Geometric Correction

An accurate two dimensional geometric correction over the entire frame is an important part of the whole reduction process. It strongly affects velocity measurements along the slit and is very critical even for point sources if narrow night sky lines shall be properly subtracted. If the spectrum contains only a point source the user may prefer to extract it from the 2D image (EXTRACT/LONG) and then proceed with the normal one-dimensional spectral reduction.

On the other hand, if the spatial information along the slit is of no interest and night sky lines do not have to be corrected for, much time can be saved by properly averaging the signal along the slit (EXTRACT/AVERAGE).

The full geometrical correction of long-slit spectra is a transformation from the raw pixel coordinates (X, Y) to the sampling space $(\lambda, s)$, where $\lambda$ is the wavelength and s is an angular coordinate in the sky along the slit. Logically, it often makes sense to separate the geometrical transformation into two orthogonal components: the dispersion relation $\lambda = \lambda(X, Y)$, which can be obtained from an arc spectrum with a fully illuminated slit and the distortion along the slit s = s(X, Y), which can be derived from the continuum spectra of point sources. Practically, these two transformations should, whenever possible, be combined into one before rectifying the data, because this saves one non-linear rebinning step, each of which necessarily leading to some loss of information.

As far as the reduction is concerned, the easiest way to achieve this is to observe the comparison lamp used for wavelength calibration through a a pin-hole mask. (Of course, this method can account only for instrumental distortions, not for differential atmospheric refraction, etc.)

In the presence of strong distortions along the slit, a 2-D modeling must be attempted and the command RECTIFY/LONG could be considered. If distortions along the slit can be neglected or suitably corrected for in a separate step, a 2-D modeling of the dispersion relation is still a valid approach. However, a separate reduction of detector row after detector row along the slit, then, often is a superior alternative. A broad overview of the major options is given in the next subsections; a detailed comparison and a Cookbook for the usage of the two methods are provided in Appendix G.