Accurate Group Delay Measurement for Radial Velocity Instruments Using the Dispersed Fixed Delay Interferometer Method. II. Application of Heterodyne Combs Using an External Interferometer Filter

Abstract

ABSTRACTA fixed delay interferometer is the key component in a DFDI (dispersed fixed delay interferometer) instrument for an exoplanet search using the radial velocity (RV) technique. Although the group delay (GD) of the interferometer can be measured with white light combs (WLCs), the measurement precision is limited by the comb visibility, and the wavelength coverage is constrained by the comb sampling. For instance, this method can calibrate only half of the SDSS-III MARVELS spectra and reach a precision of 2.2 m s-1. This article introduces an innovative method using a sine source for precision delay calibration over very broad wavelengths. The sine source is made of a monolithic Michelson interferometer fed with white light. The interferometer modulated white light (in a sinusoidal form) is fed into a DFDI instrument for calibration. Due to an optimal GD of the sine source, Fourier components from the DFDI interferometer, the sine source, and their frequency beating can be clearly separated and effectively extracted with a chirped Fourier transform to allow precision measurements of the interferometer GD over the entire range of operation wavelengths. The measurements of the MARVELS interferometer with a sine source show that this new calibration method has improved the wavelength coverage by a factor of 2 and the precision by a factor of 3. The RV measurement error induced by GD measurement uncertainties is controlled to be less than 1 m s-1, which has met the requirements for MARVELS moderate-to-high Doppler precision (∼5–30 m s-1) for exoplanet search around V ∼ 8–12 solar-type stars. Heterodyne combs using an external interferometer source can be applied in other areas of optics measurement and calibration.