November 1999 Newsletter

Stockton Astronomical Society

Valley Skies

Valley Skies - November 1999 Issue

The Telescope Nut
by Jeff Baldwin

Secondary Mirror Size and Offset

When you build a Newtonian telescope you need to design the size and placement of the secondary mirror. This seems easy to most folks, but believe it or not, it's easy to do it wrong. This little guy is more important in being engineered correctly than most people think it is, and the resultant image may pay the price for doing it incorrectly.

The secondary mirror is an oval-shaped piece of flat glass that reflects the light from the primary mirror's focus cone towards the focuser on the side of the tube. The shape is called elliptical, since a cone sliced at an angle gives us an oval figure called an ellipse. The long axis of the ellipse is called the major axis, and the short axis is called the minor axis. When you cut a cylinder out of a flat glass at a 45° angle, the length is always 1.414 times as long as the width. The obstruction of this glass will appear as a circle whose diameter is the minor axis.

The size of the secondary mirror can be calculated in about a million different ways. They all boil down to this simple rule. The minor axis (m.a.) of the secondary mirror is h/f + u, where h is the height of the remaining focus cone, f is the focal ratio of the telescope's primary mirror, and u is the unvignetted field of view. OK, it isn't really as weird as that sounds. If you have a 10" f/5.6 telescope, then f is 5.6. If it is in a 12" tube, and the focuser is 2" tall, then the height of the remaining focus cone is half of the 12 plus the 2, or a total of 8", so h = 8". The unvignetted field is the size of the light sample that the eyepiece is going to gawk at. Most folks think this needs to be as big as the eyepiece's field of view, but experimentation shows that once you get to about 0.1", no more field lightening helps, so you might as well keep it down to 0.1". Any more would increase obstruction and diffraction, and would cost more. So, With this 10" f/5.6 telescope using a 12" tube and a 2" tall focuser, we get a minor axis of m.a. = 8"/5.6 + .1" = 1.43" + .1" = 1.53". Now, the outer part of the secondary mirror is usually rough or tde or turned up from being sawed out. That means that we'd like to get a slightly larger secondary mirror to avoid that problem, and the way to do that is to buy the next size up. Try to find the secondary mirror on the market that is the smallest available larger than 1.53".

Secondary mirrors in small and slow telescopes can be mounted into the telescope so they collimate using their centers. However, if your telescope is very fast, large in aperture, or especially both large and fast, then the secondary mirror has to be mounted with an offset. This is because the mirror cuts through the light cone at a 45° angle, making the part that it cuts through near the primary larger than the part that it cuts through near the star.

Notice in the illustration that the side of the secondary mirror above the optical axis has more length than the other side. This requires that the secondary mirror is not mounted with its center on the optical axis. This needs to be accounted for with larger and/or fast optics.

To calculate this offset I have a formula that is clumsy. I also have a program that calculates it if you want to contact me. Anyway, here it is. The lengths from the major vertices to the offset mark are

and

where u is the unvignetted field of view, h is the distance from the optical axis to the first piece of glass in the eyepiece, A is the aperture of the mirror, and fl is the focal length of the telescope. Let's try one.

Let's use the 24" f/3.7 telescope with a 1.5" tall focuser and a tube diameter of 25" (12.5" radius). The focuser is inset a little, so the actual distance from the optical axis to the first piece of glass in the eyepiece is only 12.5". So h = 12.5", A = 24", u = 0.1", fl = 89.3". Therefore:

d₁ = Ö 2[(.1/2-12.5)/((-24+.1)/(2*89.3))-1)-12.5]
     = 1.414[-12.45/(-23.9/178.6-1)-12.5]
     = (1.414*12.45)/(.1338+1)-17.675
     = 15.526-17.675
     = -2.148"

d₂ = Ö 2[(-.1/2-12.5)/((24-.1)/((2*89.3)-1)-12.5]
     = 1.414[-12.55/(23.9/178.6-1)-12.5]
     = -1.414*12.55/(.1338-1)-12.5]
     = 17.746/.866-17.675
     = 20.492-17.675
     = 2.817".

This means that, measured from the vertices of the major axis, the collimation dot should be 2.15" from the ends pointing towards the star and 2.82" from the end pointing towards the mirror. These two should add up to very near the major axis of the secondary mirror. 2.82+2.15 = 4.97". The minor axis is the major axis divided by 1.414, so the minor axis should be about 4.96/1.414 = 3.51". Let's check; the minor axis should be h/f + .1 = 12.5/3.7 + .1 = 3.4 + .1 = 3.5".

In a nutshell, the minor axis is about 3.5", the major axis is 1.414 * that 3.5 = 4.96", and the offset should separate that 4.96" into two pieces, one is 2.15" and the other is 2.82". You now know exactly how to stick that secondary mirror into the telescope so that the light cone is not cut out anywhere in the light path.

If you don't want to do that arithmetic, or if you want to do it and check your work, call me and give me your numbers and we'll do it together. You can try this with smaller telescopes to see that the offset is a negligibly small number and that you don't need to worry about it.

Diffraction occurs from the secondary mirror if it is too large. Mathematically, diffraction begins to alter your image when it exceeds about 17% the diameter of the primary mirror. Lots of people go way out of their way to keep this number smaller than 17%. However, if your arithmetic shows that you need a 16.3% secondary, I don't recommend using a 17% mirror. That would mean that the edge of the mirror is being used, and that is the worst part of the secondary mirror. It would be better to go a little larger and stay on excellently figured glass than to go right on the nut and be using tde glass or turned up glass. I needed a 3.5" minor axis on the 24", but I sawed out the secondary mirror at a target of 4", and I got 3.9" with chips in about 1/8". That leaves 3.6" of good glass, and I am still less than 17% obstruction.

Well, that was somewhat of a mathematical jumble, but like I said, if the math goofs you up, holler at me. It is better to engineer your secondary mirror than to blindly stick one in and expect it to function as planned.

Enjoy ATMing, and ...

Clear Skies...Jeff Baldwin
For more information on Telescope Making jump to the ATM page.