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.

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 SPHERE is available on the instrument page.

Target Setup

Spectral Type

The target model is 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.

• Hour Angle

A coord within [-4;+4] hours at the time of the middle of total integration.

• Declination

Based on latitudes. A value between -85 and +35.

Companion

• Point Source

Point Source are sources whose spatial extend on the sky is much less than the seeing diameter. The signal to noise is computed over a circular area with diameter twice the effective seeing at the wavelength of observation. The effective seeing is given by the following formula: eff_seeing(seeing(V), λ) = seeing(V)*(λ/500nm)-1/5, where fwhm_V is the given FWHM seeing at 500nm (V-band).

• 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.

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  $${ $$\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.

Instrument setup

Instrument description

SPHERE (Spectro-Polarimetric High-contrast Exoplanet REsearch) is an extreme adaptive optics system and coronagraphic facility feeding three science instruments: IRDIS, IFS, and ZIMPOL. The primary science goal of SPHERE is imaging, low-resolution spectroscopic, and polarimetric characterization of extra-solar planetary systems. The instrument design is optimized to provide the highest image quality and contrast performance in a narrow field of view around bright targets that are observed in the visible or near infrared. SPHERE is installed at the UT3 Nasmyth focus of the VLT and includes the following sub-systems. The common path and infrastructure receives direct light from the telescope, and provides highly stabilized, AO-corrected, and coronagraphic beams to the three sub-instruments.

Mode

IRDIS (InfraRed Dual-band Imager and Spectrograph)

Dual band Imaging (DBI)

Dual-band imaging offers filter pairs in the complete spectral range. This will in particular provide essential spectral information for companions out of the IFS FoV.

Classical Imaging (CI)

Classical imaging provides a larger choice of observing parameters such as broadband filters (wider and more sensitive than DBI for faint stars) and narrowband filters.

ZIMPOL (Zurich IMaging POLarimeter)

Imaging

ZIMPOL provides an instrument mode for imaging without polarimetry. In principle, the polarimetric mode of ZIMPOL provides differential polarization signal and intensity images. But having a dedicated imaging mode ensures optimal imaging performance. The resulting data are less affected by instrumental effects (e.g. the HWP are out of the beam). Thus, if one seeks high quality imaging for targets where the polarimetric signal is not relevant then one should consider the imaging mode. Imaging provides in particular a pupilstabilized observing mode and also features which are not available in polarimetric imaging. The following list highlights the main advantages of the imaging mode:

• All polarimetric components are out of the beam. This enhances the throughput and reduces ghost effects and the scattered light level. Components which are not in the beam when compared to polarimetric imaging are: HWP1, HWP2, FLC modulator and eventually the polarization compensator and HWPZ.
• A pupil stabilized observing mode is offered for imaging which enables angular differential imaging (ADI).
• No charge shifting is required on the CCD. Therefore, one has no problems with the charge traps which appear in polarimetric imaging.
• The Filters in the common filter wheel are also available for imaging.
• The format of the resulting data is simpler.

Only minor drawbacks are related to the imaging mode when compared with the polarimetric imaging mode:

• Currently only the fast readout mode with a high readout noise of 20 e-/pix is offered.
• The two channels of ZIMPOL are strongly polarization sensitive. The total efficiency of one arm depends more strongly on the telescope pointing direction and the instrument configuration than in polarimetric mode.

IFS (Integral Field Spectrograph)

IRDIFS

This setting allows IFS observations in Y-J range, and IRDIS observations in the H band with optimum performance.

IRDIFS_EXT

Dichroics allow IFS and IRDIS to take data in parallel. IRDIFS_EXT dichroic setting allows IFS observations in the Y-H range, and IRDIS observations in K at somewhat reduced performance (particularly coronagraphic).

Derotator

Pupil Stabilized (IRDIS, IFS)

In pupil-stabilized observations the PSF variability is minimized because most of the optical elements do not move. The telescope pupil is also aligned with the Lyot stops of the instrument, which cover the M2 shadow and its spider arms. The pupil-stabilized mode provides the highest PSF stability and is recommended for coronagraphic observations and for high contrast imaging close to the star. The center of rotation is the central star. One should then be aware of the trade-off between rotation rate and the smearing of off-axis PSF

Field Stabilized (IRDIS, ZIMPOL, IFS)

In field-stabilized mode, light from a specific location in the field of view falls on a particular location on the detector, throughout the observation.

Fixed (ZIMPOL)

Instrumental polarization is best understood when the derotator is static and hence does not move.

Filter/Spectral Resolution

The available filters depend on the chosen mode, beam splitter (zimpol), coronagraph and neutral density.

Coronagraph

A coronagraph suppresses the coherent light coming from on-axis unresolved source. In SPHERE, all coronagraphs consist of a focal plane mask, followed by a pupil stop and sometimes preceded by an entrance pupil apodizer. SPHERE houses several coronagraphs to accommodate different observational needs such as spectral range or inner working angle.

Neutral Density

Since neutral densities prevent most photons from reaching the detector, their use in science templates should be avoided when possible. Instead, a coronagraph should be considered when trying to prevent saturation. If accurate photometry or astrometry of the primary target is desired, Star center and Flux observations should be considered.

• None
• ND1 (IRDIS, ZIMPOL, IFS)
• ND2 (IRDIS, ZIMPOL, IFS)
• ND3.5 (IRDIS, IFS)
• ND4 (ZIMPOL)

Observation setup

The user must supply information about the total observation time. This exposure time does not take into account instrument and telescope overheads.

• DIT

Detector on-chip integration time for one exposure (in seconds). Limits for saturation and non-linearity depend on DIT for small DITs.

• Exposure Time

The Exposure Time should exceed:

• IRDIS, IFS: DIT x n_dith

• ZIMPOL: DIT x n_dith x 2 x (n_switch + 1)

Output Setup

Differential Imaging (IRDIS)

Differential Imaging exploits the fact that the field and the pupil rotate with respect to each other. In pupilstabilized mode, most speckles are caused by instrumental artifacts and are locked up in the pupil plane, whereas the object of interest, a companion or a disk, will rotate as the field rotates. This allows distinguishing the stellar halo from the object.

Simultaneous observation of several monochromatic images can be used to reduce the impact of speckles (Sparks and Ford, 2002). For a given observation, the location of a companion around a star is constant while the location of speckles from the star increases with wavelength and their intensity decreases. For a wide enough wavelength range this allows subtraction of the speckles.

Planets and the host star have different spectral features. This information can be used to suppress speckle noise. For this, one needs simultaneous images at two similar wavelengths at which the brightness of the planet varies, e.g. in and out of a molecular band.

Stars are often unpolarized, whereas circumstellar environments and planets may be highly polarized.

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