LIGO Document T0900477-v4

Fast fitting non linear least squares algorithm of 2D gaussian beam images for LIGO optical lever

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T - Technical notes
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The aim of the project is to study the feasibility of replacing the current quadrant photodetector (QPD) readout system with a CCD in order to improve the way the Optical Level system reacquires the lock of the interferometer. Using a 2D fast centroid finding algorithm, we are able to create a more stable control signal that accounts for the thermal distortion on the surface of the suspended optics. We first examined the behavior of the system on 2 meter and 40 meter optical levers. Then, we created different fitting algorithms in MATLAB and compared the results. The two algorithms that showed the best precision and stability were then translated in C++ and optimized for fast real time execution. Both are based on the Gauss-Newton algorithm for non linear least square problems. Moreover, we effectively filtered most of the diffraction from the optics. For a lever arm of several meters, the algorithms have a short term precision under the um. Thus, the precision of the fit and long term stability of the system satisfy the Advanced LIGO's requirements.
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