Optics measurement resolution and BPM errors

We study the impact of BPM resolution on optics measurements at various levels of complexity: (1) Formula linking a given distribution of BPM resolutions to the degree of precision to which any beam trajectory can be determined based on these BPM's. (2). Formula for the precision achievable in a generalized experimental scheme measuring transfer matrices in the presence of (potentially coupled) orbit errors. (3) Formula constructed from results of (1) and (2) to relate the precision of the transfer matrix measurement to the signal-to-noise ratio of the BPM system. (4) Criterion defined to summarize how well the overall optical behavior of a large modular beam transport system can be quantified. The results from (1), (2) and (3) are used to arrive at the final analytical expression providing a generic criterion on BPM resolution for such systems. Realistic examples are discussed.