Method

Once a spectrum has been extracted, it is flux calibrated by dividing it by the grism response function pointed to in the $CALNICC_BASE/calib/grismspec.dat file. The calibrated spectrum is computed as

$$F_{{\rm CAL},l}= F_l/R_l$$ (7)

where R_l is the response for the lth wavelength bin.

  This flux calibration introduces additional uncertainties in the extracted spectra. An error $\epsilon_{{\rm Rc},l}$ is attached to each flux calibration value R_l. In addition, the uncertainty in the zero point of the wavelength calibration due to errors in the measurements of the object x coordinate leads to an error in the applied response at a particular wavelength. This uncertainty is estimated as

$$\epsilon_{{\rm Rx},l}= {\partial R_l \over \partial x} \cdot {\tt POS\_ERR}$$ (8)

where POS_ERR is the uncertainty of the zero point of wavelength calibration in pixels, i.e. the uncertainty of the x position of the object on the direct image. POS_ERR is a user supplied parameter. Realistic values are on the order of 0.5 pixels. The total error in the flux calibration is

$$\epsilon_{{\rm R},l}= \sqrt{ \epsilon_{{\rm Rx},l}^2 + \epsilon_{{\rm Rc},l}^2}$$ (9)

This error has to be taken into account in the estimate of the total uncertainty of an extracted spectrum (see section 3.5.7).