

CRIRES 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
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.
Instrument descriptions are available for CRIRES
Target Input Flux Distribution
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.
The target spectrum can also be selected from a subset of
MARCS
stellar model spectra, kindly provided by Bengt Edvardsson at the
Uppsala Astronomical Observatory. The parameter space of the MARCS
subsets are listed the following tables. Note that not all models
(referring to all possible combinations of parameters) actually exist.
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.
Target Spatial Distribution
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.
 In the AO case, the size in the spatial direction is the width (diameter) of the Airy disc:
a = 2 * 1.22*λ/D, where D=8.2m is the diameter of the telescope. If this value is smaller than 2 pixels,
then the size in the spatial direction is taken to be 2 pixels to account for the fact that a spectrum is
rarely centered on only 1 pixel.
 In the nonAO (seeing limited) case, the size in the spatial direction is
mainly given by the width of the seeing disk at the wavelength of observation, but also
the diffraction limit is considered (it mostly plays a role at longer wavelengths).
 The effective seeing is computed from the given seeing value (which refer to FWHM in the V band),
using Roddier's formula: effective_seeing = FWHM(λ)=FWHM(500nm)*(λ/500nm)^{−0.2}.
 The diffraction limit enters as the width (diameter) of the Airy disc:
2 * 1.22*λ/D, where D=8.2m is the diameter of the telescope.
 The width (considering both the effects above) is then computed like this:
a = (effective_seeing^{2} + (2 * 1.22*λ/D)^{2 })^{1/2 }
If an extended source is chosen, the S/N reference area is per pixel in the
spectral direction and integrated over 1 arcsec in the spatial direction.
The source is assumed to have a uniform intensity and the magnitude is given per square arcsec.
To consider the Doppler shift effect, select the radiobutton "Doppler". In
the table, specify the coordinates and the radial velocity of the target,
relative to the barycenter of the solar system (a negative velocity means an
approaching target). Also specify the date and time of the observation. The
program use this information (and the geographic coordinates of the Paranal
observatory lon=[70^{°},24^{'},00^{''}], lat=[24^{°},37^{'},30^{''}])
to compute the doppler shift due to the orbital and rotational movement of the
Earth (barycentric correction). In the output page, some partial results of
the computation is displayed.
Reference Source Parameters
 Target/Reference source separation: Enter the separation between the target and the reference source here. The closer the target and reference source the better the correction.
 BR Color
The (approximate) BR color of the AO or TipTilt guide star. It is used with the R magnitude to compute the flux on the wavefront sensor / tiptilt sensor. The input is only critical for extreme colors.
 Reference Source Magnitude
Stars brighter than 10th mag will be dimmed to 10th mag with a neutral density filter. Stars fainter than 17th mag do not provide significant AO correction.
Sky Conditions
Since version 6.x.x, the ETCs offer a dynamic almanac widget to facilitate the assignment of sky model parameters for 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 observatory coordinates are automatically assigned for a given instrument. The sky background model is based on the Cerro Paranal Advanced Sky Model also for instruments at la Silla, except for the altitude above sea level.
A more advanced version of the almanac is included in our SkyCalc web application, which provides more input and output options.
With the advent of instruments using new adaptive optics (AO) modes, new turbulence parameters need to be taken into account
in order to properly schedule observations and ensure that their science goals are achieved. These parameters include the coherence
time and the fraction of turbulence taking place in the atmospheric ground
layer, in addition to the seeing. Starting from Period 105, the turbulence constraints are standardised to the turbulence conditions
required by all instruments and modes, whether they are seeinglimited or AOassisted.
The handling of atmospheric constraints thus changes for both Phase 1 (proposal preparation) and Phase 2 (OB preparation).
In Phase 1, the seven current seeing categories are replaced by seven turbulence categories for all instruments.
Each category can be defined by other parameters than a pure seeing threshold, depending on the instrument.
For all instruments, all categories share the same statistical probability of realisation, which is key for an accurate
time allocation process. In Phase 2, the image quality will still be the only applicable constraint for seeinglimited modes,
whereas the same turbulence category as for Phase 1 will be used for diffractionlimited modes.
Users are encouraged to read the general description of these changes for Phase 1 and Phase 2 on
the Observing Conditions webpage, as well as instrument User Manuals for specifics per instrument.
Seeing and Image Quality
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 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 nonAO 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 gaussapproximated 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 fibrefed 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 nonAO 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 wavefront outerscale. 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 AOmodes, a model of the AOcorrected PSF is used instead.
 Slit width
Specify the width of the slit.
 Wavelengths
Note that all wavelengths are vacuum vavelengths.
 Requested wavelength
This is the the wavelength of interest. The wavelengthdependent numeric results (the signals from object and background, S/N, ...)
will refer to this particular wavelength. If any of the graphs at the bottom of the input page are selected, a cross of lightblue lines will
indicate the requested wavelength and the value of the spectrum there. When a new spectral setting is selected, the value
in the Requested Wavelength field is automatically updated to get the same value as the Reference Wavelength for the newly selected standard or free setting.
This is just a convenience feature; you can change the Requested Wavelengh to any valid value as you please.
 Wavelength range to plot
The λ(min) and λ(max) values are automatically updated to the full range when a Standard Setting is being changed.
For a Free Setting, the λ(min) and λ(max) values will be set to the corresponding full range by pressing the "set plot range" button.
In both cases, you can change the plot range if you wish to "zoom into" a subrange. Only the plots are affected; if a pixel saturates somewhere in the full spectrum (for the selected spectral setting), a warning will still be issued.
 Reference Wavelength
This wavelength refers to the center (pixel 512) of detector 3. You have the choice between selecting a standard setting or a free setting:
 Standard Setting: When this option is chosen, you must select one of the standard modes in the dropdown list.
The reference wavelength (wref) will then be assigned to the fixed value indicated in the dropdown list.
 Free Setting: When this option is chosen, you must select one of the orders in the associated dropdown list,
and enter a reference wavelength in the wref field. The entered reference wavelength must be within the range indicated
for the chosen order in the dropdown list. Don't forget to pres the "set plot range" button or you will get a reminder when you submit.
Results
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.
Note: In some of the results, the unit contains DIT, e.g.
"Object signal in reference area per DIT (at requested wavelength) : 1703.813 e/DIT" ,
to emphasize that the quantity refers to one single exposure of duration DIT, as opposed to the total integration time INT.
In principle, the unit could simply be e.
Please note!
The formula to calculate the S/N ratio includes a correction factor to
adjust the theoretical value to the observed sensitivity. The current value of this factor is:
1/1.56 = 0.64 (for λ ≤ 1.1 microns)
1/1.20 = 0.83 (for λ > 1.1 microns).
As a consequence, the displayed S/N deviates from the expectations based on photon noise, detector characteristics and spatial profile.
 S/N Ratio
The Signal to Noise Ratio (SNR or S/N) is defined for a pointlike source at the observation wavelength
in one spectral dispersion element (1 pixel). It is obtained by integrating the spectrum profile along the spatial
direction. Indicate here a value and choose a DIT, to get an estimate on how many exposures (NDIT) will be needed to achieve it.
 Exposure Time The Exposure Time is the product of DIT and NDIT.
 DIT is the detector integration time (in seconds)
 NDIT is the number of exposures of duration DIT.
 INT is the total exposure time (excluding overheads). INT = DIT x NDIT
Possible Graphs
A cross of lightblue lines will be
overplotted, indicating the requested wavelength and the value there, respectively.
Text Summary Results
 Strehl Ratio:
This is the peak intensity of the observed PSF to that of a perfect diffraction limited PSF.
 Version 5.0.1 (Dec. 19, 2013)
 Added support for FowlerNsampGrStWin windowed detector readmode
 Supporting variable RON depending on DIT
 Version 5.0.0 (July 1, 2013)
 The Sky model in the CRIRES ETC has been updated.
 All ETC version numbers have been aligned at 5.0.0 as the ETC system infrastructure was refactored and
installed on a new web server. Please report significant discrepancies to the ESO user support group usdhelp@eso.org