Tuesday, September 21, 2021

A Small Astrograph with a Large Payload


Building a large telescope is hard; designing a small telescope is hard. What exactly do I mean by that? Well, there are parts of the telescope that don't scale well with size, for example, the instrument payload, the filters, or the focusing actuators. More often than not, a design which works well on a 1m-class instrument fails to scale down to a 300mm-class instrument because the payload is incompatible with the mechanics, or is so large that it fills the clear aperture of the instrument.

A small telescope should also be...small. A good example of this is the remarkable unpopularity of equatorially-mounted Newtonians; a parabolic mirror with a 3-element corrector offers fast focal ratios and good performance, but an f/4 Newtonian is four times longer than it is wide, which gets unwieldy even for a 300mm diameter instrument.

The Argument for Cassegrain Focus

Prime focus instruments are popular as survey instruments in professional observatories. However, they fail to meet the needs of small instruments because of:

  • Excessive central obscuration. A 5-position, 2" filter wheel is about 200mm in diameter. In order to maintain a reasonable central obstruction, a 400mm clear aperture instrument is required which is marginally "small". Any larger-diameter instrumentation requires a 0.6m+ class instrument which is outside of the scope of many installations.
  • Unreasonable length. The fastest commercially available paraboloids are about f/3. Anything faster is special-order and very expensive. An f/3 prime focus system is actually longer than 3 times its diameter because of the equipment required to support the instrument payload.
  • Challenging focusing. For a very large system, actuating the instrument is the correct method for focusing because even the secondary mirror will be several tons. For a small system, reliably actuating 10+ kg of payload with no tilt or slip in a cost-effective fashion is rather unpleasant.
  • Too fast. A short prime focus system is necessarily very fast, complicating filter selection. A very fast system also performs poorly combined with scientific sensors with large pixels.
The commercially available prime focus instruments (Celestron RASA/Starizona Hyperstar, Hubble HNA, Sharpstar HNT) are designed for use with small, moderately-cooled CMOS cameras, possibly with a filter wheel in case of the Newtonian configurations. The RASA is wholly unsuited for narrowband imaging because a filter wheel would almost cover the entire aperture.

A Cassegrain system solves these issues by (1) allowing for moving-secondary focusing (2) roughly decoupling focal ratio from tube length and (3) moving the focal plane to be outside of the light path.

The 50% Central Obstruction

A 50% CO sounds bad, but by area the light loss is 25%, or less than half a stop. A 300mm nominal instrument with a 50% CO has the light gathering capacity of a 260mm system, which is pretty reasonable. The 50% CO also makes sizing the system an interesting exercise, because at some point the payload will be smaller than the secondary and prime focus makes sense again.

The Design

The Busack Medial Cassegrain is a really nice telescope that this design draws inspiration from, but it requires two full-aperture elements each with two polished sides that makes it ill-suited to mass production. Instead, we build the system as a Schmidt Corrector, an f/2 spherical mirror, and a 4E/3G integrated corrector. There's really nothing to it - by allowing the CO to grow and using the corrector to deal with the increasing aberrations, an f/4 SCT is entirely within the realm of possibility. There's a ton of freedom in the basic design, the present example makes the following tradeoffs:
  • f/4 overall system allowing for the use of an f/2 primary (which we know is cheaply manufacturable based on existing SCT's). f/4 also allows for the use of commodity narrowband filters.
  • 400mm overall tube length (not counting back focus) is a good balance between mechanical length and aberrations. 50mm between the corrector and secondary allows ample space for an internally-mounted focus actuator.
  • 160mm back focus allows for generous amounts of instrumentation including filters, tip-tilt correction, and even deformable mirrors.
  • Integrated Schmidt corrector allows for good performance with no optical compromises.
  • Corrector lenses are under 90mm in diameter and made from BK7 and SF11 glass, all easily fabricated using modern computer-controlled polishing.
The total length of the system could also be shortened, and the corrector diameters reduced, by increasing the primary-secondary separation and reducing the back focus, depending on instrument needs. Overall performance is quite good, achieving 4um spots sizes in the center and a high MTF across the field.

Actually Building It?!

Obviously, you are not going to make a 300mm Schmidt corrector and a four-element, 90mm correction assembly at home. This design is probably buildable via standard optical supply chains (the hardest part would be getting someone who is neither Celestron nor Meade to build Schmidt correctors). The correction assembly should also be further improved - there are a huge number of choices for its configuration and the 'correct' one is probably the one that is most manufacturing-friendly.

Shoot me an e-mail in case you are crazy and want to do something with the prescription for this design!