Nanometer Precision Time-Stretch Femtosecond Laser Metrology Using Phase Delay Retrieval

A femtosecond laser metrology with nanometer precision and dynamic range of centimeter incorporating time-stretch interferometry and phase delay retrieval method is proposed and experimentally demonstrated. Displacement encoded phase-sensitive temporal interferogram is generated when phase stabilized femtosecond laser pulses transmitting through a time-stretch interferometer. To avoid the chirp of temporal interferogram due to high-order dispersion, time-to-frequency mapping is established to transform the temporal interferogram to the spectral interferogram for high-speed detection. The phase delay of spectral interferogram corresponding to specific displacements is retrieved and accumulated for linear fitting. The fitted slope is the time delay between two arms in the interferometer therefore displacement can be calculated. For precision verification, the preset displacements are measured. Mean error and standard deviation are presented after sliding average of measured results in 4 μs.