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.

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 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. A summary of the input parameters is included in the result page.

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).

• Single 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.

• Airmass

The airmass can be computed from the Skycalc page: http://imagiware.com/astro/airmass.html .

• Seeing

The seeing parameter is given in arcseconds and corresponds to the full-width at half-maximum (FWHM) of the seeing disk at 500nm.
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. This is modelled as described in the following:

s_diff = 0.98 (lambda/D) 206265
where s_diff is the FWHM of the point-spread function of the telescope (in arcsec).
lambda is the central wavelength (in m).
D is the diameter of the telesscope (in m).
206265 is the conversion factor between radian and arcsec.
(The factor 1.22 usually given for the diffraction limit corresponds to the radius of the 1st Airy ring).

s_atm = seeing_opt (lambda/0.500)^−0.2 airmass^0.6 f_corr
where seeing_opt is the optical seeing (at 0.500 micron), which is the seeing parameter entered on the ETC input page, and f_corr is a correcting factor to take into account the effect of the turbulence outer scale L0. We currently use f_corr = 1.

The FWHM of the seeing disk in the VISIR ETCs is calculated like this:
s_visir = max( s_diff(lambda) , s_atm(lambda,airmass) )


• Sky

The program will invoke a flux calibrated sky model, yielding the sky background at the specified wavelength.

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.

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.

• 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

• Resulting spectrum (object+sky)

The sum of the object signal and the sky background spectrum for the central row of the spectrum.

• Object spectrum only

The total integrated counts contribution from the object, in e-/pixel/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.

Version Information

• Version 3.2.1 (Aug 31, 2007).

  Imaging ETC: Added 8 filters: B9.7, B10.7, B9.7, B11.7, B12.4 , J7.9, J8.9, J9.8, J12.2.

  Spectroscopy ETC: No changes since Version 3.1.0.

• Version 3.2.0 (June 21, 2007).

  Imaging ETC: Filter curves updated, DITs and Noise factors adjusted.

  Spectroscopy ETC: No changes since Version 3.1.0. NOTE: A bug has been identified, but not corrected: For narrow slits ( < 1 arcsec for normal seeings), the slit transmission can be up to factor 2 too big, thus overestimating the S/N by up to factor sqrt(2) ~ 1.4. This occurs only for observations of bright objects compared to the background.

• Version 3.1.0 (July 25, 2006).

  Version updated, no change in results for VISIR.

• Version 3.0.8 (June 27, 2006).

  Corrected a bug in MR spectroscopy (affected S/N results for central wavelengths in the range [12747 - 13078] nm).

  For single emission lines, the wavelength is now always placed at the (doppler shifted, if applied) reference wavelength.

  First released ETC to use new plot layout: Gif is default format. Optinal plot formats Java (interactive), pdf, ASCII data. A y-logarithmic plot is possible. Reference values indicated by overplotted horizontal and vertical lines.

• Version 3.0.6 (September 13, 2005).

  New spectral modes added.

  Introduced doppler-shift feature.

  Noise factors adjusted.

  The model for atmospheric transmission/emission updated/advanced.

  New fomula for the seeing as function of wavelength.

• Bug fixed in Version 3.0.5 (March 9, 2005).

  Spectroscopy ETC only. In the formula computing "Max. intensity at central pixel per DIT (object+sky)", the object contribution has been corrected. The effect is minor, because the sky contribution dominate.

• Version 3.0.5 (March 3, 2005)

  HR cross-dispersed mode now available in spectroscopy.

  HR long-slit spectroscopy mode: Wavelength range continously selectable in additional bands.

  Sensitivity (noise) factors adjusted.

  S/N formula corrected (better accounting for chopping/nodding). In most cases the S/N values have only changed marginally.

• Version 3.0.4 (January 7, 2005)

  Additional slit widths available in spectroscopy.

  HR long-slit spectroscopy mode: Wavelength range continously selectable in NeII band [12738-12882]nm.

  New file for telescope efficiency.

  New file for atmosphere transmission.

  Bug fixed (imaging ETC only): The formula computing the peak intensity at central PSF pixel has been corrected. In the previous version, the object contribution was not considered correctly. The change is not very significant, because the sky dominate.

  Textual label information attached to JavaApplet graphs.

• Version 3.0.0 (September 1st, 2004)

  First version.

Send comments on this document to User Support Department/DMD<usd-help@eso.org> Last modified: March 17, 2005.