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Most ATM telescopes are of known designs, but their makers can customize them to their liking. That makes them sort of unique, and adds to the satisfaction of accomplishing, sometimes very challenging, creative projects. With more complex systems, it all starts with a design created and optimized through raytracing, as the basis for elements' fabrication. And some of ATM telescopes are truly unique systems, out of common knowledge of the amateurs and professionals-alike.

  Marc Baril's 7" f/8 modified Sigler-Maksutov-Cassegrain

Making Maksutov-Cassegrain of any kind is not for the faint of heart, primarily due to the full aperture Maksutov lens corrector, whose "easy" to make spherical surfaces have to remain within tight tolerances for the surface itself, the two surfaces relative to each other, and both relative to the meniscus thickness. A good example of it is Maksutov-Cassegrain made by Marc Baril, an amateur astronomer with professional background. 

Main modification to the Sigler's design was shortening the tube length which, according to Baril, did somewhat lower system's axial correction, but still allowed a high-level performance. Here is raytrace of the prescription given in the article.

Design shows great field correction, with near-zero coma and astigmatism (it could, in fact, have 2-3 inches - or even more - smaller corrector separation without perceptibly affecting coma correction). Correction barely changes going from the field center to 0.5 degrees off axis. 

One thing to notice is that axial monochromatic correction of the starting design is a bit off (top left). It looks like undercorrection, but it is suboptimally balanced 6th/4th order spherical, with the lower order (undercorrection) being nearly twice larger than the (overcorrected) higher order. With the RMS wavefront error of 0.043, it is at the level of just a tad stronger than 1/7 wave P-V of lower order spherical. Baril mentions having a slight undercorection when arriving at the testing stage, which he removed by working the first corrector radius with a petal lap. While he thinks that what it did was slight aspherising, even just a slight strengthening of the first radius - going from 10.3507" to 10.344" - would do the trick.

After taking care of undercorrection, we come to a design with 0.982 Strehl in the e-line, 0.927 in the F, and 0.926 in C. The polychromatic (430-670nm photopic) Strehl is 0.964. If we minimize the chromatism by bringing the colors tightly together strengthening corrector radii to 10.05" and 10.481", the two lines go to 0.972 and 0.976, respectively, with the e-line at 0.98. The polychromatic Strehl goes to 0.977.

The Strehl figures are actually somewhat improved due to the 38% central obstruction, which took out the central deformation of the wavefront caused by spherical aberration. But the central obstruction did, of course, more damage than good at the level of system's PSF. Still, it's negative effect is commonly exaggerated. Baril states in his article that the biggest disadvantage of this design is its large central obstruction. How big a disadvantage it really is?

The fact is that it reduces the wavefront error in all wavelengths - the larger wavefront error, the more so. If we would take it out, these same optical surfaces would produce wavefronts of lower quality. The central line, for instance, would go from 0.183 wave RMS and 0.982 Strehl, to 0.0225 wave RMS and 0.972 Strehl. At the same time, obstruction causes 0.86 drop in the relative central intensity of the diffraction pattern, with the second 0.86 reduction factor for the energy contained in central maxima - 0.73 reduction in total - coming from the reduced central maxima size. Due to the size reduction, central maxima is not only smaller, allowing higher limiting resolution, but also significantly brighter than what 0.73 degradation factor implies. In this case, central maxima is only 7% less bright than in a perfect aperture, in this respect corresponding to 0.93 degradation factor.

So, while the nominal degradation factor is 0.74 (rounded from 0.73*0.982/0.972), it is also accompanied by 13% higher limiting resolution, and higher contrast transfer in the high frequency range. MTF compilation below illustrates the magnitude of both, loses and gains.

Here we see that the worst part of the central obstruction effect is lowering contrast transfer to the level of 33% smaller aperture in approximately 0-0.3 range of frequencies. In the 0.7-1 range the transfer increases to the level of 16% larger aperture, while over the 0.3-0.7 range we have transition from lower to higher transfer, extending all the way to the resolution limit of 16% larger aperture. Overall, nominal view favors obstructed aperture, which has contrast transfer advantage in nearly as much of the frequency range as the unobstructed, with extra high frequencies added beyond the resolution limit of unobstructed aperture.

However, to better understand the implications, MTF frequencies should be associated with magnification. With the limiting resolution at cutoff frequency λ/D in radians (times 206,265 in arc seconds), magnification at which a general detail is magnified to 5 arc minutes (likely more near threshold of detection), needed for the average eye to recognize its shape is 300D/206,265λ, or 2.64D for the aperture diameter D in mm and λ=0.00055mm (67D for D in inches). For details of Airy disc size, 2.44λ/D, corresponding to 0.41 frequency, it is 1.1D, and half as much for twice larger detail (0.2 frequency). So we could say that high magnifications start, quite approximately, at 0.3 frequency. If so, the bad part of central obstruction effect falls to the range of mid and low magnifications, while the good part covers most of the high magnification range. That said, should be noted that the largest contrast drop for this obstruction, some 25%, is at about 0.4 frequency - somewhat deeper into the high magnification range - while diminishes toward the mid-to-low magnification range (<0.3 frequencies), down to 12% at 0.2, and 5% at 0.1 frequency.

There are direct implications of different contrast levels on the limiting resolution. Taking approximate minimum contrast requirements for different object types from Rutten/Venrooij, we get that the obstructed aperture will have appreciably higher resolution limit not only for the conventional MTF limit (two bright lines, nearly identical to that for two near equally bright stars), but also for bright contrasty objects, like the surface of Moon (1 and 2, respectively). On the other hand, unobstructed aperture has higher resolution limit for bright low-contrast objects (3) and dim low-contrast objects (4).

Obviously, we can't compare apples and oranges, so whether the effect of central obstruction is good, bad, or insignificant, will depend on the specific use.

In all, the effect of central obstruction is a mixed bag, and certainly is not only bad. For photography, considerations are somewhat different, but the effect is generally considered less of a factor than for visual use.

Summing it up, while it is not possible to execute the actual optics to its theoretical optimum, it is not even necessary. No mortal soul can see the difference of one or two 1/100s in the Strehl ratio. From Baril's article, it is very likely that his commitment to making this telescope as close to its design marks as he could, did bring it to the level where the difference vs. theoretical optimum didn't matter.

Sure, performance level would have been even better with a system with slower primary, such as the original Aries' Maksutov Cassegrain, without significant difference in the tube length. But if one wants a faster system, there is a price to pay.


14.1. Early telescopes   ▐    14.3. Observatory telescopes

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