Method and apparatus for extracting common-mode alias signals in a shear atomic interferometer

Abstract

The application discloses a method and equipment for extracting same-frequency aliasing signals in a shear atomic interferometer. The same-frequency aliasing interference signals to be fitted are regarded as simple harmonic signals, fitted effective contrast and fitted effective phase are obtained based on the simple harmonic signals, and the contrast prior value of the first atomic interference signal and the contrast prior value of the second atomic interference signal are obtained by inversion. The same-frequency aliasing interference signals to be solved are regarded as simple harmonic signals, the measured effective contrast and the measured effective phase are obtained based on the simple harmonic signals, the absolute value of the phase deviation of the first atomic interference signal to be solved and the second atomic interference signal to be solved is calculated, and the phase of the first atomic interference signal to be solved and the phase of the second atomic interference signal to be solved are calculated. The application can reconstruct the atomic interference signals from the same-frequency aliasing interference signals to be solved, realizes the restoration of the original signals, and realizes the accurate separation of the atomic interference signals.

Description

Technical Field

[0001] This invention belongs to the field of precision measurement physics, specifically relating to a method and device for extracting aliased signals of the same frequency in a shearing atom interferometer, applicable to the extraction of multi-axis inertial sensing signals in a shearing cold atom interferometer and the extraction of signal overlap in a high sampling rate interferometer. Technical Background

[0002] Atomic interferometers are highly precise sensors widely used in gravity measurement, inertial navigation, and fundamental physics research. Traditional atomic interferometers often measure only a single physical quantity, while modern applications require the simultaneous measurement of multiple physical quantities (such as gravity and rotation). For example, Bouyer Canuel et al. demonstrated an atomic interferometer method for simultaneous measurement of gravity and rotation (Phys. Rev. Lett. 97, 010402, 2006), and Alex Sugarbaker et al. implemented an atomic compass for integrating multidimensional atomic optics and multiport parallel inertial sensing into systems (Phys. Rev. Lett. 111, 113002, 2013). This leads to spatial overlap of multi-atom ensembles; or the detection of atomic spatial overlap in high-sampling-rate atomic interferometry.

[0003] The current challenge lies in the fact that when multiple atomic interference signals overlap spatially and have similar or identical frequencies, traditional single-detector integration measurements or simple image fitting methods face the "parameter degeneracy" problem, meaning they cannot uniquely determine the phase information of each independent component from a single mixed image. Existing principal component analysis (PCA) methods are prone to failure when dealing with strong background noise or signals of the same frequency, necessitating a new method to process such aliased signals of the same frequency. Summary of the Invention

[0004] The purpose of this invention is to address the problems of signal aliasing and extraction difficulties in the prior art by providing a method and device for extracting aliased signals of the same frequency in a shearing atomic interferometer.

[0005] The above-mentioned objectives of the present invention are achieved through the following technical means:

[0006] A method for extracting aliased signals in a sheared atomic interferometer includes the following steps:

[0007] Step 1: Collect the mixed interference signal of the first and second atomic interference signals to obtain the homonymous mixed interference signal to be matched as the simple harmonic signal. Integrate the simple harmonic signal in the horizontal direction of space to obtain the light intensity distribution of the simple harmonic signal. The light intensity distribution based on the harmonic signal obtained in this step Perform fitting to obtain the effective contrast. and fitted effective phase ,

[0008] Statistical analysis of the effective contrast of each fit maximum value and minimum value According to the formula and The contrast prior value of the first atom interference signal was obtained through inversion. Prior value of contrast of the second atomic interference signal ,

[0009] Step 2: Integrate the co-frequency aliased interference signal to be solved in the spatial horizontal direction to obtain the interference fringe curve, and use the interference fringe curve as the intensity distribution of the simple harmonic signal. The light intensity distribution based on the harmonic signal obtained in this step Perform fitting, and obtain the effective contrast of the fitted sample. As the measured effective contrast The effective phase obtained by fitting As the measured effective phase Based on measured effective contrast and measured effective phase Calculate the phase deviation between the first and second atomic interference signals to be determined in the co-frequency aliasing interference signals to be solved. absolute value Furthermore, the phase of the first undetermined atomic interference signal is calculated. Phase of the second undetermined atomic interference signal .

[0010] The light intensity distribution of the simple harmonic signal as described above The fitting is based on the following formula:

[0011] ,

[0012] in, The background envelope of the simple harmonic signal. For spatial frequency, These are the coordinate values ​​in the horizontal direction of space. DC bias.

[0013] The phase deviation between the first and second atomic interference signals as described above absolute value Calculated based on the following formula:

[0014] .

[0015] The phase of the first atomic interference signal as described above Phase of the second undetermined atomic interference signal Calculated based on the following formula:

[0016] ,

[0017] in, It is the symbol for imaginary numbers. Depends on phase deviation The sign, when the contrast of the first atom interference signal Contrast greater than the second atomic interference signal hour, Take the positive sign; when the contrast of the first atom interference signal... Contrast of the second atomic interference signal less than or equal to hour, Take the negative sign. This is the argument operator for complex numbers.

[0018] As described above, the first atomic interference signal is 85 The Rb interference signal, the second atom interference signal is 87 Rb interference signal.

[0019] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the above-described method for extracting co-frequency aliasing signals in a shearing atomic interferometer.

[0020] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method for extracting co-frequency aliasing signals in a shearing atomic interferometer.

[0021] A computer program product includes a computer program that, when executed by a processor, implements the steps of the above-described method for extracting aliased signals in a shearing atomic interferometer.

[0022] Compared with the prior art, the present invention has the following advantages:

[0023] This invention can reconstruct atomic interference signals from aliased sheared interferograms (aliased interference signals) with the same frequency, thus restoring the original signal. Under the spectral degeneracy limit (same frequency overlap), this is achieved by introducing a priori contrast values. and contrast prior value It can still achieve precise separation of atomic interference signals, breaking through the technical bottleneck of traditional methods (PCA) under frequency degeneracy conditions. Attached Figure Description

[0024] Figure 1This is one set of in-frequency separated interference signals from a comparison group containing multiple sets of in-frequency separated interference signals.

[0025] Figure 2 This refers to one set of interferometric signals with the same frequency being mixed, which is part of a test group containing multiple sets of interferometric signals with the same frequency being mixed.

[0026] Figure 3 For processing using the method of the present invention Figure 2 The first atom interference signal obtained after inversion.

[0027] Figure 4 For processing using the method of the present invention Figure 2 The second atomic interference signal obtained after inversion. Detailed Implementation

[0028] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to embodiments. The embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0029] Example 1:

[0030] A method for extracting aliased signals in a sheared atomic interferometer includes the following steps:

[0031] Step 1, Prior Calibration: Vertical acceleration measurements were performed using a Mach-Zehnder type atomic interferometer with first and second atoms to obtain the first and second atom interference signals. Before the formal measurement, the phases of the aliased first and second atom interference signals needed to be decorrelated, i.e., the phase difference between the aliased first and second atom interference signals should be distributed between 0 and 0. The range is set to meet the extraction requirements.

[0032] In this embodiment, the first atomic interference signal is 85 The Rb interference signal, the second atom interference signal is 87 Rb interference signal,

[0033] If the first and second atomic interference signals are phase-correlated and their phase difference is fixed, then: by changing the free evolution time and the mirror rotation angle, while ensuring the interference fringe frequency remains unchanged, the phase difference between the first and second atomic interference signals can be changed, selecting a phase difference of 0. , , , The first and second atomic interference signals are mixed to obtain the desired coherent frequency mixed interference signal for acquisition, as shown in the figure. Figure 1The five phase differences are for demonstration purposes only. In actual use, acquiring more phase differences for fitting the co-frequency aliased interference signal will yield better results. Different phase differences are acceptable and do not require precise control. The co-frequency aliased interference signal is used as a simple harmonic signal.

[0034] If the phases of the first and second atomic interference signals are uncorrelated, then the actual measured co-frequency aliasing interference signal in step 2 is directly used as the simple harmonic signal.

[0035] The co-frequency aliased interferometric signal to be simulated (the co-frequency aliased interferometric signal to be solved) is the signal resulting from the aliasing of the first atomic interferometric signal and the second atomic interferometric signal. The first atomic interferometric signal and the second atomic interferometric signal in the measured co-frequency aliased interferometric signal to be simulated (the co-frequency aliased interferometric signal to be solved) share the same background envelope distribution. The intensity distribution of the co-frequency aliasing interference signal to be determined (the co-frequency aliasing interference signal to be solved) It can be modeled as:

[0036] Formula (1)

[0037] in: For shared background envelope; DC bias; and These are the contrast coefficients of the first and second atomic interference signals, respectively. and These are the phases of the first atom interference signal and the second atom interference signal, respectively; Spatial frequency; Let be the spatial horizontal coordinates of the co-frequency aliased interference signal (simple harmonic signal) to be simulated. Using the principle of superposition of complex phasors, the above equation represents the intensity distribution of the co-frequency aliased interference signal to be simulated (the co-frequency aliased interference signal to be solved). Mathematically equivalent to having a single effective contrast ratio and effective phase Light intensity distribution of simple harmonic signals Light intensity distribution of simple harmonic signals Based on the following formula:

[0038] Formula (2)

[0039] in, The light intensity distribution of the simple harmonic signal and the background envelope of the simple harmonic signal. Background envelope can be directly detected. Alternatively, a model can be used, such as the background signal of atomic clusters in this case, where the background envelope is fitted. A Gaussian model is used. The measured harmonic signal (five sets of co-frequency aliased interference signals with different phase differences to be matched / each set of co-frequency aliased interference signals to be solved) is integrated in the horizontal direction to obtain the transverse signal intensity distribution curve as the intensity distribution of the harmonic signal. Based on the above formula (2), the light intensity distribution of the simple harmonic signal Perform fitting to obtain the effective contrast. and fitted effective phase Statistical analysis of the effective contrast of each fit maximum value and minimum value According to the formula and The contrast prior value of the first atom interference signal was obtained through inversion. Prior value of contrast of the second atomic interference signal .

[0040] Step 2, Vector Inverse Solution: Perform actual measurements to obtain the co-frequency aliasing interference signal to be solved. The measured co-frequency aliasing interference signal must have the same spatial frequency as the co-frequency aliasing interference signal to be simulated in Step 1. More preferably, the contrast coefficient of the first atomic interference signal... The change does not exceed 20%, and the contrast coefficient of the second atom interference signal The change should not exceed 20%. The interference fringe curve is obtained by spatial horizontal integration of the co-frequency aliasing interference signal to be solved, and this interference fringe curve is used as the intensity distribution of the harmonic signal. Substituting into Formula 2 above, the fitted effective contrast is obtained. As the measured effective contrast The effective phase obtained by fitting As the measured effective phase Using the contrast prior value of the first atomic interference signal obtained in step 1. Prior value of contrast of the second atomic interference signal Construct a vector triangle on the complex plane, and use the law of cosines to calculate the phase deviation between the first and second atomic interference signals in the co-frequency aliasing interference signal to be solved. absolute value :

[0041] Formula (3)

[0042] This uniquely determines the phase of the first atomic interference signal in the co-frequency aliasing interference signal to be solved. Phase of the second undetermined atomic interference signal

[0043] Formula (4)

[0044] in, It is the symbol for imaginary numbers. Depends on phase deviation The sign is determined by the contrast of the first atom interference signal in the co-frequency aliasing interference signal to be solved. Contrast of the second atomic interference signal Size determines, when Greater than hour, Take the positive sign, when Less than or equal to hour, Take the negative sign. This is the argument operator for complex numbers.

[0045] Figure 1-4 For this method to 85 Rb interference signal and 87 An example of processing Rb interferometric signals with aliasing at the same frequency to be solved. Figure 1 For a set of co-frequency separated interference signals in a comparison group containing multiple sets of co-frequency separated interference signals, the phase of the first atomic interference signal in the comparison group is... Phase of the second atomic interference signal The average value of the phase difference (Mean) is 1.935 rad, and the phase difference of the first atomic interference signal in the comparison group is... Phase of the second atomic interference signal The standard deviation of the phase difference is 0.09225 rad. Figure 2 This refers to a set of interferometric signals with the same frequency being mixed, which are part of a test group containing multiple sets of interferometric signals with the same frequency being mixed. Figure 3 and Figure 4 Processed using the method of the present invention Figure 2 The first and second atomic interference signals obtained after inversion. The phase of the first atomic interference signal obtained by the test group after processing using the method of this invention. Phase of the second atomic interference signal The average value of the phase difference (Mean) is 1.965 rad. The phase of the first atomic interference signal obtained by the test group after processing with the method of this invention is... Phase of the second atomic interference signal The standard deviation of the phase difference is 0.1155 rad. This is processed using traditional methods. Figure 2 When encountering aliased signals, it is impossible to extract the required information. However, using this invention, not only can the phase of the first atomic interference signal and the phase of the second atomic interference signal be extracted from the aliased interference signal, but also... Figure 1 The phases of the first and second atomic interference signals extracted from the completely separated same-frequency interference signals are almost identical to the standard values.

[0046] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods.

[0047] Example 2:

[0048] In this embodiment, a computer device is also provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0049] Example 3:

[0050] In this embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the steps in the above-described method embodiments.

[0051] Example 4:

[0052] In this embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0053] It should be noted that the embodiments described in this invention are merely illustrative examples of the spirit of the invention. Those skilled in the art to which this invention pertains can make various modifications or additions to the described embodiments or use similar methods to substitute them, but without departing from the spirit of the invention or exceeding the scope of the invention.

Claims

1. A method for extracting aliased signals in a shearing atomic interferometer, characterized in that, Includes the following steps: Step 1: Collect the mixed interference signal of the first and second atomic interference signals to obtain the homonymous mixed interference signal to be matched as the simple harmonic signal. Integrate the simple harmonic signal in the horizontal direction of space to obtain the light intensity distribution of the simple harmonic signal. The light intensity distribution based on the harmonic signal obtained in this step Perform fitting to obtain the effective contrast. and fitted effective phase , Statistical analysis of the effective contrast of each fit maximum value and minimum value According to the formula and The contrast prior value of the first atom interference signal was obtained through inversion. Prior value of contrast of the second atomic interference signal , Step 2: Integrate the co-frequency aliased interference signal to be solved in the spatial horizontal direction to obtain the interference fringe curve, and use the interference fringe curve as the intensity distribution of the simple harmonic signal. The light intensity distribution based on the harmonic signal obtained in this step Perform fitting, and obtain the effective contrast of the fitted sample. As the measured effective contrast The effective phase obtained by fitting As the measured effective phase Based on measured effective contrast and measured effective phase Calculate the phase deviation between the first and second atomic interference signals to be determined in the co-frequency aliasing interference signals to be solved. absolute value Furthermore, the phase of the first undetermined atomic interference signal is calculated. Phase of the second undetermined atomic interference signal .

2. The method for extracting co-frequency aliasing signals in a shearing atomic interferometer according to claim 1, characterized in that, The light intensity distribution of the simple harmonic signal The fitting is based on the following formula: ， in, The background envelope of the simple harmonic signal. For spatial frequency, These are the coordinate values ​​in the horizontal direction of space. DC bias.

3. The method for extracting co-frequency aliasing signals in a shearing atomic interferometer according to claim 1, characterized in that, Phase deviation between the first and second atomic interference signals absolute value Calculated based on the following formula: 。 4. The method for extracting co-frequency aliasing signals in a shearing atomic interferometer according to claim 3, characterized in that, Phase of the first atomic interference signal to be determined Phase of the second undetermined atomic interference signal Calculated based on the following formula: ， in, It is the symbol for imaginary numbers. Depends on phase deviation The sign, when the contrast of the first atom interference signal Contrast greater than the second atomic interference signal hour, Take the positive sign; when the contrast of the first atom interference signal... Contrast of the second atomic interference signal less than or equal to hour, Take the negative sign. This is the argument operator for complex numbers.

5. The method for extracting co-frequency aliasing signals in a shearing atomic interferometer according to claim 1, characterized in that, The first atomic interference signal is 85 The Rb interference signal, the second atom interference signal is 87 Rb interference signal.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method for extracting co-frequency aliasing signals in a shearing atomic interferometer as described in any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for extracting aliased signals in a shearing atomic interferometer as described in any one of claims 1 to 5.

8. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method for extracting aliased signals in a shearing atomic interferometer as described in any one of claims 1 to 5.

Images