Interference fringe fitting method and system for cold atom interferometer gyroscope

Abstract

The present invention provides a method and system for fitting interference fringes for a cold atom interferometer gyroscope. The method comprises: obtaining a mathematical model of the interference fringes of the cold atom interferometer gyroscope, linearizing the interference fringes model based on trigonometric functions to obtain a corresponding linear function; solving the linear correlation coefficient in the linear function using the least squares method based on the currently sampled transverse fringe phase and atomic transition probability; and expanding the range of fringe initial phase values. Within the expanded range of fringe initial phase values, the interference fringes are fitted based on the linear correlation coefficient and the real-time sampled transverse fringe phase and atomic transition probability. This solution ensures the accuracy of interference fringe fitting and improves the fitting speed, meeting the real-time requirements of interference fringe fitting.

Description

Technical Field

[0001] The present invention belongs to the field of atomic interferometer gyroscopes, and in particular relates to an interference fringe fitting method and system for a cold atom interferometer gyroscope. Background Art

[0002] In the past decade, atom interferometry has been rapidly developed and widely used. Due to its high sensitivity and quantum properties, it has potential application prospects in the field of quantum precision measurement. In atom interferometry experiments, the interference fringes of matter waves can usually be fitted by modeling. The mathematical model is generally modeled as , is the vertical coordinate of the stripe, which represents the transition probability obtained by detection, Represents the horizontal coordinate of the fringe, that is, the fringe phase.

[0003] Currently, the interference fringe fitting method is based on the observed phase and transition probability Interference fringes can be fitted using the curve fitting functionality of data analysis software, such as Origin or MATLAB. In MATLAB, you can call the fit function or directly use tools such as the Curve Fitting Toolbox. This method typically only performs post-analysis and fitting based on experimental results to ensure accuracy, resulting in poor real-time performance. Summary of the Invention

[0004] In view of this, an embodiment of the present invention provides an interference fringe fitting method and system for a cold atom interferometer gyroscope, which is used to solve the problem of poor real-time performance of current interference fringe fitting.

[0005] In a first aspect of an embodiment of the present invention, a method for fitting interference fringes of a cold atom interferometer gyroscope is provided, comprising:

[0006] Obtaining a mathematical model of interference fringes of a cold atom interferometer gyroscope, and linearizing the mathematical model of interference fringes based on trigonometric functions to obtain a corresponding linear function;

[0007] Based on the currently sampled transverse fringe phase and atomic transition probability, the linear correlation coefficient in the linear function is obtained by solving it using the least square method;

[0008] The range of fringe initial phase values ​​is expanded. Within the expanded range of fringe initial phase values, the interference fringes are fitted based on the linear correlation coefficient and the real-time sampled transverse fringe phase and atomic transition probability.

[0009] In a second aspect of an embodiment of the present invention, an interference fringe fitting system for a cold atom interferometer gyroscope is provided, comprising:

[0010] A linearization module is used to obtain a mathematical model of interference fringes of a cold atom interferometer gyroscope, and linearize the mathematical model of interference fringes based on trigonometric functions to obtain a corresponding linear function;

[0011] The coefficient solving module is used to solve the linear correlation coefficient in the linear function by the least square method based on the currently sampled transverse fringe phase and atomic transition probability;

[0012] The fringe fitting module is used to expand the range of fringe initial phase values. Within the expanded range of fringe initial phase values, the interference fringes are fitted based on the linear correlation coefficient and the real-time sampled transverse fringe phase and atomic transition probability.

[0013] In a third aspect of an embodiment of the present invention, an electronic device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable by the processor, wherein the processor implements the steps of the method described in the first aspect of the embodiment of the present invention when executing the computer program.

[0014] In a fourth aspect of an embodiment of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method provided in the first aspect of the embodiment of the present invention are implemented.

[0015] In an embodiment of the present invention, the mathematical model of the interference fringes is converted into a corresponding linear function based on trigonometric functions, and the linear correlation coefficient is solved according to the actual sampling value. The interference fringes are fitted based on the linear correlation coefficient and the expanded initial phase value of the fringe. Therefore, while ensuring the fitting accuracy of the interference fringes of the cold atom interferometer gyroscope, the fitting speed is improved and the real-time requirements can be met. It has the advantages of high fitting accuracy, fast calculation speed, and suitability for embedded real-time computing. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments or descriptions of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0017] Figure 1 A schematic flow chart of an interference fringe fitting method for a cold atom interferometer gyroscope provided in accordance with one embodiment of the present invention;

[0018] Figure 2 A schematic diagram of an initial phase distribution provided by an embodiment of the present invention;

[0019] Figure 3A schematic structural diagram of an interference fringe fitting system for a cold atom interferometer gyroscope provided by one embodiment of the present invention;

[0020] Figure 4 The present invention provides a schematic structural diagram of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0021] In order to make the purpose, features, and advantages of the present invention more obvious and easy to understand, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described below are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0022] It should be understood that the terms "including" and similar expressions in the specification, claims, and drawings of the present invention are intended to cover non-exclusive inclusions. For example, a process, method, system, or apparatus comprising a series of steps or units is not limited to the listed steps or units. Furthermore, the terms "first" and "second" are used to distinguish between different objects and are not intended to describe a specific order.

[0023] As you can understand, typical interference fringes are typically obtained by scanning the transverse-axis phase in atomic gravimeters and by scanning the phase or recording the vibration phase during the interference period in atomic gyroscopes or atomic accelerometers. Fitting interference fringes based on the acquired transverse-axis phase and transition probabilities typically requires the built-in curve fitting functionality of common data analysis software (such as Origin or MATLAB). This approach ensures the accuracy of the fitting results, but is only suitable for post-analysis data analysis and does not meet real-time requirements.

[0024] The difficulty in real-time fitting interference fringes lies in the fact that the trigonometric functions sin and cos are nonlinear, making them impractical to directly perform a linear fit using the least squares method. Using MATLAB to compile the fit function into a dynamic link library or generate C code presents challenges with developing an environment and slow computation speeds, making it unsuitable for real-time computation on embedded processors such as DSPs. In terms of computational speed, a single fit has been measured to take up to 100ms, which is unacceptable for experiments with high data output rates.

[0025] Therefore, it is necessary to design a sin / cos trigonometric function fitting algorithm that can be implemented using C language (or C++ and other languages) to meet the requirements of real-time updating of the interference fringe fitting curve in atomic interferometry experiments.

[0026] See also Figure 1, a schematic flow chart of an interference fringe fitting method for a cold atom interferometer gyroscope provided by an embodiment of the present invention, comprising:

[0027] S101, obtaining a mathematical model of interference fringes of a cold atom interferometer gyroscope, and linearizing the mathematical model of interference fringes based on trigonometric functions to obtain a corresponding linear function;

[0028] A cold atom interferometer gyroscope is a gyroscope that uses the quantum properties of cold atoms to measure rotational angular velocity and linear acceleration. It includes a cold atom gyroscope and a cold atom interferometer.

[0029] The mathematical model of interference fringes is generally: Trigonometric functions represent the mapping between a set of arbitrary angles and a set of ratios, and include sine, cosine, and tangent functions. Based on the relationship between trigonometric functions, the mathematical model of interference fringes can be transformed and expressed as a linear function.

[0030] Specifically, the interference fringe mathematical model (1) is converted into formula (2) based on trigonometric function conversion:

[0031] ; (1)

[0032] Using trigonometric formulas ,have

[0033]

[0034]

[0035]

[0036] Right now ; (2)

[0037] definition , , ;

[0038] Then the linear function is expressed as:

[0039] ; (3)

[0040] Where P represents the transition probability value, P0 represents the fringe bias, and A represents the fringe amplitude. represents the fringe phase, represents the initial phase of the fringe, 、 、 Both represent linear correlation coefficients.

[0041] Thus, the nonlinear function Mathematically transformed into a linear function .

[0042] S102, based on the currently sampled transverse fringe phase and atomic transition probability, obtain a linear correlation coefficient in the linear function by using a least squares method;

[0043] The horizontal fringe phase can generally be obtained by scanning the phase or recording the vibration phase during the interference period, and the atomic transition probability can be obtained by spectral analysis, that is, measuring the spectral characteristics emitted or absorbed by the transition of atoms between different energy levels to determine the transition probability.

[0044] According to the experimentally collected horizontal fringe phase and transition probability values, a set of equations is constructed and the linear correlation coefficient in the linear function is obtained by solving it using the least squares method. That is, based on the least squares method, according to the known fringe phase and transition probability , fitting the correlation coefficient in the linear function 、 、 The value of .

[0045] Among them, based on the calculated linear correlation coefficient value and the definition of the linear correlation coefficient, the fringe bias, fringe amplitude and fringe initial phase are solved.

[0046] According to the relationship between the linear correlation coefficient and the fringe bias, fringe amplitude and fringe initial phase, that is, , , , and then the fringe bias can be obtained , fringe amplitude and the initial phase of the fringe .

[0047] S103, expanding the range of fringe initial phase values, and fitting the interference fringes within the expanded range of fringe initial phase values ​​based on the linear correlation coefficient and the real-time sampled transverse fringe phase and atomic transition probability.

[0048] It's understandable that in interference phenomena, changes in the initial phase have a significant impact on the formation and distribution of interference fringes. When two coherent waves meet and interfere, the difference in their initial phases leads to the appearance of interference fringes. Specifically, the initial phase determines the location of the peaks and troughs, affecting the distribution of light and dark in the interference fringes. If the two beams have the same initial phase, they interfere constructively, forming bright fringes. If the initial phases differ by half a period (i.e., π, or 180 degrees), they interfere destructively, forming dark fringes.

[0049] Specifically, according to the linear correlation coefficient and The positive or negative value of the fringe is used to determine the quadrant to which the fringe initial phase belongs. Based on the quadrant to which the fringe initial phase belongs, the range of the fringe initial phase value is expanded to .

[0050] Calculate the initial phase of the fringe The formula is , the effective range of phase is determined by decided, and the scope does not exceed (For example, if you use the default C language math library to calculate atan, the output range is ). However, the actual range of the interference phase is determined by arcsin2 , so the linearization process will make the initial phase The effective range is reduced by half.

[0051] Can be based on and The symbol of and The sign of The quadrant to which it should belong, re-extend the phase to , please refer to the following table for details:

[0052]

[0053] based on and initial phase The quadrant to which it belongs, combined with Figure 2 Can be obtained in Values ​​within the range, Figure 2 The figure shows the The value within the range, that is, the value within 0-360°.

[0054] In some examples, the proposed method was validated using a Xilinx Zynq XC7Z020 processor, utilizing actual atomic interferometry experimental data (primarily transition probabilities, scanning phase parameters, and vibrational phase data), and a least-squares fitting algorithm and fringe fitting program implemented in C. The experiments demonstrated accurate calculation results and significant computational speed advantages.

[0055] Specifically, 5-point fitting takes 0.14ms, 8-point fitting takes 0.18ms, 16-point fitting takes 0.27ms, 32-point fitting takes 0.54ms, and 100-point fitting takes 3.46ms. This shows that it can meet the real-time data update rate requirement of over 50Hz.

[0056] In this embodiment, by linearizing the mathematical model of the interference fringes and solving the corresponding linear correlation coefficient using the least squares method, the interference fringes are fitted in the expanded range of fringe initial phase values ​​by combining the real-time sampling values ​​and the linear correlation coefficient. This not only has high fitting accuracy and fast speed, but also can meet the real-time requirements of embedded devices.

[0057] It should be understood that the sequence numbers of the steps in the above embodiments do not imply a specific order of execution; the order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0058] Figure 3 A schematic structural diagram of an interference fringe fitting system for a cold atom interferometer gyroscope provided in an embodiment of the present invention, the system comprising:

[0059] A linearization module 310 is configured to obtain a mathematical model of interference fringes of a cold atom interferometer gyroscope and linearize the mathematical model of interference fringes based on trigonometric functions to obtain a corresponding linear function.

[0060] Specifically, the interference fringe mathematical model (1) is converted into formula (2) based on trigonometric function conversion:

[0061] ; (1)

[0062] ; (2)

[0063] definition , , ;

[0064] Then the linear function is expressed as:

[0065] ; (3)

[0066] Where P represents the atomic transition probability value, P0 represents the fringe bias, and A represents the fringe amplitude. represents the horizontal fringe phase, represents the initial phase of the fringe, 、 、 Both represent linear correlation coefficients.

[0067] The coefficient solving module 320 is used to solve the linear correlation coefficient in the linear function by the least square method based on the currently sampled transverse fringe phase and atomic transition probability;

[0068] Among them, based on the calculated linear correlation coefficient value and the definition of the linear correlation coefficient, the fringe bias, fringe amplitude and fringe initial phase are solved.

[0069] The fringe fitting module 330 is used to expand the range of fringe initial phase values, and fit the interference fringes within the expanded range of fringe initial phase values ​​based on the linear correlation coefficient and the real-time sampled transverse axis fringe phase and atomic transition probability.

[0070] The range of the initial phase value of the extended fringe includes:

[0071] According to the linear correlation coefficient and The positive or negative value of the fringe is used to determine the quadrant to which the fringe initial phase belongs. Based on the quadrant to which the fringe initial phase belongs, the range of the fringe initial phase value is expanded to .

[0072] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described systems and modules can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0073] Figure 4 FIG. 1 is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. The electronic device is used for interference fringe fitting. Figure 4 As shown, the electronic device 4 of this embodiment includes: a memory 410, a processor 420 and a system bus 430, wherein the memory 410 includes an executable program 4101 stored thereon. It can be understood by those skilled in the art that Figure 4 The electronic device structure shown in the figure does not constitute a limitation to the electronic device, and may include more or fewer components than shown in the figure, or combine certain components, or arrange the components differently.

[0074] The following combination Figure 4 A detailed introduction to the various components of electronic equipment:

[0075] Memory 410 can be used to store software programs and modules. Processor 420 executes the software programs and modules stored in memory 410 to perform various functional applications and data processing of the electronic device. Memory 410 may primarily include a program storage area and a data storage area. The program storage area may store an operating system and at least one application required for a function (such as sound playback or image playback). The data storage area may store data generated based on the use of the electronic device (such as cached data). Memory 410 may also include high-speed random access memory and non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state memory device.

[0076] Memory 410 includes an executable program 4101 for a network request method. This executable program 4101 can be divided into one or more modules / units, which are stored in memory 410 and executed by processor 420 to implement real-time interference fringe fitting, etc. These modules / units can be a series of computer program instruction segments capable of performing specific functions, and these instruction segments are used to describe the execution process of computer program 4101 in electronic device 4. For example, computer program 4101 can be divided into functional modules such as a linearization module, a coefficient solution module, and a fringe fitting module.

[0077] Processor 420 is the control center of the electronic device, connecting the various components of the entire electronic device using various interfaces and lines. By running or executing software programs and / or modules stored in memory 410 and accessing data stored in memory 410, it performs various functions of the electronic device and processes data, thereby monitoring the overall status of the electronic device. Optionally, processor 420 may include one or more processing units; preferably, processor 420 may integrate an application processor and a modem processor, wherein the application processor primarily processes the operating system, application programs, etc., and the modem processor primarily handles wireless communications. It is understood that the modem processor described above may not be integrated into processor 420.

[0078] The system bus 430 connects the various functional components within the computer and can transmit data, address information, and control information. It can be a PCI bus, an ISA bus, a CAN bus, or other types. Instructions from the processor 420 are transmitted to the memory 410 via the bus, and the memory 410 feeds data back to the processor 420. The system bus 430 is responsible for the exchange of data and instructions between the processor 420 and the memory 410. Of course, the system bus 430 can also connect to other devices, such as network interfaces and display devices.

[0079] In an embodiment of the present invention, the executable program executed by the processing 420 included in the electronic device includes:

[0080] Obtaining a mathematical model of interference fringes of a cold atom interferometer gyroscope, and linearizing the mathematical model of interference fringes based on trigonometric functions to obtain a corresponding linear function;

[0081] Based on the currently sampled transverse fringe phase and atomic transition probability, the linear correlation coefficient in the linear function is obtained by solving it using the least square method;

[0082] The range of fringe initial phase values ​​is expanded. Within the expanded range of fringe initial phase values, the interference fringes are fitted based on the linear correlation coefficient and the real-time sampled transverse fringe phase and atomic transition probability.

[0083] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described systems, devices, and modules can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0084] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0085] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some of the technical features thereof can be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for fitting interference fringes of a cold atom interferometer gyroscope, characterized in that: include: Obtaining a mathematical model of interference fringes of a cold atom interferometer gyroscope, and linearizing the mathematical model of interference fringes based on trigonometric functions to obtain a corresponding linear function; Based on the currently sampled transverse fringe phase and atomic transition probability, the linear correlation coefficient in the linear function is obtained by solving it using the least square method; The range of fringe initial phase values ​​is expanded. Within the expanded range of fringe initial phase values, the interference fringes are fitted based on the linear correlation coefficient and the real-time sampled transverse fringe phase and atomic transition probability.

2. The method according to claim 1, characterized in that The linearization processing of the interference fringe mathematical model based on trigonometric functions to obtain the corresponding linear function includes: The interference fringe mathematical model (1) is converted into formula (2) based on trigonometric function conversion: ；（1） ；（2） definition , , ; Then the linear function is expressed as: ；（3） Where P represents the atomic transition probability value, P0 represents the fringe bias, and A represents the fringe amplitude. represents the horizontal fringe phase, represents the initial phase of the fringe, 、 、 Both represent linear correlation coefficients.

3. The method according to claim 2, characterized in that The linear correlation coefficient obtained by solving the linear function by the least square method also includes: Based on the calculated linear correlation coefficient value and its definition, the fringe bias, fringe amplitude and fringe initial phase are solved.

4. The method according to claim 3, characterized in that The range of values ​​of the extended fringe initial phase includes: According to the linear correlation coefficient and The positive or negative value of the fringe is used to determine the quadrant to which the fringe initial phase belongs. Based on the quadrant to which the fringe initial phase belongs, the range of the fringe initial phase value is expanded to .

5. An interference fringe fitting system for a cold atom interferometer gyroscope, characterized in that: include: A linearization module is used to obtain a mathematical model of interference fringes of a cold atom interferometer gyroscope, and linearize the mathematical model of interference fringes based on trigonometric functions to obtain a corresponding linear function; The coefficient solving module is used to solve the linear correlation coefficient in the linear function by the least square method based on the currently sampled transverse fringe phase and atomic transition probability; The fringe fitting module is used to expand the range of fringe initial phase values. Within the expanded range of fringe initial phase values, the interference fringes are fitted based on the linear correlation coefficient and the real-time sampled transverse fringe phase and atomic transition probability.

6. The system according to claim 5, characterized in that The linearization processing of the interference fringe mathematical model based on trigonometric functions to obtain the corresponding linear function includes: The interference fringe mathematical model (1) is converted into formula (2) based on trigonometric function conversion: ；（1） ；（2） definition , , ; Then the linear function is expressed as: ；（3） Where P represents the atomic transition probability value, P0 represents the fringe bias, and A represents the fringe amplitude. represents the horizontal fringe phase, represents the initial phase of the fringe, 、 、 Both represent linear correlation coefficients.

7. The system according to claim 6, characterized in that The linear correlation coefficient obtained by solving the linear function by the least square method also includes: Based on the calculated linear correlation coefficient value and its definition, the fringe bias, fringe amplitude and fringe initial phase are solved.

8. The system according to claim 7, characterized in that The range of values ​​of the extended fringe initial phase includes: According to the linear correlation coefficient and The positive or negative value of the fringe is used to determine the quadrant to which the fringe initial phase belongs. Based on the quadrant to which the fringe initial phase belongs, the range of the fringe initial phase value is expanded to .

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the interference fringe fitting method for a cold atom interferometer gyroscope according to any one of claims 1 to 4 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed, the steps of the interference fringe fitting method for a cold atom interferometer gyroscope according to any one of claims 1 to 4 are implemented.

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