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 High-Resolution 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 up-to-date 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 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 can be obtained in various formats. A summary of the input parameters is appended to the result page.

Instrument descriptions are available for CRIRES

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 (doppler-shifted, if applied) requested wavelength, defined by its total flux and width (FWHM: full-width at half-maximum).

• 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. The template spectra can currently only be used in JHK bands.

• MARCS Stellar Model

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)




• Target Magnitude

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:

• Point Source

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 sky-projected 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 non-AO (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_seeing² + (2 * 1.22*λ/D)² )^1/2
   

• Extended Source

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.

Target Doppler Shift

• 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.
• B-R Color The (approximate) B-R color of the AO or TipTilt guide star. It is used with the R magnitude to compute the flux on the wave-front sensor / tip-tilt 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.

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.

• Seeing and Image Quality

Turbulence Category (T category)

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 seeing-limited or AO-assisted.

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 seeing-limited modes, whereas the same turbulence category as for Phase 1 will be used for diffraction-limited 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 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.

Instrument Setup

• 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 wavelength-dependent 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 light-blue 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 drop-down list. The reference wavelength (wref) will then be assigned to the fixed value indicated in the drop-down list.
  • Free Setting: When this option is chosen, you must select one of the orders in the associated drop-down 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 drop-down list. Don't forget to pres the "set plot range" button or you will get a reminder when you submit.

• S/N Ratio The Signal to Noise Ratio (SNR or S/N) is defined for a point-like 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

• Resulting spectrum (object+sky)The sum of the object signal and the sky background spectrum.
• Object spectrum onlyThe total integrated counts contribution from the object, in e-/pixel/DIT
• Sky Transmission SpectrumThe atmopheric transmission spectrum, in percent.
• Sky Emission Spectrum The atmopheric emission spectrum, in e-/pixel/DIT.
• Signal to Noise as a function of wavelength Toggling this option will display a curve showing the evolution of Signal to Noise Ratio against wavelength.
• Total efficiency and Wavelength range This option will display a curve showing the total efficiency of the system.
• Input spectrum in physical units The input flux distribution as a function of wavelength in units of nm is displayed in units of photons/cm²/s/A.
• Target PSF and Slitwidth The Point Spread Function for the target. The chosen slitwidth is indicated with two vertical overplotted blue lines.
• Enslitted Energy for the Target The Enslitted Energy in the PSF for the target, as a function of the slitwidth. The chosen slitwidth is indicated with overplotted blue lines.

• Strehl Ratio: This is the peak intensity of the observed PSF to that of a perfect diffraction limited PSF.

Version Information

• Version 5.0.1 (Dec. 19, 2013)
  
  • Added support for FowlerNsampGrStWin windowed detector read-mode
  • 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 re-factored and installed on a new web server.

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