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Wide Field Camera 3 Instrument Handbook for Cycle 24 > Chapter 9: WFC3 Exposure-Time Calculation > 9.4 Count Rates (Imaging)

9.4.1 Point SourceFor a point source, the count rate, C (e− s−1), can be expressed as the following integral over the bandpass of the filter:

• A is the area of an unobstructed 2.4-m telescope (i.e., 45,239 cm2)

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• 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.

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• 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 e− s−1 pixel−1 from the point source, Cpeak, is given by the following integral over the bandpass:

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• 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:

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• Bλ is the effective bandpass of the filter.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 SourcesFor a diffuse source, the count rate, C (e− s−1 pixel−1), which is now per pixel, due to the astronomical source can be expressed as:

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• Sλ is as above.

• 9.4.3 Emission-Line Sourceswhere 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 24 > Chapter 9: WFC3 Exposure-Time Calculation > 9.4 Count Rates (Imaging)