title: Cavity length measurement: bias from misalignment and mismatching.
abstract: SR-POEM, the sounding rocket principle of equivalence measurement, uses a set of six tracking-frequency laser gauges operating in Fabry-Perot cavities to determine the relative acceleration of two test masses (TMs) that are chemically different. One end of each cavity is a flat mirror on a TM; the other end is a concave coupling mirror mounted to a common reference plate. The tracking-frequency laser gauges work by locking a variable frequency laser to the cavity by the method of Pound, Drever, and Hall. Because the TMs are unconstrained, they are expected to rotate slightly during measurement. Although the distance measurements are intended to be based on the TEM₀₀ cavity mode, any misalignment will couple into higher-order transverse modes, particularly the TEM₁₀ and TEM₀₁. Light thus coupled will contribute a spurious signal to the cavity locking servo that causes a bias (i.e., a systematic error) in the length determination. The spurious signal proportional to the misalignment has an antisymmetric distribution at the detector and thus has a zero average, but causes a distance bias because of the inhomogeneity of the detector responsivity. To prevent such bias, SR-POEM includes a servo to keep the incoming laser beam aligned with the cavity. The required performance of that alignment servo is less stringent than has already been achieved by other projects. There is also a spurious signal proportional to the square of the misalignment that produces a symmetric distribution at the detector. This signal is also made unimportant by the operation of an alignment servo, even when operating well above the shot noise limit. We also look at the locking of a laser to a high finesse cavity and conclude that the alignment quality sets a bound on the ratio of measurement accuracy to cavity linewidth.
authors: Robert D
authors: RD
authors: Reasenberg