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NACO Exposure Time Calculator

General description

The NACO ETC is an exposure time calculator for the ESO high-resolution near-infrared camera, CONICA, which uses the Nasmyth Adaptive Optics System, NAOS.

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.

Laser Guide Star (LGS) Status

This is now supported by the NACO ETC.

Target and Reference Source Spectrum

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 the Reference Source Parameters field, information about spectral type and filter magnitude is entered for the reference source.

Spectral Type

A stellar spectral type is used to make the color correction.

The Pickles template spectra covers only the JHK bands. The target spectrum can also be selected from a subset of MARCS stellar model spectra, kindly provided by Bengt Edvardsson at the Uppsala Astronomical Observatory. The parameter space of the MARCS subsets are listed the following tables. Note that not all models (referring to all possible combinations of parameters) actually exist.

MARCS subset: Spherical Geometry
Parameter Number of
unique values
Unique Values
model 1 "st"
[Fe/H] 4 -4.00,-2.00,-1.00,0.00
Teff/K 9 4000,4500,5000,5500,6000,6500,7000,7500,8000
log(g) 5 -0.50,0.00,1.00,2.00,3.50
geometry 1 "s"
microturbulence 1 2
mass 2 1,5
total (product) 360 (this is the number of possible combinations, but only 87 models exist)

MARCS subset: Plane Parallel Geometry
Parameter Number of
unique values
Unique Values
model 1 "st"
[Fe/H] 6 -1.00,-2.00,-4.00,0.00,0.50,1.00
Teff/K 9 4000,4500,5000,5500,6000,6500,7000,7500,8000
log(g) 1 4.00
geometry 1 "p"
microturbulence 1 2
total (product) 54 (this is the number of possible combinations, but only 50 models exist)

Target / Reference Source Magnitude

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

Separation of Target and Reference Source

The target is slightly off the optical axis, because another star is used as reference source. This is particularly useful if the target is very faint, since the quality of the AO correction deteriorates rapidly for reference source magnitudes greater than V=13. The reference source must be within 30 arc seconds of the primary target.

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:

Sky Conditions

Instrument Setup


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.

Do not confuse exposure time and total observation time, the latter being a sum of exposure time and overheads in the telescope and instrument. Please consult the NACO user's manual for guidance on the choice of the integration parameters.

Possible Outputs in Imaging

For the purpose of presenting the results of the calculations of the NACO Imaging ETC, you can choose from the following output options:

Show 2-D PSF image (jpg and FITS)

Toggling this option will display two images (jpg format) of the Point-Spread Function (PSF), the first one with a linear color scale and the second one with a logarithmic color scale. In addition, a 2D FITS file with the PSF will be available for download. Note that these are monochromatic PSFs computed by the NAOS-PS software for the central wavelength of the filter used in the simulation.
The pixel scale in the fits image corresponds to lambda / 2D, with D being the diameter of the telescope. More information on the simulation parameters is available in the FITS header.

Encircled Energy as a function of Aperture Radius

Toggling this option will display a plot of the Encicled Energy (EE) as a function of the aperture radius (arcsecs). A cross of two lines will indicate the selected aperture radius r and the value EE(r). The default aperture radius is 1.22*lambda/D (D=8.2m).

S/N as a function of Exposure Time

Toggling this option will display the S/N as a function of exposure time. For point sources the S/N is calculated in the area of the diffraction limited core, radius equal to 1.22 lambda/D, which is 70 mas for an 8 m diameter telescope observing in the central K band (2.2 microns). For extended sources, the S/N is calculated per pixel element, using the surface brightness in magnitudes per square arcsec.

On the results page, the input parameters are repeated, the NACO transmission model parameters are given, sky data is given, and the S/N is plotted. See Text Summary Results for a description of the text output.Toggling both options will display a page with the input parameters, the NACO transmission model parameters, sky data and the graphs described above. Toggling no options will give you only the Text Summary Results.

Text Summary Results

All magnitudes are in the Vega system unless explicitly indicated otherwise

The text summary results are given on all results pages. Here follows a short description of the items in the text summary results.

Source spectral type: The spectral type of the target.
Source magnitude: The magnitude of the target in the chosen filter, in magnitudes for point sources, and magnitudes per square arc second for extended sources.
Source geometry: Geometry of target (point source or extended).
Reference Source separation:
Separation of reference source and target in arc seconds.
Reference Source spectral type: The spectral type of the reference source.
Reference Source magnitude:
The magnitude of the reference source.
Reference Source geometry:
Geometry of the reference source (always point source)

NAOS Wavefront sensor:
The selected wavefront sensor (visible / IR)
NAOS Transmission: Name of wavefront sensor and transmission in %.
CONICA Filter:
The used CONICA filter.
CONICA Objective: The used CONICA objective.
Detector Read-out mode: The used detector read-out mode. We offer the five combinations of read-out mode and detector mode: User Requested: The user requested exposure time or S/N setting.
DIT: Detector integration time for one exposure.
Selected signal-to-noise ratio .
Number of detector integrations.

NACO Transmission Model:

Signal-to-noise: The signal to noise is given for a target of the selected magnitude, in the filter selected and for the selected exposure time or S/N settings.
Total exposure time: NDIT*DIT , in seconds and without overhead, is the time required to reach the signal-to-noise quoted above.
Number of detector integrations: NDIT , is the number of detector integrations needed to reach the signal-to-noise quoted above.
Radius of the S/N reference area: The radius in arc seconds of the ref. area for the quoted S/N value.
Number of pixels...: Same as above, but quoted in pixels.
Total number of e-...:The number of photo-electrons on the detector array within the PSF area, counted in one DIT.
Detector Saturation and Linearity Limits: Saturation refers to the maximum number of photo-electrons that can be counted in one pixel. Additional photo-electrons are either lost, or bleed out into neighboring pixels. The Linearity Limit refers to the max. counts for which the detector response is proportional to the received photo-electrons.
In some cases, the linearity- and saturation levels is observed to depend on DIT (for small DITs, when the ratio DIT/DIT min is less than a few). In practice, this is implemented the following way, currently only for the readmode FowlerNsamp(HighSensitivity) , although it may also be relevant in other cases.
Encircled Energy:This is the fraction of light within the considered PSF area. This number must be between 0 and 1, and quantifies the efficiency of the AO system. The higher the number, the better is the correction.
Strehl Ratio: Ratio of the peak intensity of the observed PSF to that of a perfect diffraction limited PSF.
Pixel Scale...:The sky-projected angular size of a pixel element (pixel side).
Overall Transmission:The total transmission coefficient of the NACO optical system.
Sky Variability Table: This table contains some of the information given above, but for three different sky brightness cases (imaging only):Average, Bright and Dark Sky: corresponding to the typical sky variability. In the last row of the table, the so-called BLIP integration time for each sky brightness is displayed.

Version Information

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