Dealing With Diffraction In Telescopes
At left is a computer simulated image of a star as seen at high power through a telescope. Based on the Huygens Principle, the image was created by forming a unit gain circle in 3D to represent a circular aperture, then performing a 2D Fourier Transform on the pattern. The result is the interference pattern shown here, and it represents a point source (star) as seen through a telescope.
For illustration, this image is much larger that an actual star will look through your telescope. Rather than seen as a single point of light, a star in a high power telescope is seen as a small circle of light surrounded by one or more rings. The rings go on forever, but lose amplitude quickly, with only the first few being visible.
The ring pattern is a basic law of physics, but inconvenient for the user of telescopes. As you can imagine, two stars very close together have overlapping rings, and that blurs the distinction between the stars. The pattern of rings, called a diffraction pattern, limits the resolving power of a telescope.
The pattern shown is what would be seen through an astronomical refractor telescope. Refractors provide star patterns with the least amount of energy (brightness) distributed in the rings surrounding the star. Reflecting telescopes like Newtonian telescopes and Schmidt Cassegrain telescopes usually have some kind of secondary mirror in the light path that complicates the pattern, resulting in more energy being distributed to the surrounding rings and less in the central disc that's the star.
The light that is scattered into the diffraction rings makes the central star image a bit dimmer and the surrounding rings brighter. You can read more details about diffraction and different telescope designs at the diffraction tutorial.
It isn't just star images that suffer from this phenomenon. An extended image, like that of a planet, is equivalent to a large number of such diffraction limited points. Each point has energy dispersed into the rings surrounding the point. This reduces the contrast in an extended image such as Jupiter or Mars, which are composed essentially of many bright points.
The superior nature of refractors with respect to diffraction is why many telescope users prefer them. So why doesn't everyone simply buy a refractor and minimize the effects of diffraction?
The Effect Of Aperture Size On Diffraction Image
Why don't most people just use refractors? A -- because large refractors are expensive, and B -- there is another solution.
The image above shows the relationship between the nature of the diffraction image and the size of telescope. It may seem backward, but the star image actually looks smaller in a larger telescope. The central star image and its diffraction rings are both smaller with bigger aperture. That's what lets a bigger telescope separate stars that are closer together, and have better resolution on planets and other high resolution objects. The left image depicts a star diagram from a small telescope, the right a star diagram from a large telescope. In a larger telescope, the central peak is higher also, but that's not depicted in this image.
This seemingly backward result happens because a star is essentially a point source of light. It has no size in a practical sense, and a telescope can't magnify it enough to give it a size. The central disc seen in a star diffraction pattern is the smallest resolvable disc the specific telescope can create. Since it can't see things smaller, star images look that big. When you use a bigger telescope that is capable of seeing smaller images, the central disc of the star image then looks smaller.
If you checked out the diffraction tutorial, then you know that most design types of reflecting telescopes have secondary mirrors in the light path. The result of the secondary obstruction is to decrease the amplitude of the star, and increase the amplitude of the diffraction rings. That's why refractors are generally a superior design for any given aperture.
But this diagram shows that one way to reduce the effects of diffraction on resolution is to simply use a bigger telescope. Big reflectors are relatively cheap compared to refractors, and a bigger reflecting telescope, even with its central obstruction, will have an overall smaller diffraction pattern and better resolution. So planets like Saturn, Jupiter, and Mars will be resolved better, and as a bonus stars will be brighter with a bigger telescope.
The Effect Of An Apodizing On The Diffraction Image
But there is another way to have at least a small affect on the diffraction pattern without moving to a bigger telescope, especially if your telescope is a reflector of some type. The message that different sized apertures produce different sized diffraction patterns leads to another possibility. The way to take advantage of it is make a device called an apodizing screen or apodizing mask that essentially merges diffraction patterns from two different size apertures together, causing some destructive interference -- at least within the first couple of rings.
The images above represent the diffraction pattern through a refractor (left), a reflector with central obstruction (middle) and a reflector with an apodizing screen(right). Moving left to right, you can see that the introduction of an obstruction in the light path causes energy to be pushed into the surrounding diffraction pattern. The energy in the central disc is also reduced, though that is not represented in this diagram.
By putting an apodizing screen of proper dimensions in place, the result is like simultaniously looking through two apertures, the full aperture, and that of the hole in the center of the mask. The diffraction patterns of the two synthesized apertures have destructive interference in the first few (the brightest) rings, effectively reducing their effect. Even though the apodizing screen also slightly reduces the brightness of the central disc (the star), the respective difference in amplitudes between the central disc and surrounding rings is improved.
So -- how do you make an apodizing screen?
How To Make An Apodizing Screen For Your Telescope
You can make an apodizing screen with a little poster board and some window screen. You can make a simple one with just a single piece of window screen, or you can add one or two more screens (with different sized holes) to fine tune your apparatus.
The left image shows the simplest design. It's a black window screen with a single hole cut in the center. The size of the hole should be 90 % the size of your telescope objective. This single screen design is sufficient for a small telescope, say 4.5 inch or smaller. You can first cut a piece of poster board or tempered hardboard the diameter of your telescope tube, then cut a hole in that the size of your objective. That will give you a mounting surface for attaching the screen. Then make a collar for the board and slip it over the end of your telescope.
The middle image shows a two screen design. Below it you can see the resulting diffraction pattern. Note that with two screens, the second diffraction ring is nearly eliminated. The 2 screen design works well on 4.5 inch to 6 inch telescopes. The two holes in the screens should be at 90 % and 78 % the size of your telescope's objective. Rotate the two screens about 45 degrees with respect to one another before mounting.
The right image shows a three screen design. Again, below it is the diffraction pattern, with the 2nd ring gone and the 1st ring reduced in amplitude. The holes in the screens in this design are 90 %, 78 %, and 55 % the size of your telescope's objective. Rotate each screen about 30 degrees with respect to the previous screen.
How well does it work? I find it works well. When you first look in your telescope using an apodizing screen, you may be horrified. What you'll see is an awful array of scattered colors. But in the center of all that you'll see about a 100 arc-second area of clear view. This points out that the apodizing screen only works for observing small objects, such as double stars and planets. Whatever is small enough to fit in that 100 arc-second region of clear view is fair game.
I nearly always use an apodizing screen on my 6 inch f/5 Newtonian when looking at planets. I find that the subtle contrast of features on the planets is improved with the screen. In fact, I can get my apodized f/5 to perform nearly as well on such small targets as my f/10 planetary Newtonian. I also use the screen when observing bright double stars.
It costs little and is easy to construct. Go ahead and give it a try.
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