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We present an improved system for orbit and betatron phase measurementutilizing nonlinear models of BPM pickup response. We first describe thecalculation of the BPM pickup signals as nonlinear functions of beam positionusing Green's reciprocity theorem with a two-dimensional formalism. We thendescribe the incorporation of these calculations in our beam positionmeasurements by inverting the nonlinear functions, giving us beam position as afunction of the pickup signals, and how this is also used to improve ourmeasurement of the betatron phase advance. Measurements are presented comparingthis system with the linearized pickup response used historically at CESR.Comment: 7 pages, 11 figure

Orbit and optics improvement by evaluating the nonlinear beam position monitor response in the Cornell Electron Storage Ring