Photonics based microwave dynamic 3D reconstruction of moving targets

Dexin Wu; Shangyuan Li; Xiaoxiao Xue; Xuedi Xiao; Shaowen Peng; Xiaoping Zheng

doi:10.1364/OE.26.027659

1. Introduction

Compared to optical imaging, microwave imaging has the all-weather, all-time capabilities and has been widely used in many fields, such as drive assistance system, unmanned aerial vehicle (UAV), and traffic surveillance [1–3]. 3D reconstruction can provide more information about the physical structure of the targets than 2D imaging, greatly contributing to the recognition and classification of the targets in these applications [4,5]. To identify the complicated and small targets, the microwave imaging systems need to operate in a wide bandwidth and a high frequency to provide enough resolution [6,7]. Conventional electrical approaches are hard to directly generate and process high-frequency and broadband microwave signals due to the limitation of electronic devices [8,9]. To solve the problem, frequency multiplication and conversion must be employed at the cost of quality of the generated signals [10,11]. On the other hand, in order to improve the imaging performance under diverse environment conditions, the signal generator and processor need to provide fast tunability and reconfigurability, which are very difficult or even impossible with traditional technologies. Microwave photonics has been regarded as a potential field to cope with these challenges over the past decade taking its advantages of broad bandwidth, high frequency, immunity to electromagnetic interferences, flexible reconfiguration and high frequency tuning range [12–14]. Many photonic schemes have been proposed to directly generate broadband microwave signal [15–19], and microwave photonic mixer have also been proposed to realize an extremely wide bandwidth of operation and near infinite isolation [20,21]. Serval typical photonics based microwave imaging systems have been demonstrated [22–24]. In [22], a microwave photonic coherent radar is first proposed. The field trial tests prove that microwave photonics is capable of improving the performance of the conventional radar. Ref [23–26]. propose photonics assisted inverse synthetic aperture radars (ISAR) operating in X, Ku, K, and W band respectively. High-resolution and real-time imaging are demonstrated.

However, ISAR imaging is the range-doppler plane projection of a three-dimension target which leads to the loss of certain structure information. To improve the capability of ISAR, interferometric inverse synthetic aperture radar (InISAR) imaging technique is developed. Precedent researches indicate that it is feasible to get three-dimensional distribution of scatters in target using InISAR technique [27–29]. In this paper, dynamic 3D reconstruction of moving targets is proposed for the first time by establishing a photonics based InISAR. The system is based on an optical arbitrary waveform generator (OAWG) and microwave photonics assisted 3D imaging processing. The OAWG based on photonic digital-to-analogue conversion (PDAC) is used to generate a broadband linearly-frequency-modulated microwave (LFMW) signal. The echoes reflected by the targets are received by two antennas placed at different altitudes. A polarization-multiplexing dual-parallel Mach-Zehnder modulator (PM-DPMZM) together with a polarization beam splitter (PBS) and two photodetectors (PDs) are employed to mix the two receiving signals and the transmitted signal, simultaneously and separately. Combining 2D inverse synthetic aperture radar (ISAR) imaging processing and interfering the obtained two complex 2D images, the dynamic 3D reconstruction of the moving targets is achieved. In the experiment, a full X-band (8-12GHz) InISAR is established. A 3D reconstruction of two pairs of cross-placement rotary balls is demonstrated to prove the effectiveness of this system. Experimental results show that the proposed system can provide information on the stereoscopic physical structures of the targets dynamically, being favorable to identification and surveillance of complex targets. Due to the combination of OAWG and microwave photonic parallel mixing, the system can work in a wide bandwidth and high frequency. Besides, it has a high frequency tuning range, adapting to diverse environment conditions flexibly.

2. Principle

InISAR imaging is a 3D imaging technique to retrieve target altitude information contained in the phased of ISAR images, which is realized by interfering the 2D images observed by different-position receiving antennas [27–29]. Figure 1 shows the elementary InISAR geometry with one transmitting antenna and two receiving antennas. Tx(d, 0 0) and P(x, y, z) represent the transmitting antenna and a representive scattering center respectively. Rx1(0, 0, 0) and Rx2(0, 0, h) are the two receiving antennas at different altitudes. The distances from Tx, Rx1, and Rx2 to P are $R$ , $R_{1}$ , and $R_{2}$ respectively, where $R, R_{1}, R_{2} ≫ h, d$ . Suppose Tx transmits LFMW, which can be expressed as

s (t) = r e c t (\frac{\hat{t}}{T_{p}}) \exp [j 2 π (f_{c} t + k {\hat{t}}^{2} / 2)]

where

r e c t (\cdot)

is rectangle envelope,

f_{c}

is the center frequency,

T_{p}

is the pulse width,

k

is the sweeping rate,

\hat{t} = t - m T

is the fast time,

T

is the pulse repetition period, and

t_{m} = m T

is the slow time, where

m = 0, 1, \dots, M - 1

and

M

is the accumulated pulse number. After Rx1 and Rx2 receiving the echoes reflected by the scattering center, 2D imaging algorithm should be first applied. In case of transmitting LFMW, the most widely used 2D imaging algorithm includes three steps: mixing the echo and the reference signal, range alignment, and 2D Fourier transform. Suppose reference signal is the transmitted signal, the results of 2D imaging processing corresponding to Rx1 and Rx2 are respectively

\begin{array}{l} S_{1} (\hat{f}, f_{m}) = A_{1} T_{p} T_{a} \sin c [T_{p} (\hat{f} + \frac{k}{c} (R + R_{1}))] \\ \cdot \sin c [T_{a} (f_{m} + \frac{V + V_{1}}{λ})] \exp [- j \frac{2 π}{λ} (R + R_{1})] \\ S_{2} (\hat{f}, f_{m}) = A_{2} T_{p} T_{a} \sin c [T_{p} (\hat{f} + \frac{k}{c} (R + R_{2}))] \\ \cdot \sin c [T_{a} (f_{m} + \frac{V + V_{2}}{λ})] \exp [- j \frac{2 π}{λ} (R + R_{2})] \end{array}

where

\hat{f}

and

f_{m}

are the frequencies corresponding to fast time and slow time respectively,

A_{1}

and

A_{2}

are attenuation coefficients of the two transmission paths,

sinc (π a) = \sin (π a) / (π a)

,

c

is the speed of light,

T_{a} = M T

is the accumulated time,

λ

is the center wavelength of the transmitted signal, and

V

,

V_{1}

,

V_{2}

are the relative radial velocities between Tx, Rx1, Rx2 and P. As can be seen, in each 2D imaging result,

\hat{f}

and

f_{m}

are related to the range and radial velocity. Note that

h, d ≪ R, R_{1}, R_{2}

, so

R \approx R_{1} \approx R_{2} \approx y

. After range alignment, the target is equivalent to a turntable target and the radial velocity satisfies

V_{1} = V_{2} = Ω x

. Such, we have

x = \frac{f_{m} λ}{2 Ω}, y = \frac{\hat{f} c}{2 k}

The range resolution and cross range resolution are given by [6]

ρ_{r} = \frac{c}{2 B}, ρ_{a} = \frac{λ}{2 θ}

where

ρ_{r}

is the range resolution,

ρ_{a}

is the cross range resolution,

c

is the speed of light,

B

is bandwidth of the transmitted signal, and

θ

is rotation angle of the moving targets relative to range direction. Next, by interfering the two 2D image results, we can get

Δ φ = A n g l e (S_{1} S_{2}^{*}) = \frac{2 π}{λ} (R_{1} - R_{2}) = \frac{2 π}{λ} Δ R

According to geometry described in Fig. 1, we have

\begin{array}{l} x^{2} + y^{2} + z^{2} = R_{1}^{2} \\ x^{2} + y^{2} + {(z - h)}^{2} = R_{2}^{2} \\ R_{1} \approx R_{2} \approx y \end{array}

Combining Eq. (5) and Eq. (6), we can get

z = \frac{y Δ φ λ}{2 π h} + \frac{h}{2}

Thus, the 3D spatial position of the scattering center is determined. The mean square error (MSE) of the estimated

z

is expressed as

Fig. 1 The InISAR geometry with one transmitting antenna and two receiving antennas. Tx is the transmitting antenna, P is a representative scattering center, Rx1 and Rx2 are two receiving antennas placed at different altitudes, the distances from Tx, Rx1, and Rx2 to P are $R$ , $R_{1}$ , and $R_{2}$ respectively ( $R, R_{1}, R_{2} ≫ h, d$ ).

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\begin{array}{l} σ_{z}^{2} = {(\frac{\partial z}{\partial y} σ_{y})}^{2} + {(\frac{\partial z}{\partial h} σ_{h})}^{2} + {(\frac{\partial z}{\partial Δ φ} σ_{Δ φ})}^{2} \\ = {(\frac{λ Δ φ}{2 π h} σ_{y})}^{2} + {(\frac{z}{h} σ_{h})}^{2} + {(\frac{λ y}{2 π h} σ_{Δ φ})}^{2} \end{array}

It should be noted that phase wrapped problem exists when calculating the altitude coordinate according to Eq. (7), which means that when the phase difference exceeds $2 π$ , the altitude information will become vague. This problem can be solved by properly setting the length of the receiving-antenna baseline [28,29]. To eliminate the phase wrapped, the altitude coordinate should satisfy

\frac{h}{2} - \frac{R_{1} λ}{2 h} \leq z \leq \frac{h}{2} + \frac{R_{1} λ}{2 h}

For Eq. (9), it can be seen that when

h

is smaller, the

z

has a larger unambiguous range. However, Eq. (8) indicates that a smaller

h

will bring down precision of the altitude coordinate. So, it is essential to properly set the length of the receiving-antenna baseline according to the actual application.

According to the fundamental of InISAR, we design a photonics based InISAR, as the schematic diagram shown in Fig. 2. A broadband LFMW signal is generated by a PDAC-based OAWG proposed by us before [30]. After being amplified by an electrical amplifier (EA), the generated LFM microwave signal is equally split into two branches by a power splitter (PS1). In the one branch, the signal is emitted to the free space through a Tx. In the other one, the signal is equally split into two parts by another PS2, serving as two reference signals. The reflected echoes are collected by two receiving antennas placed at different altitudes (Rx1 and Rx2) and amplified by two low noise amplifier (LNA1 and LNA2) separately. A light wave from a laser diode (LD) is injected to a PM-DPMZM, which consists of two parallel DPMZMs, as shown in Fig. 2. The four RF inputs of the PM-DPMZM are driven by the two amplified echoes and two replicas of the transmitted signal respectively. All the MZMs are biased at the null point to compress the optical carrier. The polarization direction of one DPMZM’s output light is rotated 90 degrees. A polarization beam combiner (PBC) is integrated to create a polarization-multiplexed output. After it, a polarization beam splitter (PBS) is used for de-multiplexing. The de-multiplexed signals are detected by two photodetectors (PDs). Let $s (t)$ represents the transmitted LFMW, $s_{1} (t)$ and $s_{2} (t)$ represent the echoes collected by Rx1 and Rx2. Due to small modulation and carrier suppression, we only consider the first-order sidebands. According to the transmission characteristic of MZM [31], the detected two signals can be expressed as

\begin{array}{l} I_{1} (t) \propto J_{1} (β_{1}) J_{1} (β_{2}) s (t) s_{1} (t) + \frac{J_{1}^{2} (β_{1})}{4} s^{2} (t) + J_{1}^{2} (β_{2}) s_{1}^{2} (t) \\ I_{2} (t) \propto J_{1} (β_{3}) J_{1} (β_{4}) s (t) s_{2} (t) + \frac{J_{1}^{2} (β_{3})}{4} s^{2} (t) + J_{1}^{2} (β_{4}) s_{2}^{2} (t) \end{array}

where

J_{1} (\cdot)

is the first order Bessel function and

β_{i} (i = 1, 2, 3, 4)

is modulation index of the

i -th

MZM. It can be seen that mixing the reference signal and the echoes are achieved. Although the detected signals have some undesired high-frequency items, they cannot be amplified by the low-frequency EAs due to bandwidth limitation. The amplified signals are digitized by two low-speed ADCs respectively and finally conducted 2D Fourier transform and interference processing by a DSP, accomplishing the photonics assisted 3D imaging processing.

Fig. 2 Schematic diagram of the proposed photonics based microwave dynamic 3D reconstruction system and the detailed structure of the PM-DPMZM. OAWG, optical arbitrary waveform generator; EA, electrical amplifier; PS, power splitter; LNA, low noise amplifier; LD, laser diode; PM-DPMZM, polarization-multiplexing dual-parallel Mach-Zehnder modulator; PBS, polarization beam splitter; PD, photodetectors; ADC, analog-to-digital converter; DSP, digital signal processing; PR, polarization rotator; PBC, polarization beam combiner.

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3. Experiment results

In the experiment, a dynamic 3D reconstruction system is established based on the setup in Fig. 2. A LFMW signal of X-band with 4GHz bandwidth, 10us period, and 8us pulse width is generated by the OAWG. Figure 3(a) shows the temporal waveform of the generated LFMW, which is observed by a digital signal oscilloscope (DSO, Agilent DSO81204B). Figure 3(b) shows the instantaneous frequency of the generated LFM recovered by short-time Fourier transform. The generated LFM is then amplified by an X-band EA1 and split into two parts by PS1. One parts is emitted to the transmitting antenna, and the other one is split by another PS2. The echoes are amplified by two LNAs (LNA1 and LNA2). In the receiver end, a light of 16dBm at 1550nm is generated by a LD (Agilent N7714A) and injected into a PM-DPMZM (Fujitsu FTM7977HQA), which is driven by two replicas of the transmitted signal and the two amplified echoes. Output of the PM-DPMZM is divided by a PBS for de-multiplexing. The two PDs (PD1 and PD2, XPDV2120RA) have a bandwidth of 40GHz and a responsivity of 0.65 A/W. The two low-frequency EAs (EA2 and EA3) have a bandwidth from 100KHz to 500MHz. Under laboratory conditions, we use the DSO mentioned above to record the output signals and a computer to process the signal data.

Fig. 3 (a) Temporal waveform of the generated X-band LFM microwave signal using the OAWG, and (b) the recovered instantaneous frequency of the generated signal by short-time Fourier transform.

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Figure 4(a) gives the spatial position of the three antennas. The cross distance between Tx and Rx1 is 13cm. The altitude intercept between Rx1 and Rx2 is 12cm. According to the established coordinate axis and the relative distances. The coordinates of the three antennas are Tx(−13cm, 0, 0), Rx1(0, 0, 0), and Rx2(0, 0, 12cm). Figure 4(b) and Fig. 4(c) show the size of the targets consisting of two pairs of cross-placement silver-paper-packed balls placed at a turntable. The distance from each ball to the rotary center is about 25cm. The altitude difference between the two pairs balls is about 10cm. Figure 4(d) shows the relative position between the antennas and the targets. The antennas and targets are at the same altitude level approximately. The range between them is about 2.5m. According Eq. (9), in this case, the phase wrapped problem will not happen.

Fig. 4 (a) The relative position between the antennas. (b) and (c) The size of the rotary targets. (d) The relative position between the antennas and the targets. The distance from the antennas to the targets is about 2.5m.

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Adjusting the turntable to about 2.5 rotations per second. The sample rate of the DSO is set to be 50MS/s. The two mixed signals in a duration of 70ms are sampled by two channels of the DSO simultaneously and further processed by a computer. Every 10ms sampled signal is processed as a frame. Using the ISAR imaging algorithm, two 2D images are obtained for each frame. According to Eq. (4), the range resolution and cross range resolution are about 4cm and 9cm separately. Figure 5(a) and Fig. 5(b) shows the intensity information of the third-frame complex 2D images corresponding to Rx1 and Rx2, respectively. In both of the 2D images, the four balls are distinguished clearly. The two 2D images exhibit very good correlation, as they are obtained simultaneously. The video in Visualization 1 shows the whole seven-frame dynamic 2D images. To visualize the dynamic imaging results properly, the video is set to have a relative low frame rate (2fps).

Fig. 5 The third frame 2D images processed from the echoes collected by (a) Rx1 and (b) Rx2. The whole seven-frame dynamic 2D images are given in the video in Visualization 1.

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By further interfering the two complex 2D images of each frame, dynamic 3D reconstruction is achieved. Figure 6 shows the 3D reconstruction results of the third frame. The four balls are given different colors to make them clear distinguishable. It can be seen that the four balls are not placed on a horizontal level surface, which cannot be provided by a simple 2D image. From the front view in Fig. 6(b) and the left view in Fig. 6(c), the altitudes of the two pairs of balls are 11.6cm and 11.2cm, both of which match well with the real value of 10cm. In the top view given in Fig. 6(d), the separation distances between the two balls of each pair are measured to be 53.0cm and 54.2cm, which are also close to the real value of 50cm. With the 3D images, we note that it is now much easier to relate each scattering center to the target physical structures, greatly contributing to the recognition and classification of the targets. The video in Visualization 2 shows the whole seven-frame dynamic 3D reconstruction results. To evaluate the uncertainty of the phase difference used for determining the altitude of the target, we use the DSO to measure the phase jitter of the phase difference, which is about 6 degrees in 5 minutes. From Eq. (8), the standard deviation of the altitude caused by the uncertainty of the phase difference is about 1cm.

Fig. 6 3D reconstruction results of the third frame. (a) Stereoscopic view, (b) front view, (c) left view, and (d) top view. The whole seven-frame dynamic 3D reconstruction results are given in the video in Visualization 2.

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4. Conclusion

In conclusion, we propose a photonics-based system for dynamic 3D reconstruction of moving targets based on OAWG and photonics assisted 3D imaging processing. An X-band system with a 4-GHz bandwidth is established experimentally. Dynamic 3D reconstruction of two pairs of cross-placement rotary balls is achieved. The proposed system can provide information on the stereoscopic physical structures of the targets, contributing to the recognition and classification of the complex targets, showing bright prospect in drive assistance system, UAV and traffic surveillance.

Funding

National Nature Science Foundation of China (NSFC) (61690191, 61690192, 61420106003, 61621064); Natural Science Foundation of Beijing Municipality (4172029); Chuanxin Funding.

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Name	Description
Visualization 1	The video shows the dynamic 2D images observed by two receiving antennas.
Visualization 2	The video shows the dynamic 3D images.

Photonics based microwave dynamic 3D reconstruction of moving targets

Abstract

1. Introduction

2. Principle

3. Experiment results

4. Conclusion

Funding

References

Supplementary Material (2)

Cited By

Figures (6)

Equations (10)

Optics Express