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Unlike amateur telescopes, used for both, visual and photography, observatory telescopes - and the subject here are those used in the visual range of the spectrum - are generally used for photographic work. They range in sizes from fraction of a meter to eight meters, or more (segmented mirrors) in diameter. All large telescopes are based on the reflecting systems, and those sub-meter can be both, reflecting and catadioptric; very few refractors are still in observatory use. Specific uses of these telescopes vary just as much: there is an immense amount of information coming from the Universe, and with all our observatory arsenal, we are barely scratching the surface.

Since they are a part of professional operation, observatory telescopes are not only larger, but also generally more sophisticated and technologically advanced. As such, they are a special breed, puzzling and interesting not only to amateur astronomers, but also to people at large. This should open a small window into the realm of big professional telescopes, seeking to find the truth of our Universe, and our place in it.



Arguably one of the best corrected simple systems is the three-mirror system known as Paul, or Paul-Baker telescope. So when a group of astronomers from the University of Arizona's Steward Observatory were looking for a very large, ultra-fast widefield design for the Dark Matter Telescope project, it led them to the Paul-Baker, since no two-mirror system, or a Schmidt-like telescope, could achieve the needed level of correction. The telescope would be limited only by atmospheric seeing and sky background photon noise, which means it has to produce star images smaller than 0.5 arc seconds, achievable occasionally with large telescopes on best sites. The goal was the largest telescope possible with 10m focal length, needed for sufficient sampling with a 15-micron pixel (1 arc second=51 micron).

Their first design, a 6.5m f/1 Paul-Baker telescope with all three mirrors aspherized in Zemax, was capable of producing required image, but had suboptimal plate scale, and unacceptable chromatism from the dewar window. That led to the revised design, a 8.4m f/1.25 telescope with a curved dewar window and added correcting lens. This design was the starting point for the 8.4m f/1.234 Rubin Observatory Simonyi Survey Telescope (El Peñon, Cerro Pachón, Chile), with even wider, 3.5-degree field, and a bit better correction (less than 0.3 vs. less than 1/3 arc seconds design image). Since there is no prescription for the Rubin telescope, the University of Arizona's design will be used to illustrate this, we could say unique kind of a telescope. Unfortunately, prescription given in the paper isn't working, but a system with comparable performance can be reconstructed from it.

The main parameter of optical performance is ensquared energy. It is given on the bottom of every 1-arcsec square containing ray spot plots for the 0.80 energy square all values are in meters, so the 7.77-6 for the axial e-line 0.80 energy square is 7.77 microns). At 1.5 degrees off axis the polychromatic 0.80 energy square side is 24.9 microns, or nearly 0.5 arc seconds. It would probably be the subject of final optimization, generally by near-equalizing error over the field, by allowing more of an error in the inner field. At 1-degree off, the 0.80 energy square is 1/3 of arc second, becoming significantly better toward axis. Astigmatism is minimized, near zero at 1.5 degrees off, with the dominant aberration there being trefoil.

The small dot in the center of each box is the Airy disc; entirely irrelevant here, but illustrates the magnitude of aberrations in this highly corrected large telescope.

More complete picture of the aberrations is given by the Zernike terms. The main contributors are in red (piston is not an aberration in the single-aperture system, just a nominal artifact, and the defocus value - which translates to 0.33 wave RMS, i.e. 1.16 wave P-V - is evident on the astigmatism plot (best focus is not necessarily where astigmatism is at its minimum; in the presence of other aberrations it can shift to another location).

The largest single contributor is trefoil (#9). The next highest one, quadrafoil (#16) is already near negligible, adding only 15% to the trefoil (because Zernike terms add up as square root of their squared values), and even less considering secondary trefoil (#18). Most of the terms are negligible individually, but do have significance as a total, creating a higher-order aberration "noise" in this large and fact telescope.

At 1 degree off axis dominant aberration is astigmatism, but it is significantly smaller than what the longitudinal aberration graph indicates (nearly 6 waves P-V, from W=L/8F2, L being the longitudinal aberration, and F the system focal ratio). The reason is that a mix of lower- and higher-order astigmatism of opposite signs has up to four times lower error at the best focus for given longitudinal aberration, and that large central obstruction also lowers the error.



Located at Apache Point Observatory in New Mexico, the main tool of the Sloan Digital Sky Survay project, this telescope uses a two aspheric lens field correctors to achieve a well-corrected 3-degree field. As described in paper by Gunn et al. its second corrector lens is interchangeable, allowing it to be optimized for camera and spectroscopic mode. It is used to map the depths of our Universe.

The two corrector lenses have their radii given indirectly, through the value of a2 coefficient, whose full expression is a2=d2/R[1+(1-K)(d/R)2], with d being the the surface radial height, R the radius of curvature and K the surface conic. It is not clear why, because the surfaces are spherical (K=0), and (d/R)2 is negligibly small, especially for the first corrector, hence for all practical purposes a2=d2/2R, and R could be expressed directly (for the second corrector, it would give about 3% longer radius, but it would have little consequence).

Raytracing the prescription for camera mode shows, perhaps, less than expected correction-wise. The field is, as described in paper, nearly flat up to about 80% of the 1.5-degree radius, curving inward rather strongly after that. Color correction is good overall, but widely separated lines show significantly different forms of aberrations toward field edge, i.e. their best foci do not coincide. One of the requirements was near-zero distortion; according to OSLO, it just exceeds 0.1% at the field edge.

The outer portion of the field required adjustment of the detector shape. It cannot be fitted with a near-spherical curve, and requires higher order aspherics. Here, the asherics are combined with 67m curvature, which resulted in a good, but still someone uneven fit (the edge is for the best green focus; the red becomes roughly round at 99m curvature, but green out of best focus).

The paper gives no specific performance criteria for the camera mode. Final images were calculated as convolved with 0.8 arc seconds seeing FWHM, which proved to be too optimistic. For the system focal length, one arsecond is 60 microns. On the fitted field, the green line 80% energy square is 18.7 microns on axis, 15.5 microns at 1-degree, and 35.8 microns at 1.5. It indicates that the seeing is limiting factor, rather than optics.

Full spectral range of the telescope is 0.3-1 micron, but the familiar visual 0.43-0.70 range well illustrates its chromatic correction.



European Extremely Large Telescope is designed as a three-mirror anastigmtic aplanat. As described in a paper by Cayrel, the 39-meter f/0.93 ellipsoidal primary consists of 798 hexagonal segments, each 1.45m across. The 4.2m convex secondary and 4m concave tertiary are each a thin meniscus. All three mirrors are active: the primary to make possible for it to conform to the proper shape, and the other two - particularly tertiary - to correct wavefront errors, mainly those caused by atmospheric turbulence, but also those caused by mechanical deformations.

Two folding flat mirrors direct light beam to the side (Nasmyt focus). The first, 2.5m in diameter, is also active, "specified to deliver near infrared diffraction limited images with over 70% Strehl ratio in median atmospheric conditions (0.85 arcsecond seeing, t0 of 2.5ms)". The second flat, 2.2 by 2.7m, corrects for tip-tilt errors. 

Field radius is nearly 5 arc minutes, limited by the central hole in the fourth mirror (even such a small angular radius produces almost 1m image radius). The prescription gives a final f/16.6 system, somewhat slower than f/17.5 cited in the paper; not sure what is causing the difference, but the design correction level is very high.

Even at the field edge, correction is still at the level of 1/12 wave P-V of lower order spherical aberration. With the ~660m focal length, one arc second at the detector is whooping 320 microns - about 1/3 mm. The only significant aberration is field curvature.



Keeping in the company of the largest - ever wondered how much chromatism there is in the largest refractor ever built: the 40-inch Clark refractor at the Yerkes observatory in Wisconsin? I was always curious, just how much of color a quarter tone of achromat glass generates. Using general data on the Clark doublet, and Barnard's measurements, gives the following picture.

On axis, Airy disc is a barely visible dot in the center of defocused C (656nm), F(486nm), r (706nm) and g (436nm) lines. The F/C error is nearly 7 waves P-V, which puts it at the level of a 100mm f/1.8 achromat. At the field edge, coma is nearly three times the Airy disc - or 0.8 waves P-V - visually unnoticeable (about f/16 paraboloid level).


5 - 1m KLEVTSOV-CASSEGRAIN VARIETY (Vihorlatska Observatory, Slovakia)

In his book "New serial telescopes and accessories" (2014), Klevtsov gives prescription obtained from the Slovakian observatory, as a big-scale example of a telescope of the Klevtsov type.

The telescope was made in Odessa, SSSR. Original prescription is with BK7 glass (i.e. K8, its LZOS analog), but K7 glass reduces longitudinal error in the blue/violet to less than half, so that this 1-m telescope easily passes the "true apo" requirement. As with every system of this type, dominant aberration is off axis astigmatism.



One of many designs of Valery Terebizh, the Russian "master designer" as referred to by M.R. Ackerman, is a simple Richter-Slevogt (known as Houghton on the Western side) modification with widely separated corrector lenses, making possible significantly wider fields. Survey telescopes are usually of relatively small apertures, with large corrected field being the primary concern, but larger apertures can be needed for detecting fainter targets.

The Houghton-Terebizh offers 5-degree field at f/3.2. The system shown is slightly tweaked to have the axial error minimized (at no expense to off axis performance).

 Color correction even at this aperture size and relative aperture passes the "true apo" criterion. The 80% energy square is 6.6 microns on axis, and 8 microns at 2.5 degrees off (diffraction images are for the 5 wavelengths with even sensitivity).

This design can also be used as a typical survey telescope, smaller in size and faster. If rescaled to 350mm aperture and f/2.4 focal ratio - parameters of a telescope of this design used in the gamma-ray burst system observatory near Moscow, Russia (The Mobile Astronomical System of Telescope-Robot) - it still preserves a very satisfactory performance.

Note that the actual telescope is somewhat shorter, with the corrector lenses more widely separated and with the final image that would form behind the rear corrector lens, if not directed to the side with a diagonal flat).



While designed for work outside the visual spectrum, the UKIRT is based on unusual relay lens design which, with minor adjustments, could be used in the visual range as well. Here is presented its Wide Field Camera mode, as described in this online paper.

System is simplified by omitting optical window and filters, which has a minor influence on its output. The entire field covers 0.93-degree diameter, but the actually used are only four rectangular portions of it, as illustrated in the paper. The telescope is optimized to operate in four IR ranges: Y (0.97-1.07 microns), J (1.17-1.33), H(1.49-1.78) and K(2.03-2.37). As given here, the is somewhat biased toward the lower three, possibly the consequence of omitting mentioned elements.

Sub-aperture aspheric plate helps correct not only spherical aberration, but also coma and astigmatism.

The ray spot plots are given for the central line of each of the four wavebands, when refocused to their respective best focus. Above right are plots for this same system in the visual wavelengths (focused on e-line). Only minor optimization is needed to have it perform satisfactory as a visual telescope.

14.2. ATM telescopes   ▐    14.4. Commercial telescopes

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