The weak-value-amplification technique has been shown to be advantageous for precision metrology. Previous weak-value-based applications have used only a small fraction of data while discarding the rest during post-selection. Here we consider the use of the power-recycling technique to improve the sensitivity of an interferometric weak-value-based velocity measurement scheme. We discuss ways to realize this idea by introducing a power recycling mirror to make the Michelson interferometer a resonant optical cavity. In our analysis, the signal is well enhanced by the cavity and corresponding SNR...
