The Measurements

As the separation range which can be measured depends on the value of p, to measure all double stars in the range of a given telescope would require quite a number of gratings.

In practice though there is a way to overcome this problem. With a few gratings and some elementary geometry, the basic method can be considerably refined. In this case, a set of four gratings is used with slit distances of 10, 20, 30 and 40 mm. The widths of the bars separating the slits are normally half the slit distance.

The star images and their satellites can be arranged in particular configurations depending on the orientation of the grating. Provided that the pattern is carefully arranged, the grating slit distance and the grating orientation, together with a little trigonometry can deliver quite accurate results for both the PA and separation of the double star being observed. Several star patterns have been proposed by previous observers1 and the method has been continuously refined. It was extensively and successfully used and described by French and English double star observers in the 1980s.2,3,4

Obviously the most convenient method would be a grating with adjustable slit distances, thus minimizing the number of gratings and rendering trigonometric calculations superfluous. Such an instrument had already been proposed by Karl Schwarzschild in 1895.5 He used three sets of different gratings which he arranged in front of the objective glass of a 10-inch refractor like a roof with rising and descending ridge as shown in Figure 14.2. In this way he could produce variable slit distances, as seen from infinity. The instrument was adjustable by ropes from the eyepiece end.

Lawrence Richardson6 described a simpler, homemade adjustable interferometer consisting of a flat grating frame which could be tilted in front of a small 4.5-inch refractor. This was the construction which served as a model for the one described here, an easy-to-build, adjustable grating micrometer. It is made of aluminium, board and plywood and is designed for use on the popular 20-cm Schmidt-Cassegrain telescopes. Needless to say the principle of the instrument can also be used on other types of telescopes.

Figure 14.2. The

Schwarzschild adjustable diffraction micrometer used in 1895. Three pairs of interchangeable gratings (p = 70, 40 and 24 mm) were used. Reproduced from Astronomisches Nachrichten by kind permission of Wiley-VCH Verlag

Construction

This adjustable micrometer consists basically of two parts:

(1) a rectangular grating frame in front of the telescope objective or corrector lens, which can be tilted with respect to the optical axis and

(2) a flange for mounting this frame with its support onto the objective end of the tube. This flange allows the device at the same time to rotate and its orientation can be read on a 360° dial (Figure 14.3).

The apparent slit distance is varied by inclining the frame which has to be large enough to cover the telescope aperture even when tilted. On the other hand, the frame should not be larger than absolutely necessary in order to keep the instrument size within reasonable limits. Here one has to compromise: as an example, the construction shown in Figure 14.3 works with a 230 x 520 mm frame and the maximum useful tilt is about 65°. The projected slit distance varies as the cosine of the angle of inclination. Therefore the frame-tilt graduation is not in degrees but directly in corresponding cosine values, thus simplifying the reductions.

Figure 14.2. The

Schwarzschild adjustable diffraction micrometer used in 1895. Three pairs of interchangeable gratings (p = 70, 40 and 24 mm) were used. Reproduced from Astronomisches Nachrichten by kind permission of Wiley-VCH Verlag

Figure 14.3. A homemade adjustable diffraction micrometer showing the p = 25 mm grating.

Figure 14.3. A homemade adjustable diffraction micrometer showing the p = 25 mm grating.

For effective diffraction at least three or four slits should be in front of the objective so for a 20-cm telescope the largest slits will be about 25 mm wide and arranged 50 mm apart. According to the diffraction formula such a slit distance can thus be used for measuring double star separations from 5.5 to about 2.5''. For smaller separations larger telescope apertures are essential. If the 20-cm telescope is to be used for double star separations of up to 10'', say, two grating frames with 50 mm and 25 mm slit distances will do. The smaller grating - used for larger separations - will, when inclined at 65°, produces a projected slit distance of 10.6 mm, which corresponds to about 11'' separation. If wider separations are to be measured a third frame with smaller slit width could be made. However, the stability of the narrow grating strips could become a limiting factor.

In order to get reliable measures, grating frames should be precisely made. The slits and bars should be accurately parallel to each other and also to the tilting axis. Aluminium bars of width 25 mm or alternatively 12.5 mm and 1.0 mm thick are glued onto a frame made of 10 mm aluminium angle and wood. The tilting axis consists of small pivots on each frame side which turn in clamps as shown in Figure 14.4. These clamps allow a frame-exchange within seconds and they also produce just the right friction for the frame to tilt very smoothly.

Figure 14.4. Metal clamps serve as bearings for the grating frames and allow a quick exchange of frames. Note the cosine scale for reading the frame inclination.

Two lightweight side frames support the two grating frame bearings which in turn are fixed to the bottom flange as shown in the photographs. This wooden flange is provided with a cardboard collar on its back, which fits onto the end of the telescope tube. The fit should be tight enough to keep the micrometer properly in place even at low elevations but at the same time not too tight to prevent it being turned around its axis. A collar which is slightly too large is preferable because the desired clearance can then be fixed by inserting some shims of paper or felt. At the collar bottom a 1.5 mm aluminium ring is glued to its rim. This aluminium ring carries a 360° scale or dial and contributes at the same time considerably to the micrometer's stability. This scale, which indicates the double star position angle, is read by a properly set pointer or marking on the telescope tube. Having an outer diameter of 270 mm the scale allows precise reading but if desired a vernier scale could be added. To establish the dial's zero-point the grating slits have to be exactly parallel to the telescope declination axis. In this position the satellite images of a star are aligned north-south. The weight of the micrometer should be kept as low as possible in order not to disturb the balance of the telescope. The instrument shown in the photographs weighs not more than 500 g.

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