On the Possible Occurrence of Astigmatism in Star Tests

The plain fact is that there shouldn't be any. Provided that the optics themselves are of true figure, coma is the only image defect which can occur for small deviations off-axis due to imperfect collimation of a Newtonian. By the time that even rough collimation has been done, the instrument should be well within the coma-dominated regime, as explained above. Conversely, to make astigmatism dominate, the telescope would have to be miscollimated by an angle of order Q = 3/8F which is huge compared with the alignment tolerances discussed above. At this point the image distortions due to off-centring would be huge themselves - stars would appear all sorts of curious shapes even on the lowest powers and resolution would be degraded to tens of arcseconds - and the crudest of rough collimation by eye would eliminate the problem. In other words, small image distortion in a Newtonian due to small errors of collimation is never astigmatism.

If, nevertheless, the star image during hyperfine colli-mation looks fixedly like this (in order of increasing badness):

Figure 11.4.

Figure 11.4.

then you have got a small dose of astigmatism. As it can't be due to miscollimation, it must be due to distortion of figure in the optics but remember that there are four components to the optical train: main mirror, diagonal mirror, eyepiece and your eye. It should be quite easy to determine which of these is responsible for the problem, since all except the diagonal can be rotated about the optical axis without affecting the col-limation: whichever rotating component carries the axis of symmetry of the cruciform image with it, is the villain of the piece and has a distorted astigmatic figure. If this does turn out to be the main spec, it is still not cause for despair since the condition may be temporary and remediable and, in any case, if it is only as bad as the first diagram above it will have negligible effect on telescopic resolution and one can comfortably live with it, even if permanent, i.e. the telescope is still a good one. It should be noted that the machine-generated images in Figure 11.4 are something of a theoretical ideal, as they have been computed only for exact paraxial focus. In reality, astigmatism is more likely to be noticed as a distinct elongation of the star disk when slightly out of focus, this elongation reversing on passing through the focal point. This is the most characteristic symptom of astigmatism and is very pronounced even in the first case depicted above, in which the focal star disk remains virtually unaffected.

Temporary astigmatic distortion of the main mirror can be due to a variety of causes but principally three: uneven thermal expansion/contraction in changing temperatures, pinching or stressing of the disk due to overtight clamping or fit in the mirror cell, and flexure of an inadequately supported disk under its own weight. Thermal effects can easily, and frequently do, bring about a miraculous transformation of a very good mirror into one for which there are no words in polite society; unfortunately it never works this alchemy in reverse! If afflicted with this malady, there is nothing for it but to pack up for the time being while thermal relaxation takes its course or, perhaps, to pass the time with some undemanding low-power sightseeing. One can, however, take common-sense precautions to avoid those recipes which create the problem in the first place, the two worst and commonest being indoor storage at, say, 20-25 °C of an instrument that may be called into play at a moment's notice outdoors at 5 °C or below, and inadequate ventilation and other provisions for temperature stabilisation in small observatories having full exposure to the noonday sun - heating one's telescope to perhaps 40 °C is not a good preparative for high-class images a few hours later!

Mechanical distortion, whether due to pinching or to lack of adequate support of the disk, is essentially a question of mirror-cell design and management, which are dealt with extensively in the large literature of telescope making. There are two basic principles which cannot be overemphasised. Firstly, positive clamping of a mirror in its cell will almost always impair good figure and should be avoided. Secondly, gravitational flexure of a disk of thickness T scales as D4/T2, so increasing rapidly with aperture D even for a constant thickness-to-diameter ratio (T/D). The immediate consequence of this last point is that the requirements for adequate mirror support grow rapidly with size of disk, from three-point support which may suffice for full-thickness mirrors up to 10 or even 12 inches diameter, to 18 or 27-point which is necessary for virtually all mirrors of 20 inches and above. The current fashion for lightweight, thin paraboloids is very much more demanding in this respect and it is unlikely, for instance, that a 10-inch of 1-inch thickness will attain the levels of performance referred to here if carried on anything less than a nine-point support system.

Such optical woes are emphasised in this chapter because reflectors are very much more vulnerable to these conditions than refractors, as noted earlier. The conclusion does not follow, however, that Newtonians are inferior to refractors in all the most challenging fields of double-star observation. On the contrary, all the causes of temporary distortion or misalignment of mirrors are avoidable and a good Newtonian well managed will reach the Dawes limit just as well as any refractor.

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