Inversion of Fabry-Perot CCD images: use in Doppler shift measurements

We consider how to use a charge-coupled device (CCD) as an imaging device for a Fabry-Perot interferometer. When the CCD is used in a conventional manner (pixel by pixel readout), the read noise limits its usefulness. Instead, we propose using the CCD in an operational mode so that the 2-D circular symmetric Fabry-Perot interference pattern is read as a 1-D array. The recovery of the signal is effected by carrying out an Abel inversion of the 1-D array. We show how by carrying out this operation it is possible to reduce greatly the effect of read noise. Finally, we consider how this image technique reflects on the accuracy of a Doppler shift measurement.