evaluation of an alignment sensing matrix using row vector orientation

M.Mantovani Ilias Meeting WG1 ,14/11/06 Cascina

Evaluation of an alignment sensing matrix using row

vector orientationM. Mantovani, A.Freise


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 quality parameter 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


Controllability of an Alignment System

ijij sM

1 … n

s1 M11 … M1n

… … … …

sm Mm1 … Mmn

Optical Matrix

Mirror angular

movement

Signal

M =

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 (Matlab script) and we use the minimum angle between them as the figure of merit when comparing control topologies (quality parameter).


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




Evolution of the quality factor between the row vectors in the optical matrix as a function of the

demodulation phase of the q1 quadrant




The Ward technique does not need an optimization for the demodulation phase for any Gouy phase (the separation is good for all the configurations)

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)


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


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)


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.


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

evaluation of an alignment sensing matrix using row vector orientation

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