Modified weak-value-amplification technique for measuring a mirror's velocity based on the Vernier effect

A modified-weak-value-amplification(MWVA) technique of measuring the mirror's velocity based on Vernier-effect has been proposed. We have demonstrated with sensitivity-enhanced and higher signal-to-noise ratio(${\rm SNR}$) by using two cascaded Michelson interferometers. These interferometers are composed similar optical structures. One interferometer a fixed mirror acts as part Vernier-scale, while other moving sliding Vernier-scale for sensing. The envelope shifts much more than single one certain enhancement factor, which is related to free space range difference between these In addition, we calculate ${\rm SNR}$ Fisher information both MWVA traditional-weak-value-amplification(TMVA) technique. results show that our larger TWVA within time measurement window. Our numerical analysis proved efficient And principles Vernier-effect, it applicative convenient ulteriorly improving sensitivity in quantities