Abstract

We propose an imaging system with scanning feedback of an optical phased array (OPA) for moving targets with unknown speed. The system combines OPA scanning velocimetry capability with OPA-based ghost imaging to enable trajectory tracking of targets moving within the field-of-view of the system while accomplishing image reconstruction. The proposed system can perform image reconstruction for millimeter-scale moving targets placed up to 20 m away from the camera. The system can be applied in areas such as autonomous driving and high-resolution imaging.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Ghost imaging (GI) obtains object information from fluctuations in a light field, thus representing the higher-order properties of the light field [14]. Unlike traditional optical imaging that mainly relies on the distribution of the average intensity of the light field for imaging objects, GI enables detection and imaging separation, single-pixel camera imaging, and anti-interference image reconstruction [59]. GI of moving targets has been investigated and mainly focuses on calculating the target speed with respect to a reference field [1013]. This is achieved by algorithmically analyzing the results of repeatedly collecting signal light intensity information. Then, the reference light field is corrected in real time to achieve stationarity with respect to the target. A common limitation in GI of moving targets is the long time required to accurately estimate the speed of the moving object in the underlying iterative algorithm, often undermining the imaging of fast-moving targets. We believe that an optical phased array (OPA) can solve the imaging difficulties by extracting the target speed through sequential beam deflection and providing a pseudo-thermal light field for GI. Combining GI with OPA imaging has been proposed, achieving promising results [14].

Most studies on OPA have been aimed at improving chip design, reducing power consumption, and reducing loss [1520]. However, the low emission power of ordinary OPA chips and interference of background light in complex environments hinder OPA imaging and long-range communications [2124]. In addition, a general illumination method or time-of-flight imaging system may not be suitable for OPA imaging, whereas GI may offer a viable solution for OPA imaging.

To apply OPA LiDAR (light detection and ranging) technology, we propose an OPA-based GI system for imaging a moving target with an unknown speed by using a tracking algorithm. The proposed system simplifies existing solutions and does not require a reference optical path to conveniently implement image reconstruction of rapidly moving targets. Specifically, a 2D OPA-based imaging system integrating high-resolution image reconstruction for a target with unknown speed is presented in this paper. In this system, OPA controls the beam direction deflection and operates as a pseudo-thermal light source for GI-based image reconstruction. We evaluated the proposed imaging system using a 4 × 4 OPA on a silicon-on-insulator platform, in which the phase per channel is individually controlled by thermo-optic phase shifters. In addition, stochastic parallel gradient descent (SPGD) control provided the optimal tuning vector per beam direction. Experiments were conducted to verify the imaging capabilities of the proposed OPA-based GI in long-distance image reconstruction. The system was experimentally validated at 20 m from the camera in a non-laboratory environment regarding both dynamic target speed estimation and image reconstruction.

2. Scanning and image reconstruction using an OPA-based GI

The devices for GI were fabricated in a CMOS (complementary metal–oxide–semiconductor) foundry on a 300 mm silicon-on-insulator wafer with 2 μm buried oxide using lithography. The constituent components of the OPA were a fiber-to-chip edge coupler, a waveguide 1 × 2 multimode interference splitter, and free-space emitting grating coupler antennas, as shown in Fig. 1.

 figure: Fig. 1.

Fig. 1. OPA chip and performance measurement results. (a) Top-view photograph of 4 × 4 OPA chip. (b) Measured loss in fiber-to-chip edge coupler. (c) Optical microscopy image of 1 × 2 multimode interference splitter with measured insertion loss of 0.1 dB. (d) Optical microscopy image of optical antenna array with measured emission efficiency of 40%, The OPA antenna pitch is 8 microns in vertical direction, and 4 microns in horizontal direction. (e) Accumulated phase shift in thermo-optic phase shifters extracted from Mach–Zehnder interferometer transmission spectra. The optical variable phase shifter achieves a 2π phase shift by consuming 47 mW with the heater. (f) Optical response of rise and fall times of 16 and 41 μs, respectively.

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Because phase has a high sensitivity, minor manufacturing errors in the antenna array and process errors in electrode bonding considerably affect the far-field distribution, which deviates from the ideal shape. The proposed SPGD control algorithm implemented in NI LabVIEW provided the optimum tuning vector per desired beam direction, and the imaging system provided far-field feedback. The optimal 0° far-field distribution is shown in Fig. 2(a). The calibrated far-field pattern is guided to a divergence angle of 2.5° × 4.9°, which suitably agrees with the design value. By integrating automatic optimization and real-time feedback from the Fourier imaging system, a set of phase-tuning schemes with an 8 dB background suppression ratio was obtained in the 11° × 22° field of view. In addition, SPGD control generally required less than 100 iterations of the fully tuned array to provide a solution, ensuring a high calculation speed, as shown in Fig. 2(b).

 figure: Fig. 2.

Fig. 2. (a) From top left to bottom right: far-field patterns simulated and measurement after phase calibration, far-field pattern in cross-sections at θx = 0 and θy= 0 (FWHM, full width at half maximum). (b) Convergence of proposed SPGD control after approximately 100 iterations. The evaluation function used in Fig. 2(b) is the intensity ratio between selected optimized region and capture surface.

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GI applies a second-order correlation to the data collected by the two detectors on the detection arm and reference arm to restore the object image as follows [25]:

$${G^{(2)}}(x,y) = {\left\langle {I_R^{(n)}(x,y){B^{(n)}}} \right\rangle _n},$$
where IR(n) is the reference field collected by the CCD (charge-coupled device), while the n-th sampling, B(n), is the total intensity value collected by the barrel detector. By adding a velocity component to the traditional GI equation [26], the distribution of the moving target, Oμ(x(vx),y(vy)), can be described as
$${O_\mu }(x(vx),y(vy)) = \left\langle {\left( {{B_\mu } - \left\langle {{B_\mu }} \right\rangle } \right)(I(x(vx),y(vy)) - \left\langle {I(x(vx),y(vy))} \right\rangle )} \right\rangle ,$$
where vx and vy are the relative speeds of the target in the system along the corresponding axes.

Based on the conventional GI experimental method [19,26,27], the feasibility of the proposed OPA-based GI was verified on a target U shape with size of 5 × 5 mm (333 × 333 pixels in an infrared camera). In addition, image reconstruction of OPA-based GI in different environments was evaluated. Figure 3(a) shows reconstructed images obtained in three cases over 1000 iterations for conventional image reconstruction, image reconstruction with external perturbation (i.e., adding obstacles made of one-page sulfuric acid paper) along the signal optical path, and image reconstruction under thermo-optic noise conditions at a certain intensity generated by room illumination, at room temperature (300 K). The corresponding peak signal-to-noise ratio (PSNR) is shown in Fig. 3(b) [28]. The PSNR of each reconstructed image shows that OPA-based GI provides high quality reconstruction even if the imaging system suffers from phase and intensity perturbations, benefiting from the superiority of GI reconstruction and demonstrating its use in the proposed system.

 figure: Fig. 3.

Fig. 3. Simulation and experimental results of conventional GI implemented with OPA. (a) Results for OPA-based GI simulation (i), general GI experimental results (ii), GI with external perturbation experimental results (iii), and GI with thermo-optic noise experimental results (iv). (b) PSNR values of images in panel (a).

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3. Implementation and evaluation of the imaging system

Owing to its outstanding properties, GI can provide high-quality image reconstruction. In addition, OPA can control the directional beam deflection for dynamic target speed extraction, being essential for the proposed imaging system. We evaluated these two modes of operation separately in section 3.1 and then experimentally validated the proposed dynamic target imaging system with scanning feedback that integrates the two modes in section 3.2.

3.1. Separate experimental validation of image reconstruction and tracking algorithm for the OPA dynamic imaging system

GI enables image reconstruction at relatively long distances between the camera and target [2932]. Although OPA-based long-distance GI reconstruction is promising, it remains to be validated. The GI reconstruction quality is determined by two factors: reference field I(x,y) and the sum of the light field intensity following the interaction of the reference light with virtual Bμ. To verify the contribution of OPA to image reconstruction based on GI over long distances, two experiments were conducted separately.

As shown in Fig. 4(a), the signal light transmitted over a distance can be used for GI reconstruction, even if it is scattered. For experiment 1, pseudo-thermal light was generated when the transverse-electric-mode light emitted from a laser (Koheras ADJUSTIK POWER E15) with 15 dBm optical power was coupled into the OPA. In addition, a random external voltage was applied. The OPA output light was collected using a short-wave infrared lens (AZURE-NV2514SWIR). A collimating system was formed by the short-wave infrared lens and two other lenses (focal lengths of 250 and 150 mm, 2-inch diameter). The relative distance between the three components can be adjusted to easily obtain the speckle pattern that illuminates the target. The same target U was placed at 0.1 m from the OPA, and the transmitted light signal from the target was collected with an infrared pickup camera (GOLDEYE G-008 TEC1), which was placed at 20 m from the target. To facilitate the optical alignment, the infrared pickup camera was chosen as the echo detection component instead of the single-pixel detector. To demonstrate that all our experiments in this paper reconstruct the target image according to the light intensity of the echo signal rather than the field distribution, lens 3 (focal lengths of 400 mm, 2-inch diameter) is employed to converge the beam, in which case the field distribution of the echo signal can be negligible. The reference light field is stored in advance, profiting from the OPA properties. n reference optical fields IR(n) were generated by loading the OPA with n sets of random voltages, and n sets of echo signals B(n) corresponding to the reference optical fields were acquired. The reconstructed images and their PSNR values are shown in the schematics of Fig. 4(a). The PSNR of the reconstructed images in this experiment was similar to or even better than the results in the dark laboratory environment shown in Fig. 3(b). The randomness of the reference field transmitted over a certain distance can still be used to realize GI reconstruction.

 figure: Fig. 4.

Fig. 4. Feasibility verification of OPA-based GI. (a) Schematic diagram of signal light experiment and its results. (b) Schematic diagram of reference light experiment and its results.

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To distinguish the two experiments, same-size letter L was used in experiment 2 (i.e., 3.5 × 5 mm corresponding to 233 × 333 pixels in the camera). This target was placed at 20 m from the OPA, and the infrared pickup camera used to capture the light signal was placed at 0.5 m from the target. The experimental results are shown in Fig. 4(b). The pseudo-thermal light generated by the OPA can be used as the illumination light field to achieve GI reconstruction and can ensure high image reconstruction quality.

Instead of the conventional GI iterative method dynamic imaging method, OPA scanning beams are used to extract the target velocity [3335]. A 4 × 4 OPA can achieve a spatial resolution of 2.5° × 4.9°. We performed scanning with a field of view of 11° × 22° in this experiment, and approximately 5 × 4 points were required for a field-of-view scan. Scan of the entire field of view range was achieved using scanning beams optimized by SPGD algorithm. As the number of scan points in the field of view was small, SPGD-corrected directional scan voltages were sequentially loaded to the OPA phase shifters. The camera in the experiment is used to collect the light intensity rather than the field distribution. After the entire field of view was scanned once, the echo signals were superimposed to form a frame. Otsu algorithm serves to segment the target and background, and shape-center algorithm is used with it to accurately calculate the shape center position. Owing to the close distance between the target and the capture surface (compared to the speed of light c), the optical time-of-flight can be neglected with the 10Hz phase shifters modulation speed adopted. The speed of target can be calculated from the position of the center of shape change in multiple frames (5 frames are used here) and the time used for scanning [36,37]. The accuracy of speed estimation was determined by the tracking trajectories obtained using other frames according to the dynamic-programming-based track-before-detect (DP - TBD) algorithm [38,39]. The estimation diagrams and experimental setup and results are shown in Fig. 5. The estimation error was within ±5%. This preliminary verification of the algorithm property considered that only a small fraction of the scan points lies in the field of view.

 figure: Fig. 5.

Fig. 5. Target speed estimation. (a) Diagram of speed estimation algorithm, (b) schematic diagram of the experimental system, and (c) experimental results. The target shown in (b) is a 1mm diameter round reflection mirror.

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3.2. Experimental validation of the OPA dynamic imaging system in a non-laboratory environment

OPA derives from LiDAR technology and provides fast non-inertial scanning. Thus, it can be used to estimate the speed of moving targets. The scanning speed estimation of OPA combined with GI reconstruction constitutes the proposed system that enables speed estimation, tracking, and imaging of moving targets.

We conducted the experiments under the available illumination conditions of a building corridor, with the OPA chip and acquisition camera placed together and the reflection target, which consisted of a mask plate (The mask is a same-size letter L in Fig. 4(b)) and a mirror, placed at 20 m from them, the experimental system is the same as the one in Fig. 5(b), except the distance between the target and the system is increased and test target is replaced. The target was attached to an electric translation stage (Thorlabs KMTS50E/M), which uniformly moved the plane of the vertical optical axis.

The algorithm flowchart of the proposed imaging system is shown in Fig. 6(b). The voltages optimized by SPGD for scanning were sequentially applied to the OPA phase shifters. The moving speed of the target was estimated using the abovementioned algorithm, and the DP-TBD algorithm was used to track the target trajectory, as shown in Fig. 6(c). The error between the true and estimated target speed was within 5%. Overall, the tracking process stabilized, while the system switched to the imaging mode, and random voltages were loaded to the OPA phase shifter to produce pseudo-thermal light. In this experiment, the target speed was 0.4pixels/scanning. When the tracking algorithm running, the voltage modulation rate loaded on the phase shifters is 8.3 Hz with a field-of-view being scanned at 20 voltage changes. The echo signals from these 20 scans are combined to form a frame which is superimposed after normalization. The subsequent algorithm is same as the experimental procedure demonstrated in Fig. 5(a). With the velocity extraction (shape-center algorithm) and trajectory tracking (DP-TBD algorithm), the moving speed of the target can be steadily identified and then GI image reconstruction mode is adopted. The voltage modulation speed loaded on the OPA phase shifters in this case can be varied according to iterations required for the reconstruction. The reconstructed images and their PSNR according to the number of iterations are shown in Fig. 6(c) The images with serial numbers (i) – (v) on the right side of Fig. 6(c) represent images reconstructed by GI with different numbers of iterations and PSNR. The image with serial number (vi) represents the image obtained from the calibrated beams scan.

 figure: Fig. 6.

Fig. 6. Dynamic target imaging system with scanning feedback. (a) Schematic diagram of experimental system, reference field, and signal light. (b) Diagram of proposed dynamic target imaging with scanning feedback. (c) Reconstructed images and their PSNR values based on GI according to iterations and target images obtained by OPA scanning imaging.

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The reconstructed image obtained by scanning has obvious distortions because the beam quality is reduced after the reflection by the target propagates over a relatively long distance compared with the target size. The displayed scanning image is obtained by the scanning method, which requires 400 voltage changes (20 frames of superimposed images) but achieves an inferior image reconstruction quality. OPA can image relatively distant targets by GI algorithm, only requiring to acquire the reference field and total light intensity of the reflected light field for image reconstruction. GI requires more than 500 iterations to reconstruct an image with a high PSNR, which corresponds to 500 voltage changes. The spatial resolutions of both methods were almost equal. Nevertheless, as the number of elements in a scene increases, the scanning method requires more sampling time for image reconstruction, whereas GI likely maintains the sampling time for high-quality image reconstruction by adopting algorithms such as compressed sensing [4043]. The proposed system has a high imaging quality compared to conventional LiDAR scanning imaging in a non-laboratory environment.

4. Discussion and conclusion

We propose a prototype imaging system with scanning feedback, which was validated in a non-laboratory environment. A 4 × 4 OPA with independent phase control per channel was fabricated and evaluated. The OPA could scan a beam width of 2.5° × 4.9° in a field of view of 11° × 22° and ensured high background rejection in phase correcting with SPGD optimization. Moreover, target speed estimation using OPA sequential scanning was achieved by using the Otsu, shape-center, and DP-TBD algorithms. OPA-based GI was used for image reconstruction, capturing a millimeter-scale target at 20 m from the camera.

Imaging was performed in the plane perpendicular to the optical axis in this study. Nevertheless, it should be considered that 3D spatial imaging can include a component of motion along the direction of the optical axis, requiring Doppler frequency shift methods to estimate the target speed [44]. On the other hand, a uniformly moving target and simple velocity measurement algorithm were employed in this study, and the velocity measurement, tracking, and imaging capabilities of the OPA-based imaging system were demonstrated experimentally. With more OPA antennas and higher spatial resolution, more algorithms can be devised to improve the imaging performance. Furthermore, high-speed acquisition component such as high bandwidth single-pixel detector or photon counter, and computation systems such as designs and craft readout and digital signal processing (DSP) electronics, OPA controlled by electro-optical phase shifters may improve data processing and the imaging speed of the system [45,46]. In practical scenarios, the proposed system can work in alternating tracking and imaging modes to achieve tracking of targets with variable motion states.

The proposed imaging system can perform speed estimation and image reconstruction for dynamic targets, achieving suitable results and a resolution in the order of 1.5 millimeters for object imaging at a distance up to 20 m. The proposed imaging system may be applied in a variety of fields such as autonomous driving and high-resolution imaging.

Funding

National Natural Science Foundation of China (62005207); Open Research Fund of State Key Laboratory of Pulsed Power Laser Technology under grant (SKL 2019 KF 06); Natural Science Foundation of Shaanxi Province under grant (2019JQ-648).

Acknowledgments

The chip used was produced in cooperation with Chongqing United Microelectronics Center. The authors would like to thank the editor and anonymous reviewers for their valuable comments on this paper.

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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References

  • View by:

  1. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
    [Crossref]
  2. V Strekalov D, V Sergienko A, N Klyshko D, and YH Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
    [Crossref]
  3. S Bennink R, J Bentley S, and W Boyd R, ““Two-Photon” Coincidence Imaging with a Classical Source,” Phys. Rev. Lett. 89(11), 113601 (2002).
    [Crossref]
  4. G Scarcelli, V Berardi, and Y Shih, “Can Two-Photon Correlation of Chaotic Light Be Considered as Correlation of Intensity Fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006).
    [Crossref]
  5. G Wang L, S Qamar, Y Zhu S, and S Zubairy M, “Hanbury Brown–Twiss effect and thermal light ghost imaging: A unified approach,” Phys. Rev. A 79(3), 033835 (2009).
    [Crossref]
  6. W C Chan K, N O’Sullivan M, and W Boyd R, “High-order thermal ghost imaging,” Opt. Lett. 34(21), 3343–3345 (2009).
    [Crossref]
  7. S Aspden R, R Gemmell N, A Morris P, S Tasca D, L Mertens, G Tanner M, A Kirkwood R, A Ruggeri, A Tosi, W Boyd R, S Buller G, H Hadfield R, and J Padgett M, “Photon-sparse microscopy: visible light imaging using infrared illumination,” Optica 2(12), 1049–1052 (2015).
    [Crossref]
  8. K Chan, N O’Sullivan M, and W Boyd R, “Optimization of thermal ghost imaging: High-order correlations vs. background subtraction,” Opt. Express 18(6), 5562–5573 (2010).
    [Crossref]
  9. X Zhang, H Yin, R Li, J Hong, S Ai, W Zhang, C Wang, J Hsieh, Q Li, and P. Xue, “Adaptive ghost imaging,” Opt. Express 28(12), 17232–17240 (2020).
    [Crossref]
  10. L Hu, X Jin, and G. Zeng, “Lensless ghost imaging for moving objects,” Opt. Eng. 50(12), 7005–7007 (2011).
    [Crossref]
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2021 (2)

2020 (6)

2019 (5)

2018 (2)

Y. He, G. Wang, G Dong, S Zhu, H Chen, A Zhang, and Z Xu, “Ghost Imaging Based on Deep Learning,” Sci Rep 8(1), 6469 (2018).
[Crossref]

L Luo C, P Lei, L Li Z, J Quan Q, X Xin J, D Feng, and Z Min L, “Long-distance ghost imaging with an almost non-diffracting Lorentz source in atmospheric turbulence,” Laser Phys. Lett. 15(8), 085201 (2018).
[Crossref]

2017 (1)

M. Lyu, W. Wang, H Wang, H Wang, G Li, N Chen, and G Situ, “Deep-learning-based ghost imaging,” Sci Rep 7(1), 17865 (2017).
[Crossref]

2016 (3)

2015 (4)

2014 (3)

2013 (3)

2012 (2)

H Shapiro J and W Boyd R, “The physics of ghost imaging,” Quantum Inf. Process. 11(4), 949–993 (2012).
[Crossref]

C Zhao, W Gong, M Chen, E Li, H Wang, W Xu, and S Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

2011 (1)

L Hu, X Jin, and G. Zeng, “Lensless ghost imaging for moving objects,” Opt. Eng. 50(12), 7005–7007 (2011).
[Crossref]

2010 (1)

2009 (4)

G Wang L, S Qamar, Y Zhu S, and S Zubairy M, “Hanbury Brown–Twiss effect and thermal light ghost imaging: A unified approach,” Phys. Rev. A 79(3), 033835 (2009).
[Crossref]

W C Chan K, N O’Sullivan M, and W Boyd R, “High-order thermal ghost imaging,” Opt. Lett. 34(21), 3343–3345 (2009).
[Crossref]

Y Bromberg, O Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

O Katz, Y Bromberg, and Y Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

2006 (1)

G Scarcelli, V Berardi, and Y Shih, “Can Two-Photon Correlation of Chaotic Light Be Considered as Correlation of Intensity Fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006).
[Crossref]

2004 (1)

A Gatti, E Brambilla, M Bache, and L A Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

2002 (1)

S Bennink R, J Bentley S, and W Boyd R, ““Two-Photon” Coincidence Imaging with a Classical Source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref]

1996 (1)

T. Itoh, H. Sueda, and Y. Watanabe, “Motion compensation for ISAR via centroid tracking,” IEEE Trans. Aerosp. Electron. Syst. 32(3), 1191–1197 (1996).
[Crossref]

1995 (2)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
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V Strekalov D, V Sergienko A, N Klyshko D, and YH Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
[Crossref]

1993 (1)

J Arnold, S Shaw, and H Pasternack, “Efficient target tracking using dynamic programming,” IEEE Trans. Aerosp. Electron. Syst. 29(1), 44–56 (1993).
[Crossref]

1986 (1)

Y Takeda, “Velocity profile measurement by ultrasound Doppler shift method,” International Journal of Heat and Fluid Flow 7(4), 313–318 (1986).
[Crossref]

1985 (1)

Y Barniv, “Dynamic Programming Solution for Detecting Dim Moving Targets,” IEEE Trans. Aerosp. Electron. Syst. AES-21(1), 144–156 (1985).
[Crossref]

Ai, S

Akter, M

U Sara, M Akter, and S Uddin M, “Image quality assessment through FSIM, SSIM, MSE and PSNR—a comparative study,” JCC 07(03), 8–18 (2019).
[Crossref]

Arnold, J

J Arnold, S Shaw, and H Pasternack, “Efficient target tracking using dynamic programming,” IEEE Trans. Aerosp. Electron. Syst. 29(1), 44–56 (1993).
[Crossref]

Aspden R, S

Aßmann, M

M Aßmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3(1), 1–5 (2013).
[Crossref]

Bache, M

A Gatti, E Brambilla, M Bache, and L A Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

Barniv, Y

Y Barniv, “Dynamic Programming Solution for Detecting Dim Moving Targets,” IEEE Trans. Aerosp. Electron. Syst. AES-21(1), 144–156 (1985).
[Crossref]

Bayer, M.

M Aßmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3(1), 1–5 (2013).
[Crossref]

Bennink R, S

S Bennink R, J Bentley S, and W Boyd R, ““Two-Photon” Coincidence Imaging with a Classical Source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref]

Bentley S, J

S Bennink R, J Bentley S, and W Boyd R, ““Two-Photon” Coincidence Imaging with a Classical Source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref]

Berardi, V

G Scarcelli, V Berardi, and Y Shih, “Can Two-Photon Correlation of Chaotic Light Be Considered as Correlation of Intensity Fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006).
[Crossref]

Bo, Z

E Li, Z Bo, M Chen, W Gong, and S Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
[Crossref]

Bovington J, T

Bowers J, E.

Bowman, R

Boyd R, W

Brambilla, E

A Gatti, E Brambilla, M Bache, and L A Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

Brand, M

Bromberg, Y

Y Bromberg, O Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

O Katz, Y Bromberg, and Y Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Buller G, S

Cai, Y

Chan, K

Chan K, W C

Chang Y, C

Chen, H

Chen, M

W. Gong, C. Zhao, H Yu, M Chen, W Xu, and S Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci Rep 6(1), 26133 (2016).
[Crossref]

X Li, C Deng, M Chen, W Gong, and S Han, “Ghost imaging for an axially moving target with an unknown constant speed,” Photonics Res. 3(4), 153–157 (2015).
[Crossref]

E Li, Z Bo, M Chen, W Gong, and S Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
[Crossref]

C Zhao, W Gong, M Chen, E Li, H Wang, W Xu, and S Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

Chen, N

M. Lyu, W. Wang, H Wang, H Wang, G Li, N Chen, and G Situ, “Deep-learning-based ghost imaging,” Sci Rep 7(1), 17865 (2017).
[Crossref]

Chen, X

Coldren L, A

Cole D, B

Coolbaugh, D

Cui, X

Dauler, E. A.

Dave U, D

Davenport M, L

Deng, C

C Deng, W Gong, and S Han, “Pulse-compression ghost imaging lidar via coherent detection,” Opt. Express 24(23), 25983–25994 (2016).
[Crossref]

X Li, C Deng, M Chen, W Gong, and S Han, “Ghost imaging for an axially moving target with an unknown constant speed,” Photonics Res. 3(4), 153–157 (2015).
[Crossref]

Dong, G

Y. He, G. Wang, G Dong, S Zhu, H Chen, A Zhang, and Z Xu, “Ghost Imaging Based on Deep Learning,” Sci Rep 8(1), 6469 (2018).
[Crossref]

Dostart, N

Doylend J, K

Edgar M, P

Farshid, A

Feldkhun, D

Feng, D

L Luo C, P Lei, L Li Z, J Quan Q, X Xin J, D Feng, and Z Min L, “Long-distance ghost imaging with an almost non-diffracting Lorentz source in atmospheric turbulence,” Laser Phys. Lett. 15(8), 085201 (2018).
[Crossref]

Firooz, A.

Fleddermann, R

Francis S, P

Gatti, A

A Gatti, E Brambilla, M Bache, and L A Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

Gemmell N, R

Gong, W

C Deng, W Gong, and S Han, “Pulse-compression ghost imaging lidar via coherent detection,” Opt. Express 24(23), 25983–25994 (2016).
[Crossref]

X Li, C Deng, M Chen, W Gong, and S Han, “Ghost imaging for an axially moving target with an unknown constant speed,” Photonics Res. 3(4), 153–157 (2015).
[Crossref]

E Li, Z Bo, M Chen, W Gong, and S Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
[Crossref]

C Zhao, W Gong, M Chen, E Li, H Wang, W Xu, and S Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

Gong, W.

W. Gong, C. Zhao, H Yu, M Chen, W Xu, and S Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci Rep 6(1), 26133 (2016).
[Crossref]

Gordillo O, A J

Gu J, H

Hadfield R, H

Han, S

C Deng, W Gong, and S Han, “Pulse-compression ghost imaging lidar via coherent detection,” Opt. Express 24(23), 25983–25994 (2016).
[Crossref]

W. Gong, C. Zhao, H Yu, M Chen, W Xu, and S Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci Rep 6(1), 26133 (2016).
[Crossref]

X Li, C Deng, M Chen, W Gong, and S Han, “Ghost imaging for an axially moving target with an unknown constant speed,” Photonics Res. 3(4), 153–157 (2015).
[Crossref]

E Li, Z Bo, M Chen, W Gong, and S Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
[Crossref]

C Zhao, W Gong, M Chen, E Li, H Wang, W Xu, and S Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

He, Y.

Y. He, G. Wang, G Dong, S Zhu, H Chen, A Zhang, and Z Xu, “Ghost Imaging Based on Deep Learning,” Sci Rep 8(1), 6469 (2018).
[Crossref]

He, Z,

Heck M, J R

Hong, J

Hosseini E, S

Hsieh, J

Hu, L

L Hu, X Jin, and G. Zeng, “Lensless ghost imaging for moving objects,” Opt. Eng. 50(12), 7005–7007 (2011).
[Crossref]

Hu H, K

Hulme J, C

Itoh, T.

T. Itoh, H. Sueda, and Y. Watanabe, “Motion compensation for ISAR via centroid tracking,” IEEE Trans. Aerosp. Electron. Syst. 32(3), 1191–1197 (1996).
[Crossref]

Ji, X

Jia, L

Jiang, L

Jin, M

Jin, X

L Hu, X Jin, and G. Zeng, “Lensless ghost imaging for moving objects,” Opt. Eng. 50(12), 7005–7007 (2011).
[Crossref]

Jonathan, P

Kang, G

G Kang, H Kim S, B You J, S Lee D, and H Park H, “Silicon-Based Optical Phased Array Using Electro-Optic p-i-n Phase Shifters,” IEEE Photonics Technol. Lett. 31(21), 1685–1688 (2019).
[Crossref]

Katz, O

O Katz, Y Bromberg, and Y Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Y Bromberg, O Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Kerman, A. J.

Khilo, A

Kim S, H

G Kang, H Kim S, B You J, S Lee D, and H Park H, “Silicon-Based Optical Phased Array Using Electro-Optic p-i-n Phase Shifters,” IEEE Photonics Technol. Lett. 31(21), 1685–1688 (2019).
[Crossref]

Kirkwood R, A

Klyshko D, N

V Strekalov D, V Sergienko A, N Klyshko D, and YH Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
[Crossref]

Kohno, Y

Komatsu, K

Leake, G

Lee D, S

G Kang, H Kim S, B You J, S Lee D, and H Park H, “Silicon-Based Optical Phased Array Using Electro-Optic p-i-n Phase Shifters,” IEEE Photonics Technol. Lett. 31(21), 1685–1688 (2019).
[Crossref]

Lei, P

L Luo C, P Lei, L Li Z, J Quan Q, X Xin J, D Feng, and Z Min L, “Long-distance ghost imaging with an almost non-diffracting Lorentz source in atmospheric turbulence,” Laser Phys. Lett. 15(8), 085201 (2018).
[Crossref]

Li, E

E Li, Z Bo, M Chen, W Gong, and S Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
[Crossref]

C Zhao, W Gong, M Chen, E Li, H Wang, W Xu, and S Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

Li, G

M. Lyu, W. Wang, H Wang, H Wang, G Li, N Chen, and G Situ, “Deep-learning-based ghost imaging,” Sci Rep 7(1), 17865 (2017).
[Crossref]

Li, Q

Li, R

Li, X

X Li, C Deng, M Chen, W Gong, and S Han, “Ghost imaging for an axially moving target with an unknown constant speed,” Photonics Res. 3(4), 153–157 (2015).
[Crossref]

Li, Y

F Wang P, Z Luo G, Y Xu, Y Li, Y Su, J Ma, R Wang, Z Yang, X Zhou, Y Zhang, and J Pan, “Design and fabrication of a SiN-Si dual-layer optical phased array chip,” Photonics Res. 8(6), 912–919 (2020).
[Crossref]

Li Z, L

L Luo C, P Lei, L Li Z, J Quan Q, X Xin J, D Feng, and Z Min L, “Long-distance ghost imaging with an almost non-diffracting Lorentz source in atmospheric turbulence,” Laser Phys. Lett. 15(8), 085201 (2018).
[Crossref]

Lin H, Z

Lipson, M

Liu W, T

Liu W, T.

Lugiato, L A

A Gatti, E Brambilla, M Bache, and L A Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref]

Luo C, L

L Luo C, P Lei, L Li Z, J Quan Q, X Xin J, D Feng, and Z Min L, “Long-distance ghost imaging with an almost non-diffracting Lorentz source in atmospheric turbulence,” Laser Phys. Lett. 15(8), 085201 (2018).
[Crossref]

Luo G, Z

F Wang P, Z Luo G, Y Xu, Y Li, Y Su, J Ma, R Wang, Z Yang, X Zhou, Y Zhang, and J Pan, “Design and fabrication of a SiN-Si dual-layer optical phased array chip,” Photonics Res. 8(6), 912–919 (2020).
[Crossref]

Lyu, M.

M. Lyu, W. Wang, H Wang, H Wang, G Li, N Chen, and G Situ, “Deep-learning-based ghost imaging,” Sci Rep 7(1), 17865 (2017).
[Crossref]

Ma, J

F Wang P, Z Luo G, Y Xu, Y Li, Y Su, J Ma, R Wang, Z Yang, X Zhou, Y Zhang, and J Pan, “Design and fabrication of a SiN-Si dual-layer optical phased array chip,” Photonics Res. 8(6), 912–919 (2020).
[Crossref]

McClelland D, E

Mertens, L

Miller S, A

Min L, Z

L Luo C, P Lei, L Li Z, J Quan Q, X Xin J, D Feng, and Z Min L, “Long-distance ghost imaging with an almost non-diffracting Lorentz source in atmospheric turbulence,” Laser Phys. Lett. 15(8), 085201 (2018).
[Crossref]

Mohanty, A

Molnar, R. J.

Morris P, A

Nakano, Y

O’Sullivan M, N

Onural, D

Ozeki, Y

Padgett M, J

Pan, J

F Wang P, Z Luo G, Y Xu, Y Li, Y Su, J Ma, R Wang, Z Yang, X Zhou, Y Zhang, and J Pan, “Design and fabrication of a SiN-Si dual-layer optical phased array chip,” Photonics Res. 8(6), 912–919 (2020).
[Crossref]

Pan, S.

Park H, H

G Kang, H Kim S, B You J, S Lee D, and H Park H, “Silicon-Based Optical Phased Array Using Electro-Optic p-i-n Phase Shifters,” IEEE Photonics Technol. Lett. 31(21), 1685–1688 (2019).
[Crossref]

Pasternack, H

J Arnold, S Shaw, and H Pasternack, “Efficient target tracking using dynamic programming,” IEEE Trans. Aerosp. Electron. Syst. 29(1), 44–56 (1993).
[Crossref]

Peters J, D

Phare C, T

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Popovic M, A

Qamar, S

G Wang L, S Qamar, Y Zhu S, and S Zubairy M, “Hanbury Brown–Twiss effect and thermal light ghost imaging: A unified approach,” Phys. Rev. A 79(3), 033835 (2009).
[Crossref]

Qiu, P

Quan Q, J

L Luo C, P Lei, L Li Z, J Quan Q, X Xin J, D Feng, and Z Min L, “Long-distance ghost imaging with an almost non-diffracting Lorentz source in atmospheric turbulence,” Laser Phys. Lett. 15(8), 085201 (2018).
[Crossref]

Qubaisi K, A

Roberts L, E

Roberts S, P

Rosenberg, D.

Ruggeri, A

Sara, U

U Sara, M Akter, and S Uddin M, “Image quality assessment through FSIM, SSIM, MSE and PSNR—a comparative study,” JCC 07(03), 8–18 (2019).
[Crossref]

Scarcelli, G

G Scarcelli, V Berardi, and Y Shih, “Can Two-Photon Correlation of Chaotic Light Be Considered as Correlation of Intensity Fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006).
[Crossref]

Sergienko, A. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
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W. Gong, C. Zhao, H Yu, M Chen, W Xu, and S Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci Rep 6(1), 26133 (2016).
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U Sara, M Akter, and S Uddin M, “Image quality assessment through FSIM, SSIM, MSE and PSNR—a comparative study,” JCC 07(03), 8–18 (2019).
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Laser Phys. Lett. (1)

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G Wang L, S Qamar, Y Zhu S, and S Zubairy M, “Hanbury Brown–Twiss effect and thermal light ghost imaging: A unified approach,” Phys. Rev. A 79(3), 033835 (2009).
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[Crossref]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
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Phys. Rev. Lett. (4)

V Strekalov D, V Sergienko A, N Klyshko D, and YH Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
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W. Gong, C. Zhao, H Yu, M Chen, W Xu, and S Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci Rep 6(1), 26133 (2016).
[Crossref]

M. Lyu, W. Wang, H Wang, H Wang, G Li, N Chen, and G Situ, “Deep-learning-based ghost imaging,” Sci Rep 7(1), 17865 (2017).
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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. OPA chip and performance measurement results. (a) Top-view photograph of 4 × 4 OPA chip. (b) Measured loss in fiber-to-chip edge coupler. (c) Optical microscopy image of 1 × 2 multimode interference splitter with measured insertion loss of 0.1 dB. (d) Optical microscopy image of optical antenna array with measured emission efficiency of 40%, The OPA antenna pitch is 8 microns in vertical direction, and 4 microns in horizontal direction. (e) Accumulated phase shift in thermo-optic phase shifters extracted from Mach–Zehnder interferometer transmission spectra. The optical variable phase shifter achieves a 2π phase shift by consuming 47 mW with the heater. (f) Optical response of rise and fall times of 16 and 41 μs, respectively.
Fig. 2.
Fig. 2. (a) From top left to bottom right: far-field patterns simulated and measurement after phase calibration, far-field pattern in cross-sections at θx = 0 and θy= 0 (FWHM, full width at half maximum). (b) Convergence of proposed SPGD control after approximately 100 iterations. The evaluation function used in Fig. 2(b) is the intensity ratio between selected optimized region and capture surface.
Fig. 3.
Fig. 3. Simulation and experimental results of conventional GI implemented with OPA. (a) Results for OPA-based GI simulation (i), general GI experimental results (ii), GI with external perturbation experimental results (iii), and GI with thermo-optic noise experimental results (iv). (b) PSNR values of images in panel (a).
Fig. 4.
Fig. 4. Feasibility verification of OPA-based GI. (a) Schematic diagram of signal light experiment and its results. (b) Schematic diagram of reference light experiment and its results.
Fig. 5.
Fig. 5. Target speed estimation. (a) Diagram of speed estimation algorithm, (b) schematic diagram of the experimental system, and (c) experimental results. The target shown in (b) is a 1mm diameter round reflection mirror.
Fig. 6.
Fig. 6. Dynamic target imaging system with scanning feedback. (a) Schematic diagram of experimental system, reference field, and signal light. (b) Diagram of proposed dynamic target imaging with scanning feedback. (c) Reconstructed images and their PSNR values based on GI according to iterations and target images obtained by OPA scanning imaging.

Equations (2)

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G ( 2 ) ( x , y ) = I R ( n ) ( x , y ) B ( n ) n ,
O μ ( x ( v x ) , y ( v y ) ) = ( B μ B μ ) ( I ( x ( v x ) , y ( v y ) ) I ( x ( v x ) , y ( v y ) ) ) ,

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