THE STEVICK-PAUL OFF-AXIS REFLECTING TELESCOPE

The convex secondary mirror is placed just to the side of the light entering the telescope, leaving a little room for a light baffle. It is positioned afocally, so as to send parallel light on to the tertiary.

The concave tertiary mirror is positioned exactly twice as far to the side of the entering beam as was the convex secondary, and its own radius of curvature distant from the secondary. Because the tertiary mirror receives parallel light from the secondary, it forms an image at its focus, just as it would with starlight.

The focal plane lies within the system of mirrors, but is accessible to the eye with the inclusion of a flat diagonal. This fourth mirror does not obstruct light and corrects the reverted image that plagues telescopes having an odd number of reflections. It is angled to throw the image out of the telescope at 90 degrees to the sec.-tert. beam.

Although diffraction limited performance is possible down to about f/5.6, focal plane tilt, which increases with decreasing f-ratio, constrains the design to more moderate f-ratios. I have chosen to restrict my designs to f/10 or longer. This way image anamorphism is kept under 2 percent and focal plane tilt need not exceed 10 degrees.

The prototype telescope is a 10 inch f/6.2 design. This size was chosen because I already had the paraboloidal primary mirror and I wanted to test the system quickly; only two spherical mirrors had to be made. Eyepieces won't tolerate being tilted in the fat f/6 light cone, but it delivers an excellent image if the eyepiece is square. However, this leaves the top and bottom of the field out of focus and is why I recommend more moderate f-ratios be considered. With shallower cones of light the eyepiece can then be tilted to match the focal plane.

I employ a value for the radius of curvature of the spherical mirrors that is .4 that of the primary r.o.c.. This `radius ratio' has been found to be optimum, but telescopes are possible with different radius ratios.

Telescopes with radius ratios less than .4 are more compact, at least down to .33 where increasing pri.-sec. spacing lengthens the instrument again. They have a smaller primary tilt and smaller diameters for the spherical mirrors. However, they suffer a more steeply tilted focal plane.

Telescopes with radius ratios greater than .4 are longer. They have a larger primary tilt and larger diameters for the spherical mirrors. They do, however, enjoy a less steeply tilted focal plane.

By a stroke of good fortune, the eyepiece falls quite close to the balance point in an instrument designed with the preferred ratio of .4. It is in a convenient position for viewing and its arc of travel is short.

The tertiary mirror must be larger than the secondary by twice the clear field. Required minimum diameters of the spherical mirrors are determined with these equations:

[Eqn 1]	Sec. diam. = A*D+(1-A)*d	where:	A = radius ratio
[Eqn 2]	Tert. diam. = A*D+(3-A)*d		D = primary diameter
			d = diam. of clear field

Mirror tilts have a fixed relationship among themselves. The primary tilt determines all the others. In a Stevick-Paul, the paraboloidal primary mirror must have a tilt a bit larger than that required for freedom from obscuration, to allow for an effective light baffle. The equations are as follows:

[Eqn 3]	Pri. tilt:	T1 = C/N	where:	C is selected from the table
				N = pri. f-ratio

[Eqn 4]	Sec. tilt:	T2 = k*T1	where:	k = (1+A)/(2*A)
				A = radius ratio
[Eqn 5]	Tert.tilt:	T3 = T2-T1

[Eqn 6]

Focal plane tilt is approximated as 4*T3

The last three equations are valid for all possible values of the radius ratio. The numbers for the primary tilt are empirically derived to assure freedom from stray light and are valid for a ratio of .4 only.

The spaces between the surfaces can be found simply as:

[Eqn 7]	pri.-sec.	e1 = F1+F2	where:	F1 = primary f.l.
				F2 = secondary f.l.
[Eqn 8]	sec.-tert.	e2 = R3		R3 = tertiary r.o.c.
[Eqn 9]	tert.-f.p.	e3 = F3		F3 = tertiary f.l.
			note:	F2 is negative

The focal plane lies within the system of mirrors and a flat diagonal is needed to throw it clear. The diagonal mirror is positioned in the cone of light converging to the focus, figure 2. If it is placed to catch all the light for a 1 inch diameter field, and at the same time, kept from infringing on any of the field rays between the secondary and tertiary mirrors (upper position), not enough residual cone will exist to get the focal plane free. The only solution to this dilemma seems to be an increase in the tilts of all the mirrors. This would lengthen the available cone of light but would increase the focal plane tilt dramatically.

The solution is to nestle the diagonal mirror up against the central beam of light passing between the secondary and tertiary mirrors (middle position). Therefore, the diagonal intrudes into the light at the lower edge of the field, but is out of the way at the center and the upper part of the field. The diagonal mirror is then slid along the central beam toward the tertiary mirror (lowest position) until it catches only enough of the rays forming the top edge of the field to produce a one-half magnitude loss due to vignetting. These two compromises, acceptable intrusion at the lower part of the field, and acceptable vignetting of the edge of the field, have minimized tilt angles while still providing sufficient free cone to the focuser.

In this design, free cone is more important than residual cone. The length of cone which can be fielded by the diagonal mirror is the residual cone. I define free cone as that part of the residual cone which exists on the observers side of the parallel sec.-tert. beam. I look for at least 4 inches. A low profile focuser would be required if less free cone were available.

A light baffle surrounds the converging cone of light from the primary mirror, fitting into the notches made where the several light paths cross. Trying to keep the baffle out of the road of all field rays would result in the need for higher tilt angles. Following the philosophy of permitting a small loss in illumination at the edge of the field, the baffle is sized to just pass the central beam intact. This means vignetting technically begins immediately away from the center of the field, but because the baffle is so far from the focus, it blocks less than 10 percent of the light at the field edge. Vignetting arising from the placement of the diagonal mirror is far greater than that from the baffle.

With the baffle thus sized, the required primary tilt is not much larger than the theoretical minimum. By raytracing the light that just makes it through the baffle, I look to see that it approaches no closer than 1 inch to the field center. This means a field 2 inches in diameter is free of stray light. Even 2 inch O.D. eyepieces would thus be protected from washout. The table of primary tilts reflects this design philosophy.

Tolerances for spherical aberration are the same in a Newtonian and a Stevick-Paul telescope since the primary f-ratio is preserved in the final system; therefore, any long focus primary mirror that could be left spherical in a Newtonian may also be left spherical in this telescope.

Curator: Hartmut Frommert [contact]
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