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VIMOS Exposure Time Calculator

VIMOS Exposure Time Calculator

User Manual

Table of Contents

Title page

Prepared By: A. Zanichelli
Approved by: O. Le Fevre

Revised by: B. Garilli

Version Information


This document is intended to provide information and help for the VIMOS Exposure Time Calculator, which can be operated to simulate observations both in imaging and in spectroscopic (MOS and IFU) modes.
The general features of VIMOS ETC as well as the basic formulae used to compute S/N or Exposure Time are described in Section 2, while a description of input parameters and their meaning is given in Section 3. The computations performed by the code are listed in Sections 4 and 5. A description of ETC output is given in Section 6.

Some general conventions used in this document:

Some conventions specific for spectroscopy:


The ETC works by simulating four main "components" of an observation: the source, the atmosphere, the telescope, and the instrument.
Spectral energy distribution, redshift, magnitude, and surface brightness profile characterize the simulated source. A sky spectrum, magnitude, and extinction as a function of wavelength, airmass, ImageQualityFWHM, describe the atmosphere.
A spectral energy distribution is described with a bag of optical rays, sampling the spectrum in lambda. Each optical ray is thus characterized by wavelength, intensity, and two directional angles (Alpha, Gamma). These angles are referred respectively to Y and X axis of the optical system.
The simulated telescope is characterized by its effective area, and transmission as a function of wavelength.
The simulated instrument is characterized by:
  1. Slit or slit+IFU for spectroscopy.
  2. Grism + order sorting filter for spectroscopy, or filters if in imaging mode.
  3. Lens.
  4. Detector.

A filter is described by a transmission curve as a function of wavelength. A grism is described by its angular dispersion, central wavelength and transmission curve. A further transmission curve is used to describe the order-sorting filter. The lens component describes the sum of all the lenses present in the instrument, by means of system focal length (telescope + instrument) and an "overall" (i.e. due to all the lenses + folding mirror of the instrument) transmission curve.
Grism and lens are the two components, which perform geometrical transformations of the coordinates of the input optical ray. That is, if the ray enters the instrument with directional angles inAlpha=0, inGamma=0, along Y and X respectively, after grism and lens these angles will be different from 0 and the light is dispersed onto the CCD.
The detector (CCD) is characterized by its responsive quantum efficiency, gain, readout noise, dark current, saturation, plate scale.

For what concerns the instrument optical components, with the exception of the IFU lenses optical transmission and the Intermediate resolution grism, numbers/curves used for this version of the ETC are measured values, stored in the ETC Calibration Database. For what concerns the CCD, we used values listed in the EEV 44-82 CCD Test Report.
In the following subsections we briefly describe how the ETC computes the S/N or Exposure Time in the three observing modes.


Here we report the formulae used for S/N or Exposure Time calculations. For details on how these formulae are applied to the different source geometries and observing modes, refer to the next Sections.

1) Given the S/N, evaluate the Exposure Time:
Evaluate the time for 1 exposure:

2) Given the Exposure time, evaluate the S/N:
Evaluate S/N for 1 exposure of t seconds:

S = count rate from the source (e- / s).
B = count rate from the sky (e- / s).
ff = flat-field accuracy.
F = ff 2(S + B) 2
NDC = detector noise due to dark current (e- / s).
RON 2 = (ron 2 ) * n_pix
ron = detector readout noise in e-
n_pix = number of pixels. See next Sections for different meanings depending on observing mode.
t = exposure time in seconds.
S/N = Signal to Noise Ratio.


For what concerns S/N or Exposure Time calculations in imaging mode, three options are given: pointlike sources, extended sources and integral photometry. For pointlike sources, the S/N is evaluated over the PSF area. For extended sources, the S/N is computed per pixel and the source surface brightness is assumed to be uniform. The third option, called "Integral Photometry", evaluates the S/N over the selected aperture area.


The S/N or Exposure Time you get from the spectroscopic ETC is NOT over one resolution element along dispersion, BUT over just 1 pixel, that is a dispersion element.

2.3.1 MOS

The ETC for MOS spectroscopy supports pointlike and extended sources. Extended sources can be characterized by a uniform surface brightness, or by a De Vaucouleurs or Exponential law.
Some VERY IMPORTANT points to be kept in mind by the user are:

Pointlike sources : given the exposure time, the evaluate S/N is the one you would get over 1 pixel in the dispersion direction and npsf pixels in the spatial direction, where npsf is the number of pixels in (ImageQualityFWHM) arcsecs.

Extended sources:given the exposure time, the evaluated S/N is the one you would get over 1 pixel in the dispersion direction and n_ext pixels (in the X direction). Where: n_ext is the number of pixels inside 2*projected semi-major axis (= 2*r_eff for De Vaucouleurs or Exponential profiles, see Sec. 3.2)

2.3.2 IFU

The two options are again pointlike or extended sources, but their meaning is different from MOS.

Pointlike sources: here we consider integral spectroscopy, i.e. the signal from all fibers covering the source is summed to obtain a single spectrum. The number of fibers on the source, nfib, is computed as the ratio between the source area and the area of 1 microlens. This number is an approximation, as it is not possible to take into account the actual microlens geometrical disposition on the source.

Extended sources: this option is intended as bidimensional spectroscopy, that is we consider the spectrum from just 1 fiber. The S/N is thus computed summing signal, sky, etc. over fib_pix pixels.


In this section a description of the input parameters you are requested to provide in the ETC input form is reported. More details on how they are used in the computations are found in Section 4. The ETC input form is divided in various parts, some of them different when in imaging or in spectroscopic observing modes.


Here you can select the spectral energy distribution of the source you want to observe. The options are: flat spectrum, blackbody, template SED from list, or user-defined spectral energy distribution. This part of the input form is the same for each observing mode.

Flat spectrum: constant flux at each lambda.

BlackBody: if you select this option, you must provide the temperature in K.

A template SED. The flux scale is of no interest, as the SED will be scaled to the desired magnitude.
Template SEDs from list do not include intrinsic galactic absorption.

In this section of the input form you can also set the source reshift. Redshifting is applied to template distributions .


Here you can choose source geometry. Different input parameters are foreseen in the three observing modes.
Surface brightness profiles are currently allowed only for MOS spectroscopy.


The three possibilities are: pointlike (seeing limited) sources, extended sources, and integral photometry.

For pointlike sources the user must provide:
  1. Total magnitude in one of the associated broad band filters. It is assumed that the total light coming from the source falls inside a circle of radius = ImageQualityFWHM.
S/N : Exposure Time are computed over the whole PSF area.

For extended sources the user must provide:
  1. Mean surface brightness in mag/arcsecs 2 again in one of the associated filters.
S/N : Exposure Time are computed over one pixel.

The user must provide:
  1. Aperture magnitude (mag) they want to reach.
  2. Aperture radius (arcsecs).
S/N : Exposure Time are computed over the aperture area.


Here the two possibilities are: pointlike or extended sources. Different input parameters are expected in the two cases.

Requested parameters are the same as for pointlike sources in the imaging case.

Requested parameters are:
  1. Magnitude (mag/arcsecs 2) in one of the associated broad band filters. For De Vaucouleurs and Exponential profiles, this is intended as the central surface brightness.
  2. Surface brightness distribution.
  3. Projected semi-major axis.
Three surface brightness distributions are provided: uniform, i.e. a constant surface brightness; De Vaucouleurs profile to represent elliptical galaxies; Exponential law to represent spirals.
Values of surface brightness and effective radius / projected semi-major axis are intended outside the atmosphere, i.e. before applying ImageQualityFWHM PSF convolution and atmospheric extinction.
It is assumed that the source major axis lies along the slit, and the profile is computed only along the spatial direction (i.e. slit length).
De Vaucouleurs and Exponential profiles:
In both cases, the given magnitude is intended as the CENTRAL surface brightness, and the projected semi-major axis is intended as the effective radius along the slit. These profiles are normalized to 1 at the central pixel and are then convoluted with the PSF before computations.
Subsampling of pixels is applied in the computation of the spatial profile.
Uniform surface brightness profile:
The intensity is set to 1 for (:projected radius) < x < (+projected radius) and to zero elsewhere.
Also this profile is convoluted with the PSF, so to smooth the distribution at the edges.

NOTE: no cosmology is applied to the surface brightness profiles, i.e. what you give is what you observe, irrespective of source redshift. We have chosen this approach because we think it is handier for the users to scale surface brightness and radius with his preferred cosmology, than obliging them to use our idea of universe.


Source geometries for IFU spectroscopy: pointlike or extended. Parameters have the same meaning as the ones in the corresponding case of the imaging mode. See Section 4.3.6 and following for a description of the meaning of source geometries in IFU spectroscopy (different from MOS).


This part of the input form is common to all the observing modes.
Requested parameters:

Sky Conditions