SNRΒΆ

The SNR is calculated based on the user input exposure time, instrument configuration, and simulated target spectrum. For spectroscopic modes, these values are calculated at a particular wavelength specified by the user in Section 2 of the ETC forms.

Please make sure the wavelength that appears in this section is covered by the selected mode.

For the stare modes, the total photon counts from the various light sources are computed by multiplying the pysynphot-derived count rate (in photons/sec) by the user input exposure time, using encircled energy tables for the point source target. For the scan modes, the encircled energy of the point spread function has been collapsed to a single row to simulate scanning perpendicular to the row. Each photon count term is depicted below with a c subscript. All terms are calculated for a particular extraction region (aka photometric extraction aperture) that covers Npix pixels. Some terms, shown in parentheses, are optional in that they apply only to certain exposures. Thermal background, for example, only applies when an infrared detector is used.

We start with equation (i),

SNR  = \frac{S_c}{N}        \ \ (i)

where:
Sc = Source counts
N = Noise

N = \sqrt{S_c + N_{pix} B G_c + (N_{pix} N_{read} P) + N_{pix} N_{read} R N^2}

where:
B Gc = Background counts per pixel
RN = Read Noise
P = Background per pixel per exposure added using the post-flash option (optional parameter for ACS and WFC3 UVIS)

B G_c = (Sky_c) + D C_c + (Thermal_c)

where:
DCc = Dark Current counts
Skyc = Sky counts = (Earth Shine) + (Zodiacal Light) + (Geocoronal Emission Lines)
(Thermalc) = Thermal Background counts (optional)
(Earth Shine) = (optional parameter)
(Zodiacal Light) = (optional parameter)
(Geocoronal Emission Lines) = (optional parameter)

So if equation (i) is fully expanded with each of its individual terms substituted it becomes equation (ii):

SNR = \frac{S_c}{\sqrt{S_c + N_{pix} [(Sky_c) + DC_c + (Thermal_c) + (N_{read} P )+ N_{read} R N^2]}} \\ (ii)

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