# VISIR Exposure Time Calculator

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# Important notes and bug reports

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.

## Input Spectrum

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/λo)α, where λo 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 = λo.

• ### 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.

## Doppler Shift

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

The sky background radiance and transmission model in the VISIR ETC is based on the Cerro Paranal advanced sky model, developed by a team at the University of Innsbruck as part of the Austria in-kind contribution to ESO. See also the SkyCalc web application.

• ### Seeing

• Since version 6.0.0, 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 point sources in the ETC.

With the seeing now consistently defined as the atmospheric PSF FWHM outside the telescope at zenith at 500 nm, the IQ FWHM is modeled by the ETC considering the transfer functions of the atmosphere, telescope and instrument, with s=seeing, λ=wavelength, x=airmass and D=telescope diameter:

{ \small \begin{aligned} \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} \\ \end{aligned} } .

For fibre-fed instruments, the instrument transfer function is not applied.

For non-AO instrument modes, the atmospheric PSF FWHM with the given seeing $$s$$ (arcsec), airmass $$x$$ and wavelength $${\small \lambda }$$ (nm) is modeled as a gaussian profile with:

 \begin{aligned} & {\small \mathit{FWHM}}_{\text{atm}}(\mathit{s},\mathit{x},\lambda) = \mathit{s} \cdot x^{0.6} \cdot (\lambda/500\text{ nm})^{-0.2} \cdot \sqrt{1+F_{\text{Kolb}} \cdot 2.183 \cdot ({r_0}/L_{0})^{0.356}} \text{,} \\ & \small{\text{where}} \end{aligned} \begin{aligned} {r_0} & = 0.976 \cdot 500.0 \cdot 10^{-9}\text{ nm } / \mathit{s} \cdot (180/\pi \cdot 3600) \cdot (\lambda/500.0\text{ nm})^{1.2} \cdot x^{-0.6} \\ F_{\text{Kolb}} & = 1/(1+300 \cdot D/L_{0})-1 \end{aligned} $${ L_{0} }$$ is the wave-front outer-scale. We have adopted a value of $${ L_{0} }$$=23 m, which is the generally accepted value for Paranal. D is the telecscope diameter in meters. $${r_0}$$ is the Fried parameter at the requested wavelength and airmass. $$F_{\text{Kolb}}$$ is the Kolb factor (ESO Technical Report #12). If the argument of the square root $${\small (1+F_{\text{Kolb}} \cdot 2.183 \cdot ({r_0}/L_{0})^{0.356}) < 0 }$$, which happens when the Fried parameter $${\small {r_0} }$$ reaches its threshold of $${\small r_{\text{t}} = L_{0} \cdot (1.0/2.183)^{1/0.356} }$$, the value of $${\small \mathit{FWHM}}_{\text{atm}}$$ is set to $${\small 0.0 }$$.

For AO-modes, a model of the AO-corrected PSF is used instead.

Seeing statistics:

The Paranal seeing statistics is based on the so-called UT seeing measurements obtained from the UT1 Cassegrain Shack-Hartmann wavefront sensor used for active optics.

The measurements are deconvolved in order to represent the seeing outside the dome (i.e. they are corrected for the instrument+telescope resolution).

The La Silla seeing statistics is based on the DIMM FWHM measurements corrected for the instrumental resolution.

These data come from http://www.eso.org/gen-fac/pubs/astclim/paranal/seeing/singcumul.html

• ### Airmass

• The airmass of the observed target. The airmass must be ≥ 1.

• ### PWV

• The precipitable water vapor PWV is the vertically integrated total mass of water vapor per unit area for a column of atmosphere. PWV=2.5 mm is close to the median value for Paranal. Details about the seeing and PWV at Paranal are available from http://www.eso.org/gen-fac/pubs/astclim/paranal.

## 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.

## 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.

## 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 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 6.0.1 (March 03, 2015)
Noise factors in the VISIR imaging ETC were adjusted; the sensitivity and S/N estimates have changed compared to version 6.0.0.
• ##### Version 6.0.0 (February 26, 2015)
A unified convention for seeing and image quality applied in all ETCs offered from CfP P96.

• ##### Version 5.0.0 (July 1, 2013)

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. Please report significant discrepancies to the ESO user support group usd-help@eso.org

• ##### Version 3.3.1 (June 18, 2012).

Sky model updated (Austria in-kind SM-01), now supporting explicit PWV as well as season typical atm. profiles

Cosmetic changes in input and output pages

• ##### Version 3.3.0 (Apr 24, 2012).

New prototype version for AQUARIUS detector. All noise factors set to 1.

Using first version of Austria in-kind sky background model SM01