Experimental demonstration of deep frequency modulation interferometry.

Katharina-Sophie Isleif,Felipe Guzmán Cervantes,Moritz Mehmet,Thomas S Schwarze,Gerhard Heinzel,Oliver Gerberding

doi:10.1364/oe.24.001676

Abstract

Experiments for space and ground-based gravitational wave detectors often require a large dynamic range interferometric position readout of test masses with 1 pm/√Hz precision over long time scales. Heterodyne interferometer schemes that achieve such precisions are available, but they require complex optical set-ups, limiting their scalability for multiple channels. This article presents the first experimental results on deep frequency modulation interferometry, a new technique that combines sinusoidal laser frequency modulation in unequal arm length interferometers with a non-linear fit algorithm. We have tested the technique in a Michelson and a Mach-Zehnder Interferometer topology, respectively, demonstrated continuous phase tracking of a moving mirror and achieved a performance equivalent to a displacement sensitivity of 250 pm/Hz at 1 mHz between the phase measurements of two photodetectors monitoring the same optical signal. By performing time series fitting of the extracted interference signals, we measured that the linearity of the laser frequency modulation is on the order of 2% for the laser source used.

Highlights

New interferometer schemes using different phase modulation techniques, like digital interferometry (DI) [1,2,3,4] and deep phase modulation (DPM) [5, 6], are currently investigated to simplify the optical part of future experiments in gravitational physics and for metrology experiments
This article reports on the implementation of deep frequency modulation interferometry by investigating two interferometer types
A Mach-Zehnder Interferometer was used to validate the functionality and continuous longterm readout given by deep frequency modulation and the sophisticated fit algorithm, operating in the frequency domain, that was originally designed for deep phase modulation

Summary

Introduction

New interferometer schemes using different phase modulation techniques, like digital interferometry (DI) [1,2,3,4] and deep phase modulation (DPM) [5, 6], are currently investigated to simplify the optical part of future experiments in gravitational physics and for metrology experiments. One recently proposed scheme to simplify optical set-ups is the so-called deep frequency modulation (DFM) [10], a type of frequency modulated continuous wave (FMCW) technique [11] that uses strong laser frequency modulations in unequal arm length interferometers in combination with a phase readout based on fitting the complex amplitudes of the modulation harmonics [5]. This fit algorithm is an alternative to established windowing based, multiplexingcapable stration phase extraction methods [12].

Phase measurement performance

Conclusion and outlook