Telescope contrast and resolution

[Ags]

I've had a thread going in the Physics section for a few years regarding diffraction and Airy discs. I was trying to calculate telescope resolution and contrast for different optical designs. I eventually cracked the problem and spent today feeding some telescopes through my simulator. Because a lot of work has gone into this, and it needs more explanation than a forum post allows, I set up a blog for myself.

http://opticsandalgorithms.blogspot.nl/2015/04/calculating-diffraction-patterns.html

At the bottom of the page you can find a table of various telescopes and their resolutions and contrast levels for different targets.

Of course even if my maths is perfect (and I can't believe my lovely SE4 comes out as badly as it does) I do not take into account manufacturing errors, so my results may be more applicable to high-end instruments like TMB apos than more affordable instruments like an ST80.

[Altais]

Very interesting. How do your results depend on the wavelength of the light? And when manufacturers quote angular resolution based on the Rayleigh criterion, what is the convention when it comes to wavelength (since the Rayleigh criterion is a function of wavelength)?

[Ags]

The convention is to use the peak sensitivity of the human eye which is ~510nm at night.

http://en.m.wikipedia.org/wiki/Spectral_sensitivity

At higher frequencies, the Airy disc gets smaller. I think observers in the 18th century noted color fringing in diffraction rings.

[Altais]

I see. Looks like the reflecting telescopes you have simulated actually perform somewhat better than the Rayleigh criterion would imply then. Good to know. 

[Ags]

No, the Rayleigh criterion is simply miscalculated for scopes with a central obstruction. The formula typically given for the Rayleigh limit applies specifically to refractors, which have more energy in their airy disc, but it is slightly broader than the same disk in an obstructed telescope.

[Altais]

Yes. My point was that if the angular resolution of a reflector quoted by the manufacturer is based on the Rayleigh limit for a refractor of the same aperture (as was my understanding from your blog post), then it is worth noting that the actual (theoretical) resolution for the reflectors in your simulation is in fact better than this. 

[Ags]

Yes, firstly I was relieved when my simulator matched the Rayleigh formula for refractors, and also that it showed the slight resolution boost obstructed instruments enjoy :-)

[Ags]

It took all day, but I calculated the diffraction patterns of 20 different telescopes (mostly variations of Newtonian). It's too late to upload all the results, but I did make a start on publishing the pictures of the diffraction patterns:

http://opticsandalgorithms.blogspot.nl/2015/04/refractor-diffraction-patterns.html

Edited April 12, 2015 by Ags

[YKSE]

Very interesting work Agnes, thanks for sharing

I have difficulty in accessing the source code link giving in your blog, can't download it either.

[Ags]

What problem are you having accessing the source code?

[YKSE]

Sorry, just opened it in google chrome. It must be that my Internet Explorer is of older version.

[Ags]

Good to hear.

I've been working on a more detailed report of various scopes, Newtonians 100 to 300mm, refractors 60 to 180mm, SCTs 150 to 280mm, plus more maks. For the Newts I give results for 25, 30 and 35% obstructions. I hope to post it tomorrow night.

[Ags]

I fed 28 telescopes through my telescope simulator and have some more telescope contrast/resolution data.

http://opticsandalgorithms.blogspot.nl/2015/04/contrast-and-resolution-of-different.html 

Aperture rules!

[YKSE]

Agnes,

A question about your calculation of refractors, are those achromats or perfect APOs? I'd assume that there're some differences in fine contrast between these two types, because of the chromatic aberrations in achromats.

[Xplode]

Numbers for newtonians seems weird, for 30% obstruction contrast increases with bigges scoper as you would expect, with 25% obstruction the 250mm has better numbers than the 300mm which seems weird to me

[Ags]

Thanks for pointing that out 250/25% seems off. I'm running that one again...

[Ags]

The simulation is done at one wavelength (510nm) so an achro would do ok theoretically! But I believe the results would only be applicable to long-tube achros and to apos.

I think I know what went wrong with the large newts - being very large, they are undersampled. I will redo the 300 newts too

Edited April 14, 2015 by Ags

[Ags]

Debugging the large newt issue is proving achingly slow, and I'm running out of ideas for the root cause... 

[Ags]

I finally figured out where my maths went wrong... It was a simple arithmetic error combined with a logic error; I have reconsidered how to calculate contrast and will redo the calculations accordingly.

[Ags]

I have been making slow but steady progress. I increased the number of samples per sub by a factor of 9, and also doubled the resolution of the final spot diagram to 1200x1200 pixels. I also found a way of detecting when the pattern is undersampled. I hope to put up some new contrast data tomorrow.

[Ags]

I mustered the courage to post a new set of scope contrast data:

http://opticsandalgorithms.blogspot.nl/2015/04/contrast-and-resolution-of-different.html

I increased the precision of the resolution calculations slightly, but now calculate contrast as the ratio of intensity in a cental 1 arc second radius versus a circle representing a given target size - 10 arc seconds for Mars and 30 arc seconds for Jupiter and Saturn. so a elescope which got all the light within an arc second of the focal point would get a contrast ratio of 1.0, and a scope that just produces an unfocused blur would have a contrast tending towards 0.

I hope i have not made any new mathematical errors, but i only seem to get time to work on this at 2am, so as in life there can be no guarantees.

[Ags]

I added an animation of the effect of central obstruction size. This is a central obstruction growing from 0% to 50% by diameter in a 130mm scope. The generated image is 60 arc seconds across (one Jupiter, with a bit of black sky around the edges).

http://i.imgur.com/UqEtSVv.gif

http://opticsandalgorithms.blogspot.com/2015/05/animation-of-central-obstruction.html

Edited May 8, 2015 by Ags

[Ags]

I created a graph showing the ratio of contrast to central obstruction size:

[Ags]

As a companion piece to the post of central obstructions and contrast, I did a similar calculation for contrast with cetnral obstruction fixed at 25% and vanes varying from 0 to 5mm.

http://opticsandalgorithms.blogspot.nl/2015/05/animation-of-diffraction-of-spider.html

Here is the graph corresponding to the C.O. graph in the previous post:

[alpal]

On 12/05/2015 at 07:06, Ags said:

I created a graph showing the ratio of contrast to central obstruction size:

Thanks for that.

Why isn't the contrast ratio 1.0 for no obstruction?

There used to be a Newtonian calculator on the net which gave contrast ratio

for the design of your choice.

I can't find it anymore after exhaustive searches.

There is some intellectual content here about it here:

https://www.telescope-optics.net/obstruction.htm

but that's all I can find.

Can anyone find that calculator for me please?

PS - it's not here:

https://stellafane.org/tm/newt-web/newt-web.html

although maybe that program used to have it 10 years ago?

 

cheers

Allan