Time delay interferometric ground-based semi-physical experimental verification scheme

Abstract

The application provides a time delay interferometric ground semi-physical experimental verification scheme, which comprises the following steps: (1) based on a space gravitational wave detection task and a load configuration scheme, acquiring a space gravitational wave detection task core measurement, and recording measurement data; (2) constructing an algebraic relationship of a time delay interferometric scheme capable of effectively eliminating laser frequency noise and secondary noise such as optical platform jitter, and calculating a first generation time delay interference and a first generation basic combination solution according to the algebraic relationship; (3) repeating the above step (2) for multiple rounds, compensating for the difference of the equivalent interference measurement arm length, and further suppressing laser frequency noise. The application has reasonable concept, and a semi-physical simulation platform of an equivalent million kilometer arm length unequal arm Michelson interferometer is built by combining a lock arm frequency stabilization system and an electronic phase delay system, so that effective suppression of laser frequency noise is realized.

Description

Technical Field

[0001] This invention relates to the field of time-delay interferometry (TDI) technology, specifically to a ground-based semi-physical experimental verification scheme for time-delay interferometry. Background Technology

[0002] The core objective of time-delay interferometry (TDI) is to effectively eliminate noise (such as noise induced by gravitational waves and other interference) by delaying and interferometrically synthesizing laser signals from multiple detection points. Space-based gravitational wave detectors, such as LISA, rely on detection arrays consisting of three or more satellites. 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-based semi-physics experiments are crucial for verifying TDI (Transient Direction Induction) technology in space-based gravitational wave detectors. These experiments typically simulate specific physical processes in the space environment, testing TDI's performance by reproducing its operation in a ground-based environment. The objectives of these ground-based semi-physics experiments include:

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

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

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

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

[0008] Several key experimental methods have been proposed and applied in laboratory and ground-based facilities for validating TDI technology:

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

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

[0011] (3) High-precision noise modeling: In order to test the noise suppression effect of TDI technology, known noise sources, such as electromagnetic noise and vibration noise, will be added to the interferometer 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 future directions of existing ground-based semi-physics experiments are as follows:

[0014] (1) Difficulty in simulating the space environment: Ground-based experiments cannot perfectly replicate the conditions of the space environment (such as vacuum, microgravity, etc.), which limits the verification of some technologies. Therefore, the experimental scheme needs to optimize the simulation process as much as possible to make it closer to the space conditions.

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

[0016] (3) Long-term stability and real-time processing capability: Space probes usually need to work stably for a long time in extreme environments; ground-based semi-physical 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 technical cooperation: The realization of TDI technology involves knowledge from multiple fields such as laser technology, optical systems, data processing, and space physics; future research will require cooperation from experts in various fields to further optimize the technology and experimental schemes.

[0018] The existing technologies for ground-based semi-physical experiments are as follows:

[0019] (1) Noise modeling and simulation: Noise modeling is very important in ground-based semi-physical experiments. Experiments usually simulate the effects of ground vibration, minor vibrations of buildings, air flow and other factors on the signal. By simulating these noise sources, it is possible to test how TDI technology can effectively eliminate these interferences and obtain clearer gravitational wave signals.

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

[0021] The existing technical problems with ground-based semi-physical experiments are as follows:

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

[0023] ① Ground noise interference: Ground-based gravitational wave detection experiments are affected by various environmental noises such as building vibration, earthquake noise, and air flow, making it difficult to distinguish gravitational wave signals from noise components in the interference signal, which seriously affects the effectiveness of TDI technology;

[0024] ② Differences between experimental environment and space conditions: There are significant differences between the ground experimental environment and the working conditions of space probes, especially the microgravity and vacuum conditions, which are difficult to replicate. As a result, the experimental verification process of TDI technology lacks application testing in a real environment.

[0025] ③ Signal processing precision 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 precision requirements for signal delay synthesis are extremely high, and existing experimental schemes are difficult to achieve sufficiently high sensitivity and stability.

[0026] ④ Limitations of the verification scheme: Existing ground verification experiments often use a single test method and lack a comprehensive experimental scheme that can fully verify the performance of TDI technology under various noise environments; existing schemes fail to fully simulate noise sources and operating conditions in the space environment, thus affecting the comprehensive verification of TDI technology.

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

[0028] To address the technical problems existing in the background art mentioned above, this invention proposes a time-delayed interferometric ground-based semi-physical experimental verification scheme. Its concept is reasonable. It will combine the locking arm frequency stabilization system and the electronic phase delay system to build a semi-physical simulation platform for an unequal-arm Michelson interferometer with an equivalent million-kilometer arm length, thereby achieving effective suppression of laser frequency noise.

[0029] To address the aforementioned technical problems, this invention provides a time-delayed interferometry ground-based semi-physical experiment verification scheme, which includes the following steps:

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

[0031] (2) Construct an algebraic relationship for a time delay interference scheme that effectively eliminates secondary noise such as laser frequency noise and optical platform jitter. Calculate the solution of the first-generation time delay interference and the first-generation basic combination based on this algebraic relationship. If there is still a large residual laser frequency noise after the first-generation time delay interference, the second-generation time delay interference can be selected. The second-generation time delay interference is still calculated based on the aforementioned algebraic relationship.

[0032] (3) Repeat step (2) above multiple times to compensate for the difference in the equivalent interferometric measurement arm length and further suppress laser frequency noise.

[0033] The time-delayed interferometric ground semi-physical experiment verification scheme, wherein the core measurement of the mission in step (1) includes laser interferometric ranging data between six satellites via three measuring arms; each laser interferometric ranging data between satellites consists of the test quality from the inertial sensor of the first satellite to the local optical platform, the inter-satellite optical platform, and the test quality from the optical platform of the second satellite to the local platform;

[0034] Each satellite contains six core scientific measurement data streams, and each optical platform includes inter-satellite interpolation interferometry s(t), local test quality to optical platform interferometry ε(t), and adjacent optical platform reference interferometry τ(t):

[0035]

[0036] In equations (1)-(7) above, 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, λ represents the laser wavelength; N(t) is other readout noise; where the subscripts of all characters in equations (1)-(7) indicate according to Figure 1 The numbers are labeled, with counterclockwise labeled 1, 2, 3, and clockwise labeled 1′, 2′, 3′. The numbers 1, 2, and 3 represent the numbers of three different satellites. The superscripts of all characters in formulas (1)-(6) indicate the optical platform represented by s, ε, or τ. N opt (t) represents optical path noise.

[0037] The time-delayed interferometric ground-based semi-physical experiment verification scheme, wherein the specific process of step (2) is as follows:

[0038] Define the time delay operator:

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

[0040] Construct the algebraic relationship for a time-delay interferometry scheme that effectively eliminates secondary primary 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 equation (9) above, F j Let f(H) be the solution to the time-delay interferometry scheme, and η be the polynomial in terms of the delay operator; f(H) be the polynomial of the gravitational wave signal; O be the polynomial of secondary noises such as phase meter readout noise and inertial sensor displacement noise; η be the inter-satellite test quality to test quality interferometric measurement data formed by splicing; D is the time delay operator in the previous formula; t represents time.

[0043] Then, the solution of the time delay interference and the basic combination of the first generation time delay interference is calculated by the above algebraic relation (9).

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

[0045] A semi-physical simulation platform for an equivalent million-kilometer-long unequal-arm Michelson interferometer was constructed by combining a locked-arm frequency stabilization system and an electronic phase delay system. Through this simulation platform, laser parasitic delay and phase-locked return were processed and then interfered with the local laser beat frequency to obtain frequency or phase measurement data y1(t) and y2(t). To achieve noise assessment, the experimental platform included the ultra-stable reference carrier laser interferometric data y0(t). The measurement signal contained local laser frequency instability noise.

[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 interferometry formed by the two arms of a space gravitational wave detection mission in orbit. The data from this interferometry are as follows:

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

[0050] The accuracy of this interferometry is affected by the laser frequency noise p(t-L2)-p(t-L1); based on the Michelson type time-delay interferometric data processing algorithm of the space gravitational wave detection mission, the time-delayed ground fiber interferometric data are combined as follows:

[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 combination data is 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] Ultimately, this achieves effective suppression of laser frequency noise.

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

[0058] The time-delay interferometric ground-based semi-physical experimental verification scheme of this invention is reasonably conceived. It combines a locking arm frequency stabilization system and an electronic phase delay system to build a semi-physical simulation platform for an unequal-arm Michelson interferometer with an equivalent million-kilometer arm length, thereby achieving effective suppression of laser frequency noise.

[0059] Applying the time-delay interferometry ground-based semi-physical experimental verification scheme of this invention, a semi-physical simulation experimental platform integrating a frequency noise suppression system was successfully constructed within the main vacuum chamber of the picometer-level laser interferometry experimental platform at the Huairou Campus of the Institute of Mechanics, Chinese Academy of Sciences. This platform effectively simulates the on-orbit scientific operation of two measurement arms, L3 and L2, of the three-star gravitational wave detection array, generating measurement data. It enables the implementation of various arm-locking frequency stabilization techniques and the semi-physical verification of first-generation and second-generation Michelson-type time-delay interferometry data processing technologies. The vacuum chamber, located in a Class 1000 cleanroom, has an inner diameter of four meters and can maintain a noise level better than 10 for extended periods. -5The vacuum chamber is equipped with an optical experimental table, suspension mechanism, heat sink and other necessary devices. The cables are connected to the integrated frequency noise suppression semi-physical simulation system in the chamber, thereby realizing the control of the experiment and the acquisition of data.

[0060] Based on the application of the time-delay interferometry ground-based semi-physical experiment verification scheme of this invention, relying on 10 -5 The Pa-level ultra-high vacuum environment and active temperature control system can effectively suppress gas refractive index fluctuations and phase noise; experimental data show that the phase noise spectral density at 0.1 Hz is less than 10. -6 rad / √Hz, meeting the requirements for space applications.

[0061] The time-delay interferometry ground-based semi-physical experiment adopts a split optical module architecture, supports rapid switching of the locking arm frequency stabilization scheme, and the phase delay system has a parallel processing capability of 128 channels with a time delay resolution of 0.1ps, providing a hardware foundation for the pre-research of third-generation noise reduction algorithms.

[0062] This invention constructs an equivalent mega-kilometer-scale interferometer arm based on an electronic phase delay system, breaking through the physical arm length limitations of ground-based laboratories and realizing the detection of 10-kilometer-scale gravitational waves in space at Taiji. 6 Simulation of laser frequency noise suppression characteristics of a km-scale ultra-long interferometer arm. Compared with traditional kilometer-scale delay schemes, the electronic phase delay system increases the equivalent arm length by three orders of magnitude and extends the noise suppression bandwidth to the critical frequency band of 0.1 mHz-1 Hz.

[0063] The verification scheme of this invention can be used to complete the design of an integrated system for suppressing and eliminating laser frequency noise. The design specifications meet the requirements of suppressing laser frequency noise by no less than 8 orders of magnitude in the 0.1mHz to 0.1Hz frequency band and by no less than 6 orders of magnitude in the 0.1Hz to 1Hz frequency band.

[0064] The verification scheme of this invention can be used to complete laser measurement link noise analysis, including the reliability, completeness, and stability analysis of the noise source, covering the 1 pm / Hz range within the measurement frequency band. 1 / 2 The above noise levels are addressed. A numerical simulation system design for an integrated laser frequency suppression and elimination system was completed. The design accuracy of the modeling and analysis is better than 0.05 pm / Hz in the 0.1 mHz to 1 Hz frequency band. 1 / 2 .

[0065] The verification scheme of this invention can be used to complete the design of a semi-physical simulation platform for an integrated laser frequency suppression and elimination system. The semi-physical simulation design specifications meet the requirements of suppressing laser frequency noise by no less than 8 orders of magnitude in the 0.1mHz to 0.1Hz frequency band and by no less than 6 orders of magnitude in the 0.1Hz to 1Hz frequency band.

[0066] To address the discrepancy between the ground-based semi-physical simulation noise level and the actual on-orbit noise index in integrated frequency noise suppression, the verification scheme of this invention can be used to complete the research on equivalence and consistency evaluation methods, ensuring that the initial laser frequency noise (1mHz to 1Hz) does not exceed 30Hz / Hz. 1 / 2 The assessment requirements.

[0067] The verification scheme of this invention can be used to design a time-delay interferometry system, with design specifications showing a reduction in laser frequency noise of no less than 6 orders of magnitude in the 0.1 mHz to 0.1 Hz frequency band and no less than 5 orders of magnitude in the 0.1 Hz to 1 Hz frequency band. The verification scheme of this invention can also be used to design a numerical simulation system for time-delay interferometry, with a design accuracy of better than 0.05 pm / Hz in the 0.1 mHz to 1 Hz frequency band. 1 / 2 . Attached Figure Description

[0068] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0069] Figure 1 This is a laser image of the core interferometric data from the space gravitational wave detection mission involved in the time-delay interferometry ground-based semi-physical experiment verification scheme of this invention;

[0070] Figure 2 This is a diagram of the Michelson-type TDI combination involved in the time-delay interferometry ground-based semi-physical experimental verification scheme of this invention;

[0071] Figure 3 This is a diagram of the Sagnac-type TDI combination involved in the time-delay interferometry ground-based semi-physical experimental verification scheme of this invention;

[0072] Figure 4 This is a diagram of the symmetrical Sagnac TDI combination involved in the time-delayed interferometry ground-based semi-physical experimental verification scheme of this invention;

[0073] Figure 5 This is a diagram showing the missing TDI combination involved in the time-delay interferometry ground-based semi-physical experimental verification scheme of the present invention;

[0074] Figure 6 This is a schematic diagram of the unequal-arm Michelson laser interferometer involved in the time-delay interference ground-based semi-physical experimental verification scheme of the present invention;

[0075] Figure 7This is a diagram of the unequal-arm Michelson interferometry formed by the on-orbit dual-arm measurement of the space gravitational wave detection mission involved in the time-delay interferometry ground-based semi-physical experiment verification scheme of the present invention.

[0076] Figure 8 The diagram shows the unequal-arm Michelson-type time-delay interferometry scheme for space gravitational wave detection involved in the time-delay interferometry ground-based semi-physical experimental verification scheme of this invention.

[0077] Figure 9 This is the logical optical path diagram of the time-delay interferometry ground-based semi-physical experimental verification scheme and the Michelson interferometer semi-physical simulation platform of the present invention. Detailed Implementation

[0078] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] The present invention will be further explained below with reference to specific embodiments.

[0080] This embodiment provides a time-delayed interferometric ground-based semi-physical experiment verification scheme, which is designed based on the space gravitational wave detection mission and payload configuration scheme. The core measurement data of the mission includes laser interferometric ranging data between six satellites via three measurement arms. Each satellite ranging data path is composed of three laser interferometric measurements connected end-to-end: the test quality of the first satellite's inertial sensor to the local optical platform, the inter-satellite optical platform, and the optical platform of the second satellite to the local test quality. The measurement data is recorded below. Each satellite contains six core scientific measurement data paths. Each optical platform includes inter-satellite extrapolated interferometry s(t), local test quality to optical platform interferometry ∈(t), and adjacent optical platform reference interferometry τ(t):

[0081]

[0082]

[0083]

[0084] In equations (1)-(7) above, 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, λ represents the laser wavelength, and N(t) is other readout noise including platform instability, temperature fluctuations, fiber optics, etc.; where the subscripts of all characters in equations (1)-(7) indicate according to Figure 1 The markings are arranged counterclockwise as 1, 2, 3, and clockwise as 1′, 2′, 3′. The numbers 1, 2, and 3 represent the numbers of three different satellites. The superscripts of all characters in formulas (1)-(6) above represent the optical platforms represented by s, ε, or τ. The measurement signal subscripts are marked according to a counterclockwise rotation around the constellation, such as... Figure 1 As shown.

[0085] Define the time delay operator (where i represents the satellite number):

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

[0087] Construct the algebraic relationship for a time-delay interferometry scheme that effectively eliminates secondary primary 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] In equation (9) above, F j Let f(H) be the solution for the time-delay interferometry scheme, f(H) be the polynomial of the delay operator, O be the polynomial of secondary noise such as phase meter readout noise and inertial sensor displacement noise, η be the inter-satellite test quality to test quality interferometric measurement data 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] The solution to the time delay interferometry and the basic combination of the first-generation time delay interferometry can be calculated from the above algebraic relation (9). If there is still a large residual laser frequency noise after the first-generation time delay interferometry processing, the second-generation time delay interferometry technology can be selected. Its optical path combination configuration is as follows: Figure 2-5 As shown.

[0091] All possible combinations of the first-generation time-delay interferometry scheme can be obtained by combining the above-mentioned basic scheme. The first-generation scheme is suitable for relatively ideal mission trajectory situations where the influence of arm length variation is negligible. When the influence of three-star arm length variation is significant, and there is still a large residual laser frequency noise after the first-generation time-delay interferometry processing, the second-generation time-delay interferometry technique can be selected. The second-generation scheme is still derived from the above-mentioned basic scheme. Its principle is to compensate for the difference in equivalent interferometric measurement arm length by repeating the first-generation scheme multiple times, thereby further suppressing laser frequency noise.

[0092] This time-delay interferometric ground-based semi-physical experimental verification scheme will combine a locked-arm frequency stabilization system and an electronic phase delay system to build a semi-physical simulation platform for a Michelson interferometer with unequal arm lengths equivalent to one million kilometers. A schematic diagram is shown below. Figure 6 As shown:

[0093] The two measurement arms in the diagram represent components of the electronic experimental system, with arm lengths capable of dynamic simulation without drag control. This simulation platform processes the laser beam through time delay and phase-locked return, then interferes with the local laser beat frequency to obtain frequency or phase measurement data y1(t) and y2(t). For noise assessment, the interferometer semi-physical simulation platform includes the local ultra-stable reference carrier laser interferometric data y0(t). The measurement signal from the semi-physical experimental platform includes local laser frequency instability noise.

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

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

[0096] In equation (10) above, N(t) represents other noises, including platform instability, temperature fluctuations, and optical fiber. Figure 6 The optical path in the simulation depicts the unequal-arm Michelson interferometry formed by the two arms of a space gravitational wave detection mission in orbit, as shown below. Figure 7 As shown.

[0097] The data from this interferometry measurement are as follows:

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

[0099] The measurement accuracy of the unequal-arm Michelson interferometry formed by the two arms of the space gravitational wave detection mission is affected by the laser frequency noise p(t-L2)-p(t-L1). Based on the Michelson-type time-delay interferometric data processing algorithm of the space gravitational wave detection mission, the time-delayed ground-based fiber optic interferometric data is combined, and the optical path is shown below. Figure 8 As shown.

[0100] Combine time-delayed ground-based fiber optic interferometric 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 equations (13)-(14) above, D refers to the time delay operator, where the subscripts 1 and 2 of the time delay operator D indicate which detector is which, such as... Figure 1 As shown in the image;

[0104] The Michelson-type time delay combination data is as follows:

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

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

[0107] Effective suppression of laser frequency noise is achieved.

[0108] The logical optical path of the Michelson interferometer semi-physical simulation platform involved in the time-delay interferometry ground-based semi-physical experimental verification scheme of this invention is as follows: Figure 9 As shown, this simulation demonstrates the on-orbit scientific operation of two measurement arms of the three-star gravitational wave detector constellation, ARM12 (composed of satellite 1 (S / C1) and satellite 2 (S / C2)) and ARM13 (composed of satellite 1 (S / C1) and satellite 3 (S / C3)), and generates measurement data. It enables the implementation of various arm-locking frequency stabilization techniques and semi-physical verification of first-generation and second-generation Michelson-type time-delay interferometric data processing technologies.

[0109] Based on experimental requirements, the Michelson interferometer semi-physical simulation platform uses an ultrastable laser to generate a carrier laser (or reference laser), which is connected to the Michelson interferometer semi-physical simulation platform inside the vacuum chamber via optical fiber. The integrated test system uses a 1064nm Nd:YAG solid-state ultrastable laser, model SLS-1064-300-1000, as the carrier laser source. Figure 9As shown, the carrier laser is split into two main carrier lasers, ARM12 and ARM13, which are respectively connected to the semi-physical simulation system of the ARM12 and ARM13 measuring arms. The optical path design of these two measuring arms is consistent; therefore, the principle and optical path design of the semi-physical simulation will be introduced using the L12 measuring arm as an example in the following text.

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

[0111] Taking the ARM12 measuring arm as an example, the reference carrier laser, after beam splitting, is connected to the No. 1 electro-optic modulator (EMO-1). Based on the numerical simulation input, the signal generator generates the independent frequency instability noise P1(t) of the No. 1 laser L1 of satellite 1, driving EMO-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 3MHz / Hz1 / 2@0.1mHz~30kHz / Hz1 / 2@10mHz, and P0≤300Hz / Hz1 / 2 is the frequency instability noise of the carrier ultra-stable laser. The laser modulated by EMO-1 undergoes heterodyne interference with the reference carrier laser, and the signal is output as the No. 1 beat frequency signal via a photodetector (PD), with frequency noise P1(t). The photodetector used in this experiment is the GD4542-20MHz-12K from the 44th Research Institute of China Electronics Technology Group Corporation. Its performance parameters are shown in the table below. The photodetector has a low noise equivalent power density, which meets the accuracy requirements of the experiment.

[0112] The beat frequency signal No. 1 is acquired by a multi-function phase meter (PM), generating and storing data product No. 1. Data product No. 1, along with the beat frequency data product No. 9 corresponding to the L1' simulated laser of the ARM13 measuring arm, serves as an important reference data product for simulating the initial laser frequency noise of L1 and L1', and is used as a reference benchmark for verifying the frequency stabilization performance index of the locking arm and the time delay interferometry processing performance index.

[0113] To accurately read frequency instability noise signals and feed the information back to the delay system, this experiment requires high measurement accuracy from the phase meter. The multi-functional phase meter used in this experiment is a self-developed product, with a phase measurement accuracy of 2π×10⁻⁶. -6 With a frequency measurement accuracy better than 0.1 mHz and a bandwidth of 1 MHz to 20 MHz, it can meet the measurement requirements of experiments.

[0114] The frequency offset between the interfering beams is achieved by an acousto-optic modulator (AOM). This experiment uses the SGTF150-1064-1P acousto-optic modulator manufactured by the 26th Research Institute of China Electronics Technology Group Corporation (CETC). Its performance parameters are shown in the table below. It features fast response time, low insertion loss, and low power consumption, meeting the experimental requirements.

[0115] The L1 simulated laser signal, after passing through EOM-6, undergoes heterodyne interference with the reference carrier laser. This interference is then processed by a PD to generate beat frequency signal #2. The beat frequency data, acquired and stored by a multi-function phase meter, is then precisely delayed (τ) by an electronic delay system (EPD) to measure the flight time τ of the laser signal from S / C1 to S / C2 within the solar system's center of mass frame. 12 Flight time data τ 12 The orbit (including drag-free and attitude control) is generated based on numerical simulation of the formation system. Simultaneously, 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, and typical incident gravitational wave signals, are simulated and superimposed onto the electrical signal data. Implementing a time delay for the noise is a crucial step in this experiment. A host computer controls the data acquisition card to apply a time delay of 10s to 20s to the noise. The acquisition card used is the NI USB 6289 data acquisition card, and the host computer program is written in LabVIEW. The USB 6289 data acquisition card has an analog input sampling rate of 500kS / s, a time resolution of 50ns, and a sampling rate of 1.54MS / s for the three channels of analog output. The input / output voltage is between -10V and 10V.

[0116] After a time delay τ 12 The subsequent electronic beat frequency signal drives EOM-2, which converts the time-delayed frequency noise P1(t-τ) of the analog laser L1 into P1(t-τ). 12 The simulated laser signal, consisting of gravitational wave coupling H12(t), Doppler frequency shift D12(t), and other noise analog signal N12(t), is modulated onto the reference carrier laser to generate a simulated laser signal propagated through ARM12. The total frequency noise is P1(t-τ). 12 )+P0(t).

[0117] A reference carrier laser is input to EOM-3. Based on numerical simulation input, a signal generator produces independent frequency instability noise P2(t) for laser L2 (S / C2), driving 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 L1 at time τ... 12The previous semi-physical simulation laser signal was heterodyne-interfered and collected by a photodetector to generate beat frequency signal No. 3. The signal contains gravitational wave signal, Doppler frequency shift, other noise, and frequency noise P1(t-τ). 12 The signal is acquired 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 final frequency noise output of the L2 semi-physical equivalent analog laser source is P1(t-τ). 12 )+P0(t) realizes the phase-locked return laser after the laser moves from S / C1 to S / C2.

[0118] The phase-locked return laser, after EOM-4 modulation compensation, undergoes heterodyne interference with the reference carrier laser. The resulting beat frequency signal (signal 4) is acquired by a photodetector, with a frequency noise of P1(t-τ). 12 The beat frequency data, acquired and stored by a multi-functional phase meter, generates Data Product No. 4. This beat frequency data, through an electronic delay system (EPD), precisely delays the flight time τ of the laser signal from S / C2 to S / C1 in the solar system's center of mass system. 21 Flight time data τ 21 Orbit generation is based on numerical simulation of the formation system. Simultaneously, 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 and TTL noise, as well as typical incident gravitational wave signals, are simulated and superimposed onto the electrical signal data. After a time delay τ... 21 The subsequent electronic beat frequency signal drives EOM-5, which returns the phase-locked analog laser L2 and the frequency noise P1(t-τ) after time delay. 12 -τ 21 ) and gravitational wave coupling H21(t), H12(t-τ) 12 Doppler frequency shifts D21(t), D12(t-τ) 12 Other noise analog signals N21(t), N12(t-τ) 12 The signal is modulated onto a reference carrier laser to generate a simulated laser signal propagated through an ARM12, with a total frequency noise of P1(t-τ). 12 -τ 21 At this step, the measuring arm ARM12 has achieved the equivalent semi-physical simulation data laser signal received from S / C1, via phase-locked return from S / C2 to S / C1, reflecting the dynamic effects of orbit and satellite attitude, as well as the coupling of typical gravitational wave signals. This laser signal undergoes heterodyne interferometry with the reference carrier laser signal, and the beat frequency signal No. 5 is acquired by the PD. A phase meter then collects and stores this signal, generating data product No. 5, which contains a total frequency noise of P1(t-τ). 12 -τ 21 ).

[0119] The ARM12 phase-locked loop return semi-physical analog laser signal modulated by EOM-5 is heterodyne-interfered with the L1 semi-physical analog signal. The signal is then acquired by a PD to generate beat frequency signal 6, which is collected and stored by a phase meter and input to the lock arm sensor and controller. The lock arm and sensor controller for this experiment were developed by the project team at the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences.

[0120] Data from test masses 6 and 14, used as semi-physical simulation data for the Samsung formation dual-arm measurement, serve as key input data for time-delay interferometry. Simultaneously, semi-physical simulation data from test masses 8 and 16 are also used as input data for time-delay interferometry. To construct a complete Samsung heterodyne interferometry measurement link, a ground-based inertial reference system was built, and a test mass interferometer was established between the test masses and the optical platform. The two test masses achieve low-interference free motion of translational degrees of freedom through an inverted pendulum and a secondary suspension system, achieving a residual acceleration index of 1×10⁻⁶ for the translational degrees of freedom. -12 m / s 2 / Hz1 / 2. This implements a semi-physical equivalent simulation of the two measuring arms of Samsung, the inertial reference with a total of four translational degrees of freedom, and the four test mass interferometers in this test experiment.

[0121] The aforementioned data products, after processing by the first and second generation unequal-arm Michelson-type time-delay interferometry data, generate X1 and X2 time-delay interferometry channel data products. These are compared with the noise amplitude spectral density of data products 5 and 13 (or data products 1 and 9) in the absence of gravitational wave signals, achieving independent verification of the performance indicators of the time-delay interferometry technology. By adjusting orbital simulation data and inputting fixed arm length configurations and dynamic formations under this control without drag, the performance and applicability of the first and second generation time-delay interferometry technologies are verified respectively.

[0122] The X1 and X2 first-generation and second-generation unequal-arm Michelson-type time-delay interferometric channel data products were compared with the initial class physical simulation data laser frequency noise data products No. 1 and No. 9 to verify and evaluate the performance indicators of the time-delay interferometric integrated frequency suppression system. Simultaneously, by adjusting the input modulated gravitational wave signal, orbital configuration, drag-free and attitude control effects, and load anomalies, the performance indicators of the integrated laser frequency noise suppression system in improving the gravitational wave detection signal-to-noise ratio, the robustness of frequency noise suppression, and the factors affecting potential performance loss were fully verified.

[0123] This invention is well-conceived and combines a locking arm frequency stabilization system with an electronic phase delay system to build a semi-physical simulation platform for an unequal-arm Michelson interferometer with an equivalent million-kilometer arm length, thereby achieving effective suppression of 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, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions 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 interferometry ground-based semi-physical experiment verification scheme, characterized in that, Includes the following steps: (1) Based on the space gravitational wave detection mission and payload configuration scheme, acquire the core measurement data of the space gravitational wave detection mission and record the measurement data; (2) Construct an algebraic relationship for a time-delay interferometry scheme that effectively eliminates laser frequency noise and secondary noise from optical platform jitter. Calculate the solution for the first-generation time-delay interferometry and the first-generation basic combination based on this algebraic relationship. If residual laser frequency noise still exists after the first-generation time-delay interferometry, then the second-generation time-delay interferometry is selected. The second-generation time-delay interferometry is also calculated based on the aforementioned algebraic relationship. The specific process is as follows: Define the time delay operator: （8）； Construct the algebraic relationship for a time-delay interferometry scheme that effectively eliminates both laser frequency noise and secondary noise from optical platform jitter: （9）； In equation (9) above, F j Let f(H) be the solution for the time-delayed interferometry scheme, and let O be the polynomial in terms of the delay operator; f(H) is the polynomial of the gravitational wave signal; O is the polynomial of the phase meter readout noise and the secondary noise of the inertial sensor displacement noise. The data represents the inter-satellite test quality to test quality interferometry data constructed by splicing together the data; D is the time delay operator in the previous formula; t represents time. Then, the solution to the time delay interference and the first-generation time delay interference basic combination is calculated using the above algebraic relation (9); (3) Repeat step (2) above multiple times to compensate for the difference in equivalent interferometric measurement arm length and further suppress laser frequency noise. The specific process is as follows: A semi-physical simulation platform for an equivalent million-kilometer-long unequal-arm Michelson interferometer was constructed by combining a locked-arm frequency stabilization system and an electronic phase delay system. Through this simulation platform, laser parasitic delay and phase-locked return processing were performed, followed by beat frequency interference with the local laser to obtain frequency or phase measurement data y1(t) and y2(t). To achieve noise assessment, the experimental platform included the ultra-stable reference carrier laser interferometric data y0(t). The measurement signal contained local laser frequency instability noise. （10）; （11）; The above optical path simulates the unequal-arm Michelson interferometry formed by the two arms of a space gravitational wave detection mission in orbit. The data from this interferometry are as follows: （12）; The accuracy of this interferometry is affected by laser frequency noise. The impact; based on the Michelson type time-delay interferometric data processing algorithm of the space gravitational wave detection mission, the ground fiber interferometric data after time delay are combined: （13）； （14）； The Michelson-type time delay combination data is as follows: (15); Ultimately, this achieves effective suppression of laser frequency noise.

2. The time-delay interferometry ground-based semi-physical experiment verification scheme as described in claim 1, characterized in that, The core measurement in step (1) includes laser interferometric ranging data between six satellites via three measuring arms. Each satellite laser interferometric ranging data consists of the test quality from the inertial sensor of the first satellite to the local optical platform, the inter-satellite optical platform, and the test quality from the optical platform of the second satellite to the local platform. Each satellite contains six core scientific measurement data streams, and each optical platform includes inter-satellite interferometry. From local test quality to optical platform interferometry and adjacent optical platform reference interferometry : （1）； （2）； （3）； （4）； （5）； （6）； （7）； In equations (1)-(7) above, t represents time, H represents the gravitational wave signal, and p is the laser frequency noise. This refers to the noise caused by displacement of the optical platform. To test the mass displacement jitter noise, For fiber optic noise, L represents the distance between satellites. The wavelength of the laser is represented; N(t) represents other readout noise; the subscripts of all characters in formulas (1)-(7) are labeled according to Figure 1, proceeding counterclockwise according to 1, 2, 3, and clockwise according to To represent this, the numbers 1, 2, and 3 represent the numbers of three different satellites; the superscripts of all characters in formulas (1)-(6) are represented in s, The optical platform represented; This indicates optical path noise.

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