14.4. Behind store window
Commercial telescopes nowadays come in a great variety of types, sizes and quality. What all of them very much have in common is that, with rare exceptions, they don't come with more detailed information on the quality of their optical output. At best, what those interested get is a surface quality indicator, an LA plot and/or ray spots of the telescope they are expected to lay down their hard earned money for. It is not going to change any time soon, but with modern ray trace programs at hand, and a sufficient information about specific telescope, we can at least find out what its design limits are. With sufficient data - assuming high fabrication quality - it will be pretty close to what the actual telescope's performance level is.
For those like me, curious about what just about any telescope actually delivers, not so much because of the quality concern, but more to find out how it actually works (without breaking it open to look inside :), that is just a treat hard to resist. The raytrace program used is OSLO EDU.
1 - 180mm f/7 apo refractor
For no particular reason, this "look inside" series starts with a 180mm f/7 apo using Ohara FPL55 glass, announced by Stellarvue. Again, this is not the actual instrument's design, but the data available is sufficient to create a system that will well illustrate performance level this refractor is capable of. Taking as the mating glass Ohara's S-BSL7 - the equivalent of Schott's BK7, the least expensive and, at the same time, the highest quality optical glass available - gives following results.
The lens is closer to f/7.1, but it wouldn't cause appreciable difference. The rear gap is widened to minimize the higher order spherical residual (kinda alike the TOA, but with significantly smaller separation), without which the central line would be at about 0.02 wave RMS. It is possible it could be achieved with some other approach, like different glasses, but this is probably the simplest way to deal with it.
The central line Strehl is 0.997, and the photopic polychromatic Strehl is 0.955. The system comfortably passes the "true apo" criteria in the F and C, which requires chromatic correction of 0.80 Strehl, or better, as well as in the red r line, but falls just short of 1/2 wave P-V, or less, requirement in the violet g line. With a bit of tweaking, it could probably just pass the "true apo" criteria in all four.
While it is not realistic to expect any actual instrument to have better than 1/100 wave RMS central line correction - which nearly certainly means less than 0.95 polychromatic Strehl - chromatic correction should remain close to design values. Anyway, the difference between, say, 0.94 and 0.96 Strehl even on the most demanding details is for all practical purposes imperceptible (contrast-wise on extended details, it should be similar to the difference between 14% and 17% linear central obstruction).
The conclusion is: if well made, this kind of a lens can deliver at the level of a "true apo".
2 - 180mm f/7 fluorite apo refractor
2 - 180mm f/7 fluorite apo refractor
Does fluorite guarantee superior performance? Another contender in the same aperture and focal ratio as the above lens is the TEC's fluorite triplet apo. While the only information available on this lens' design is that it uses fluorite as the middle element, we can again look at the available mating glasses and see what is the best that comes out.
After trying a good number of combinations with matching glasses according to both, PF,e (for the F/C correction) and Pg,F (for the violet), the best - with a few very close behind - was the one with two glasses that have similar, but opposite in sign deviation from the ideal match: BK7 and K10. Its design parameters are shown below.
Performance level of this fluorite triplet is practically identical to that of the above FPL55 triplet, with the latter having only a slightly better polychromatic Strehl, mainly due to the possibility to lower the higher order spherical residual (not possible with an oiled triplet, due to its radii and gaps constraints). It is, of course, possible that fluorite triplet design could be better than this one, but such glass combination is not readily apparent - and the same applies to the FPL55 triplet.
It comes to what is pretty much a common knowledge, and it is that there is nothing magical about fluorite itself vs. other extra low dispersion glasses. In the end, it is the design and fabrication quality what decides how well a lens will perform.
3 - Takahashi Mewlon 210
Takahashi's Dall Kirkham reflector comes in three sizes: 210mm, 250mm and the 300mm big gun. It is often speculated how much of off axis coma they generate. Luckily, Takahashi gives design specifications for all three, which makes it easy to create the exact optical design. The three are very similar, having ~f/3 primary and 4x secondary magnification. Since the primary is enlarged (+10mm on the diameter) it is not clear whether the focal ratios given were calculated vs. effective aperture or the actual diameter. It is assumed the latter, but it wouldn't make significant difference if it is the former.
The reason for enlarged primary is the displaced stop, placed at the primary's focus. It has no appreciable effect on coma, but reverses the sign of astigmatism, reducing field curvature nearly in half.
Here's the raytrace for the smallest Mewlon, 210mm f/2.9/11.5 Dall-Kirkham system. Diffraction limited field, limited by coma, is 0.055 degrees in radius if measured by the RMS wavefront error (0.0745 wave, for 546nm wavelength), and 0.63 degrees according to the P-V wavefront error (0.42 wave).
OSLO is inconsistent here, since the P-V/RMS ratio for primary coma is 320.5 (astigmatism is negligibly small in comparison this close to axis, and has no appreciable effect on the wavefront error). Taking 0.059 degrees, i.e. 2.5mm off axis, as the diffraction limited field radius, implies that its linear field is comparable to that of a f/6.1 paraboloid (from F=[h/48W]1/3, where h is the off-axis height, and W is the P-V wavefront error - taken as 0.42 wave - both in the same units). Of course, the corresponding angular field is proportionally smaller in the Mewlon. Also, it has proportionally larger image scale, which means that the linear diffraction image of the aberration is nearly twice larger. No effect on visual observation, since the objective's magnification is a part of total magnification (objective x eyepiece), but results in better sampling with any given CCD chip.
The system has 32% central obstruction diameter.
4 - AP 10" f/14.6 Maksutov-Cassegrain
One of the cult telescopes in the amateurs' circles, the Astro-Physics' take on the Gregory-Maksutov design, never had its optics specs published, but since they are determined by the system parameters, it is possible to reconstruct them in the way that there is no appreciable difference in the performance level vs. the actual design.
The purpose of aspherizing the primary is to remove the residual coma, with the extra benefit of somewhat relaxing corrector's radii, hence reducing the higher-order spherical aberration residual as well. The limit to aspherization is set by the coma introduced by it. If it is chosen to eliminate coma, with the standard corrector thickness of 1/10 the aperture diameter, it results in a design below.
The central line is just short of 0.95 Strehl (0.947 without its 23.6% central obstruction, 0.958 with it dialed in, due to it taking out the central wavefront deformation), and it is the main reason why the polychromatic Strehl is also below 0.95 (around 0.94 when unobstructed, which implies that the Strehl degradation factor due to the chromatism is only ~0.99). There are only two practical ways to somewhat improve the central line correction: one is with a thicker meniscus, and the other with more strongly aspherized primary.
With 32mm thick meniscus, the central line's Strehl increases to 0.966 (0.971 with the obstruction), with a slightly larger (minimum size) secondary, and nearly 2" longer back focus.
With the primary conic increased to -0.23 (at which coma at 0.25 degree off axis reaches diffraction limit - shown below ray spot plots - and design still could be called "coma free" in practical sense) the Strehl increases to 0.956 (0.962 with the obstruction). With both, thickness and conic increase, the central line's Strehl goes to 0.975.
A 3% increase in the contrast averaged over MTF frequencies - which is what the Strehl value represents - is hardly noticeable at all. So the actual design may, and may not have these enhancements (with Roland's drive for perfection, it is more likely than not). Much more of a factor is seeing: even as good as 1 arcsec would lower the average Strehl of a perfect 10" aperture down to about 0.5 (D/r0~1.8). Yet, such 10" aperture still can deliver stunning views.
An interesting detail is the star test. These instruments with the balanced 4th and 6th order spherical show more asymmetry in out of focus images than the standard, 4th order spherical aberration alone. It was pointed out more than once by those manufacturing such telescopes (including Roland) that a highly corrected telescope of this type will still show noticeably different in- and out of focus images. Can we trust them, considering conflict of interest? The bottom row shows OSLO simulations for the design in question with 0.97 central line Strehl (the one with thicker meniscus).
5 - ARIES' original 10" Maksutov-Cassegrain (?)
Seems that quit a few amateurs believe that larger MC telescopes - and 10" would belong to that category - have to be aspherized in order to be well corrected. That, however, holds true only if the primary is kept at f/3, or so. Allowing for somewhat slower primary relaxes the required corrector radii, making possible to have significantly larger all-spherical systems well corrected.
More so, such systems can be also coma-free. Commercially-made MC that fits the requirement of a slower primary is the original Aries' 10" f/13.5 telescope from the 1990's. While I'm not aware of the official prescription, a design can be made to illustrate its performance level. It will be a f/4/14.5 system with separated secondary mirror.
Correction level is stunning: the central line Strehl is 0.99+, and so are the ratios in F and C (needless to say, the polychromatic Strehl too). Field curvature is mild, and the minimum obstruction size is 27% by diameter. Needed optical tube is longer, but not excessively long. Angular field that fits 2-inch barrel is nearly 3/4 of a degree in diameter.
The system could be easily rescaled to fit the original Aries, without appreciable change in the performance level.
6 - TAKAHASHI TSA 102 apo triplet
One in the series of exquisite Takahashi refractors, the TSA 102 had its optical design revealed during its marketing campaign. Here's how it raytraces.
On the design level, there is no chromatism to speak about. Polychromatic Strehl in the 430-670nm range comes to 0.992, while in the optimized wawelength it is 0.9998. The polychromatic MTF is practically coinciding with that of a perfect aperture.
There is some residual coma, which probably wasn't present in the final design. While it is visually unnoticeable, it does make point image asymmetrical, and enlarges the 80% energy circle at 1-degree off axis by nearly 1/3. And it is easily removed by adjusting the outer radii (R1=344mm, R6=-944mm, with R3=179.5mm and the second gap increased to 0.45mm to minimize spherical aberration).
Just how good this triplet is illustrates the fact that its polychromatic
Strehl is still as high as 0.962 even when scaled down to f/6, although
the tolerances are much tighter. That is one of the Takahashi's secrets:
they don't push the envelope, making it possible to execute design to a
near (practical) perfection.