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KMOS Exposure Time Calculator

Important notes and bug reports

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.

General description

These programs provide an HTML/Java based interface and 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 signal-to-noise, 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, signal-to-noise ratios, instrument efficiencies, PSF size etc.. The optional graphs are displayed within Java applets allowing interactive manipulation. The results are also provided in ASCII and GIF formats for further analysis and printing. Finally, a summary of the input parameters is appended to the result page.


Spectral Type

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.

Target Magnitude

You must select the filter and filter magnitude for proper scaling of the template spectrum. Available filters are V, J, H and K. For extended sources, the magnitude must be given per square arc second.

Target Spatial Distribution

Point Source

A point source 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 sky-projected pixel size. The reference area for the S/N is circular with a radius equal to FWHM of the Image Quality PSF at the airmass and wavelength of observation.

Extended Source (per pixel)

The target object is assumed to have a uniform intensity and the S/N on the result page is given per spatial pixel on the detector. Note that the magnitude (or the flux for an emission line) is always given per arcsec2 for extended sources.

Extended Source (with a given area)

The source is assumed to have a uniform intensity over the given area (Ω) on the sky, the number of pixels in the S/N area is Ω / pixelScale2. To obtain the S/N per arcsec2, enter Ω=1 here. Note that Ω should not exceed the 14×14 pixels IFU area (0.2 arcsec/pix * 14 pix)2 = 7.84 arcsec2.
Note that the magnitude (or the flux for an emission line) is always given per arcsec2 for extended sources.

Sky Conditions

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 in-kind contribution to ESO.

Seeing and Image Quality

Since version 6.0.0, the definitions of seeing and image quality used in the ETC follow the ones given in Martinez, Kolb, Sarazin, Tokovinin (2010, The Messenger 141, 5) originally provided by Tokovinin (2002, PASP 114, 1156) but corrected by Kolb (ESO Technical Report #12):

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 long-exposure 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 non-AO point sources in the ETC.

With the seeing consistently defined as the atmospheric PSF FWHM outside the telescope at zenith at 500 nm, the ETC models the IQ PSF as a gaussian, considering the gauss-approximated transfer functions of the atmosphere, telescope and instrument, with s=seeing, λ=wavelength, x=airmass and D=telescope diameter:

Image Quality
\( { \begin{equation} \mathit{FWHM}_{\text{IQ}} = \sqrt{\mathit{FWHM}_{\text{atm}}^2(\mathit{s},x,\lambda)+\mathit{FWHM}_{\text{tel}}^2(\mathit{D},\lambda)+\mathit{FWHM}_{\text{ins}}^2(\lambda)} \end{equation} } \)

For fibre-fed instruments, the instrument transfer function is not applied.

The diffraction limited PSF FWHM for the telescope with diameter D at observing wavelength λ is modeled as:
\( \begin{equation} \begin{aligned} \mathit{FWHM}_{\text{tel}} & = 1.028 \frac{\lambda}{D} \text{, } & \text{ with } \lambda \text{ and D in the same unit}\\ & = 0.000212 \frac{\lambda}{D} \text{arcsec, } & \text{ with } \lambda \text{ in nm and D in m}. \end{aligned} \end{equation} \)
For point sources and non-AO instrument modes, the atmospheric PSF FWHM with the given seeing \(s\) (arcsec), airmass \(x\) and wavelength \({ \lambda }\) (nm) is modeled as a gaussian profile with:
$${\mathit{FWHM}}_{\text{atm}}(\mathit{s},\mathit{x},\lambda) = \mathit{s} \cdot x^{0.6} \cdot (\frac {\lambda} {500})^{-0.2} \cdot \sqrt{[1+F_{\text{Kolb}} \cdot 2.183 \cdot ({r_0}/L_{0})^{0.356})]}$$
Note: The model sets \({ \mathit{FWHM}}_{\text{atm}}\)=0 if the argument of the square root becomes negative \({ [1+F_{\text{Kolb}} \cdot 2.183 \cdot ({r_0}/L_{0})^{0.356}] < 0 }\) , which happens when the Fried parameter \({ {r_0} } \) reaches its threshold of \({ r_{\text{t}} = L_{0} \cdot [1/(2.183 \cdot F_{\text{Kolb}})]^{1/0.356}}\). For the VLT and \({ L_{0} = 46m}\) , this corresponds to \({ r_{\text{t}} = 5.4m} \).
\({ L_{0} }\) is the wave-front outer-scale. We have adopted a value of \({ L_{0} }\)=46m (van den Ancker et al. 2016, Proceedings of the SPIE, Volume 9910, 111).

\(F_{\text{Kolb}} \) is the Kolb factor (ESO Technical Report #12):
$$F_{\text{Kolb}} = \frac {1}{1+300 {\text{ }} D/L_{0}}-1$$
For the VLT and \({ L_{0} }\)=46m, this corresponds to \(F_{\text{Kolb}} = -\)0.981644.
\( {r_0} \) is the Fried parameter at the requested seeing \(s\), wavelength \({ \lambda }\) and airmass \(x\):
$$r_0 = 0.100 \cdot s^{-1} \cdot (\frac{\lambda}{500})^{1.2} \cdot x^{-0.6} \text{ m, } \text{ } \text{ } \text{ } \text{ with } s \text{ in arcsec } \text{and } \lambda \text{ in nm.} $$

For AO-modes, a model of the AO-corrected PSF is used instead.

Seeing statistics:

The Paranal seeing statistics is based on the so-called UT seeing measurements obtained from the UT1 Cassegrain Shack-Hartmann 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/gen-fac/pubs/astclim/paranal/seeing/singcumul.html


The airmass of the observed target. The airmass must be ≥ 1

Moon Phase

Number of days from New Moon.


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/gen-fac/pubs/astclim/paranal.

Instrument Setup

Angular Resolution Scale

KMOS has a fixed camera with a single spatial scale. The spatial scale along the slice is 0.2arcsecs and the slice width is 0.2arcsecs. This ensures the same spatial sampling of 0.2 arcsecs on the sky. At the detector, the slice width is sampled by two pixels in the spectral direction.


This refers to the combination of filter and grating that determine the (fixed) wavelength range of observations. The available gratings are IZ, YJ, H, K or HK, the the latter with spectral resolving power around half of that of the other gratings.


You must supply information about the total observation time. This can be done in terms of DIT (Detector Integration Time), which is the duration of individual exposures, and NDIT (Number of DIT's), which is the number of exposures. The total exposure time is the product of DIT times NDIT. This exposure time does not take into account instrument and telescope overheads.
Alternatively, you can specify a signal to noise ratio, in which case the ETC will compute the minimal number of individual exposures (each of duration DIT) required to reach the requested S/N ratio.

S/N Ratio

The Signal to Noise Ratio (SNR or S/R) is defined for a point-like source at the central observation wavelength. Indicate here a value and choose a DIT, to get an estimate on how many exposures (NDIT) will be needed to achieve it.
Please note that the ETC estimates the S/N in one pixel although the spectral resolution element is two pixels (see Angular Resolution Scale above). In the case of background limited observations between the OH lines, this will be a conservative estimate of the S/N achievable in the spectral resolution element.

Exposure Time

The Exposure Time is the product of DIT and NDIT.

Possible Graphs

Text Summary Results

Version Information

Send comments and questions to usd-help@eso.org