Moving Real-Target Imaging of a Beam-Broaden ISAL Based on Orthogonal Polarization Receiver and Along-Track Interferometry

Abstract

In response to the application requirement of wide-range high-resolution imaging of non-cooperative moving real targets by inverse synthetic-aperture ladar (ISAL), experiments were conducted on the depolarization effect of target materials, and the polarization selection of ISAL receiving and transmitting channels was discussed. Considering the impact of target depolarization and the demand for along-track interferometry, combined with beam-broaden and high-gain amplifiers, an ISAL system design method that can stably image multiple non-cooperative real targets has been proposed. Under the condition of broadening the transmitting and receiving beams to 3° in the elevation direction for non-cooperative moving vehicles, echo data with a duration of 1 s is obtained. The spatial correlation algorithm combined with along-track interferometry is used to estimate the vibration phase error. The sub-aperture Range-Doppler algorithm is used for imaging. The ISAL imaging results of the moving vehicle validated the high-resolution imaging ability of ISAL and its potential for stable imaging of non-cooperative moving real targets.

1. Introduction

Compared to traditional optical imaging systems, synthetic-aperture ladar (SAL) and inverse synthetic-aperture ladar (ISAL) are not limited by the diffraction limit for imaging resolution [1]. Compared to microwave synthetic-aperture radar based on the principle of synthetic aperture, SAL/ISAL has advantages such as higher resolution and shorter imaging time [2,3]. Therefore, SAL/ISAL has great potential for development in high-resolution remote sensing applications.

However, there are also many problems with SAL/ISAL. 1. Due to limitations in laser power density and the number of receiving channels, the beamwidth of SAL/ISAL transceivers is generally narrow, making it difficult to obtain a large observation swath [4]. 2. The currently publicly reported SAL/ISAL experiments mainly focus on observing corner cubes or specially designed targets with high reflectivity, and have not yet met the application requirements for imaging real targets [5,6,7]. This is because real targets have characteristics such as non-cooperation, low reflectivity, and depolarization, which make ISAL imaging difficult. 3. Due to the short wavelength of the laser, atmospheric turbulence and vibrations of the radar or target on the order of micrometers can introduce large vibration phase errors in the echo signal of SAL/ISAL, which can lead to severe defocusing of the imaging results [8,9,10,11,12]. 4. Due to the strict requirements for polarization in coherent detection used by SAL/ISAL, the receiving channel based on an all-fiber optical path requires the use of single-mode polarization-maintaining fiber for reception, which determines that the echo signal must be received with linear polarization. However, due to the influence of atmospheric refractive index or target surface complex refractive index, the atmosphere and most real targets have a depolarization effect on the laser signal, which may significantly reduce the echo signal-to-noise ratio (SNR) of the receiving and transmitting channels with the same linear polarization system [13], making it difficult to apply the vibration phase estimation method based on interferometry [14], and making it difficult to achieve stable imaging for different real targets. 5. The linear frequency-modulated signals commonly used in synthetic-aperture radar exhibit poor linearity in the laser band, which significantly affects the imaging results [15,16]. Extensive research has been conducted on these issues in the existing literature; however, there is limited research that simultaneously addresses system design and imaging processing, and experimental studies focusing on non-cooperative real targets are also scarce.

Since the imaging SNR of SAL/ISAL can still be improved through signal processing after analog-to-digital converter (ADC) sampling. The transmitting and receiving beams can be broadened to form a larger observation width, and the resulting losses can be compensated for by setting amplifiers and combining signal processing [17]. In addition, the real targets exhibit uneven imaging scenes, irregular scattering properties, and unstable depolarization effects [18], which will reduce the estimation accuracy of the vibration phase error by the spatial correlation algorithm (SCA). To solve this problem, multiple receiving channels can be set up, and interferometry processing between channels can be used to achieve an accurate estimation of vibration phase error further to achieve high-resolution imaging. Furthermore, to reduce the system’s sensitivity to depolarization effects, the polarization state of the transmitted signal in the experimental system is set to circular polarization. Additionally, a vertical polarization receiving channel and a horizontal polarization receiving channel are established, enabling the system to perform stable motion compensation and imaging for a variety of real targets. Utilizing the characteristics of Binary Phase Shift Keying (BPSK) signals, such as their large time–bandwidth product, excellent autocorrelation, low sidelobe levels, and ease of generation [19], a BPSK signal with a code length of 2000 and a pulse width of 1 μs is employed to image real targets.

2. Depolarization Effect of Laser Signals for Different Targets

Due to the shorter wavelength of the laser, the interaction between the laser and the target surface is more likely to occur, resulting in a corresponding increase in the probability of multiple scattering. Therefore, in addition to the influence of the atmosphere, the structure, coating, and surface roughness of the target can also change the polarization state of the laser echo signal. Based on the influence of target characteristics on the polarization state of laser signals, targets can be classified into polarization-maintaining targets (when transmitting vertically polarized laser, the majority of the polarization state of the laser signal reflected by the target is still the vertical polarization component), generally depolarized targets (when transmitting vertically polarized laser, the vertical polarization component and horizontal polarization component of the laser signal reflected by the target are close), and severely depolarized targets (when transmitting vertically polarized laser, the majority of the polarization state of the laser signal reflected by the target is the horizontal polarization component).

2.1. The Influence of Depolarization Effect on Interferometry

The short wavelength of ISAL makes it extremely sensitive to vibration. Even small vibrations can modulate the frequency spectrum of the echo signal, significantly increasing its Doppler bandwidth, causing the azimuth imaging results to be out of focus and increasing the difficulty of imaging. The factors determining the Doppler bandwidth of the signal are the amplitude and frequency of the vibration during the imaging time. The Doppler bandwidth corresponding to a sinusoidal vibration with an amplitude of 100 μm and a frequency of 50 Hz is as high as 40 kHz. For moving targets, vibrations of this magnitude are common; thus, it is necessary to estimate and compensate for vibration phase errors.

Along-track interferometry is a commonly used method for estimating vibration phase errors [14,19]. This method involves deploying two receiving channels in the along-track direction, which is equivalent to two channels observing the target twice at the same distance and from the same perspective at different slow-time ($t_k$ and $t_k+\Delta t$). On this basis, the difference value of the vibration phase error (the interferometric phase) can be obtained through interferometric processing, and then the interferometric phase is integrated to estimate the vibration phase error. The difference value of the vibration phase error obtained through along-track interferometry can be expressed as:

$$\Delta {\phi }_v\left(t_k\right)=\mathrm{unwrap}\left\{\mathrm{angle}\left[s_1\left(\widehat{t},t_k\right)\cdot s_2{\left(\widehat{t},t_k+\Delta t\right)}^{*}\right]\right\}$$

(1)

where $\widehat{t}$ is the fast-time, $t_k$ is the slow-time, $\Delta t=d/‖\stackrel{\rightharpoonup }{v}‖$ is the delay difference between the two channels, $d$ is the length of the interferometric baseline, $\stackrel{\rightharpoonup }{v}$ is the target velocity vector parallel to the baseline, $s_1\left(\widehat{t},t_k\right)$ is the echo signal received by channel-1 at $t_k$, and $s_2\left(\widehat{t},t_k+\Delta t\right)$ is the echo signal received by channel-2 at $t_k+\Delta t$; unwrap represents unwrapping the phase, angle represents taking the phase of the signal, and ^∗ represents conjugate processing of the signal.

The echo signal received by the channel-i at $t_k+\Delta t_i$ is the pulse-compressed echo signal in the slant range direction, which can be expressed as:

$$s_i\left(\widehat{t},t_k+\Delta t_i\right)={\displaystyle \sum _{m=1}^M\left\{\begin{array}{l}{\rho }_m\cdot {\sigma }_m\cdot \exp \left(j\cdot {\phi }_m\right)\cdot \mathrm{sinc}\left\{B_r\cdot \left[\widehat{t}-2\cdot \frac{R_{m,i}\left(t_k+\Delta t_i\right)}{C}\right]\right\}\\ \cdot \exp \left[-j\cdot \frac{4\pi \cdot R_{m,i}\left(t_k+\Delta t_i\right)}{\lambda }\right]\cdot \exp \left[j\cdot {\phi }_v\left(t_k+\Delta t_i\right)\right]\end{array}\right\}}$$

(2)

where ${\rho }_m$ is the depolarization loss coefficient of the m-th scattering point, ${\sigma }_m$ is the backscattering coefficient of the m-th scattering point, ${\phi }_m$ is the initial phase of the m-th scattering point, $B_r$ is the bandwidth of the transmitted signal, $R_{m,i}\left(t_k+\Delta t_i\right)$ is the distance from the m-th scattering point to the equivalent phase center of the i-th channel at $t_k+\Delta t_i$, $\lambda$ is the wavelength of the transmitted signal, $C$ is the speed of light, and ${\phi }_v\left(t_k+\Delta t_i\right)$ is the vibration phase error at time $t_k+\Delta t_i$.

To achieve the target vibration phase error estimation, the interferometry processing is performed after the registration of $s_1\left(\widehat{t},t_k\right)$ and $s_2\left(\widehat{t},t_k+\Delta t\right)$. At this time, the interferometric phase can be represented as $\Delta {\phi }_v\left(t_k\right)={\phi }_v\left(t_k\right)-{\phi }_v\left(t_k+\Delta t\right)$. Afterward, the estimation of the vibration phase error can be achieved by integration:

$${\phi }_v\left(t_k\right)={\displaystyle {\int }_0^{t_k}\Delta {\phi }_v\left(K\right)dK}$$

(3)

Based on the above analysis, it can be seen that the accuracy of phase error estimation for along-track interferometry depends on the amplitude and phase consistency between channels and the SNR. For ISAL linear polarization receivers based on all-fiber optic paths and coherent systems, if the ISAL observation object is depolarized, the depolarization effect of the target will significantly reduce the SNR of the echo signal, which will seriously affect the accuracy of phase error estimation and imaging resolution. Therefore, it is necessary to study how to overcome the influence of depolarization on different targets to ensure the amplitude and phase consistency between channels and the SNR, so that the system can effectively estimate phase errors and achieve stable imaging for various targets.

2.2. Study on the Depolarization Effect of Different Targets

At the wavelength of 1550 nm, typical polarization-maintaining targets include smooth-surfaced metals and flat mirrors; typical generally depolarized targets include reflective stickers and rough-surfaced metals; and typical severely depolarized targets include buildings and coated products. We use a vertical polarization laser with a polarization extinction ratio of 23 dB and a BPSK signal with a code length of 2000 (the main side lobe ratio after pulse compression is approximately 33 dB) as the transmitted signal. The polarization state of receiving channel-1 is set to vertical polarization (defined as the polarization maintaining channel, PMC), and the polarization state of receiving channel-2 is set to horizontal polarization (defined as the depolarization channel, DPC). Observe different targets separately and observe the same target multiple times to solve the problem of possible large errors in single experimental results. Set up a controlled experiment, switch the polarization states of channel-1 and channel-2, and observe again to solve measurement errors caused by inconsistent channels. At the same time, verify the accuracy of the echo data phenomenon using a polarizer in front of the infrared camera.

The results of statistical averaging of multiple sets of experimental data are shown in Figure 1. The loss of laser signal in the vertical polarization direction due to atmospheric and incident angle (approximately 1° away from the normal direction) is considered to be 1.5 dB. The experimental results show that the smooth-surfaced metal has better polarization performance, with a loss of about 1.5 dB in the vertical polarization direction of the laser signal, corresponding to a difference of 17 dB in the echo intensity between the PMC and the DPC. The reflective sticker shows a more obvious depolarization phenomenon, with a loss of about 6.5 dB in the vertical polarization direction of the laser signal, corresponding to a difference of 7 dB in the echo intensity between the PMC and the DPC. However, the wall shows a more serious depolarization phenomenon, with a loss of about 11 dB in the vertical polarization direction of the laser signal, corresponding to a difference of −2 dB in the echo intensity between the PMC and the DPC. At this time, the energy of the echo signal is mainly concentrated in the DPC.

In addition, we have conducted this experiment for more targets, and the results show that most targets are depolarized. The experimental results also show that in the target area, most of the coherence coefficients are greater than 0.6. This indicates that there is still strong coherence between the two orthogonal polarization states of the echo signals, which provides conditions for interferometry processing. On this basis, the principle that the two echo signals at the same time have approximately the same vibration characteristics can be used to estimate the vibration phase error through interferometry processing between channels.

2.3. Study on the Depolarization Effect of Targets Corresponding to Light Sources with Different Polarization States

The above results show that when both the transmitting and receiving channels use the linearly polarized laser, the energy loss caused by target depolarization will not be conducive to the stable imaging of various targets by the ISAL system. If the transmitting laser is changed to circularly polarized and still uses vertical and horizontal polarization for receiving, the impact of target depolarization on imaging stability should be alleviated. The literature [13] shows that when using a linearly polarized laser source, the SNR of the vertical polarization channel is usually low, limiting the observation accuracy and observation distance. Compared with the linearly polarized laser source, the circularly polarized laser source may have more obvious advantages.

Therefore, we conducted experiments on transmitting a linearly polarized laser and a circularly polarized laser for different targets. The observation object of the experiment is a road. The oblique angle is about 1°, the downward angle is about 20°, and the oblique distance is about 24 m. Taking asphalt pavement and reflective stickers attached to the roadside as targets, the infrared image of their layout is shown in Figure 2a. By moving the laser spot, we can obtain the echo signals of reflective stickers and asphalt pavement, respectively. The 1/4 wave plate with known optical axis direction is used to adjust the polarization state, and the 1/4 wave plate is placed in front of the transmitting collimator. The polarization state is detected by the polarizer, which is placed in front of the infrared camera with a central wavelength of 1550 nm.

When transmitting a vertically polarized laser, the light intensity of the laser source in the infrared camera with vertical polarization (V) and horizontal polarization (H) is shown in Figure 2b, and it can be seen that the degree of vertical polarization is better. When transmitting the circularly polarized laser, the light intensity of the laser source in the infrared camera with vertical polarization and horizontal polarization is shown in Figure 2c, and the light intensity of the two channels of the reflective sticker is shown in Figure 2d when transmitting vertically polarized laser, and the light intensity of the two channels of the reflective sticker is shown in Figure 2f when transmitting the circularly polarized laser. When transmitting the circularly polarized laser, the pulse compression results of the two channels of the reflective sticker are shown in Figure 2e, and the pulse compression results of the two channels of the reflective sticker are shown in Figure 2g when transmitting the circularly polarized laser.

The experimental results show that when transmitting vertically polarized laser, for reflective stickers, which are generally depolarized targets, the echo intensity of the vertically polarized receiving channel is greater than that of the horizontally polarized receiving channel. For asphalt pavement, which is a severely depolarized target, the echo intensity of the vertically polarized receiving channel is less than that of the horizontally polarized receiving channel. When transmitting the circularly polarized laser, for both depolarized targets, the echo intensity of the two linearly polarized receiving channels with orthogonal polarization states is similar, and compared to the case of transmitting the linearly polarized laser, the echo intensity of both channels is slightly improved.

3. Introduction to Experimental System

The optical system used in the ISAL experimental system in this paper is shown in Figure 3a, including a transmission channel (TC), two orthogonal polarization receiving channels (RC), and a transmission reference channel (TRC) for pulse compression. To expand the observation width in the range direction, both the transmitting and receiving channels used cylindrical lenses to broaden the beam in the elevation direction. The transmitted and received laser spots after the beam broaden are shown in Figure 3b and Figure 3c, respectively. The azimuth width of the transmitting beam is 1.5 mrad, the elevation width is 50 mrad, the azimuth width of the receiving beam is 1.2 mrad, and the elevation width is 80 mrad. TC comprises a fiber collimator, a 1/4 wave plate, and a cylindrical lens. RC comprises a fiber collimator, a polarizer, and a cylindrical lens. TRC is used to record the transmitted BPSK signal and achieve pulse compression of the echo signal. The polarization states of each channel and their geometric relationships are shown in Figure 3d.

The ISAL system mainly comprises the optical system, signal generator, echo signals sampling module, and computer. The system diagram is shown in Figure 4. The ISAL system is placed on a general three-axis stable platform to reduce the impact of platform vibration on imaging quality. The center wavelength of the laser is 1.55 μm, and the average emission power is 5 W. High pulse repetition frequency (PRF) is used to avoid Doppler frequency aliasing caused by vibration, so PRF is selected to be 100 kHz. The signal generator generates the clock signal while generating the broadband phase modulation electrical signal required by the Mach–Zehnder (MZ) modulator and the wide-pulse modulation electrical signal required by the Acousto-Optic Modulator (AOM) pulse modulator. Finally, a BPSK signal with a pulse width of 1 μs, a subcode width of 0.5 ns, a number of symbols of 2000, and a bandwidth of 2 GHz is generated. The echo signals sampling module mainly comprises the balanced photodetector (BPD), amplifier, and analog-to-digital converter (ADC). The ADC has a quantization bit of 12 and a sampling rate of 4 GS/s. The corresponding quantization power threshold at a load of 50 Ω is −68.2 dBm. To ensure detection sensitivity, both the echo power and equivalent noise power need to be greater than the ADC’s quantization power threshold. By increasing the amplifier gain, small signal sampling can be ensured. Therefore, the ISAL system in this article sets the RF amplifier to 50 dB. In addition, in order to facilitate observation of the target, a short-wave infrared camera is also configured during the experiment.

4. ISAL Imaging Experiment of Moving Target

4.1. Signal Processing Flow

Due to the relative motion between the ISAL system and the target in the direction of laser propagation, there is a Doppler frequency shift between the echo signal and the transmitted signal. BPSK signals are Doppler-sensitive, and the larger the pulse width of BPSK, the greater the impact of Doppler frequency shift on the pulse compression effect. In this paper, the ISAL system used a BPSK signal with a pulse width of 1 μs, which has a Doppler tolerance of 500 kHz and a corresponding target radial velocity of 0.3875 m/s. The ISAL system’s PRF is 100 kHz, and the Doppler bandwidth that can be processed is 50 kHz, corresponding to a target radial velocity of 0.03875 m/s. Therefore, for moving target echo signals, in order to achieve more ideal pulse compression and avoid Doppler frequency aliasing, it is necessary to first perform Doppler compensation on the echo signal. On this basis, vibration phase error estimation and compensation are performed to achieve image focusing in azimuth direction and achieve ideal imaging resolution.

The literature [10,14,19] introduces the method of estimating the vibration phase error of a translational target based on dual-channel and multi-channel echo signals, and the literature [12] proposes a method of estimating the vibration phase error of a rotational target based on multi-channel echo signals. Therefore, when the coherence of multi-channel echo signals is good, it is feasible to estimate the vibration phase error through interferometry processing. However, the large Doppler bandwidth in interferometry processing will affect the unwrapping of the interferometric phase, so the baseline length needs to be set short to prevent the interferometric phase from being entangled. The baseline length needs to meet the following conditions:

$$\max \left\{\left|{\phi }_v\left(t_k+d/‖\stackrel{\rightharpoonup }{v}‖\right)-{\phi }_v\left(t_k\right)\right|\right\}<\pi \mathrm{rad}$$

(4)

The SCA algorithm can approximately extract the differential value of the vibration phase error between adjacent pulses in the echo signal. To reduce the Doppler bandwidth of the vibration and thus alleviate the problem of interferometric phase wrapping, the SCA can be used to roughly estimate and compensate for the vibration phase error of the echo signal first. Then, the along-track interferometry method can be used to accurately estimate and compensate for the vibration phase error. At this point, Equation (2) can be rewritten as:

$$s_{i,sca}\left(\widehat{t},t_k+\Delta t_i\right)={\displaystyle \sum _{m=1}^M\left\{\begin{array}{l}{\rho }_m\cdot {\sigma }_m\cdot \exp \left(j\cdot {\phi }_m\right)\cdot \exp \left\{j\cdot \left[{\phi }_v\left(t_k+\Delta t_i\right)-{\phi }_{sca}\left(t_k+\Delta t_i\right)\right]\right\}\\ \cdot \mathrm{sinc}\left\{B_r\cdot \left[\widehat{t}-2\cdot \frac{R_{m,i}\left(t_k+\Delta t_i\right)}{C}\right]\right\}\cdot \exp \left[-j\cdot \frac{4\pi \cdot R_{m,i}\left(t_k+\Delta t_i\right)}{\lambda }\right]\end{array}\right\}}$$

(5)

where ${\phi }_{sca}\left(t_k\right)={\displaystyle \sum _{j=1}^k\mathrm{unwrap}\left[\mathrm{angle}\left({\epsilon }_{j,j-1}\right)\right]}$ is the phase error estimated by SCA, and ${\epsilon }_{j,j-1}$ is the complex coherence coefficient between the j-th pulse and its previous pulse in the echo.

The outdoor experiment scene and observation geometry of the ISAL system in this paper are shown in Figure 5. The imaging target was the vehicles traveling on the road, with the transmission laser spot located in the center of the road, and its elevation width was 1 m. The oblique distance between the ISAL system and the targets is 20 m, the height difference is about 9 m, the oblique angle ${\theta }_{\mathrm{s}}$ = 7.7°, and the depression angle $\varphi$ = 24.2°.

The signal processing flow of this paper is as follows.

• Preprocess: the echo signal and the transmitted reference signal are preprocessed first, including Hilbert transform and harmonic interference removal.
• Parameter estimation: estimate the oblique angle, depression angle, and oblique distance according to the measured observation geometry, estimate the target motion velocity according to the infrared camera video, and conduct Doppler compensation for the echo signal in combination with the estimated parameters. The equation for calculating the Doppler frequency to be compensated is as follows:

  $$f_{\mathrm{d}}={\displaystyle \frac{2V}{\lambda }}\cdot \sin {\theta }_{\mathrm{s}}\cdot \cos \varphi$$

  (6)

  where ${\theta }_{\mathrm{a}}$ is the azimuth beamwidth. The compensated echo signal and the TRC signal are conjugate-multiplied in the fast frequency domain to achieve pulse compression. Then, the estimated parameters are fine-tuned based on the time and frequency domains of the pulse compression results until the ideal pulse compression result is obtained.

3.

Registration: perform fast-time alignment and slow-time alignment on data from two channels.

4.

Estimation and compensation of vibration phase error: the signals of the two channels after registration are used for coarse-estimation of the vibration phase error using SCA, and then the vibration phase error is fine-estimation using the along-track interferometry.

5.

Construction of matched filter: after compensating for the vibration phase error, the second-order phase generated by translational motion in the phase of the echo signal occupies the main component, and the matched filter is constructed according to the target motion velocity, and the frequency modulation rate of the matched filter is as follows:

$$K_a=2V^2/\lambda R=0.4\mathrm{MHz}/\mathrm{s}$$

(7)

6.

Imaging: divide the sub-aperture according to the method in the literature [13] and use the Range-Doppler (RD) algorithm for imaging. The sub-aperture imaging results are then stitched and azimuthally multi-look processed to obtain the final imaging result. The duration of the imaging sub-aperture depends on the synthetic-aperture time. The relationship between the synthetic-aperture time T and the azimuth beamwidth, the slant distance R, the target movement speed V, the oblique angle, and the depression angle is as follows:

$$T={\displaystyle \frac{R{\theta }_a}{V\cos {\theta }_s\cos \phi }}$$

(8)

The above equation is the maximum synthetic-aperture time calculated. The synthetic-aperture time corresponds to the number of slow-time pulses. Considering the slow-time Fourier transform, the number of pulses is usually rounded to the integer power of 2. In this paper, the synthetic-aperture time is 5.12 ms (512 pulses). The sub-aperture duration is divided into 5.12 ms for imaging, and the corresponding matched filter bandwidth is set to 2 kHz. At this time, the corresponding lateral imaging resolution ${\rho }_a=V/B$.

4.2. ISAL Imaging Results

The ISAL system shown in Figure 4 is used to conduct ISAL imaging experiments on moving targets. First, the experiment was carried out on the tricycle, which was pasted with the reflective stickers for calibration (the length of the reflective stickers along the track is 2 cm). The transmission laser spot, the infrared image corresponding to the tricycle, and the reflective stickers are shown in Figure 6a. The size of the tricycle and the spacing of the reflective stickers are shown in Figure 6b.

The time–frequency analysis results of the 4109th range-gate (where the reflective stickers are located) of the echo signals from RC-1 and RC-2 are shown in Figure 7a,b. It can be seen that the Doppler bandwidth caused by vibration is about 45 kHz, and the Doppler curves of RC-1 and RC-2 are relatively close. Firstly, the SCA is used for coarse-estimation and compensation of the vibration phase error, and then the along-track interferometry is used for fine-estimation and compensation of vibration phase error. The time–frequency analysis results of the 4109th range-gate after compensation are shown in Figure 7c,d, indicating that the Doppler bandwidth of the echo signal is substantially reduced. It should be noted that after compensation, due to the second-order phase generated by the target’s lateral motion, the echo signals at each point exhibit the characteristics of chirp signals.

There is a certain oblique angle in the observation geometry in this paper, so the target moving too fast will lead to a large Doppler frequency shift. If the moving velocity is too fast, it will lead to spectrum aliasing, which will affect the accuracy of the algorithm in this paper. When designing the system, it is necessary to ensure that the pulse repetition frequency of the system is at least twice the Doppler bandwidth of the echo signal. The Doppler bandwidth of the signal is related to the azimuth beamwidth, depression angle, oblique angle, and other factors, which can be expressed as:

$$B_{\mathrm{a}}={\displaystyle \frac{2V}{\lambda }}\cdot {\theta }_{\mathrm{a}}\cdot \sin {\theta }_{\mathrm{s}}\cdot \cos \varphi$$

(9)

The pulse repetition frequency of this system is 100 kHz, and the corresponding maximum Doppler bandwidth is 50 kHz. In this experiment, in addition to the 45 kHz Doppler bandwidth caused by vibration, the residual Doppler bandwidth is about 5 kHz. From this, it can be calculated that the maximum allowable velocity of this method in theory is about 26 m/s.

The range direction profile of the imaging results is shown in Figure 8a. The bandwidth of the BPSK signal after the Hilbert transform is 1 GHz, corresponding to a range resolution of 15 cm. This also corresponds well to the 3 dB width in the range direction profile. According to the infrared camera image and observation geometry, the lateral velocity of the target is estimated to be approximately 2.4–2.6 m/s. The azimuth direction profile of the imaging results is shown in Figure 8b. Based on the correspondence between the reflective sticker spacing and the imaging results, the estimated lateral velocity is 2.51 m/s. After compensating for the vibration phase error, the second-order phase of the real data corresponds to the second-order phase of the lateral velocity of 2.51 m/s, as shown in Figure 8c. It can be seen that the two are relatively close, which also verifies the accuracy of the target lateral velocity, on the other hand.

The imaging results of ISAL on a tricycle under the conditions of transmitting a laser with different polarization states are shown in Figure 9 and

Table 1. Image quality assessment.

	Figure 9a	Figure 9b	Figure 9c	Figure 9d
Image entropy	12.8836	12.7063	12.6604	12.6036
Contrast ratio	8.0256	9.1473	10.0486	10.0971

. Figure 9a,b show the imaging results of RC-1 and RC-2 when the vertically polarized laser is transmitted. Figure 9c,d show the imaging results of RC-1 and RC-2 when the circularly polarized laser is transmitted. The azimuth beam divergence angle is 1.2 mrad, and the corresponding synthetic-aperture duration is about 9 ms. Divide the sub-aperture duration according to 5.12 ms for imaging, set the matching filter bandwidth to 2 kHz, and the corresponding lateral imaging resolution is about 1 mm.

The focusing effect of imaging results is evaluated by image entropy and image contrast, as shown in Table 1. The equations for image entropy and contrast are as follows:

$$\left\{\begin{array}{c}\begin{array}{cc}H\left(I\right)=-{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^{K}p\left(j,k\right)\cdot \ln p\left(j,k\right),}}& p\left(j,k\right)={\displaystyle \frac{|I\left(j,k\right){|}^2}{{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K|I\left(j,k\right){|}^2}}}}\end{array}\\ \begin{array}{cc}C\left(I\right)={\displaystyle \frac{1}{u}}\sqrt{{\displaystyle \frac{1}{JK}}\cdot {\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K{\left(\left|I\left(j,k\right)\right|-u\right)}^2}}},& u={\displaystyle \frac{{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^K\left|I\left(j,k\right)\right|}}}{JK}}\end{array}\end{array}\right.$$

(10)

where $p\left(j,k\right)$ is the normalized power of the image, $I\left(j,k\right)$ is the complex image, $u$ is the average intensity of the image, and $J$ and $K$ are the number of two-dimensional pixels in the image, respectively. The smaller the image entropy and the higher the contrast, the better the focusing effect.

From the above imaging results, it can be observed that when transmitting a vertically polarized laser, the contrast ratio of the imaging results in RC-2 is higher than that in RC-1, indicating that the depolarization effect of the targets is significant. In addition, due to the influence of the targets’ roughness and incidence angle, the depolarization characteristics at different positions of the targets are also not consistent. Taking the first reflective sticker in the above imaging results as an example, the imaging results of RC- 1 after interpolation processing are shown in Figure 10a. The echo intensity on both sides of the reflective sticker is higher, while the echo intensity at the center of the reflective sticker is weaker. The imaging results of RC-2 are shown in Figure 10b, which is opposite to the phenomenon in Figure 10a. The imaging results of RC-1 and RC-2 are synthesized in a non-coherent accumulation manner, as shown in Figure 10c. It can be seen that, after fusion processing, the echo intensity of each scattering point on the reflective sticker is relatively uniform, and the imaging quality is improved.

Based on the above experimental results and signal processing methods, ISAL imaging experiments were conducted on non-cooperative vehicles driving on the road. The infrared images of the non-cooperative vehicles and their two receiving channels’ synthesized ISAL imaging results when transmitting the circularly polarized laser are shown in Figure 11. When transmitting the linearly polarized laser, due to the low SNR and inaccurate phase error estimation, it is impossible to image non-cooperative vehicles. When transmitting the circularly polarized laser, the SNR of the echo signals received by orthogonal polarization two receiving channels meets the use requirements of along-track interferometry. The infrared image of the non-cooperative vehicle and the ISAL imaging results after two-channel synthesis are shown in Figure 11. Based on the infrared images, the estimated lateral velocity is about 5.2 m/s, the length of the vehicle is about 4.6 m, and the width is about 1.8 m. Due to the large size of the vehicle, the laser spot can only cover its upper surface, so ISAL only images its roof. From the imaging results, it can be seen that the contour of the car’s upper surface is clear and can correspond well with the infrared image.

5. Discussion

ISAL is a kind of ladar system based on coherent detection technology, which adopts an all-fiber optical path to ensure its stability and coherence in the changing environment. ISAL has the advantages of high imaging resolution and short imaging time, and has great development potential in high-resolution remote sensing applications.

Due to the use of an all-fiber optical path and a single-mode polarization-maintained fiber, ISAL can only use a linear polarization receiver. At this time, the depolarization effect of the atmosphere and most real targets on the laser will significantly reduce the echo signal-to-noise ratio of the same linear polarization system in the receiving and transmitting channels, which makes it difficult to apply the vibration phase estimation method, and to stably image various targets. Therefore, the current publicly reported ISAL experiments have not yet met the application requirements for imaging real targets.

In this paper, the imaging of ISAL moving targets based on orthogonal polarization and along-track interferometry is studied. The experimental results in Section 2.2 indicate that the depolarization effect of real targets on lasers is severe. The depolarization effect of targets toward lasers will greatly reduce the SNR of ISAL systems, which will make it difficult for ISAL to stably perform high-resolution imaging of real targets. In order to reduce the depolarization effect of real targets on laser signals, Section 2.3 conducted a study on the depolarization effect of targets on laser signals under different polarization states. The experimental results showed that when the circularly polarized laser was transmitted, for the depolarization target, the echo intensity of the two orthogonal polarization receiving channels was close, and the echo intensity of the two channels was slightly improved compared to the case of transmitting the linearly polarized laser.

On this basis, this paper conducted ISAL imaging experiments on moving real targets. The beam divergence angle after receiving and transmitting elevation beam broaden is about 3°, the echo data duration is 1 s, the vibration Doppler frequency range based on SCA coarse-compensation and along-track interferometry fine-compensation is about 45 kHz, the imaging range resolution is 15 cm, and the azimuth resolution is mm.

The experimental results show that emitting the circularly polarized laser and using two channels of orthogonal polarization reception can balance the echo energy of different targets and the effect of forward interference, making the system more stable in imaging multiple real targets. The experimental results also indicate that using the beam-broaden method and increasing the gain of the electronic amplifier can help ISAL to perform wide-range imaging of real targets, which is of great significance for the research of ISAL.

In order to reduce the amount of data and computation, we adopt the scheme of transceiver beam broaden to achieve wide-range imaging while reducing the number of receiving channels. However, due to the large beam-expansion degree, and the small receiving aperture and transmission power, the laser power density on the target is small. At present, imaging is only conducted for non-cooperative moving targets that are close to each other. Later, the receiving aperture will be increased and the transmission power will be increased to image the long-distance non-cooperative moving targets.

6. Conclusions

At present, the observation objects in the publicly reported SAL/ISAL experiments are mainly corner reflectors or specially designed targets with high reflectivity, which have not yet met the application requirements for imaging real targets. The main reason for this problem is that most real targets have a depolarization effect on the laser, which may significantly reduce the SNR of the echo in the same polarization system of the transmitting and receiving channels, making vibration phase estimation methods based on interferometry difficult to apply. In order to solve the problem of ISAL imaging non-cooperative moving targets, this research designed a dual-channel orthogonal polarization receiving inverse synthetic-aperture ladar with a wavelength of 1550 nm, a transceiver beam divergence angle of 3°, and an average transmit power of 5 W. The designed system successfully obtained ISAL imaging results of non-cooperative vehicles, which proved the stability of the system.

The depolarization effects on laser signals are tested for polarization-maintaining targets, generally depolarized targets, and severely depolarized targets. The experimental results show that for the ladar based on an all-fiber optical path and linear polarization receiving channel, the SNR of the echo signal is greatly reduced when the linear polarization laser is transmitted. If the circular polarization laser is transmitted, the problem of excessive energy loss when the target is seriously depolarized can be effectively avoided, and the echo intensity of each channel can be relatively close when detecting different targets. At the same time, the experimental results also show that most of the coherence coefficients of the echo signals are greater than 0.6; that is, the two echo signals with orthogonal polarization still have strong coherence. All of these provide conditions for interferometry processing. On this basis, the research of a beam-broaden ISAL imaging of moving real-target based on orthogonal polarization and along-track interferometry is carried out, and the vibration phase error is estimated and compensated.

The imaging results of tricycle targets with reflective stickers show that the ISAL imaging results obtained when the circularly polarized laser is transmitted have a higher image SNR and smaller image entropy than when the linearly polarized laser is transmitted. The image quality can be further improved after the fusion processing of the imaging results of the vertical polarization receiving channel and the horizontal polarization receiving channel.

ISAL imaging experiments were carried out on non-cooperative vehicles traveling on the road. When the linear polarized laser was transmitted, due to low SNR and inaccurate phase error estimation, it was impossible to image non-cooperative vehicles. When the circularly polarized laser was transmitted, the SNR of the two-channel echo signals received by the orthogonal polarization receiver met the requirements of the along-track interferometry. After the phase error compensation and fusion processing of the orthogonal polarization echo signals, the ISAL imaging results of the non-cooperative vehicle were successfully obtained, which shows that the system in this paper has good performance.

In conclusion, the method proposed in this paper can simultaneously address the impact of the target depolarization effect on echo energy and the problem of vibration error estimation based on along-track interferometry, enabling the ISAL system to stably compensate for motion and image multiple real targets. This research work is conducive to the stable imaging of various targets by the ISAL system, which will greatly improve the observation efficiency of ISAL and lay a foundation for further imaging of non-cooperative moving targets over a long distance.