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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

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

Sky Model

The sky background model is based on the Cerro Paranal Advanced Sky Model, also for instruments at la Silla, except for the different altitude above sea level. The observatory coordinates are automatically assigned for a given instrument.

Since version P101, the ETCs include a dynamic almanac widget to facilitate assignment of accurate sky model parameters for a given target position and time of observation.

Alternatively, the almanac mode can be overridden to allow manual assignment of airmass and moon phase. In that case, the sky model will use fixed typical values for all remaining parameters (which can be seen in the output page by enabling the check box "show skymodel details").

The almanac is updated dynamically by a service on the ETC web server, without the need to manually update the web application.

Notes about the algorithms, resources and references for the almanac are available here

Almanac Usage

Hovering the mouse over an input element in the almanac normally displays a pop-up "tooltip" with a short description.


The upper left part of the almanac box refers to the date and time of observation.
This can be done with a UT time or a MJD. A date/time picker widget will appear when the UT input field is clicked, but the UT can also be assigned manually. In any case, the UT and MJD fields are dynamically coupled to be mutually consistent.

The two +/- buttons can be used to step forward or backward in time by the indicated step and unit per click. The buttons can be held down to step continuously until released.

The third of night corresponding to the currently selected time is indicated. This is an input parameter to the airglow component in the sky model. Twilight levels (civil, nautical and astronomical) referring to the sun altitude ranges are also indicated in the dynamic text. These levels refer to the sun altitude:


The target equatorial coordinates RA and dec can be assigned manually in the two input fields or automatically using the SIMBAD resolver to retrieve the coordinates.
If the lookup is successful, an "info" link will open a window in which the raw SIMBAD response can be inspected.
The units can be toggled between decimal degrees and hh:mm:ss [00:00:00 - 23:59:59.999] for RA and dd:mm:ss (or dd mm ss) for dec. A whitespace can be used as separator instead of a colon.

Output Table

The table dynamically displays the output from the server back-end service, including temporal and spatial coordinates for the target, Moon and Sun. The bold-faced numbers indicate the parameters normally relevant in the phase 1 proposal for optical instruments. The numbers appear in red color if they are out of the range supported by the sky model.

Visiblity Plot

The chart dynamically shows the altitude and equivalent airmass as function of time for the moon and target, centered on midnight for the currently selected date.
The green line, which refers to the currently selected time, can be dragged left and right to change the time, dynamically coupled with the sections in the Time section.

A more advanced version of the almanac is included in our SkyCalc web application, which provides more input and output options.

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