Diffraction influences telescopic images by the effect it has on incoming starlight as we have seen in Chapter 10. It can also be used as the basis for a simple micrometer.

When it comes to measuring the position angles and separations of double stars, sophisticated and expensive precision instruments usually come to mind. However, if you can accept a limited selection of double stars then accurate measurements with very simple devices, the so-called diffraction grating micrometers, are possible. These micrometers, especially in their simplest forms, are very easy and inexpensive to build.

When a telescope object glass or mirror is masked by a coarse grating as shown in Figure 14.1, diffraction of each star image will produce an array of satellite images on both sides of the star in a line perpendicular to the grating slits (Figure 14.5a below). The brighter the star and the wider the grating slits, the greater the number of visible satellites. These satellite images are actually rectangular-shaped spectra but this is only apparent with brighter stars. The central image is the zero order image, the neighbouring satellites are the first order images and so on. For measurement purposes though, only the zero and first-order images of each component are of interest. The basis of this micrometer is that the distance between the zero and first order images is fixed for a given grating and

Figure 14.1. The author's 20-cm Schmidt-Cassegrain equipped with a 50-mm grating. The first-order images are 2.3 arcseconds from the zero-order image. See also Figure 14.5a below. The position angles can be read on a 360° scale.

Figure 14.1. The author's 20-cm Schmidt-Cassegrain equipped with a 50-mm grating. The first-order images are 2.3 arcseconds from the zero-order image. See also Figure 14.5a below. The position angles can be read on a 360° scale.

depends on the separation of the slits. For a given grating therefore, this distance, once determined, can be used to measure both the position angle and separation of double stars.

Experience has shown that gratings whose slit width is equal to the bar width give the best results because this corresponds to the maximum brightness of the first-order images. The critical dimension of a grating is the slit distance, p. The angular separation in seconds of arc between the zero and first order images is given by:

206,265 X

where l is the grating slit width (in mm) and d is the bar width (also in mm), so that p = (l + d). The wavelength of the starlight, X, varies from about 5620 A (5.62 x 10-4 mm) for an early B star to 5760 A(5.76 x 10-4 mm) for an early M star but these values depend slightly on the observer, and so X is known as the effective wavelength. To use the micrometer to its full accuracy each observer needs to determine his or her effective wavelength for a range of spectral types.

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