Effect of spectral resolution on weak-value based parameter estimation

There was a long-standing postulation that the precision of weak-value based metrology using post-selection and spectral analysis is limited by the resolution of spectrometer. Current proposals releasing this limitation require either initially Gaussian spectrum or giving up the weak value amplification approximation, both of which make extra restrictions and increase the difficulty of implementation. However, we find that this compromise is unnecessary. Rather than the spectral resolution, the precision of weak-value based metrology mainly relies on how accurate we know about the initial pointer state. Moreover, the relation between knowledge of the initial pointer state and the error-ratio of output is provided and numerically simulated. Our results suggest that the detection devices of weak-value based metrology can be significantly simplified, thus made it a more convenient technique for real-world applications.