  Many advanced techniques have been developed, tested and implemented in the
last decades in almost all circular accelerators across the world to measure
the linear optics. However, the greater availability and accuracy of beam
diagnostics and the ever better correction of linear magnetic lattice
imperfections (beta beating at 1% level and coupling at 0.1%) are reaching what
seems to be the intrinsic accuracy and precision of different measurement
techniques. This paper aims to highlight and quantify, when possible, the
limitations of one standard method, the harmonic analysis of turn-by-turn beam
position data. To this end, new analytic formulas for the evaluation of lattice
parameters modified by focusing errors are derived. The unexpected conclusion
of this study is that for the ESRF storage ring (and possibly for any third
generation light source operating at ultra-low coupling and with similar
diagnostics), measurement and correction of linear optics via orbit beam
position data are to be preferred to the analysis of turn-by-turn data.
