Development and characterization of a SoC-based phase readout system for deep frequency modulation
Creators: name: Vorndamme, Christoph
Publisher: name: Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) / Laser Interferometry and Gravitational Wave Astronomy
Year: 2017
Subjects: Interferometry
Deep Frequency Modulation
Phase Readout

description: In this thesis the implementation of a digital phase readout system for a laser interferometry technique called deep frequency modulation (DFM) is described.
            Gravitational wave and geodesy missions require to track the motion of test masses with pm/Hz^(1/2) precision over a large dynamic range. DFM is one technique with which such precision can be reached. Central properties of DFM-based setups are the utilization of compact optical hardware on the one hand and sophisticated readout methods on the other hand. The former makes these setups easily scalable in terms of readout channels and therefore a promising candidate for future missions in which multiple testmasses have to be tracked in multiple degrees of freedom.
            The DFM technique utilizes a homodyne interferometer with intentional arm-length mismatch and a frequency modulated laser source to generate a characteristic interference pattern. This pattern depends non-linearly on four parameters which are determined by the phase readout system: A scalefactor which includes laser power, detector efficiency and contrast, modulation depth, modulation phase and interferometer phase. The latter can then be utilized to track a test mass movement.
            In order to extract these parameters a readout scheme as well as a hardware to implement it is needed. In this thesis the implementation of two different readout algorithms is shown. One utilizes the fact that, neglecting the DC value, the signal energy is distributed over integer multiples of the modulation frequency. It takes long segments of data and demodulates the signal at exactly these frequencies. In this way the first ten complex amplitudes are obtained. An analytic model connects the complex amplitudes with the four parameters and leads to an overdetermined system of equations. This can then be solved for the parameters via a non-linear fit. The second readout method is based on a Kalman filter. The Kalman filter combines measurement information with so called process models, i.e. models of the parameter dynamics. Together with knowledge about the uncertainty in the system the Kalman filter is the optimal state estimator for linear stochastic systems. To apply the Kalman filter to DFM several adjustments have to be made. Therefore it is shown how to adjust the Kalman filter for non-linear systems and how to derive a process model empirically.
            In contrast to previously built phase readout systems this thesis shows its implementation on a system on a chip (SoC) which combines, besides other components, a CPU with a field-programmable gate array (FPGA). The utilization of both on a single chip enables real-time processing on a single device. Furthermore this thesis shows the implementation of necessary communication interfaces which can be used as the base for other applications.
            Finally the phase readout system and both of its readout methods are tested in an electrical and an optical testbed. Null measurements are utilized to determine non-common noise sources in distinct readout channels as well as the noise performance of the system. At frequencies above 100 mHz both readout methods show phase noise equivalent to a path length noise of 1 pm/Hz^(-1/2). Limiting noise sources at lower frequencies are analyzed and discussed, as well as alternatives and improvements for the current setup.