CalculationsΒΆ

Exposure Time and S/N Calculation

To specify the exposure parameters, you can give either the exposure time (in seconds), in which case the program will calculate the count rates due to the source, background, and the resulting S/N ratio. Or, you can give the required S/N ratio, in which case the program will calculate the required exposure time to achieve this S/N ratio and the corresponding integrated counts. Further details follow:

If you select the exposure time:

The program takes the filter transmission, throughputs of the optics and the efficiency of the detector, and calculates the expected countrate for the specified instrument configuration and finds the S/N ratio and the integrated counts from the source, the sky background, and the detector background for the specified exposure time.

If you select the S/N ratio:

The ETC takes the filter transmission, throughputs of the optics and the efficiency of the detector, and calculates the expected count rate for the specified instrument configuration and finds the required exposure time so that the observation will have the specified S/N. This exposure time is then used to calculate the integrated counts from the source and different backgrounds.

Specifying the Wavelength (spectroscopic exposures):

The S/N and associated counts values listed on the main output page are calculated at a specified wavelength, sometimes called the observation wavelength. The observation wavelength must be in the inclusive throughput range for the instrument, detector, spectral element(s) and disperser central wavelength (if applicable) chosen for this observation.

CTE corrections and the ETC:

Phase I proposers should note that the ETC applicable to CCDs (ACS, STIS, WFC3) does not take into account the effects of CTE when predicting S/N ratios.

The Pixel-based CTE correction code currently only works for ACS (Anderson & Bedin). It corrects the CTE trails by restoring the flux to the source, but it will not improve the S/N in the source to be equivalent to that without the effects of CTE.

Proposers are advised to consult the relevant ISRs (e.g., ACS ISR 12-03 by Ubeda & Anderson and ACS ISR 12-05 by Chiaberge for ACS, STIS ISR 03-03R by Bohlin & Goudfrooij and subsequent ISRs for STIS) to determine the percentage of flux lost and increase their exposure times accordingly.

Proposers should also be aware of these issues:

  • The effects of CTE can be minimized by placing the source close to a readout amplifier. For the same total exposure time, the CTE losses are reduced by taking fewer longer exposures rather than more shorter exposures.
  • CTE degrades S/N through flux loss of the source into CTE trails, increased noise from CTE trails of warm pixels/cosmic rays, and increased noise in dark calibration files.
  • In WFC3 and ACS, the post-flash mode can help mitigate CTE effects, particularly for low S/N sources, and for low background levels; for more details, please see the white paper on CTE in the WFC3 ETC.

WFC3 scan mode:

In scan mode, the exposure parameters refer to the S/N calculation only. The ETC in scan mode does not support Time calculations. You can give either the scan rate in arcsec/sec and the scan length in arcsec, or the exposure time in seconds and the scan length in arcsec. The ETC will report the complementary quantity accordingly.

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