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Wide Field Camera 3 Instrument Handbook for Cycle 26 > Chapter 9: WFC3 Exposure-Time Calculation > 9.4 Count Rates (Imaging)

 9.4 Count Rates (Imaging)
9.4.1 Point Source
For a point source, the count rate, C (e s−1), can be expressed as the following integral over the bandpass of the filter:
where:
 • A is the area of an unobstructed 2.4-m telescope (i.e., 45,239 cm2)
 • Fλ is the flux from the astronomical source in erg cm−2 s−1 Å−1.
 • The factor λ/hc (where h is Planck’s constant and c is the speed of light) converts ergs to photons.
 • QλTλ is the system fractional throughput, i.e., the probability of detecting an electron per incident photon, including losses due to obstructions of the full 2.4-m OTA aperture. It is specified this way to separate out the instrument sensitivity Qλ and the filter transmission Tλ.
 • εf  is the fraction of the point-source energy encircled within Npix pixels.
 • Sλ is the total imaging point-source sensitivity in units of e− s−1 Å−1 per incident erg cm−2 s−1 Å−1.
The peak es−1 pixel−1 from the point source, Cpeak, is given by the following integral over the bandpass:
where:
 • Fλ, and Sλ are as above.
 • εf(1) is the fraction of energy contained within the peak pixel.
If the flux from the source can be approximated by a flat continuum (Fλ = constant) and εf is roughly constant over the bandpass, then:
We can now define an equivalent bandpass of the filter, Bλ, such that:
where:
 • Speak is the peak sensitivity.
 • Bλ is the effective bandpass of the filter.
The count rate from the source can now be written as:
In Tables 9.1 and 9.2 above, we give the value of:
for each of the filters.
where V is the visual magnitude of the source, the quantity under the integral is the mean sensitivity of the detector+filter combination (also tabulated in Tables 9.1 and 9.2), and ΑΒν is the filter-dependent correction for the deviation of the source spectrum from a constant Fν spectrum. This latter quantity is tabulated for some representative astronomical spectra in Appendix A:.
9.4.2 Diffuse Sources
For a diffuse source, the count rate, C (es−1 pixel1), which is now per pixel, due to the astronomical source can be expressed as:
where:
 • Iλ is the surface brightness of the astronomical source, in erg cm−2 s−1 Å−1 arcsec−2.
 • Sλ is as above.
 • mx and my are the plate scales in arcsec pixel−1 along orthogonal axes.
For a source where the flux is dominated by a single emission line, the count rate can be calculated from the equation
where C is the observed count rate in e s−1, (QT)λ is the system throughput at the wavelength of the emission line, F(λ) is the emission-line flux in units of erg cm−2 s−1, and λ is the wavelength of the emission line in angstroms. (QT)λ can be determined by inspection of the plots in Appendix A:. See Section 9.9.4 for an example of count-rate estimation for an emission-line source.

Wide Field Camera 3 Instrument Handbook for Cycle 26 > Chapter 9: WFC3 Exposure-Time Calculation > 9.4 Count Rates (Imaging)