... signal^2.1

The formula 2.3 is appropriate in normal observing configurations where the Point Spread Function of the detected image is determined by the seeing observing conditions. In the case of the UVES ETC, when the seeing observing conditions are very poor or when one would like to have a very high spectral resolution it is possible to insert an Image Slicer along the optical path. In this case the number of integration pixels along the spatial direction is determined by the effective slit height, which is dependent from the image slicer characteristics. In that case $n_{pix}=int((\mbox{slit height/pix scale}) +0.5)$, where int() returns the integer part of a number.

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... fly.^2.2

For the UVES instrument, which allows the use of Image Slicers, one has to use a slightly different formula for an input source of intensity. If the incident flux has a gaussian distribution with sperical radial simmetry as:

$$I(\rho)=\frac{I_{0}}{2\sqrt{2}} \exp{ \displaystyle\left[ ... ...o^{2}}{2}(\frac{2.35482}{seeing})^{2} \displaystyle\right] }$$

$$T_{x}=erf\displaystyle \left[ \frac{IS_{width}}{2\sqrt{2}} ... ...t}}{2\sqrt{2}} \frac{2.35482}{seeing} \displaystyle \right]$$

Where $\rho$ is the radial coordinate, seeing is the observed seeing in arcseconds, IS_width and IS_height are the image slicers width and height in arcseconds.

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