Study On Optimization And Matching Of Quadrant Photoreceiver In Differential Wavefront Sensing

To realize the spaceborne gravitational-wave detection,the Tian Qin project plans to send three satellites into Earth orbit,forming a triangular array with sides about 170,000kilometers long.Long-baseline laser interferometers will be established between satellites and optical readout systems will be set up inside the satellites to measure the motions of the test masses.The overall displacement resolution of the optical metrology system has to achieve 1 pm/Hz^1/2@6 m Hz.Based on the principle of differential wavefront sensing（DWS）,quadrant photoreceiver（QPR）is one of the key equipment used to measure the displacement and angular variation of interferometric lasers simultaneously.The function of the QPR is photoelectric conversion and its performance is important for the accuracies of displacement and angle.According to the requirement of the laser interferometry system in the Tian Qin project,the design analysis,optimization,and multi-channel matching of QPR in DWS measurement were studied in this thesis.To meet the requirements of displacement and angular measurement,the bandwidth,the gain,the signal-to-noise ratio（C/N₀）,and the angular measurement accuracy of QPRs in the two types of interferometry systems were analyzed.Because of the inter-satellite Doppler frequency shift and the attenuation of the power due to long-distance propagation,the long-baseline interferometry provides strict requirements for the above four aspects.To decrease the coupling error caused by the multi-Do F motion of the test mass,angular measurement accuracy should be guaranteed in the optical readout system.According to the task requirements,this thesis carries out analysis,design,and experimental research on the QPRs and DWS.The main results and conclusions include the following four aspects.By analyzing the influence of QPR on displacement and angular measurement according to the transfer function and noise transfer models of the trans-impedance amplifier circuit,an optimization scheme of the output’s C/N₀ was proposed.The test results of the self-made photoreceiver show that its bandwidth is 30 MHz,and the electronic noise is 46 n V/Hz^1/2 with a signal frequency of 30 MHz.By optimizing the circuit parameters and laser power,the C/N₀ of the photoreceiver’s output signal is improved by 2 to 3 d B-Hz.The improvement of the C/N₀ translates to a 0.11 pm/Hz^1/2 decrease of the photoreceiver contribution to the Tian Qin readout displacement noise.To measure the angular background noise of the system,a measurement scheme based on integrated optical devices was proposed with the advantage of a reduced optical axis jitter effect.A laser intensity modulator and a dual-tone acousto-optic modulator were used to replace the interferometer to generate equivalent interference light fields.The angular measurement background noises of the photoreceivers in the heterodyne frequencies of10 k Hz and MHz band were tested respectively.The test results show that the prototypes can reach 2 nrad/Hz^1/2@6 m Hz and 20 nrad/Hz^1/2@6 m Hz at heterodyne frequencies of10 k Hz and 10 MHz,respectively.Based on the Gaussian Beam model,a numerical model of DWS was established to analyze the influence of nonlinearity in DWS on angular measurement and the tilt-to-length coupling effect on displacement measurement.The DWS angular measurement range of QPRs with different diameters was measured by a Mach-Zehnder Interferometer with a fast piezo tip/tilt platform.The experimental results are in agreement with the numerical model within±0.5 mrad,which verifies the nonlinear effect of DWS.The influence of key components of the trans-impedance amplifier circuit on the consistency of multichannel phase frequency response was analyzed,and a multi-channel consistency calibration test scheme was proposed.The consistency of the multi-channel phase-frequency response of QPR and phasemeter was calibrated by using a dual-tone acousto-optic modulator.The calibration results with a standard deviation less than 0.4 mrad are given.Using the calibration results to match the multiple channels of the phase reading system can meet the requirements of the angular measurement accuracy of the optical metrology system.