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SINFONI Exposure Time Calculator


	SINFONI 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.

General description

The SINFONI ETC is an exposure time calculator for the ESO Spectrograph for INtegral Field Observations in the Near Infrared, SINFONI, which uses the SINFONI AO module. 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. The ETCs are maintained on the ESO web servers 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.

Target

In the Target Input Flux Distribution field, you can select a spectral type and filter magnitude for the target. Alternatively, you can choose to specify the target with a blackbody temperature (and a filter magnitude). In both cases, the flux will be scaled to the specified magnitude in the selected band.
You can also choose to specify a single emission line instead; an analytic Gaussian, centered on the wavelength parameter, defined by its total flux and full-width at half-maximum (FWHM) width.

Spectral Type

The target model can be defined by the target's 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.

Target Magnitude

All magnitudes are in the Vega system - unless otherwise indicated.

You must select the filter and filter magnitude for proper scaling of the template spectrum. Available filters are V, J, H and K. For extended sources, the magnitude must be given per square arc second.

Target Spatial Distribution

The geometry of the target will affect the signal to noise, since extended sources will cover a wider area of the detector. You can either select:

Point Source

If point source is chosen, the target object is assumed to be an emitter with negligible angular size. This can be selected for objects with an angular radius of much less than the sky-projected pixel size. The reference area for the S/N depends on the configuration:

In the AO/25 mas case, the reference area is the diffraction limited core of the PSF; a disk with radius=1.22 lambda/D, which is 70 mas for an 8 m diameter telescope observing in the K band.
In the AO/100 mas and AO/250 mas cases, the reference area is to a disk with a radius that encloses 50% of the object's total flux.
In the non-AO case, the reference area is the Image Quality disk at the wavelength of observation. See the seeing section.

The target object is assumed to have a uniform intensity and the S/N on the result page is given per 2 pixels of the detector. (We use 2 pixels to obtain a square area on the sky). Note that the magnitude (or the flux for an emission line) is always given per arcsec² for extended sources.

Extended Source (with a given area)

The source is assumed to have a uniform intensity over the given area (Ω) on the sky. Since we use 2 pixels to obtain a square area on the sky, in this case the number of pixels in the S/N area is 2 × Ω / pixelScale². To obtain the S/N per arcsec², enter Ω=1 here. Note that the magnitude (or the flux for an emission line) is always given per arcsec² for extended sources.

Reference Source Parameters

Target/Reference source separation

The entered separation between target and reference star refers to the value at Zenith. The ETC will scale the given separation d(Zenith) to an effective separation d(X) at the given airmass X, using different formulas for NGS and LGS:

NGS: d(X) = d(Zenith) * X^8/5 , d(X)≤30"
LGS: d(X) = d(Zenith) * X^3/2 , d(X)≤60"

Note that the AO-performance model is currently limited to effective separations d(X)≤30" in NGS mode and d(X)≤60" in LGS mode. Choose a value from the drop-down menu. Stars brighter than 10th mag will be dimmed to 10th mag with a neutral density filter. Stars fainter than 17th mag do not provide significant AO correction.

Atmosphere

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

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

$ { \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 ${ L_{0} = 23m}$ , this corresponds to ${ r_{\text{t}} = 2.63m} $.

${ L_{0} }$ is the wave-front outer-scale. We have adopted a value of ${ L_{0} }$=23m, which is the generally accepted value for Paranal (Dali Ali et al. 2010, A&A 524, A73; Martin et al. 2000, A&AS, 144, 39).

$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 ${ L_{0} }$=23m, this corresponds to $F_{\text{Kolb}} = -$0.990737.

$ {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

Airmass

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

Instrument Setup

Angular Resolution Scale

Choose one of the three available spatial scales. Note that a pixel projects to a non-square area on the sky, namely for pixelscale x, the size of the projection is x*x/2.

Grating

This refers to the combination of filter and grating determining the (fixed) wavelength range of observations. The entire J, H, K or H+K band is fit onto the detector, respectively.

Results

You must supply information about the total observation time. This can be done in terms of DIT (Detector Integration Time), which is the duration of individual exposures, and NDIT (Number of DIT's), which is the number of exposures. The total exposure time is the product of DIT times NDIT. This exposure time does not take into account instrument and telescope overheads.
Alternatively, you can specify a signal to noise ratio, in which case the ETC will compute the minimal number of individual exposures (each of duration DIT) required to reach the requested S/N ratio.

S/N Ratio

The Signal to Noise Ratio (SNR or S/R) is defined for a point-like source at the central observation wavelength. Indicate here a value and choose a DIT, to get an estimate on how many exposures (NDIT) will be needed to achieve it.

Exposure Time

The Exposure Time is the product of DIT and NDIT.

DIT is the detector integration time (in seconds)
NDIT is the number of exposures of duration DIT.
INT is the total exposure time (excluding overheads). INT = DIT x NDIT

Possible Graphs

Resulting spectrum (object+sky) The sum of the object signal and the sky background spectrum.
Object spectrum only The total integrated counts contribution from the object, in e-/pixel/DIT
Sky spectrum only The sky contribution on the same area as the one covered by the object, 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.
Total efficiency and Wavelength range This option will display a curve showing the total efficiency of the system.
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.

Text Summary Results

Encircled Energy on Target: This is the fraction of the object's total flux contained in those pixels over which the S/N is calculated, i.e. "Number of Pixels in PSF spatial profile" on the results page.
Strehl Ratio: This is the peak intensity of the observed PSF to that of a perfect diffraction limited PSF.

Version Information

Version 6.0.1 (February 29, 2016) The J-grism throughput model updated with improved efficiency.
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 5.1.0 (April 9, 2014)
Detector parameters updated as given in the User manual P94. The detector RON now depends on the DIT. Added an warning appering if any pixels in the resulting spectrum exceeds the level at which persistence may occur, see sec. 2.6 of the User Manual.
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