Designing a Telescope: What Equations Do I Need?

[Tyrion101]

I would like to design a telescope from the ground up, the only parts that I will not be making myself will be the mirrors and eyepieces. I've already decided I needed focal length equations, what others will I need to build it? I'm going to go for a truss tube dobsonian, (I've seen some ideas for ultra lightweights that I'd like to play with) which means I'll need some other equations I'm not familiar with. I've not decided on aperture size yet, I guess that will depend on what I can afford mirror wise. So any ideas? I figured here would be the best place to ask.

 

[jedishrfu]

for telescope parts:

http://www.telescope.com/home.jsp

and here's an article on building a dobsonian scope:

http://www.popularmechanics.com/science/space/telescopes/4286700

 

[Drakkith]

Try this site as well: https://stellafane.org/tm/dob/

 

[Greg Bernhardt]

Here is another pretty good tutorial on building a telescope from Space.com here
http://www.space.com/24114-how-to-build-a-telescope-science-fair-projects.html

 

[elegysix]

You will need to consider the spot size, field of view, field curvature and off-axis aberrations that result from the mirror you use, as well as know what is acceptable for how you will be using the scope. I would recommend using some ray tracing software to aid you with the design. (such as zemax, it can tell you many of those things)

Some of the smaller diameter mirrors (I forget what the limit is - maybe 8" diameter?) a spherical surface meets the 1/4 (might be 1/8, been a few years since I've worked on them) wave criteria, even though the surface should be a parabola. This makes manufacturing your mirror much simpler.

I don't know how set you are on a dobsonian, but if you go for a cassegrain, be sure to purchase the mirrors as a paired set.

 

[Chronos]

The Dobsonian Telescope, by Kriege and Berry is highly regarded. While focused more on large apertures, it includes plans that are adaptable to more modest scopes.

 

[Drakkith]

Some of the smaller diameter mirrors (I forget what the limit is - maybe 8" diameter?) a spherical surface meets the 1/4 (might be 1/8, been a few years since I've worked on them) wave criteria, even though the surface should be a parabola. This makes manufacturing your mirror much simpler.

My optics book has a spot diagram (spot blur) of various F-ratio 200 mm spherical mirrors and specifically talks about using a spherical instead of a parabloidal mirror. It says that as long as the spot blur is smaller than the airy disk it is acceptable to use a spherical mirror. Since the airy disc increases in size relative to the spot blur with increasing focal ratio, a slower f-ratio is needed. For an 8 inch (200 mm) mirror the fastest f-ratio is f/12. Anything faster than f/12 will have the airy disk smaller than the spot blur, meaning that your mirror is not diffraction limited.

For example, at f/4, an 8-inch spherical mirror has a spot blur that is about 10-20 times the diameter of the airy disk. At f/6 the spot blur is about five times the size of the airy disk. An f/8 mirror would probably be the fastest usable mirror where the blur could be accepted, but the spot blur is still twice the size of the airy disk, so I wouldn't recommend it. At f/10 the airy disk and the spot blur are almost the same size, and at f/12 the airy disk finally exceeds the spot blur, meaning that only an f/12 spherical mirror or slower is diffraction limited.

Reference: Fig 5.4, Telescope Optics: A Comprehensive Manual for Amateur Astronomers, by Rutten and van Venrooij.

 

[elegysix]

Yes that's exactly right, I forgot to mention that it depends on the f number.
(It's been 4 or 5 years since I made optics - and I haven't had any courses on this stuff. Just 2.5 years manufacturing experience)

 

[Tyrion101]

I'm going for a 16 inch scope, I want to design it so that it's eyepiece will be at eye height when straight up, I'm about 5 foot 10, so the eyepiece would be a couple inches shorter, I don't want to have to contort to uncomfortable positions when I look straight up. Is this feasible with a 16" mirror?

 

[cpman]

With a mirror at least F/4.5 or faster, it is reasonable to assume that the eyepiece is less than 5'10", even with the mount, as the optical length of a 16" F/4.5 is 72". With compensation for the fact that the optical path is bent, the OTA will probably be close to 65" long.

Unfortunately, faster mirrors are much more difficult to figure to a high quality, and will be more expensive than a slower mirror. However, F/4.5 isn't too fast, so shouldn't be that much more than an F/6 for instance.
From my experience, an F/4.5 shouldn't have awful coma, and if you haven't used something without coma before, you'll be satisfied with the views.

I'm not able to get numbers for a typical 16" F/4.5 Newtonian though, as I don't have my computer with me.

Hope I helped!

 

[Chronos]

At the zenith position, the eyepiece of an f4.5 mirror will be a bit high. For example, the eyepiece height for a 16" Lightbridge, f4.5, is between 67 and 68". Of course, most of the time you won't be viewing the sky directly overhead, so the ep should be at a comfortable height for the average person. f4.5 is about as fast as it gets for a mass produced 16" mirror. Faster mirrors get expensive in a hurry.

 

[davenn]

At the zenith position, the eyepiece of an f4.5 mirror will be a bit high. For example, the eyepiece height for a 16" Lightbridge, f4.5, is between 67 and 68". Of course, most of the time you won't be viewing the sky directly overhead, so the ep should be at a comfortable height for the average person. f4.5 is about as fast as it gets for a mass produced 16" mirror. Faster mirrors get expensive in a hurry.

That would depend on the mount the telescope was on

My Meade DS10 10" f4.5 Newtonian, has a f/l of 1120mm, a tad over 3ft
It was on a reasonably short pier. The only time it approached standing/crouching height
was when it was aiming towards the zenith ... I still had to bend over a bit

Being a tall guy 6'3" I always found the scope too low to the ground for comfortable use
And renting the home, I was unable to mount it on a taller pier


Dave

 

[tfr000]

You need not do a lot of math for the first cut at a Newtonian-style scope. Basically, the focuser will be at about the focal length from the primary mirror, minus half the diameter of the tube to account for the secondary's fold in the light path.
That's all I did for an 8" f/8 Newtonian I built many years ago - it worked fine. Ray-tracing and all that isn't necessary, unless you're going to be grinding some exotic optics.