9.3 Calculating Sensitivities from Tabulated Data

Most observers will use the ETC or stsynphot to determine count rates and sensitivities for WFC3 observations. However, it is also possible to calculate count rates and signal-to-noise ratios (SNRs) manually, 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 SNR 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 were derived using on-orbit data acquired over ~10 years (see WFC3 ISR 2021-04 and WFC3 ISR 2024-06 for the latest UVIS and IR photometric calibration). Monitoring of the photometric performance shows that the WFC3/UVIS detector sensitivity changes by ~0.1 - 0.2 % per year, depending on the filter; WFC3/IR sensitivity losses are ~0.1% per year, also filter-dependent. The values listed in Table 9.1 (UVIS) and Table 9.2 (IR) are calculated for a 'reference epoch' defined at MJD = 55008 (June 26, 2009). A Jupyter notebook shows how to use stsynphot to compute sensitivity values for any WFC3 observing mode, 'obsmode', i.e. a combination of the desired 'instrument, detector, filter, date, and aperture'. This may be used to determine the UVIS tabular values for any observation date. The new time-dependent inverse sensitivities provide a photometric internal precision of < 0.5% for wide-, medium-, and narrow-band filters. As of early 2024, the WFC3/IR inverse sensitivities do not include any time-dependence, and the values listed in Table 9.2 are valid for all observation dates. Current estimates of the IR photometric uncertainties are ~2% for broad-band filters and 5-10% for narrow-band filters. For a more detailed discussion about WFC3 photometric calibration, see Section 9.1 of the Data Handbook.

Sensitivity data for the G280 grism listed in Table 9.1 is derived from ground-based calibration during Thermal Vacuum testing, as described in WFC3 ISR 2009-01. Sensitivity data for the G102 and G141 grisms provided in Table 9.2 were established by observing the white dwarf spectrophotometric standard stars GD153 and GD71 at several positions across the field (WFC3 ISRs 2009-17, 2009-18, and 2011-05).  For more detail on the calibration of the WFC3 grisms, see Section 9.3 of the Data Handbook.

For the latest set of photometric inverse sensitivities (zeropoints), see the WFC3 Photometric Calibration website.

Filter throughputs are presented in graphical form as a function of wavelength for both chips, UVIS1 and UVIS2, and all 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. Here 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 Tokunaga & Vacca 2005, PASP, 117, 421).  For further discussion on synphot formulae, see the synphot documentation on photometric properties.
   

   $$//<![CDATA[ \begin{array}{l}\displaystyle \lambda_p=\sqrt{\frac{\int Q_{\lambda}T_{\lambda} \lambda d\lambda} {\int Q_{\lambda}T_{\lambda} \lambda^{-1} d\lambda }}\end{array} //]]>$$

3. The bandpass 'efficiency', defined as the integral ∫Q_λT_λ λ^-1 dλ, is used to determine the count rate when given the astronomical magnitude of the source. In the latest python-based stsynphot software (Lim et al. 2016), this dimensionless quantity 'efficiency' is equivalent to the result for 'qtlam' in the older IRAF STSDAS synphot task 'bandpar'.
   
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 dλ, defined 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 (see Section 9.4). The sensitivity integral is equivalent to PHOTFLAM^-1, where PHOTFLAM is a header keyword defined as the 'inverse sensitivity', representing the flux density (erg cm^-2 s^-1 Å^-1) of a source that produces a count rate of 1 e⁻ s⁻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 (in 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:

• C, the count rate of the source in e⁻ s⁻¹ over some selected area on the detector containing N_pix ­pixels.
• P_cr , the peak count rate of the source in e⁻ s⁻¹ pixel ⁻¹, 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 the WFC3/UVIS Channel, provided for both UVIS1 and UVIS2. Values for the quad filters are listed in the UVIS1 column, but are specific to the spectral element associated with each detector amplifier. For more discussion, see Section 6.5.

Table 9.2: Sensitivity Data for the WFC3/IR Channel.