Exposure Time Calculator

The user can use the Exposure Time Calculator (click here to go to the ETC webpage ) and find a user guide below on this page. However, the ETC involves intensive computing that may require more than one minute before displaying the results to the PIs, especially at higher spectral resolution. We therefore also provide pre-computed values for a limited number of cases.

On this page:


Pre-computed values

Several test cases have been pre-computed to allow the PIs for a quicker access to SNR or exposure time values. We have used the ETC and only changed a couple of parameters: the spectral resolution and the use of apodization or not. We fix the exposure time per step at 5s and compute the continuum SNR at specific wavelength. The total required exposure time is thus a simple multiplication of the spectral resolution.

How to use those pre-computed values?

First, select the line of interest, the spectral resolution, and the observing conditions required for your observations.
Then, either use the graph or the formula to derive the continuum SNR you would achieve with 5s exposures. If the SNR does not satisfy your needs or exceeds them, scale the exposure time accordingly (i.e. if you want to double the SNR, multiply the exposure time per step by 4).
Then, compute the number of steps required to properly sample the spectra at the resolution you require (the ratio between number of steps and spectral resolution is given in each section).
Finally, multiply the number of steps by the exposure time, without forgetting to add the overheads to each step (3.25s is the default value).

HII regions

The first test cases we made available are for HII regions, looking at the Hα, Hβ, Oii and Oiii lines. The HII region has a metallicity of 8.39 and the Hα surface brightness is fixed at $10^{-13}$ erg/s/cm2/arcsec2. No background is added.
For each line, the first series of tests are in the best observing conditions possible (AM 1.2, seeing 0.8", Moon 20%, clouds 0 mag). The other series of tests are in slightly worse conditions (AM 1.2, seeing 0.8", Moon 50%, clouds 0 mag), (AM 1.2, seeing 0.8", Moon 80%, clouds 0 mag), (AM 1.2, seeing 0.8", Moon any, clouds 0 mag). Those four series are then done at AM 1.5.

Hα line

The relations between SNR and spectral resolution have been derived for R<2000.
At a wavelength of 656.3nm, in the SN3 filter, the ratio between the number of steps for the interferogram and the spectral resolution is 0.273.

(AM 1.2, seeing 0.8", Moon 20%, clouds 0 mag)
SNR^2 = 24 * R + 620 (no apodization)
SNR^2 = 26 * R/2 + 730 (apodization)

(AM 1.5, seeing 0.8", Moon 20%, clouds 0 mag)
SNR^2 = 21 * R + 700 (no apodization)
SNR^2 = 23 * R/2 + 400 (apodization)

(AM 1.2, seeing 0.8", Moon 50%, clouds 0 mag)
SNR^2 = 23 * R + 760 (no apodization)
SNR^2 = 26 * R/2 + 600 (apodization)

(AM 1.5, seeing 0.8", Moon 50%, clouds 0 mag)
SNR^2 = 20 * R + 580 (no apodization)
SNR^2 = 22 * R/2 + 520 (apodization)

(AM 1.2, seeing 0.8", Moon 80%, clouds 0 mag)
SNR^2 = 21 * R + 620 (no apodization)
SNR^2 = 24 * R/2 + 470 (apodization)

(AM 1.5, seeing 0.8", Moon 80%, clouds 0 mag)
SNR^2 = 18 * R + 590 (no apodization)
SNR^2 = 20 * R/2 + 380 (apodization)

(AM 1.2, seeing 0.8", Moon any, clouds 0 mag)
SNR^2 = 16 * R + 540 (no apodization)
SNR^2 = 18 * R/2 + 430 (apodization)

(AM 1.5, seeing 0.8", Moon any, clouds 0 mag)
SNR^2 = 13 * R + 410 (no apodization)
SNR^2 = 15 * R/2 + 230 (apodization)

Hβ line

The relations between SNR and spectral resolution are derived for R<1500 range. At spectral resolution greater than about 2000, the SNR reaches a plateau at about 100 without apodization.
At a wavelength of 486.1nm, in the SDSSg filter, the ratio between the number of steps for the interferogram and the spectral resolution is 1.02.

(AM 1.2, seeing 0.8", Moon 20%, clouds 0 mag)
SNR^2 = 4.3 * R + 30 (no apodization)
SNR^2 = 4.9 * R/2 + 50 (apodization)

(AM 1.5, seeing 0.8", Moon 20%, clouds 0 mag)
SNR^2 = 3.6 * R + 40 (no apodization)
SNR^2 = 4.1 * R/2 + 40 (apodization)

(AM 1.2, seeing 0.8", Moon 50%, clouds 0 mag)
SNR^2 = 3.7 * R + 40 (no apodization)
SNR^2 = 4.2 * R/2 + 20 (apodization)

(AM 1.5, seeing 0.8", Moon 50%, clouds 0 mag)
SNR^2 = 3.1 * R + 40 (no apodization)
SNR^2 = 3.5 * R/2 + 40 (apodization)

(AM 1.2, seeing 0.8", Moon 80%, clouds 0 mag)
SNR^2 = 2.3 * R + 30 (no apodization)
SNR^2 = 2.6 * R/2 + 20 (apodization)

(AM 1.5, seeing 0.8", Moon 80%, clouds 0 mag)
SNR^2 = 1.8 * R + 20 (no apodization)
SNR^2 = 2.1 * R/2 + 10 (apodization)

(AM 1.2, seeing 0.8", Moon any, clouds 0 mag)
SNR^2 = 0.66 * R + 5 (no apodization)
SNR^2 = 0.74 * R/2 + 7 (apodization)

(AM 1.5, seeing 0.8", Moon any, clouds 0 mag)
SNR^2 = 0.50 * R + 5 (no apodization)
SNR^2 = 0.56 * R/2 + 4 (apodization)

Oii line

The Oii line is part of a doublet and as such, each line is contaminated by wiggles originating from the other line. Those wiggles change with the spectral resolution, but can be removed after apodization. Without apodization, the peak intensity of each line seems to go up and down as the resolution increases though. With NB2 apodization, a resolution of about 1300 is required to perfectly separate both lines.
The relations between SNR and spectral resolution are derived within the 1300-10000 range.
At a wavelength of 372.6nm, in the SN1 filter, the ratio between the number of steps for the interferogram and the spectral resolution is 0.277.

(AM 1.2, seeing 0.8", Moon 20%, clouds 0 mag)
SNR^2 = 1.5 * R + 460 (no apodization)
SNR^2 = 1.8 * R/2 + 110 (apodization)

(AM 1.5, seeing 0.8", Moon 20%, clouds 0 mag)
SNR^2 = 1.3 * R + 420 (no apodization)
SNR^2 = 1.5 * R/2 + 130 (apodization)

(AM 1.2, seeing 0.8", Moon 50%, clouds 0 mag)
SNR^2 = 1.4 * R + 580 (no apodization)
SNR^2 = 1.6 * R/2 + 130 (apodization)

(AM 1.5, seeing 0.8", Moon 50%, clouds 0 mag)
SNR^2 = 1.2 * R + 370 (no apodization)
SNR^2 = 1.4 * R/2 + 120 (apodization)

(AM 1.2, seeing 0.8", Moon 80%, clouds 0 mag)
SNR^2 = 0.94 * R + 320 (no apodization)
SNR^2 = 1.1 * R/2 + 80 (apodization)

(AM 1.5, seeing 0.8", Moon 80%, clouds 0 mag)
SNR^2 = 0.76 * R + 270 (no apodization)
SNR^2 = 0.90 * R/2 + 60 (apodization)

(AM 1.2, seeing 0.8", Moon any, clouds 0 mag)
SNR^2 = 0.24 * R + 90 (no apodization)
SNR^2 = 0.29 * R/2 + 20 (apodization)

(AM 1.5, seeing 0.8", Moon any, clouds 0 mag)
SNR^2 = 0.19 * R + 70 (no apodization)
SNR^2 = 0.22 * R/2 + 20 (apodization)

Oiii line

The relations between SNR and spectral resolution are derived for R<2000 range.
At a wavelength of 500.7nm, in the SDSSg filter, the ratio between the number of steps for the interferogram and the spectral resolution is 1.06.

(AM 1.2, seeing 0.8", Moon 20%, clouds 0 mag)
SNR^2 = 32 * R + 340 (no apodization)
SNR^2 = 35 * R/2 + 500 (apodization)

(AM 1.5, seeing 0.8", Moon 20%, clouds 0 mag)
SNR^2 = 27 * R + 300 (no apodization)
SNR^2 = 30 * R/2 + 480 (apodization)

(AM 1.2, seeing 0.8", Moon 50%, clouds 0 mag)
SNR^2 = 28 * R + 360 (no apodization)
SNR^2 = 31 * R/2 + 390 (apodization)

(AM 1.5, seeing 0.8", Moon 50%, clouds 0 mag)
SNR^2 = 23 * R + 340 (no apodization)
SNR^2 = 26 * R/2 + 180 (apodization)

(AM 1.2, seeing 0.8", Moon 80%, clouds 0 mag)
SNR^2 = 17 * R + 280 (no apodization)
SNR^2 = 19 * R/2 + 170 (apodization)

(AM 1.5, seeing 0.8", Moon 80%, clouds 0 mag)
SNR^2 = 14 * R + 180 (no apodization)
SNR^2 = 15 * R/2 + 120 (apodization)

(AM 1.2, seeing 0.8", Moon any, clouds 0 mag)
SNR^2 = 4.8 * R + 80 (no apodization)
SNR^2 = 5.4 * R/2 + 50 (apodization)

(AM 1.5, seeing 0.8", Moon any, clouds 0 mag)
SNR^2 = 3.7 * R + 50 (no apodization)
SNR^2 = 4.1 * R/2 + 60 (apodization)


Using the SITELLE Exposure Time Calculator

The Exposure Time Calculator (ETC) for SITELLE is made of an input table, a result table, and a plot area. The user enters the parameters for their source in the input table. The result table will show the most important parameters for the PI. The plot area displays the input spectrum of the source, the observed spectrum, and the SNR spectrum.

Input table

The input table comprises 5 sections: the source emission definition, the background emission definition, the instrument settings, the observing conditions, and the computation mode.

Source emission

Definition of the source emission

The first section of the input table defines the emission from the source. Five types of sources are available: stars, galaxies, H II regions, emission line spectrum, and user supplied. Each type is associated to a few specific parameters, and all share two global parameters.
The global parameters, optional, allow the user to define a redshift (either in z or velocity) and some extinction.
The specific parameters are:

  • for the stars: spectral type (i.e. temperature), metallicity, and magnitude
  • for the galaxies: metallicity, age, and brightness
  • for the H II regions: metallicity, and Hα brightness
  • for the emission line spectrum: position, integrated flux, and width of the line
  • for the user supplied spectrum: a filename

Background emission

Definition of the background emission

The second section of the input table is optional and defines the emission from the background, diluted and assumed constant across the entire field of view. The parameters available to define the background emission are exactly the same as those available to define the source.

Instrument settings

Definition of the instrument settings

To define the instrument settings, the user has to select a filter, a reference wavelength used to compute the SNR, the spectral resolution (λ/Δλ) requested at that wavelength, the binning (if any), and whether or not the user will use apodization techniques.
If the user decides to use the Norton-Beer apodization, the actual resolution of the observed spectrum will be twice lower than the requested spectral resolution.

Observing conditions

Definition of the observing conditions

To define the observing conditions, the user needs to select a seeing value (0.8, 1.0, or 1.2 arcsec), an airmass limit (1.2 or 1.5), a Moon phase (new, crescent, quarter, full), and enter a value for cloud extinction.
Regarding the Moon phase, the ETC assumes the worst case scenario in terms of distance between the Moon and the target.

Computation mode

Definition of the computation mode

Here, the user can chose between computing a SNR value for a given exposure time (either per step, or for the whole interferogram), and computing an exposure time for a given SNR value. The SNR either is defined as a continuum value, or results from a fit to an emission line.

Result table

Result table

While the user modifies parameters in the input table, the result table are automatically updated, except for the value that the PI wants to compute (SNR or exposure time). This table shows to the user, for instance, the spectral resolution (λ/Δλ) at both ends of the selected filter, and the number of steps in the interferogram. Additionally, if the PI enters an exposure time per step, the table displays the computed total exposure time for the interferogram, taking into account the overheads as defined by the selected binning.
After the user has submitted their parameters to the ETC, the result table will also display either the computed SNR value at the wavelength of interest, or the exposure times (per step and total), depending on the PI's selection. It will also display a message to let the user know whether the ETC encountered an issue or not.

Plot area

Plot area

In this area, the ETC updates automatically the input spectrum each time the user changes a parameter in the input table. After the user has submitted their parameters to the ETC, the left panel also displays the observed (i.e. simulated) spectrum and the fit to the emission line at the wavelength that the user has selected. On the right panel, a spectrum of the SNR is provided.