Terahertz three-dimensional imaging method and system based on Hilbert transform

Abstract

The invention relates to the technical field of SAR imaging, and provides a terahertz three-dimensional imaging method and system based on Hilbert transform, and the method comprises the steps: collecting echo real number signals of an object to be detected and each equivalent channel of a standard part; respectively predicting p numbers at two ends of the echo real number signal by using an autoregression model to obtain a continuation digital signal; performing fast Fourier transform on the continuation digital signal to obtain a frequency spectrum; performing Hilbert transform on the frequency spectrum in a frequency domain to obtain an analysis frequency spectrum; sequentially carrying out processing and inverse Fourier transform on the analysis frequency spectrum to obtain time domain complex data; respectively deleting p data at two ends of the time domain complex data to obtain target data; the target data of the to-be-measured object is corrected based on the target data of the standard component, the corrected data of each equivalent channel is input into the backward projection algorithm to generate the three-dimensional image of the to-be-measured object, the phase information of the digital signal is extracted by adopting the method of combining the AR model and the Hilbert transform, and the hardware complexity is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of SAR imaging technology, and particularly relates to a terahertz three-dimensional imaging method and system based on Hilbert transform. BACKGROUND

[0002] The frequency of terahertz wave is between millimeter wave and infrared light, and the wavelength is smaller compared with millimeter wave; meanwhile, the bandwidth of terahertz wave is very large, so terahertz wave is suitable for realization of large bandwidth and narrow antenna beam, and is easy to finely image the target in imaging detection. Terahertz wave has good penetration, and is more likely to obtain information inside the object; and the photon energy of terahertz wave is millielectron-volt, and will not cause harmful ionization reaction on human body. Therefore, terahertz imaging technology has been widely researched and applied in the field of composite material nondestructive testing and imaging.

[0003] Terahertz wave is combined with synthetic aperture radar (SAR) technology, and has high imaging resolution. In order to reduce the number of array elements of the antenna array and the construction cost of the imaging system, the multiple input multiple output (MIMO) technology is adopted, so that the number of observation channels and degrees of freedom is much more than the actual number of physical array elements.

[0004] The existing SAR imaging system generally adopts an array transmitting module to perform two-dimensional plane scanning on the measured object, and after the scattered signal passes through the receiving module, the in-phase (I) and quadrature (Q) intermediate frequency digital signals are obtained by using the quadrature intermediate frequency receiver, so that the amplitude and phase of the complex signal can be directly obtained, and then the three-dimensional imaging is performed by using the SAR imaging algorithm, but the hardware complexity is increased. In order to reduce the hardware complexity, the MIMO array terahertz imaging system can adopt a real number sampling receiver mode, and each intermediate frequency signal is digitally collected to only obtain the real number signal, but this brings the problem of lacking the signal phase. SUMMARY

[0005] In order to solve the problem of lacking the complex signal phase in the MIMO array terahertz imaging system in the prior art, a first object of the present application provides a terahertz three-dimensional imaging method based on Hilbert transform, comprising:

[0006] Respectively collecting echo real number signals of each equivalent channel of the measured object and the standard part;

[0007] Using an autoregressive model to respectively predict p numbers at both ends of the echo real number signals, and obtaining extended digital signals;

[0008] Performing fast Fourier transform on the extended digital signals to obtain a frequency spectrum;

[0009] performing Hilbert transform on the spectrum in frequency domain to obtain an analytic spectrum;

[0010] sequentially performing windowing filtering processing and inverse Fourier transform on the analytic spectrum to obtain time domain complex data;

[0011] respectively deleting p data at two ends of the time domain complex data to obtain target data;

[0012] correcting the target data of the object based on the target data of the standard part, and inputting the data of each equivalent channel after correction into a back projection algorithm to generate three-dimensional imaging of the object.

[0013] Specifically, the calculation formula of the Hilbert transform is:

[0014] ,

[0015] In the formula, Spec_H[k] is the analytic spectrum, and Spec[k] is the spectrum.

[0016] Specifically, the windowing filtering processing is Kaiser windowing.

[0017] Specifically, the main lobe width of the Kaiser window is dynamically set based on the maximum and minimum distance difference between the transmitting antenna and the object.

[0018] Specifically, a three-dimensional coordinate system of the object and the transmitting antenna and the receiving antenna is constructed based on the size of the object, a scattering point is selected according to the shape of the object, the maximum distance and the minimum distance of the object to different equivalent channels are estimated, the maximum time interval and the minimum time interval between the transmitting signal and the echo signal are calculated, and the bandwidth and the center frequency of each equivalent channel are sequentially estimated.

[0019] Specifically, the main lobe width of the Kaiser window is equal to the bandwidth.

[0020] The second object of the application is to provide a terahertz three-dimensional imaging system based on Hilbert transform, which is characterized by comprising:

[0021] a signal source generating a linear frequency modulation pulse sequence;

[0022] a one-dimensional motion device on which the object is placed, the one-dimensional motion device driving the object to move at a constant speed;

[0023] a terahertz transmitting module including M transmitting elements linearly arranged above the one-dimensional motion device, and sequentially transmitting linear frequency modulation signals based on a preset spatial scanning sequence;

[0024] The terahertz receiving module comprises N receiving array elements linearly arranged above a one-dimensional motion device, and the transmitting array elements are arranged in parallel with the receiving array elements and used for receiving echo signals scattered by a to-be-detected object.

[0025] The digital acquisition card converts the collected echo signals into echo real signals through analog-digital conversion.

[0026] The processor processes the echo real signals by using the above-mentioned terahertz three-dimensional imaging method based on Hilbert transform.

[0027] Compared with the prior art, the present application has the following beneficial effects:

[0028] The present application uses an AR model to extend the data at both ends of the signal, and then performs Hilbert transform on the signal to extract the phase information of the digital signal. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 It is a schematic diagram of the terahertz three-dimensional imaging system of the present application.

[0030] Figure 2 It is a flowchart of the present application. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below with reference to the embodiments.

[0032] As shown in the figure, the present application provides a terahertz three-dimensional imaging method based on Hilbert transform, which is applied to a MIMO array terahertz imaging system.

[0033] The MIMO array terahertz imaging system is as follows: Figure 1As shown, including a one-dimensional motion device and a parallel array of terahertz MIMO transceiving antenna array arranged on the one-dimensional motion device. The measured object is placed on the one-dimensional motion device, and is uniformly moved along the Y axis under the driving of the one-dimensional motion device, which meets the assumption of "one step and one stop". Assuming that the measured object moves j D =1, 2, …J D times, the target can be uniformly sampled in the Y direction J times. The antenna array adopts time division multiplexing transmission mode, and only one antenna transmits at each time, and all receiving antennas receive simultaneously. Assuming that there are M transmitting elements and N receiving elements, M*N equivalent channels will be formed, that is, M*N spatial sampling can be performed on the X axis. The signal source generates a linear frequency modulation signal, which is transmitted by the terahertz transmitting module, scattered by the measured object, and de-linear frequency modulation processed by the terahertz receiving module. The rear end adopts a digital acquisition card to collect digital intermediate frequency real signals. Assuming that the measured object target moves along the Y axis every time, the sampling point number of the system on the fast time is k D . The three-dimensional test data Data[k D ][i][j D ] of the measured object is finally obtained, wherein the sampling point number k D =1, 2, …K D ; the X-axis spatial sampling number i=1, 2, …M*N; and the Y-axis movement number j D =1, 2, …J D .

[0034] The present application adopts a flat metal plate as a standard piece for data calibration, and the standard piece adopts the same test method as the measured object. The standard piece is placed on the one-dimensional motion device and moved along the Y axis. The three-dimensional calibration data Cal[k C ][i][j C ] of the standard piece is finally obtained, wherein the sampling point number k C =1, 2, …K C ; the X-axis spatial sampling number i=1, 2, …M*N; and the Y-axis movement number j C =1, 2, …J C .

[0035] Since the key to imaging is to obtain the phase information of the signal, the Hilbert transform is used to obtain the phase information of the digital signal (including test data and calibration data). In order to eliminate the waveform distortion caused by the end effect of the signal waveform after the Hilbert transform, the present application adopts an autoregressive (AR, autoregressive) model to extend the data at both ends of the signal, and then performs Hilbert transform on the signal.

[0036] Specifically, taking the echo real signal of the to-be-tested object as an example, the test data deal[k] = Data[k][m][n] (k = 1, 2, … K, and K is even) collected by selecting the mth equivalent channel and the nth Y-axis movement collection are processed. The signal processing procedure is as follows:

[0037] The deal[k] is further forward and backward predicted p times by using an L-order AR model, and a new sequence extended digital signal deal new [k] is obtained, k = 1, 2, … K+2p.

[0038] The fast Fourier transform is performed on the extended digital signal deal new [k], and the frequency spectrum Spec[k] is obtained. The Hilbert transform is performed on the frequency spectrum Spec[k] in the frequency domain, and the analytic frequency spectrum Spec H [k] is obtained, and the calculation formula is as follows:

[0039]

[0040] At this time, Spec H [k] corresponds to the frequency spectrum of the complex signal.

[0041] Since the terahertz signal is relatively weak after scattering and other interference is introduced, it is necessary to filter and denoise the signal. Due to the geometric arrangement of the antenna array, the round trip distance from the transmitting antenna to the measured target and from the measured target to the receiving antenna is different for different transmitting antennas and receiving antennas, that is, the MxN equivalent channels formed are inconsistent with the round trip distance of the measured target. At the same time, since the to-be-tested object also has a geometric size, for the same equivalent channel, the round trip distance from the transmitting antenna to the measured target and from the measured target to the receiving antenna has a maximum distance and a minimum distance. Therefore, the bandwidth of the filter can be adaptively set according to the maximum and minimum distances of different equivalent channels and the to-be-tested object.

[0042] The present application adopts Kaiser window to perform windowing filtering in the frequency domain, combines the geometric size of the to-be-tested object, dynamically designs the bandwidth of the frequency domain filter according to the maximum and minimum round trip distances of the transmitting and receiving antennas of the mth channel and the to-be-tested object, so that the main lobe width of the Kaiser window is equal to the bandwidth of the frequency domain filter.

[0043] The terahertz transmitting module transmits a linear frequency modulation continuous wave, and after passing through an ideal scattering point, the terahertz receiving module receives the scattered signal. The system adopts a mixing method to obtain a difference frequency signal, and the difference frequency signal output in the complex form is expressed as:

[0044]

[0045] In the formula, A is the signal amplitude; f0 is the starting frequency of the frequency-modulated continuous wave of the signal; K is the modulation slope; and τ is the time interval between the transmitted signal and the echo signal, i.e., the delay.

[0046] ,

[0047] R t R is the distance between the scattering point and the transmitting antenna. r is the distance between the scattering point and the receiving antenna, and c is the speed of light.

[0048] In the above formula, the frequency of the difference frequency signal S(t) corresponding to a single scattering point can be considered as f=Kτ. Therefore, after the transmitted signal passes through a series of scattering points of the object under test, the bandwidth and center frequency of the difference frequency signal are determined by the maximum and minimum values ​​of τ.

[0049] First, measure the size of the object under test, construct a three-dimensional coordinate system between the object under test and the transmitting and receiving antennas, and calculate the maximum and minimum distances from the object under test to different equivalent channels.

[0050] like Figure 1 As shown, the i-th equivalent channel is selected as an example. Assume its corresponding transmit antenna coordinates are (x... t ,y t The coordinates of the receiving antenna are (x, 0). r ,y r ,0), Select the scattering point of the object to be measured according to the shape of the object and construct the position coordinates (x, 0), m ,y m ,z m If the four endpoints and center point of the object under test are selected, the time interval between the transmitted signal and the echo signal can be calculated:

[0051] ,

[0052] In the formula, τ m R is the time interval between the transmitted signal and the echo signal. tm R is the distance from the transmitting antenna to the object under test. rm This is the distance from the receiving antenna to the object under test.

[0053] According to Kτ m Maximum time interval τ max and minimum time interval τ min The bandwidth B and center frequency f of the received signal in the i-th equivalent channel can be estimated. c ,

[0054] ,

[0055] ,

[0056] Thus, the bandwidth and center frequency of the filter of the signal corresponding to different equivalent channels are adaptively set in the signal processing process.

[0057] Since the analytical spectrum Spec H [k] is 0 in the right half of the symmetric center, Kaiser window only needs to be applied to the analytical spectrum Spec H [k] in the left half. The analytical spectrum after windowing is Spec Win [k], k = 1, 2, … K + 2p.

[0058] The inverse Fourier transform is performed on Spec Win [k] to obtain time-domain complex data deal h [k], k = 1, 2, … K + 2p.

[0059] The first p data and the last p data of the time-domain complex data deal h [k] are removed to obtain target data deal complex [k] of the object to be measured with phase information, k = 1, 2, … K.

[0060] Based on the above method, the echo real signals Data[k D ][i][j D ] and Cal[k C ][i][j C ] of each equivalent channel of the object to be measured and the standard part are obtained, and the complex target data Data complex [k D ][i][j D ] and Cal complex [k C ][i][j C ] are obtained after processing, i.e., the phase information of the echo real signal of the object to be measured and the phase information of the echo real signal of the standard object. The target data Data complex [k D ][i][j D ] of the object to be measured is corrected by using the target data Cal complex [k D ][i][j D ] of the standard part. The data of each equivalent channel after correction is input into a back projection (BP) algorithm to generate three-dimensional imaging of the object to be measured. The back projection algorithm projects the value corresponding to the time delay in the target data onto the pixel points of the imaging grid, and finally forms an image through coherent accumulation of the projection values of all azimuth sampling moments.

[0061] The above-described embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that the technical solutions recorded in the foregoing embodiments can still be modified, or some technical features can be replaced by equivalent ones; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A terahertz three-dimensional imaging method based on Hilbert transform, characterized in that, include: Real echo signals from each equivalent channel of the test object and the standard part were collected respectively. By using an autoregressive model to predict p numbers at each end of the echo real signal, the extended digital signal is obtained. The spectrum is obtained by performing a fast Fourier transform on the extended digital signal; Perform a Hilbert transform on the spectrum in the frequency domain to obtain an analytical spectrum; The analytical spectrum is processed sequentially and subjected to inverse Fourier transform to obtain complex data in the time domain; Delete the p data points at both ends of the complex data in the time domain to obtain the target data; The target data of the test object is corrected based on the target data of the standard part, and the corrected data of each equivalent channel is input into the back projection algorithm to generate a three-dimensional image of the test object.

2. The terahertz three-dimensional imaging method based on Hilbert transform according to claim 1, characterized in that, The formula for calculating the Hilbert transform is as follows: ， In the formula, Spec_H[k] is the analytical spectrum, and Spec[k] is the spectrum.

3. The terahertz three-dimensional imaging method based on Hilbert transform according to claim 1, characterized in that, The windowing filtering process is a Kaiser window.

4. The terahertz three-dimensional imaging method based on Hilbert transform according to claim 3, characterized in that, The width of the main lobe of the Kaiser window is dynamically set based on the difference between the maximum and minimum round-trip distance between the transceiver antenna and the object under test.

5. The terahertz three-dimensional imaging method based on Hilbert transform according to claim 4, characterized in that, A three-dimensional coordinate system is constructed based on the dimensions of the object under test (DUT) and the transmitting and receiving antennas. Scattering points are selected according to the shape of the DUT. The maximum and minimum distances from the DUT to different equivalent channels are estimated. The maximum and minimum time intervals between the transmitted and echo signals are calculated. The bandwidth and center frequency of each equivalent channel are then estimated sequentially.

6. The terahertz three-dimensional imaging method based on Hilbert transform according to claim 5, characterized in that, The width of the main lobe of the Kaiser window is equal to the bandwidth.

7. A terahertz three-dimensional imaging system based on Hilbert transform, characterized in that, include: A signal source, wherein the signal source generates a linear frequency modulated pulse sequence; A one-dimensional motion device, on which an object to be measured is placed, and the one-dimensional motion device drives the object to be measured to move at a uniform speed. The terahertz transmitting module includes M transmitting array elements linearly arranged above a one-dimensional motion device, which transmit linear frequency modulated signals in turn based on a preset spatial scanning sequence; The terahertz receiving module includes N receiving array elements arranged linearly above a one-dimensional motion device. The transmitting array elements are arranged in parallel with the receiving array elements and are used to receive the echo signal scattered by the object under test. The digital acquisition card converts the acquired echo signal into a real echo signal via analog-to-digital conversion. The processor processes the echo real signal using the terahertz three-dimensional imaging method based on Hilbert transform as described in any one of claims 1-6.

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