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Broadband photonic beam processor for simultaneous beamforming and high-resolution imaging

Xiaoxue Chen, Shangyuan Li, Luhang Xing, Jinghan Yu, Xiaoxiao Xue, and Xiaoping Zheng

Open Access Open Access

Abstract

In this paper, a broadband photonic beam processor is presented for the all-optical multifunction integrated receiver. By implementing echo signals with optical beam multi-domain processing based on space-to-time mapping and time-to-frequency mapping, the non-mechanical control of expected beam pointing is enabled while the target within the beam can be imaged simultaneously. A proof-of-concept experiment with a 4-element phased array is performed in Ka band. The beam pointing is set to be 0° and 12.5°, where two-dimensional images of moving targets inside the beam region are obtained, respectively. The suppression ratio to the beam region outside is measured to be 26.8 dB. And the range and cross-range imaging resolution is 0.042 m × 0.051 m. A comparison with a cascade mode of single-function microwave photonic modules shows that the multifunction integrated photonic beam processor has reduced the system loss by 32.4 dB. The proposed beam processor enables multi-element broadband phased arrays with less complexity and power consumption.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

The appearance of phased array technology effectively overcomes the weaknesses of conventional mechanically rotated antennas in stabilization and accuracy. It has been commonly used in communications, missile warning, radio astronomy, and air-to-ground surveillance, etc [1–5]. Adjusting the phase and magnitude of each branch flexibly to steer the main beam significantly facilitates the reconnaissance of the whole airspace. Despite the obvious benefits of rapid beam steering without any mechanical motion, phase shifters and accessories circuits complicate the array architecture and lead to the rising cost [6]. Moreover, due to the dispersion effect of traditional phase shifters within the microwave band, the bandwidth is constrained by the problem of beam squint [7]. The beam pointing assigned by signals over wide bandwidth deviates from the expected direction with changes of the carrier frequency. The photonic true time delay (TTD) method based on microwave photonic technology provides a possibility to solve this problem [8–11]. While overcoming the aperture effect to realize broadband beamforming, it also offers advantages such as higher frequency, larger bandwidth and lower propagation loss [12–14]. Many scholars constantly pay attention on the area of photonic TTD. Some approaches are based on switching optical paths in different lengths by mechanical or electrical methods [15–18], while others focus on changing the refractive index of light in transmission [19–23]. As rising requirements for reduction of the size of arrays, the growth for the miniaturization and integration of phased array based on TTD has also been fueled synchronously [24–26]. In [24], a photonic TTD beamforming network based on a miniature microresonator frequency comb source and the dispersive time delay is proposed to achieve arbitrary microwave beam pattern control.

The beamformer utilizing photonic TTD has proved to be significant for detection of non-cooperative targets in space by steering control of the main beam [27]. However, the output of most beamformers is sampled and digitalized directly by analog-to-digital converters (ADC) at Nyquist sampling rate according to the prior studies. Consequently, the limitation in operation bandwidth and memory depth for ADCs hinders the enhancement on imaging resolution within millimeter wave and sub-terahertz frequencies, and thus disables further fast and precise identification of the target. The present available microwave photonic imaging methods indicate their superiority in providing employed microwave signals with broadband and higher operational frequencies, decreasing the mass of data to relieve the pressure on the back-end electrical ADC and favoring desired high-resolution imaging [28–30]. In [28], a high-resolution inverse synthetic aperture radar imaging system in W-band with a bandwidth of 8 GHz is investigated and experimentally demonstrated with a sampling rate of 100 MSa/s in the receiver. In [29], a K-band microwave photonic bistatic radar system with balanced I/Q de-chirping is proposed and successfully distinguishes two overlapping targets along the monostatic radar line of sight.

Nevertheless, there is only a single function regardless of aforementioned beamformers based on photonic TTD or microwave photonic imaging implements with enhanced resolution, which is unfavorable for collaboration of spatial search and high-resolution detection. To cope with the diversification and complexity of environment, the performance on two-dimensional resolution of beamformers has to be improved. One solution is to cascade optical beamformers and microwave photonic imaging modules. Since the interface between the two single-function microwave photonic modules is in the form of electricity, the low efficiency of opto-electronic and electro-optical conversion naturally contributes to more system loss and power consumption. Another solution is to combine microwave photonic imaging with digital beamforming. A photonics-based K-band phased array radar at 22-26 GHz is presented for realization of airspace search and precise recognition [30]. But the system has to be configured with the same number of receivers as the number of phased-array radar elements, which is adverse to the scale expansion of array elements (AEs). Integrating multiple functions into an optical module not only avoids the unnecessary relay conversion loss under the cascade mode, but also can simplify system layout and maintenance by optical multiplexing. However, the all-optical interconnection architecture of optical beamformers and microwave photonic imaging modules has not been reported yet.

In this paper, a broadband photonic beam processor for simultaneous beamforming and high-resolution imaging is proposed, considering the new demand for beamformers. Integrated through the optical beam multi-domain processing (OBMP) module, consisting of space-to-time mapping (STM) and time-to-frequency mapping (TFM), the two microwave photonic functions are implemented at the same time. Besides, all receiving AEs are multiplexed into one channel, which heavily reduces the amount of the back-end electrical components. As a promising substitute for current beamformers, it is applicable to military warning, drones, intelligent transportation and other fields for better performance. A broadband photonic beam processor fed by a four-element receive array is devised and demonstrated at the Ka-band centered in 35 GHz millimeter wave with 4 GHz bandwidth. On the one hand, the beam pointing has been steered to be 0° and 12.5°, respectively, for beamforming. On the other hand, the graphs of moving targets at the beam region can be obtained simultaneously for high-resolution imaging, while obstacles outside the beam region will not cause misjudgment with the suppression ratio of 26.8 dB. The corresponding range and cross-range resolution are 0.042 m and 0.051 m respectively. A comparison with a cascade mode of two single-function microwave photonic modules is also conducted, showing the proposed processor reduces the system loss by 32.4 dB and is well-suited for future wideband large-scale applications with high efficiency.

2. Principle of operation

The schematic diagram of the broadband photonic beam processor with N elements is illustrated in Fig. 1. The linear frequency modulated (LFM) echo waveform of each AE received by the antenna array is sent to the corresponding microwave input port of the photonic beam processor and then amplified. The light source provides the optical carrier with different wavelengths for electro-optical conversion, which can be implemented by multiple modulators. Taking the Mach-Zehnder modulator for example, the optical field of each AE can be expressed as:

$${E_i}(t )= {E_{ci}}{e^{j{\omega _{ci}}t}}\cos \left( {\frac{{{m_i}}}{2}\cos ({{\omega_e}({t - {\gamma_i}} )+ \pi k{{({t - {\gamma_i}} )}^2}} )+ {\varphi_i}} \right),$$
where Eci and ωci are the amplitude and optical carrier frequency of i th AE (AEi, i = 1, 2, …, N), mi is the corresponding modulation indice, ωe is the initial frequency of LFM signal, γi is the relative delay of the echo signal at AEi to the transmitted signal, k stands for the chirp rate of the LFM and φi denotes the direct-current bias of the modulation.

 figure: Fig. 1.

Fig. 1. The schematic diagram of the proposed photonic beam processor. E/O: electro-optical conversion; OBMP: optical beam multi-domain processing; STM: space-to-time mapping; TFM: time-to-frequency mapping; AE: array element; AM: amplitude manipulation; TDR: temporal-delay regulation; TFC: time-to-frequency converter; Sum: summation of N elements; O/E: opto-electronic conversion; LPF: low-pass filter.

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Then the optical signals of all channels pass through the OBMP for the all-optical multifunction integrated receive, which is mainly composed of a block of STM and a block of TFM, as depicted in Fig. 1. In this former block, the modulated optical signal maps the spatial location of every AE along the time domain. The amplitude manipulation (AM) is implemented in every AE to resist the deterioration of the consistency among multiple elements caused by the uneven response of actual electronic and opto-electronic components. By imposing temporal-delay regulation (TDR) on each AE, the difference in incremental delay compensation is antisymmetric to that of the relative delay of the echo signal at AEi to steer the main beam for the specific direction. Taking the delay compensation τ1 of the first AE as the reference link with a fixed value, the incremental delay compensation τi can be expressed as:

$$\left\{ \begin{array}{l} {\tau_i} = {\tau_1} - ({i - 1} )\frac{{d\sin {\theta_0}}}{c},\\ {\gamma_i} = {\gamma_1} + ({i - 1} )\frac{{d\sin \theta }}{c}, \end{array} \right. ({i = 1,2,\ldots ,N} ),$$
where c is the speed of light, d is the interval spacing distance between adjacent AEs, θ0 is the expected beam pointing for the receiving direction of specific airspace, θ is the incident direction of the echo waveform and γ1 is the relative delay of the echo signal at the reference element to the transmitted signal. Due to the incoherence of optical carriers, the multi-channel signals are multiplexed by the combiner to one way, which is written as:
$${E_{ST}}(t )= \sum\limits_{i = 1}^N {{E_{ci}}{e^{j{\omega _{ci}}({t - {\tau_i}} )}}{a_i}\cos \left( {\frac{{{m_i}}}{2}\cos ({{\omega_e}({t - {\tau_i} - {\gamma_i}} )+ \pi k{{({t - {\tau_i} - {\gamma_i}} )}^2}} )+ {\varphi_i}} \right)} .$$

Then the output of STM block is injected into the latter of OBMP. In the block of TFM, the signals loaded with delay information through STM are mapped to single-frequency signals by photonic multiplication operation with the optical cosinoidal replica Er(t) of the emitted LFM signal:

$${E_r}(t) = \cos ({{m_r}{s_e}(t )+ {\varphi_r}} ),$$
where se(t) is the emitted signal, mr and φr is the amplitude and phase factor in the photonic multiplier. Taking the chirp rate k as the TFM factor, the delay difference of AEs is transformed to the different single frequency, which can be expressed as:
$${f_j} - {f_i} = k[{({{\tau_j} + {\gamma_j}} )- ({{\tau_i} + {\gamma_i}} )} ],i,j = 1,2,\ldots ,N.$$

To proceed, the optical signal via TFM processing is fed to a low-speed photodetector (PD) for opto-electronic conversion and superposition of all AEs. After filtered in a low-pass filter (LPF), the output electrical signal through square-law detection can be obtained as:

$$\begin{aligned} i(t )\propto &[{{E_{ST}}(t ){E_r}(t )} ]\cdot {[{{E_{ST}}(t ){E_r}(t )} ]^ \ast }\\ &\mathop \approx \limits^{LPF} \sum\limits_{i = 1}^N {\frac{{{a_i}{E_{ci}}^2}}{2}{J_1}({{m_i}} ){J_1}({{m_r}} )\cos ({2\pi {f_i}t} )} , \end{aligned}$$
where Jn is the nth-order Bessel function of the first kind. From Eq. (6), the output of the photonic beam processor is the superposition of N-channel single-frequency signals, as shown in Fig. 2(a). Through the Fourier transform (FT) in digital signal processing, the frequency-domain expression I(ω) of the output electrical signal can be written as:
$$I(\omega )\propto \sum\limits_{i = 1}^N {{a_i}{E_{ci}}^2\delta ({\omega - {\omega_i}} )} .$$

 figure: Fig. 2.

Fig. 2. (a) The profile of the signal for beamforming in frequency domain through OBMP. (b) The simulated phased array pattern of the proposed photonic beam processor in Ka band under the condition of the antenna spacing at half-wavelength.

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According to the principle of FT, there is a symmetry property between time domain and frequency domain as follows:

$$F[{x(t )} ]= X({j\omega } )\mathop \Rightarrow \limits^{Fre - shift} F[{x(t ){e^{ {\mp} j{\omega_0}t}}} ]= X({j({\omega \pm {\omega_0}} )} ),$$
where F[·] denotes the operation of FT. From the view of time domain, taking the first AE as the benchmark (optionally other elements) and assuming all AEs have the same amplitude response a1Ec12 = a2Ec22 = … = aNEcN2, the ultimate output y(t) with amplitude consistency for the photonic beam processor can be expressed as:
$$y(t )= \sum\limits_{i = 1}^N {{y_1}(t )\cdot {e^{j2\pi ({{f_i} - {f_1}} )t}}} .$$

Here, y1(t) stands for the temporal expression of the benchmark. Consequently, according to Euler's formula, the normalized response y(θ) of the photonic beam processor with N receiving AEs can be given as:

$$|{y(\theta )} |= \left|{\frac{{\sin \left[ {\frac{{N\pi dkt}}{c}({\sin \theta - \sin {\theta_0}} )} \right]}}{{N\sin \left[ {\frac{{\pi dkt}}{c}({\sin \theta - \sin {\theta_0}} )} \right]}}} \right|.$$

Therefore, the receiving main beam points to the main maximum direction when θ = θ0. Under the ideal condition of the antenna spacing at half-wavelength, the polar plot in Fig. 2(b) shows the simulated phased array pattern of the proposed photonic beam processor with ten AEs while the beam pointing θ0 is set at 0°, 15°, 30°, respectively in Ka band. Considering the backward suppression effect of the antenna itself, the angle detection range without grating lobes is limited within ±90°.

Based on this frequency processing of frequency shift and superposition, the proposed OBMP module also allows the use of high-resolution imaging through converting broadband signal to the narrow band. As a result, low-speed electrical ADC can be employed to signal acquisition and real-time processing. While realizing the flexible control of beam pointing, due to the highly efficient processing ability for broadband signals, two-dimensional image of the target in the main beam can be obtained through inverse synthetic aperture radar (ISAR) technology. The theoretical range resolution and cross-range resolution can be expressed as [28]:

$$\left\{ \begin{array}{l} \Delta x = \frac{c}{{2B}}\\ \Delta y = \frac{c}{{2{\omega_r}{T_r}{f_c}}} \end{array} \right.,$$
where B is the bandwidth of the echo signal, ωr is the rotational angular velocity of the target, Tr is the sampling accumulation time, and fc is the carrier frequency of the echo signal. From Eq. (11), the high efficiency of hardware processor has enabled the steady improvement on the range resolution and cross-range resolution. Within the all-optical interconnection structure, the broadband photonic beam processor can be exploited for the realization of optical beam steering and precise imaging simultaneously. All the receiving AEs are multiplexed into one channel for TFM combined with wavelength division multiplexing, which greatly reduces the scale of back-end electrical components and simplifies the hardware complexity of the system. Moreover, it helps to achieve the multifunction integrated reception with the expansion ability of AEs.

3. Experiment results and discussion

As a proof of principle, the proposed photonic beam processor with four AEs is demonstrated experimentally. Figure 3(a) shows the block diagram of the system applying the proposed photonic beam processor as the receiver. At the transmitter, the LFM signal of 33-37 GHz is generated by up-converting to the baseband signal from the arbitrary waveform generator (AWG, Tektronix, AWG70002A). The signal is split into two parts. One is radiated into free space from a horn antenna, and the other is sent to the receiver side as the replica. The spectrum is depicted in Fig. 3(b), where the signal-to-noise ratio is up to 50 dB recorded by a spectrum analyzer (Rohde & Schwarz, FSWP 50). The echo signal reflected by the target is received by phased array antennas consisting of four identical horn components (A-INFO, BI320), which are parallel placed by a spacing distance d ≈ 2 cm, nearly 2.5 times of the operating wavelength. The target is located at a range r = 2.75 m away from the origin, which can be regarded as a point target in far field.

 figure: Fig. 3.

Fig. 3. (a) Block diagram of the experimental setup applying the proposed photonic beam processor. (b) Spectrum of the emitted LFMW in 33-37 GHz. (c) The detailed experimental configuration of the proposed photonic beam processor for simultaneous beamforming and imaging. MZM: Mach-Zehnder modulator; VOAs: variable optical attenuators; PD: photodetector; LPF: low-pass filter; ADC: analog-to-digital converter; DSP: digital signal processing.

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Figure 3(c) illustrates the detailed experimental configuration of the proposed photonic beam processor. For each receiving AE, the echo wave is amplified by an electrical amplifier (Centellax, OA4MVM3) firstly and then modulates the optical carrier. The four optical carriers are generated by the multi-channel tunable laser (Agilents, N7714A). The wavelengths of the light wave in each channel are 1538.19 nm, 1539.77 nm, 1541.35 nm and 1542.94 nm, respectively. They are injected into the Mach-Zehnder modulator (MZM, Fujitsu, FTM 7938) for electro-optical conversion and sent to OBMP. In the block of STM, variable optical attenuators (VOAs) are applied for the AM of every AE, and the incremental delay compensation for TDR is realized by adjustable optical delay lines in the experiment, which is set up according to different expected beam pointing for beamforming. The multi-channel signals composed of different light wavelengths loaded with temporal delay information are combined into one channel by a wavelength division multiplexer. Then the output of STM block is forwarded to another MZM, as a photonic multiplication operation block for TFM where the optical spectrum is structured jointly with the replica of the emitted signal according to Eq. (4), taking the chirp rate of the LFM as the TFM factor. After the conversion to single-frequency signal from the temporal broadband echo wave carrying the information of beam direction and target features, the ultimate optical signal is detected by a PD with a bandwidth of 3 GHz. Due to the incoherence of each optical carrier, the optical-carried echo signal of each channel at the PD is beat with the optical replica independently and thus superimposed. At the same time, the nonlinearity in phase originating from the emitted signal or the nonideality of experimental devices in each AE can also be superimposed, leading to the phase distortion of the output. This may reduce the accuracy of the ranging to a certain extent, and increase the spurs and side lobes for the ISAR imaging further, which can be addressed through the pre-distortion or post-compensation technique [31,32] and does not affect the principle verification. The narrowband signal is filtered out by an LPF to remove the out-of-band noise and spurious components, and sampled by the real-time oscilloscope (OSC, Keysight, UXR0134A). After digital signal processing, the beam at the processor can focus on the specific direction of the airspace to obtain the image of the target within the beam region.

3.1 Performance demonstration

The performance for simultaneous beamforming and two-dimensional imaging of the photonic beam processor is verified by four balls packaged with silver paper as targets. In experiment, the four balls rotate around the center with a rotation radius of 20 cm and an angular velocity of 200 r/min. The cross-range resolution is 0.051 m according to Eq. (11). Firstly, the incremental delay imposed on the adjacent AE is set to zero, to serve for steering the beam to the desired angle θ0 = 0 °. At the same time, the four targets are made an angle θ = 0° with the central axis of the receiver array in Fig. 4(a). Figure 4(b) depicts the imaging result through inverse synthetic aperture method, where there are four clear scattering points. Then moving the balls with an angular displacement Δθ = 12.5°, there is hardly any visualized photograph observed in Fig. 4(c) and 4(d), when the main beam still points at 0°. Subsequently, while the balls remain stationary, as shown in Fig. 4(e), we adjust the beam direction to an angle of θ0 = 12.5° by TDR between adjacent AEs of about 14.4 ps from Eq. (2). The targets are imaged again in Fig. 4(f). Figure 4(g) and 4(h) illustrate the placement and its corresponding imaging result under the condition that the four balls are relocated at θ = 0°, confirming that the stuff outside the beam will not cause interference to the detection inside the beam. It is demonstrated that the receiver side can be focused on the expected specific space direction by realizing the beam steering and detecting targets in high resolution within the present region. Moreover, due to the adjustable optical delay lines with a capable minimal increment of 0.5 ps in the experiment, the beam pointing can be steered with a tuning resolution of 0.43° according to Eq. (2), which meets the demand for detection of the targets located at a small angle and can be improved further by replacement of more precise delay components for TDR.

 figure: Fig. 4.

Fig. 4. Configuration and image results of the four balls packaged by silver paper in different directions. (a) The targets are placed at 0° while the beam pointing at 0°. (b) The corresponding image results of (a). (c) The targets are placed at 12.5° while the beam pointing at 0°. (d) The corresponding image results of (c). (e) The targets are placed at 12.5° while the beam pointing at 12.5°. (f) The corresponding image results of (e). (g) The targets are placed at 0° while the beam pointing at 12.5°. (h) The corresponding image results of (g).

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To investigate the performance of beam directivity shown in Fig. 4, a metal plate is chosen as the target. The beam pointing is set to be 0° through OBMP. Figure 5(a) and 5(b) show the ranging profiles of the metal plate at an angle of 12.5° when the beam is steered to point at 12.5° and 0°, respectively. It can be seen that the suppression ratio is about 26.8 dB. Keeping the beam pointing unchanged at 0°, and then adjusting the location of the metal plate to be the same direction, the receiver side can range the plate again. Therefore, the photonic beam processor realizes the all-optical multifunction integration of beamforming and high-resolution imaging while the targets outside the region hardly affect the detection of targets inside the region. Furthermore, two metal plates are employed to evaluate the range resolution of the presented beam processor. The spacing distance Δr of the two targets can be computed through the frequency separation between peaks obtained from the output of the processor. By moving a metal plate close to the other one gradually, it can be observed that the two plates can still be distinctive from each other while Δr is decreased to 0.042 m, as shown in Fig. 5(c). The result is well matching with the measured data between the two plates and close to the theoretical resolution according to Eq. (11). Furthermore, due to the large volume of the horn antennas at receive, the spacing distance of the adjacent element is nearly 2.5 times of the operating wavelength, thus leading to the limitation of the beamforming range by grating lobes. Although the adjustable optical delay lines in experiment cover the compensation range of over 300 ps, which is enough to support the tuning of the main beam at Ka-band over the full capable region, the steering of the beam pointing is still restricted between ±25°, which can be further expanded by utilizing array antennas with smaller size, such as Vivaldi antennas [33] rather than horn antennas.

 figure: Fig. 5.

Fig. 5. (a) The ranging result of the metal plate when it is placed at 12.5° with the beam pointing at 12.5°. (b) The ranging result of the metal plate when it is placed at 12.5° with the beam pointing at 0°. (c) Range profile of the two metal plates is separated by 0.042 m.

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3.2 Comparison with a cascade receive mode of single-function modules

Presently, the input and output of microwave photonic modules are both fabricated with an electric-based signal. When one single-function microwave photonic module is intended for connecting with the other single-function module for diversification of functions, twice electro-optical conversions must be implemented. Due to the low conversion efficiency, electrical amplifiers are often required to compensate for the system loss. However, the aforementioned photonic beam processor based on OBMP realizes the all-optical multifunction integrated receive mode, where there is only one electro-optical conversion needed to perform both functions of beamforming and imaging concurrently in the optical domain. Consequently, it reduces the number of devices required and optimizes the system loss resulting from the inefficient conversion between photonics and microwave, making it highly competitive with the traditional implementations. In comparison with the classical cascade receive mode of two single-function microwave photonic modules, the improvement of the processor on system loss at receiver is evaluated through experimental analysis.

The schematic diagram of the cascade mode is shown in Fig. 6(a). Firstly, the echo signal of each receive AE is imposed delay in the optical domain to control the beam pointing in the module of optical beamforming network (OBFN). Then it is transformed to an electrical signal to send to the next step. In the module of microwave photonic imaging, the beamforming signal is converted to the optical domain to implement dechirping process. As can be seen, the two-stage electro-optical and opto-electronic conversion have been introduced in the cascade mode for the achievement of the dual functions, inevitably leading to more extra system loss owing to low conversion efficiency. Electrical amplifiers are demanded for the power compensation between the two modules. In the experiment, an electrical amplifier with a gain of 21 dB is employed. As shown in Fig. 3(a), we replace the cascade modules with the photonic beam processor as the receiver and take a metal plate as the target. Meanwhile, the devices with the same performance parameters are adopted and the other receiver power conditions are kept unchanged. With the same input power, the echo waveform and the response of the target are shown as the red line in Fig. 6(b) and 6(c), where their all-optical multifunction integrated counterparts are shown as the blue line in Fig. 6(b) and 6(c). Compared with the cascade mode of optical analog beamforming network and microwave photonic imaging, the proposed photonic beam processor can perform simultaneous optical beamforming and high-resolution imaging with only one electro-optical conversion, which has reduced the system loss by 32.4 dB. The all-optical multifunction integrated receiving mode of the photonic beam processor provides beneficial properties for phased array including operational conveniences and reduced power consumption. Besides, by contrast with the digital solution in [26], it is obvious that the beam processor has simplified deployment significantly, leading to the receiving end no more required individual signal sampling and processing blocks in each element. The photonic beam processor enables the receiver side with further effective identification capability and practical feasibility for large-scale applications.

 figure: Fig. 6.

Fig. 6. (a) The schematic diagram of the cascade mode. EC: electrical coupler. PD: photodetector; Amp: amplifier. sr(t): the replica of the emitted signal. (b) The output waveform of the metal plate with different receive modes. (c) The peak response of the metal plate in different receive modes.

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4. Conclusion

In summary, the proposed photonic beam processor based on OBMP has less complexity and power consumption than the cascade mode of single-function microwave photonic modules when both rapid beam steering and imaging are demanded for applications. The real-time beamforming and imaging can be realized by rapid processing of the low-frequency narrowband signal obtained from STM and TFM. Since the multi-channel signal is merged into one channel, the complexity of system architecture and requirements for hardware is greatly diminished, making it much more possible to expand the scale of array. In the current experiment, the performance of optical beamforming and high-resolution imaging of the proposed photonic beam processor with four AEs are both verified. The beam pointing can be steered to 0° and 12.5° respectively with a suppression ratio of 26.8 dB, while a two-dimensional imaging experiment is demonstrated with the range and cross-range resolution of 0.042 m × 0.051 m. In comparison with the cascade mode of optical beamforming network and microwave photonic imaging module, the system loss of the beam processor has been decreased 32.4 dB by means of all-optical multifunction integrated receive. For practical applications, the demand for the fast scanning of the main beam in real scenarios may be considered. Accordingly, programmable adjustable optical delay lines can be applied to the beam processor to impose the incremental delay compensation. And the proposed processor can achieve this without theoretical bounds in this case. The scanning step and rate are determined by the corresponding minimum delay increment and switching time, respectively. More improvement on the performance of the photonic beam processor can be further gained, provided operation over signal with higher frequency and wider bandwidth and increase of AEs, intending for coordinated recognition of non-cooperative targets under modern complicated scenarios.

Funding

National Key Research and Development Program of China (2019YFB2203301); National Natural Science Foundation of China (61690191, 62127805).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)
Fig. 1.
Fig. 1. The schematic diagram of the proposed photonic beam processor. E/O: electro-optical conversion; OBMP: optical beam multi-domain processing; STM: space-to-time mapping; TFM: time-to-frequency mapping; AE: array element; AM: amplitude manipulation; TDR: temporal-delay regulation; TFC: time-to-frequency converter; Sum: summation of N elements; O/E: opto-electronic conversion; LPF: low-pass filter.

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Fig. 2.
Fig. 2. (a) The profile of the signal for beamforming in frequency domain through OBMP. (b) The simulated phased array pattern of the proposed photonic beam processor in Ka band under the condition of the antenna spacing at half-wavelength.

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Fig. 3.
Fig. 3. (a) Block diagram of the experimental setup applying the proposed photonic beam processor. (b) Spectrum of the emitted LFMW in 33-37 GHz. (c) The detailed experimental configuration of the proposed photonic beam processor for simultaneous beamforming and imaging. MZM: Mach-Zehnder modulator; VOAs: variable optical attenuators; PD: photodetector; LPF: low-pass filter; ADC: analog-to-digital converter; DSP: digital signal processing.

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Fig. 4.
Fig. 4. Configuration and image results of the four balls packaged by silver paper in different directions. (a) The targets are placed at 0° while the beam pointing at 0°. (b) The corresponding image results of (a). (c) The targets are placed at 12.5° while the beam pointing at 0°. (d) The corresponding image results of (c). (e) The targets are placed at 12.5° while the beam pointing at 12.5°. (f) The corresponding image results of (e). (g) The targets are placed at 0° while the beam pointing at 12.5°. (h) The corresponding image results of (g).

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Fig. 5.
Fig. 5. (a) The ranging result of the metal plate when it is placed at 12.5° with the beam pointing at 12.5°. (b) The ranging result of the metal plate when it is placed at 12.5° with the beam pointing at 0°. (c) Range profile of the two metal plates is separated by 0.042 m.

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Fig. 6.
Fig. 6. (a) The schematic diagram of the cascade mode. EC: electrical coupler. PD: photodetector; Amp: amplifier. sr(t): the replica of the emitted signal. (b) The output waveform of the metal plate with different receive modes. (c) The peak response of the metal plate in different receive modes.

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Equations (11)

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E i ( t ) = E c i e j ω c i t cos ⁡ ( m i 2 cos ⁡ ( ω e ( t − γ i ) + π k ( t − γ i ) 2 ) + φ i ) ,
{ τ i = τ 1 − ( i − 1 ) d sin ⁡ θ 0 c , γ i = γ 1 + ( i − 1 ) d sin ⁡ θ c , ( i = 1 , 2 , … , N ) ,
E S T ( t ) = ∑ i = 1 N E c i e j ω c i ( t − τ i ) a i cos ⁡ ( m i 2 cos ⁡ ( ω e ( t − τ i − γ i ) + π k ( t − τ i − γ i ) 2 ) + φ i ) .
E r ( t ) = cos ⁡ ( m r s e ( t ) + φ r ) ,
f j − f i = k [ ( τ j + γ j ) − ( τ i + γ i ) ] , i , j = 1 , 2 , … , N .
i ( t ) ∝ [ E S T ( t ) E r ( t ) ] ⋅ [ E S T ( t ) E r ( t ) ] ∗ ≈ L P F ⁡ ∑ i = 1 N a i E c i 2 2 J 1 ( m i ) J 1 ( m r ) cos ⁡ ( 2 π f i t ) ,
I ( ω ) ∝ ∑ i = 1 N a i E c i 2 δ ( ω − ω i ) .
F [ x ( t ) ] = X ( j ω ) ⇒ F r e − s h i f t ⁡ F [ x ( t ) e ∓ j ω 0 t ] = X ( j ( ω ± ω 0 ) ) ,
y ( t ) = ∑ i = 1 N y 1 ( t ) ⋅ e j 2 π ( f i − f 1 ) t .
| y ( θ ) | = | sin ⁡ [ N π d k t c ( sin ⁡ θ − sin ⁡ θ 0 ) ] N sin ⁡ [ π d k t c ( sin ⁡ θ − sin ⁡ θ 0 ) ] | .
{ Δ x = c 2 B Δ y = c 2 ω r T r f c ,
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