Optical Instrument Exposure Time Calculator 


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.
See also: Frequently Asked Questions
The Optical ETC is an exposure time calculator for the ESO optical instruments SUSI, EMMI, VLT Test Camera, FORS, and the WFI (Wide Field Imager on the 2.2m in La Silla). 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. As the ETCs are maintained on the ESO Web servers, they provide the most uptodate 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 signaltonoise, 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, signaltonoise 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. Finally a summary of the input parameters is appended to the result page.
The model includes an input spectrum (e.g. a template star spectrum), atmospheric parameters , optical instrument path and observation criteria. The model generates output graphs describing the spectral illumination of the CCD, the instrument efficiency or the signal to noise as a function of the exposure time or Image Quality.
The target model is a spectral distribution constant with the wavelength.
The target model is a blackbody defined by its temperature and monochromatic apparent magnitude at a given wavelength. Temperature is expected in Kelvin and wavelengt in one of the band filters U, B, V, R or I.
The target model can be defined by a template spectrum . As with the blackbody it will be scaled to the provided magnitude and band filter U, B, V, R or I.
For point sources the resolution is limited by the PSF at the wavelength and airmass of observation. In imaging mode the signal to noise is computed over an area of diameter twice the Image Quality FWHM. In spectroscopy the reference area is the number of spatial pixels covered by twice the Image Quality PSF FWHM along the slit, and 1 pixel in the spectral direction. The number of pixels is calculated as Npix=2*FWHM(PSF)/plate_scale, rounded to the nearest integer.
Indicate the object magnitude in the broad band filter associated to the filter that you define in the Instrument Setup. For extended sources the magnitude is given per square arcsecond.
For extended sources, the brightness geometry is assumed uniformly distributed. The magnitude is given per square arcsecond. In imaging mode the resulting S/N numbers are displayed for one pixel as well as per square arcsecond. In spectroscopy mode, for extended sources the resulting S/N is calculated over one pixel along the dispersion and one arcsec along the slit.
Days from new moon 
Sky Brightness  

U 
B 
V 
R 
I 
z 

0 
22.0  22.7  21.8  20.9  19.9  18.8 
3 
21.5  22.4  21.7  20.8  19.9  18.8 
7 
19.9  21.6  21.4  20.6  19.7  18.6 
10 
18.5  20.7  20.7  20.3  19.5  18.3 
14 
17.0  19.5  20.0  19.9  19.2  18.1 
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 longexposure 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:
\( { \small \begin{equation} \begin{aligned} \mathit{FWHM}_{\text{IQ}} & = \sqrt{\mathit{FWHM}_{\text{atm}}^2(\mathit{s},x,\lambda)+\mathit{FWHM}_{\text{tel}}^2(\mathit{D},\lambda)+\mathit{FWHM}_{\text{ins}}^2} \\ \end{aligned} \end{equation} } \) .
For fibrefed instruments, the instrument transfer function is not applied. For nonAO 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:
\(
\begin{equation}
\begin{aligned}
& {\small \mathit{FWHM}}_{\text{atm}}(\mathit{s},\mathit{x},\lambda) = \mathit{s} \cdot x^{0.6} \cdot (\lambda/500\text{ nm})^{0.2} \cdot \sqrt{1+F_{\text{Kolb}} \cdot 2.183 \cdot ({r_0}/L_{0})^{0.356}} \text{,} \\
& \small{\text{where}}
\end{aligned}
\end{equation}
\) \( \begin{equation} \begin{aligned} {r_0} & = 0.976 \cdot 500.0 \cdot 10^{9}\text{ nm } / \mathit{s} \cdot (180/\pi \cdot 3600) \cdot (\lambda/500.0\text{ nm})^{1.2} \cdot x^{0.6} \\ F_{\text{Kolb}} & = 1/(1+300 \cdot D/L_{0})1 \end{aligned} \end{equation} \) \({ L_{0} }\) is the wavefront outerscale. 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 \({\small 0.0 }\). 
The Paranal seeing statistics is based on the socalled UT seeing measurements obtained from the UT1 Cassegrain ShackHartmann 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/genfac/pubs/astclim/paranal/seeing/singcumul.html
Here you will see the combined efficiency of the M1M3 mirrors.
Set the corresponding FORS collimator resolution (Standard or High)
The filter is selected from a list with an option menu. Some filter curves can be found in the web tool for characteristic curves.
This option reduces the transmission by 50% to take the polarisation Wollaston prism into account
Select the disperser. Characteristics of the FORS grisms are described in the FORS manual. Echelle modes can be selected in the REMD EMMI mode. See the EMMI manual for details. This model computes results corresponding approximately to one Echelle order centered at the wavelength selected by the user. The blaze function is not taken into account in this model.
Select the slit width from the list of predefined values.
The simulation takes into account the readout noise levels for the relevant readout mode. For details see the User Manual.
A curve of signaltonoise as a function of exposure time is generated. The centre value and a range to both sides of the centre value are provided.
A curve of signaltonoise as a function of exposure time is generated. The centre value and a range to both sides of the centre value are provided (in seconds).
The result graphs are Java based applications. A static version of the graphs is also provided in GIF and ASCII format.
Source Geometry: "Point source" or "Extended" depending on the source geometry. Some results are computed differently for pointsources ort extended sources.
Signal to Noise over PSF area: Signal to noise computed using the formula: S/N = object_signal / sqrt (object_signal + sky_signal*Npsf + Npsf*CCDnoise**2)
Number of pixels for PSF area: For pointsources this is the area over which the S/N is estimated. It is a circular area of radius given by the Image Quality FWHM by the plate scale. This value corresponds to "Npsf" in the signaltonoise formula.Plate scale: The plate scale of the system, in arcsecs per pixel.
Electrons in the PSF area: The total flux contribution from the object, integrated over the PSF area, and expressed in electrons. This value corresponds to "object_signal" in the signaltonoise formula.
Sky background value: The flux contribution from the sky for one pixel of the detector. This value corresponds to "sky_signal" in the signal to noise formula.
Detector readout noise level: CCD readout noise in electrons/pixel. This value corresponds to CCDnoise in the signaltonoise formula.
Peak pixel value: This value is the sum of the sky background level (sky_signal) and the fraction of the object signal falling on one pixel at the center of the profile (object_signal_max).
Detector saturation: The detector saturation level. A message will be displayed if the maximum intensity is greater than this limit. Please note that the actual saturation level may depend on the CCD readoutmode.
PSF extension: number of pixels over which the signaltonoise is estimated. This value is computed as twice the Image Quality FWHM divided by the plate scale.
Signal to Noise at central pixel: Signal to noise on the central pixel, computed using the formula: S/N = object_signal_max / sqrt (object_signal_max + sky_signal + CCDnoise**2). Only this signal to noise is computed for extended sources.
The input flux distribution for the selected target is diplayed in units of 1e20 ergs/cm**2/s/A
This option will display a curve showing the efficiency in terms of detected photons against wavelength.
Toggling this option will display the object spectrum as seen by the detector, in units of e/Angstrom/sec
Toggling this option will display a curve showing the evolution of Signal to Noise Ratio against Image Quality in arcseconds.
Toggling this option will display a curve showing the Signal to Noise Ratio as a function of Exposure Time.
Spectroscopy results such as efficiency, signal, signaltonoise estimates are dependent on the wavelength and given over the wavelength range in graphics form. A summary of results is provided in text form for the central pixel of the range (also corresponding to the central wavelength).
Wavelength Range: The respective wavelength associated to the first and last pixel of the detector for the given configuration and dispersion, in nanometers.
For the Echelle modes of the spectroscopic EMMI ETC, the wavelength range corresponds approximately to one Echelle order, centered at the userspecified central wavelength. The blaze function is not taken into account in this model.
Central Wavelength: The wavelength of the central pixel, in nanometers.
Dispersion: The dispersion of the spectrum, in nanometers per pixel.
Plate scale: The plate scale of the system, in arcsecs per pixel.
FWHM of the image_quality profile: The fullwidth at halfmaximum of the slit spatial profile. This value is the Image Quality divided by the plate scale.
Efficiency at central wavelength: Total efficiency of the system at central wavelength, including atmospheric extinction, telescope transmission, optics and detector efficiency, in percent.
Object signal at central pixel: The total flux contribution from the object, integrated over the slit, and expressed in electrons per pixel along the dispersion direction. The value is given at the central wavelength and corresponds to "object_signal" in the signaltonoise formula.
Sky background level at central pixel: The flux contribution from the sky for one row along the dispersion direction, in electrons per pixel along the dispersion direction. The value is given at the central wavelength and corresponds to "sky_signal" in the signal to noise formula.
Max. intensity at central pixel (object+sky): This value is the sum of the sky background level and the fraction of the object signal falling on one pixel at the center of the slit profile.
AD/Detector saturation level: The truncation level of the AD converter for the default gain mode. A message will be displayed if the maximum intensity is greater than this limit. Please note that the actual saturation level may depend on the CCD readoutmode, and that the saturation is here tested only for the central wavelength.
Detector readout noise level: CCD readout noise in electrons/pixel. This value corresponds to CCDnoise in the signaltonoise formula.
Detector dark current: CCD dark current in e/pixel/hour. This value corresponds to DarkCurrent in the signaltonoise formula.
PSF extension: number of pixels over which the signaltonoise is estimated. This value is computed as twice the Image Quality FWHM divided by the plate scale. This value corresponds to "Npsf" in the signaltonoise formula.
Signal to Noise at central pixel: Signal to noise at central wavelength, computed using the formula: S/N = object_signal / sqrt (object_signal + sky_signal*npsf + Npsf*DarkCurrent*ExpTime + Npsf*CCDnoise**2).
The total integrated counts contribution from the object, in e/pixel. The integration is done along the slit. The counts are expressed in electrons per pixel along the dispersion direction.
The sky contribution on each row of the detector, in e/pixel. This value is not integrated along the slit.
The input flux distribution for the selected target is diplayed in units of 1e20 ergs/cm**2/s/A
Toggling this option will display a curve showing the evolution of Signal to Noise Ratio against wavelength.
This option will display a curve showing the total efficiency of the system, and a second graph showing the dispersion relation.
Produces a FITS file with the 2D simulated spectrum as seen on the detector
