Externally Dispersed Interferometer Prototype for Sensitive Radial Velocimetry: Theory

ABSTRACT. A theory of operation of a wideband interferometric Doppler spectroscopy technique, called externally dispersed interferometry (EDI), is presented. The first EDI prototype was tested on sunlight and detected the 12 m s1 amplitude lunar signature in Earth’s motion. The hybrid instrument is an undispersed Michelson interferometer having a fixed delay of about 1 cm, in series with an external spectrograph of about 20,000 resolution. The Michelson provides the Doppler shift discrimination, while the external spectrograph boosts net white-light fringe visibility by reducing cross talk from adjacent continuum channels. A moire ́ effect between the sinusoidal interferometer transmission and the input spectrum heterodynes high spectral details to broad moiré patterns, which carry the Doppler information in its phase. These broad patterns survive the blurring of the spectrograph, which can have several times lower resolution than grating-only spectrographs typically used now for the Doppler planet search. This enables the net instrument to be dramatically smaller in size (∼1 m) and cost. The EDI behavior is compared and contrasted to the conventional grating-only technique. 1