Folding a Newtonian Telescope
Until about a year ago this team was building a telescope with something like a Nasmyth design. James Nasymth invented the idea of using three mirrors in a telescope to eventually direct the optical path perpendicular to the telescope tube through a primary axis of rotation for the mount. The result is that as the telescope rotates about that axis, the eyepiece does not move, nor does any kind of instrument that might be installed there. Professionals use this kind of design on their telescopes to avoid mechanical problems caused by very large and massive instruments at the prime focus. Our interest was to get the eyepiece down to the height of a standing or sitting person, eliminating the need for a ladder in the public observatory at Robert Ferguson Observatory.
We weren’t quite Nasymth, but the concept was the same. The primary (40-inch) mirror is a concave paraboloid shape. It reflects the incoming light from the sky to a secondary on that same optical axis that is a convex hyperboloid. The light, still on the same axis, then encounters a third mirror, this time a flat, tilted at 45 degrees to the optical axis, bouncing the light through the side of the tube. That’s where we deviated from the original Nasmyth design – we allowed the final optical axis to be closer to the front of the telescope (optically), meaning it would not be at the mechanical altitude axis of rotation, but rather a few inches above that. The result was an eyepiece height for visual users that wasn’t stationary, but was still reachable for most individuals without a ladder.
During the first star tests we did of the optical components of the telescope, we incorporated the Nasmyth convex hyperboloid secondary mirror. Those first tests showed we had some significant astigmatism in the system. We removed the secondary from the system and placed a video system at prime focus where we validated that the primary mirror was the source of most if not all of the astigmatism. Other blog entries since that time 18 months ago tell the story of learning how to make and use a Bath interferometer to better test the primary mirror in the shop and our eventual arrival at an acceptable figure as evaluated by both interferometry and star tests. While that process was unfolding, we were thinking about our challenges with the secondary mirror.
Testing the surface of the secondary mirror was not something we were entirely confident we could do. Our experience with the primary, where we tested to the best of our ability with a multi-zone Foucault shadow test, made us less confident of our tests of the secondary curve. We also learned something first-hand about the behavior of the Nasymth-Cassegrain optical design in practice – the placement of the secondary along the optical axis is very critical and requires fine adjustment to bring the focal plane into a desired location. When we first tried locating that focal plane, we found that we had incorrectly estimated that location by several feet (!) but that by adjusting the location of the secondary less than 2 inches, we corrected that location. While we could successfully get a focal plane where we wanted it, our telescope will be operated by a large team of docents who would be asked to make these kinds of fine adjustments if the primary mirror was every collimated, and the touchiness of the secondary location worried us in that situation.
We had considered a folded Newtonian design early in the project and had discarded it as impractical for a mirror the size of ours. The basics of a folded Newtonian include the same paraboloid primary mirror reflecting the optical path to a flat secondary mirror (the fold). The secondary reflects the optical path back down the main optical axis to a diagonal mirror on that axis, where it bounces out to the focal plane beyond the circumference of the optical tube assembly (OTA). We had planned that the primary be a short focal ratio and the mirror, with astigmatism, was at about f/3.6 (the ratio of the focal length to the diameter of the mirror). In order to bring the focal plane near to where we wished it in the mechanical design, the secondary flat mirror would be, well, huge.
The other problem that a folded Newtonian design had to solve was coma. In a reflecting telescope with a paraboloid primary mirror, when you are observing the image of a star at the center of the field, on axis, you get a nice, compact, point-like image. But when you look at the edge of the field at stars that are off-axis, forming a small angle with the pointing direction of the optical system, you get images that look like comets, all pointing toward the center of the field. This is true for all Newtonians, folded or otherwise. Small amateur-built telescopes don’t visibly suffer from this aberration of the image because the effect is small above focal ratios of f/8 or so. Coma gets increasingly difficult to ignore as you reach for smaller focal ratios.
It turned out that by the time we were having these deliberations, Mel Bartels, for whom an asteroid is named and who authored the earliest versions of the software we are using on Project 40 drive systems, had been experimenting with short focal ratio reflectors, like an f/2.8 6-inch design documented at http://www.bbastrodesigns.com/6inchF2.8/6%20Inch%20F2.8%20Telescope.html. Further, he had inspired others to similar experiments and there were now dozens of examples documented at amateur web sites demonstrating the challenges and rewards of this design. In particular, many of these designers had adopted a coma corrector from Paracorr that solved the coma problem by inserting a lens assembly in front of the eyepiece, eliminating the coma aberration with specific eyepieces.
With a potential solution for the coma problem of a short focal ratio Newtonian, the team evaluated the options for reducing the size of the secondary mirror. We are working with a focal length of 144 inches. When the telescope is pointing straight up at the zenith, the eyepiece will be at its greatest height above the floor. The mount places the primary surface about 23 inches above the floor and we would like the eyepiece to be no higher than 60 inches above the floor. The primary-secondary distance (x) plus the secondary-diagonal distance (y) plus the radius of the OTA plus a couple of inches to get the focal plane out to a usable location (z) gives us a formula for the height of the eyepiece above the floor: h = 23 + (x – y) and a constraint on those values: x + y + z = 144. Since z isn’t going to change for our design, consider it a constant of 24 inches and with a target of 60 inches for h, we can solve the two equations to reach x = 78.5 inches. The diameter of the on axis light cone at a distance x from the primary mirror is D’ = D (1 – x/F), where D’ is the diameter of the light cone at x, D is the diameter of the primary mirror, and F is the focal length of the primary. At the design distance of 78.5 inches, the secondary would need to be 18.2 inches in diameter and the diagonal would need to have a minor axis of 6.7 inches.
To reduce both of those diameters the team explored a design that tilted the secondary mirror to move the prime focus outside of the OTA without reflecting off of a diagonal mirror. Eventually the diagonal mirror was restored, but as a standard eyepiece diagonal (not one mounted on a spider). With this design, we reduce z to the back focus or distance from the final bounce off of the diagonal mirror to the prime focus, about 6 inches when using the Paracorr. And y is also reduced because the optical path is traversing a diagonal line from the center of the secondary to the edge of the OTA. With some optimization, we settled on a 30 degree bounce off of the secondary (by tilting the secondary by 15 degrees) and that gives a y’ corresponding to the altitude of that triangle of y’ = y cos 30. When you do the rest of the math, the secondary distance from the primary is 83.9 inches where a 16.7 inch diameter secondary will capture all of the light from the primary. We were able to refine that design by allowing the zenith height to creep above 60 inches because we would rarely point that high in the sky and by sacrificing a half inch around the circumference of the primary mirror where a turned edge was only going to give us some scattered light in any case. The result was a secondary 16 inches in diameter, which is 30% less area covered than the 18.2 inch diameter secondary we started with.
The final problem we had to solve was a mental one – it was hard to allow ourselves to accept a 16 inch diameter secondary mirror, so much bigger than even the 6-inch diagonal we had purchased for the Nasmyth design. So we recalculated and recalculated and asked each other questions (like, how are we going to make a 16 inch flat mirror!) over and over again until last June. By that time, we were seeing enough progress in the interferometry of the primary mirror that it was time to make a decision. And because we didn’t believe that we could make the flat ourselves, we checked the budget, suspended our belief that secondary mirrors are not that big, put the secondary mirror out to bid, and chose Custom Scientific to make the mirror for us. The order was placed in July and they delivered it in September, a month ahead of schedule.
In the meantime, we were exploring the Paracorr coma corrector on the Televue web site. The design as it comes from the maker includes a rotating tube at the eyepiece end that has lettered locations on a helical track that give you the ability to precisely control the distance from the ocular to the exit lens of the corrector. Each eyepiece would have its own letter setting for optimal performance of the corrector. This was workable for the docent team that would be operating the telescope, but would definitely require some training. Then we found a reference to the SIPS – an integration of a Starlight Instruments feather-touch focuser with a Type 2 Paracorr corrector. A review by one of the early purchasers locked us in on this solution. In operation, he reported that he could use any eyepiece with the corrector, rough focus with the main focus adjustment to get the image of a star in the center of the field looking point-like, and then use the feather-touch fine focus adjustment to make the stars at the edge of the field point-like. This is so much like normal focusing with the small addition of paying attention to the center and then to the edge images that we settled on this solution for the telescope.
With the focuser now on the corrector, our previous thinking about the human end of the telescope, with a classic focuser (rack and pinion or Crayford) aimed at the secondary, became a design with a standard diagonal mirror mounted to point at the secondary, reflecting the light up to the corrector-focuser-eyepiece assembly for easy use by the observer. While we calculated that with a back focus of only 6 inches to the prime focus the diagonal mirror could have a 2 inch minor axis, we decided to give ourselves a little more room for error and chose a 3 inch diagonal mirror. Finding one became an interesting problem, but our friends at Orion located one for us.
With the SIPS and the 3 inch diagonal in hand, we had to find a way to integrate those. Since the location of the input of the Paracorr with respect to the primary mirror does not change once set, we realized that we could hard-integrate it to the diagonal. There is a small amount of adjustment that can be had from the SIPS as its input end also allows rotation on a large thread that moves the lens assembly in and out of the mounting tube about half an inch. The SIPS/Paracorr body has a small lip that is 70mm in diameter and the 3 inch diagonal body has a similar lip with a diameter of 80mm, so we designed a cylinder 90mm in outside diameter with inside diameters of 70 and 80mm at each end and only 20mm high. The design carries hex allen set screws to lock each of the diagonal and SIPS to the adapter, integrating them as a unit. We farmed out the fabrication to emachineshop.com, and, in the meantime, did a 3D print in plastic to validate the design.
You can see that this design change has been a journey, as has the whole project, filled with small, incremental insights that each solved problems that were revealed as we committed to earlier insights. More than once we have been required to make leaps over obstacles that seemed too much for our skills or patience. The motivation to persevere through the set backs and to tackle the problems with a fresh mind set from time to time was the desire to bring this telescope to our docents and our visitors at Robert Ferguson Observatory. We know what that community deserves, and we have been determined to bring it.