## Choice of echelle grating

A choice of two gratings is provided with UES, one with 31.6 lines/mm and one with 79.0 lines/mm. It is important to realise that the choice of grating is not determined by the spectral resolution required, as in a conventional first order spectrograph such as ISIS. Instead, the choice of grating is determined by a trade-off between wavelength coverage and the quality of sky subtraction.

In order to see why this is the case, its worth briefly restating the basic equations governing diffraction by a grating. The grating equation describes the condition for constructive interference:

The angular dispersion is obtained by differentiating this:

The dispersion is a function only of the angles at which the grating is used, and not a function of the groove spacing. The two UES gratings have nearly the same blaze angle (64.95 degrees for the 31.6 echelle and 63.96 degrees for the 79.0 echelle), and hence are used with similar values of i and . This means that at a given wavelength they provide almost identical spectral resolution as can be seen from Tabs. 15 and 16.

The difference between the two gratings is that, at any given wavelength, the grating equation implies they must be operated at a different interference order. For example, observations at 5000Å would use either the 31.6 lines/mm grating in order m 114, or the 79.0 lines/mm grating in order m 45 (see Tabs. 15 and 16 ). The principal effect of this is that the wavelength range of each order, normally referred to as the Free Spectral Range (FSR) is different. The FSR is given by:

At any given wavelength, the 79.0 lines/mm grating will have 2.5 times the free spectral range of the 31.6 lines/mm grating; the orders are 2.5 times longer, and hence 2.5 times further apart. Since the dispersion is the same, this means that for a fixed detector size, the 79.0 lines/mm grating provides less wavelength coverage, but more space between the orders to measure the sky background.

When deciding which echelle to use, it is therefore necessary to consider how long a slit you need to get adequate sky subtraction, and how many exposures will be required to cover the required wavelength range.

The inter-order spacing with both echelles at various wavelengths is summarised in Tab. 18. This assumes no focal modifier lenses are in the beam. The slitlength used should be slightly shorter than this inter-order spacing, in order to leave a gap between the orders.

It is possible to estimate the number of exposures required to cover a given wavelength range using the data in Tabs. 15 and 16. These tables give the length and separation on the detector of each order.

This calculation can be carried out much more easily using graphical means, and the ECHWIND programme has been developed for this purpose. ECHWIND draws a complete echellogram on an image display, together with a box representing the size and shape of the detector in use. The position of individual spectral lines can also be marked on the display. The user can then move the detector window around using the mouse. At each position, the screen displays the minimum and maximum wavelengths and order numbers falling on the detector. The position of the detector window can be marked on the screen so as to ease preparation of observations where multiple overlapping wavelength ranges are required. The output of the programme is the central wavelength and order number of each exposure.

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Mon Mar 14 16:50:31 GMT 1994