Estimation of Exposure Time

The number of photons per pixel in the spectrum expected to be obtained for each wavelength range (U,B,V,R,I) can be calculated by the following equation:

$N_{\rm photon} = a_{\rm band} \times 10^{-m_{\rm band}/2.5} \times T_{\rm exp} \times f$

In this equation, $a_{\rm band}$ is a constant for each wavelength range given in Table , $m_{\rm band}$ is a magnitude in that band, $T_{\rm exp}$ is the exposure time, and $f$ is the fraction of the light entering the slit (which depends on the slit width and the seeing disk during the observation).

Table 8: Coefficients for the foton-per-pixel equation

Band (Wavelength)	$a_{\rm band}$
U (3670Å)	$5.4 \times 10^{5}$
B (4360Å)	$6.3 \times 10^{5}$
V (5450Å)	$8.5 \times 10^{5}$
R (6380Å)	$8.0 \times 10^{5}$
I (7970Å)	$2.7 \times 10^{5}$

The S/N ratio achieved with a given exposure time for objects with a given brightness can be estimated by the HDS Exposure Time Calculator (ETC) available in the following Web page.

To determine the flux emitted from the source, user can define the brightness of the object in a given band, its redshift, and spectral energy distribution (power law, blackbody of a given temperature or template stelar spectrum from the available library).

For the instrument setting we encourage to use on of the standard ones, but if a non-standard is selectet, one can choose between the red and blue grating and define the central wavelength. The ADC and image rotators are optional and can also be included. The Messia 5 CCD control system is set by default, as it is currently in use. User can also select one of the binning options, and choose between the normal slit (which width needs to be defined) and one of the image slicers. Other parameters are the size of the seeing disk and exposure time.

As the output, the ETC firstly gives various information related to the efficiency, readout time, dark current, etc. In the output table below a simplified echelle format is simulated - for each echelle order its location and wavelength range are given. Disoersion, source flux, peak couns and S/N ratio is calculated for the center of each order. Lines marked orange refer to orders that might be partially damaged by a bad column. Lines marked red mean saturation in a given order. In case one of the ISes is selected, the last two columns show how much the number of photons and S/N are improved relatively to the normal slit. Please read carefully all the notes below the table.