Nonlinear Error Calibration Technique for Fast Rotating Optical Delay Lines
Objective As devices can change the relative delay time of reference light and detection light in optical detection systems,optical delay line(ODL)is widely employed in terahertz time-domain spectroscopy(THz-TDS),optical coherence tomography,ultrafast time resolution spectroscopy,and pump-probe technique.In particular,ODL is adopted to scan and detect THz-TDS signals by changing the relative delay of femtosecond and terahertz(THz)pulses in THz-TDS.As such,ODL is a key component that affects the accuracy,signal-to-noise ratio,and spectral resolution of THz signals.In the THz-TDS system,the ODL nonlinearity directly affects the accuracy and consistency of the sampling signal of the THz-TDS system.The nonlinear delay time change leads to the nonlinear actual sampling interval of the system,which brings the nonlinear change in the optical path of the femtosecond laser pulses(FLP)and thus causes the line position error of the THz spectrum.The greater nonlinear error of the THz sampling signal results in more severe distortion of the collected THz signals and greater difficulty in subsequent data processing.Therefore,it is urgent to solve the nonlinear problem of various rotating optical delay line(RODL)delay time.We design a fast rotating optical delay line(FRODL)composed of multiple turntable reflection surfaces(TRSs)and construct a polarized Michelson interference system.Based on the actual calibration results of the total delay time and delay time interval of the FRODL structure,nonlinear error calibration of the actual delay time of FRODL is achieved.Methods We first design a FRODL composed of multiple TRSs and analyze the structure and working principle of FRODL.Then,the feasibility of the FRODL optical path is further verified,and the optical path structure of FRODL at different rotation angles is simulated to obtain the theoretical working angle of FRODL.Combined with the theoretical mathematical model of FRODL,the theoretical delay time of FRODL is obtained,and the theoretical nonlinearity is fitted using the least squares method.Then,considering the signal ratio of the excitation signal,a fiber optic coupling structure is adopted.Based on the coupling power fluctuations during the actual coupling process of FRODL,the actual working range of FRODL is determined.Then,a polarization Michelson interferometer measurement system is built,and the delay time and delay time interval generated by the actual rotation angle of the TRS on each side of the FRODL are calibrated multiple times to obtain the average delay time of the TRS on each side of the FRODL.Additionally,the least squares method is adopted to fit the nonlinear error size and actual nonlinearity of the actual delay time interval.Finally,we also build the THz-TDS system,collect the THz signal under FRODL operation,and utilize the cubic spline interpolation algorithm to calibrate the nonlinear error of the THz signal.Results and Discussions The designed FRODL structure consists of a turntable,a coupling lens,a focusing lens,and a planar reflector(Fig.1).The simulation results show that the theoretical working range of FRODL is[-2.5°,2.5°]and the theoretical delay time can reach 43.522 ps.The fitted ideal delay time is 43.465 ps,and the sensitivity of the ideal delay time to rotation angle is 8.693 ps/(°).The theoretical nonlinearity of FRODL is 0.304％,which means the linearity can reach 99.696％(Fig.3).The calibration results of the polarization Michelson interferometer measurement system show that the average delay time of TRS is 43.504 ps,and the ideal delay time after fitting is 43.522 ps,with a small difference between the two values.The nonlinear error of the FRODL target sampling interval is 52.724％less than 0.05 ps,and there is a nonlinear error of 47.276％with a sampling interval exceeding 0.05 ps.The maximum nonlinear error is 0.094 ps,and the actual nonlinearity of FRODL is 0.215％(Fig.6).Finally,by adopting cubic spline interpolation twice,we obtain the actual delay time of FRODL is matched with the sampling point signal and the calibrated THz equally spaced time-domain waveform(Fig.7).Conclusions We provide a design concept for FRODL and verify by simulation and experiments that the working angle of the FRODL structure can reach 5°.Based on polarization Michelson interference calibration technology,the actual delay time of FRODL is tested.The experimental results show that the delay time of the FRODL is greater than 43.5 ps,and the maximum error of the FRODL before calibration is 0.094 ps,with a linearity of 99.785％.To address the nonlinear errors in THz waveform acquisition in the THz TDS system,we employ the cubic spline interpolation method to obtain the actual delay time corresponding to the encoder angle of each TRS sampling point.By recording the actual delay time corresponding to the encoder angle position,the nonlinearity of the THz sampling signal is calibrated.The FRODL delay time error after calibration is determined by the error accuracy of the cubic spline interpolation algorithm.By leveraging cubic spline interpolation to perform equidistant interpolation on the calibrated non equidistant time-domain THz waveform,the spectral transformation error of the non-equidistant time-domain THz waveform is solved.The calibrated equidistant time-domain THz waveform not only maintains the accuracy of time-domain THz signal sampling but also has spectral accuracy.
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