The Exposure Time is calculated based on the user input SNR, instrument configuration and input source spectrum. For spectroscopic modes, this value is calculated at a particular wavelength which is specified by the user in Section 2 of the ETC forms.
Please make sure the wavelength entered in this section is covered by the selected mode.
With this information, the count rate terms (in photons/sec) are retrieved from pysynphot. Each photon count rate term is depicted below with an r subscript.
Taking formula (ii) from the previous page and expanding the count terms, we get the following:
This can be easily changed to:
Then solving for t gives us: