Modified weak-value-amplification technique for measuring a mirror's velocity based on the Vernier effect
Jing-Hui Huang, Feifan He, Xue-Ying Duan, Guang-Jun Wang, Xiangyun Hu
Abstract
A modified weak-value-amplification (MWVA) technique to measure a mirror's velocity based on the Vernier effect is proposed. To demonstrate its enhanced sensitivity and higher signal-to-noise ratio (SNR), we use two cascaded Michelson interferometers with similar optical structures. One has a fixed mirror and acts as a fixed part of the Vernier scale, while the other, with a moving mirror, acts as a sliding part of the Vernier scale for velocity sensing. The envelope of the cascaded interferometers shifts much more than a single one with a certain enhancement factor, which is related to the free space range difference between them. In addition, we calculate the SNR based on the Fisher information with both the MWVA and traditional weak-value-amplification (TWVA) techniques. The results show that both the SNR and the sensitivity with our MWVA technique is greater than that of the TWVA technique within the range of our time measurement window. In particular, MWVA can present a viable and effective alternative to the TWVA technique out of the limit of resolution. Furthermore, by using the principles of the Vernier effect, it is applicable and convenient to improve the sensitivity and SNR in measuring other quantities with the TWVA technique.