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Wide Field Camera 3 Instrument Handbookfor Cycle 22 > Chapter 9: WFC3 Exposure-Time Calculation > 9.4 Count Rates (Imaging)

9.4
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 cm2 s−1 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 1
per incident erg cm2 s−1 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.
Alternatively, we can write the count-rate equation in terms of V magnitudes:
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:WFC3 Filter Throughputs.
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 cm2 s−1 1 arcsec2.
Sλ is as above.
mx and my are the plate scales in arcsec pixel−1 along orthogonal axes.
9.4.3 Emission-Line Sources
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:WFC3 Filter Throughputs. See Section 9.9.4 for an example of count-rate estimation for an emission-line source.

Wide Field Camera 3 Instrument Handbookfor Cycle 22 > Chapter 9: WFC3 Exposure-Time Calculation > 9.4 Count Rates (Imaging)

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