System Throughput and SNR / Exposure Time Estimation

A decision on a suitable exposure time will require the combination of

- The overall spectral response of the system (Figure 2.4).

- The spectral transmission of the filters (Chapter 3 and Appendix A).

- The spectral energy distribution and spatial profile of the target.

- The point response function and pixel size of the instrument (Chapter 5).

- Criteria for specifying desirable charge levels.

When the transmissions of filters *T*(lambda) are combined with the overall system response *Q*(lambda), we obtain **detective quantum efficiency** plots (electrons-per-photon as a function of lambda) for each filter. These DQE plots link the output of the CCD to the photon flux at the input to an unobscured 2.4 m telescope.
These calibrations exist in the STScI Calibration Data Base, and are accessible with the STSDAS SYNPHOT package or with the XCAL software. The XCAL and SYNPHOT Users Guides should be consulted for further details. We include here a sufficient calibration for exposure planning.

In Table 6.1 the **dimensionless efficiency** and the mean wavelength for each filter are tabulated together with the effective width, the equivalent Gaussian dimensionless width, the maximum transmission, the derivative of the mean wavelength with respect to spectral index, the pivot wavelength, average wavelength, and wavelength of maximum transmission. The parameters are defined as follows. The dimensionless efficiency is

The **mean wavelength** is defined in Schneider, Gunn, and Hoessel Ap. J., 264, 337 (1983)

This rather unconventional definition has the property that the correspondingly defined mean frequency is just
. It is in some sense halfway between the conventional frequency mean and the wavelength mean. The **pivot wavelength** is defined as

The effective dimensionless Gaussian width is defined implicitly by

where the integration limits eliminate unrealistic contributions from imperfect blocking far from the bandpass. The effective width of the bandpass is

The final two columns in Table 6.1 are defined as follows. In the next-to-last column me/sec is the zero-point magnitude for 1 e^{-} s^{-1} (with AB_nu=0). The final column gives twfsky, which is the exposure time (in seconds) needed to make the sky noise equal to 5 e^{-} RMS (i.e. ~read noise) in the WFC for a sky level of V=23.3 mag arcsec^{-2}.

#### Table 6.1: System Efficiencies and Zeropoints.

#### Table 6.2: AB_nu as a Function of Wavelength.