Noise studies of externally dispersed interferometry for Doppler velocimetry

Externally Dispersed Interferometry (EDI) is the series combination of a fixed-delay field-widened Michelson interferometer with a dispersive spectrograph. This combination boosts the spectrograph performance for both Doppler velocimetry and high resolution spectroscopy. The interferometer creates a periodic comb that multiplies against the input spectrum to create moire fringes, which are recorded in combination with the regular spectrum. Both regular and high-frequency spectral components can be recovered from the data--the moire component carries additional information that increases the signal to noise for velocimetry and spectroscopy. Here we present simulations and theoretical studies of the photon limited Doppler velocity noise in an EDI. We used a model spectrum of a 1600K temperature star. For several rotational blurring velocities 0, 7.5, 15 and 25 km/s we calculated the dimensionless Doppler quality index (Q) versus wavenumber v. This is the normalized RMS of the derivative of the spectrum and is proportional to the photon-limited Doppler signal to noise ratio.