# General description

The web application 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 regularly updated to reflect the known performance of ESO instruments.

The exposure time calculator consists of two pages.
Input page: 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.
Output page: The results page presents the computed results, including number of counts for the object and the sky, signal-to-noise ratios, instrument efficiencies, etc. The optional graphs are displayed in several formats. In addition a summary of the input parameters is appended to 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.

The exposure time calculator models the observation chain which includes the target spectral distribution, atmosphere parameters, instrument configuration, and detector setup. An instrument description for VISTA is available on the instrument page.

## Input Spectrum

The following options are available to describe the input spectrum of the target.

• ### Uniform

• The flux density is constant at all wavelengths (F(λ) = const.) The flux density level is determined from the specified object magnitude.

• ### Spectral Type

• The target model can be defined by a 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.

• ### Blackbody

• The target model is a blackbody defined by its temperature, expressed in Kelvin. The intensity distribution is scaled to the object magnitude.

• ### Object Magnitude

• Enter the V (650 nm), Z (880 nm), Y (1030 nm), J (1250 nm) , H (1650 nm), or K (2160 nm) magnitude, ideally closest in wavelength to the selected filter.

NOTE! For the Uniform and Template Spectra, currently the Target Magnitude can ONLY be given in the same band as the Filter.

Zero points used for conversion into photon fluxes are taken from the following references: Wilson, 1972, ApJ, 177, 533, and from Hewett et al., 2006, MNRAS, 367, 454.

• ### 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. Line flux is given in 10-16 erg.cm-2.s-1.

NB: When requesting a single line as input spectrum, the magnitude parameter is not taken into account. Only the line flux will be used to determine the signal magnitude.

NB: The FWHM of a single line is limited by the sampling. If the requested FWHM is too narrow, it will be replaced by the minimum supported value, and a warning will be issued in the beginning of the result page.

• ### Source Geometry

• Point Source
• Extended Source

For extended sources, the magnitude is given per square arcsecond. The reference area for the signal-to-noise calculation can either be circular with the specified angular diameter, or it can be set to one detector pixel.

## Atmosphere

• ### Airmass

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

• ### Seeing and Image Quality

• 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 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  $${ $$\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)}$$ }$$

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{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}
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.

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

• ### Sky Model

• Since ETC version 6.0.0, the sky background radiance and transmission model in the VIRCAM ETC is based on the Cerro Paranal advanced sky model.

## Instrument Setup

• ### Filter

• Choosing the instrument filter determines for which band the exposure time will be computed. For information about the filters (incl. transmission curves), please refer to the Instrument Description and the User Manual.

• ### Detector Mode

• The average pixel scale is 0.34 arcsec/pixel.

The read-out mode is Double Correlated. The read-out noise varies from detector to detector, but on average it is 23 electrons.

## Results

The DIT (Detector on-chip integration time per single shot in seconds) is needed as input for all of the following cases:

Specify an exposure time per pixel,
OR
Specify a signal-to-noise ratio to be achieved,
OR
Specify an observing strategy.

The observing strategy constitutes of:

• Ndit = the number of exposure coadds
• Nexp = the number of exposure loops
• the microstepping pattern (NxM), which uses either no-interleaving 1x1 (i.e. no microstepping), or 2x2 interleaving to improve sampling in good conditions,
• Njitter = the number of jitters; note that for VIRCAM there is a list of possible jitter patterns or one can use random jitters, in which case Njitter is a free parameter
• Npaw = the number of pawprints taken within a tile. Currently the choices for Npaw are 1, 3 or 6.

In all cases, the exposure time for each exposure is DIT*Ndit, with the specified DIT. However, the VIRCAM focal plane is not fully covered with detectors and therefore some larger offsets (pawprint offsets) are used to obtain a tile, an image with more uniform coverage of the focal plane. The total exposure time per pixel after taking NxM microstep exposures + Njitter dithered exposures + Npaw pawprint offsets + Nexp exposure loops depends on the Npaw parameter value. In case one chooses Npaw=1, then each pixel will be exposed once for each pawprint offset and the total exposure time per pixel will be given by Ndit*Nexp*NxM*Njitter. The Npaw=3 (Tile3 patterns) result in vertical stripes, where the pixels along these vertical stripes are exposed at least twice (except for the edges of the tile). In case of Npaw=6 each pixel in a final tile will be exposed at least twice (except for the edges of the tile). Therefore most of the pixels in a tile covered with Npaw=3 and Npaw=6 will have total exposure time per pixel defined by Ndit*Nexp*NxM*Njitter*2. For more details please see the VISTA User manual.

The output form will give you estimates for SNR or Exposure Time, together with output graphs you selected.

Do not confuse exposure time (which is the total exposure time per pixel used for calculation of S/N) and total observation time, the latter being a sum of exposure time, including additional offset exposures and overheads in the telescope and instrument. Please consult the user manuals for guidance on the choice of the integration parameters.

## Possible graphical Outputs

• ### Input spectrum in physical units

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

• ### CCD Illumination, Object only

• The total integrated counts contribution from the object per pixel as a function of wavelength, in e-/pixel/DIT.

• ### Sky Transmission Spectrum

• The sky transmission in percent as a function of wavelength.

• ### System efficiency

• This option will display a curve showing the total efficiency in percent of the system.

• ### S/N as a function of Exposure Time

• The S/N as a function of Exposure Time

• Version 6.2.0 (August 30, 2016)
The new sky model has been updated with adjusted ozone and CO2 abundances and minor changes in the moonlight model.
The outer-scale parameter L0 in the seeing/IQ model was changed. This has changed the size of the S/N reference area and consequently many numerical results, in particular at long wavelengths.

• Version 6.0.0 (February 26, 2015) A unified convention for seeing and image quality applied in all ETCs offered from CfP P96.
A new advanced sky model enabled.
• 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

 Send comments and questions to usd-help@eso.org