Measurement of beta-function and phase using response matrix

The response matrix relates beam motion at the BPM locations to changes in corrector magnet strengths. A method for extracting the beta-function and phase of the beam position monitors and the corrector magnets from the measured response matrix based on storage ring theoretical model is presented. The accuracy of beta and phase thus calculated is limited by the accuracy of response matrix measurement and calibration of BPM and correctors. The error function represents the accuracy of the tune used for iteration. The correct tune corresponds to the minimum error function, which can be used to determine the actual tune.