MOANA: optical design

How many more telescopes do you need? Just one more or so goes the joke.

This section goes over the design decisions of MOANA, a carbon fiber 10″ f/4.5 corrected Newtonian Astrograph. This is my 3^rd telescope build so far, and it benefited from many of the -sometime hard- lessons learned on the previous designs.

Here are the specifications, as defined at the start of the project:

Optical Specifications.

• A speed faster than f/5. Except for planetary/solar, I feel life is too short for anything slower than f/5.
• A focal length around 1,000-1,200mm. I already have a couple of wide or super wide field system based on telephoto lenses plus a 200mm Borg and a 600mm Hyperstar. So the next step up in focal length was in the 1,000-1,200mm range. Systems with a longer focal become either slow or big (simply because f = F/D), and increasingly more difficult to guide. If one wants to maintain a reasonable speed, they also get expensive: as a general rule of thumb, the weight and price of a system increases with the power 3 of its diameter, so multiply by 2 the diameter, increase by a factor 2³=8 weight and cost (we can assume in first approximation cost is proportional to mass).
• An instrument diffraction limited (or very close to it) over the sensor considered. Any instrument that does not meet this criteria (and there are still some sold commercially today) is an inexcusable optical design failure.
• Better than 90% vignetting over the sensor, a spec very often overlooked in commercial instruments. Many refractors for example boast a full frame illumination, but have over 60% vignetting at the edge of the sensor!
• Enough back focus for a filter wheel + a standard 17mm back focus camera.

Mechanical specifications.

• Weight and portability. Although MOANA is mostly designed as an observatory instrument, I wanted it to be transportable in a regular hatchback car. I also wanted the telescope to be portable enough so a single person could carry it and put it in station without help, and without the fear of breaking one’s back or dropping the instrument. Last I wanted my mount (AP 1100 GTO) to carry it without struggling. I am not upgrading to a bigger mount any time soon.
• Very stable focus when temperature changes. Quite simple: I am not interested in refocusing every 15mn when the temperature drops with the night.
• Ease and stability of collimation. Collimation needs to be a quick, easy and reproducible process, that takes no more than 15mn, can be done at night or during day light. Collimation needs to remain stable for at least a night, ideally months if the instrument is not moved. Again, this is very simple: I prefer the night to be spent observing, not collimating.
• Realistic collimation tolerances for all optical parts. I have seen many commercial instruments with incredible performance on paper. However what really matters is that those performance are achieved only under perfect collimation. The tolerances, which tell you how fast performance degrades when collimation quality degrades, are often not provided. This results in either chronic under-performance by the system (poor images), or a constant uphill battle and headache for the user to attain and stay within collimation tolerances. Riccardi Honders, Hyperstar, and many other system fall into this category. I was not having any of that for MOANA: I needed the instrument to be robust enough so a slight imperfection in collimation would not have a catastrophic outcome. The instrument needs to stay in a remote observatory with wild temperature swings, and keep performing nights after nights, at all angles.
• A system realistic to build for an amateur with limited tooling, time, knowledge and skills.

Last but not least: final cost, and adherence to the budget forecast. The cost spec was simple: MOANA should not be more expensive than a high quality equivalent commercial instrument (eg: ASA Newtonian). This is a major challenge, as commercial instrument clearly benefit from an economy of scale. In particular, the cost of CNC machined part goes down dramatically as the number of part in the series increases. The other aspect is adherence to budget: it would be very easy to underestimate cost, or the amount of work involved.

Choice of the optical formula: the constraint on fabricability, tolerance, collimation and cost oriented me towards a Corrected Newtonian. The best Corrected Newtonian optical formula is without a doubt the Hyperbolic Newtonian. However, when I started the project (5 years ago) the optical correctors and main mirrors for the Hyperbolic Newtonian were, and generally still are, relatively rare (ASA makes a large professional Hyperbolic Newtonian & corrector, Hubble Optics sells mirrors and correctors for this formula to amateurs). The Parabolic Newtonian has the following advantages over the hyperbolic: can work or be tested on a small field without a corrector, wide range of correctors commercially available (Wynne correctors, Paracorr), can be used with a generic focal increaser (PowerMate or equivalent) for planetary or long focal work, could be used visually with the right eye pieces and without the corrector. Further many manufacturers make parabolic primaries, offering a wide choice. In the end I went for the safe, well documented and traditional Parabolic Corrected Newtonian.

The coma corrector, or corrector (as it may also helps with field flattening) is central in the optical design of MOANA. In fact the whole telescope is designed around and for the corrector. This philosophy is quite the opposite of most cheap commercial Newtonian telescopes, where the coma corrector is too often an afterthought slapped in after the owner realizes the off axis image is unacceptable for photography.

Optimizing the choice of primary mirror – coma corrector -sensor size. Once the Newtonian has been adopted formula, this is the most important step. There are 3 elements: primary mirror, coma corrector and sensor size. Each of those elements put constraints on the other two, and an iterative process was used to optimize the system.

• for the system to remain truly portable the primary diameter needs to be at or below 10″ (25cm) -at least for me and what I am comfortable to haul.
• then to not compromise too much on the secondary mirror size and still keep low vignetting over the entire sensor, the instrument becomes limited to an APS-C sensor as the biggest sensor that can be illuminated.

Let’s pause here for a second. Full frame sensors have a huge advantage: they cover more field of view. They have a few disadvantages:

• they are expensive.
• The filter for those sensors are also extremely expensive.
• The filter wheels for those sensors are big, heavy and expensive.
• the correctors for those sensor are big (at least 3″ diameter), heavy, complex and expensive. This is because the coma increases linearly with the field angle. So correctors for bigger fields become increasingly more complex, with more glass, possibly the use of exotic glass, more extreme lens shape.
• the focuser to carry the corrector, filter wheel and sensor needs to be oversized, heavy and expensive.
• The secondary mirror, in charge of illuminating the corrector, needs to be big. It becomes heavy, makes a large obstruction which reduces the illumination, disrupt the diffraction pattern and decreases contrast.

Now on the telescope: the bigger the telescope, the bigger the field of illumination. The sensor size that can be illuminated increases linearly with the primary mirror diameter when a particular design is scaled at constant f/number.

For example, any 16″ Newtonian should effortlessly illuminate a full frame sensor, while any 10″ should effortlessly illuminate an APS-C sensor.

Notwithstanding the above statements, by making compromises (mostly an oversize secondary mirror) a particular instrument can be pushed towards some desired performance, like a wider illumination circle. For example ASA had their 8 inch Newtonian astrograph advertised as compatible with full frame sensors. The price to pay is a very large secondary mirror for that scope (with correlative large central obstruction percentage) and some vignetting.

From those consideration, I decided MOANA would be required to illuminate an APS-C sensor only. That is, I found it was better to design a top performer on a cheaper, lighter APS-C sensor imaging train rather than an average performer compromised to illuminate a full frame sensor. The ability to make those choice eyes wide open is the huge advantage of making one’s own instrument. Also there is no right or wrong here: the question is what characteristic is most desirable, and what is an acceptable compromise to get there. From the above, it is also be clear if I ever design a 16″ Newtonian telescope, it will have at least a 3 inches Wynne corrector and will be designed to illuminate a full frame sensor: this is the natural thing to do with such diameter.

Back to the primary -corrector -sensor optimization. At this point we have a 10 inch telescope, to illuminate an APS-C sensor. A 2 inch diameter corrector minimum is required to maintain vignetting specs. What corrector should be chosen? Chapter 14.2 of the Smith-Ceragioli-Berry book (“Coma Corrector for Newtonian Telescopes”) is a highly recommended read on the question. From here there were 2 considerations. First: each corrector is optimized for a particular f/number value. Second: corrector collimation (or alignment) specs become quickly unforgiving when the f/number of the primary is fast (say faster than f/3.5) or when the corrector is also a focal reducer.

So the coma corrector and the f/number of the primary mirror are chosen together.

At this point we have chosen D the diameter of the telescope, and defined a range for F, the focal length (1,000 to 1,200mm). The focal ratio, or telescope speed, f is also f=F/D. A very important fact in optic is: focusing tolerance is proportional to f². This means an f/6 system, for example, would be 4 time more tolerant to focus and collimation errors than an f/3 system. This explains why fast system, very attractive on paper can be a total pain to focus and collimate. Faster primary mirrors are also more expensive (more glass needs to be removed, more time spent on parabolization) and more difficult to test.

In the end I went for f/4.5, and a corrector optimized for that focal, the Paracorr type 2.

On the Paracorr type 2, 2 inches: it is very wide spread in the amateur community, and has been extensively used with good results. The alignment and collimation tolerance are forgiving. I tested one on a previous telescope and knew exactly where I was going. There are drawbacks however: the optical formula is a secret of Televue so it cannot be ray traced for a particular system, the documentation coming with the corrector is a bunch of hand drawn diagrams on Televue’s website (when the industry standard has been clean Zemax plots for years), and the adapters provided by Televue have back focus values inconsistent with the corrector’s drawing (I think the drawing are correct and the back focus values have been mixed up with external measurement).

Conclusions: at this point the following parameters have been defined:

• the primary diameter D=10″.
• the focal ratio f/4.5.
• From the above, the focal length, F=10″*4.5=1,142mm
• the coma corrector (Paracorr type 2, 2 inches)
• the sensor to illuminate: APS-C. That is an image circle of 29mm diameter, illuminated without vignetting.

From there I used Atmos (the free version) and plugged in the above parameters. One parameter I did not have yet was the optical axis-focal plane distance. That measurement is constrained by the entry light cone diameter, and the fact I did not want the paracorr to protrude inside this light cone. It is also constrained by the secondary diameter. The secondary mirror size has discrete values, which I took from the supplier (Antares Optics).

From here I iteratively searched the values of the optical axis-focal plane distance E in Atmos, within my acceptable range, until I got out of Atmos a secondary size D2 compatible with the manufacturer specs of an existing secondary mirror (minor axis of the secondary equal to 78 mm). In scientific language, I inverted for E, knowing D2, and using Atmos as a black box. It seems complicated but it is really a 5mn process.

This iterative process lead me to an optical axis-focal plane distance of E=245 mm, fully constraining the Newtonian design, including the optimal secondary offset (Dx=3mm).

The last step was to ray trace the design in the free version of Oslo. The fact that the Paracorr design is secret is a problem. So for my ray tracing I used the coma corrector described in Smith-Ceragioli-Berry p389. That design is understood to be akin to the first Paracorr. The promise is that the actual ray tracing with the Paracorr type 2 would be very similar and slightly better than what I would come up with with the SCB corrector.

Here is the Oslo “.len” file.

And here are the ray tracing results done in Oslo.