CRIRES Exposure Time Calculator 


Note: These tools are only provided for the technical assessment of feasibility of the observations. Variations of the atmospheric conditions can strongly affect the required observation time. Calculated exposure times do not take into account instrument and telescope overheads. Users are advised to exert caution in the interpretation of the results and kindly requested to report any result which may appear inconsistent.
The CRIRES ETC is an exposure time calculator for the ESO HighResolution IR Echelle Spectrometer using the AO system MACAO. The ETC interface allows to set the simulation parameters and examine interactively the model generated graphs. The ETC programs allow easy comparison of the different options relevant to an observing program, including target information, instrument configuration, variable atmospheric conditions and observing parameters. The ETCs are maintained on the ESO web servers to always provide uptodate information reflecting the known performance of ESO instruments.
These programs consist of two pages. The observation parameters page presents the entry fields and widgets for the target and reference source information, expected atmospheric conditions, instrument configuration, observation parameters such as exposure time or signaltonoise, and results selection. An "Apply" button submits the parameters to the model executed on the ESO Web server. The results page presents the computed results, including number of counts for the object and the sky, signaltonoise ratios, instrument efficiencies, PSF size etc. The optional graphs can be obtained in various formats. A summary of the input parameters is appended to the result page.
In the Target Input Flux Distribution field, you can select a spectral type and filter magnitude for the target.
Alternatively, you can choose to specify the target with a blackbody temperature (and a filter magnitude).
In both cases, the flux will be scaled to the specified magnitude in the selected band.
You can also choose to specify a single emission line instead;
an analytic gaussian, centered on the (dopplershifted, if applied) requested wavelength,
defined by its total flux and width (FWHM: fullwidth at halfmaximum).
The target model can be defined by the target's spectral type. It uses a template spectrum, which is scaled to the provided magnitude and filter. The spectral type is used to make the color correction. The template spectra can currently only be used in JHK bands.
MARCS subset: Spherical Geometry  
Parameter  Number of unique values 
Unique Values 
model  1  "st" 
[Fe/H]  4  4.00,2.00,1.00,0.00 
Teff/K  9  4000,4500,5000,5500,6000,6500,7000,7500,8000 
log(g)  5  0.50,0.00,1.00,2.00,3.50 
geometry  1  "s" 
microturbulence  1  2 
mass  2  1,5 
total (product)  360 (this is the number of possible combinations, but only 87 models exist) 
MARCS subset: Plane Parallel Geometry  
Parameter  Number of unique values 
Unique Values 
model  1  "st" 
[Fe/H]  6  1.00,2.00,4.00,0.00,0.50,1.00 
Teff/K  9  4000,4500,5000,5500,6000,6500,7000,7500,8000 
log(g)  1  4.00 
geometry  1  "p" 
microturbulence  1  2 
total (product)  54 (this is the number of possible combinations, but only 50 models exist) 
All magnitudes are in the Vega system  unless otherwise indicated.
You must select the filter and filter magnitude for proper scaling of the template spectrum. Available filters are V,J,H,K,L and M. For extended sources, the magnitude must be given per square arc second.
The geometry of the target will affect the signal to noise, since extended sources will cover a wider area of the detector. You can either select:
If point source is chosen, the target object is assumed to be an emitter with negligible angular size.
This can be selected for objects with an angular radius of much less than the skyprojected pixel size.
The reference area for the S/N computation depends on the configuration, the reference area has a rectangular shape and the
size a*b depends on the configuration. In the direction of dispersion, b = 1 pixel.
The sky background radiance and transmission model in the CRIRES ETC is based on the Cerro Paranal advanced sky model.
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 airmass of the observed target. The airmass must be ≥ 1.
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.
A cross of lightblue lines will be overplotted, indicating the requested wavelength and the value there, respectively.
