CN110501707B - Electromagnetic vortex imaging method based on orbital angular momentum bimodal multiplexing - Google Patents
Electromagnetic vortex imaging method based on orbital angular momentum bimodal multiplexing Download PDFInfo
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Abstract
The electromagnetic vortex imaging method based on orbital angular momentum bimodal multiplexing comprises the steps of firstly constructing a uniform circular array, changing the frequency of an excitation signal emitted by the uniform circular array and the number of orbital angular momentum modes, and sequentially generating vortex electromagnetic waves which have different frequencies and carry different orbital angular momentum modal multiplexing to irradiate a target by the uniform circular array; sequentially receiving vortex electromagnetic wave target echo data multiplexed in different frequencies and different modes by adopting a single receiving array element antenna, and performing phase compensation processing on the vortex electromagnetic wave target echo data; and processing each target echo data after the phase compensation processing by adopting a Hilbert transform method, demodulating target information carried by a single orbital angular momentum mode, reconstructing frequency-single-mode two-dimensional echo data, and performing two-dimensional Fourier transform on the frequency-single-mode two-dimensional echo data to obtain a target two-dimensional image. Compared with vortex electromagnetic wave imaging which does not utilize modal multiplexing and carries single modal orbital angular momentum in a traversing manner, the method reduces orbital angular momentum traversal by half, and improves electromagnetic vortex imaging efficiency.
Description
Technical Field
The invention relates to the technical field of electromagnetic vortex imaging, in particular to an electromagnetic vortex imaging method based on orbital angular momentum bimodal multiplexing.
Background
As an all-weather and long-distance information acquisition mode, radar high-resolution imaging has very important application in the fields of space target monitoring, remote sensing mapping, ocean observation and the like. The existing high-resolution imaging radar mainly obtains the distance high resolution by transmitting a broadband signal, and forms a large virtual synthetic aperture by the relative motion of the radar and a target to obtain the azimuth high resolution. However, in practical applications, a certain key area is often subjected to a long-time uninterrupted gaze observation, and the radar and the target are in a relatively static observation geometric condition. Under the condition, the traditional radar high-resolution imaging system cannot meet the synthetic aperture requirement, and the imaging resolution is difficult to guarantee.
In recent years, orbital angular momentum has been widely used in the fields of optical communication, quantum imaging, microwave imaging, and the like. The traditional plane waves have difference only in the distance direction, and the direction perpendicular to the propagation direction contains the same phase information, so that the traditional plane waves cannot provide direction resolution under the staring observation geometrical condition.
Unlike conventional plane waves, electromagnetic waves carrying orbital angular momentum have a helical phase front, called vortex electromagnetic waves, with phase differences in both the distance and azimuth directions. When the vortex electromagnetic wave irradiates the target, the distance direction and the azimuth direction of the target can be scaled by phase difference information, and the echo information can provide difference information required for distinguishing the distance direction and the azimuth direction. By utilizing the phase wavefront difference and processing the vortex electromagnetic wave echo, high-resolution imaging of the radar target can be realized. The electromagnetic vortex imaging realizes two-dimensional resolution of the target distance direction and the azimuth direction by utilizing vortex electromagnetic waves, does not depend on relative motion of a radar and a target, is expected to form complementation with imaging modes such as synthetic aperture/inverse synthetic aperture and the like, and provides a new imaging mode.
The azimuth resolution of electromagnetic vortex imaging is related to the range of orbital angular momentum modes, and the higher the number of the modes, the higher the azimuth resolution. In order to obtain high azimuth resolution, electromagnetic vortex imaging needs to irradiate a target by using vortex electromagnetic waves of various modes. At present, electromagnetic vortex imaging mainly utilizes vortex electromagnetic waves carrying single orbital angular momentum to sequentially irradiate a target, different modes need to be traversed, and the electromagnetic vortex imaging efficiency is limited.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide an electromagnetic vortex imaging method based on orbital angular momentum bimodal multiplexing. Vortex electromagnetic waves multiplexed by the orbital angular momentum mode carry a plurality of orbital angular momentum modes, when the vortex electromagnetic waves multiplexed by the modes irradiate a target, single mode information is demodulated through target echo processing, and the vortex electromagnetic waves which are equivalent to the vortex electromagnetic waves carrying single orbital angular momentum are traversed for multiple times, so that the irradiation time of the vortex electromagnetic waves is expected to be reduced, and the electromagnetic vortex imaging efficiency is improved.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that:
the electromagnetic vortex imaging method based on orbital angular momentum bimodal multiplexing comprises the following steps:
s1, constructing a uniform circular array for generating vortex electromagnetic waves carrying positive and negative bimodal multiplexing;
s2, changing the frequency f of an excitation signal transmitted by a uniform circular array and the number l of orbital angular momentum modes, wherein the uniform circular array sequentially generates vortex electromagnetic wave irradiation targets with different frequencies and carrying different orbital angular momentum mode multiplexing; sequentially receiving vortex electromagnetic wave target echo data multiplexed in different frequencies and different modes by adopting a single receiving array element antenna;
s3, performing phase compensation processing on each target echo data received by a single receiving array element antenna;
and S4, processing each target echo data after phase compensation processing by adopting a Hilbert transform method, demodulating target information carried by a single orbital angular momentum mode, and reconstructing frequency-single mode two-dimensional echo data.
And S5, carrying out two-dimensional Fourier transform on the frequency-single-mode two-dimensional echo data to obtain a target two-dimensional image.
In S1 of the present invention, N identical transmitting antenna elements are arranged at equal intervals on a circumference with a radius of a to form a uniform circular array. One of the transmitting antenna array elements is randomly selected as an initial transmitting array element, and the azimuth angle of the initial transmitting array element is set to be zero degree. Starting from the initial transmitting array element along the anticlockwise direction of the circumference, sequentially numbering all transmitting antenna array elements on the uniform circular array as 1,2,3, … and N, wherein the azimuth angle of the nth transmitting antenna array element is phin＝2π(n-1)/N。
In order to generate vortex electromagnetic waves carrying positive and negative bimodal multiplexing, the amplitude and the phase of an excitation signal of each transmitting antenna array element are designed according to array parameters of a uniform circular array and orbital angular momentum modal numbers of modal multiplexing, and the method comprises the following steps:
when the bimodal multiplexing orbital angular momentum mode number of the vortex electromagnetic wave carrying positive and negative bimodal multiplexing generated by the uniform circular array is +/-l, the excitation signal of the nth transmitting antenna array element of the uniform circular array is cos (l phi)n) I.e. the amplitude of the excitation signal of the nth transmit antenna element is | cos (l φ)n) I, the phase of the excitation signal of the nth transmitting antenna array element is ≈ cos (l phi)n) Wherein | represents an absolute value, phi represents an angle value, phinIs the azimuth angle of the nth transmit antenna element. When all transmitting antenna array elements in the uniform circular array simultaneously apply excitation signals according to the requirements, and the frequency of the excitation signals is f, any point in space
Electric field strength value of
Can be expressed as
Wherein i is an imaginary number unit, l is a multiplexed orbital angular momentum mode number, and N is a uniform circular arrayThe number of elements of the transmitting antenna on, r represents a point
R, theta,
Are respectively a point
Distance, pitch angle and azimuth angle in polar coordinates, rnRepresenting the position vector of the nth transmit antenna element. k 2 pi f/c represents the wave number of the emitted monochromatic signal (c is the propagation speed of light in vacuum), and Jl(kasin θ) is a first class of Bessel function of order l.
In the invention S2, the frequency f of the excitation signal transmitted by the uniform circular array and the orbital angular momentum mode number l are changed, and the frequency f of the excitation signal sequentially transmitted by the uniform circular array is set as f1,f2,…,fPThe orbital angular momentum mode number is l ═ l1,±l2,…,±lQP, Q are the excitation signal frequency and the orbital angular momentum transmission times, respectively. The receiving frequency of a single receiving array element antenna is fpThe orbital angular momentum mode number is +/-lqIs recorded as spqWherein P is 1,2,3 … P; q is 1,2,3 … Q. The target data under the excitation signal frequency and different orbital angular momentum mode numbers form a frequency-multiplexing mode echo data set with dimension of P × Q, which is recorded as sPQEach column of the frequency-multiplexing mode echo data set is a vortex electromagnetic wave target echo signal with the same orbital angular momentum mode number and different excitation signal frequencies, and each column is a vortex electromagnetic wave target echo signal with the same excitation signal frequency and different orbital angular momentum mode numbers.
In the present invention S2, the target includes M scattering points, and the backscattering coefficient of the M-th scattering point is σmThe polar coordinate of the m-th scattering point is
By single jointReceiving vortex electromagnetic wave target echo with excitation signal frequency f and orbital angular momentum modal number +/-l by an array element antenna, wherein the target echo can be expressed as:
wherein f ═ f1,f2,…,fP，l＝±l1,±l2,…,±lQ。
In S3 of the present invention, a method for performing phase compensation processing on each target echo data received by a single receiving array element antenna is as follows:
for each target echo data s received by single receiving array element antennapqFirstly, according to the corresponding orbital angular momentum mode number lqIs multiplied by
To compensate for the common phase;
secondly according to the orbital angular momentum mode number lqWave number k of transmission signalpCalculating the array radius a and the pitch angle theta of the target
For the target echo data s according to the formula (3)pqMultiplying by the phase term Ψpq。
Thus, the target echo data s received for a single receiving element antennapqAfter the phase compensation processing is carried out, the obtained target echo data SpqThe expression of (a) is as follows:
likewise, for single receptionEach target echo data s received by array element antennapqTarget echo data S obtained after phase compensation processingpqA new P x Q dimensional data matrix can be constructed, denoted SPQ。
The implementation method of the S4 of the invention is as follows:
s4.1 demodulating target echo Sr carrying positive mode informationpq；
The receiving frequency f obtained after the phase compensation processingpThe orbital angular momentum mode number is +/-lqTarget echo data SpqPerforming Hilbert transform to demodulate at a frequency fpThe orbital angular momentum mode number is lqAs shown in equation (5), where H [ · is]Are hilbert transformed symbols.
S4.2 demodulating the target echo Sr carrying the negative mode informationp′q；
Firstly, the target echo data S after phase compensation processing is requiredpqRespectively performing Hilbert transform processing on the real part data and the imaginary part data, and subtracting the Hilbert transform result of the imaginary part data from the Hilbert transform result of the real part data to obtain S'pqAs shown in equation (6):
wherein Re (S)pq) For the phase-compensated processed target echo data SpqReal part of, Im (S)pq) For the phase-compensated processed target echo data SpqThe imaginary part of (c).
Then, S'pqTaking the conjugate, the frequency f can be demodulatedpThe orbital angular momentum mode number is-lqThe target echo data of (2) as shown in equation (7).
S4.3 demodulating the target echo Sr which carries the positive mode informationpqAnd a target echo Sr 'carrying negative mode information'pqForming a new P × 2Q dimension frequency-single mode echo data, wherein the range of orbital angular momentum mode number is l ═ -lQ,-lQ-1,…-l1,l1,…,lQ。
When vortex electromagnetic waves with orbital angular momentum dual-mode multiplexing are emitted to irradiate a target through the designed uniform circular array, target echoes under 2Q modes can be reconstructed only through Q times of emission and reception, the orbital angular momentum traversal is reduced by half, and the electromagnetic vortex imaging efficiency is improved.
In the invention, in S5, the two-dimensional fourier transform is performed on the new frequency-single mode echo data of dimension P × 2Q finally obtained in S4, so that a target two-dimensional image can be obtained.
Electromagnetic vortex imaging system based on orbital angular momentum bimodal multiplexing includes:
and the uniform circular array is used for generating vortex electromagnetic wave irradiation targets with different frequencies and carrying different orbital angular momentum modal multiplexes. The design of the uniform circular array has been described in detail above and will not be described in detail here.
And the single receiving array element antenna is used for receiving vortex electromagnetic wave target echo data multiplexed in different frequencies and different modes.
The phase compensation module is used for performing phase compensation processing on each target echo data received by a single receiving array element antenna;
the target information demodulation reconstruction module is used for performing Hilbert transform on each target echo data after phase compensation processing, demodulating target information carried by a single orbital angular momentum mode, and reconstructing frequency-single mode two-dimensional echo data;
and the target two-dimensional image acquisition module is used for carrying out two-dimensional Fourier transform on the frequency-single-mode two-dimensional echo data to obtain a target two-dimensional image.
The invention has the beneficial technical effects that:
the invention utilizes vortex electromagnetic waves multiplexed by orbital angular momentum modes to carry out target two-dimensional imaging. The vortex electromagnetic wave carrying orbital angular momentum has a unique phase wavefront structure, and can carry richer target azimuth distribution information, and the wavefront phase of the vortex electromagnetic wave is no longer a plane. The vortex electromagnetic wave is used for imaging, the relative motion between the target and the radar is not depended on, and the two-dimensional imaging of the target is realized under the staring observation condition. Compared with vortex electromagnetic wave imaging which does not utilize modal multiplexing and carries single modal orbital angular momentum in a traversing manner, the electromagnetic vortex imaging method based on orbital angular momentum dual-modal multiplexing reduces orbital angular momentum traversing by half, and improves electromagnetic vortex imaging efficiency.
Drawings
FIG. 1 is a schematic diagram of an electromagnetic vortex imaging flow based on orbital angular momentum bimodal multiplexing according to the present invention;
FIG. 2 is a schematic diagram of electromagnetic vortex imaging based on orbital angular momentum bimodal multiplexing in one embodiment of the invention;
FIG. 3 is a two-dimensional result of a point spread function of the method of the present invention and a single modality traversal imaging method; wherein, fig. 3(a) is the point spread function imaging result obtained by the electromagnetic vortex imaging method based on orbital angular momentum bimodal multiplexing, and fig. 3(b) is the point spread function imaging result obtained by imaging only traversing vortex electromagnetic waves carrying a single mode without mode multiplexing
FIG. 4 is a comparison of the orientation dimension point spread function of the method of the present invention and a single modality traversal imaging method;
FIG. 5 is a numerical simulation imaging result of the method of the present invention, wherein FIG. 5(a) is a model of the scattering points of an aircraft target. FIG. 5(b) is a result of a numerical simulation of the target of FIG. 5(a) using the method of the present invention.
Detailed Description
In order to facilitate the practice of the invention, further description is provided below with reference to specific examples.
Referring to fig. 1, the present embodiment provides an electromagnetic vortex imaging method based on orbital angular momentum bimodal multiplexing, including the following steps:
s1, constructing a uniform circular array for generating vortex electromagnetic waves carrying positive and negative bimodal multiplexing.
Referring to fig. 2, N identical transmitting antenna elements are arranged at equal intervals on a circumference with a radius a to form a uniform circular array. One of the transmitting antenna array elements is randomly selected as an initial transmitting array element, and the azimuth angle of the initial transmitting array element is set to be zero degree. Starting from the initial transmitting array element along the anticlockwise direction of the circumference, sequentially numbering all transmitting antenna array elements on the uniform circular array as 1,2,3, … and N, wherein the azimuth angle of the nth transmitting antenna array element is phin＝2π(n-1)/N。
In order to generate vortex electromagnetic waves carrying positive and negative bimodal multiplexing, the amplitude and the phase of an excitation signal of each transmitting antenna array element are designed according to array parameters of a uniform circular array and orbital angular momentum modal numbers of modal multiplexing.
When the bimodal multiplexing orbital angular momentum mode number of the vortex electromagnetic wave carrying positive and negative bimodal multiplexing generated by the uniform circular array is +/-l, the excitation signal of the nth transmitting antenna array element of the uniform circular array is cos (l phi)n) I.e. the amplitude of the excitation signal of the nth transmit antenna element is | cos (l φ)n) I, the phase of the excitation signal of the nth transmitting antenna array element is ≈ cos (l phi)n) Wherein | represents an absolute value, phi represents an angle value, phinIs the azimuth angle of the nth transmit antenna element. When all transmitting antenna array elements in the uniform circular array simultaneously apply excitation signals according to the requirements, and the frequency of the excitation signals is f, any point in space
Electric field strength value of
Can be expressed as
Wherein i is an imaginary number unit, l is a multiplexing orbital angular momentum mode number, N is a transmitting antenna array element number on the uniform circular array, and r represents a point
R, theta,
Are respectively a point
Distance, pitch angle and azimuth angle in polar coordinates, rnRepresenting the position vector of the nth transmit antenna element. k 2 pi f/c represents the wave number of the emitted monochromatic signal (c is the propagation speed of light in vacuum), and Jl(kasin θ) is a first class of Bessel function of order l.
S2, changing the frequency f of an excitation signal transmitted by a uniform circular array and the number l of orbital angular momentum modes, wherein the uniform circular array sequentially generates vortex electromagnetic wave irradiation targets with different frequencies and carrying different orbital angular momentum mode multiplexing; and a single receiving array element antenna is adopted to sequentially receive vortex electromagnetic wave target echo data multiplexed in different frequencies and different modes.
Changing the frequency f of the excitation signal transmitted by the uniform circular array and the orbital angular momentum mode number l, and setting the frequency f of the excitation signal sequentially transmitted by the uniform circular array as f ═ f1,f2,…,fPThe orbital angular momentum mode number is l ═ l1,±l2,…,±lQP, Q are the excitation signal frequency and the orbital angular momentum transmission times, respectively. The receiving frequency of a single receiving array element antenna is fpThe orbital angular momentum mode number is +/-lqIs recorded as spqWherein P is 1,2,3 … P; q is 1,2,3 … Q. The target data under the excitation signal frequency and different orbital angular momentum mode numbers form a frequency-multiplexing mode echo data set with dimension of P × Q, which is recorded as sPQWherein each column of the frequency-multiplexing modal echo data set is a vortex electromagnetic wave target echo signal with the same orbital angular momentum modal number and different excitation signal frequenciesAnd each action is a vortex electromagnetic wave target echo signal with the same excitation signal frequency and different orbital angular momentum mode numbers.
Let the target contain M scattering points, the M-th scattering point has a backscattering coefficient of sigmamThe polar coordinate of the m-th scattering point is
Receiving vortex electromagnetic wave target echo data with excitation signal frequency f and orbital angular momentum modal number +/-l by using a single receiving array element antenna, wherein the target echo data can be expressed as follows:
wherein f ═ f1,f2,…,fP，l＝±l1,±l2,…,±lQ。
And S3, performing phase compensation processing on each target echo data received by a single receiving array element antenna.
Amplitude envelope J in vortex electromagnetic wave target echo data received by single receiving array element antennal(kasinθm) The sign of (1) changes with the orbital angular momentum mode number l, and the sign destroys the relation between the azimuth and the orbital angular momentum, and affects the azimuth resolution, so that the phase compensation is carried out on the vortex electromagnetic wave target echo signal.
For each target echo data s received by single receiving array element antennapqFirstly, according to the corresponding orbital angular momentum mode number lqIs multiplied by
To compensate for the common phase; secondly according to the orbital angular momentum mode number lqWave number k of transmission signalpCalculating the array radius a and the pitch angle theta of the target
For the target echo number according to equation (3)According to spqMultiplying by the phase term Ψpq。
Thus, the target echo data s received for a single receiving element antennapqAfter the phase compensation processing is carried out, the obtained target echo data SpqThe expression of (a) is as follows:
similarly, each target echo data s received by a single receiving array element antennapqTarget echo data S obtained after phase compensation processingpqA new P x Q dimensional data matrix can be constructed, denoted SPQ。
And S4, processing each target echo data after phase compensation processing by adopting a Hilbert transform method, demodulating target information carried by a single orbital angular momentum mode, and reconstructing frequency-single mode two-dimensional echo data.
Target echo data S obtained after phase compensation processingpqSimultaneously carrying echo information of a positive mode and a negative mode, and carrying out phase compensation processing on target echo data SpqAnd performing Hilbert transform processing to demodulate a target echo carrying single positive mode (l is more than or equal to 0) information. When the frequency emission times and the orbital angular momentum emission times are P, Q respectively, the total number of the demodulated positive mode echo data is P × Q.
S4.1 demodulating target echo Sr carrying positive mode informationpq；
The receiving frequency f obtained after the phase compensation processingpThe orbital angular momentum mode number is +/-lqTarget echo data SpqPerforming Hilbert transform to demodulate at a frequency fpThe orbital angular momentum mode number is lqAs shown in equation (5), where H [ · is]Are hilbert transformed symbols.
In order to demodulate a target echo carrying information of a single negative mode (l is less than 0), the Hilbert transform is required to be deformed.
S4.2 demodulating target echo Sr 'carrying negative mode information'pq；
Firstly, the target echo data S after phase compensation processing is requiredpqRespectively performing Hilbert transform processing on the real part data and the imaginary part data, and subtracting the Hilbert transform result of the imaginary part data from the Hilbert transform result of the real part data to obtain S'pqAs shown in equation (6):
wherein Re (S)pq) For the phase-compensated processed target echo data SpqReal part of, Im (S)pq) For the phase-compensated processed target echo data SpqThe imaginary part of (c).
Then, S'pqTaking the conjugate, the frequency f can be demodulatedpThe orbital angular momentum mode number is-lqThe target echo data of (2) as shown in equation (7).
Similarly, when the frequency transmission times and the orbital angular momentum transmission times are P, Q, respectively, the demodulated negative mode echo data are P × Q.
S4.3 demodulating the target echo Sr which carries the positive mode informationpqAnd a target echo Sr 'carrying negative mode information'pqForming a new P × 2Q dimension frequency-single mode echo data, wherein the range of orbital angular momentum mode number is l ═ -lQ,-lQ-1,…-l1,l1,…,lQ。
When vortex electromagnetic waves with orbital angular momentum dual-mode multiplexing are emitted to irradiate a target through the designed uniform circular array, target echoes under 2Q modes can be reconstructed only through Q times of emission and reception, the orbital angular momentum traversal is reduced by half, and the electromagnetic vortex imaging efficiency is improved.
And S5, performing two-dimensional Fourier transform on the new frequency-single-mode echo data with dimension of P multiplied by 2Q finally obtained in the step S4 to obtain a target two-dimensional image.
FIG. 3 is a comparison of the present invention with a point spread function simulation that does not utilize modal multiplexing, but only traverses modes carrying a single orbital angular momentum.
The method of the invention is adopted, namely, the vortex electromagnetic wave is transmitted by utilizing the uniform circular array, the number of the transmitting antenna array elements is 80, the circumference radius of the uniform circular array is 0.6m, the ideal point target distance is 1000m, and the azimuth angle is 0.5 pi. The frequency of the transmitted signal is 9.9GHz-10.1GHz, and the frequency sampling interval is 1 MHz. When the method provided by the invention is adopted, when the uniform circular array emits the bimodal multiplexing vortex electromagnetic wave to irradiate the target, the orbital angular momentum mode number l is [0, +/-15 ], and the irradiation is carried out for 16 times in total.
When the target is irradiated by adopting the vortex electromagnetic wave which does not utilize mode multiplexing and only carries a single orbital angular momentum mode in a traversing way, the number l of the orbital angular momentum modes is [ -15,15], and the irradiation is carried out for 31 times.
Wherein, fig. 3(a) is a point spread function imaging result obtained by the electromagnetic vortex imaging method based on orbital angular momentum bimodal multiplexing, and fig. 3(b) is a point spread function imaging result obtained by imaging only by traversing vortex electromagnetic waves carrying a single mode without mode multiplexing. FIG. 4 is a comparison of the method of the present invention with a single modality traversal imaging orientation dimension point spread function. It can be seen from the point spread function two-dimensional imaging result and the azimuth dimension distribution that, compared with the electromagnetic vortex imaging using the vortex electromagnetic wave carrying a single mode, the method provided by the invention can demodulate twice the orbital angular momentum information, i.e. half of the mode traversal time can be reduced on the premise of obtaining the same azimuth dimension resolution.
FIG. 5 is a result of numerical simulation imaging of a multiple scatter point target according to the method of the present invention. FIG. 5(a) is a model of the scattering points of an aircraft object. The number of the array elements is 200, the radius of the array elements is 1.8m, the target model is at 1005m-1025m, and the azimuth angle is distributed between 0-0.25 pi. The frequency is 9.9GHz-10.1GHz, the frequency sampling interval is 1MHz, the signal-to-noise ratio of the received signal is 10dB, the modal range of the transmitted bimodal multiplexing vortex electromagnetic wave is [0, +/-50 ], and the total number of irradiation is 51. Fig. 5(b) is the result of numerical simulation imaging of the target by the method of the present invention, and it can be seen from the figure that the imaging method proposed by the present invention is also suitable for two-dimensional imaging of a multi-scattering point target under single-array-element receiving condition.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (7)
1. The electromagnetic vortex imaging method based on orbital angular momentum bimodal multiplexing is characterized by comprising the following steps of:
s1, constructing a uniform circular array for generating vortex electromagnetic waves carrying positive and negative bimodal multiplexing;
s2, changing the frequency f of an excitation signal transmitted by a uniform circular array and the number l of orbital angular momentum modes, wherein the uniform circular array sequentially generates vortex electromagnetic wave irradiation targets with different frequencies and carrying different orbital angular momentum mode multiplexing; sequentially receiving vortex electromagnetic wave target echo data multiplexed in different frequencies and different modes by adopting a single receiving array element antenna;
s3, performing phase compensation processing on each target echo data received by a single receiving array element antenna;
s4, processing each target echo data after phase compensation processing by adopting a Hilbert transform method, demodulating target information carried by a single orbital angular momentum mode, and reconstructing frequency-single mode two-dimensional echo data;
s4.1 demodulating target echo Sr carrying positive mode informationpq；
The receiving frequency obtained after the phase compensation processing is fpThe orbital angular momentum mode number is +/-lqTarget echo data SpqPerforming Hilbert transform to demodulate to obtain a frequency fpThe orbital angular momentum mode number is lqAs shown in equation (5), where H [ · is]Is a Hilbert transform symbol;
s4.2 demodulating target echo Sr 'carrying negative mode information'pq；
Firstly, the target echo data S after phase compensation processing is requiredpqRespectively performing Hilbert transform processing on the real part data and the imaginary part data, and subtracting the Hilbert transform result of the imaginary part data from the Hilbert transform result of the real part data to obtain S'pqAs shown in equation (6):
wherein Re (S)pq) For the phase-compensated processed target echo data SpqReal part of, Im (S)pq) For the phase-compensated processed target echo data SpqAn imaginary part of (d);
then, S'pqTaking the conjugate, the frequency f can be demodulatedpThe orbital angular momentum mode number is-lqTarget echo data Sr'pqAs shown in equation (7);
s4.3 demodulating the target carrying the positive mode informationEcho SrpqAnd a target echo Sr 'carrying negative mode information'pqForming a new P × 2Q dimension frequency-single mode echo data, wherein the range of orbital angular momentum mode number is l ═ -lQ,-lQ-1,…-l1,l1,…,lQ；
And S5, carrying out two-dimensional Fourier transform on the frequency-single-mode two-dimensional echo data to obtain a target two-dimensional image.
2. The orbital angular momentum bimodal multiplexing-based electromagnetic vortex imaging method of claim 1, wherein in S1, N identical transmitting antenna elements are arranged at equal intervals on a circle with a radius a to form a uniform circular array; randomly selecting one of the transmitting antenna array elements as an initial transmitting array element, wherein the azimuth angle of the initial transmitting array element is set to be zero degree; starting from the initial transmitting array element along the anticlockwise direction of the circumference, sequentially numbering all transmitting antenna array elements on the uniform circular array as 1,2,3, … and N, wherein the azimuth angle of the nth transmitting antenna array element is phin＝2π(n-1)/N。
3. The electromagnetic vortex imaging method based on orbital angular momentum bimodal multiplexing of claim 2, wherein in S1, when the orbital angular momentum mode number of bimodal multiplexing of the vortex electromagnetic waves carrying positive and negative bimodal multiplexing generated by the uniform circular array is +/-l, the excitation signal of the nth transmitting antenna array element of the uniform circular array should be cos (l phi)n) I.e. the amplitude of the excitation signal of the nth transmit antenna element is | cos (l φ)n) I, the phase of the excitation signal of the nth transmitting antenna array element is ≈ cos (l phi)n) Wherein | represents an absolute value, phi represents an angle value, phinThe azimuth angle of the nth transmitting antenna array element is obtained; when all transmitting antenna array elements in the uniform circular array simultaneously apply excitation signals according to the requirements, and the frequency of the excitation signals is f, any point in space
Electric field strength value of
Expressed as:
wherein i is an imaginary number unit, l is a multiplexing orbital angular momentum mode number, N is a transmitting antenna array element number on the uniform circular array, and r represents a point
R, theta,
Are respectively a point
Distance, pitch angle and azimuth angle in polar coordinates, rnA position vector representing an nth transmit antenna element; k 2 pi f/c represents the wave number of the emitted monochromatic signal, c is the propagation speed of light in vacuum, Jl(kasin θ) is a first class of Bessel function of order l.
4. The orbital angular momentum bimodal multiplexing-based electromagnetic vortex imaging method of any one of claims 1 to 3, wherein: in S2, the frequency f of the excitation signals transmitted by the uniform circular array and the number l of orbital angular momentum modes are changed, and the frequency f of the excitation signals sequentially transmitted by the uniform circular array is set to f1,f2,…,fPThe orbital angular momentum mode number is l ═ l1,±l2,…,±lQP, Q are respectively the excitation signal frequency and the orbit angular momentum transmitting times; the receiving frequency of a single receiving array element antenna is fpThe orbital angular momentum mode number is +/-lqIs recorded as spqWherein P is 1,2,3 … P; q is 1,2,3 … Q; the frequency of the excitation signal and the number of different orbital angular momentum modesWill form a frequency-multiplexing mode echo data set forming dimension P x Q, which is denoted as sPQ。
5. The orbital angular momentum bimodal multiplexing-based electromagnetic vortex imaging method of claim 4, wherein: in S2, the target includes M scattering points, and the backscattering coefficient of the M-th scattering point is σmThe polar coordinate of the m-th scattering point is
Receiving a vortex electromagnetic wave target echo with an excitation signal frequency of f and orbital angular momentum modal number of +/-l by using a single receiving array element antenna, wherein the target echo can be expressed as:
wherein f ═ f1,f2,…,fP，l＝±l1,±l2,…,±lQ。
6. The orbital angular momentum bimodal multiplexing-based electromagnetic vortex imaging method of claim 5, wherein: the implementation method of S3 is as follows:
for each target echo data s received by single receiving array element antennapqFirstly, according to the corresponding orbital angular momentum mode number lqIs multiplied by
To compensate for the common phase;
secondly according to the orbital angular momentum mode number lqWave number k of transmission signalpCalculating the array radius a and the pitch angle theta of the target
For the target echo data s according to the formula (3)pqMultiplying by the phase term Ψpq；
Target echo data s received by single receiving array element antennapqAfter the phase compensation processing is carried out, the obtained target echo data SpqThe expression of (a) is as follows:
for each target echo data s received by single receiving array element antennapqTarget echo data S obtained after phase compensation processingpqA new P x Q dimensional data matrix can be constructed, denoted SPQ。
7. The orbital angular momentum bimodal multiplexing-based electromagnetic vortex imaging method of claim 6, wherein: in S5, the two-dimensional fourier transform is performed on the new frequency-single mode echo data of dimension P × 2Q finally obtained in S4, so that a target two-dimensional image can be obtained.
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