A microwave imaging system and imaging method based on folded feed active transmit array

Abstract

The application discloses a microwave imaging system and imaging method based on a folded feed active transmitarray. In the application, the folded feed active transmitarray is composed of a feed, a polarization rotation reflectarray and a programmable transmitarray, the distance of the feed is shortened to 1 / 3 of the focal length by using twice reflection of incident waves between the programmable transmitarray and the polarization rotation reflectarray, and the profile of the imaging system is reduced. The programmable transmitarray has the characteristics of wide band, low insertion loss, low cost and convenient control. In the imaging process, random focusing beams are generated by the folded feed active transmitarray to perform sparse sampling on the imaging plane, and the scattering echo of a target object is obtained by using multiple receiving antennas, and combined with a compression sensing algorithm, an image of the target object can be quickly reconstructed from a small amount of measurement signals, and the whole system has the advantages of low profile, low loss, low hardware cost, high integration, fast imaging speed and the like.

Description

Technical Field

[0001] This invention relates to the field of microwave imaging technology, and in particular to a microwave imaging system and imaging method based on a folded feed active transmission array. Background Technology

[0002] Microwave imaging is a method of acquiring information about target objects using electromagnetic waves in the microwave frequency band. It has wide applications in medicine, geographic resource exploration, military applications, and security inspection. Microwaves refer to electromagnetic waves with frequencies in the range of 300MHz-300GHz. These waves have excellent penetrating power through rain, fog, walls, clothing, plastics, and other media. Utilizing this property, microwave imaging can detect the shape, material properties, and spatial location of objects hidden beneath media, and it can achieve all-weather detection, which is impossible with optical imaging. Furthermore, microwaves do not harm the human body, and the resolution of microwave imaging has now reached the millimeter level, sufficient to detect dangerous items hidden under clothing, such as handguns, knives, and explosives. This makes it ideal for security inspection systems in public places such as airports and train stations. Thanks to advancements in semiconductor technology, microwave imaging systems offer higher hardware integration and lower costs. In recent years, microwave imaging technology has been extensively researched. Although some progress has been made, high-resolution, real-time imaging, and low-cost large-aperture microwave imaging systems, especially those used for human body security inspections, still face many challenges.

[0003] In recent years, the development of sparse signal processing and compressed sensing theory has provided new solutions for microwave imaging. The compressed sensing (CS) theory proposed by Dohono et al. in 2006 states that for a signal with sparse characteristics, the original signal can be accurately recovered from a small number of incoherent measurements when the sampling frequency is lower than the Nyquist sampling frequency. In microwave imaging, researchers both domestically and internationally, such as the DRSimth research group at Duke University and the Cui Tiejun research group at Southeast University, have proposed various microwave imaging systems and methods based on compressed sensing theory. The introduction of compressed sensing theory makes hardware design more flexible. Incoherent measurements are often achieved through random beams, and some low-cost antenna structures, such as the currently most common frequency-diversity antennas and programmable metasurfaces, can be used to generate random beams. Compared with traditional microwave imaging systems, compressed sensing-based microwave imaging systems have the advantages of low cost, fast imaging speed, and high resolution.

[0004] Frequency-diversity antennas refer to antennas with different radiation characteristics at different operating frequencies, such as resonant cavities with etched slots of different sizes. To generate a sufficient number of incoherent measurements, these antennas often need to operate over a wide frequency band. Although these antennas have advantages such as low cost, low profile, and ease of fabrication, they require a large bandwidth, wasting spectrum resources. Furthermore, broadband RF transceivers increase the cost of the imaging system. To address this issue, the research group of Cui Tiejun at Southeast University proposed using programmable metasurfaces in microwave imaging systems. By programming and changing the characteristics of the metasurface units, such as transmission or reflection characteristics, a sufficient number of incoherent measurement modes can be generated at a single frequency, greatly saving spectrum resources. Programmable metasurfaces are also low-cost and their aperture is easily scalable. However, most programmable metasurfaces have high losses, which reduces the signal-to-noise ratio of the imaging measurement signal. For large-aperture programmable metasurfaces, to ensure that each metasurface unit is effectively illuminated, the distance between the feed and the metasurface needs to be increased, increasing the system profile. These drawbacks hinder the widespread application of imaging systems based on programmable metasurfaces in practical applications. Summary of the Invention

[0005] To address the problems existing in the background art, this invention provides a microwave imaging system and imaging method based on a folded feed active transmission array. The programmable transmission array unit structure adopts a transceiver antenna form, realizing a programmable transmission array with low insertion loss and 1-bit 0° / 180° phase modulation. By placing the feed of the programmable transmission array in the middle of a designed polarization rotating reflector array, and placing the polarization direction of the feed orthogonal to the polarization direction of the programmable transmission array, the electromagnetic waves radiated by the feed pass through the programmable transmission array only after two reflections. This effectively shortens the distance between the feed and the programmable transmission array to 1 / 3 of the focal length, realizing a low-cost, low-profile, low-loss, and high-resolution microwave imaging system.

[0006] This invention is achieved through the following technical solution:

[0007] I. A microwave imaging system based on a folded feed active transmission array

[0008] The system includes a feed, a polarized rotating reflector array, a support frame, a receiving antenna, a programmable transmission array, a logic voltage control module, an RF transceiver module, a power combining module, and a microcontroller system.

[0009] The polarized rotating reflector array and the programmable transmission array are arranged vertically at intervals and are fixedly connected by a bracket. The feed is fixedly installed in the middle of the polarized rotating reflector array, and multiple receiving antennas are arranged at intervals on the sides of the programmable transmission array. The feed, polarized rotating reflector array, bracket, and programmable transmission array form a folded feed active transmission array, which is used to generate a randomly focused beam to illuminate the imaging target object. The feed is connected to the transmit port of the RF transceiver module, the receive port of the RF transceiver module is connected to the output port of the power combining module, the input port of the power combining module is connected to multiple receiving antennas, the programmable transmission array is connected to the logic voltage control module, and both the RF transceiver module and the logic voltage control module are connected to the microcontroller system.

[0010] The programmable transmission array is composed of Np identical transmission elements arranged uniformly in two dimensions, with the spacing between the transmission elements being half the wavelength of the center operating frequency of the programmable transmission array.

[0011] The transmission unit comprises an upper antenna structure layer, a first dielectric layer, an upper metal ground layer, a second dielectric layer, a DC bias circuit layer, a third dielectric layer, a lower metal ground layer, a fourth dielectric layer, and a lower antenna structure layer arranged in sequence. The upper antenna structure layer is connected to the upper metal ground layer, and from top to bottom, the upper antenna structure layer is also connected to the lower metal ground layer and the lower antenna structure layer in sequence. The DC bias circuit layer is directly connected to the lower antenna structure layer, and the DC bias circuit layer is connected to the logic voltage control module.

[0012] The upper antenna structure layer includes four upper rectangular metal rings, two PIN diodes, and three upper rectangular metal strips. The three upper rectangular metal strips are arranged sequentially and at intervals along a straight line in the middle of the upper surface of the first dielectric layer. From left to right, they are referred to as the first upper rectangular metal strip, the second upper rectangular metal strip, and the third upper rectangular metal strip. The first and second upper rectangular metal strips are connected by a PIN diode, and the second and third upper rectangular metal strips are connected by another PIN diode. The two ends of the second upper rectangular metal strip are connected to the positive terminal of one PIN diode and the negative terminal of the other PIN diode, respectively. Two corresponding upper rectangular metal rings are laid on the upper surface of the first dielectric layer on both sides of the first and third upper rectangular metal strips, so that the four upper rectangular metal rings are laid in a matrix array on the upper surface of the first dielectric layer. The four upper rectangular metal rings and the third upper rectangular metal strip are connected to the upper metal ground layer, the lower metal ground layer, and the lower antenna structure layer in sequence through their respective vias. The first upper rectangular metal strip is connected to the upper metal ground layer through a second blind via, and the second upper rectangular metal strip is directly connected to the lower antenna structure layer through its corresponding via.

[0013] The DC bias circuit layer includes an L-shaped DC wire and a fan-shaped microstrip line laid on the upper surface of the third dielectric layer. The first branch of the L-shaped DC wire is disposed directly below the first upper rectangular metal strip. The end of the first branch of the L-shaped DC wire is directly connected to the lower antenna structure layer through a first blind hole. The end of the second branch of the L-shaped DC wire is connected to the logic voltage control module.

[0014] The lower antenna structure layer includes four lower rectangular metal rings and two lower rectangular metal strips laid on the lower surface of the fourth dielectric layer. The four lower rectangular metal rings and the four upper rectangular metal rings of the upper antenna structure layer are arranged in a one-to-one vertical overlap. The four lower rectangular metal rings are connected to the four upper rectangular metal rings through corresponding vias. The two lower rectangular metal strips are a long lower rectangular metal strip and a short lower rectangular metal strip respectively. The long lower rectangular metal strip and the short lower rectangular metal strip are arranged at intervals. The long lower rectangular metal strip is disposed directly below the first upper rectangular metal strip and the second upper rectangular metal strip. The short lower rectangular metal strip is disposed directly below the third upper rectangular metal strip. The long lower rectangular metal strip is directly connected to the DC bias circuit layer through a first blind hole. The long lower rectangular metal strip is directly connected to the second upper rectangular metal strip through the via closest to the short lower rectangular metal strip. The short lower rectangular metal strip is connected to the third upper rectangular metal strip through its own via, the lower metal ground layer and the upper metal ground layer in sequence.

[0015] The polarization rotation reflectarray is formed by two-dimensional uniform arrangement of Nr reflection units with the same structure. The spacing between the reflection units is 1 / 3 wavelength of the center operating frequency of the polarization rotation reflectarray.

[0016] The reflection unit includes an upper metal reflection layer, a fifth dielectric layer and a lower metal reflection layer. The upper metal reflection layer and the lower metal reflection layer are respectively laid on the upper and lower surfaces of the fifth dielectric layer. The upper metal reflection layer is a "king" - shaped metal, and the "king" - shaped metal is laid in the middle of the upper surface of the fifth dielectric layer. The "king" - shaped metal is a symmetric structure, and there is a 45° angle between its symmetry axis and the side length of the fifth dielectric layer. The upper and lower metal strips of the "king" - shaped metal are set as arc - shaped, and the middle metal strip is linear. The center of the arc - shaped metal strip is located at the center of the linear metal strip. The lower metal reflection layer is a rectangular metal patch, and the area of the lower metal reflection layer is the same as the area of the lower surface of the fifth dielectric layer.

[0017] II. A microwave imaging method based on a folded feed active transmitarray

[0018] The method uses the microwave imaging system based on a folded feed active transmitarray as described above. The method includes the following steps:

[0019] Step 1: Randomly generate the beam focusing point coordinates (x d , f , f , y f , f dThe target phase state of each transmission element in the programmable transmission array is calculated based on the beam focus point coordinates.

[0020] Step 2: Transmit the target phase state of the programmable transmission array to the logic voltage control module, and the logic voltage control module controls each transmission element in the programmable transmission array to be in the target phase state.

[0021] Step 3: The electromagnetic wave signal generated by the RF transceiver unit enters the feed source. The electromagnetic field radiated by the feed source in the main polarization direction illuminates the programmable transmission array, producing the first reflection. The first reflected wave illuminates the polarization rotating reflection array, producing the second reflection and polarization rotation. Then, it is transmitted through the programmable transmission array. During the transmission process, the programmable transmission array performs phase modulation, ultimately forming a randomly focused beam that illuminates the beam focus point coordinates (x, y) on the imaging plane. f ,y f ,f d );

[0022] Step 4: The random focusing beam interacts with the target object on the imaging plane to generate reflected waves. The reflected waves are received by multiple receiving antennas and transmitted to the power combiner for synthesis. Then, the output port of the power combiner is transmitted to the radio frequency transceiver circuit to obtain the transmission coefficient of the current measurement.

[0023] Step 5: Repeat steps 1-4 M times, each time generating different random beam focus point coordinates and corresponding programmable transmission array target phase states, and finally obtain the transmission coefficients of the M measurements.

[0024] Step 6: Construct an imaging model based on the random focused beam pattern of each measurement, the radiation pattern of the receiving antenna, and the geometric relationship between the imaging system and the imaging plane. Substitute all the measurement data from M measurements into the imaging model and combine it with the compressed sensing algorithm to complete the reconstruction of the reflectivity of the target object.

[0025] In step 1, the calculation formula for the target phase state of each transmission unit in binarization is as follows:

[0026]

[0027]

[0028] in, This indicates that the coordinate is r i (x i ,y i The continuous target phase state of the transmission element at (,0). Represents coordinate r i (x i ,y i The target phase state binarized at the transmission element at (x, 0),i With y i Let x and y represent the coordinates of the i-th transmission element in the x and y directions, respectively. f With y f Let f represent the coordinates of the beam focusing point in the x and y directions, respectively. d Let k be the distance between the programmable transmission array and the imaging plane, k0 be the wavenumber in free space, and n be an integer greater than or equal to 0. For the transmission phase of the center cell of the programmable phase-modulated surface, The phase distribution generated by the feed on the programmable phase modulation surface.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] First, this invention achieves a low-profile folded feed active transmission array by integrating the design of the feed source, polarization deflection reflective surface and programmable transmission array. By utilizing the two reflections generated between the programmable transmission array and the polarization deflection reflective surface by the electromagnetic waves radiated by the feed source, the distance between the feed source and the programmable transmission array is effectively shortened to 1 / 3 of the focal length, reducing the profile height of the entire imaging system, which is beneficial for realizing a highly integrated large-aperture microwave imaging system.

[0031] Secondly, the programmable transmission array unit of the present invention adopts the form of a transceiver antenna, and uses positive and negative DC bias voltages to control the on / off state of the PIN tube in the control unit to achieve 1-bit 0 / 180° phase modulation. Compared with the transmission array using frequency selective surface (FSS), it has the advantages of low insertion loss, simple structure, convenient control and wide bandwidth.

[0032] Third, this invention uses a randomly focused beam to perform incoherent measurements on the imaging plane, resulting in low correlation between different measurements. Combined with compressed sensing algorithms, the reflectivity distribution of the imaging plane can be accurately reconstructed from undersampled data. Compared with traditional imaging methods based on the Nyquist sampling theorem, this invention has a faster imaging speed, requires less data storage, and further reduces the hardware and computational costs of the imaging system.

[0033] Fourth, the aperture of the imaging system of the present invention can be expanded according to the size of the target object, which is highly flexible and has a wide range of applications. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the microwave imaging system based on the folded active transmission array of the present invention.

[0035] Figure 2 This is a schematic diagram of the multilayer PCB structure of the programmable transmission array unit of the present invention.

[0036] Figure 3This is a schematic diagram of the upper antenna structure layer of the programmable transmission array unit of the present invention.

[0037] Figure 4 This is a schematic diagram of the lower antenna structure layer of the programmable transmission array unit of the present invention.

[0038] Figure 5 This is a schematic diagram of the equivalent control circuit of the PIN tube of the programmable transmission array unit of the present invention.

[0039] Figure 6 This is the transmission amplitude modulation result of the programmable transmission array unit in the embodiment.

[0040] Figure 7 This is the transmission phase modulation result of the programmable transmission array unit in the embodiment.

[0041] Figure 8 In the embodiment, the programmable transmission array unit is in Figure 7 The phase difference is shown in the two transmission phase states.

[0042] Figure 9 This is a schematic diagram of the multilayer PCB structure of the polarized rotating reflective array unit of the present invention.

[0043] Figure 10 This is a schematic diagram of the upper metal layer structure of the polarized rotating reflective array unit of the present invention.

[0044] Figure 11 The simulation results of the reflection coefficient of the polarized rotating reflection array in the embodiment are shown.

[0045] Figure 12 This is a hardware circuit block diagram of the microwave imaging system based on the folded feed active transmission array of the present invention.

[0046] Figure 13 These are two different phase states of the programmable transmission array unit in the embodiment, and the corresponding random focus field distribution on the imaging plane.

[0047] Figure 14 This is the simulation image reconstruction result of the embodiment.

[0048] In the diagram: 1. Feed source, 2. Polarized rotating reflector array, 3. Support, 4. Receiving antenna, 5. Programmable transmission array, 6. Target object, 7. Upper rectangular metal ring, 8. First PIN diode, 9. Second PIN diode, 10. Upper rectangular metal strip, 11. First dielectric layer, 12. Upper metal ground layer, 13. Second dielectric layer, 14. L-shaped DC conductor, 15. Fan-shaped microstrip line, 16. Third dielectric layer, 17. First blind via, 18. Lower metal ground layer, 19. Fourth dielectric layer, 20. Lower rectangular metal ring, 21. Lower rectangular metal strip, 22. Second blind via, 23. Via, 24. Upper metal reflector layer, 25. Fifth dielectric layer, 26. Lower metal reflector layer. Detailed Implementation

[0049] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0050] like Figure 1 and Figure 12 As shown, the present invention includes a feed 1, a polarized rotating reflector array 2, a support 3, a receiving antenna 4, a programmable transmission array 5, a logic voltage control module, an RF transceiver module, a power combining module, and a microcontroller system.

[0051] A polarized rotating reflector array 2 and a programmable transmission array 5 are arranged vertically at intervals, and are fixedly connected by a bracket 3. A feed 1 is fixedly installed in the middle of the polarized rotating reflector array 2, with its output port facing the programmable transmission array 5. Multiple receiving antennas 4 are arranged at intervals to the sides of the programmable transmission array 5. The feed 1, polarized rotating reflector array 2, bracket 3, and programmable transmission array 5 form a folded feed active transmission array to generate a randomly focused beam to illuminate the imaging target object 6. The feed 1 is connected to the transmit port of the RF transceiver module. The receiving port of the RF transceiver module is connected to the output port of the power combining module, and the input port of the power combining module is connected to multiple receiving antennas 4. The L-shaped DC conductor 14 in the DC bias circuit layer of the programmable transmission array 5 is connected to the logic voltage control module. Both the RF transceiver module and the logic voltage control module are connected to a microcontroller system. The microcontroller system is connected to a control terminal (such as a computer) via a serial port. Commands are sent from the computer to the microcontroller system to control the RF transceiver module and the logic voltage control module to perform measurements. The measurement data is acquired by the microcontroller system and transmitted to the computer for image reconstruction. A specific embodiment of the microwave imaging system based on a folded feed active transmission array of the present invention is as follows: Figure 1 As shown, target object 6 is located at z = f d Within the xy two-dimensional imaging plane, where the z-axis direction is perpendicular to the surface of the programmable transmission array, f dThe distance between the programmable transmission array and the imaging plane is indicated. The folded feed active transmission array, which consists of feed 1, polarized rotating reflective array 2, support 3 and programmable transmission array 5, serves as the transmitting end to illuminate the target object 6.

[0052] The programmable transmission array 5 contains multiple two-dimensional uniformly arranged units with 1-bit 0 / 180° phase modulation capability. Through a specific coding mode, the incident wave generated by the feed 1 can be phase-modulated to form a randomly focused beam that illuminates the surface of the target object 6. After the incident wave interacts with the target object 6, it generates a scattered wave, which is received by multiple receiving antennas 4 located around the folded active transmission array, thus completing a measurement of the target object.

[0053] To obtain more information about the target object, the encoding mode of the programmable transmission array can be changed to generate multiple different randomly focused beams for multiple measurements of the target object. For computational convenience, the imaging plane is divided into N pixels. Assuming the total number of measurements is M, during the m-th measurement, the folded active transmission array is positioned at any pixel r on the imaging plane. n The incident field generated at point is denoted as Based on the principle of electromagnetic scattering and the Born approximation, we can obtain the value located at r. r The scattered echo signal received by the receiving antenna at that location is:

[0054]

[0055] Where f(r) n ) indicates that it is located at r n The reflectance of a pixel, E0(r) r ) indicates that the receiving antenna is at r r The field distribution at the aperture surface is related to the operating mode of the receiving antenna, g(r r ,r n )=exp(-jk|r r -r n |) / (4π|r r -r n |) is the Green's function in free space. According to the theory of electromagnetic wave propagation in free space, E rx (r n )=E0(r r )g(r r ,r n This can be equivalent to the receiving antenna at any pixel point r in the imaging plane. n The field distribution generated at that location. For all M measurements, combining the above scattering field expression and considering the noise present in the actual measurements, a simplified imaging model is obtained:

[0056] g = Hf + n

[0057] Where g represents a measurement matrix of size M×1, containing the scattered echo signals obtained from M incoherent measurements, and H represents a transmission matrix of size M×N, where the (m,n)th element of matrix H is represented as... The image can be calculated based on the random focusing beamform of each measurement, the radiation pattern of the receiving antenna, and the geometric relationship between the imaging system and the imaging plane; f represents the reflectivity distribution matrix of the imaging plane to be solved, with a size of N×1; n represents the noise matrix with a size of M×1. The imaging method used in the embodiment is based on the above imaging model, employing a fast-converging two-step iterative shrinking threshold algorithm (TwIST) to reconstruct the image of the target object from the measurement data obtained from M incoherent measurements.

[0058] The programmable transmission array 5 is composed of Np identical transmission elements arranged uniformly in two dimensions. The spacing between two adjacent transmission elements is half the wavelength of the center operating frequency of the programmable transmission array 5.

[0059] like Figure 2 As shown, the transmission unit includes an upper antenna structure layer, a first dielectric layer 11, an upper metal ground layer 12, a second dielectric layer 13, a DC bias circuit layer, a third dielectric layer 16, a lower metal ground layer 18, a fourth dielectric layer 19, and a lower antenna structure layer arranged in sequence. The first upper rectangular metal strip of the upper antenna structure layer is connected to the corresponding position of the upper metal ground layer 12 through a second blind hole 22. The upper antenna structure layer is also connected to the upper metal ground layer 12, the lower metal ground layer 18, and the lower antenna structure layer in sequence from top to bottom through vias 23. Specifically, the upper rectangular metal patch 7, the first upper rectangular metal strip 11, the second upper rectangular metal strip 12, the third upper dielectric layer 13, the fourth dielectric layer 19, the fifth upper dielectric layer 11, the sixth upper dielectric layer 12, the seventh upper dielectric layer 13, the eighth upper dielectric layer 14, the ninth upper dielectric layer 15, the eleventh upper dielectric layer 16, the eleventh lower dielectric layer 17, the eleventh lower dielectric layer 18, the eleventh lower dielectric layer 19, the eleventh lower dielectric layer 19, the eleventh lower dielectric layer 10, the eleventh lower dielectric layer 1 ...2, the eleventh lower dielectric layer 13, the eleventh lower dielectric layer 14, the eleventh lower dielectric layer 15, the eleventh lower dielectric layer 16, the eleventh lower dielectric layer 17, the eleventh lower The three upper rectangular metal strips are connected to the lower rectangular metal patch 20 and the short lower rectangular metal strip in the lower antenna structure layer through the corresponding vias 23, passing through the upper metal ground layer 12 and the lower metal ground layer 18 in sequence. The second upper rectangular metal strip is directly connected to the long lower rectangular metal strip in the lower antenna structure layer through the corresponding via 23. The L-shaped DC conductor 14 of the DC bias circuit layer is directly connected to the long lower rectangular metal strip of the lower antenna structure layer through the first blind via 17. The DC bias circuit layer is not connected to the lower metal ground layer 18. The DC bias circuit layer is connected to the logic voltage control module.

[0060] like Figure 3As shown, the upper antenna structure layer includes four upper rectangular metal rings 7, two PIN tubes, and three upper rectangular metal strips 10. The three upper rectangular metal strips 10 are arranged sequentially and at intervals along a straight line in the middle of the upper surface of the first dielectric layer 11, and are referred to as the first upper rectangular metal strip, the second upper rectangular metal strip, and the third upper rectangular metal strip from left to right. The first and third upper rectangular metal strips have the same shape, while the first and second upper rectangular metal strips may have the same or different shapes. The interval between the first and second upper rectangular metal strips is the same as the interval between the second and third upper rectangular metal strips. The first upper rectangular metal strip and the second upper rectangular metal strip are connected by a PIN tube (i.e., the first PIN tube 8), and the second upper rectangular metal strip and the third upper rectangular metal strip are connected by another PIN tube (i.e., the second PIN tube 9). The two ends of the second upper rectangular metal strip are respectively connected to the positive terminal of one PIN tube and the negative terminal of the other PIN tube, that is, the two PIN tubes are oriented in the same direction. Two corresponding upper rectangular metal rings 7 are laid on the upper surface of the first dielectric layer 11 on both sides of the first upper rectangular metal strip and the third upper rectangular metal strip, so that the four upper rectangular metal rings 7 are laid in a matrix array on the upper surface of the first dielectric layer 11. The four upper rectangular metal patches 7 and the third upper rectangular metal strip are connected to the upper metal ground layer 12, the lower metal ground layer 18 and the lower antenna structure layer in sequence through their respective vias 23. The four upper rectangular metal patches 7 are connected to the four lower rectangular metal patches 20 in the lower antenna structure layer through their corresponding vias 23. The two vias 23 of each rectangular metal patch are located at the two corners closest to the adjacent rectangular metal patch on the same side as the upper rectangular metal strip. The third upper rectangular metal strip is connected to the short lower rectangular metal strip. The via 23 of the third upper rectangular metal strip is located at one end near the PIN tube. The first upper rectangular metal strip is connected to the upper metal ground layer 12 through the second blind hole 22. The second blind hole 22 of the first upper rectangular metal strip is located at one end near the PIN tube. Through holes are opened in the middle of the upper metal ground layer 12 and the lower metal ground layer 18. The second upper rectangular metal strip is directly connected to the long lower rectangular metal strip of the lower antenna structure layer through the corresponding via 23. The via 23 of the second upper rectangular metal strip is located in the middle of itself. The second upper rectangular metal strip is not connected to the upper metal ground layer 12 and the lower metal ground layer. That is, the via 23 of the second upper rectangular metal strip passes through the through hole in the middle of the upper metal ground layer 12 and the lower metal ground layer.

[0061] The DC bias circuit layer includes an L-shaped DC conductor 14 and a fan-shaped microstrip line 15 laid on the upper surface of the third dielectric layer 16. The first branch of the L-shaped DC conductor 14 is located directly below the first upper rectangular metal strip. The end of the first branch of the L-shaped DC conductor 14 is directly connected to the long lower rectangular metal strip of the lower antenna structure layer through the first blind hole 17. A through hole is opened in the middle of the lower metal ground layer. The first blind hole 17 passes through the through hole of the lower metal ground layer, that is, the end of the first branch of the L-shaped DC conductor 14 is not connected to the lower metal ground layer. The second branches of the L-shaped DC conductor 14 do not overlap with the four upper rectangular metal patches 7 and the four lower rectangular metal patches 20. The end of the second branch of the L-shaped DC conductor 14 is connected to the logic voltage control module.

[0062] like Figure 4 As shown, the lower antenna structure layer includes four lower rectangular metal rings 20 and two lower rectangular metal strips 21 laid on the lower surface of the fourth dielectric layer 19. The four lower rectangular metal rings 20 are arranged vertically to overlap with the four upper rectangular metal rings 7 of the upper antenna structure layer. The vias 23 on the four lower rectangular metal patches 20 are also vertically to overlap with the vias 23 on the four upper rectangular metal patches 7. The four lower rectangular metal rings 20 are connected to the four upper rectangular metal rings 7 through corresponding vias 23. The two lower rectangular metal strips 21 are a long lower rectangular metal strip and a short lower rectangular metal strip, respectively. The long lower rectangular metal strip and the short lower rectangular metal strip are arranged alternately. The long lower rectangular metal strip is located directly below the first upper rectangular metal strip and the second upper rectangular metal strip, and the short lower rectangular metal strip is located below the first upper rectangular metal strip and the second upper rectangular metal strip. The long lower rectangular metal strip is positioned directly below the third upper rectangular metal strip. In specific implementation, the long lower rectangular metal strip is directly connected to the first branch end of the L-shaped DC conductor 14 of the DC bias circuit layer through the first blind hole 17. The long lower rectangular metal strip is not connected to the lower metal ground layer. The long lower rectangular metal strip is directly connected to the second upper rectangular metal strip through the via 23 closest to the short lower rectangular metal strip. The long lower rectangular metal strip is not connected to the upper metal ground layer 12 and the lower metal ground layer 18. That is, the via 23 of the long lower rectangular metal strip passes through the through hole in the middle of the upper metal ground layer 12 and the lower metal ground layer 18. The short lower rectangular metal strip is connected to the third upper rectangular metal strip through the via 23 located near one end of the long lower rectangular metal strip, passing through the lower metal ground layer 18 and the upper metal ground layer 12 in sequence.

[0063] The working principle of a 5-element programmable transmission array to achieve 1-bit 0 / 180° phase modulation is as follows: Figure 5The diagram shows the equivalent control circuit for the two PIN diodes in the upper antenna structure layer. The positive terminal of the first PIN diode 8 and the negative terminal of the second PIN diode 9 are both grounded. Both the negative terminal of the first PIN diode 8 and the positive terminal of the second PIN diode 9 are connected to the logic voltage control module. When the logic voltage control module generates a positive voltage, the first PIN diode 8 is OFF and the second PIN diode 9 is ON, activating the upper antenna structure layer 7 of the programmable transmission array unit from the right side. When the logic voltage control module generates a negative voltage, the first PIN diode 8 is ON and the second PIN diode 9 is OFF, activating the upper antenna structure layer 7 of the programmable transmission array unit from the left side. Therefore, when the logic voltage control module generates positive and negative bias voltages respectively, the upper antenna structure layer of the programmable transmission array unit is equivalent to rotating 180° in space. The transmission phase of the unit differs by 180° between the two states corresponding to the positive and negative bias voltages, and the transmission phase state of each unit can be controlled individually.

[0064] To further illustrate the phase modulation principle of the programmable transmission array 5, an example is provided below.

[0065] The selected size of the programmable transmission array element is 6.5mm × 6.5mm. All dielectric layers are made of RO4350b material with a relative permittivity of 3.48. The thickness of the first dielectric layer 11 and the fourth dielectric layer 19 is 1.216mm, and the thickness of the second dielectric layer 13 and the third dielectric layer 16 is 0.1mm. The external dimensions of the rectangular metal rings in the upper and lower antenna structure layers are 1.675mm × 1.8mm, and the internal dimensions are 0.8mm × 1.1mm. The PIN diode is model MA4AGFCP910. Full-wave simulation of this structure was performed using the electromagnetic simulation software CST. When the first PIN diode 8 and the second PIN diode 9 are respectively turned on, the changes in transmission amplitude and transmission phase are as follows: Figure 6 and Figure 7 As shown. From Figure 6 As can be seen, the transmission amplitude is basically the same in both PIN diode states. The operating frequency band with insertion loss less than 2dB is 21.35-33.3GHz, and the relative bandwidth is 43.7%. The transmission phase of the two PIN diode states is as follows: Figure 7 As shown, its phase difference is as follows Figure 8 As shown, within the indicated bandwidth, the phase difference between the two PIN diode states remains essentially constant at 180 degrees, meeting the 1-bit 0 / 180° phase modulation requirement of the imaging system. Furthermore, the programmable transmission array can polarize linearly polarized electromagnetic waves whose polarization direction is parallel to the long sides of the upper and lower rectangular metal patches, i.e., as shown... Figure 3 The x-direction polarized electromagnetic wave shown has a transmission effect and a reflection effect on electromagnetic waves perpendicular to this polarization direction. The cross-polarization suppression ratio is better than 40dB.

[0066] For a traditional active transmissive array, it is usually composed of a feed source and a programmable transmissive array. In order to effectively irradiate each unit in the programmable transmissive array, the feed source often needs to be placed at a relatively large focal length. Therefore, the overall profile of the active transmissive array is relatively high, which limits its application. To solve this problem, a folded-feed active transmissive array is adopted in the present invention, which is composed of a feed source 1, a polarization-rotating reflective array 2, a bracket 3, and a programmable transmissive array 5. The method for implementing the folded-feed active transmissive array is as follows: Select a linearly polarized feed source 1 and install the feed source 1 at the center of the polarization-rotating reflective surface 2. The polarization-rotating surface 2 and the programmable transmissive array 4 are respectively installed on both sides of the bracket 3, as Figure 1 shown, where the polarization directions of the feed source 1 and the programmable transmissive array 4 are placed orthogonally to each other. Assume that the feed source 1 radiates electromagnetic waves in the y-polarization direction and irradiates the surface of the programmable transmissive array 4. Since the incident wave and the polarization of the programmable transmissive array are orthogonal to each other and cannot be transmitted, a first reflection occurs. The reflected wave irradiates the polarization-reflective surface, causing a 90-degree polarization rotation and a second reflection. The polarization direction of the second reflected wave becomes the x-direction and can penetrate the programmable transmissive array. By using the two reflections that occur between the programmable transmissive array 5 and the polarization-rotating reflective array 2 for the incident wave, the distance between the feed source 1 and the programmable transmissive array 5 can be shortened to 1 / 3 of the focal length, effectively reducing the system profile.

[0067] The polarization-rotating reflective array 2 is formed by two-dimensionally arranging Nr reflective units with the same structure uniformly. The distance between two adjacent reflective units is 1 / 3 wavelength of the center operating frequency of the polarization-rotating reflective array 2.

[0068] As Figure 9 and Figure 10 shown, the reflective unit includes an upper metal reflective layer 24, a fifth dielectric layer 25, and a lower metal reflective layer 26; the upper metal reflective layer 24 and the lower metal reflective layer 26 are respectively laid on the upper and lower surfaces of the fifth dielectric layer 25; the upper metal reflective layer 24 is a "king" - shaped metal, and the "king" - shaped metal is laid in the middle of the upper surface of the fifth dielectric layer 25. The "king" - shaped metal is a symmetric structure, and there is a 45° angle between its symmetry axis and the side length of the fifth dielectric layer 25. The upper and lower metal strips of the "king" - shaped metal are set as arc - shaped, and the middle metal strip is linear. The center of the arc - shaped metal strip is located at the center of the linear metal strip; the fifth dielectric layer 25 is made of a dielectric material with a relative dielectric constant of 2.45; the lower metal reflective layer 26 is a rectangular metal patch, and the area of the lower metal reflective layer 26 is the same as the area of the lower surface of the fifth dielectric layer 25, so that the lower metal reflective layer 26 completely covers the lower surface of the fifth dielectric layer 25.

[0069] As Figure 10As shown, the dimensions of the polarization rotating surface unit in this embodiment of the invention are: l1 = 3.65 mm, l2 = 0.8 mm, r1 = 1.4 mm, r2 = 1.1 mm, w1 = 0.3 mm, w2 = 0.25 mm, θ1 = 45°, the dielectric layer thickness is 1.58 mm, the dielectric material is Taconic TLX-8, and the dielectric constant is 2.45. Full-wave simulation of this structure was performed using the electromagnetic simulation software CST. The incident wave polarization direction was set as follows... Figure 9 The y-polarization direction is shown, and the incident direction is +z. The simulated reflection coefficient is as follows. Figure 11 As shown, where This represents the ratio between the reflected wave in the y-polarization direction and the incident wave in the y-polarization direction. This represents the ratio of the reflected wave in the x-polarization direction to the incident wave in the y-polarization direction. Figure 11 As can be seen, within the 20-36GHz frequency band, Less than -20dB A value close to 0 dB indicates that the incident wave in the y-polarization direction undergoes a 90-degree polarization rotation after passing through the polarization rotating reflection array of this invention, efficiently converting it into an electromagnetic wave in the x-polarization direction. Similarly, the incident wave in the x-polarization direction can also be converted into a reflected wave in the y-polarization direction, satisfying the requirements of a folded feed active transmission array.

[0070] Based on the above embodiments, this embodiment provides a microwave imaging method based on a folded feed active transmission array, which employs the following steps during imaging:

[0071] Step 1: Randomly generate the coordinates (x, y) of a beam focus point on the imaging plane on the computer. f ,y f ,f d The target phase state of each transmission element in the programmable transmission array 5 is calculated based on the beam focus point coordinates.

[0072] Located at r i (x i ,y i The formula for calculating the target phase state of the transmission element binarized at (0) is as follows:

[0073]

[0074]

[0075] in, Indicates that it is located at r i (x i ,y i The continuous phase state of the transmission element at (,0). For the binarized target phase state of the transmission unit located at this location, xi With y i Let x and y represent the coordinates of the i-th transmission element in the x and y directions, respectively. f With y f Let f represent the coordinates of the beam focusing point in the x and y directions, respectively. d Let k be the distance between the programmable transmission array and the imaging plane, k0 be the wavenumber in free space, and n be an integer greater than or equal to 0. This refers to the transmission phase state of the center cell of the programmable phase-modulating surface. The phase distribution generated by the feed on the programmable phase modulation surface.

[0076] Step 2: The computer transmits the binary target phase state of the programmable transmission array 5 to the microcontroller in the form of 0 and 1 binary data, where 0 represents the 0° phase state and 1 represents the 180° phase state. The microcontroller further transmits the binary data to the logic voltage control module. The logic voltage control module converts the binary data into the corresponding analog voltage signal to control the state of the PIN tubes of each transmission unit, thereby controlling the programmable transmission array 5 to be in the target phase state.

[0077] Step 3: The electromagnetic wave signal generated by the RF transceiver unit enters the feed 1 through the output port. The electromagnetic field radiated by the feed 1 in the main polarization direction illuminates the programmable transmission array 5. Since the polarization direction of the programmable transmission array is orthogonal to the polarization direction of the feed, the electromagnetic wave in the main polarization direction generated by the feed cannot be transmitted, resulting in the first reflection. The first reflected wave illuminates the polarization rotating reflection array 2, resulting in the second reflection, and the polarization direction is rotated by 90°. The polarization direction of the second reflected wave is the same as that of the programmable transmission array, and then it is transmitted through the programmable transmission array 5. During the transmission process, the programmable transmission array 5 performs phase modulation, and finally forms a randomly focused beam that illuminates the beam focus point coordinates (x, y) on the imaging plane. f ,y f ,f d );

[0078] Step 4: The random focusing beam interacts with the target object 6 on the imaging plane to generate a reflected wave. The reflected wave is received by multiple receiving antennas and then transmitted to the power combiner through the output ports of the multiple receiving antennas for synthesis. The power combiner is then transmitted to the radio frequency transceiver circuit through its output port to obtain the current transmission coefficient, thus realizing a transmission coefficient measurement. The transmission coefficient is acquired by the microcontroller and transmitted to the computer to complete a random sampling.

[0079] Step 5: Repeat steps 1-4 M times, each time generating different random beam focus point coordinates and the corresponding programmable transmission array 5 phase state, and finally obtain the transmission coefficients of the M measurements.

[0080] Step 6: Construct an imaging model based on the random focused beam pattern, the radiation pattern of the receiving antenna, and the geometric relationship between the imaging system and the imaging plane for each measurement. Substitute all the measurement data from M measurements into the imaging model and combine it with the compressed sensing algorithm to complete the reflectivity reconstruction of the target object 6.

[0081] The technical effects of the present invention will be further described in detail below with reference to simulation experiments of embodiments of the present invention.

[0082] Without loss of generality, assume the programmable transmission array has Np = 16 × 16 elements with a spacing of 6.5 mm, the polarized rotating reflection array has Nr = 28 × 28 elements with a spacing of 3.65 mm, the imaging plane is 12λ × 12λ, where λ is the wavelength corresponding to the operating frequency of 24 GHz, i.e., 12.5 mm, the imaging plane is divided into N = 40 × 40 grids, the total number of measurements is M = 250, and the imaging distance is f. d =8cm. For example Figure 13 , Figure 13 (a) and (c) show the phase state of each element in the programmable transmission array under two different measurement modes, respectively. Figure 13 (b) and (d) show the random focused field distribution generated by the folded active transmission array on the imaging plane under corresponding phase states. It can be seen that the generated field distribution differs under different measurement modes, and the use of random focused beams can further reduce the correlation between different measurement modes. To verify the effectiveness of the imaging system and imaging method of this invention, [further details are needed]. Figure 14 The "T"-shaped target pattern in (a) is imaged, where the white portion represents a reflectance of 1 and the black portion represents a reflectance of 0. To make the simulation results more realistic, Gaussian white noise is added to the measurement matrix g to reduce its signal-to-noise ratio to 20 dB. The image reconstruction result using the TwIST algorithm is as follows. Figure 14 As shown in (b), the position and outline of the "T" shaped pattern can be clearly reconstructed, achieving accurate imaging.

[0083] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A microwave imaging system based on a folded-feed active transmitarray, characterized in that, Includes a feed (1), a polarized rotating reflector array (2), a support (3), a receiving antenna (4), a programmable transmission array (5), a logic voltage control module, an RF transceiver module, a power combining module, and a microcontroller system; The polarized rotating reflector array (2) and the programmable transmission array (5) are arranged vertically at intervals. The polarized rotating reflector array (2) and the programmable transmission array (5) are fixedly connected by a bracket (3). The feed source (1) is fixedly installed in the middle of the polarized rotating reflector array (2). Multiple receiving antennas (4) are arranged at intervals on the side of the programmable transmission array (5). The feed source (1), the polarized rotating reflector array (2), the bracket (3) and the programmable transmission array (5) form a folded feed source active transmission array, which is used to generate a random focusing beam to illuminate the imaging target object (6). The feed source (1) is connected to the transmitting port of the radio frequency transceiver module. The receiving port of the radio frequency transceiver module is connected to the output port of the power combining module. The input port of the power combining module is connected to multiple receiving antennas (4). The programmable transmission array (5) is connected to the logic voltage control module. Both the radio frequency transceiver module and the logic voltage control module are connected to the microcontroller system.

2. The microwave imaging system based on folded feed active transmitarray of claim 1, wherein, The programmable transmission array (5) is composed of Np identical transmission units arranged in a two-dimensional uniform manner, with the spacing between the transmission units being half the wavelength of the center operating frequency of the programmable transmission array (5).

3. The microwave imaging system based on folded feed active transmitarray of claim 2, wherein, The transmission unit includes an upper antenna structure layer, a first dielectric layer (11), an upper metal ground layer (12), a second dielectric layer (13), a DC bias circuit layer, a third dielectric layer (16), a lower metal ground layer (18), a fourth dielectric layer (19), and a lower antenna structure layer arranged in sequence. The upper antenna structure layer is connected to the upper metal ground layer (12), and the upper antenna structure layer is also connected to the lower metal ground layer (18) and the lower antenna structure layer in sequence from top to bottom. The DC bias circuit layer is directly connected to the lower antenna structure layer, and the DC bias circuit layer is connected to the logic voltage control module.

4. The microwave imaging system based on folded feed active transmitarray of claim 3, wherein, The upper antenna structure layer includes four upper rectangular metal rings (7), two PIN diodes, and three upper rectangular metal strips (10). The three upper rectangular metal strips (10) are arranged sequentially and at intervals along a straight line in the middle of the upper surface of the first dielectric layer (11), and are referred to as the first upper rectangular metal strip, the second upper rectangular metal strip, and the third upper rectangular metal strip from left to right. The first and second upper rectangular metal strips are connected by a PIN diode, and the second and third upper rectangular metal strips are connected by another PIN diode. The two ends of the second upper rectangular metal strip are respectively connected to the positive terminal of one PIN diode and the negative terminal of the other PIN diode. The upper surfaces of the first dielectric layer (11) on both sides of the first upper rectangular metal strip and the third upper rectangular metal strip are each covered with two corresponding upper rectangular metal rings (7), so that the four upper rectangular metal rings (7) are laid in a matrix array on the upper surface of the first dielectric layer (11). The four upper rectangular metal rings (7) and the third upper rectangular metal strip are connected to the upper metal ground layer (12), the lower metal ground layer (18) and the lower antenna structure layer in sequence through their respective vias (23). The first upper rectangular metal strip is connected to the upper metal ground layer (12) through the second blind hole (22), and the second upper rectangular metal strip is directly connected to the lower antenna structure layer through the corresponding via (23).

5. The microwave imaging system based on folded feed active transmitarray of claim 4, wherein, The DC bias circuit layer includes an L-shaped DC conductor (14) and a fan-shaped microstrip line (15) laid on the upper surface of the third dielectric layer (16). The first branch of the L-shaped DC conductor (14) is located directly below the first upper rectangular metal strip. The end of the first branch of the L-shaped DC conductor (14) is directly connected to the lower antenna structure layer through the first blind hole (17). The end of the second branch of the L-shaped DC conductor (14) is connected to the logic voltage control module.

6. The microwave imaging system based on folded feed active transmitarray of claim 4, wherein, The lower antenna structure layer includes four lower rectangular metal rings (20) and two lower rectangular metal strips (21) laid on the lower surface of the fourth dielectric layer (19). The four lower rectangular metal rings (20) are arranged one above the other with the four upper rectangular metal rings (7) of the upper antenna structure layer. The four lower rectangular metal rings (20) are connected to the four upper rectangular metal rings (7) through corresponding vias (23). The two lower rectangular metal strips (21) are a long lower rectangular metal strip and a short lower rectangular metal strip, respectively, and the long lower rectangular metal strip and the short lower rectangular metal strip are arranged at intervals. The long lower rectangular metal strip is located directly below the first and second upper rectangular metal strips, and the short lower rectangular metal strip is located directly below the third upper rectangular metal strip. The long lower rectangular metal strip is directly connected to the DC bias circuit layer through the first blind via (17). The long lower rectangular metal strip is directly connected to the second upper rectangular metal strip through the via (23) located closest to the short lower rectangular metal strip. The short lower rectangular metal strip is connected to the third upper rectangular metal strip through its own via (23) via the lower metal ground layer (18) and the upper metal ground layer (12).

7. The microwave imaging system based on folded feed active transmitarray of claim 1, wherein, The polarization rotation reflection array (2) is formed by two-dimensionally arranging Nr reflection units with the same structure, and the spacing between the reflection units is 1 / 3 wavelength of the central operating frequency of the polarization rotation reflection array (2).

8. The microwave imaging system based on folded feed active transmitarray of claim 7, wherein, The reflection unit includes an upper metal reflection layer (24), a fifth dielectric layer (25), and a lower metal reflection layer (26); the upper metal reflection layer (24) and the lower metal reflection layer (26) are respectively laid on the upper and lower surfaces of the fifth dielectric layer (25); the upper metal reflection layer (24) is a "king" - shaped metal, and the "king" - shaped metal is laid in the middle of the upper surface of the fifth dielectric layer (25). The "king" - shaped metal is a symmetric structure, and there is a 45° angle between its symmetry axis and the side length of the fifth dielectric layer (25). The upper and lower metal bars of the "king" - shaped metal are set as arc - shaped, the middle metal bar is linear, and the center of the arc - shaped metal bar is located at the center of the linear metal bar; the lower metal reflection layer (26) is a rectangular metal patch, and the area of the lower metal reflection layer (26) is the same as the area of the lower surface of the fifth dielectric layer (25).

9. A microwave imaging method based on a folded feed active transmission array, characterized in that, The method uses a microwave imaging system based on a folded active transmission array according to any one of claims 1 - 8, and the method includes the following steps: Step 1: randomly generate a beam focus point coordinate on an imaging plane calculating the target phase state of each transmissive unit in the programmable transmissive array (5) according to the beam focus point coordinate Step 2: Transmit the target phase state of the programmable transmission array (5) to the logic voltage control module, and the logic voltage control module controls each transmission unit in the programmable transmission array (5) to be in the target phase state; Step 3: The electromagnetic wave signal generated by the radio frequency transceiver unit enters the feed source (1). The electromagnetic field radiated by the feed source (1) in the main polarization direction is irradiated onto the programmable transmission array (5), resulting in the first reflection. The first reflected wave is irradiated onto the polarization rotating reflection array (2), resulting in the second reflection and polarization rotation. Then, it is transmitted through the programmable transmission array (5). During the transmission process, the programmable transmission array (5) performs phase modulation, and finally forms a randomly focused beam that illuminates the beam focus point coordinates on the imaging plane. ; Step 4: The random focused beam interacts with the target object (6) on the imaging plane to generate a reflected wave. After the reflected wave is received by multiple receiving antennas, it is transmitted to the power combiner for combination, and then transmitted from the output port of the power combiner to the radio frequency transceiver circuit, thereby obtaining the currently measured transmission coefficient; Step 5: Repeat steps 1 - step 4 for M times, each time generating different random beam focusing point coordinates and the corresponding target phase state of the programmable transmission array (5), and finally obtaining the transmission coefficients measured M times; Step 6: Construct an imaging model according to the form of the random focused beam measured each time, the radiation form of the receiving antenna, and the geometric relationship between the imaging system and the imaging plane. Substitute the M - time measurement data into the imaging model, and combine with the compressive sensing algorithm to complete the reconstruction of the reflectivity of the target object (6).

10. The method of claim 9, wherein, In the said step 1, the calculation formula for the binary target phase state of each transmission unit is as follows: in, Indicates the location at coordinates The continuous target phase state of the transmission unit. Representing coordinates The target phase state in the binarized transmission unit. and Let x and y represent the coordinates of the i-th transmission element in the x and y directions, respectively. and These represent the coordinates of the beam focusing point in the x and y directions, respectively. The distance between the programmable transmission array and the imaging plane. Let n be the wave number in free space, n be an integer greater than or equal to 0, and φ(0,0,0) be the transmission phase of the center element of the programmable phase-tuning surface. The phase distribution generated by the feed on the programmable phase modulation surface.

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