VISIR Exposure Time Calculator

Note: This Exposure Time Calculator is 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 Infrared ETC is an exposure time calculator for the ESO infrared instrument VISIR. The HTML/Java based 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. Being maintained on the ESO Web servers, the ETCs are maintained to always provide up-to-date information reflecting the known performance of ESO instruments.

The input page presents the entry fields and widgets for the target information, expected atmospheric conditions, instrument configuration, observation parameters such as exposure time or signal-to-noise, and output 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 as images and interactive Java applets as well as ASCII and PDF formats for further analysis and printing.

Note: These tools are only provided for technical assessment of observation feasibility. Variations of the atmospheric conditions can strongly affect the required observation time. Calculated exposure time do not take into account instrument and telescope overheads. Users are advised to exert caution in the interpretation of the results and to report any result which may be suspected to be inconsistent.

Instrument description is available for VISIR

From the following, choose the spectrum shape you want for your target.

• Uniform (continuum)

The flux density is constant at all wavelengths: F(λ) dλ = constant.

• Blackbody

The flux density distribution model F(λ) is a blackbody BB(T,λ) defined by its temperature T in unit Kelvin. (This is identical with a greybody spectrum with exponent α=0).

F(λ) dλ = BB(T,λ) dλ= 2hc dλ λ^-5[exp(hc/λkT)-1]^-1.

• Greybody

The flux density distribution model F(λ) is a greybody GB(T,λ,α). This is proportional to a blackbody BB(T,λ) multiplied by the wavelength λ to the power of the exponent α. A pure blackbody is thus a greybody with α=0.

F(λ) dλ = GB(T,λ,α) dλ = BB(T,λ) dλ (λ/λ_o)^α, where λ_o is a reference wavelength.

This can also be expressed as:
F(λ) dλ = GB(T,λ,α) dλ = constant * 2hc * dλ * λ^-5-α[exp(hc/λkT)-1]^-1 , where the constant has the value constant = λ_o^-α.

• Object Flux

If the target model is one of those selected above, the flux will be scaled to the specified flux in mJy at the central wavelength of the selected filter (imaging) or spectral setting (spectroscopy).

• Emission Line

The input spectrum is a single emission line. It is an analytic Gaussian, centered on the wavelength parameter, defined by its total flux and full-width at half-maximum (FWHM).
The minimal width is internally defined by the ETC and set equal to the model's sampling of the wavelength range for the selected configuration (filter or spectral setting). In the case that the width set by the user is smaller than the minimal width, the minimal width is used for the calculations and a warning is issued.
When the single line input option is used (in the section Input Flux Distribution), the (doppler shifted, if applied) wavelength of the line is used as reference instead of the central wavelength of the selected spectral setting.

• Source Geometry

  • Point Source

    Point Source is a source which is unresolved at the wavelength specified by the user. The spatial extent of the area over which the S/N is computed is equal to the FWHM of the PSF at the obserserving wavelength (the FWHM is limited by the effective seeing in the shorter wavelengths, and the telescope diffraction limit in the longer wavelengths).

  • Extended Source

    The value of the flux specified by the user corresponds to a flux per square arcsecond.
    In imaging, the signal-to-noise ratio for extended sources is calculated for an area of 1 square arcsec on the detector.
    In spectroscopy, the signal-to-noise ratio for extended sources is calculated for an area of 1 arcsec in the spatial direction and 1 pixel in the dispersion direction.

To consider the Doppler shift effect, select the radiobutton "Doppler". This is useful with an input spectrum having significant spectral features, like the single line option. In the table, specify the coordinates and the radial velocity of the target, relative to the bary-center 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.

Sky Conditions

• 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.

  
  

  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.
  

  Almanac

  By default, the airmass and moon phase parameters are entered manually. The sky model will use fixed typical values for all remaining relevant parameters (which can be seen in the output page by enabling the check box "show skymodel details").

  Alternatively, a dynamic almanac widget can be enabled to facilitate assignment of accurate sky model parameters for a given target position and time of observation. The sky radiation model includes the following components: scattered moonlight, scattered starlight, zodiacal light, thermal emission by telescope and instrument, molecular emission of the lower atmosphere, emission lines of the upper atmosphere and airglow continuum.

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

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

  Time

  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:

  • Astronomical Twilight −18^° ≥ alt_☉ < −12^°
  • Nautical Twilight −12^° ≥ alt_☉ < −6^°
  • Civil Twilight −6^° ≥ alt_☉ < 0^°

  Target

  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.

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  Instrument Setup

  The other setup sections differ whether you are working in imaging or spectroscopy mode.

  Imaging ETC

  • Filter

  The filters available for the instrument is listed in the pulldown menu. In the square bracket is listed the position of the filter in the filterwheel, as well as the wavelength range of the filter.

  • Objective

  Select the pixel scale.

  Spectroscopy ETC

  • Grating

  Select the resolution mode of the spectrograph and the central wavelength of the spectral range.
  For the HR cross-dispersed mode, the ETC computes results for one echelle order, usually the main order, but it is possible to select an echelle order which is offset from the main order. Information about the order will be given on the output page.
  Please note: When the single line input option is used (in the section Input Flux Distribution) , the (doppler shifted, if applied) wavelength of the line is used as reference instead of the central wavelength of the selected spectral setting.

  • Slit

  Slits can be selected from the pull-down menu.

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  Results

  Set a Signal to Noise Ratio (SNR) to achieve and get an Exposure Time estimation, or the opposite: given an exposure time, estimate the SNR you would get. Total integration time (without overheads) INT=NDIT*DIT. In reality, the optimal DIT depends on the atmospheric conditions at the time of observation - the actual partition of NDIT is done on-the-fly. In this model, a DIT typical for the chosen filter is assigned, and NDIT is computed according to the S/N or INT requested by the user.

  The output form will give an estimate of the SNR or Exposure Time, together with graphs you selected for output. These graphs are interactive Java applets and may require that you setup your browser to enable Java applets.

  To set up the observation, either a SNR or an exposure time must be user-defined. The simulation computes then the associated value.

  • S/N Ratio

  Indicate here a value of the Signal to Noise Ratio (SNR) and get an estimation of the exposure time required to achieve it.

  • Exposure Time

  Indicate here the total exposure time to get an estimate of the Signal to Noise Ration for the observation.

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  Possible Outputs in Imaging

  • S/N as a function of Exposure Time

  Toggling this option will display a curve showing the evolution of Signal to Noise Ratio as a function of Exposure Time.

  • Signal to Noise vs Wavelength

  Toggling this option will display a curve showing the SNR spectrum.

  • Input spectrum in physical units

  The input flux distribution is displayed in units of ergs/cm²/s/A

  Possible Outputs in Spectroscopy

  • Resulting spectrum (object+sky)

  The sum of the object signal and the sky background spectrum in the pixel of peak intensity.

  • Object spectrum only

  The total integrated counts contribution from the object in the reference area, in e-/DIT.

  • Sky spectrum only

  The sky contribution on each row of the detector, 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.

  • 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.

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  Version Information

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  Send comments and questions via https://support.eso.org/