KMOS Exposure Time Calculator 


The sky background radiance and transmission model in the KMOS ETC is based on the Cerro Paranal advanced sky model, developed by a team at the University of Innsbruck as part of the Austria inkind contribution to ESO.
Seeing is an inherent property of the atmospheric turbulence, which is independent of the telescope that is observing through the atmosphere; Image Quality (IQ), defined as the full width at half maximum (FWHM) of longexposure stellar images, is a property of the images obtained in the focal plane of an instrument mounted on a telescope observing through the atmosphere.
The IQ defines the S/N reference area for point sources in the ETC.
With the seeing now consistently defined as the atmospheric PSF FWHM outside the telescope at zenith at 500 nm, the IQ FWHM is modeled by the ETC considering the transfer functions of the atmosphere, telescope and instrument, with s=seeing, λ=wavelength, x=airmass and D=telescope diameter:
\( { \small \begin{equation} \begin{aligned} \mathit{FWHM}_{\text{IQ}} & = \sqrt{\mathit{FWHM}_{\text{atm}}^2(\mathit{s},x,\lambda)+\mathit{FWHM}_{\text{tel}}^2(\mathit{D},\lambda)+\mathit{FWHM}_{\text{ins}}^2} \\ \end{aligned} \end{equation} } \) .
For fibrefed instruments, the instrument transfer function is not applied. For nonAO instrument modes, the atmospheric PSF FWHM with the given seeing \(s\) (arcsec), airmass \(x\) and wavelength \({\small \lambda }\) (nm) is modeled as a gaussian profile with:
\(
\begin{equation}
\begin{aligned}
& {\small \mathit{FWHM}}_{\text{atm}}(\mathit{s},\mathit{x},\lambda) = \mathit{s} \cdot x^{0.6} \cdot (\lambda/500\text{ nm})^{0.2} \cdot \sqrt{1+F_{\text{Kolb}} \cdot 2.183 \cdot ({r_0}/L_{0})^{0.356}} \text{,} \\
& \small{\text{where}}
\end{aligned}
\end{equation}
\) \( \begin{equation} \begin{aligned} {r_0} & = 0.976 \cdot 500.0 \cdot 10^{9}\text{ nm } / \mathit{s} \cdot (180/\pi \cdot 3600) \cdot (\lambda/500.0\text{ nm})^{1.2} \cdot x^{0.6} \\ F_{\text{Kolb}} & = 1/(1+300 \cdot D/L_{0})1 \end{aligned} \end{equation} \) \({ L_{0} }\) is the wavefront outerscale. We have adopted a value of \({ L_{0} }\)=23 m, which is the generally accepted value for Paranal. D is the telecscope diameter in meters. \( {r_0} \) is the Fried parameter at the requested wavelength and airmass. \(F_{\text{Kolb}} \) is the Kolb factor (ESO Technical Report #12). If the argument of the square root \({\small (1+F_{\text{Kolb}} \cdot 2.183 \cdot ({r_0}/L_{0})^{0.356}) < 0 }\), which happens when the Fried parameter \({\small {r_0} } \) reaches its threshold of \({\small r_{\text{t}} = L_{0} \cdot (1.0/2.183)^{1/0.356} } \), the value of \({\small \mathit{FWHM}}_{\text{atm}}\) is set to \({\small 0.0 }\). 
The Paranal seeing statistics is based on the socalled UT seeing measurements obtained from the UT1 Cassegrain ShackHartmann wavefront sensor used for active optics.
The measurements are deconvolved in order to represent the seeing outside the dome (i.e. they are corrected for the instrument+telescope resolution).
The La Silla seeing statistics is based on the DIMM FWHM measurements corrected for the instrumental resolution.
These data come from http://www.eso.org/genfac/pubs/astclim/paranal/seeing/singcumul.html
The precipitable water vapor PWV is the vertically integrated total mass of water vapor per unit area for a column of atmosphere. PWV=2.5 mm is close to the median value for Paranal. Details about the seeing and PWV at Paranal are available from http://www.eso.org/genfac/pubs/astclim/paranal.