Characterisation and Optimisation of Phase Readout Algorithm for Deep Frequency Modulation Interferometry

Abstract

Precise optical path length change measurement is the core of all ground based and space based gravitational wave detectors and satellite geodesy missions which use optical readout techniques. The Deep Frequency Modulation (DFM) technique is able to perform with the required sensitivity of pm/√Hz over a large dynamic range along with the added advantage of being able to provide absolute length measurement in the same setup, making it a possible candidate for future missions in which multiple test masses have to be tracked in multiple degrees of freedom. Here, the complexity is shifted from the optical side to the digital phase extraction part. DFM utilises a compact optical setup, with a frequency modulated laser and an unequal arm length interferometer which is easily scalable. The characteristic DFM interferometric signal depends on four parameters, namely a scaling factor, effective modulation index, modulation phase and the test mass phase, which are extracted using an analytical model from the IQ demodulated measured signal with a non-linear fit algorithm. The test mass phase here obtained by tracking the test mass motion is used to measure the path length change. In this thesis, the software phase readout routine with spectral decomposition and nonlinear fit algorithm utilising Levenberg Marquardt minimisation algorithm is the main focus. Experimental verification of the technique which was done in a testbed in the lab here in AEI Hannover, revealed inconsistent behaviour of the fit routine with respect to physical measurables. Investigations to understand the causes was carried out by creating realistic DFM-like signals, considering all the effects observed. Simulation to characterise the physical parameters and intrinsic fit routine parameters lead to deeper understanding of the cost function (sum of squares function, SSQ) and it’s variation on the parameter space. The revelation of the modulation phase (ψ) drift, due to the difference in the clock speeds of the signal generator and the data acquisition module, was detrimental. The ψ drift along with the noise in the system affected the SSQ minimisation and lead to wrong parameter estimates with the fit routine. Further steps in the thesis involved the optimisation of the fit routine to prevent the fit failure and to achieve the desired performance.