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Volume 48, 1915
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Art. LI.—The Star Test for Telescopic Mirrors

[Read before the Wanganui Philosophical Society, 17th May, 1915]

In the manufacture of mirrors for telescopic work the usual test is that known as Foucault's shadow test. This test used in connection with the zonal one is very convenient for workshop use, but it has its drawbacks. It will be found that the depth of the shadow varies according to the length of focus of the mirror, and it is affected also by the size of the hole through which the light shines and by the amount of light in the room. It is very easy, therefore, to be deceived by the shadow test: it takes, also, some experience to know what shadow should be seen. Theoretically, the zonal test should be satisfactory, but the necessary measurements are so small and delicate that I should not care to depend on it. There therefore remains one test for the final figure of a mirror, which I think is supreme: this is the star test. I will endeavour to describe it, premising that, as a mirror is specially made for viewing the stars, testing it on the stars seems quite a rational proceeding.

Focus the mirror on to a bright star and then rack it slightly out of focus both inside and outside the focal point. The image swells into a ring of light with a dark centre, the shadow of the flat. This should be exactly similar at equal distances on each side of the focal point. If, on the other hand, with the eye-piece slightly outside the focus the ring of light with the dark centre is seen, but with it slightly inside the focus there is a disc of light with a star-like point in the centre, the figure of the mirror is elliptic. If the reverse appears—that is, with the eye-piece inside the focal point there is a disc of light with a dark centre, and with it outside the focal point the telescope shows a disc of light with a bright star in the centre—the figure is a hyperbola. On throwing the eye-piece still farther out of focus it will be found, if the figure is elliptical, that inside the focal point the disc of light expands with a fairly large dark spot in the centre, while outside the focal point, at an equal distance, the disc of light will have a small black spot in the centre. If the mirror should unfortunately prove hyperbolic, outside the focal point the disc of light will have a large black spot, while inside the focal point, at a similar distance, the disc of light will have a small black spot. If the expanded disc is hairy or ragged when inside but well defined outside the focus, the edge of the mirror is turned down.

With a perfect mirror, throwing the eye-piece out of focus at equal distances on each side of the focal point, the mirror should show the outside edge of the disc slightly heavier than inside; and it should contain concentric rings of light each slightly fainter than the one immediately outside it, and in the centre there should be a black spot. Each image at an equal distance from the focal point should be an exact copy of the other. In making these experiments the eye-pieces should, if possible, be achromatic, and for the results to be critical a bright star, such as Sirius, Canopus, Arcturus, or either of the Pointers, should be used, and an eye-piece of fairly high power. I used in these experiments three achromatic eye-pieces—180, 260, and 360—and also a low-power negative one of about 100. The mirror can only be perfectly balanced with one power. Any power from 180 to 260 would be a good power to finally correct it with. If the series of rings do not shade down-uniformly it shows that there are zones in the

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mirror. A good hint can be obtained from Cooke,* and after making the necessary alterations I have no hesitation in quoting from him:—

“If on racking towards the mirror it is found that the central rings look feeble while the edge rings, and especially the outer one, look massive and luminous, while on racking out of focus away from the mirror the central rings look relatively brighter and the outer rings look weak in comparison to what they appeared when within focus, then the inference is that the edge rays fall short or come to a focus at a point nearer to the mirror than the focus for the central rays, or, in other words, there is positive aberration.

“If, on the other hand, the central rings when inside focus look about as luminous or even more so than the outer ring which is thin and weak, while on racking outside focus the complementary effect of a massive and luminous outside ring enclosing comparatively feeble central rings is observed, then the inference is that the edge rays come to focus at a point farther from the mirror than the focus for the central rays, and this fault is negative aberration.”

It will thus be seen that the general disc of light gives a general idea of the figure. The black spot in the centre being larger on one side or the other shows at once whether the mirror is under- or over-corrected; and the outside ring of light viewed at equal distances inside and outside the focus, with a succession of stops getting smaller and smaller, shows at once the figure of each successive zone, and whether polished too long or too short in focus; or, if absolutely equal, quite correct.

When finally silvered and tested this way it gives at once the general figure and the individual zones. If there are zones in the mirror they are easily seen in the expanded discs of light, as these zones appear brighter or darker than the normal disc.

If the edge is badly turned down there will probably be a ring-system outside the focus, with a heavy outside ring, while inside of the focal point the disc of light will be faint on its margin, with a hairy and confused edge. It is useful to have a number of stops made reducing the aperture, and then to compare the outside ring as the aperture gets smaller. This outside ring should be the best-defined ring on the disc, and should be exactly equally bright inside and outside of focus at equal distances. If this is not the case there is a zone at the edge of the circle to which the mirror is stopped down, and it can be ascertained in manner previously mentioned whether it is polished too deep or not deep enough.

Another defect easily detected by the out-of-focus method is astigmatism. Astigmatism may be caused either by the large mirror, the eye-piece, or the eye of the observer; or the small flat may, if not flat, show a similar defect. The appearance of the out-of-focus image will be an oval instead of a circular disc.

If it is caused by a defective eye-piece the long diameter of the oval image will rotate as the eye-piece rotates. If it is caused by the eye of the observer it is only necessary to move the head a quarter of a circle round the eye-piece to see if the oval rotates. There remains the chance of the flat being in fault. If the large mirror is turned 90° and the oval image does not rotate the flat is in fault. If the oval rotates with the large mirror the fault lies with the mirror—that is, it is astigmatic: one diameter is ground and polished slightly flatter than the other diameter. This method of testing is particularly suited to finally testing large mirrors after they

[Footnote] *“Telescopic Objectives.” London: De Little and Sons, 1896.

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have been mounted, as a few minutes' scrutiny of a large star will show at once whether the figure is good or bad without removing the mirror from its tube. A high power must be used for large mirrors. Very large mirrors seldom have absolutely first-class figures for dividing double stars, but are sufficiently good for photography, as the halation hides the minor faults which make the difference between a perfect mirror and a good one. Until mirrors are figured with the same care as achromatics they will never give satisfaction; and I may add that a perfect flat is as essential as a perfect mirror. If the flat is concave it will give, slightly out of focus, an oval disc of light instead of a circle, and quite spoil the definition.

In conclusion, I should like to acknowledge my debt to Nichol's Cyclopaedia, published in 1837, and to Cooke's book on “Telescopic Objectives.”