Evaluation of an alignment sensing matrix using row vector orientation

1. Evaluation of an alignment sensing matrix using row vector orientation M. Mantovani, A.Freise

2. Introduction • The original design of the automatic alignment system has never been implemented in its pure form. The system design is being continuously discussed from the point of view of the controllability and the noise performances. • Study of the robustness of an alignment system: • Developed a method to obtain a qualityparameter which corresponds to the robustness of a given alignment control system starting from the optical lay-out • Applied this method to simple optical configurations like the single Fabry-Perot cavity • Studied the controllability of a complex system like the full Virgo interferometer

3. Controllability of an Alignment System Method to evaluate the quality of a control or sensing matrix: using the distribution of the matrix‘ row vectors in the system's parameter space. In an over-determined system (e.g. VIRGO) we select the subset of diode signals which provides maximally separated vectors (Matlabscript) and we use the minimum angle between them as the figure of merit when comparing control topologies (quality parameter). Signal Optical Matrix Mirror angular movement M =

4. Single Cavity Example (Ward) Analysis of the controllability for a single FP cavity by using the Ward technique Evolution of the optical matrix coefficients as a function of the demodulation phase of the q1 quadrant The row elements are evolving in phase

5. Single Cavity Example (Ward) Analysis of the controllability for a single FP cavity by using the Ward technique Evolution of the quality factor between the row vectors in the optical matrix as a function of the demodulation phase of the q1 quadrant

6. Single Cavity Example (Ward) Analysis of the controllability for a single FP cavity by using the Ward technique Separation angle by choosing the most separated set of sub-vectors for each choice of Gouy and demodulation phase Separation angle by choosing a fixed set of sub-vectors (the one that optimize the system in one initial configuration) The Ward technique does not need an optimization for the demodulation phase for any Gouy phase (the separation is good for all the configurations)

7. Single Cavity Example (Anderson) Evolution of the separation angle between the better decoupled row vectors in the optical matrix as a function of the demodulation phase of the q1 quadrant Evolution of the separation angle between the not optimized row vectors in the optical matrix as a function of the demodulation phase of the q1 quadrant

8. Single Cavity Example (Anderson) Analysis of the controllability for a single FP cavity by using the Anderson technique Separation by choosing the most separated set of sub-vectors for each choice of Gouy and demodulation phase Separation by choosing a fixed set of sub-vectors (the one that optimizes the system in one initial configuration) The Anderson technique needs an optimization for the demodulation phase (for all the Gouy phases we can always find a demodulation phase which is good for all the configurations)

9. Full Virgo (Anderson) Quality factor obtained by choosing the most separated set of sub-vector for each choice of Gouy and demodulation phase Quality factor obtained by choosing the most separated set of sub-vector for each choice of Gouy and demodulation phase considering also the DC signals VIRGO configuration: Result of the study on the controllability of a complex configuration as the VIRGO alignment system. The chosen alignment control system can thus control all the required degrees of freedom and it can be improved by tuning the parameters of the optical readouts.

10. Conclusions • We have studied the dependence of the controllability of a simple system (a FP cavity using the Ward and the Anderson technique) on the parameters of the optical readout in order to validate and check the performance the chosen test method . • Applying the method to the VIRGO configuration, we could confirm that the current Virgo alignment control configuration represents a feasible solution. • Noise propagation studies in progress • Using the described method and a noise model we can optimize the VIRGO ASC system