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Effects of distortions

The optical system of LDSS-2 produces small radial distortions amounting to approximately 2% of the radius at the field edge. We may distinguish two types of distortion:

• Non-chromatic distortion which is the amount by which the centroid of an image of a point source deviates from the position predicted in the absence of distortion. Generally the prediction is made by adopting the reduction factor appropriate for the centre of the field (given roughly by the ratio of the telescope to camera focal ratios ). This amounts to a maximum of 2% of the radius at the field edge.

• Chromatic distortion which is the amount by which the centroid of an image of a point source varies with wavelength. The largest distortion predicted from ray-tracing is 20m ( arcsec) at about 3 arcmin off axis.

For spectroscopic observations, the effect of these distortions can be accounted for by the extraction routines in LEXT.

The non-chromatic distortion will manifest itself as an additional non-linearity in the dispersion (in addition to that caused intrinsically by the grism) which will depend on the location of the spectrum in the field. The normal way to reduce LDSS spectroscopic data is to use a wavelength calibration exposure (Section 5.5.2) to determine the non-linear pixel-to-wavelength conversion separately for each spectrum. If the spectra are then resampled correctly, this source of distortion will be exactly accounted for. However, this effect can introduce a small error if an object is positioned far from the centre of the slit in the cross-dispersion () direction. In this case there will be a offset between the object and the centroid of the slit which is where the wavelength calibration was determined. Since the wavelength calibration depends on position, this introduces a small error.

The non-chromatic distortion will also cause the centroid of the spectrum in the cross-dispersion direction to vary with position in the field, in addition to the variation in centroid caused by differential (i.e. wavelength-dependent) atmospheric refraction. This is normally accounted for in the reduction by the extraction software keeping track of the centroid shift as a function of wavelength.

The chromatic distortion merely adds additional distortion that is also dependent on the wavelength of the light that falls at that position. It can therefore be accounted for using the standard procedures mentioned above.

For spectroscopic data, it is therefore not necessary to remove the distortion explicitly. Indeed it would be undesirable to attempt this since it would mean resampling the data unnecessarily which always adds noise.