a go. My work was done with a monochrome camera. With a color camera, it  is much easier.

Post 'em when you get 'em.

### #5 Cotts

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Posted 08 January 2019 - 12:55 PM

Assuming your 90mm is 1100mm f.l. and the camera data you gave, with no Barlow.:

FOV: 17.82' x 13.37'

Image Scale: 0.41"/pixel

If I have your scope's focal length wrong, calculate for yourself here: http://www.12dstring.me.uk/fovcalc.php

The image scale is the important figure.

The best compromise for resolution and camera sensitivity is to put the resolving power of the scope onto TWO pixels of your camera.   For a 90mm scope the Rayleigh resolving power is 1.6 arc seconds.  (Think of a circle 1.5" in diameter for this)  You are putting the resolving power onto nearly four pixels without even using a Barlow.  (1.6 div. by 0.41)  Adding a barlow will not improve the resolution in your images; it will actually only make your image dimmer (light of object spread over more pixels) requiring longer exposures.....so I do not recommend using a barlow at all...

Dave

### #6 Cotts

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Posted 08 January 2019 - 01:02 PM

Assume the yellow circle represents the Airy Disc produced by your telescope out to the first minimum of the diffraction pattern..  The grid represents the pixel array.

Undersampled.

Oversampled

Just right

Dave

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### #7 George Bailey

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Posted 08 January 2019 - 01:03 PM

For a 2.2u pixel size, max f for the SYSTEM should be no greater than 11 to have proper Nyquist sampling.

You are probably already about at or above this without a barlow with your scope with that camera.

### #8 gregj888

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Posted 08 January 2019 - 01:56 PM

For Speckle (ya, I know but hold on) we split the Airy disk over 4-10 pixels.  I haven't seen much benefit past 4-5 and limiting mag degrades pretty fast.  The primary reason for doing this as far as I know is to increase the base line measurements for the angles improving their accuracy.  It may also help with the separation when processing with Fourier but I haven't chased that down to verify it one way or the other.

Airy disk over 2 is considered a great compromise of resolution and limiting mag, but I'm unclear how really applies to Nyquist.  This may be partly my fault as I was given this as a base suggestion by the AO guys at the Keck and passed it on years ago and related it to Nyquest.  Note it was fairly specific and makes more sense with an AO system.  2-4 pixels over the seeing blur makes more sense in most case, IMHO.

For planetary imaging, my understanding is an imaging scale closer to Speckle is used.  I've assumed this has to do with the processing algorithms as much as the capture.  It's easy to believe there can be information hidden in the overlapping airy disks of an extended object.

IMHO, there are no rules when talking about pixels across the Airy disk.  It all relates to what you are doing.  For speckle ~5, planetary is probably close, general long exposure high resolution imaging ~2 (though seeing can effect it), wide field survey/occultation/comet/SN could go lower ~0.25?  Fainter objects in a shorter time likes lower numbers until noise kicks in.

### #9 Tom Glenn

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Posted 08 January 2019 - 06:44 PM

The rule of thumb of taking the pixel diameter in microns, and multiplying by 5, to arrive at the F ratio to image at, really does work quite well to maximize the sampling without using too much (and useless) magnification.  Optical theory gets confusing very quickly, but you don't really need to understand the theory to arrive at the proper sampling rate.  The 5x rule works very well, but if you want another way of calculating image scale that achieves the same result, you can take the Dawes limit of your scope and divide by 3.  This gives the approximate value in arcsec/pixel that you want to image at to achieve maximum resolution.  If you want to know your sampling rate (image scale) you can calculate it using the focal length and pixel size using this website as an example (there are many others):

http://astronomy.tools/calculators/ccd

The use of barlows is only required in order to achieve the proper image scale, which depends entirely on the diameter of the pixels in your camera and focal length of the scope.  Barlows are not something to be used simply because you feel like the result may be better with a 3x (or 5x, etc) versus a 2x barlow.  It's not a random decision.  Different size pixels require different F ratios in order to maximize the sampling.  If the pixels are small enough such that the F ratio of the scope is already 5x the pixel diameter, you would not need to use a barlow at all.  If you exceed the generally accepted maximum sampling rate, your resolution does not improve, but your image quality degrades.  There are certain types of imaging in which exceptions to these rules can be made, but for extended objects such as planets and the Moon, you won't gain anything by using an F ratio above 5x the pixel diameter, although it's better to be slightly above than below this value if the seeing is excellent.   Also, these values are typically calculated for green light (wavelength 550nm), which is the center of the visual spectrum, and the human eye is most sensitive to green light.  Imaging in red or IR light reduces the optimal F ratio somewhat, as the Airy disk size increases with wavelength.

This is all you really need to know to select the appropriate image scale, but reading about optical theory can be very interesting.  The following website provides a good brief discussion of resolution and the Airy Disk:

https://www.telescop..._resolution.htm

Part of the confusion when reading optical theory is that often terminology is not used correctly, or consistently, even in technical literature.  The "Airy Disk" does not refer to the central diffraction maximum of a point source (this is called the spurious disk), but rather to the region that encompasses the spurious disk and extends all the way to the mid-point between the first maximum and the first minimum of the Airy pattern.  Formulas for computing these values can become confusing, because you need to be aware of whether you are calculating the angular value in radians or in arcseconds.  The most rigorous definition of "resolution" for point sources is the Rayleigh criterion, which requires that the central maximum of the point spread function (PSF) for one point source exactly coincides with the first minimum of the other point source.  This distance allows two point sources (stars) to be completely resolved.  The angular separation of two equal point sources of light that satisfies the Rayleigh criterion is half of the diameter of the Airy Disk.  However, point sources can be resolved at angular separations somewhat less than this, although the PSFs start to significantly overlap.  The Dawes limit was actually determined empirically by visual observation, and is very similar to the theoretical limit of the minimum distance that two equal PSFs can be before they become indistinguishable.  This diffraction limit is also very close to the FWHM value (Full Width at Half Maximum) of the PSF, which is a value that you will see often when talking about measuring the size of a star in an image.

The relation of the FWHM limit of resolution to the Nyquist sampling theorem is that according to Nyquist, you have to sample at a rate of 2x the smallest detail (or highest frequency) you wish to record.  Importantly, this was originally used to describe the conversion of analog to digital signals for recording audio waves, which do not have multiple dimensions.  It is not precisely transferable to imaging without making some adjustments for both the Gaussian spread of the Airy pattern as well as the fact that pixels have two dimensions (you can read more about that here).  If you make the general adjustments for these factors, you arrive at a modified Nyquist sampling rate of ~3.3x for imaging.  So if you take the Dawes limit for your scope, and divide by 3.3, this will give you the image scale in arcsec/pixel which will record information at a diffraction limited level.  But note, this number isn't necessarily exact, because it relied on a few assumptions along the way.  However, following this guideline will achieve near diffraction limited results in good conditions.  Even without knowing any of this theory, any planetary imager can tell you that when you sample at approximately 1/3 the Dawes limit (meaning 3 pixels span one FWHM of the PSF for a point source) you will get more detail in your image than if you sample with only 2 pixels (assuming excellent seeing).  But going much above 3 pixels per FWHM does not add to the resolution of the image, and does have negative effects because the irradiance per pixel is greatly reduced (frame rate is reduced and noise increases).

Note that for maximum resolution, the 3.3x pixel sampling rate refers to the number of pixels that need to span approximately the FWHM of the Airy disk, not the Airy Disk itself.  The full Airy Disk measures twice the diameter of the Rayleigh criterion, which is itself slightly higher than the FWHM value.  Also worth pointing out is that you can ignore all of this theory, and simply multiple the pixel value by 5 and this tells you the F ratio to image at.  The math all works out to be about the same!  And finally, this only applies to capturing information under conditions in which you are truly diffraction limited.  This may be easy to do with smaller scopes, but with larger instruments, the seeing conditions will almost never be good enough for the theoretical maximum resolution to be obtained, so your images can often benefit by sampling at a reduced rate, which improves your frame rate and SNR.

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### #10 Tom Glenn

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Posted 09 January 2019 - 03:59 AM

An additional point to the above is that if you look at George's post (#7), he references another CN post that provides a description of the derivation of the "5x" pixel rule of thumb.  Of note, the calculation makes use of the FWHM value that I mention above, and makes the assumption that you should aim for a sampling rate of 2.75x.  This is fine, but does illustrate how some of this becomes arbitrary.  The 2.75x value comes from averaging the 2.5-3x range referenced in the linked post, although I just described above how another theoretical calculation suggests that a value of 3.3x should be used.  ​As I write this I'm realizing that an additional source of confusion is that the "5x" and "2.75x" values are referencing different quantities, with the former referring to multiplying the pixel size in microns by 5 to arrive at an F ratio, while the latter is reporting the number of pixels that should span a FWHM (the sampling rate). Sorry for any confusion!

Does any of this matter?  In practice not really, but if you use the 3.3x value in the formula, then the "5x" pixel rule becomes a "6x" pixel rule in green light of 550nm.  So under these assumptions, a 3um pixel should be imaged at F/18 rather than F/15 if you use a green filter and had the seeing conditions that would support diffraction limited imaging.  In practice, you might not have a barlow combination that can easily achieve these exact F ratios in your scope, however, so close is good enough.  Also of note, if we use a value of 650nm for the wavelength of light, since many people image with red filters, then this brings the ideal F ratio back down to 5x the pixel size even when using my 3.3x sampling factor (it becomes a "4x" rule using the original calculation).  So despite all of these calculations and theories, if you simply use a 5x rule of thumb you will be very close to the ideal sampling rate without having to worry about much else.  But as others (and myself) have stated, you really do have to factor in the seeing conditions, because oversampling the seeing will compromise frame rate and SNR for no reason, so you have to make a judgement call based on the conditions.  Although if conditions are very poor, it's probably not worth imaging anyway.

And to circle back to the OP......those suggesting that no barlow be used with the combination of a 90mm Mak-Cass and 2.2um pixels are correct.  Depending on the exact focal length of the Mak-Cass (most operate at somewhere between F/12 and F/14), then this combination is already adequately sampled (and in fact on the higher end of desirable) without a barlow.  Using even a 2x barlow in this situation would severely degrade the image quality, and a 5x barlow would completely destroy it.

Edited by Tom Glenn, 09 January 2019 - 04:14 AM.

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