07. Exposure Meter Calculation

For a precision RV (PRV) instrument, the exposure time is often taken to be an integer multiple of the p-mode oscillation time period of the Target star (O(10mins)). One way to calculate this would be to take the midpoint (mean) value for the time of the observation. This would be fine, if the flux levels remained constant throughout the exposure. However, since sky conditions change through an exposure duration of the order of 10 mins, the next generation of PRV instruments use an exposure meter to measure the flux as a function of time. Note that to correct for higher order effects : chromatic change in the atmosphere, i.e. differential change of the flux in red vs blue, some instruments now use chromatic exposure meter (Landoni 2013, Blackman 2017).

They use this flux time series to calculate the flux weighted barycentric velocity. The flux is also used to calculate the flux weighted midpoint of observation.

However it is important to note that at the 1 cm/s the barycentric velocity at the flux weighted midpoint is not equal to the flux weighted barycentric velocity.

In BCPy, we have now included a function which takes an array with the flux values at each of the JDUTC time steps (flux time stamp from Exposure meter) and uses that to calculate the weighted barycentric velocity for the observation. Therefore the correction is calculated at each JDUTC and an average weighted by the exposure meter fluxes is returned. The Exposure meter should have a cadence of minimum 1 min for cm/s.

Further it outputs a JDUTCMID. This is the flux weighted midpoint time, which can be used as the actual time stamp for the radial velocity at that Epoch.

Example shown in Sample Script