9.3 Calculating Sensitivities from Tabulated Data

Most observers will use the ETC or synphot to determine count rates and sensitivities for WFC3 observations. However, it is also possible to calculate count rates and S/N ratios by hand, and this exercise will give the observer better insight into the sensitivity calculations. The formulae and tabular values required to calculate sensitivities for the WFC3 imaging and spectroscopic modes are provided in this section. Using them, one can calculate the expected count rates and the S/N ratio achieved in a given exposure time, based on the spectral energy distribution of a source. The formulae are given in terms of sensitivities, but we also provide transformation equations between throughput (QT) and sensitivity (S) for imaging and spectroscopic modes.

The tabular data presented here was derived using on-orbit data that was processed with ground-based flat field reference files. (See WFC3 ISR 2009-30 and WFC3 ISR 2009-31.) These flat fields are in error by up to several percent on large spatial scales. More accurate zeropoints (see Online arrow below) have been determined by using better flat fields (see Sections 5.4.3 and 5.7.4) and by deriving filter-specific solutions instead of making a low-order fit across wavelengths. Monitoring of photometric performance over the first year of operations has shown the WFC3/UVIS detector to be stable to rms ~ 0.5% (WFC3 ISR 2010-14) and the WFC3/IR detector to be stable to rms ~ 0.5% to 1.0%, depending on filter (WFC3 ISR 2011-08).

For more accurate photometric zeropoints, see the WFC3 Photometric Zeropoints website.

Throughputs are presented in graphical form as a function of wavelength for each of the imaging filters and grisms in Appendix A. Given the source characteristics and the sensitivity of the WFC3 configuration, calculating the expected count rate over a given number of pixels is straightforward. The additional information required is the encircled energy fraction (ε_f) in the peak pixel, the plate scale, and (for the spectroscopic modes) the dispersions of the grisms.

The sensitivity information is summarized in Tables 9.1 and 9.2. In these two tables, and in the following discussion, the filter transmission functions are denoted T(λ), and the overall system response function (apart from the filter transmission) is denoted Q(λ). The terms “counts” and “count rates” always refer to the number of detected electrons, which is converted to data numbers, or DNs, upon readout according to the gain factors for the detectors. The measured gain is 1.55 e⁻/DN for the UVIS channel and ~2.4 e⁻/DN for the IR channel (see Table 5.1).

In Tables 9.1 and 9.2, the following quantities are listed:

1. The filter or grism designation.

2. The “pivot wavelength” for that filter or grism, λ_p. Pivot wavelength is a source-independent measure of the characteristic wavelength of a bandpass, defined such that it is the same if the input spectrum is given in units of F_λ or F_ν (see A. TokunagW.Vacca 2005, PASP, 117, 421):

   $$\lambda_p=\sqrt{\frac{\int Q(\lambda)T(\lambda)\lambda d\lambda} {\int Q(\lambda)T(\lambda)d\lambda /\lambda}}.$$

3. The integral ∫Q_λT_λ dλ/λ, used to determine the count rate when given the astronomical magnitude of the source.
   
4. The ABmag zero-point, defined as the AB magnitude of a source with a flat F_ν that yields 1 e⁻ s⁻¹ with the specified configuration.
   
5. The sensitivity integral, ∫S_λ d_λ, defined (see Section 9.4) as the count rate that would be detected from a flat F_λ source with a flux of 1 erg cm⁻² s⁻¹ Å⁻¹.
   
6. The ensquared energy, defined as the fraction of PSF flux enclosed in the default photometry aperture (5 × 5 pixels for the UVIS and 3 × 3 pixels for the IR).
   
7. The fraction of the total PSF flux in the central pixel for a centered stellar source, useful for determining the peak count rate to check for saturation (see also Appendix D).
   
8. The sky background count rate (e⁻ s⁻¹), which is the count rate that would be measured with average zodiacal background and average earth-shine. For the IR channel, this quantity also includes the thermal background from HST and the instrument. It does not include the contribution from the detectors themselves (i.e., dark current and read noise).

The next two sections describe how to calculate two quantities:

• The count rate in e⁻ s⁻¹, C, from your source over some selected area on the detector containing N_pix ­pixels.
• The peak count rate in e⁻ s⁻¹ pixel ⁻¹, P_cr, from your source, which is useful for avoiding saturated exposures.

We consider the cases of point sources and diffuse sources separately in each of the following imaging and spectroscopy sections.

Table 9.1: Sensitivity Data for WFC3/UVIS Channel.  

Table 9.2: Sensitivity Data for WFC3/IR Channel.