A precise method for measuring the resonance frequency of hyperpolarized noble gas FID signals

Abstract

The application discloses a kind of hyperpolarized inert gas FID signal resonance frequency accurate measurement method, belong to atomic molecule and optical physics, signal detection and analysis field.For the FID signal of hyperpolarized inert gas, since signal itself oscillation decay with time, the length of sampling time is limited therefore the resolution of spectrum is limited, in turn, the precision of magnetic field measurement is influenced.The present application significantly improves the frequency resolution by refining spectrum and frequency estimation in succession, and has important significance for improving the precision of magnetic field measurement.

Description

Technical Field

[0001] The present invention aims to propose a precise measurement method for the resonance frequency of a hyperpolarized noble gas FID signal applicable to the field of atomic magnetometers, and belongs to the fields of atomic, molecular and optical physics, signal detection and analysis. Background Art

[0002] With the rapid development of quantum technology and magnetic field sensing, the accuracy and sensitivity of magnetic field measurements have continued to improve, and the highly promising atomic magnetometer has experienced rapid development. Unlike traditional magnetometers, atomic magnetometers rely on atomic spin, manipulate atoms through optical means, and then detect the ambient magnetic field based on the atomic spin state. Among them, FSP magnetometers, developed from optically pumped magnetometers, obtain magnetic field information by optically detecting the free spin precession of atomic spin polarization, a typical signal of which is the free induction decay (FID) signal. This type of magnetometer avoids the systematic readout errors of feedback-driven magnetometers while retaining the advantage of measuring the magnetic field mechanism by measuring frequency. It is a highly promising atomic magnetometer.

[0003] The free induction decay (FID) signal is an observable resonance signal in the field of nuclear magnetic resonance or electron paramagnetic resonance (EPR) generated by the nonequilibrium nuclear spin magnetization around the magnetic field. Assuming the magnetization vector of the atomic ensemble is polarized along the z-axis and undergoes Larmor precession about the z-axis under the influence of an external magnetic field, free induction decay (FID) occurs when a radio frequency pulse with a frequency close to the atomic Larmor precession frequency is applied to the ensemble. The experimental FID signal is obtained by detecting and digitizing the voltage in the detection coil surrounding the sample. FID signals are often used to measure sample relaxation, the ambient magnetic field, and magnetic field gradients in atomic magnetometers. J. Murday measured the magnetic field gradient by analyzing the FID signal and analyzed that the main sources of systematic errors are the resonance condition, the time delay of the finite radio frequency pulse, and the nonorthogonality of the gradient and the cylindrical axis. E. Breschi et al. used the FID signal to calibrate a three-dimensional magnetic coil and measure the three-axis components of the residual magnetic field.

[0004] The FID signal is an oscillating, decaying signal whose frequency reflects the Larmor precession frequency of the atom, and thus the magnitude of the ambient magnetic field. Since this ambient magnetic field is typically the shielded field of the atomic magnetometer, its amplitude is relatively small, often in the nanoT range, and therefore requires high frequency resolution. Directly Fourier transforming the signal yields low frequency resolution. Due to the picket fence effect, the frequency between two adjacent points in the spectrum cannot be measured, directly affecting the accuracy of the magnetic field measurement. Therefore, a refined estimate of the FID signal's spectrum is necessary.

[0005] In order to solve the problem of insufficient spectral resolution of the FID signal, the application provides an accurate measurement method of the resonance frequency of the hyperpolarized noble gas FID signal suitable for a shielding environment. The method is aimed at the problem of low spectral resolution caused by the limited time length of the hyperpolarized noble gas FID time domain signal, and proposes a local DFT (Discrete Fourier Transform) and parabolic interpolation refinement estimation method, which reduces the error caused by the fence effect and can further improve the frequency resolution of the limited time length hyperpolarized noble gas FID signal, and has important significance for improving the accuracy of magnetic field measurement. SUMMARY

[0006] The application aims to design a spectral refinement method suitable for a system with limited time and fixed sampling rate, focuses on the frequency extraction of the hyperpolarized noble gas FID signal, and provides an accurate measurement method of the resonance frequency of the hyperpolarized noble gas FID signal, which is a fixed sampling point, high-precision and fast frequency refinement estimation method. The method mainly includes two parts: spectral resolution refinement and frequency estimation, which helps to accurately obtain the frequency of the FID signal and provides guarantee for accurate acquisition of the true value of the magnetic field.

[0007] The technical solution of the application is as follows:

[0008] An accurate measurement method of the resonance frequency of the hyperpolarized noble gas FID signal, characterized by comprising the following steps:

[0009] Step 1: obtaining the free induction decay FID signal from the hyperpolarized noble gas FID signal acquisition experimental device, performing FFT (Fast Fourier Transform) on the FID signal to obtain the FFT spectrum, and determining the target frequency band from the FFT spectrum;

[0010] Step 2: magnifying the target frequency band locally to find two points with the maximum amplitude, which are k1 and k2, respectively;

[0011] Step 3: using DFT (Discrete Fourier Transform) to refine the frequency between k1 and k2;

[0012] Step 4: finding three points with the maximum amplitude after refinement, and performing parabolic fitting;

[0013] Step 5: calculating the abscissa point of the derivative of the parabola being zero, which is the accurate estimation solution of the resonance frequency of the hyperpolarized noble gas FID signal.

[0014] The step 4 includes the following parabolic formula:

[0015] y=ax 2 +bx+c

[0016] Where y represents the amplitude of the ordinate, x represents the frequency of the abscissa, and a, b, and c represent the coefficients of the parabola expression. The following simultaneous equations are established to solve a, b, and c by refining the three points with the largest amplitude, P1(x1, y1), P2(x2, y2), and P3(x3, y3):

[0017] y1=ax1 2 +bx1+c

[0018] y2=ax2 2 +bx2+c

[0019] y3=ax3 2 +bx3+c

[0020] This results in a parabolic function y=ax that opens downward after fitting. 2 +bx+c.

[0021] The step 5 includes the formula: y′=2ax0+b=0

[0022] y' represents the derivative of the parabolic function y, x0 represents the abscissa point where the parabolic derivative is zero, and x0 is the accurate estimate of the resonant frequency of the hyperpolarized noble gas FID signal.

[0023] The improved resolution of the spectrum is defined as the difference between the horizontal coordinate x0 and the horizontal coordinate f(k1) corresponding to the maximum amplitude point k1 before refinement, that is, Δf′=|x0-f(k1)|, which is used to measure the effect of spectrum refinement and frequency estimation. When the value is small, it proves that the true value of the frequency is near the spectrum line before refinement. When the value is large, it proves that the true value of the frequency is far away from the spectrum line before refinement.

[0024] The target frequency band in step 1 is between 0 and 10 Hz.

[0025] The target frequency band in step 1 is the spectrum peak area of ​​the FFT spectrum.

[0026] In step 2, k1 and k2 are frequency points of adjacent peaks, and k1<k2.

[0027] The step 3 includes the following DFT formula:

[0028]

[0029] Where X(k) represents the frequency domain signal, N is the number of sampling points, n is the sampling point number, x(n) represents the time domain signal, e is a natural constant, j is an imaginary unit, and k is the frequency point number;

[0030] Using the idea of ​​continuous instead of discrete, interpolation is performed between X(k1) and X(k2). The specific interpolation value is,

[0031]

[0032] Where D is the refinement multiple. Since k1 and k2 are adjacent points and k1 is on the left, k1+1=k2. The corresponding number of the refined point is k1=k 10 ,k 11 ,k 12 ,k 13 ,...,k 1D =k2, the frequency difference between each point is Δf / D, where Δf is the frequency resolution before refinement, and the formula is,

[0033] Δf=f s / N

[0034] where f s is the sampling rate, and N is the number of sampling points.

[0035] The hyperpolarized noble gas FID signal acquisition experimental device includes a pump light emitter, a first half-wave plate, a first beam expander, a second half-wave plate, a first wedge block, a second wedge block, a first Glan-Thompson prism, a first quarter-wave plate, and an atomic gas chamber, which are sequentially connected in series along the positive direction of the Z axis. A coil and a magnetic shielding barrel are sequentially arranged outwardly from the periphery of the atomic gas chamber.

[0036] The hyperpolarized noble gas FID signal acquisition experimental device includes a detection light emitter, a second beam expander, a third half-wave plate, a third wedge block, a fourth wedge block, a second Glan-Thompson prism, an atomic gas chamber and a fourth half-wave plate, which are connected in series along the negative direction of the X-axis. The fourth half-wave plate is connected to the second photodiode through the transmission side of the first beam splitter for signal output, and the reflection side of the first beam splitter is connected to the first photodiode for signal output.

[0037] The technical effects of the present invention are as follows: A method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal belongs to the fields of atomic, molecular, and optical physics, as well as signal detection and analysis. Because the FID signal of a hyperpolarized noble gas oscillates and decays over time, obtaining its spectrum requires sampling within a finite timeframe. However, the sampling rate cannot be increased infinitely, resulting in a limited spectral resolution, which in turn affects the accuracy of magnetic field measurements. By sequentially refining the spectrum and then estimating the frequency, the present invention significantly improves the frequency resolution, which is of great significance for improving the accuracy of magnetic field measurements.

[0038] The present invention has the following features: (1) It provides an estimation method for low-frequency signals and high-resolution spectra; (2) It facilitates high-precision measurement of magnetic fields using FID; and (3) Accurate FID signal frequency and magnetic field measurements provide a guarantee for residual magnetic field measurements using an atomic magnetometer. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 The present invention is a flow chart of a method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal. Figure 1 The method includes the following steps: 1. performing FFT (Free Induction Decay, FID) on the obtained FID signal to determine the target frequency band; 2. locally amplifying the target frequency band to find the two points with the largest amplitude; 3. performing frequency refinement between these two points using DFT (Discrete Fourier Transform, DFT); 4. finding the three points with the largest amplitude after refinement and performing parabola fitting; and 5. calculating the horizontal coordinate of the point where the parabola derivative is zero, which is the accurate frequency estimate.

[0040] Figure 2 The present invention is a schematic diagram of the structure of an FID signal acquisition experimental device involved in implementing a method for accurately measuring the resonance frequency of a hyperpolarized noble gas FID signal.

[0041] Figure 3 The figure is a schematic diagram of the FID time domain signal collected by implementing a method for accurately measuring the resonance frequency of a hyperpolarized noble gas FID signal according to the present invention. Figure 3 The vertical axis is voltage / mV, and the vertical axis scale values ​​are from 1.84-1.86···1.98-2; the horizontal axis is time / s, and the horizontal axis scale values ​​are from 0-10-···-90-100. Figure 3 The upper right middle portion includes a locally enlarged waveform of the time domain signal.

[0042] Figure 4 It is a schematic diagram of spectrum refinement and frequency estimation results obtained by implementing a method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal according to the present invention. Figure 4 Included in the figure are the Fourier transform spectrum diagram at the upper left and the refined spectrum diagram at the lower left (involving initial points, refinement points, and fitted parabola), the Fourier transform local spectrum diagram at the upper right and the refined local spectrum diagram at the lower right (involving initial points, refinement points, and fitted parabola). Figure 4 The vertical axis of each figure is amplitude, and the horizontal axis is frequency / Hz.

[0043] The reference numerals are listed as follows: 1-pump light emitter; 2-first half-wave plate; 3-first beam expander; 4-second half-wave plate; 5-first wedge block; 6-second wedge block; 7-first Glan-Thompson prism; 8-first 1 / 4 wave plate; 9-coil; 10-atomic gas chamber; 11-magnetic shielding barrel; 12-detection light emitter; 13-second beam expander; 14-third half-wave plate; 15-third wedge block; 16-fourth wedge block; 17-second Glan-Thompson prism; 18-fourth half-wave plate; 19-first photodiode; 20-second photodiode; 21-first beam splitter. DETAILED DESCRIPTION

[0044] Below is the attached figure ( Figures 1-4 ) and Examples illustrate the present invention.

[0045] Figure 1 The present invention is a flow chart of a method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal. Figure 2 The present invention is a schematic diagram of the structure of an FID signal acquisition experimental device involved in implementing a method for accurately measuring the resonance frequency of a hyperpolarized noble gas FID signal. Figure 3 The figure is a schematic diagram of the FID time domain signal collected by implementing a method for accurately measuring the resonance frequency of a hyperpolarized noble gas FID signal according to the present invention. Figure 4 This is a schematic diagram of spectrum refinement and frequency estimation results obtained by implementing a method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal of the present invention. Figures 1 to 4 As shown, a method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal includes the following steps: Step 1, obtaining a free induction decay (FID) signal from a hyperpolarized noble gas FID signal acquisition experimental device, performing a fast Fourier transform (FFT) on the FID signal to obtain an FFT spectrum, and determining a target frequency band from the FFT spectrum; Step 2, locally amplifying the target frequency band to find two points with the largest amplitudes, namely k1 and k2; Step 3, performing frequency refinement between k1 and k2 using a discrete Fourier transform (DFT); Step 4, finding three points with the largest amplitudes after refinement and performing parabola fitting; Step 5, calculating the abscissa point where the parabola derivative is zero, which is the accurate estimated solution for the resonant frequency of the hyperpolarized noble gas FID signal.

[0046] Step 4 includes the following parabola formula:

[0047] y=ax 2 +bx+c

[0048] Where y represents the amplitude of the ordinate, x represents the frequency of the abscissa, and a, b, and c represent the coefficients of the parabola formula. The following simultaneous equations are established by using the three points with the largest amplitude after refinement, P1(x1, y1), P2(x2, y2), and P3(x3, y3), to solve a, b, and c:

[0049] y1=ax1 2 +bx1+c

[0050] y2=ax2 2 +bx2+c

[0051] y3=ax3 2 +bx3+c

[0052] This results in a parabolic function y=ax that opens downward after fitting. 2 +bx+c.

[0053] The step 5 includes the formula: y′=2ax0+b=0

[0054] y' represents the derivative of the parabolic function y, x0 represents the abscissa point where the parabolic derivative is zero, and x0 is the accurate estimate of the resonant frequency of the hyperpolarized noble gas FID signal.

[0055] The improved resolution of the spectrum is defined as the difference between the abscissa x0 and the abscissa f(k1) corresponding to the point k1 with the maximum amplitude before refinement, i.e., Δf′ = |x0 - f(k1)|, which is used to measure the effectiveness of spectrum refinement and frequency estimation. The target frequency band in step 1 is between 0 and 10 Hz. The target frequency band in step 1 is the peak region of the FFT spectrum. k1 and k2 in step 2 are adjacent frequency points with the maximum amplitude in the spectrum, and k1 < k2.

[0056] The step 3 includes the following DFT formula:

[0057]

[0058] Where X(k) represents the frequency domain signal, N is the number of sampling points, n is the sampling point number, x(n) represents the time domain signal, e is a natural constant, j is an imaginary unit, and k is the frequency point number;

[0059] Using the idea of ​​continuous instead of discrete, interpolation is performed between X(k1) and X(k2). The specific interpolation value is,

[0060]

[0061] Where D is the refinement multiple. Since k1 and k2 are adjacent points and k1 is on the left, k1+1=k2. The corresponding number of the refined point is k1=k 10 ,k11 ,k 12 ,k 13 ,...,k 1D =k2, the frequency difference between each point is Δf / D, where Δf is the frequency resolution before refinement, and the formula is,

[0062] Δf=f s / N

[0063] where f s is the sampling rate, and N is the number of sampling points.

[0064] The hyperpolarized noble gas FID signal acquisition experimental device includes a pump light emitter 1, a first half-wave plate 2, a first beam expander 3, a second half-wave plate 4, a first wedge 5, a second wedge 6, a first Glan-Thompson prism 7, a first quarter-wave plate 8, and an atomic gas cell 10, which are sequentially connected in series along the positive direction of the Z axis. A coil 9 and a magnetic shielding barrel 11 are sequentially arranged outward from the periphery of the atomic gas cell 10. The hyperpolarized noble gas FID signal acquisition experimental device includes a detection light emitter 12, a second beam expander 13, a third half-wave plate 14, a third wedge 15, a fourth wedge 16, a second Glan-Thompson prism 17, an atomic gas cell 10, and a fourth half-wave plate 18, which are sequentially connected in series along the negative direction of the X axis. The fourth half-wave plate 18 is connected to a second photodiode 20 via a transmission side of a first beam splitter 21 for signal output, and is connected to a first photodiode 19 via a reflection side of the first beam splitter 21 for signal output.

[0065] A method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal comprises the following steps:

[0066] (1) Perform FFT (Fast Fourier Transform) on the obtained FID signal, observe the obtained spectrum, find the spectrum peak, and thus determine the target frequency band that needs to be refined.

[0067] (2) Observe the local amplification of the target frequency band and find the two points with the largest FFT amplitude in the target frequency band.

[0068] (3) Use the idea of ​​continuous instead of discrete and use DFT to refine the frequency between these two points.

[0069] (4) Find the three points with the largest amplitude after refinement, perform parabola fitting, and obtain a parabola opening downward.

[0070] (5) Calculate the horizontal coordinate corresponding to the point where the derivative of the fitted parabola is zero, which is the accurate estimate of the FID frequency.

[0071] A method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal, characterized in that the method comprises the following steps:

[0072] Step (1) performs FFT (Fast Fourier Transform) on the experimentally measured hyperpolarized noble gas FID signal, observes the obtained spectrum, finds the spectrum peak, and thus determines the target frequency band that needs to be refined.

[0073] Step (2) is based on step (1), observing the local amplification of the target frequency band, and finding the two points k1 and k2 (adjacent points, k1 < k2, set X(k1) > X(k2)) with the largest FFT amplitude in the target frequency band, which are generally peak points.

[0074] Step (3) uses DFT to refine the frequency between these two points, where the DFT formula is:

[0075]

[0076] Here we use the continuous instead of discrete idea to interpolate and refine between X(k1) and X(k2). The specific interpolation value is,

[0077]

[0078] Where D is the refinement multiple. Since k1 and k2 are adjacent points and k1 is on the left, k1+1=k2. The corresponding number of the refined point is k1=k 10 ,k 11 ,k 12 ,k 13 ,...,k 1D =k2, the frequency difference between each point is Δf / D, where Δf is the frequency resolution before refinement, and the formula is,

[0079] Δf=f s / N (3)

[0080] where f s is the sampling rate, and N is the number of sampling points.

[0081] Step (4) Find the three points P1(x1,y1), P2(x2,y2), and P3(x3,y3) with the largest amplitude after refinement, and perform parabola fitting. Let the formula of the parabola be,

[0082] y=ax 2 +bx+c (4)

[0083] Substituting the coordinates of the three points, we have,

[0084] y1=ax1 2 +bx1+c

[0085] y2=ax2 2 +bx2+c (5)

[0086] y3=ax32 +bx3+c

[0087] The simultaneous equations are used to obtain a, b, and c, which are substituted into formula (4) to obtain a parabolic function that opens downward after fitting.

[0088] Step (5) calculates the maximum point of the fitted parabola, that is, the point where the derivative is zero. According to the formula,

[0089] y′=2ax0+b=0 (6)

[0090] The corresponding horizontal coordinate x0 is obtained, which is the accurate estimate of the FID frequency.

[0091] The collected FID low-frequency time domain signal is first used to select the frequency band using FFT (the target frequency band is generally between 0-10Hz), and then DFT discrete Fourier transform is performed between the two maximum values ​​of the selected frequency band. The three refined points are selected for parabola fitting, and the maximum value of the fitted function is the frequency estimation point.

[0092] The improved resolution of the spectrum is defined as the difference between the abscissa x0 and the abscissa f(k1) corresponding to the maximum amplitude point k1 before refinement, that is, Δf′=|x0-f(k1)|, which is used to measure the effect of spectrum refinement and frequency estimation.

[0093] The experimentally measured 21 Taking the FID signal of Ne atom as an example, the process of spectrum refinement and frequency estimation using the present invention is specifically described.

[0094] A method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal comprises the following steps:

[0095] (1) According to Figure 2 Build the experimental device using 21 Ne atomic FID signal excitation and collection, the gas cell is equipped with 21 Ne atoms, pumped by pump light 21 The Ne atom is placed at a high energy level to produce macroscopic polarization. The coil is energized to generate an oscillating magnetic field in the direction perpendicular to the pump light. The oscillating magnetic field is then turned off, and the detection light intensity in the x direction is detected by a photodiode. The current signal is then converted into a voltage signal and collected into a computer for processing.

[0096] (2) The experimental data is processed by matlab. 21The FID time domain signal of Ne atom is imported into MATLAB with a length of 38620. The original data is cropped to remove the non-FID part (including the part before oscillation attenuation and the part after attenuation to near zero). The remaining data is x, and the data length N=length(x)=19491. The fft function is used for calculation and the spectrum coordinate of the cropped FID time domain data is plotted and marked as Fw.

[0097] (3) Find the convex peak in the spectrum. Observe that the frequency here is between 2.7 and 2.9 Hz. After zooming in on the image, we can find that the discrete points in this frequency band have the largest amplitude, X1 (f(k1), Fw(k1)), and the second largest amplitude, X2 (f(k2), Fw(k2)). k1 = 272, k2 = 273. At this time, the difference between the horizontal coordinates of the two points, that is, the resolution of the spectrum, is Δf = 0.0103 Hz.

[0098] (4) Since the Larmor precession frequency of atomic spin is linearly related to the magnitude of the magnetic field, the formula is:

[0099] ω=γB

[0100] Where ω is the Larmor precession angular velocity, γ is the gyromagnetic ratio, and B is the magnitude of the magnetic field. According to the formula, the resolution of the magnetic field can be calculated by the spectral line resolution of the spectrum, where 21 The gyromagnetic ratio of Ne atom is a fixed constant, which can be calculated by looking up the table of nuclear magnetic dipole and electric quadrupole moments (reference: Stone N J. Table of nuclear magnetic dipole and electric quadrupole moments [J]. Atomic Data and Nuclear Data Tables, 2005, 90 (1): 75-176.) based on its magnetic moment, Lande factor and nuclear spin quantum number. The resolution of the magnetic field at this time is calculated as,

[0101]

[0102] For high-precision magnetic field measurement, the resolution of the magnetic field is poor at this time and does not meet the accuracy requirements of magnetic field measurement, so it needs to be refined.

[0103] (5) The refinement factor D is set to 5. The interpolation between X1 and X2 is calculated according to formula (2). The four points X1 and X2 are removed and their vertical coordinates are calculated, that is, the discrete Fourier transform amplitude.

[0104]

[0105] The frequency resolution after refinement becomes 1 / 5 of the original one.

[0106]

[0107] The magnetic field resolution after spectrum refinement is calculated according to formula (7):

[0108]

[0109] After refinement, the magnetic field resolution has dropped below 1 nT. At this time, parabolic interpolation will be able to more accurately estimate the true value of the FID signal resonance frequency.

[0110] (6) The refined points are represented in the original spectrum, and the three points with the largest amplitude in the frequency band are taken as X′1, X′2, and X′3. The sort function is used to obtain:

[0111]

[0112] Substitute X′1, X′2, and X′3 into formulas (4) and (5) to obtain the parabola coefficients, or use the polyfit function in Matlab to fit it to obtain a downward-opening parabola.

[0113] (7) The parabola is differentiated to obtain the point where the derivative is zero, whose horizontal coordinate is x0 = 2.7931 Hz. This frequency is the estimated frequency. The horizontal coordinate of the maximum amplitude point X1 before spectrum refinement is f(k1) = 2.79 Hz. The frequency resolution after refinement is defined as the difference between the estimated frequency and the frequency of the maximum amplitude point. The frequency resolution after refinement is,

[0114] Δf′=|x0-f(k1)|=|2.7931-2.79|Hz=0.0031Hz (12)

[0115] (8) The effect of spectrum refinement and frequency estimation is measured by the percentage of resolution improvement. The degree of frequency resolution refinement can be calculated by formula (12). Through spectrum refinement and frequency estimation, the resolution is improved by about 70%.

[0116] (9) The results of using the present invention to refine the estimated frequency are shown in Figure 3 and Figure 4 .

[0117] Any content not described in detail in this specification is prior art known to those skilled in the art. It should be noted that the above description is intended to help those skilled in the art understand the present invention, but does not limit the scope of protection of the present invention. Any equivalent substitution, modification, improvement, and / or simplification of the above description that does not depart from the essence of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal, characterized in that: The following steps are involved: Step 1: obtaining a free induction decay (FID) signal from a hyperpolarized noble gas FID signal acquisition experimental device, performing a fast Fourier transform (FFT) on the FID signal to obtain an FFT spectrum, and determining a target frequency band from the FFT spectrum; Step 2: locally amplify the target frequency band and find the two points with the largest amplitude, namely k1 and k2; Step 3, use DFT discrete Fourier transform to refine the frequency between k1 and k2; Step 4: Find the three points with the largest amplitude after refinement and perform parabola fitting; Step 5: Calculate the abscissa point where the parabola derivative is zero, which is the accurate estimated solution for the resonant frequency of the hyperpolarized noble gas FID signal.

2. The method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal according to claim 1, characterized in that: Step 4 includes the following parabola formula: y=ax 2 +bx+c Where y represents the amplitude of the ordinate, x represents the frequency of the abscissa, and a, b, and c are the coefficients of the parabola formula. The following simultaneous equations are established by refining the three points with the largest amplitude, P1(x1, y1), P2(x2, y2), and P3(x3, y3), to solve a, b, and c: y1=ax1 2 +bx1+c y2=ax2 2 +bx2+c y3=ax3 2 +bx3+c This results in a parabolic function y=ax that opens downward after fitting. 2 +bx+c.

3. The method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal according to claim 2, wherein: The step 5 includes the formula: y′=2ax0+b=0 y' represents the derivative of the parabolic function y, x0 represents the abscissa point where the parabolic derivative is zero, and x0 is the accurate estimate of the resonant frequency of the hyperpolarized noble gas FID signal.

4. The method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal according to claim 3, wherein: The improved resolution of the spectrum is defined as the difference between the abscissa x0 and the abscissa f(k1) corresponding to the maximum amplitude point k1 before refinement, that is, Δf′=|x0-f(k1)|, which is used to measure the effect of spectrum refinement and frequency estimation.

5. The method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal according to claim 1, wherein: The target frequency band in step 1 is between 0 and 10 Hz.

6. The method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal according to claim 1, wherein: The target frequency band in step 1 is the spectrum peak area of ​​the FFT spectrum.

7. The method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal according to claim 1, wherein: In step 2, k1 and k2 are frequency points of adjacent peaks, and k1<k2.

8. The method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal according to claim 1, wherein: The step 3 includes the following DFT formula: Where X(k) represents the frequency domain signal, N is the number of sampling points, n is the sampling point number, x(n) represents the time domain signal, e is a natural constant, j is an imaginary unit, and k is the frequency point number; Using the idea of ​​continuous instead of discrete, interpolation is performed between X(k1) and X(k2). The specific interpolation value is, Where D is the refinement multiple. Since k1 and k2 are adjacent points and k1 is on the left, k1+1=k2. The corresponding number of the refined point is k1=k 10 ,k 11 ,k 12 ,k 13 ,...,k 1D =k2, the frequency difference between each point is Δf / D, where Δf is the frequency resolution before refinement, and the formula is, Δf=f s / N where f s is the sampling rate, and N is the number of sampling points.

9. The method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal according to claim 1, wherein: The hyperpolarized noble gas FID signal acquisition experimental device includes a pump light emitter, a first half-wave plate, a first beam expander, a second half-wave plate, a first wedge block, a second wedge block, a first Glan-Thompson prism, a first quarter-wave plate, and an atomic gas chamber, which are sequentially connected in series along the positive direction of the Z axis. A coil and a magnetic shielding barrel are sequentially arranged outwardly from the periphery of the atomic gas chamber.

10. The method for accurately measuring the resonant frequency of a hyperpolarized noble gas FID signal according to claim 1, characterized in that: The hyperpolarized noble gas FID signal acquisition experimental device includes a detection light emitter, a second beam expander, a third half-wave plate, a third wedge block, a fourth wedge block, a second Glan-Thompson prism, an atomic gas chamber and a fourth half-wave plate, which are connected in series along the negative direction of the X-axis. The fourth half-wave plate is connected to the second photodiode through the transmission side of the first beam splitter for signal output, and the reflection side of the first beam splitter is connected to the first photodiode for signal output.

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