A technical question re exposure

[pberrett]

Hi wonderful people

This question is for those more technically inclined.

I have been reading up on exposure, resolution and aperture. As I understand it in astrophotography aperture is king because a bigger telescope = more light = more saturated and detailed imaged (i.e > resolution).

This can be compensated for however. As an example take a 12" aperture telescope which takes an image with an exposure time of 10 seconds (all other things being equal and assuming one is tracking the object). If one only had a 6" telescope one could compensate by increasing the exposure time (I assume by a factor of 4 = (6^2/3^2) = relative difference in areas of telescope.

My question is whether in doing so one can achieve the same resolution image with the 6" telescope as was achieved with the 12" telescope or whether the use of a smaller telescope restricts the resolution in a way that can't be compensated by longer exposures.

Hoping someone can help.

Thanks Peter

[Merlin66]

Visually or imaging??
Visually the smaller aperture always has lower resolution (all things being equal, seeing etc)
With imaging it comes down to plate scale (arcsec/pixel), seeing, guiding etc etc.

[pberrett]

Imaging.
I am interested to see whether a small telescope can produce a highly detailed image or not.

[Merlin66]

Smaller apertures will be limited by the seeing.

[Outcast]

Have a look in the beginners and deep space imaging sections of the forum. There are folk achieving incredibly fine detail with as little as 61mm of aperture.

What you're asking is incredibly more complex than just an aperture & exposure length as was alluded to in an earlier response.

Pixel size, pixel number, sample ratios, sensor size, tracking accuracy, seeing conditions, cooled/uncooled camera... all these & more affect image quality & resolution achievable.

[Startrek]

It appears you have some technical background
Can I suggest you read some of Craig Stark’s tutorials under “Fishing for Photons” circa 2009 to 2012
He wrote a number of very good articles in relation to image scale, signal to noise ratio etc... in imaging
it may answer some of your questions

Craig is a Professor of Neurobiology an avid Astrophotographer , he also invented PHD guiding software

[pberrett]

Thanks

I will check that out.

cheers Peter

[JA]

Hi Peter,

Your question about resolution or the ability to resolve (and capture) detail in an object is governed by controlled / limited by a number of factors:
1. the atmosphere,
2. the optics,
3. the imaging system & settings,
4. the mount tracking precision and
5. processing skills and experience

There are many provisos one could put on an answer to your question, which is focused primarily on the OPTICS, but generally speaking as far as OPTICAL resolution is concerned the larger the aperture the better the resolution, all else being equal. This is in accordance with the Rayleigh Limit / Dawes Limit criteria, essentially diffraction limitations on light passing through an aperture, which is also a function of the wavelength of the light. The only other governing parameter optically is the extent to which optical aberrations and/or contrast might reduce the performance further.

If I had to draw a logical line in the sand I'd say that for 2 instruments of equal focal length, equal image circle size and "optical quality", as hard to define as that is, the larger aperture instrument will provide higher resolution. The ability to use or record an image at that higher resolution depends on all the aforementioned factors 1, 2, 3, 4 and 5. Any shortcomings in these factors will only serve to limit this resolution further.

On the issue of exposure duration: Of course exposure duration and/or stacking images for greater overall exposure duration will help produce a cleaner (less noisy) image as the signal to noise ratio is increased, but it will not resolve what the optics cannot see due to aperture limitations.

I will link something further later...

EDIT >Now added....
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/Raylei.html

https://en.wikipedia.org/wiki/Angular_resolution

https://courses.lumenlearning.com/austincc-physics2/chapter/27-6-limits-of-resolution-the-rayleigh-criterion/#:~:text=Diffraction%20limits%20res olution.,diffraction%20pattern%20of %20the%20other.

Best
JA

[Merlin66]

Look at Rob's images which show what can be achieved with smaller aperture set-ups.
http://www.iceinspace.com.au/forum/showthread.php?t=187637&highlight=Rob

[pberrett]

Impressive!