Time delay interference ground semi-physical experiment verification scheme

Abstract

The invention provides a time delay interference ground semi-physical experiment verification scheme, which comprises the following steps of: (1) based on a space gravitational wave detection task and a load configuration scheme, acquiring core measurement of the space gravitational wave detection task, and recording measurement data; (2) constructing an algebraic relationship of a time delay interference scheme for effectively eliminating secondary noise such as laser frequency noise and optical platform jitter, and calculating according to the algebraic relationship to obtain a solution of first-generation time delay interference and a solution of first-generation basic combination; and (3) repeating the step (2) for multiple rounds to compensate the difference of the equivalent interference measurement arm length and further suppress the laser frequency noise. The half-physical simulation platform is reasonable in conception, the half-physical simulation platform of the Michelson interferometer with the unequal arms and equivalent to the million kilometer arm length is built by combining an arm locking frequency stabilization system and an electronic phase time delay system, and effective suppression of laser frequency noise is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of time delay interferometry (TDI), and particularly to a time delay interferometry ground semi-physical experimental verification scheme. Background Art

[0002] The core objective of time delay interferometry (TDI) technology is to effectively eliminate noise (such as noise caused by gravitational waves and other interferences) through the delay and interference synthesis of laser signals from multiple detection points. Space gravitational wave detectors, such as LISA, rely on a detection array composed of three or more satellites, and the relative positions and time delays between these satellites can be used to significantly reduce system noise and improve the detection sensitivity of low-frequency gravitational wave signals.

[0003] Ground semi-physical experiments are crucial for the verification of TDI technology in space gravitational wave detectors. These experiments usually simulate specific physical processes in the space environment and test the performance of TDI by reproducing its working principle in the ground environment. Among them, the objectives of ground semi-physical experiments include:

[0004] (1) Signal delay and synthesis verification: The experiment needs to verify whether the delay synthesis process between multiple signal sources in TDI technology can eliminate noise as expected and accurately reconstruct gravitational wave signals;

[0005] (2) Noise suppression test: Ground semi-physical experiments can simulate different noise sources and test how TDI technology eliminates these noises in space;

[0006] (3) Technical reliability evaluation: These experiments also need to test the reliability and stability of the TDI system during long-term operation, especially considering that space gravitational wave detectors may need to operate stably for a long time.

[0007] The existing ground semi-physical experimental schemes and methods are as follows:

[0008] When verifying TDI technology, several main experimental methods have been proposed and applied in laboratories and ground facilities:

[0009] (1) Laboratory simulation: Through a high-precision laser interferometer, a laboratory can simulate the signal reception and processing process of a space detector. By adjusting the time delay and phase of the signal, the effect of the TDI method under different conditions can be tested;

[0010] (2) Satellite orbit simulation: Some experimental schemes simulate the signal transmission delay between multiple satellites in a ground device to reproduce the actual relative motion between satellites in space, which helps to understand the working performance of TDI under actual space conditions;

[0011] (3) High-precision noise modeling: To test the noise suppression effect of TDI technology, known noise sources such as electromagnetic noise and vibration noise are added to the interferometer in the experiment to simulate the interference that may be encountered in space;

[0012] (4) Virtual experiments and simulations: Some experiments may use computer simulation technology to simulate various signal processing and noise suppression processes of TDI. These simulations can test different experimental design schemes without the need for real hardware.

[0013] The challenges and development directions of existing ground-based hardware-in-the-loop experiments are as follows:

[0014] (1) Difficulty in simulating the space environment: It is difficult to perfectly replicate the conditions of the space environment (such as vacuum, microgravity, etc.) in ground-based experiments, which limits the verification of some technologies to a certain extent; therefore, the experimental scheme needs to optimize the simulation process as much as possible to make it close to space conditions;

[0015] (2) High-precision signal processing: The successful implementation of TDI depends on the extremely high-precision processing of weak signals; as the experimental scheme progresses, developing more efficient and low-error signal processing methods will become the focus of research;

[0016] (3) Long-term stability and real-time processing ability: Detectors in space usually need to work stably for a long time in extreme environments; ground-based hardware-in-the-loop experiments need to evaluate the stability of the TDI system during long-term experimental operation and verify its ability to process signals in real time in the space environment;

[0017] (4) Interdisciplinary technology cooperation: The implementation of TDI technology involves knowledge in multiple fields such as laser technology, optical systems, data processing, and space physics; future research will require the cooperation of experts in various fields to further optimize the technology and experimental scheme.

[0018] The relevant technologies of existing ground-based hardware-in-the-loop experiments are as follows:

[0019] (1) Noise modeling and simulation: In ground-based hardware-in-the-loop experiments, noise modeling is very important; experiments usually simulate the influence of factors such as ground vibration, minute vibrations of buildings, and air flow on signals; by simulating these noise sources, it is possible to test how effectively the TDI technology eliminates these interferences and obtains clearer gravitational wave signals;

[0020] (2) Signal processing technology: The techniques of signal delay synthesis and noise filtering are the core parts of TDI technology; in ground-based experiments, through precise time delay and signal synthesis algorithms, experimental data can be finely processed to maximize the detection sensitivity.

[0021] The technical problems of existing ground-based hardware-in-the-loop experiments are as follows:

[0022] Currently, time delay interferometry (TDI) has been applied to some extent in space gravitational wave detectors. Especially in space gravitational wave detection projects such as LISA (Laser Interferometer Space Antenna) and Taiji, low-frequency gravitational waves can be effectively detected through the laser interferometry of multi-satellite systems. However, although the TDI technology has relatively mature application solutions in the space environment, its verification and implementation in the ground experimental environment still face many challenges. The main problems include:

[0023] ① Ground noise interference: Ground gravitational wave detection experiments are affected by various environmental noises such as building vibrations, seismic noises, and airflows, making it difficult to distinguish gravitational wave signals from noise components in the interference signals, seriously affecting the effectiveness of the TDI technology.

[0024] ② Differences between the experimental environment and space conditions: There are significant differences between the ground experimental environment and the working conditions of space detectors. In particular, microgravity and vacuum conditions are difficult to replicate, resulting in a lack of application tests in the real environment during the experimental verification process of the TDI technology.

[0025] ③ Signal processing accuracy and complexity: TDI relies on the time delay and precise synthesis of multiple signal sources to eliminate noise and reconstruct gravitational wave signals. However, in ground experiments, due to noise sources and equipment errors, the accuracy requirements for signal delay synthesis are extremely high, and existing experimental schemes are difficult to achieve sufficient sensitivity and stability.

[0026] ④ Limitations of verification schemes: Existing ground verification experiments often adopt single test methods and lack comprehensive experimental schemes that can fully verify the performance of the TDI technology in various noise environments. Existing schemes fail to fully simulate noise sources and operating conditions in the space environment, thus affecting the all-round verification of the TDI technology.

[0027] In summary, it is necessary to further innovate the existing technology. Summary of the Invention

[0028] In view of the technical problems existing in the above background technology, the present invention proposes a time delay interferometry ground semi-physical experimental verification scheme. Its concept is reasonable. An equivalent million-kilometer arm length unequal-arm Michelson interferometer semi-physical simulation platform will be built by combining a locked-arm frequency stabilization system and an electronics phase time delay system to effectively suppress laser frequency noise.

[0029] To solve the above technical problems, a time delay interferometry ground semi-physical experimental verification scheme provided by the present invention includes the following steps:

[0030] (1) Based on the space gravitational wave detection mission and payload configuration scheme, obtain the core measurement data of the space gravitational wave detection mission and record the measurement data;

[0031] (2) Construct the algebraic relationship of the time-delay interference scheme that can effectively eliminate secondary noises such as laser frequency noise and optical platform jitter. Calculate the solutions of the first-generation time-delay interference and the first-generation basic combination according to this algebraic relationship; and in the case that there is still a large residual laser frequency noise after the first-generation time-delay interference processing, the second-generation time-delay interference processing can be selected, and the second-generation time-delay interference processing is still calculated based on the aforementioned algebraic relationship;

[0032] (3) Repeat the above step (2) in multiple rounds to compensate for the differences in the equivalent interference measurement arm lengths and further suppress the laser frequency noise.

[0033] In the time-delay interference ground semi-physical experimental verification scheme, in the step (1), the core measurement of the mission includes the laser interferometric ranging data between 6 satellites in three measurement arms; each laser interferometric ranging data between satellites consists of the test mass in the inertial sensor of the first satellite in the link to the local optical platform, the inter-satellite optical platform, and the second satellite optical platform to the local test mass;

[0034] Each satellite contains a total of 6 core scientific measurement data, and each optical platform includes the inter-satellite extrapolation interference measurement s(t), the interference measurement ε(t) from the local test mass to the optical platform, and the reference interference measurement τ(t) between adjacent optical platforms:

[0035]

[0036] In the above formulas (1)-(7), t represents time, H represents the gravitational wave signal, p is the laser frequency noise, Δ is the optical platform displacement jitter noise, δ is the test mass displacement jitter noise, μ is the fiber noise, L represents the distance between satellites, and λ represents the wavelength of the laser; N(t) is other readout noises; where the subscripts of all characters in formulas (1)-(7) are marked according to Figure 1 in a counterclockwise order as 1, 2, 3, and in a clockwise order as 1′, 2′, 3′, and the numbers 1, 2, 3 respectively represent the numbers of three different satellites; the superscripts of all characters in formulas (1)-(6) represent the optical platforms represented by s, ε, or τ; N opt (t) represents the optical path noise.

[0037] In the time-delay interference ground semi-physical experimental verification scheme, the specific process of the step (2) is as follows:

[0038] Define the time-delay operator:

[0039] D i f(t) = f(t - L i ) (8);

[0040] Construct an algebraic relation for the time-delay interference scheme that effectively eliminates secondary major noises such as laser frequency noise and optical platform jitter:

[0041] ∑ j＝{1,2,3,1′,2′,3′} F j (D1, D2, D3, D 1′ D 2′ D 3′ )η j (t) = f(H) + O(t) (9);

[0042] In the above formula (9), F j is the solution of the time-delay interference scheme, which is a polynomial about the delay operator; f(H) is a polynomial of the gravitational wave signal; O is a polynomial of secondary noises such as the phase meter readout noise and the inertial sensor displacement noise; η is the inter-satellite test mass to test mass interference measurement data formed by splicing; D is the time-delay operator in the previous formula; t represents time;

[0043] Then, the solutions of the time-delay interference and the first-generation time-delay interference basic combination are calculated from the above algebraic relation (9).

[0044] In the time-delay interference ground semi-physical experimental verification scheme, the specific process of realizing the compensation for the difference in the equivalent interference measurement arm length and further suppressing the laser frequency noise in step (3) is as follows:

[0045] Build an equivalent million-kilometer arm length unequal-arm Michelson interferometer semi-physical simulation platform by combining the locked-arm frequency stabilization system and the electronics phase time-delay system; through this simulation platform, after processing the laser passing time delay, phase-locked return, etc., interfere with the local laser beat frequency to obtain the frequency or phase measurement data y1(t) and y2(t); for noise evaluation, the experimental platform includes the ultra-stable reference carrier laser interference data y0(t); the measurement signal includes the frequency instability noise of the local laser:

[0046] y1(t) = p(t - L1) - p(t) + N1(t) (10);

[0047] y2(t) = p(t - L2) - p(t) + N2(t) (11);

[0048] The above optical path simulates the unequal-arm Michelson interference measurement of the two arms in orbit for the space gravitational wave detection mission, and the data of this interference measurement is:

[0049] y2(t) - y1(t) = p(t - L2) - p(t - L1) + N2(t) - N1(t) (12);

[0050] The measurement accuracy of this interferometry is affected by the laser frequency noise p(t - L2) - p(t - L1); According to the Michelson type time delay interferometry data processing algorithm for the space gravitational wave detection mission, the time-delayed ground fiber optic interferometry data is combined:

[0051] D1y2(t) = p(t - L2 - L1) - p(t - L1) + N2(t - L1) (13);

[0052] D2y1(t) = p(t - L1 - L2) - p(t - L2) + N1(t - L2) (14);

[0053] The Michelson-type time delay combined data is obtained as follows:

[0054] X1(t) = (D1y2(t) + y1(t)) - (D2y1(t) + y2(t)) = N2(t - L1) +

[0055] N1(t) - N1(t - L2) - N2(t) (15);

[0056] Finally, the effective suppression of laser frequency noise is achieved.

[0057] Adopting the above technical solution, the present invention has the following beneficial effects:

[0058] The time delay interferometry ground semi-physical experimental verification scheme of the present invention is reasonably conceived. An equivalent non-equal-arm Michelson interferometer semi-physical simulation platform with an arm length of one million kilometers will be built by combining the locked-arm frequency stabilization system and the electronics phase time delay system to effectively suppress the laser frequency noise.

[0059] Applying the time delay interferometry ground semi-physical experimental verification scheme of the present invention, a semi-physical simulation experimental platform with an integrated frequency noise suppression system has been successfully built in the main vacuum chamber of the picometer-level laser interferometry experimental platform in the Huairou Campus of the Institute of Mechanics, Chinese Academy of Sciences. The built semi-physical simulation experimental platform with an integrated frequency noise suppression system is used to equivalently simulate the on-orbit scientific operation of the two measurement arms L3 and L2 of the three-star formation for space gravitational wave detection, and generate measurement data. It can realize various locked-arm frequency stabilization technical solutions and the semi-physical verification of the first-generation and second-generation Michelson-type time delay interferometry data processing technologies. The vacuum chamber is located in a thousand-class clean room with an inner diameter of four meters and can maintain a vacuum better than 10 -5The vacuum level is Pa; an optical experiment table, a suspension mechanism, a heat sink and other necessary devices are arranged in the vacuum chamber, and the cables are connected to the integrated frequency noise suppression hardware-in-the-loop simulation system in the chamber, so as to realize the control of the experiment and the acquisition of data.

[0060] On the premise of applying the time delay interference ground hardware-in-the-loop experiment verification scheme of the present invention, relying on a 10 -5 Pa-level ultra-high vacuum environment and an active temperature control system, the gas refractive index fluctuation and phase noise can be effectively suppressed; the experimental data shows that the phase noise spectral density is lower than 10 -6 rad / √Hz at 0.1 Hz, meeting the requirements of space application indicators.

[0061] The time delay interference ground hardware-in-the-loop experiment adopts a split optical module architecture, supports the rapid switching of the locked arm frequency stabilization scheme, the phase delay system has the parallel processing ability of 128 channels, and the time delay resolution reaches 0.1 ps, providing a hardware basis for the pre-research of the third-generation noise reduction algorithm.

[0062] The present invention constructs an equivalent interferometer arm length of one million kilometers based on the electronic phase time delay system, breaks through the limitation of the physical arm length of the ground laboratory, and realizes the simulation of the laser frequency noise suppression characteristics of the 10 6 km-level ultra-long interferometer arm in the Taiji space gravitational wave detection. Compared with the traditional kilometer-level delay scheme, the electronic phase time delay system increases the equivalent arm length by three orders of magnitude, and the noise suppression bandwidth is extended to the key frequency band of 0.1 mHz - 1 Hz.

[0063] Using the verification scheme of the present invention, the integrated system design of laser frequency noise suppression and elimination can be completed, and the design index meets the requirement of suppressing the laser frequency noise by no less than 8 orders of magnitude in the frequency band of 0.1 mHz to 0.1 Hz and no less than 6 orders of magnitude in the frequency band of 0.1 Hz to 1 Hz.

[0064] Using the verification scheme of the present invention, the noise analysis of the laser measurement link can be completed, and the reliability, completeness and stability analysis of the noise source can be completed, including the noise above 1 pm / Hz 1 / 2 in the measurement frequency band. The numerical simulation system design of the integrated laser frequency suppression and elimination system is completed, and the design accuracy of modeling and processing analysis is better than 0.05 pm / Hz in the frequency band of 0.1 mHz to 1 Hz 1 / 2 .

[0065] Using the verification scheme of the present invention, the hardware-in-the-loop simulation platform design of the integrated laser frequency suppression and elimination system can be completed, and the hardware-in-the-loop simulation design index meets the requirement of suppressing the laser frequency noise by no less than 8 orders of magnitude in the frequency band of 0.1 mHz to 0.1 Hz and no less than 6 orders of magnitude in the frequency band of 0.1 Hz to 1 Hz.

[0066] Aiming at the difference between the noise level in the ground semi-physical simulation for integrated frequency noise suppression and the actual noise index in orbit, the verification scheme of the present invention can be used to complete the research on the equivalence and consistency evaluation methods, meeting the evaluation requirement that the initial laser frequency noise is not greater than 30 Hz / Hz from 1 mHz to 1 Hz. 1 / 2 The evaluation requirements are met.

[0067] Using the verification scheme of the present invention, the time delay interferometry system design can be completed. The design index is that the suppression of laser frequency noise is not less than 6 orders of magnitude in the frequency band of 0.1 mHz to 0.1 Hz and not less than 5 orders of magnitude in the frequency band of 0.1 Hz to 1 Hz. Using the verification scheme of the present invention, the numerical simulation system design of the time delay interferometry technology can be completed, and the design accuracy of modeling and processing analysis is better than 0.05 pm / Hz in the frequency band of 0.1 mHz to 1 Hz. 1 / 2 . BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0069] Figure 1 It is a laser diagram of the core interference data of the space gravitational wave detection mission related to the time delay interferometry ground semi-physical experimental verification scheme of the present invention;

[0070] Figure 2 It is a Michelson-type TDI combination diagram related to the time delay interferometry ground semi-physical experimental verification scheme of the present invention;

[0071] Figure 3 It is a Sagnac-type TDI combination diagram related to the time delay interferometry ground semi-physical experimental verification scheme of the present invention;

[0072] Figure 4 It is a symmetric Sagnac TDI combination diagram related to the time delay interferometry ground semi-physical experimental verification scheme of the present invention;

[0073] Figure 5 It is a measurement missing TDI combination diagram related to the time delay interferometry ground semi-physical experimental verification scheme of the present invention;

[0074] Figure 6 It is a schematic diagram of an unequal-arm Michelson laser interferometer related to the time delay interferometry ground semi-physical experimental verification scheme of the present invention;

[0075] Figure 7This is the unequal-arm Michelson interference measurement diagram formed by the on-orbit two-arm measurement in the space gravitational wave detection mission involved in the time-delay interference ground semi-physical experimental verification scheme of the present invention;

[0076] Figure 8 This is the diagram of the unequal-arm Michelson-type time-delay interference scheme in the space gravitational wave detection involved in the time-delay interference ground semi-physical experimental verification scheme of the present invention.

[0077] Figure 9 This is the logical optical path diagram of the Michelson interferometer semi-physical simulation platform in the time-delay interference ground semi-physical experimental verification scheme of the present invention. Detailed implementation manners

[0078] Next, the technical solutions of the present invention will be described clearly and completely in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0079] Next, a further explanatory description of the present invention will be made in conjunction with specific implementation manners.

[0080] A time-delay interference ground semi-physical experimental verification scheme provided in this embodiment is designed based on the space gravitational wave detection mission and the payload configuration scheme. The core measurement data of the mission includes 6-way laser interference ranging data between satellites in three measurement arms. Among them, each way of ranging data between satellites is respectively composed of three-way laser interference measurements that are connected end to end from the inertial sensor test mass of the first satellite in the link to the local optical platform, the inter-satellite optical platform, and the optical platform of the second satellite to the local test mass. The measurement data is recorded as follows: Each satellite contains a total of 6-way core scientific measurement data, and each optical platform includes the inter-satellite extrapolation interference measurement s(t), the interference measurement ∈(t) from the local test mass to the optical platform, and the reference interference measurement τ(t) between adjacent optical platforms:

[0081]

[0082]

[0083]

[0084] In the above formulas (1)-(7), H represents the gravitational wave signal, p is the laser frequency noise, Δ is the displacement jitter noise of the optical platform, δ is the displacement jitter noise of the test mass, μ is the fiber noise, L represents the distance between satellites, λ represents the wavelength of the laser, and N(t) is other readout noises caused by platform instability, temperature fluctuations, fibers, etc.; the subscripts of all characters in formulas (1)-(7) are marked according to Figure 1 as follows. It is carried out counterclockwise as 1, 2, 3 and clockwise as 1′, 2′, 3′. The numbers 1, 2, 3 respectively represent the numbers of three different satellites; the superscripts of all characters in the above formulas (1)-(6) represent the optical platform represented by s, ε, or τ. The measurement signal subscripts are marked according to the counterclockwise rotation around the constellation, as shown in Figure 1 .

[0085] Define the time delay operator (i represents the i-th satellite):

[0086] D i f(t) = f(t - L i ) (8);

[0087] Construct the algebraic relation of the time delay interference scheme that effectively eliminates secondary main noises such as laser frequency noise and optical platform jitter:

[0088] ∑ j＝{1,2,3,1′,2′,3′} F j (D1, D2, D3, D 1′ D 2′ D 3′ )η j (t) = f(H) + O(t) (9);

[0089] Among them, in the above formula (9), F j is the solution of the time delay interference scheme, which is a polynomial about the delay operator, f(H) is a polynomial of the gravitational wave signal, O is a polynomial of secondary noises such as the readout noise of the phase meter and the displacement noise of the inertial sensor, η is the interference measurement data from the test mass to the test mass between satellites formed by splicing; D is the time delay operator in the previous formula, j has been explained in the formula, and t represents time.

[0090] From the above algebraic relation (9), the solutions of time delay interference and the basic combination of the first-generation time delay interference can be calculated. If there is still a large residual laser frequency noise after the first-generation time delay interference processing, then the second-generation time delay interference technology scheme can be selected, and its optical path combination configuration is as shown in Figures 2-5 .

[0091] All possible combination schemes of the first-generation time-delay interferometry can be obtained by combining the above basic schemes. The first-generation scheme is applicable to the relatively ideal mission orbit situation where the influence of the arm length change can be ignored. In the case where the influence of the arm length change in the three-star system is relatively large and there is still a large residual laser frequency noise after the first-generation time-delay interferometry processing, the second-generation time-delay interferometry technical scheme can be selected. The second-generation scheme is still calculated based on the above basic scheme. Its principle is to compensate for the difference in the equivalent interferometric arm length by repeating the first-generation scheme multiple times, further suppressing the laser frequency noise.

[0092] This ground-based hardware-in-the-loop experimental verification scheme for time-delay interferometry will build an equivalent non-equal-arm Michelson interferometer hardware-in-the-loop simulation platform by combining the locked-arm frequency stabilization system and the electronics phase time-delay system. The schematic diagram is as Figure 6 shown:

[0093] In the figure, the two measurement arms are respectively composed of the electronics experimental system, and the arm lengths can be dynamically simulated without drag control. Through this simulation platform, after processing the laser passing time delay, phase-locked return, etc., the laser is beat-interfered with the local laser to obtain the frequency or phase measurement data y1(t) and y2(t). To realize the noise evaluation, the hardware-in-the-loop simulation platform of the interferometer includes the local ultra-stable reference carrier laser interferometry data y0(t). The measurement signals of the hardware-in-the-loop experimental simulation platform include the frequency instability noise of the local laser:

[0094] y1(t) = p(t - L1) - p(t) + N1(t) (10);

[0095] y2(t) = p(t - L2) - p(t) + N2(t) (11);

[0096] In the above formula (10), N(t) is other noise caused by platform instability, temperature fluctuation, optical fiber, etc. Figure 6 The optical path in simulates the non-equal-arm Michelson interferometric measurement of the two arms in orbit for the space gravitational wave detection mission, as shown in the following Figure 7 shown.

[0097] The data of this interferometric measurement is:

[0098] y2(t) - y1(t) = p(t - L2) - p(t - L1) + N2(t) - N1(t) (12);

[0099] The measurement accuracy of the non-equal-arm Michelson interferometric measurement of the two arms in orbit for the space gravitational wave detection mission is affected by the laser frequency noise p(t - L2) - p(t - L1). According to the Michelson type time-delay interferometry data processing algorithm for the space gravitational wave detection mission, the ground fiber optic interferometry data after time delay is combined. The optical path is as followsFigure 8 as shown

[0100] Combine the time-delayed ground fiber optic interference data

[0101] D1y2(t) = p(t - L2 - L1) - p(t - L1) + N2(t - L1) (13);

[0102] D2y1(t) = p(t - L1 - L2) - p(t - L2) + N1(t - L2) (14);

[0103] In the above equations (13)-(14), D refers to the time-delay operator, where the subscripts 1 and 2 of the time-delay operator D respectively represent the number of the detector, as shown in the image in Figure 1 as shown

[0104] The Michelson-type time-delay combined data obtained is:

[0105] X1(t) = (D1y2(t) + y1(t)) - (D2y1(t) + y2(t)) = N2(t - L1) +

[0106] N1(t) - N1(t - L2) - N2(t) (15);

[0107] Effectively suppress the laser frequency noise

[0108] The logical optical path of the Michelson interferometer semi-physical simulation platform involved in the time-delay interference ground semi-physical experimental verification scheme of the present invention is as shown in Figure 9 as shown, equivalently simulate the on-orbit scientific operation of the two measurement arms ARM12 (formed by satellite 1 (S / C1) and satellite 2 (S / C2)) and ARM13 (formed by satellite 1 (S / C1) and satellite 3 (S / C3)) of the three-star formation for space gravitational wave detection, and generate measurement data. It can implement various lock-arm frequency stabilization technology schemes, as well as the semi-physical verification of the first-generation and second-generation Michelson-type time-delay interference data processing technologies

[0109] Based on the experimental requirements, the Michelson interferometer semi-physical simulation platform selects an ultra-stable laser to generate carrier laser (or reference laser), which is connected to the Michelson interferometer semi-physical simulation platform in the vacuum chamber by optical fiber. The carrier laser source of the integrated test system selects a 1064nm Nd:YAG solid ultra-stable laser, model SLS-1064-300-1000. As shown in Figure 9As shown in the figure, the carrier laser is mainly split into two paths of carrier lasers, namely the measurement arm ARM12 and ARM13, and are respectively connected to the semi-physical simulation systems of the AMR12 and ARM13 measurement arms. The optical path designs of these two measurement arms are the same. Therefore, the principle and optical path design of the semi-physical simulation will be introduced below taking the L12 measurement arm as an example.

[0110] The Michelson interferometer semi-physical simulation platform uses a total of 12 electro-optic modulators (EOMs) to achieve the equivalent simulation of the frequency instability noise of four independent lasers in two measurement arms, as well as the modulation of the laser phase and the compensation function of the frequency instability noise. The model of the electro-optic modulator used in the experiment is NIR-MPX-LN-0.1, its electro-optic bandwidth is 150 MHz, the half-wave voltage is 1.5 V, and the working wavelength is between 950 nm and 1150 nm.

[0111] Taking the ARM12 measurement arm as an example, after the reference carrier laser is split, it is connected to the 1st electro-optic modulator (EMO-1). Based on the numerical simulation input, the independent frequency instability noise P1(t) of the 1st laser L1 of satellite 1 is generated by the signal generator, driving EOM-1 to modulate P1(t) into the carrier laser. The total frequency noise is P1(t)+P0(t), where the amplitude spectral density level of P1(t) is 3 MHz / Hz1 / 2@0.1 mHz~30 kHz / Hz1 / 2@10 mHz, and P0≤300 Hz / Hz1 / 2 is the frequency instability noise of the carrier ultra-stable laser. The laser modulated by EOM-1 is heterodyne interfered with the reference carrier laser, and via the photodetector (PD), the 1st beat signal is output, and the frequency noise is P1(t). In this experiment, the photodetector used is GD4542-20MHz-12K from the 44th Research Institute of China Electronics Technology Corporation. The performance parameters are shown in the following table. The noise equivalent power density of this photodetector is low, meeting the accuracy requirements of the experiment.

[0112] The 1st beat signal is collected by the multifunctional phase meter (PM), generating the 1st data product and storing it. The 1st data product, as well as the 9th beat data product corresponding to the L1' analog laser of the ARM13 measurement arm, are important reference data products for the initial laser frequency noise of L1 and L1', and are the reference benchmark data for verifying the performance indicators of the locked-arm frequency stabilization and the time-delay interference processing performance indicators.

[0113] To accurately read the frequency instability noise signal and feedback information to the delay system, this experiment has very high requirements for the measurement accuracy of the phase meter. The multifunctional phase meter used in this experiment is a self-developed product, and its phase measurement accuracy reaches 2π×10 -6 rad / √Hz, the frequency measurement accuracy is better than 0.1 mHz, and the frequency band range is 1 MHz~20 MHz, which can meet the measurement requirements of the experiment.

[0114] The frequency offset between the interfering lights is achieved by an acousto-optic modulator (AOM). In this experiment, an SGTF150-1064-1P model acousto-optic modulator produced by the 26th Research Institute of China Electronics Technology Corporation is used. Its performance parameters are shown in the following table. It has the characteristics of fast response time, small insertion loss, low power consumption, etc., meeting the requirements of the experiment.

[0115] After the L1 analog laser signal passes through the laser signal after EOM-6 again and heterodyne interferes with the reference carrier laser, the 2nd beat frequency signal is generated by PD acquisition. The 2nd beat frequency data collected and stored by the multifunctional phase meter passes through the electronic time delay system (EPD), and is accurately delayed by the flight time τ of the laser signal from S / C1 to S / C2 in the barycentric coordinate system of the solar system. 12 The flight time data τ 12 is generated based on the numerical simulation orbit of the formation system (including drag-free and attitude control). At the same time, other key interferences and noises 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 and superimposed on the electrical signal data here. Implementing the time delay of noise in this experiment is a crucial step. The upper computer controls the data acquisition card to delay the noise for 10 s to 20 s. The data acquisition card used is the USB 6289 data acquisition card of NI Corporation, and the upper computer program is written in LabVIEW. The USB 6289 data acquisition card has an analog input sampling rate of 500 kS / s, a time resolution of 50 ns, and an analog output sampling rate of 1.54 MS / s for three channels. The input / output voltage is between -10 V and 10 V.

[0116] After the time delay τ 12 the electronic beat frequency signal drives EOM-2 to modulate the frequency noise P1(t - τ 12 ) of the analog laser L1 after time delay, as well as the gravitational wave coupling H12(t), Doppler frequency shift D12(t), and other noise simulation signals N12(t) onto the reference carrier laser, generating a simulated laser signal propagated through ARM12. The total frequency noise is P1(t - τ 12 ) + P0(t).

[0117] The reference carrier laser is connected to EOM-3. Based on the numerical simulation input, the signal generator generates the independent frequency instability noise P2(t) of the 2nd laser L2 of S / C2, which drives EOM-3 to modulate P2(t) into the carrier laser. The total frequency noise is P2(t) + P0(t). The semi-physical simulation laser signal of laser L2 at time t and the flight time τ of L1 12Heterodyne interference is performed on the previous hardware-in-the-loop simulated laser signal, and the 3rd beat frequency signal is collected by a photodetector. The signal contains gravitational wave signals, Doppler frequency shifts, other noises, 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) to drive EOM-4, so that the frequency noise finally output by the L2 hardware-in-the-loop equivalent simulated laser light source is P1(t - τ 12 ) + P0(t), realizing the phase-locked return of the laser after going from S / C1 to S / C2.

[0118] The phase-locked return laser modulated and compensated by EOM-4 undergoes heterodyne interference with the reference carrier laser, and the 4th beat frequency signal is collected by a photodetector. The frequency noise is P1(t - τ 12 ). It is collected, stored by a multifunctional phase meter, and the 4th data product is generated. This beat frequency data is accurately delayed by the electronic time delay system (EPD) by the flight time τ 21 of the laser signal from S / C2 to S / C1 in the barycentric coordinate system of the solar system. 21 The flight time data τ 21 is generated based on the numerical simulation orbit of the formation system. 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 and superimposed on the electrical signal data here. After the time delay τ 12 of the electronic beat frequency signal, EOM-5 is driven to phase-lock and return the analog laser L2, and the frequency noise P1(t - τ 21 - τ 12 ), gravitational wave couplings H21(t), H12(t - τ 12 ), Doppler frequency shifts D21(t), D12(t - τ 12 ), and other noise simulation signals N21(t), N12(t - τ 12 - τ 21 ) are modulated onto the reference carrier laser to generate a simulated laser signal propagated through ARM12, with a total frequency noise of P1(t - τ 12 - τ 21 ) + P0(t). Up to this step, the measurement arm ARM12 is realized to be launched from S / C1 to S / C2, phase-locked and returned to S / C1, and the equivalent hardware-in-the-loop simulated data laser signal affected by the orbit, satellite attitude dynamics, and coupled typical gravitational wave signals is obtained. This laser signal undergoes heterodyne interference with the reference carrier laser signal, and the 5th beat frequency signal is obtained by PD collection, collected and stored by a phase meter, and the 5th data product is generated, which contains a total frequency noise of P1(t - τ

[0119] The phase-locked return semi-physical analog laser signal after being modulated by EOM-5 is heterodyne interfered with the L1 semi-physical analog signal. The 6th beat frequency signal is generated through PD acquisition, collected and stored by the phase meter, and input to the locking arm sensing and controller. The locking arm and sensing controller in this experiment are developed by the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, the project team.

[0120] The 6th and 14th data are used as the semi-physical analog data for the double-arm measurement of the three-star formation, which are the key input data for the time-delay interference processing. At the same time, the 8th and 16th test mass interferometer semi-physical analog data are also used as the input data for the time-delay interference processing. 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. The two test masses achieve low-interference free movement of 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 1×10 -12 m / s 2 / Hz1 / 2. The semi-physical equivalent simulation of the two measurement arms of the three stars, a total of four translational degrees of freedom of the inertial reference, and four test mass interferometers in this test experiment is realized.

[0121] The above data products, after being processed by the first-generation and second-generation unequal-arm Michelson-type time-delay interference data, generate the X1 and X2 time-delay interference channel data products. Without the gravitational wave signal, they are compared with the noise amplitude spectral density of the 5th and 13th data products (or the 1st and 9th data products) to realize the independent verification of the technical performance indicators of the time-delay interference. By adjusting the orbital simulation data, inputting the fixed arm length configuration and the dynamic formation under the control of drag-free, the performance and applicable range of the first-generation and second-generation time-delay interference technologies are respectively verified.

[0122] The X1 and X2 first-generation and second-generation unequal-arm Michelson-type time-delay interference channel data products are compared with the noise amplitude spectral density of the 1st and 9th data products of the laser frequency noise of the initial class physical simulation data, and the verification and evaluation of the performance indicators of the time-delay interference integrated frequency suppression system can be realized. At the same time, by adjusting the input modulated gravitational wave signal, orbital configuration, drag-free and attitude control influence, payload anomaly and other signals, the performance indicators of the integrated laser frequency noise suppression system for improving the signal-to-noise ratio of gravitational wave detection, the robustness of frequency noise suppression, and the dependent factors of potential performance loss are fully verified.

[0123] The concept of the present invention is reasonable. An unequal-arm Michelson interferometer semi-physical simulation platform with an equivalent arm length of one million kilometers will be built by combining the locking arm frequency stabilization system and the electronic phase time-delay system to effectively suppress the laser frequency noise.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A time-delay interference ground semi-physical experimental verification scheme, characterized in that, It includes the following steps: (1) Based on the space gravitational wave detection mission and payload configuration scheme, obtain the core measurement data of the space gravitational wave detection mission, and record the measurement data; (2) Construct the algebraic relationship of the time-delay interference scheme that can effectively eliminate secondary noises such as laser frequency noise and optical platform jitter, and calculate the solutions of the first-generation time-delay interference and the first-generation basic combination according to this algebraic relationship; and in the case that there is still a large residual laser frequency noise after the first-generation time-delay interference processing, the second-generation time-delay interference processing can be selected, and the second-generation time-delay interference processing is still calculated based on the aforementioned algebraic relationship; (3) Repeat the above step (2) in multiple rounds to achieve compensation for the difference in the equivalent interference measurement arm length and further suppress the laser frequency noise.

2. The time-delay interference ground semi-physical experimental verification scheme according to claim 1, characterized in that The core measurement in the step (1) includes the laser interferometric ranging data between 6 satellites in three measurement arms; the laser interferometric ranging data between each pair of satellites consists of the test mass in the inertial sensor of the first satellite in the link to the local optical platform, the inter-satellite optical platform, and the second satellite optical platform to the local test mass; Each satellite contains a total of 6 core scientific measurement data, and each optical platform includes the inter-satellite extrapolation interference measurement s(t), the interference measurement ε(t) from the local test mass to the optical platform, and the reference interference measurement τ(t) between adjacent optical platforms: In the above equations (1)-(7), t represents time, H represents the gravitational wave signal, p is the laser frequency noise, Δ is the displacement jitter noise of the optical platform, δ is the displacement jitter noise of the test mass, μ is the fiber optic noise, L represents the distance between satellites, λ represents the wavelength of the laser; N(t) is other readout noise; where the subscripts of all characters in equations (1)-(7) are labeled according to Figure 1, counterclockwise as 1, 2, 3, and clockwise as 1′, 2′, 3′, and the numbers 1, 2, 3 respectively represent the numbers of three different satellites; the superscripts of all characters in equations (1)-(6) represent the optical platforms represented by s, ε, or τ; N opt (t) represents the optical path noise.

3. The time-delay interference ground semi-physical experimental verification scheme according to claim 1, characterized in that The specific process of the step (2) is as follows: Define the time-delay operator: D i f(t) = f(t - L i ) (8); Construct the algebraic relationship of the time-delay interference scheme that can effectively eliminate secondary main noises such as laser frequency noise and optical platform jitter: ∑ j＝{1,2,3,1′,2′,3′} F j (D1,D2,D3,D 1′ D 2′ D 3′ )η j (t)=f(H)+O(t) (9); In the above equation (9), F j is the solution of the time-delay interference scheme and is a polynomial about the delay operator; f(H) is a polynomial of the gravitational wave signal; O is a polynomial of secondary noises such as the phase meter readout noise and the inertial sensor displacement noise; η is the inter-satellite test mass to test mass interference measurement data formed by splicing; D is the time-delay operator in the previous formula; t represents time; Then calculate the solutions of the time-delay interference and the first-generation time-delay interference basic combination from the above algebraic relationship (9).

4. The time-delay interference ground semi-physical experimental verification scheme according to claim 1, characterized in that The specific process of achieving compensation for the difference in the equivalent interference measurement arm length and further suppressing the laser frequency noise in the step (3) is as follows: Build an equivalent million-kilometer arm-length unequal-arm Michelson interferometer semi-physical simulation platform by combining the arm-locking frequency stabilization system and the electronics phase time-delay system; through this simulation platform, after processing the laser passing time delay, phase-locked return, etc., interfere with the local laser beat frequency to obtain the frequency or phase measurement data y1(t) and y2(t); for noise evaluation, the experimental platform includes the ultra-stable reference carrier laser interferometry data y0(t); the measurement signal includes the frequency instability noise of the local laser: y1(t) = p(t - L1) - p(t) + N1(t) (10); y2(t) = p(t - L2) - p(t) + N2(t) (11); The above optical path simulates the unequal-arm Michelson interferometric measurement of the two arms in orbit of the space gravitational wave detection mission, and the data of this interferometric measurement is: y2(t) - y1(t) = p(t - L2) - p(t - L1) + N2(t) - N1(t) (12); The measurement accuracy of this interferometric measurement is affected by the laser frequency noise p(t - L2) - p(t - L1); according to the Michelson type time-delay interference data processing algorithm combination of the space gravitational wave detection mission, combine the time-delayed ground fiber interferometry data: D1y2(t) = p(t - L2 - L1) - p(t - L1) + N2(t - L1) (13); D2y1(t) = p(t - L1 - L2) - p(t - L2) + N1(t - L2) (14); The Michelson - type time - delay combined data is obtained as follows: X1(t) = (D1y2(t) + y1(t)) - (D2y1(t) + y2(t)) = N2(t - L1) + N1(t) - N1(t - L2) - N2(t) (15); Finally, the effective suppression of the laser frequency noise is achieved.

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