Results of an “end-to-end” test of the new method using random test data. Top left: Doppler shifts with a nominal (no aberration) PSF. Top right: Doppler shifts with an aberrant PSF and correction, produced from the same underlying data. The correction recovers the test results well – at lower right the magnitude of the difference between the two is shown to be under 5 km/s except for very low signal regions adjacent to high signal ones. The uncorrected Doppler shifts (lower center) show far larger differences, overwhelming the actual signal in this test dataset. The line fit intensity is shown at the lower left for reference.