Optical Instrument 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.

See also: Frequently Asked Questions

Input Parameters

The model includes an input spectrum (e.g. a template star spectrum), atmospheric parameters , optical instrument path and observation criteria. The model generates output graphs describing the spectral illumination of the CCD, the instrument efficiency or the signal to noise as a function of the exposure time or Image Quality.

• Input Flux Distribution

  • Continuum

    The target model is a spectral distribution constant with the wavelength.

  • Blackbody

    The target model is a blackbody defined by its temperature and monochromatic apparent magnitude at a given wavelength. Temperature is expected in Kelvin and wavelengt in one of the band filters U, B, V, R or I.

  • Template spectrum

    The target model can be defined by a template spectrum . As with the blackbody it will be scaled to the provided magnitude and band filter U, B, V, R or I.

  • MARCS

    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)

  • Upload

    Users can upload a file with the spectral flux distibution to the ETC server.

    Supported formats:

    • A FITS 2-D image in the primary HDU with NAXIS1 = 2 and NAXIS2 = <N>, where <N> is the number of points in the spectrum. The filename extension must be .fits, for example sed.fits
    • ASCII: Text file with two numerical columns, separarted by any number of spaces or tabs. The filename extension must be .dat, for example sed.dat

    In both cases the values in the first column should be the wavelength in nm units and ascending order; the second column is the the flux density in a unit proportional to erg/cm2/s/A. The absolute flux scale is not significant since the spectrum will be scaled to the given magnitude in the given band. The maximum file size is 2 MB.
    
    NOTE! The wavelength range of the uploaded spectrum must cover the spectral range of the selected instrument mode as well as the wavelength range of the photometric band in which the magnitude is given.

• Spatial Distribution

  • Seeing Limited

    For point sources the resolution is limited by the PSF at the wavelength and airmass of observation. In imaging mode the signal to noise is computed over an area of diameter twice the Image Quality FWHM. In spectroscopy the reference area is the number of spatial pixels covered by twice the Image Quality PSF FWHM along the slit, and 1 pixel in the spectral direction. The number of pixels is calculated as Npix=2*FWHM(PSF)/plate_scale, rounded to the nearest integer.

  • Extended Source

    For extended sources, the brightness geometry is assumed uniformly distributed. The magnitude is given per square arcsecond. In imaging mode the resulting S/N numbers are displayed for one pixel as well as per square arcsecond. In spectroscopy mode, for extended sources the resulting S/N is calculated over one pixel along the dispersion and one arcsec along the slit.

  • Object Magnitude

    Indicate the object magnitude in the broad band filter associated to the filter that you define in the Instrument Setup. For extended sources the magnitude is given per square arcsecond.

• 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.

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

• Instrument Setup

  • Resolution

    Set the corresponding FORS collimator resolution (Standard or High)

  • Filter

    The filter is selected from a list with an option menu. Some filter curves can be found in the web tool for characteristic curves.

  • Polarimetry mode

    This option applies factor ~0.67 to the transmission to take the polarisation Wollaston prism into account

  • Grating/Grism

    Select the disperser. Characteristics of the FORS grisms are described in the FORS manual. Echelle modes can be selected in the REMD EMMI mode. See the EMMI manual for details. This model computes results corresponding approximately to one Echelle order centered at the wavelength selected by the user. The blaze function is not taken into account in this model.

  • Slit

    Select the slit width from the list of predefined values.

  • Detector

    The simulation takes into account the read-out noise levels for the relevant read-out mode. For details see the User Manual.

  Results

  Possible Outputs in Imaging

  • Text Summary Results

    Source Geometry: "Point source" or "Extended" depending on the source geometry. Some results are computed differently for point-sources ort extended sources.

    Signal to Noise over PSF area: Signal to noise computed using the formula: S/N = object_signal / sqrt (object_signal + sky_signal*Npsf + Npsf*CCDnoise**2)

    Number of pixels for PSF area: For point-sources this is the area over which the S/N is estimated. It is a circular area of radius given by the Image Quality FWHM by the plate scale. This value corresponds to "Npsf" in the signal-to-noise formula.

    Plate scale: The plate scale of the system, in arcsecs per pixel.

    Electrons in the PSF area: The total flux contribution from the object, integrated over the PSF area, and expressed in electrons. This value corresponds to "object_signal" in the signal-to-noise formula.

    Sky background value: The flux contribution from the sky for one pixel of the detector. This value corresponds to "sky_signal" in the signal to noise formula.

    Detector read-out noise level: CCD read-out noise in electrons/pixel. This value corresponds to CCDnoise in the signal-to-noise formula.

    Peak pixel value: This value is the sum of the sky background level (sky_signal) and the fraction of the object signal falling on one pixel at the center of the profile (object_signal_max).

    Detector saturation: The detector saturation level. A message will be displayed if the maximum intensity is greater than this limit. Please note that the actual saturation level may depend on the CCD readout-mode.

    PSF extension: number of pixels over which the signal-to-noise is estimated. This value is computed as twice the Image Quality FWHM divided by the plate scale.

    Signal to Noise at central pixel: Signal to noise on the central pixel, computed using the formula: S/N = object_signal_max / sqrt (object_signal_max + sky_signal + CCDnoise**2). Only this signal to noise is computed for extended sources.

  • Graphs

    Input spectrum in physical units

    The input flux distribution for the selected target is diplayed in units of ergs/cm²sup>/s/A

    Total efficiency

    This option will display a curve showing the efficiency in terms of detected photons against wavelength.

    CCD Illumination

    Toggling this option will display the object spectrum as seen by the detector, in units of e-/Angstrom/sec

    Signal to Noise vs Image Quality

    Toggling this option will display a curve showing the evolution of Signal to Noise Ratio against Image Quality in arcseconds.

    S/N as a function of Exposure Time

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

  Possible Outputs in Spectroscopy

  • Text Summary Results

    Spectroscopy results such as efficiency, signal, signal-to-noise estimates are dependent on the wavelength and given over the wavelength range in graphics form. A summary of results is provided in text form for the central pixel of the range (also corresponding to the central wavelength).

    Wavelength Range: The respective wavelength associated to the first and last pixel of the detector for the given configuration and dispersion, in nanometers.
    For the Echelle modes of the spectroscopic EMMI ETC, the wavelength range corresponds approximately to one Echelle order, centered at the user-specified central wavelength. The blaze function is not taken into account in this model.

    Central Wavelength: The wavelength of the central pixel, in nanometers.

    Dispersion: The dispersion of the spectrum, in nanometers per pixel.

    Plate scale: The plate scale of the system, in arcsecs per pixel.

    FWHM of the image_quality profile: The full-width at half-maximum of the slit spatial profile. This value is the Image Quality divided by the plate scale.

    Efficiency at central wavelength: Total efficiency of the system at central wavelength, including atmospheric extinction, telescope transmission, optics and detector efficiency, in percent.

    Object signal at central pixel: The total flux contribution from the object, integrated over the slit, and expressed in electrons per pixel along the dispersion direction. The value is given at the central wavelength and corresponds to "object_signal" in the signal-to-noise formula.

    Sky background level at central pixel: The flux contribution from the sky for one row along the dispersion direction, in electrons per pixel along the dispersion direction. The value is given at the central wavelength and corresponds to "sky_signal" in the signal to noise formula.

    Max. intensity at central pixel (object+sky): This value is the sum of the sky background level and the fraction of the object signal falling on one pixel at the center of the slit profile.

    AD/Detector saturation level: The truncation level of the AD converter for the default gain mode. A message will be displayed if the maximum intensity is greater than this limit. Please note that the actual saturation level may depend on the CCD readout-mode, and that the saturation is here tested only for the central wavelength.

    Detector read-out noise level: CCD read-out noise in electrons/pixel. This value corresponds to CCDnoise in the signal-to-noise formula.

    Detector dark current: CCD dark current in e-/pixel/hour. This value corresponds to DarkCurrent in the signal-to-noise formula.

    PSF extension: number of pixels over which the signal-to-noise is estimated. This value is computed as twice the Image Quality FWHM divided by the plate scale. This value corresponds to "Npsf" in the signal-to-noise formula.

    Signal to Noise at central pixel: Signal to noise at central wavelength, computed using the formula: S/N = object_signal / sqrt (object_signal + sky_signal*npsf + Npsf*DarkCurrent*ExpTime + Npsf*CCDnoise**2).

  • Graphs

    Object spectrum only

    The total integrated counts contribution from the object, in e-/pixel. The integration is done along the slit. The counts are expressed in electrons per pixel along the dispersion direction.

    Sky spectrum only

    The sky contribution on each row of the detector, in e-/pixel. This value is not integrated along the slit.

    Input spectrum in physical units

    The input flux distribution for the selected target is diplayed in units of ergs/cm²sup>/s/A

    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.

    Standard deviation of Stokes parameters as a function of wavelength

    The standard deviation in percent for U/I, Q/I, or V/I for weakly polarized sources in the object spectrum. The Stokes I spectrum is equal to the object spectrum (polarimetric mode) converted to ADU and normalized to 1s integration time.

    Total efficiency and Wavelength range

    This option will display a curve showing the total efficiency of the system, and a second graph showing the dispersion relation.

    2D Simulated Image

    Produces a FITS file with the 2D simulated spectrum as seen on the detector

• Version Information

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