Wavelength calibration

The extraction of the orders and the calculation of the coefficients of interpolation for the wavelength calibration are performed, just after the exposure, by the ELODIE reduction software. These coefficients are used in formula (1) to establish the relation between pixels and wavelengths.

$$\lambda(x,k) = {1 \over k}\sum_{i=0}^3\sum_{j=0}^5 A(i,j)T_{i}(\tilde{x})T_{j}(\tilde{k}^{-1})$$ (1)

where $k \in [91, 157]$ is the order of the spectrum, $x \in [1, 1024]$ the number of the pixel in a given order, T_i and T_j the values of the Chebyshev polynomial of order i and j at the points $\tilde{x}$and $\tilde{k}^{-1}$ and A(i,j) the coefficients of the interpolation. In equation (1), $\tilde{x}$ and $\tilde{k}^{-1}$ are x and 1/k normalized on the [-1,1] interval by a linear transformation.