Fitting method for high reflectivity measurement with phase-shift cavity ring-down technique

The frequency dependences of both amplitude and phase-shift of the first harmonic of the ring-down signal are measured by a lock-in amplifier in a phase-shift cavity ring-down technique (PS-CRD). With different frequency ranges, the cavity decay time values fitted with either amplitude-frequency curve or phase-shift-frequency curve differ in a wide range, with a maximum error of roughly 8%. By defining a root-mean-square error function including both the amplitude error term and phase-shift error term, the maximum error is significantly diminished to 1.3% and the root-mean-square error is as small as 0.5%. The cavity decay time is statistically determined to be 0.791 μs with different frequency ranges. On the other hand, experimental parameters (i.e., the instrumental response time and th