THE STEVICK-PAUL OFF-AXIS REFLECTING TELESCOPE

All Stevick-Paul telescopes follow simple rules of construction. Refer to figure 3. We already know the distances between the surfaces. We need only calculate a1. This is the first axis distance. It is determined from the primary tilt as:

[Eqn 10] a1 = sin(2*T1)*e1 where: e1 = pri.-sec. space

The second axis distance will be twice the first.

[Eqn 11] a2 = 2*a1

The third axis distance will be one-half the first.

[Eqn 12] a3 = a1/2

Using equation 10 for the first axis distance, we find that its value for the 8" we are designing is 5.9737... inches. This is so close to 6 inches that we shall call it 6 inches even. It is always permissible to round up this figure slightly for constructional ease. Our axis distances are then:
a1 = 6", a2 = 12", a3 = 3".

We have enough information now to locate the centers of the surfaces on a large sheet of paper. Use the long edge of the paper as a guide; light should enter the telescope parallel to this edge. Mark the center of the primary mirror first, a bit higher up than its semi-aperture from the bottom edge. Draw a line the length of the paper through this point, and parallel to its lower edge. Then, using the known spacings and axis distances, locate the other three centers. Draw the path of the principal ray with a long straight edge, connecting the centers of the four surfaces (You may have already drawn the one between the secondary and tertiary surfaces in order to locate the focus.)

To accurately lay in the light rays of interest, we need to angle the mirror surfaces just as they will be in the final instrument. Bisect the three angles, then with a square or protractor, draw the three mirror surfaces at right angles to these constructs. The focal plane, which for now lies inside the system of mirrors, has no angle to bisect but is quite easy to draw in with a carpenter's square, as it is always oriented perpendicular to the incoming light.

Using a ruler, mark the full diameter of the primary mirror, then place tick marks to locate the diameter of light at the edges of the clear field on the last three surfaces. For the secondary and tertiary mirrors, this is the required minimum diameters for these mirrors. For the focal plane this will be the clear field itself.

Lastly, place another set of tick marks on the secondary and tertiary mirrors that represent the diameter of the central beam of light only. It has a value of A*D and is the same for both of them. For the 8" telescope the value is 3.2 inches.

[Eqn 13]	central beam diam. = A*D	where:	D = pri. diam.
			A = radius ratio

Taking again our straight edge, we shall lay in some of the light paths. In order to avoid confusion, not all possible light rays will be drawn. Start by drawing in the full beam of light entering the telescope. These two rays will be parallel to the edge of the paper, and of the same diameter as the primary mirror.

The next lines to be drawn will connect the edges of the primary mirror to the corresponding tick marks on the secondary surface marking the diameter of the central beam. At this point we have produced the first V notch marking the location of the top edge of the light baffle.

Starting where we just left off, draw parallel lines from the secondary mirror to the same set of tick marks on the tertiary surface. We can now see the second V notch, inverted from the first, that marks the location of the bottom edge of the light baffle.

Changing now, we pick up the wider set of tick marks on the tertiary mirror and connect them to the marks previously placed in the focal plane indicating the edge of the clear field. Of the two rays we just drew, the upper one intersects the lowest (closest to the primary) of the parallel rays between the secondary and tertiary mirrors right where the top edge of the diagonal mirror is to be placed.

To send light across the parallel beam at right angles to it, the diagonal will have a tilt somewhat less than 45 degrees.

[Eqn 14] diagonal tilt T4 = (45-T3)

Again, in the 8" f/11.75, this mirror will be tilted 42.72 degrees. This optical angle is measured against the principal ray passing through the center of the diagonal mirror.

A protractor can be used to draw in the diagonal but the easiest way is to score around the residual cone with a hobby knife letting the bottom cut extend a bit farther than we think is needed. Fold the flap of paper thus released at right angles across the parallel beam, beginning the fold at the intersection point. Crease the paper once it is properly oriented. We can now measure the free cone available on the eyepiece side of the parallel beam. Now unfold the paper and scribe the diagonal along the crease. The major axis of the diagonal mirror can now be measured. Divide by 1.4 to get the required minor axis diameter.

Some amateurs may opt to send the light out the side panel of the telescope instead of across the parallel beam. This is perfectly permissable. The focuser will then be in close proximity to the altitude axis resulting in a nearly stationary eyepiece. In this configuration the diagonal mirror will be on its side with one side up against the parallel beam. For this, fold the cone of paper straight back on itself instead of across the parallel beam, crease, then measure the required minor axis directly.

We can now finish the specifications of the 8" f/11.75 telescope. Measuring the diagonal mirror from the paper and dividing by 1.4 shows it must have a minor axis of 1.6 inches. We will specify the next larger standard size of 1-5/8 inches. The top of this slightly oversized mirror will be kept against the parallel beam while the rest sticks down. We can also measure the separation of the diagonal and tertiary mirrors along the principal ray. It is 28.75 inches, leaving 8.85 inches of residual cone. Almost 5 inches of free cone is available.

Here then is the finished design.

Curator: Hartmut Frommert [contact]
[Schiefspiegler Home] [SEDS]