A Simple Yolo Design:

Arthur S. Leonard invented the Yolo telescope in the mid 1960's.  What a terrific design!  Imagine, grinding and polishing two surfaces, and putting a scope together that can perform as well as or better than a refractor of the same size.  So...  Why aren't there more Yolos out there?   I think that for most amateur telescope makers, it looks just way too complicated,  especially the math that's involved.

It turns out that if you follow a few design rules,  producing a Yolo should be much simpler.

The first rule:
Both mirrors have the same curvature.  With the yolo design this is generally the case. Even if they differ by 5%,  similiar results are achieved.

The second rule:
The mirrors are spaced such that the distances are the same.  That is the mirror to mirror distance the the same as the secondary to focus distance.  It turns out that this spacing should be 0.191 times the radius of curvature.  This was derived from one of Leonards equations.  More precisely,

                                         spacing =  R * (3 - SQRT(5)) / 4.
The third rule:
The mirror tilts of the primary and secondary are both the same.
If these three rules are followed,  Voila!  comma is cancelled and what you are left with is some astigmatism.  This can be removed by adding a cylindrical lens ahead of the eyepiece,  or by mechanically bending one of the mirrors.  I am bending the primary since I can adjust the tension of the bending bracket while observing at the eyepiece.  Arthur Leonard suggests bending an oversized secondary mirror.  That's a good idea since the bending pressure points would be located outside the illuminated area of the secondary mirror.
There also is a similiar design for the Schiefspiegler telescope:

Rule 1: 
The primary and secondary must have equal but opposite curvatures.  This is generally the case.
Rule 2:
The mirrors are positioned such that the distances are the same.  Similiar to the Yolo, but the formula is different:

             spacing = R * 0.309

   or       spacing = R * (SQRT(5) - 1) / 4
.
Rule 3:
The secondary tilt is 4 times the primary tilt.

Voila!  Comma is cancelled and you have some astigmatism left.  It's common to place a cylindrical lens in the light path ahead of the eyepiece.  I would try a bending bracket on the primary to adjust it in, rather than the secondary. 

Possible 8 inch F25 design:
Surface    Radius                 Tilt        Separation
1             249.68  250.32      2.5        77.25
2             250                      10.0      77.25
A special thanks to Dave Stevick for providing the spot diagram & ray tracing program WinSpot.  It's easy to use.  You can examine numerous provided telescope designs or start creating your own.  You can find it at Dave Stevicks Weird Telescope Page.

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