# A.2 Throughputs and Signal-to-Noise Ratio Data

## A.2.1 Sensitivity Units and Conversions

This appendix contains plots of throughputs for each WFC3 filter. Section 9.3 explains how to use these throughputs to calculate expected count rates from your source.

The first figure for each filter gives the integrated system throughput based on on-orbit observations of spectrophotometric standards. This is the combination of the efficiencies of the detector and of the optical elements in the light path. The throughput is defined as the number of detected counts/second/cm2 of telescope area relative to the incident flux in photons/cm2/s. For both the UVIS and IR channels, "counts" is the number of electrons detected. In both channels the detected counts obey Poisson statistics, except that at short wavelengths in the UVIS channel, a single incoming photon has a finite chance of producing multiple electrons in the CCD. Section 5.4.2 describes this phenomenon, which was measured to have a much smaller effect in the UVIS detectors compared to theoretical predictions. The plots in this appendix have been corrected to remove multiple electrons generated by UV photons, using a correction that is intermediate between the theoretical and measured UVIS "quantum yields." The throughput includes all obscuration effects in the optical train (e.g., due to the HST secondary).

All wavelength measurements for the UVIS and IR channel filters were done in a gaseous medium: air for UVIS measurements and helium for IR measurements. The results have been converted to vacuum wavelengths using the indices of refraction of the gaseous media. The UVIS laboratory measurements were done at a temperature of 20°C, whereas the filters are operated on orbit at 0°C; this may lead to wavelength shifts which are expected to be small. The IR laboratory measurements were done at a temperature of –30°C, whereas the filters are operated on orbit at –35°C; this may lead to wavelength shifts which are expected to be very small.

Note that the tables in the synphot package and the WFC3 Exposure Time Calculator all assume vacuum wavelengths for both the UVIS and IR filter transmission data.

Because we have applied a correction to the throughputs for quantum yield in order to derive appropriate counting statistics for the source, the sensitivity calculations shown here are conservative in background- or read-noise-dominated regimes; the additional signal electrons from the enhanced UV quantum yield will increase the detection of faint sources in the 200–300 nm range somewhat vs. these sample calculations.

To recalculate the throughput with the most recent detector QE tables in synphot, you can create total-system-throughput tables (instrument plus OTA) using the synphot calcband task. calcband takes any valid obsmode command string as input and produces a table with two columns of data called "wavelength" and "throughput" as its output. For example, to evaluate the throughput for the F475W filter and the UVIS detector, Chip 1, you would use the command calcband wfc3, uvis1, f475w sdssg_thpt. The resulting throughput table is stored in an IRAF table, sdssg_thpt. The table can be converted to standard text format with tdump "sdssg_thpt" datafile="sdssg_thpt.txt" columns="wavelength,throughput".

## A.2.2 Signal-to-Noise Ratio

For each imaging mode, plots are provided to estimate the signal-to-noise ratio (S/N) for a representative source. The first figure shows S/N for point sources. The second figure shows S/N for uniform extended sources of area 1 arcsec2.

The different line styles in the S/N figures delineate regions where different sources of noise dominate. If the total noise from backgrounds (read noise, sky, thermal, dark) is larger than the noise from the source, the observation is considered to be background-dominated, and the line style reflects which background source is largest. Note that for the WFC3 detectors, the dark current can never be the largest source of noise when a source is background-dominated, because the read noise is always larger than the dark count noise when exposures are 1000 s or less. The point- and extended-source S/N figures assume average sky levels. These plots also indicate where an observation will saturate the full well of the detector.

For point sources, an aperture size of 5 × 5 pixels has been used for the UVIS channel, while an aperture size of 3b × b3 pixels has been used for the IR channel. For extended sources, a 1 arcsec2 aperture was used. The read noise has been computed assuming a number of readouts NREAD= integer (t/1000 s), where t is the exposure time, with a minimum NREAD=2.

In situations requiring more detailed calculations (non-stellar spectra, extended sources, other sky background levels, unknown target V magnitude, etc.), the WFC3 Exposure Time Calculator should be used.

Follow these steps to use the signal-to-noise plots:

1. Determine the AB magnitude of your source at the wavelength of interest. There are several ways to do this.
-Examine Tables A.1A.2, or A.3 and find ABν for the desired spectral type and filter. Sum the magnitude of the target and ABν derived from the table.
-Alternatively, compute ABMAG (=V+ABν) from the source flux, using the relation.

or

2. Find the appropriate plot for the filter in question, and locate V+ABν on the horizontal axis. Then read off the signal-to-noise ratio for the desired exposure time, or vice-versa.

Note that the plots show the S/N as a function of source magnitude for exposure times as short as 0.1 s, although the minimum exposure time for the UVIS channel is actually 0.5 s.