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If such are the results achievable with the decidedly primitive amateur-built telescope described earlier, it must follow that similar performance is within reach of virtually any Newtonian having a good mirror at f/5-6 or longer, adequately supported on a mounting of sufficient stability and rigidity. Those further refinements which the author's instrument so conspicuously lacks - permanently mounted optics of modern low-expansion glass in a telescope having a clock drive or at least good manual slow motions - will, of course, make this easier but are not indispensable. The real essentials for such subarcsecond performance are listed here, together with some general points of advice on the conduct of this type of double-star observation:

(i) While any good instrument is worth giving a fair trial on subarcseconders, it is unlikely, in the case of reflectors especially, that a system having a primary f-ratio of less than 5 will achieve the level of performance described above, even if claimed to be "diffraction limited" (a decidedly loose phrase): equation (11.3) makes it clear that colli-mation tolerances for critical imaging quality become almost impossibly tight at F < 5, in addition to which these deeper curves of the main mirror are more difficult for the optician to control by most of the methods of figuring and testing still in use, so that such "fast" paraboloids are rarely as good as the best of longer focus. In general it is clear for reflectors that the longer the focus the better, within reason; even F =12 or 15 would certainly not be excessive here.

(ii) It goes without saying that such extremes of imaging performance can only be expected of good optics, of course, but it would be a mistake to suppose that the author's 12.5-inch is wildly exceptional in this respect. Calver was undoubtedly a master optician but he was working with both materials and methods which made his job decidedly more difficult than that of his modern successor; there must be many more recent mirrors in amateur hands which are just as good as this 1908 glass. It is probably true that any paraboloid as good as, or perhaps a little better than, the Rayleigh quarter-wave criterion will deliver the sort of results described here, if well managed and satisfying the other necessary conditions. Remember, however, that the Rayleigh criterion means that the extreme distortion peak-to-valley of the wavefront must not exceed one quarter of the relevant wavelength of light used; a phrase such as "a one-tenth wave mirror" may, in extremis (and often does!), mean that the mean deviation of the glass from perfect figure does not exceed one tenth of a test wavelength (usually He-Ne laser at 6328A) which is itself considerably larger than the 5100-5300A value relevant to visual observation. In such terms, a surface only just satisfying the Rayleigh criterion would be described as "one-thirteenth wave", so beware ambiguous descriptions of optical quality from telescope retailers, manufacturers and others!

(iii) On the needlessly controversial subject of magnification, the only rule is that there are no rules, and any attempt to set hard and fast limits to what may be used on a given aperture is merely an arbitrary and unhelpful constraint hampering the realisation of the telescope's uttermost capabilities. The wise observer will give full play to the instrument's whole range of powers without prejudice and finally settle on that magnification which best reveals the details sought, irrespective of whether that also yields the crispest, aesthetically most satisfying image. The last is a merely cosmetic consideration. As to high, or even very high, powers - say from 40 per aperture-inch upwards - be neither obsessed with, nor afraid of them. It should be pointed out that the "resolving magnification" is the theoretical minimum for visibility of small detail, not a maximum; oft-repeated attempts to set this as an upper limit to useful magnification, taking 1' as the smallest detail resolvable by the eye and Dawes' or Rayleigh's limits as the smallest that one may be attempting to see with the telescope, are fallacious on all counts: visual acuity varies hugely from one individual to another but the typical night-time resolution of a normal eye is 22 to 3', not 1, while Table 11.1 of subarcsecond double-star appearances shows that we may very well be in quest of detail as small as 0.5 times the Dawes limit, to magnify which up to comfortable visibility therefore requires a power of at least 65 per aperture-inch, a figure itself not in any sense an upper limit. This is quite in line not only with the author's experience with the 12.5-inch mirror (x65.8 per inch) and Jerry Spevak's with the 70mm objective (x72.4 per inch, see Chapter 10) but also that of most observers of such close visual pairs. You may be able to reach these subarcsec-ond limits at substantially lower magnifications but I shall be surprised! (iv) A vital corollary of the last point is that the whole mechanical construction of the telescope must be such that both its rigidity and smoothness of movement are able to handle the high magnifications necessary. This is a rather demanding requirement, which in larger apertures is virtually certain to be incompatible with the lightweight construction favoured for portable telescopes, many of which are hugely under-engineered in this respect. For a reflector over about 6 inches aperture, a permanently mounted instrument is certainly better than a portable for this class of observing and it is evident from this consideration and point (i) that the popular f/4.5 Dobsonian of large aperture is just about the worst possible choice here. Such telescopes are not the tools of high-resolution astronomy.

(v) Full and thorough collimation of a reflector's optics as frequently as may be needed to maintain their precise alignment is an absolute essential, as discussed earlier. Equation (11.2) now makes it very obvious that the smallest errors of squaring-on at the arcminute level will be quite sufficient for coma to swamp many of the finer features in Table 11.1.

(vi) The quality of the seeing is of vital importance. Don't waste time attempting to observe subarc-seconders when the Airy disks of these stars are not visible (say, seeing III Antoniadi or worse).

(vii) These pairs should only be observed when at a large elevation above the horizon, preferably within about 1 hour of meridian passage, and certainly not when below about 35°. Below 40° elevation, elongation of star disks due to atmospheric spectrum becomes increasingly evident and the seeing steadily deteriorates due to the lengthening visual ray within the turbulent atmosphere. Resist the temptation to try for subarcseconders which never rise above these elevations in your sky-the results will only be gibberish.

(viii) This sort of observing does not require phenomenal eyesight; the author is slightly short-sighted and certainly of only average visual acuity even when corrected for myopia. What it does emphatically require is a mental receptiveness to every nuance of what is seen, a power of concentration which devours to the last drop what the eye has to offer. This ability to use one's eyes takes training and practice, of which something has already been said earlier. It is remarkable how widely telescope users differ in this respect, even among active observers, but fancy equipment is no substitute here for essential observing skills. In training the eye to this activity it makes obvious sense not to be too ambitious at first but to start with pairs at several times the Dawes limit and then work steadily downwards. The furthest fringes of subarcsecond double-star observing are undoubtedly an extreme sport, a sort of "athletics for the eyes", which demands fitness as with any such activity. Illness, tiredness or significant alcohol intake are all quite incompatible with peak performance, which depends as much on the observer as it does on the instrument.

Spectacle wearers must, necessarily, abandon their glasses for this work, as the high magnifications used require eyepieces whose eye-relief is much too small to accommodate them. This is no problem whatever to those suffering only from pure long- or short-sight as simple re-focus of the telescope takes care of all, but astigmatism is a more serious matter. Uncorrected, this will cause spurious elongation of star disks with obviously undesirable consequences, so the astigmatic observer who would pursue this game must resort either to contact lenses or to a tight-fitting eyepiece cap carrying the appropriate corrective glass (e.g. old spectacle lens or a piece cut centrally from one).

(ix) Unequal close pairs are much more difficult than equal pairs at the same separation, especially in reflectors generating accentuated diffraction rings, in which an inequality of even 1 magnitude may cause considerable difficulty in the clear sighting of a companion anywhere near the first ring, and a magnitude disparity of 2 or only a little more makes it practically invisible. Most of the remarks above concern approximately equal pairs (magnitude difference less than 1, say) and it makes sense to begin with these on first setting out to crack subarcseconders. An illustrative example here is Albireo, the bright component of which is itself a very close double (MCA55) having a brightness inequality of about 2 magnitudes: at 0.38' ' this is very much more difficult in the author's 12.5-inch (e.g. obs. 1996.80) than an equal pair such as 5 Equ at 0.33'' , probably, in fact, as difficult as any pair successfully observed with that telescope. The effects of seeing and of use of different optical systems on the detectabil-ity of these unequal pairs is altogether a more complex affair than the corresponding questions for equal doubles, and their observation consequently yields much less reproducible results.

(x) For all really doubtful or difficult cases, Herschel's advice could not be bettered: while leaving the eyepiece and focus untouched alternate in quick succession between views of the target double and of a nearby single star at about the same altitude, so using the roundness of the latter as a "control" or comparison for the observed disk shape of the double. If the comparison star shows any significant elongation, the entire observation should be rejected. (xi) Lastly, we come to perhaps the most important point of all for any observations which may with any justification be challenged or doubted, in which category should probably be included all alleged sightings of pairs equal or unequal, separated by less than twice the Dawes limit for the instrument used. As a matter of elementary scientific method it is essential that the observer has some independent means of checking each observation and so proving its validity to the sceptic (quite possibly the observer themselves). This requires that the observation is always made "blind" with respect to some observable parameter of the pair, the observer having deliberately gone to the eyepiece not knowing everything about the current appearance of the target, so that the only possible source of knowledge of the parameter is the observation itself. The observed value can then, post-obs., be checked against the "correct" or expected value as an objective criterion of verification (OCV). The most obvious choice of OCV is the position angle. Thus, and only thus, can observer prejudice, the phenomenon common in some less rigorous visual astronomy of "seeing what you expect to see", be eliminated and these extremes of double-star observation be securely founded on objective detection of the chosen targets. (This is flatly contrary to the (bad) advice given in some handbooks but it must be recognised that questionable observations made in the absence of any OCV, or where none is possible (e.g. as in claims to have seen the central star of the Ring Nebula M57 with small telescopes), are quite meaningless.) If in any doubt about PA at the first observation of a difficult pair where the seeing is less than ideal, do not check the value then but re-observe the target on better nights until confident of the result, and only then consult the OCV.

To conclude, enough has surely now been said to make a powerful case for the reflecting telescope as fully the equal of the refractor, aperture for aperture, in at least some of the most demanding classes of doublestar observation. The author hopes that this may be an encouragement to users of good reflectors to venture into a deeply fascinating field of observation from which the speculum has too often been unjustifiably excluded by false preconceptions of the superiority of the lens.

References

1 Conrady, A.E., 1919, Mon. Not. R.. Astron. Soc., 79, 582.

2 Couteau, P., 1981, Observing Visual Double Stars, MIT Press, p. 32.

3 Born, M. and Wolf, E., 1999, Principles of Optics, 7th edn, Cambridge University Press, p. 424.

4 Born, M. and Wolf, E., Chapter IX, esp. pp. 520-2 and refs. given there, esp. Wolf 1951, pp. 106-8.

5 Ceravolo, P., Dickinson, T. and George, D., March 1992, Sky & Telescope, Optical Quality in Telescopes, 253.

6 Taylor, H.D., 1983, The Adjustment and Testing of Telescope Objectives, 5th edn, Adam Hilger, Bristol, pp. 41-4, in which the ray, or geometrical optics, picture is used.

7 Dimitroff, G. and Baker, J.G., 1947, Telescopes and Accessories, Harvard University Press, pp. 42-3.

8 Berrevoets, C., 2000, Aberrator, Version 2.52 ( I am indebted to Cor Berrevoets for the use of this excellent programme to generate Figures 11.1-11.4, and to David Randell for drawing my attention to Aberrator and to its availability as internet freeware at http://aberrator. astronomy.net (the version now available is Version 3.0 -Editor).

10 Sidgwick, J.B., 1979, Amateur Astronomer's Handbook, 4th edn, Pelham, London, Chapter 12,

11 Griffin, R.F., June 1991, Sky & Telescope, Gamma Persei Eclipsed, 598.

Further Reading

Hysom, E. J., 1973, J. Brit. Astron. Assoc., 83, 246-8.

Chapter 12

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