Time delay interference technology and arm locking frequency stabilization integrated semi-physical experiment verification method

Abstract

The invention provides a time delay interference technology and locking arm frequency stabilization integrated semi-physical experiment verification method. The method comprises the following steps: (1) constructing a locking arm frequency stabilization system; (2) constructing an arm locking frequency stabilization and time delay interference technology semi-physical simulation platform; (3) setting function and technical indexes of a semi-physical simulation platform of the arm locking frequency stabilization and time delay interference technology, and selecting data measurement and acquisition equipment, a data processing tool and a test environment; (4) carrying out a semi-physical simulation platform function verification experiment of the arm locking frequency stabilization and time delay interference technology; and (5) testing and verifying the performance indexes of the semi-physical simulation platform of the arm-locking frequency stabilization and time delay interference technology. According to the method, the suppression ratio of the laser frequency noise can be greatly improved, and the signal-to-noise ratio of the gravitational wave signal relative to the laser frequency noise and other additional noise of a link is remarkably improved, so that the feasibility of an optimization strategy is verified.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of time delay interferometry (TDI), and particularly relates to a time delay interferometry technology and a lock-arm frequency stabilization integrated semi-physical experimental verification method. BACKGROUND

[0002] In 2003, B.S. Sheard et al. first proposed the laser lock-arm technology, based on the basic delay interference principle, and they gave a feedback model of a single-arm lock-arm. In order to compensate for the low phase margin of the single-arm lock-arm system under high gain, B.S. Sheard proposed a design criterion: a 1 / sp (p>1) type filter is used in a lower frequency band, and a 1 / sα (0<α<1) type filter is used in a higher frequency band. By using the design scheme, the frequency noise is sufficiently suppressed in most of the frequency intervals except that it is slightly amplified near the zeros of the system transfer function.

[0003] In order to improve the noise suppression near the zeros of the system transfer function, in 2005, Markus Herz proposed an enhanced lock-arm scheme. This scheme introduces an auxiliary arm (such as another idle arm of LISA / Taiji) on the basis of a single-arm (main arm) lock-arm. The auxiliary arm and the main arm have different lengths, so they have different zero frequencies. The noise remaining in the main arm lock-arm near the zero frequency can be measured in the auxiliary arm through interference. The measured signal controls the main laser through forward feedback, thereby improving the noise suppression near the zero frequency, and the initial transient damped oscillation near the zero frequency can also be suppressed.

[0004] In 2008, A. Sutton et al. proposed a double lock-arm scheme, which ingeniously uses the information of two interference arms to form an error signal, greatly improving the noise suppression performance of the system. However, a potential problem of the double lock-arm is that the length difference of the two arms cannot be too small. When the length difference of the two arms is equal to 130 km, the closed-loop measurement noise of the direct double lock-arm at 3 mHz is almost equal to the noise requirement of the LISA system, and when the length difference of the two arms is less than 130 km, the closed-loop measurement noise cannot meet the noise requirement of the LISA. Another problem of the direct double lock-arm is the frequency pulling caused by the Doppler effect. Although various lock-arm schemes have the problem of frequency pulling, in the direct double lock-arm, the frequency pulling rate caused by the differential lock-arm part is inversely proportional to the difference in transmission delay of the two arms, and when the delay difference is very small, the frequency error caused by the frequency pulling can be higher than that of the single-arm lock-arm.

[0005] In order to reduce the frequency pulling error of the direct double lock arm, K. McKenzie et al. proposed an improved double lock arm scheme in 2009. It is a linear combination of common mode lock arm and direct double lock arm. Under this improved scheme, the potential frequency pulling error of the differential lock arm part at low frequency is eliminated by the filter, and the total frequency pulling error of the system is mainly provided by the common mode lock arm part, which is inversely proportional to the average transmission delay of the two arms. Compared with the direct lock arm scheme (the transmission delay of the two arms is very small), the frequency pulling error is greatly reduced.

[0006] In 2022, Huazhong University of Science and Technology proposed a new single-arm lock arm technology, which equivalently realized the frequency division of the link reflected laser phase with the help of optical frequency comb and electronic frequency divider, thereby avoiding the problem that the lock arm sensor has zero points at the frequency integer multiples corresponding to the inverse of the transmission delay. By selecting a smaller frequency division coefficient, better noise suppression effect can be obtained.

[0007] Overall, in the past 20 years, due to the limited application (currently only applicable to the unique scene of long baseline interferometer measurement), the research on laser lock arm technology is not very high, and it belongs to a small field, and there are few related research results. In view of the complexity of the laser lock arm problem in the multi-source disturbance environment, there is no laser lock arm scheme suitable for intelligent identification and suppression of noise in the multi-source disturbance environment.

[0008] In view of the above, it is necessary to further innovate the existing technology. SUMMARY

[0009] In view of the technical problems in the above background art, the present application provides a time delay interferometry technology and a lock arm frequency stabilization integrated semi-physical experimental verification method, which has a reasonable concept. In view of the instability of the single-arm lock arm system and the multi-source noise coupling problem, a nonlinear constraint multi-parameter collaborative optimization strategy for the controller is proposed. The optimization result overcomes the inherent instability problem of the single-arm lock arm frequency stabilization system, greatly improves the suppression ratio of the laser frequency noise, significantly improves the signal-to-noise ratio of the gravitational wave signal relative to the laser frequency noise and other additional noises of the link, and verifies the feasibility of the optimization strategy.

[0010] To solve the above technical problems, the present application provides a time delay interferometry technology and a lock arm frequency stabilization integrated semi-physical experimental verification method, which comprises the following steps:

[0011] (1) first construct a lock arm frequency stabilization system;

[0012] (2) construct a lock arm frequency stabilization and time delay interferometry technology semi-physical simulation platform;

[0013] (3) Set the function and technical index of the lock arm frequency stabilization and time delay interferometry semi-physical simulation platform, and select the data measurement and collection equipment, data processing tool and test environment;

[0014] (4) Perform the function verification experiment of the lock arm frequency stabilization and time delay interferometry semi-physical simulation platform;

[0015] (5) Perform the performance index test verification of the lock arm frequency stabilization and time delay interferometry semi-physical simulation platform.

[0016] The time delay interferometry and lock arm frequency stabilization integrated semi-physical experimental verification method, wherein the method for the lock arm frequency stabilization system constructed in step (1) is as follows: considering different laser propagation links that can be generated between multiple spacecrafts, a general lock arm structure is established, and a corresponding link phase difference and a lock arm sensor transfer function are obtained; further considering technical noise and interference originating from system instability, a complete noise model is established, and the influence of the lock arm sensor and the controller transfer function on each target parameter of the system is analyzed; at the same time, an analytical model and numerical calculation are combined to solve the dependence of the lock arm system detection sensitivity base and various disturbances, sensor functions and feedback digital filters, and the boundary conditions of each parameter and function that meet the requirements of gravitational wave detection are obtained; finally, based on the complete noise model, the general lock arm sensor and the data-driven feedback controller, the lock arm frequency stabilization of the local laser is realized.

[0017] The time delay interferometry and lock arm frequency stabilization integrated semi-physical experimental verification method, wherein the lock arm frequency stabilization system constructed in step (1) includes a data input layer, a control architecture layer and an optimization output layer;

[0018] The data input layer is responsible for system data modeling and has multiple output interfaces; the control architecture layer is responsible for feedback system structure design and is a multiple input multiple output interface; the optimization output layer is responsible for parameter optimization and output and is a multiple input multiple output interface;

[0019] The data type input by the data input layer mainly includes noise and control parameters; the data input layer needs to complete mathematical modeling of noise signals of shot noise, displacement noise, acceleration noise, laser frequency noise, detector and phase meter reading noise and analog-to-digital converter clock noise, give the transfer function of the gravitational wave signal in the lock arm frequency stabilization system, and also model all feedback controllers to obtain the control parameters in the feedback controller; all noise model data and controller parameters will be transmitted to the control architecture layer for dynamic evolution;

[0020] The noise data of the data output layer is handed over to the optimization output layer after the dynamic evolution of the control architecture layer is completed; the optimization output layer first obtains laser frequency noise suppression ratio, phase margin, gravitational wave sensitivity, other technical noise peak gain and zero-pole position index information of the closed-loop system through a data analysis module, then performs weight distribution and linear and nonlinear combination on the indexes through a target extraction module to obtain a unique output target function, the independent variable of the function being the input parameters of the controllers; then a specific optimization algorithm is used to optimize the target function; after the target function reaches the optimal value, the corresponding controller parameter values are returned to the data input layer.

[0021] The time delay interferometry and lock-arm frequency stabilization integrated semi-physical experimental verification method, wherein the lock-arm frequency stabilization and time delay interferometry semi-physical simulation platform constructed in step (2) mainly comprises an ultra-stable laser, a first measurement arm ARM12 and a second measurement arm ARM13; the ultra-stable laser is used to generate carrier laser, and the carrier laser is split into two carrier lasers by a beam splitter and is connected to the semi-physical simulation system of the first measurement arm ARM12 and the second measurement arm ARM13 respectively.

[0022] The time delay interferometry and lock-arm frequency stabilization integrated semi-physical experimental verification method, wherein the functions of the lock-arm frequency stabilization and time delay interferometry semi-physical simulation platform set in step (3) include:

[0023] (3.1.1) equivalent simulation of million-kilometer baseline interferometric measurement;

[0024] (3.1.2) ground semi-physical simulation of inertial reference system;

[0025] (3.1.3) equivalent simulation of key noises and interferences of inter-satellite laser interferometric measurement system;

[0026] (3.1.4) ground equivalent verification of laser frequency noise suppression and elimination function performance.

[0027] The time delay interferometry and lock-arm frequency stabilization integrated semi-physical experimental verification method, wherein the technical indexes of the lock-arm frequency stabilization and time delay interferometry semi-physical simulation platform set in step (3) include integrated laser frequency suppression and elimination; the integrated laser frequency suppression and elimination meets the requirement that the laser frequency noise suppression is not less than 8 orders of magnitude in the 0.1mHz-0.1Hz frequency band and not less than 6 orders of magnitude in the 0.1Hz-1Hz frequency band.

[0028] The time delay interferometry and the integrated semi-physical experiment verification method of the lock arm frequency stabilization, wherein: the data measurement and collection selected in the step (3) includes a signal generator capable of generating analog data and a multifunctional phase meter capable of measuring phase; and the multifunctional phase meter and the signal generator are synchronized using an ultra-stable clock.

[0029] The data processing tool selected in the step (3) is time delay interferometry data processing software.

[0030] The time delay interferometry and the integrated semi-physical experiment verification method of the lock arm frequency stabilization, wherein the test environment selected in the step (3) specifically includes a laboratory environment, an internal environment of a vacuum chamber, and an external environment of a laboratory.

[0031] The temperature of the laboratory environment is: temperature 20±2℃, humidity <20%, and hundred-level purification.

[0032] The internal environment of the vacuum chamber is: test gas pressure 10 -5 Pa;

[0033] The external environment of the laboratory is: there is no large construction site within a range of 500m outside the experiment, and the test is carried out at night.

[0034] The time delay interferometry and the integrated semi-physical experiment verification method of the lock arm frequency stabilization, wherein the specific steps of the step (4) of the lock arm frequency stabilization and the time delay interferometry semi-physical simulation platform function verification experiment include:

[0035] (4.1) Precision evaluation of laser interferometer

[0036] Turn on the acousto-optic modulator AOM, adjust the frequency deviation between the reference carrier lasers, turn off the modulation functions of all signal generators and electro-optic modulators EOM, turn on each interferometer, realize heterodyne interference measurement between the reference carrier lasers, and continuously measure for a duration of ≥10 hours; read out the data through each phase meter to evaluate the noise floor of each interferometer; the test evaluation index should reach 1μm / Hz 1 / 2 @0.1mHz~0.01μm / Hz 1 / 2 @10mHz, which meets the experimental interferometer precision index requirements;

[0037] (4.2) Precision evaluation of simulated laser frequency noise

[0038] Turning on the signal generator, driving the corresponding electro-optic modulator EOM to simulate the laser signal of the corresponding independent laser, turning off the digital phase-locked loop PLL control signal, and continuously operating the integrated system for ≥10 hours; obtaining the phase meter channel data corresponding to the heterodyne interference signal output by the interferometer, and obtaining the semi-physical simulation laser frequency noise data; residual error analysis of the original simulation data, to evaluate the semi-physical simulation accuracy of the laser frequency noise;

[0039] (4.3) Measurement arm phase delay precision evaluation

[0040] Turning off the electro-optic modulator EOM in front of each measurement arm, based on the signal generator, driving the electro-optic modulator EOM behind the measurement arm, modulating the characteristic or pseudo-code signal into the corresponding simulated laser signal; correlation analysis of the data of the corresponding channel of the phase meter of the measurement arm, to obtain the actual electronic delay time data sequence; and the residual error of the input simulation delay data sequence, to obtain the delay precision evaluation of the front measurement arm to the rear measurement arm;

[0041] (4.4) Test mass translational degree of freedom residual acceleration noise test evaluation

[0042] The test mass is in a suspended and stationary state, and the corresponding phase meter readout data is converted into residual acceleration data of the test mass in the re-measurement axis direction through the test mass interferometer; the suspension system and the test mass interferometer are continuously operated for ≥10 hours, and the test data precision should reach 1×10 -12 m / s 2 / Hz 1 / 2 .

[0043] The time delay interference technology and the integrated semi-physical experimental verification method of the locked arm frequency stabilization, wherein the specific steps of step (5) locked arm frequency stabilization and time delay interference technology semi-physical simulation platform performance index test verification are as follows:

[0044] (5.1) Locked arm frequency stabilization system performance test

[0045] First, ensure that all components in the locked arm frequency stabilization and time delay interference technology semi-physical simulation platform are operating normally, and only the Doppler frequency shift caused by relative orbital motion is retained in the electronic delay system EPD superimposed signal; the integrated verification system is continuously operated for ≥10 hours; then, compare the laser frequency noise data of adjacent simulated lasers before and after the locked arm control, to give a test evaluation of the performance index of the locked arm frequency stabilization system in different frequency bands; and then test and verify the conversion relationship of the locked arm frequency stabilization system to the gravitational wave signal and the change of the signal-to-noise ratio;

[0046] By adjusting and changing the lock arm sensing and control scheme, the orbit parameter, the gravitational wave signal, other related noise forms and possible data abnormal factors, the robustness, performance and dependence of related factors of the lock arm frequency stabilization system are tested and analyzed, and the optimization scheme selection is selected.

[0047] (5.2) Time delay interferometric data processing technology performance test

[0048] The lock arm sensing controller is closed to the driving control of the adjacent electro-optical modulator, only the Doppler frequency shift caused by the relative orbit motion is reserved in the electronic delay system EPD superposition signal, other components in the lock arm frequency stabilization and time delay interferometric technology semi-physical simulation platform are normally operated, and the integrated verification system is continuously operated for greater than or equal to 10 hours.

[0049] The time delay interferometric technology is verified and evaluated in different frequency bands to suppress the performance index of the laser frequency noise.

[0050] The conversion relationship of the time delay interferometric processing to the gravitational wave signal and the verification and evaluation of the signal-to-noise ratio change are analyzed.

[0051] By adjusting and changing the lock arm sensing and control scheme, the orbit parameter, the gravitational wave signal, other related noise forms and possible data abnormal factors, the robustness, performance and dependence of related factors of the lock arm frequency stabilization system are tested and analyzed, and the optimization scheme selection is selected.

[0052] (5.3) Integrated frequency noise suppression system performance test

[0053] All components in the lock arm frequency stabilization and time delay interferometric technology semi-physical simulation platform are normally operated, the integrated verification system is continuously operated for greater than or equal to 10 hours, and the performance verification of the lock arm frequency stabilization and time delay interferometric integrated frequency noise elimination technology is performed.

[0054] By adjusting and changing the lock arm sensing and control scheme, the orbit parameter, the gravitational wave signal, other related noise forms and possible data abnormal factors, the robustness, performance and dependence of related factors of the lock arm frequency stabilization system are tested and analyzed, and the optimization scheme selection is selected.

[0055] By adopting the technical scheme, the present application has the following beneficial effects:

[0056] The time delay interference technology and the integrated semi-physical experiment verification method of the lock arm frequency stabilization have reasonable conception, the technical scheme of the data-driven multi-parameter collaborative optimization of the star-borne lock arm frequency stabilization is proposed for the complexity of the problem of the laser lock arm in the multi-source disturbance environment, the hierarchical structure is adopted, the data input layer is responsible for the noise data modeling and the controller parameter selection, the control architecture layer is responsible for the lock arm frequency stabilization feedback system architecture design, and the optimization output layer is responsible for the optimization and output of the controller parameters, the mathematical characteristics of various technical noises and interference factors of the lock arm system are analyzed, the mathematical model of various noises of the lock arm system is established, the generation method of the noise is given, and simulation verification is carried out, the general model of the general lock arm architecture is established, the characteristics of the single-arm lock arm and the double-arm lock arm structure are analyzed, the general steps of the numerical simulation of the control architecture layer in the MATLAB / Simulink environment are given in combination with the single-arm lock arm and the double-arm lock arm, and the method of dynamically modulating the control parameters in real time in the simulation by using the S function is proposed, aiming at the instability of the single-arm lock arm system and the multi-source noise coupling problem, the nonlinear constraint multi-parameter collaborative optimization strategy of the controller is proposed, the optimization result overcomes the inherent instability problem of the single-arm lock arm frequency stabilization system, greatly improves the suppression ratio of the laser frequency noise, significantly improves the signal-to-noise ratio of the gravitational wave signal relative to the laser frequency noise and other additional noises of the link, and thus the feasibility of the optimization strategy is verified.

[0057] The mathematical characteristics of various technical noises and interference factors of the lock arm system are analyzed, the mathematical model of various noises of the lock arm system is established, the generation method of the noise is given, and simulation verification is carried out, on the basis of the electronic phase delay technology for constructing a very long baseline, the physical simulation of the satellite formation configuration change and various noise sources involved in the interferometric measurement link is carried out, the noise interference is modeled in the wide spectrum range of 0.1mHz-1Hz of the main frequency band of gravitational wave detection based on the difference of the frequency spectrum characteristics of various noises, the equivalence of the arm length and the time delay is analyzed and explained, the lock arm frequency stabilization and time delay interference technology semi-physical simulation platform is constructed based on the lock arm frequency stabilization and time delay interference data processing technology principle, and the integrated system performance index test verification experiment is carried out, the principle consistency of the semi-physical simulation noise and the on-orbit noise is verified, and when the semi-physical simulation noise is improved by 3 orders of magnitude, the relative suppression effect is consistent.

[0058] Based on the application, intelligent identification and accurate suppression of laser frequency noise in a multi-source disturbance environment can be realized, and the sensitivity level of the star-borne laser interferometer gravitational wave detector can be improved as much as possible. BRIEF DESCRIPTION OF DRAWINGS

[0059] In order to more clearly illustrate the technical solutions in the specific embodiments or prior art of the present application, the drawings required to be used in the description of the specific embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0060] Figure 1 The structural principle diagram of the lock arm frequency stabilization system involved in the time delay interference technology and the lock arm frequency stabilization integrated semi-physical experimental verification method of the present application;

[0061] Figure 2 The internal structure principle diagram of the control architecture layer involved in the time delay interference technology and the lock arm frequency stabilization integrated semi-physical experimental verification method of the present application;

[0062] Figure 3 The logic optical path schematic diagram of the lock arm frequency stabilization and time delay interference technology integrated test system involved in the time delay interference technology and the lock arm frequency stabilization integrated semi-physical experimental verification method of the present application;

[0063] Figure 4 The phase meter measurement typical result diagram involved in the time delay interference technology and the lock arm frequency stabilization integrated semi-physical experimental verification method of the present application. DETAILED DESCRIPTION

[0064] The technical solutions of the present application will be described clearly and completely below in combination with the drawings. Obviously, the described embodiments are some embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor belong to the protection scope of the present application.

[0065] The present application will be further explained and described below in combination with specific embodiments.

[0066] The time delay interference technology and the lock arm frequency stabilization integrated semi-physical experimental verification method provided by the present embodiment mainly include the following steps:

[0067] S100, constructing a lock arm frequency stabilization system

[0068] The following figure gives the scheme of the lock arm frequency stabilization system of the present project. Considering that different kinds of laser propagation links may be generated between multiple spacecrafts, an establishment like Figure 1The general lock arm structure is shown, and the corresponding link phase difference Φ1, Φ2, Φ3, Φ4 and the lock arm sensor transfer function F(Φ1, Φ2, Φ3, Φ4) are obtained; further considering the technical noise and interference (such as pointing jitter, laser intensity noise, etc.) originating from system instability, a complete noise model is established, combined with classical theories such as random process analysis and feedback control, the influence of the lock arm sensor and the controller transfer function on the system target parameters under general conditions is analyzed; at the same time, the dependence of the lock arm system detection sensitivity base and various disturbances, sensor functions, feedback digital filters, etc. is solved by combining analytical models with numerical calculations, and the boundary conditions of each parameter and function to meet the requirements of gravitational wave detection are obtained. Finally, based on the complete noise model, the general lock arm sensor, and the data-driven feedback controller, the local laser is locked and stabilized in frequency.

[0069] The lock arm frequency stabilization system includes a data input layer, a control architecture layer, and an optimization output layer; the data input layer is responsible for system data modeling, the control architecture layer is responsible for feedback system structure design, and the optimization output layer is responsible for parameter optimization and output. The data input layer has multiple output interfaces, and the control architecture layer and the optimization output layer are both multiple input and multiple output interfaces. The data input layer mainly includes two data types of noise and control parameters; the data input layer needs to complete the mathematical modeling of noise signals such as shot noise, displacement noise, acceleration noise, laser frequency noise, detector and phase meter reading noise, analog-to-digital converter clock noise, etc., and give the transfer function of the gravitational wave signal in the lock arm frequency stabilization system; in addition, all feedback controllers are modeled to obtain control parameters in the feedback controller, including the number of zeros and poles, gain coefficients, etc. All noise model data and controller parameters will be transmitted to the control architecture layer for dynamic analysis.

[0070] The internal structure of the control architecture layer is shown in Figure 2 The frequency noise of the spacecraft 1 laser reaches spacecraft 2 and 3 through delays τ12 and τ13, respectively, and the gravitational wave signal is added to the laser frequency noise through the corresponding transfer function during transmission; the link output noise passes through controller 1 and controller 2 to weakly lock the local lasers of spacecraft 2 and 3, and technical noise such as shot noise, reading noise, and clock noise is added during the locking process; after locking, the frequency noise of the lasers of spacecraft 2 and 3 returns to spacecraft 1 through delays τ21 and τ31, respectively, and technical noise such as displacement noise and acceleration noise is added during the entire link transmission process; the noise signals of the two feedbacks pass through controller 3 to generate a feedback signal, and the final output of the lock arm frequency stabilization signal is obtained by subtracting the original spacecraft 1 laser frequency noise. Figure 2All the red terminals represent the signals output from the data input layer (mathematical models of various noises, parameter forms of the controller, transfer functions of gravitational waves, etc.), and the black terminals represent the output information provided to the optimization output layer. Figure 2 This example uses two laser transmission links (spacecraft 1-2-1 and spacecraft 1-3-1). This architecture can be expanded to include more links. The final number of links to use will depend on the optimization results for different link combinations.

[0071] After the noise data from the data output layer completes its dynamic evolution at the control architecture layer, it is passed to the optimization output layer. This layer first uses the data parsing module to obtain metrics such as the laser frequency noise suppression ratio, phase margin, gravitational wave sensitivity, peak gain of other technical noise, and the zero-pole locations of the closed-loop system. The target extraction module then weights these metrics and applies linear and nonlinear combinations to produce a unique output objective function, whose independent variables are the input parameters of each controller. This objective function is then optimized using a specific optimization algorithm (such as gradient descent). Once the objective function reaches its optimal value, the corresponding controller parameter values ​​are returned to the data input layer.

[0072] S200, build a semi-physical simulation platform for locking arm frequency stabilization and time delay interference technology

[0073] Based on the principle of locking arm frequency stabilization and time delay interference data processing technology, a semi-physical simulation platform for locking arm frequency stabilization and time delay interference technology was constructed, and integrated system performance index test and verification experiments were carried out. The semi-physical simulation experimental platform for the integrated frequency noise suppression system was built in the main vacuum chamber of the picometer-level laser interference experimental platform. The vacuum chamber is located in a Class 1000 clean room with an inner diameter of four meters and can maintain a temperature better than 10°C for a long time. -5 The chamber is equipped with essential equipment such as an optical experiment table, a suspension mechanism, and a heat sink. Cables are connected to the chamber's integrated frequency noise suppression semi-physical simulation system via a through-chamber flange, enabling data collection for experimental control.

[0074] The logic optical path of the integrated system semi-physical simulation platform is as follows Figure 3 The simulation shows the equivalent on-orbit scientific operation of the two measurement arms of the three-satellite gravitational wave detection formation: the first measurement arm ARM12 (composed of the first satellite (S / C1) and the second satellite S / C2) and the second measurement arm ARM13 (composed of the first satellite S / C1 and the third satellite S / C3), and generates measurement data. This simulation can implement various locking arm frequency stabilization technology solutions and semi-physical verification of first- and second-generation Michelson-type time delay interferometry data processing techniques.

[0075] Based on the experimental requirements, the semi-physical simulation platform selects the super stable laser to generate the carrier laser (or reference laser), and accesses the semi-physical simulation platform in the vacuum chamber through the optical fiber. The carrier laser light source of the integrated test system selects the 1064nm Nd:YAG solid super stable laser, model SLS-1064-300-1000. The performance parameters of the laser are as follows,

[0076] Table 1 Performance parameters of super stable laser

[0077] Parameter Stabilized output power >100mW Frequency drift 972Hz / 3hours Frequency stability <300 Hz / Hz 1 / 2 ]] Power stability <0.05% / 3hours

[0078] As shown in Figure 3 , the carrier laser is divided into two paths of the first measurement arm ARM12 and the second ARM13, and is connected to the semi-physical simulation system of the AMR12 and the ARM13 measurement arm respectively. The optical path design of the two measurement arms is consistent, therefore, the principle and optical path design of the semi-physical simulation are introduced below taking the L12 measurement arm as an example.

[0079] This project uses 12 electro-optic modulators EOM to realize the equivalent simulation of the frequency instability noise of four independent lasers of two measurement arms, and the modulation of laser phase and the compensation function of frequency instability noise. The electro-optic modulator used in the experiment is NIR-MPX-LN-0.1, the electro-optic bandwidth is 150MHz, the half-wave voltage is 1.5V, and the working wavelength is between 950nm and 1150nm.

[0080] Taking the ARM12 measurement arm as an example, after the reference carrier laser is divided, it is connected to the No. 1 electro-optic modulator EMO-1, and based on the numerical simulation input, the independent frequency instability type noise P1(t) of No. 1 laser L1 of S / C1 is generated by the super frequency laser, which drives No. 1 electro-optic modulator EOM-1 to modulate P1(t) into the carrier laser, and the total frequency noise is P1(t)+P0(t), wherein the amplitude spectrum density level of P1(t) is 3MHz / Hz 1 / 2 @0.1mHz~30kHz / Hz 1 / 2 @10mHz,P0≤300Hz / Hz 1 / 2 The frequency instability type noise of the carrier super stable laser. After the laser modulated by No. 1 electro-optic modulator EOM-1 is heterodyne interfered with the reference carrier laser, it is output by the photodetector PD, and the frequency noise is P1(t). The photodetector used in this experiment is GD4542-20MHz-12K of China Electronics Forty-fourth Research Institute, and the performance parameters are shown in the following table. The noise equivalent power density of the photodetector is low, which meets the accuracy requirements of the experiment.

[0081] Table 2 Performance parameters of photodetector

[0082] Parameter Technical index Operating wavelength 1064nm Photosensitive surface diameter 1200±5μm Quadrant interval ≤12μm Linear output voltage amplitude ≥1Vpp AC crosstalk ≤5％ Voltage responsivity ≥13KV / W Gain consistency ≤5％ Noise equivalent power density ≤ 4.5 pW / Hz 1 / 2 ]] Operating voltage ±5V Operating temperature 22±3℃

[0083] The 1st beatnote signal is collected by the multifunctional phase meter PM to generate the 1st data product and store it. The 1st data product, and the 9th beatnote data product corresponding to the measurement arm L1' of the ARM13 simulating laser are L1 and L1', which are important reference data products of the simulated initial laser frequency noise of the L1 and L1', and are reference datum for verifying the performance index of the locking arm and the performance index of the time delay interference processing.

[0084] In order to accurately read the frequency instability noise signal and feed back the information to the delay system, the measurement accuracy of the phase meter is required to be high in the experiment. The multifunctional phase meter used in the experiment is a self-developed product, as shown in the figure, and the phase measurement accuracy thereof reaches Figure 4 The frequency measurement accuracy is better than 0.1 mHz, the frequency band range is 1 MHz-20 MHz, and the measurement requirement of the experiment can be met.

[0085] The frequency offset between the interference lights is realized by the acousto-optic modulator AOM. The SGTF150-1064-1P type acousto-optic modulator produced by the 26th Research Institute of China Electronics Corporation is used in the experiment, and the performance parameters thereof are shown in the following table. The acousto-optic modulator has the characteristics of fast response time, small insertion loss, and low power consumption, and meets the requirements of the experiment.

[0086] Table 3 Performance parameters of the acousto-optic modulator

[0087] Parameter Wavelength 1064nm Insertion loss 2.0dB Polarization extinction ratio 22dB Rise time 20ns Frequency shift frequency 150MHz 3dB frequency shift bandwidth 40MHz Drive power 1.5W

[0088] After the L1 simulating laser signal again passes through the EOM-6, the laser signal is heterodyne interfered with the reference carrier laser, collected by the PD to generate the 2nd beatnote signal, collected and stored by the multifunctional phase meter, and accurately delayed by the electronic time delay system EPD in the flight time τ of the laser signal from S / C1 to S / C2 in the barycenter system of the solar system. 12 12 ​​Based on the numerical simulation of the formation system orbit (including no drag and attitude control), the orbit is generated. At the same time, other key interference and noise in the inter-satellite laser measurement link from S / C1 to S / C2, such as Doppler frequency shift based on relative orbital motion, TTL noise, etc., as well as typical incident gravitational wave signals, are simulated to be superimposed into the electrical signal data. The time delay of the noise is a key step in this experiment, and the data acquisition card is controlled by the host computer to delay the noise for 10s-20s. The data acquisition card used is the USB 6289 data acquisition card of NI company, and the host computer program is written by LabVIEW. The analog input sampling rate of USB 6289 data acquisition card is 500kS / s, the time resolution is 50ns, and the sampling rate of three channel analog output is 1.54MS / s. The input / output voltage is between-10V and 10V.

[0089] After the time delay τ 12 , the electronic beat frequency signal drives EOM-2, modulates the frequency noise P1(t-τ 12 ) of the analog laser L1 after the time delay and the gravitational wave coupling H 12 (t), Doppler shift D 12 (t) and other noise simulation signals N 12 (t) to the reference carrier laser to generate the simulated laser signal propagated through ARM12, and the total frequency noise is P1(t-τ 12 )+P0(t).

[0090] The reference carrier laser accesses EOM-3, and based on the numerical simulation input, the signal generator generates the independent frequency instability noise P2(t) of the No.2 laser L2 of S / C2, drives EOM-3, and modulates P2(t) to the carrier laser, and the total frequency noise is P2(t)+P0(t). The heterodyne interference is performed between the semi-physical analog laser signal of the laser L2 at time t and the semi-physical analog laser signal of L1 before the time of flight τ 12 , and the photoelectric detector is used to collect the No.3 beat frequency signal, which contains the gravitational wave signal, Doppler shift, other noise, and frequency noise P1(t-τ 12 )-P2(t). This signal is collected by a phase meter, and a compensation signal is output based on a digital phase-locked loop PLL, which drives EOM-4 to make the final output frequency noise of the L2 semi-physical equivalent analog laser source P1(t-τ 12 )+P0(t), so as to realize the phase-locked return laser after the laser from S / C1 to S / C2.

[0091] The phase-locked return laser modulated by EOM-4 is subjected to heterodyne interference with the reference carrier laser, and the photoelectric detector is used to collect the No.4 beat frequency signal, and the frequency noise is P1(t-τ 12), via the multi-function phase meter, and stored, and a 4th data product is generated. This beat frequency data, via the electronic path delay system (EPD), is precisely delayed by the time of flight τ of the laser signal from S / C2 to S / C1 in the heliocentric system 21 . The time of flight data τ 21 is based on the formation system numerical simulation orbit. At the same time, other key interferences and noises in the inter-satellite laser measurement link from S / C2 to S / C1 such as Doppler frequency shift based on relative orbital motion, TTL noise, etc., as well as typical incident gravitational wave signals, are simulated here to be superimposed into the electrical signal data. The electronic beat frequency signal after the delay τ 21 drives the EOM-5 to lock the phase of the simulated laser L2 back and pass through the delayed frequency noise P1(t-τ 12 -τ 21 ) and the gravitational wave coupling H 21 (t), H 12 (t-τ 12 ), Doppler frequency shift D 21 (t), D 12 (t-τ 12 ), other noise simulation signals N 21 (t), N 12 (t-τ 12 ) modulate the reference carrier laser to generate a simulated laser signal that propagates through the ARM12, with the total frequency noise being P1(t-τ 12 -τ 21 )+P0(t). At this step, the measurement arm ARM12 is achieved by S / C1 transmitting to S / C2 phase-locked return to S / C1, receiving the orbit, satellite attitude dynamic influence, and coupling typical gravitational wave signal. The equivalent semi-physical simulation data laser signal is achieved. This laser signal is heterodyne interfered with the reference carrier laser signal, and the 5th beat frequency signal is obtained by PD collection, phase meter collection and storage, and a 5th data product is generated, which contains the total frequency noise P1(t-τ 12 -τ 21 ).

[0092] The ARM12 phase-locked return semi-physical simulation laser signal modulated by EOM-5 is heterodyne interfered with the L1 semi-physical simulation laser signal, and the 6th beat frequency signal is generated by PD collection, phase meter collection and storage, and input to the lock arm sensing and controller.

[0093] The lock arm sensor and controller processes the physical simulation data of the two measurement arms ARM12 and ARM13, outputs laser phase feedback control signals for L1 and L1', drives EOM-6 and EOM-12 respectively, realizes the lock arm frequency stabilization phase compensation of the simulated satellite laser L1 and L1' of S / C1, finally completes the lock arm frequency stabilization control closed loop, and outputs the frequency stabilized laser simulation signal after lock arm frequency stabilization control, which enters the time delay loop again.

[0094] The lock arm frequency stabilized L1 semi-physical simulation laser signal is heterodyne interfered with the reference carrier laser, generates the 7th beat frequency signal after being collected by the PD, and is collected, stored and data products are generated by the multifunctional phase meter. The 7th beat frequency data is the laser frequency noise after lock arm frequency stabilization control At the same time, it contains the incident gravitational wave signal converted by the lock arm transfer function and other related noise signals. By comparing the noise amplitude spectral density of the 7th beat frequency data and the 1st beat frequency data without gravitational wave and other related modulation noise signals, and the noise amplitude spectral density of the 15th beat frequency data and the 9th beat frequency data, the lock arm frequency stabilization performance index evaluation is realized.

[0095] At the same time, the 6th and 14th data are the semi-physical simulation data of the three-star formation double-arm measurement, which are the key input data of the time delay interference processing. The 8th and 16th test mass interferometer semi-physical simulation data are also the input data of the time delay interference processing. In order to build a complete three-star heterodyne interference measurement link, a ground inertial reference system is built, and a test mass interferometer is established between the test mass and the optical platform. Two test masses realize low disturbance free motion in the translational degree of freedom through the inverted pendulum and the secondary suspension system, and the residual acceleration index of the translational degree of freedom reaches 1x10 -12 m / s 2 / Hz 1 / 2 . The semi-physical equivalent simulation of the three-star two measurement arms, four translational degrees of freedom of the inertial reference and four test mass interferometers is realized in the test experiment.

[0096] The above data products, after being processed by the first generation and the second generation unequal arm Michelson-type time delay interference data, generate X1 and X2 time delay interference channel data products. In the case of not containing gravitational wave signals, the noise amplitude spectral density is compared with the 5th and 13th data products (or the 1st and 9th data products), and the independent verification of the performance index of the time delay interference technology is realized. By adjusting the orbit simulation data, inputting the fixed arm length configuration and the dynamic formation under the condition of no drag and this station control, the performance and application range of the first generation and the second generation time delay interference technology are verified respectively.

[0097] X1, X2 first generation, second generation unequal arm Michelson-type time delay interferometer channel data product, with initial class physical simulation data laser frequency noise 1, 9 data product noise amplitude spectrum density comparison, can realize the verification and evaluation of the overall performance index of the integrated frequency suppression system of the lock arm frequency stabilization and time delay interferometer. At the same time, by adjusting the input modulation gravitational wave signal, orbital configuration, non-drag and attitude control influence, load anomaly and other signals, the performance index of the integrated laser frequency noise suppression system on the signal-to-noise ratio improvement of gravitational wave detection, the robustness of frequency noise suppression, and the dependent factors of potential performance loss are fully verified.

[0098] S300, set the function and technical index of the lock arm frequency stabilization and time delay interferometer technology semi-physical simulation platform;

[0099] S310, set the function of the lock arm frequency stabilization and time delay interferometer technology semi-physical simulation platform

[0100] S311, million kilometers of interference baseline interferometric measurement equivalent simulation;

[0101] S312, inertial reference system ground semi-physical simulation;

[0102] S313, key noise and interference equivalent simulation of inter-satellite laser interferometric measurement system;

[0103] S314, ground equivalent verification of laser frequency noise suppression and elimination function performance.

[0104] S320, set the technical index table 4 of the lock arm frequency stabilization and time delay interferometer technology semi-physical simulation platform

[0105]

[0106] Test conditions: initial laser frequency noise 10mHz~1Hz not more than 30kHz / Hz 1 / 2 , low frequency inflection point 10mHz, not more than 3MHz / Hz at 0.1mHz 1 / 2 ; vacuum degree reaches 1×10 -5 Pa; temperature stability mK / Hz 1 / 2 order of magnitude; acceleration noise of inertial reference system 1×10 -12 m / s 2 / Hz 1 / 2 .

[0107] S400, set the test equipment and test environment of the lock arm frequency stabilization and time delay interferometer technology semi-physical simulation platform;

[0108] S410, select test equipment and tools

[0109] S411, data measurement and collection

[0110] The simulation data generation signal generator selected in this experiment is Keysight 33500B. The multifunctional phase meter for realizing phase measurement is a self-developed device, and the phase meter and the signal generator are synchronized using an ultra-stable clock.

[0111] S412, data processing tool

[0112] The time delay interference data processing tool software of this experiment is a self-developed program module.

[0113] The data processing tool for performance evaluation of the lock arm frequency stabilization and time delay interference integrated system is a self-developed program module.

[0114] S420, select test environment

[0115] S421, laboratory environment: temperature: 20±2℃; humidity: <20%; hundred-level purification;

[0116] S422, internal environment of vacuum cavity: test gas pressure: ~10 -5 Pa;

[0117] S423, external environment of laboratory: there is no large construction site within 500m of the experiment, and the test is carried out at night.

[0118] S500, function verification experiment of lock arm frequency stabilization and time delay interference integrated verification system

[0119] Turn on the laboratory air conditioner and set the temperature to 20℃. Stable for 2 hours. Connect the hardware according to the connection relationship shown in Figure 3 . Turn on the ultra-stable laser and preheat for half an hour.

[0120] S510, precision evaluation of laser interferometer

[0121] Turn on the acousto-optic modulator AOM, adjust Figure 3 the frequency deviation between the reference carrier lasers; turn off all signal generators and EOM modulation functions.

[0122] Turn on Figure 3 each interferometer to realize heterodyne interference measurement between the reference carrier lasers, and the continuous measurement time is ≥10 hours. The phase meter 1-7 and 9-15 can realize the evaluation of the noise floor of each interferometer.

[0123] The test evaluation index should reach 1μm / Hz 1 / 2 @0.1mHz~0.01μm / Hz 1 / 2 @10mHz, then it meets the interferometer precision index requirements of this experiment.

[0124] S520, analog laser frequency noise precision evaluation

[0125] Turn on the signal generator, drive EOM-1, EOM-3, EOM-7, EOM-9 to simulate independent laser L1, L1', L2, L3 laser signal. Turn off the PLL control signal, and the integrated system runs continuously for more than 10 hours.

[0126] Obtain the semi-physical simulation of laser frequency noise data by heterodyne interferometer output heterodyne interference signal 1, 4, 9, 11 phase meter channel data, and residual error analysis with original simulation data to evaluate the semi-physical simulation precision of laser frequency noise.

[0127] S530, phase delay precision evaluation

[0128] Turn off EOM-3. Based on the signal generator, drive EOM-1 to modulate the characteristic or pseudo-code signal into the L1 analog laser signal. The data correlation analysis of phase meter channel 1 and channel 3 can obtain the actual electronic delay time τ 12 (t) data sequence. With the residual error of the input simulation delay data sequence, the S / C1→S / C2 measurement arm delay precision evaluation can be obtained.

[0129] Turn off EOM-4, drive EOM-3 to modulate the characteristic or pseudo-code signal into the L2 analog laser signal. The data correlation analysis of phase meter channel 4 and channel 5 can obtain the actual electronic delay time τ 21 (t) data sequence. With the residual error of the input simulation delay data sequence, the S / C2→S / C1 measurement arm delay precision evaluation can be obtained.

[0130] Turn off EOM-9. Based on the signal generator, drive EOM-7 to modulate the characteristic or pseudo-code signal into the L1' analog laser signal. The data correlation analysis of phase meter channel 9 and channel 11 can obtain the actual electronic delay time τ 13 (t) data sequence. With the residual error of the input simulation delay data sequence, the S / C1→S / C3 measurement arm delay precision evaluation can be obtained.

[0131] Turn off EOM-10, drive EOM-9 to modulate the characteristic or pseudo-code signal into the L3 analog laser signal. The data correlation analysis of phase meter channel 12 and channel 13 can obtain the actual electronic delay time τ 31 (t) data sequence. With the residual error of the input simulation delay data sequence, the S / C3→S / C1 measurement arm delay precision evaluation can be obtained.

[0132] The time delay precision should be better than 10 ns.

[0133] S540, Test Mass Translational Degree of Freedom Residual Acceleration Noise Test Evaluation

[0134] The test mass is suspended and stationary. The test mass interferometer reads the data from phases 8 and 16, converts the data to the test mass, and then measures the residual acceleration data in the axial direction. The suspension system and the test mass interferometer operate continuously for ≥ 10 hours.

[0135] The test data accuracy should reach 1×10 -12 m / s 2 / Hz 1 / 2 .

[0136] S600, lock-arm frequency stabilization and time delay interferometry technology integrated system performance index test verification

[0137] Turn on the laboratory air conditioner, set the temperature to 20℃, and stabilize for 2 hours. Figure 3 Connect the hardware as shown in the figure. Turn on the ultra-stable laser and preheat it for half an hour.

[0138] S610, lock arm frequency stabilization system performance test

[0139] First, ensure that all components in the semi-physical simulation platform of the locking arm frequency stabilization and time delay interference technology operate normally, and only the Doppler frequency shift caused by the relative orbital motion is retained in the EPD superposition signal. The semi-physical simulation platform of the locking arm frequency stabilization and time delay interference technology runs continuously for ≥10 hours.

[0140] Phase meter measurement channels 1 and 2 provide the laser frequency noise data for the L1 simulated laser before and after arm-locking control, respectively. Phase meter measurement channels 9 and 10 provide the laser frequency noise data for the L1' simulated laser before and after arm-locking control, respectively. Comparing the amplitude spectral density of the data from these two measurement channels (channels 1 and 2, and channels 9 and 10, respectively) allows for a test evaluation of the performance of the arm-locking frequency stabilization system across different frequency bands.

[0141] A characteristic high-amplitude gravitational wave signal was added to the EPD superposition signal. The locking arm sensor controller was turned off for EOM-6 and EOM-12, while all other components operated normally. Phase meter heterodyne interferometry data No. 5 and No. 13 were acquired. The locking arm sensor controller was turned on for EOM-6 and EOM-12, and the integrated platform was run repeatedly using the same simulation data. Phase meter heterodyne interferometry data No. 5 and No. 13 were acquired again. This test verified the conversion relationship between the locking arm frequency stabilization system and the change in signal-to-noise ratio.

[0142] By adjusting the change of the lock arm sensing and control scheme, the track parameters, gravitational wave signals, other related noise forms, possible data anomalies and other factors, test and analyze the robustness of the lock arm frequency stabilization system, the dependence of performance and related factors, and the selection of optimization scheme.

[0143] S620, time delay interferometric data processing technology performance test

[0144] Turn off the driving control of the EOM-6 and EOM-12 by the lock arm sensing controller, only keep the Doppler frequency shift caused by the relative orbital motion in the EPD superposition signal, and other components in the lock arm frequency stabilization and time delay interferometric technology semi-physical simulation platform operate normally. The integrated verification system runs continuously for ≥10 hours.

[0145] Phase meter No. 6 and No. 14 data are used as the semi-physical simulation data of the heterodyne interferometric measurement of the three-star formation double-arm, which are the key input data for time delay interferometric processing. The simulated inter-satellite heterodyne interferometric data of No. 6 and No. 14 are combined with the semi-physical simulation data of the test mass interferometer of No. 8 and No. 16. The first-generation and second-generation Michelson-type time delay interferometric channel output data products X1(t) and X2(t) are generated. The time delay interferometric data products are compared with the data of No. 1 and No. 9 phase meter channels and No. 5 and No. 13 phase meter channels in terms of noise amplitude spectral density, which can realize the verification and evaluation of the suppression performance index of the time delay interferometric technology in different frequency bands on laser frequency noise.

[0146] Add a characteristic strong amplitude gravitational wave signal to the EPD superposition signal, turn off the driving of EOM-6 and EOM-12 by the lock arm sensing controller, and other components operate normally. Obtain the heterodyne interferometric data of No. 5 and No. 13 phase meters. Compare the first-generation and second-generation Michelson-type time delay interferometric channel output data products X1(t) and X2(t). Analyze the verification and evaluation of the conversion relationship and signal-to-noise ratio change of the time delay interferometric processing on the gravitational wave signal.

[0147] By adjusting the change of the track parameters, gravitational wave signal types and parameters, other related noise forms and amplitudes, possible data anomalies and other factors, test and analyze the robustness of the time delay interferometric technology, the dependence of performance and related factors. The applicable scope of the first-generation and second-generation time delay interferometric technology scheme.

[0148] S630, integrated frequency noise suppression system performance test

[0149] All components in the lock arm frequency stabilization and time delay interferometry technology semi-physical simulation platform are in normal operation. The integrated verification system is continuously operated for ≥10 hours. The first generation and second generation Michelson type time delay interferometry channel output data products X1(t), X2(t) are obtained by combining the phase data of the 6th, 14th, 8th and 16th phase meters. The X1(t), X2(t) are compared with the noise amplitude spectral density of the initial signal of the 1st and 9th phase meter channels of the simulated lasers L1 and L1', so as to realize the performance verification of the lock arm frequency stabilization and time delay interferometry integrated frequency noise elimination technology.

[0150] By adjusting the lock arm sensing and control scheme, the orbital parameter, the type and intensity of the gravitational wave signal, other related noise forms, possible data anomalies and other factors, the robustness of the integrated frequency noise suppression system, the dependence of the performance and related factors, and the optimization scheme selection are tested and analyzed.

[0151] The present application concept is reasonable. In view of the instability of the single-arm lock arm system and the multi-source noise coupling problem, a nonlinear constraint multi-parameter collaborative optimization strategy for the controller is proposed. The optimization result overcomes the inherent instability problem of the single-arm lock arm frequency stabilization system, greatly improves the suppression ratio of the laser frequency noise, significantly improves the signal-to-noise ratio of the gravitational wave signal relative to the laser frequency noise and other additional noises in the link, and thus verifies the feasibility of the optimization strategy.

[0152] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A time delay interferometry technology and a locked-arm frequency stabilization integrated semi-physical experimental verification method, characterized in that: The following steps are involved: (1) First build the locking arm frequency stabilization system; (2) Construct a semi-physical simulation platform for arm-locking frequency stabilization and time-delay interferometry technology; (3) Set the functions and technical indicators of the semi-physical simulation platform for the locking arm frequency stabilization and time delay interferometry technology, and select data measurement and acquisition equipment, data processing tools and test environment; (4) Conduct functional verification experiments on the semi-physical simulation platform for arm-locking frequency stabilization and time-delay interferometry technology; (5) Conduct performance index testing and verification of the semi-physical simulation platform for arm locking frequency stabilization and time delay interference technology.

2. The time delay interferometry technology and the integrated semi-physical experimental verification method for locking arm frequency stabilization according to claim 1 are characterized in that: The method for performing arm frequency stabilization on the arm lock frequency stabilization system constructed in the step (1) is as follows: considering different types of laser propagation links that may be generated between multiple spacecraft, a universal arm lock structure is established to obtain the corresponding link phase difference and arm lock sensor transfer function; further considering the technical noise and interference caused by system instability, a complete noise model is established to analyze the influence of the arm lock sensor and controller transfer function on various target parameters of the system; at the same time, a combination of analytical model and numerical calculation is used to calculate the dependence of the detection sensitivity base of the arm lock system on various disturbances, sensor functions, and feedback digital filters, and obtain the boundary conditions of various parameters and functions that meet the requirements of gravitational wave detection; finally, based on the complete noise model, the universal arm lock sensor and the data-driven feedback controller, the arm lock frequency stabilization of the local laser is achieved.

3. The time-delayed interferometry technology and the integrated semi-physical experimental verification method for locking arm frequency stabilization according to claim 1 are characterized by: The locking arm frequency stabilization system constructed in step (1) includes a data input layer, a control architecture layer and an optimization output layer; The data input layer is responsible for system data modeling and has multiple output interfaces; the control architecture layer is responsible for feedback system structure design and has a multi-input and multi-output interface; the optimization output layer is responsible for parameter optimization and output and has a multi-input and multi-output interface; The data input layer primarily accepts noise and control parameters. It must mathematically model the noise signals, including shot noise, displacement noise, acceleration noise, laser frequency noise, detector and phase meter reading noise, and analog-to-digital converter clock noise, to provide the transfer function of the gravitational wave signal in the locked-arm frequency stabilization system. Furthermore, it must model all feedback controllers to obtain their control parameters. All noise model data and controller parameters will be passed to the control architecture layer for dynamic evolution. After the noise data of the data output layer completes its dynamic evolution at the control architecture layer, it is passed to the optimization output layer. The optimization output layer first obtains the laser frequency noise suppression ratio, phase margin, gravitational wave sensitivity, other technical noise peak gain, and zero-pole position indicator information of the closed-loop system through the data analysis module. Then, the target extraction module performs weight assignment and linear and nonlinear combination on these indicators to obtain a unique output objective function. The independent variables of this function are the input parameters of each controller. The objective function is then optimized using a specific optimization algorithm. After the objective function reaches the optimal value, the corresponding controller parameter value is returned to the data input layer.

4. The time-delayed interferometry technology and the integrated semi-physical experimental verification method for locking arm frequency stabilization according to claim 1 are characterized by: The arm-locking frequency stabilization and time-delay interference technology semi-physical simulation platform constructed in step (2) mainly includes an ultra-stable laser, a first measuring arm ARM12 and a second measuring arm ARM13; the ultra-stable laser is used to generate a carrier laser, and the carrier laser is divided into two carrier lasers through beam splitting and respectively connected to the semi-physical simulation system of the first measuring arm ARM12 and the second measuring arm ARM13.

5. The time delay interferometry technology and the integrated semi-physical experimental verification method for locking arm frequency stabilization according to claim 1 are characterized in that: The functions of the semi-physical simulation platform for the arm-locking frequency stabilization and time-delayed interferometry technology set in step (3) include: (3.1.1) Equivalent simulation of interferometry based on a million-kilometer interferometric baseline; (3.1.2) Ground-based semi-physical simulation of inertial reference system; (3.1.3) Equivalent simulation of key noise and interference in intersatellite laser interferometry system; (3.1.4) Ground equivalent verification of the performance of the laser frequency noise suppression and elimination function.

6. The time delay interferometry technology and the integrated semi-physical experimental verification method for locking arm frequency stabilization according to claim 1 are characterized in that: The technical indicators of the semi-physical simulation platform of the arm-locking frequency stabilization and time-delayed interference technology set in the step (3) include integrated laser frequency suppression and elimination; the integrated laser frequency suppression and elimination satisfies the requirement of suppressing laser frequency noise by no less than 8 orders of magnitude in the frequency band of 0.1mHz to 0.1Hz, and no less than 6 orders of magnitude in the frequency band of 0.1Hz to 1Hz.

7. The time-delayed interferometry technology and the integrated semi-physical experimental verification method for locking arm frequency stabilization according to claim 1 are characterized by: The data measurement and acquisition selected in step (3) includes a signal generator capable of generating analog data and a multifunctional phase meter capable of measuring phase; and the multifunctional phase meter and the signal generator are synchronized using an ultra-stable clock; The data processing tool selected in step (3) is time delay interferometry data processing software.

8. The time delay interferometry technology and the integrated semi-physical experimental verification method for locking arm frequency stabilization according to claim 1 are characterized in that: The test environment selected in step (3) specifically includes the laboratory environment, the internal environment of the vacuum chamber, and the external environment of the laboratory: The laboratory environment temperature is: 20±2°C, humidity <20%, and Class 100 purification; The internal environment of the vacuum chamber is: test pressure 10 -5 Pa; The external environment of the laboratory is as follows: there is no large-scale construction site within 500m outside the laboratory, and all tests are carried out at night.

9. The time delay interferometry technology and the integrated semi-physical experimental verification method for locking arm frequency stabilization according to claim 1, characterized in that: The specific steps of the functional verification experiment of the semi-physical simulation platform of the locking arm frequency stabilization and time delay interference technology in step (4) include: (4.1) Laser interferometer accuracy evaluation Turn on the acousto-optic modulator (AOM), adjust the frequency deviation between the reference carrier lasers, and turn off the modulation functions of all signal generators and electro-optic modulators (EOMs). Turn on each interferometer to perform heterodyne interferometry between the reference carrier lasers, with a continuous measurement time of ≥10 hours. Read data from each phase meter to evaluate the noise floor of each interferometer. The test evaluation index should reach 1μm / Hz. 1 / 2 @0.1mHz~0.01μm / Hz 1 / 2 @10mHz, it meets the accuracy requirements of the experimental interferometer; (4.2) Accuracy evaluation of simulated laser frequency noise Turn on the signal generator to drive the corresponding electro-optical modulator (EOM) to simulate the laser signal of the corresponding independent laser, turn off the digital phase-locked loop (PLL) control signal, and ensure that the integrated system operates continuously for ≥10 hours. Obtain semi-physical simulated laser frequency noise data by outputting the phase meter channel data corresponding to the heterodyne interference signal from the interferometer, and analyze the residuals compared to the original simulation data to evaluate the accuracy of the semi-physical simulation of laser frequency noise. (4.3) Measurement arm phase delay accuracy evaluation The electro-optical modulator (EOM) at the front of each measurement arm is turned off, and the electro-optical modulator (EOM) at the rear of the measurement arm is driven by a signal generator to modulate the characteristic or pseudo-code signal into the corresponding simulated laser signal. A data correlation analysis is performed on the corresponding channel of the phase meter of the measurement arm to obtain the actual electronic delay time data sequence. The residual error with the input simulated delay data sequence is used to obtain the corresponding delay accuracy assessment from the front measurement arm to the rear measurement arm. (4.4) Test evaluation of residual acceleration noise of translational degree of freedom of test mass The test mass is in a suspended static state. The test mass interferometer is used to read the data from the corresponding phase meter, convert it into the test mass, and then measure the residual acceleration data in the axial direction. The suspension system and the test mass interferometer are operated continuously for ≥10 hours. The test data accuracy should reach 1×10 -12 m / s 2 / Hz 1 / 2 .

10. The time delay interferometry technology and the integrated semi-physical experimental verification method for locking arm frequency stabilization according to claim 1, characterized in that: The specific steps of the step (5) of testing and verifying the performance indicators of the semi-physical simulation platform of the locking arm frequency stabilization and time delay interference technology are as follows: (5.1) Locking arm frequency stabilization system performance test First, ensure that all components in the semi-physical simulation platform for arm-locking frequency stabilization and time-delay interferometry technology operate normally, that only the Doppler frequency shift caused by relative orbital motion is retained in the electronic delay system's EPD superposition signal, and that the integrated verification system operates continuously for ≥10 hours. Then, compare the laser frequency noise data of adjacent simulated lasers before and after arm-locking control to test and evaluate the performance indicators of the arm-locking frequency stabilization system in different frequency bands. Finally, test and verify the conversion relationship of the arm-locking frequency stabilization system to gravitational wave signals and the change in signal-to-noise ratio. By adjusting and changing the locking arm sensing and control scheme, orbital parameters, gravitational wave signals, other related noise forms, and possible data anomalies, the robustness of the locking arm frequency stabilization system, the dependence of its performance on related factors, and the selection of optimization schemes are tested and analyzed; (5.2) Time delay interferometry data processing technology performance test The locking arm sensor controller's drive control of the adjacent electro-optical modulator is turned off, and only the Doppler frequency shift caused by relative orbital motion is retained in the electronic delay system's EPD superposition signal. Other components in the locking arm frequency stabilization and time delay interferometry semi-physical simulation platform operate normally. The integrated verification system operates continuously for ≥10 hours. Verify and evaluate the performance of time delay interferometry technology in suppressing laser frequency noise in different frequency bands; Analyze the conversion relationship of gravitational wave signals and the verification and evaluation of the signal-to-noise ratio changes caused by time delay interferometry processing; By adjusting orbital parameters, gravitational wave signal type and parameters, other related noise forms and amplitudes, possible data anomalies and other factors, the robustness of the time delay interferometry technique and the dependence of its performance on related factors are tested and analyzed; (5.3) Integrated frequency noise suppression system performance test All components in the semi-physical simulation platform for the arm-locking frequency stabilization and time-delay interferometry technology operate normally, and the integrated verification system runs continuously for ≥10 hours to verify the performance of the integrated frequency noise elimination technology for the arm-locking frequency stabilization and time-delay interferometry technology; By adjusting and changing the locking arm sensing and control scheme, orbital parameters, gravitational wave signal type and intensity, other related noise forms and possible data anomaly factors, the robustness of the integrated frequency noise suppression system, the dependence of performance on related factors, and the selection of optimization schemes are tested and analyzed.

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