SDN 0003.17 

Slit Losses

The following tables provide information on slit losses. All calculations assumed that the seeing profile was a Gaussian. Table 1 shows calculations, for a 0.1 arcsec slit, of slit throughput (neglecting any diffraction effects) and of the decentering required to produce a 5% decrease in the throughput. Note that this is 5% of the transmitted light, not 5% of the total light.

Table 1: Narrow Slit Losses

As can be seen, the allowable decenter is not a strong function of seeing; there is (not surprisingly) a minimum at the point where the seeing size is comparable to the slit width. This minimum is equivalent to a decenter in the focal plane of just under 10 mm.

Since the allowable decenter is not a strong function of image diameter, it is clear that the allowable decenter for AO image profiles will be similar. If we imagine an AO profile as consisting of the superposition of a sharp gaussian and a broader residual profile, we can see that allowable decenters will typically be £0.02 arcsec.

It should be pointed out that, for image profiles that are comparable to the slit in width, or narrower, the velocity zero-point of the spectrum is set by the centering of the image more than by the positioning of the slit, and the sky background cannot be used for the

zero-point determination. In this case, one must rely on atmospheric absorption lines in the object spectrum. Spectra can, in principle, have zero-points defined to <0.1 pixel, which corresponds to positioning accuracy of <0.005 arcsec, or <3 mm in the focal plane.

A second comparison of light losses is for the 0.1 and 0.3 arcsec slits. This is mainly of interest in determining where the trade-off is in signal to noise. There are two cases to consider. One is where the length of the slit used for object extraction is constant in arcseconds on the sky. This would most likely apply when the 0.15 arcsec pixels of the larger slit sample the image reasonably well, i.e. for image FWHM ³0.2 arcsec. In this case, the throughput improvement required for the 0.3 arcsec slit to be best is Ö3 or 1.732. The other case is where the slit length used is constant in pixels (usually a small number), in which case a factor of 3 improvement is needed.

Table 2: Comparison of 0.1” and 0.3” Slits

The second case discussed above would most plausibly apply only for very good seeing, which is when the narrow slit is already favored. Hence we need consider only the first case. This indicates that the narrow slit is favored only when the seeing FWHM is 0.15 arcsec or better. In the absence of adaptive optics, such seeing is extremely rare, occurring less than 10% of the time. With an operating AO system, the situation changes, provided Strehl ratios of ~0.3 or better can be produced.

The calculations do not include diffraction effects; the GNIRS optics are somewhat oversized, so that use of a narrow slit will not lead so severe additional light losses for most wavelengths.

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