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How does diffraction work?


Ags

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I thought I could get an approximate measure of the light scatter in a telescope by simply making a ratio of edge to area - edges contribute diffraction and area contributes unscattered light. Of course it is a simplification too far: a thin spider vane will cause less scattering even though by my approximation it contributes the same amount of edge-length as a fat vane.

So how is it that the shape of the telescope opening affects the degree of diffraction? Going back to the spider vane, a photon getting scattered on one edge of the spider vane cannot know what is happening on the other edge of the spider vane, or how far away the other edge is...

On a similar note, a nearly circular opening, like the aperture blades on a camera lens, causes blindingly obvious diffraction artifacts in an image. Is it really true that a 90% approximation of a circle produces so much more diffraction than a true circle, or does a polygon merely concentrate a roughly similar amount of diffraction into highly visible spikes?

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A perfect circle with no obstruction will show no diffraction. Ever seen diffraction through a APO refractor? I hope not. Diffraction is what happens to light when it passes near the edge of an object. In this case, star light passing over the edge of the spider vanes. In most cases, diffraction is bad because it spreads star light out instead of focusing it all to a common point. They are also distracting to some people. If I were a serious astrophotographer, I might care, but for the most part, I think it looks pretty cool. Except on clusters. Now that is annoying.

I can't really explain why there is diffraction on cameras. For that, I'd need some one else to explain. I'm also kind of curious where it come from because the aperture is essentially octagonal not circular with spider vanes in the way.

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A perfect circle with no obstruction definitely shows diffraction. It is called the Airey disc and is shown by all telescopes regardless of design. The apo won't show diffraction spikes, but it will show diffraction.

In fact... The diffraction introduced by the circular edge of the telescope is worse at small apertures - so the typically small-apertured APO can be at a disadvantage.

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Light "bends" at any "edge" this bending is called diffraction. The aperture of any telescope presents an edge, even the edge of a mirror or lens. A secondary obstruction such as a Newtonian secondary, adds more diffraction, and the first "diffraction ring" of the star pattern is brighter with that additional edge". The bigger the obstruction, the more diffraction there will be. This "first diffraction ring" is responsible for deterioration of image quality, as fine detail is masked by the brightness of the added diffraction. The refarctor has, thus, less diffraction and higher image quality. Chromatic abberation colours this image, unfortunately, with a Creamy insead of white sharp detail, and also adds fringe colours. The apo has none of theses failings ( at least hardly noticeable) consequently is a telescope showing finer detail. Diffraction will always remain.

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I'm trying to find a mathematical approximation that is better than edge/area, that takes account of the difference between for example a thin vane and a fat vane... I don't want to get my head around Fourier transforms! :embarassed:

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Diffraction is a lot more complicated than reflection or refraction. It's essentially an interference effect: wave-fronts meet an obstruction and interfere with each other beyond it. (If you think in photons then yes, it's a non-local effect, because that's what interference is). So to do it properly you need messy calculations or simulations, and you would presumably want the latter. These links might help, otherwise try looking around for others (keywords some combination of telescope/diffraction/simulation). If you don't want diffraction spikes in your Newtonian then use a curved secondary holder. The diffraction won't have gone away: it's just making a different sort of pattern at the eyepiece.

http://www.falstad.com/diffraction/

http://www.beugungsb...iffraction.html

http://www.telescope...ction_image.htm

http://www.astronomy...com/spider.html

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Right. The diffraction doesn't go away, it is simply spread about in the focal plane so that it beome too feint to see. In short messages such as this, it is almost impossible to explain it properly, it takes quite a bit more than the few words in these posts. Acey got a good point across. If anyone REALLY wants to know more about diffraction, and how diffraction gratings work in spectroscopes, drop me a PM and I will send enough info to possibly make things clear. I dare say Acey would probably do the same thing, too, but I can't speak for him.

I would prefer to take the route suggested by acey, ie, simulations rather than calculations. The latter is complex, but if you are a mathematician you will already have been through them, but simulations and diagrams show what's going on to make life almost :grin::huh: pleasant! :huh:

(home made experiment equipment. simple yet effective.)

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  • 2 years later...

Old thread, but I found this today, maybe I can adapt it to simulate some more common astronomical apertures:

http://www.falstad.com/diffraction/

It includes ring and disc apertures, so that's maks and fracs covered. Just need to figure out how to add in spider vanes (of various widths, straight and curved). Also would be nice to add in polygon apertures (i.e. camera lenses).

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I have built a telescope model using ray tracing rather than fancy mathematics. It's rather slow, but I understand what I have done. Initial tests look promising, at least I get a central spike as expected for an airy disc. But it looks like I will have to make my virtual CCD much higher in resolution.

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Well, I have got my diffraction calculator working and I ran a few smaller telescopes through it. It is the Airy disc (showing power, amplitude squared).

EDIT: Looks like my maths is wrong! Watch this space!

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No, the ray tracing is very slow. I need to add multithreading and some optimizations to speed it up. I figure I can get it 30x faster, but even that is not enough. I am currently only calculating the cross-section of the pattern - to generate the full image of the diffraction pattern will be hundreds of times slower.

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Going back to my original post, you cannot make an approximation of diffraction by making a ratio of edge to surface area. The reason is that all points of the aperture contribute equally to the diffraction pattern, which is why spider vane width makes a difference. The way to understand it is by the Huygens-Fresnel principle, which lets you analyze wavefronts as being the sum of smaller wavefronts. So for example, reflection is not analysed as a photon bouncing off a barrier at the angle of reflection, but instead as radial wavefronts spreading out from every point on the reflective surface; the interference between these wavelets results in the observed reflected wave.

So in the case of an Airy disc, the point of focus is the point at which all wavelets interfere constructively with each other (because the light has to travel exactly the same distance down the telescope tube, off the mirror, and to the focal point, so the waves are in phase). As you move away from point of focus, the "agreement" between the wavelets breaks down rapidly, but not linearly, which what we see in the graph of the Airy disc. The wider the aperture, the more quickly the wavelets will disagree with each other and interfere destructively, meaning the Airy disc gets smaller as aperture increases.

http://en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle

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Bother! I knew my graphs looked wrong somehow... I had the central obstruction diameter out by a factor of two. So the "maks" in my graph are actually monsters with 60-70% central obstructions!  :Envy:

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 I am currently only calculating the cross-section of the pattern - to generate the full image of the diffraction pattern will be hundreds of times slower.

Not necessarily. Symmetry is your friend.  For example,  you already have enough data from your cross-section to generate a disc and rings for a refractor (spherically symmetric diffraction artifacts). A 'standard' four spiked Newtonian star will only require 1/8th of the diffraction image calculated.

Good luck with your challenge.

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Well, I don't want to make assumptions I am getting the data right (i.e. just assuming I have achieved rotational symmetry), and I eventually want to look at asymmetrical scenarios like focuser drawtubes sticking into the optical path...

I did a low res calculation of a small newtonian (150mm aperture, 29% obstruction, 4 1mm thick spider vanes) and made this animation as I added the iterations of my sampling together. It took 2.5 hours of calculating on my laptop, with a total of 64 "subs".

kaHwpbS.gif

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Tiki, I have followed your suggestion and introduced support for symmetry; I allow for reflection on either axis or both, so I get to save 75% of processing time for the average Newtonian.

I have done lots of work to clean up the code and make it easy to add different kinds of visualizations to the data. I just need to make it easier to add different obstructions to the light path. 

I have also added the ability to write out the results as a text file, not just as an image. This lets me do some maths after the fact on the data, so I can start finding meaningful ways to compare the different scopes for resolution and contrast.

I took too much time today wrestling with displaying the diffraction patterns in a "realistic" way - the previous animation was processed i Gimp, but I wanted my program to produce a moderately accurate view of the patterns by itself. This was the best I managed so far (although the middle brightnesses are still too bright):

WJiJtQ7.png

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