Of prime concern here is not the issue of obtaining the largest possible field of view from the telescope at full resolution, since wide-field observation is, almost by definition, not high-resolution imaging. In any case, most of us have to make do with the fixed F and D of the telescope we have and are, therefore, stuck with the fixed 0max value those imply. The real issue for practical observing, if the telescope is to be used as a serious optical instrument and not merely as a crude "light bucket", is that of sufficiently accurate collimation of the optics to guarantee maximum image quality and full, unimpaired resolution somewhere (preferably the centre!) in the field of an eyepiece of sufficient power to reveal that resolution to the eye. If, through failure of collimation, the optical axis of the primary mirror falls outside such a field by more than 0max, the telescope will never reach its limiting resolution however good the "seeing" may be and even this is a hopelessly sloppy criterion since it allows nothing for the aberrations of the eyepiece when used far off-axis. The matter is certainly not trivial as typical fields of these very high-power eyepieces are only of the same order of magnitude as 0max itself.

The usual collimation procedure10 of looking into the telescope in daylight through an axial pinhole and centring/rendering concentric the reflections of the main mirror in the diagonal and of the diagonal in the main mirror will, if carried through carefully, bring the optical axis into coincidence with the centre of the eyepiece field to within a tolerance of order 10'. At this point, the telescope, if of good quality, will very likely yield quite pretty and satisfying images even of planets at moderately high powers (approximately 20 per inch of aperture) and stars will appear round or point-like up to about these magnifications; it will not, however, reach the limiting resolution for that aperture, falling short of this by a factor of 2 or more in all probability. This is well illustrated by a typical experience with the author's 12.5-inch. After full collimation on 1996.80, the telescope completely split and separated y2 Andromedae (OX 38) at x825 in good but not perfect seeing, when the pair was at 0.50''. A few nights later, after a hurried setting-up in which it had not been possible to complete the final stages of collimation, there was no trace of the companion visible at that power in the same instrument, despite superlative seeing and the star on the meridian. The residual aberrations which blotted out the little star on this occasion were nevertheless still so small as to be completely inappreciable in planetary images; Saturn that night was magnificent at x352.

To go beyond this sort of 30-50% performance there are two further stages which must be completed, what one might call "fine collimation" and "hyperfine colli-mation", the first a refinement of the usual daylight procedure, the second using night-time star tests. No progress can be made on either of these unless the telescope is fitted with fine adjustment screws controlling the squaring-on of the main mirror cell, which are themselves driven by controls within comfortable reach of the eyepiece. Note that it is vital that the observer is able to alter the attitude of the main mirror at will while looking through the eyepiece. Given how very simple it is to contrive this on the majority of Newtonians, it is remarkable how few instruments, commercial or home-made, are fitted with the necessary gear. Having equipped the telescope with this, one can proceed with daylight fine collimation. Mark the centre of the main mirror surface (the pole of the paraboloid) with a round spot at least 1/8 inch across -Tippex is very suitable - the precise size is of no importance but what is absolutely vital is that it be plainly visible from the eyepiece drawtube, be exactly concentric with the pole of the mirror and be fairly accurately circular. Point the telescope at the daylit sky and look along the axis of the drawtube, accurately defined by a "dummy" eyepiece or high-power eyepiece from which the lenses have been removed. Having made the usual adjustments to the diagonal, use the mirror-tilt fine adjust screws to move the reflection of the diagonal in the main mirror until its centre falls exactly on that of the Tippex pole-mark. This should be done by winding the adjust screws, and hence the reflection of the diagonal, to and fro repeatedly while watching through the drawtube, until absolutely satisfied of complete concentricity of diagonal-reflection and pole-mark, so far as the eye can judge. This will probably have taken col-limation to within 2' or 3' of target. All of this assumes the mounting of the diagonal to be rigid, without per-

ceptible play; the small shifts in position (e.g. rotation about the optical axis) of a floppy diagonal can easily introduce randomly changing collimation errors of 10' or more, so defeating all one's best efforts. Nor can it be assumed that collimation is an infrequent necessity, let alone a once-for-all ritual; even a permanently mounted instrument is subject to frequent shifts and distortions (mechanical flexure, thermal expansion and contraction, etc.) at the arcminute level and my personal experience is that serious attempts on subarcsec-ond double stars require recollimation at each observing session. However, once in the habit of it, the process takes only a couple of minutes - hardly a major chore.

For the final, hyperfine stage one has to wait for a class I or II (Antoniadi) night, to push the telescope to its absolute limits. This stage is, of course, only relevant to observing on such nights, in any case. Charge the telescope with a power of x50 to x80 per inch of aperture (e.g. ---inch eyepiece and Barlow pushed well in) and focus on a second or third magnitude star. An immediate test of the quality of the telescope is that even at this power the star should come crisply to focus so that the central disk is almost pinprick-like (this may well be surrounded by a fainter and much larger fuzzle of instrumental and atmospheric origin but ignore that to start with) and unless the instrument is of uncommonly long f-ratio there will be virtually no depth of focus - the tiniest displacement of the eyepiece in or out will noticeably de-focus the star image. (The theoretical depth of focus is ±8F2AX where AX is the maximum tolerable wavefront deformation arising from malfocus.1 If we adopt the Rayleigh tolerance limit AX = X/4, this becomes ±2F2X: e.g. ± 99X at f/7, which is just over 0.05 mm.)

It is, however, the diffraction rings which are far the most sensitive indicators of image degradation due to atmosphere, bad optics or imperfect collimation, which is why one so rarely sees the ideal Airy pattern of the books under real field conditions - and which, rather than the central disk, are therefore used for monitoring hyperfine collimation. The rings are, in particular, extremely sensitive to coma due to miscollimation and will show a very pronounced lopsidedness at a far lower level of maladjustment than is needed to make the central disk go visibly out of round. The result in a Newtonian can be a really quite serious loss of resolution as all the light previously distributed evenly and symmetrically around the rings is dumped into a collection of much brighter short arcs all to one side, creating a sort of false image several times the size of the Airy disk. It seems that this degree of comatic distortion occurs at about the 2-3' level of collimation error one can hope to achieve at the fine collimation stage -depending, of course, on f-ratio but that is my experience at f/7.

Assuming that fine collimation has been carried out with sufficient care and that the optics are of reasonable quality, a close look at the halo or fuzzle surrounding the main star image should reveal that it is at least partly composed of very roughly concentric bright arcs vaguely centred on the star disk. In a Newtonian of typical proportions there are likely to be three or four quite bright arcs (often a lot brighter than the theoretical Airy ring pattern, as noted in the first section of the chapter) and you will be doing extremely well at this stage to see them as arcs of more than about 120°. Unless the night is a true class I (i.e. very rarely at most sites) the rings are not easily seen on full aperture the first time one tries this; they will be fragmented, distorted crinkly-wise and constantly on the jitter. If previous adjustments have brought the telescope within 2 or 3' of true, you will be operating by now well within the coma-dominated regime discussed earlier and an idealised version of what you will see (ignoring atmospheric interference) is shown in Figure 11.2. What you almost certainly will not see is a complete set of circular rings.

Coma in a Newtonian off-axis is external; that is to say the light of the diffraction rings is displaced to the side furthest away from the optical axis. The remedy to the state of affairs shown here - the final hyperfine collimation - is therefore simple (in principle!): while keeping close watch through the eyepiece, wind the fine-adjust controls on the main mirror very slowly so as to displace the distorted image (Figure 11.3), re-centring the star in the field as this adjustment proceeds. It may well be that the outer arcs will disappear during this process but the important thing is that the innermost arc should expand tangentially so as to encircle the central image as a complete ring of uniform brightness. If that state is achieved, you will be in the fortunate position of having a telescope which will reveal detail right down to its diffraction limit -atmosphere permitting!

Figure 11.2. The effect of slight miscollimation in a reflector.

It should now be evident why such insistent emphasis was placed earlier on the need for the collimation controls to be within comfortable reach of an observer actually looking through the instrument, for without

Figure 11.3.

Correcting the miscollimation.

such provision fine collimation will obviously be almost impossible and, in view of the very high powers needed during this stage, hyperfine collimation will be absolutely out of the question. This last stage of collimation, using the structure of star images, must be conducted with the telescope at full aperture but it may take some initial practice for less experienced observers to see the relevant details of the diffraction pattern. Readers unaccustomed to such high-power observation and to the appearance of the Airy rings may find it helpful to follow the suggestions made in the section below on "How to See the Diffraction Limit of any Telescope" before attempting star tests and hyperfine adjustment.

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