2 Differential atmospheric refraction in IFS: Its effects and correction

To illustrate the effects of differential atmospheric refraction (hereafter DAR) in IFS systems we are going to present a simplified case. Let us assume that the object is a star with a constant continuum, i.e. $F_{\lambda}({\rm continuum})=$ const. (Fig. 1 left), and the parallactic angle is 0 deg (i.e. the differential atmospheric refraction takes place along the N-S direction). At the telescope focal plane, the star image is sampled by an array of square apertures.

In the absence of DAR the images of the star at all the wavelengths are coincident, and the spectra obtained from any aperture are basically the same (Obviously, the counts and, therefore, the S/N vary from aperture to aperture depending on their sampling of the seeing). However, when DAR is present the images of the star at different wavelengths are not in positional agreement. In our example they shifted along the N-S direction. Now each aperture gives a different spectrum. To illustrate this let us consider two individual apertures, A₁ and A₂, orientated along PA 0 deg in such a way that the maximum of the star in $\lambda_{1}$ is at the centre of A₁, and the maximum of the star in $\lambda_2$ is at the centre of A₂ (see Fig. 1 centre). In such a situation aperture A₁ loses part of the light of the object's spectrum at wavelengths larger than $\lambda_{1}$. Similarly, aperture A₂ does not include part of the blue light of the star's spectrum. Consequently, the spectra inferred from A₁ and A₂ differ between them and from the actual spectrum of the object (see Fig. 1). The fluxes obtained in this way at different wavelengths from the same aperture (fibre) spectrum are not directly comparable. In fact, in the previous example, the only comparable fluxes are those obtained in $\lambda_{1}$ from aperture A₁ ($F_{\lambda_1}(A_1)$), and in $\lambda_2$ from aperture A₂ ($F_{\lambda_2}(A_2)$). In other words, if differential atmospheric refraction is present, the way to obtain the flux at a particular $\lambda$ is to centre an aperture at the maximum of the star at this wavelength. If the complete spectrum is required, we should have centred as many apertures as spectral resolution elements, the actual spectrum being $F_{\lambda_i}=F_{\lambda_i}(A_i)$, where $F_{\lambda_i}(A_i)$ is the flux of an aperture centred on the maximum of the star in $\lambda_i$.Obviously it is not possible to have all these apertures on the focal plane simultaneously, especially if the number of spectral elements is in the order of 1000. However, if the object is properly sampled, $F_{\lambda_i}(A_i)$ may be well determined by interpolation between $F_{\lambda_i}(A_1)$ and $F_{\lambda_i}(A_2)$. This is the basic method that we have applied for correcting for differential atmospheric refraction, and whose results are shown in the next section. Obviously, in a real case, the direction of differential atmospheric refraction and the distribution of the apertures are such that the interpolation must be done in two dimensions.

  

Figure 1: Effects of differential atmospheric refraction on IFS. The spectra obtained from two different apertures differ between them and from the real one