Vectorial Digitelligent Optics for High-Resolution Non-Line-of-Sight Imaging

Yinghui Guo; Yunsong Lei; Mingbo Pu; Fei Zhang; Qi Zhang; Xiaoyin Li; Runzhe Zhang; Zhibin Zhao; Rui Zhou; Yulong Fan; Xiangang Luo

doi:10.1016/j.eng.2024.11.013

Engineering ›› 2025, Vol. 45 ›› Issue (2) :76 -84. DOI: 10.1016/j.eng.2024.11.013

Research Subwavelength Optics—Article

research-article

Vectorial Digitelligent Optics for High-Resolution Non-Line-of-Sight Imaging

Yinghui Guo ^a^,^b^,^c^,^d^,^#
, Yunsong Lei ^a^,^b^,^c^,^d^,^#
, Mingbo Pu ^a^,^b^,^c^,^d^,^*
, Fei Zhang ^a^,^b^,^c^,^d
, Qi Zhang ^a^,^b^,^c
, Xiaoyin Li ^a^,^b^,^c
, Runzhe Zhang ^a^,^b^,^c^,^d
, Zhibin Zhao ^a^,^b^,^c^,^d
, Rui Zhou ^e
, Yulong Fan ^a^,^b
, Xiangang Luo ^a^,^b^,^d^,^*

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Abstract

Object imaging beyond the direct line of sight is significant for applications in robotic vision, remote sensing, autonomous driving, and many other areas. Reconstruction of a non-line-of-sight (NLOS) screen is a complex inverse problem that comes with ultrafast time-resolved imager requirements and substantial computational demands to extract information from the multi-bounce scattered light. Consequently, the echo signal always suffers from serious deterioration in both intensity and shape, leading to limited resolution and image contrast. Here, we propose a concept of vectorial digitelligent optics for high-resolution NLOS imaging to cancel the wall’s scattering and refocus the light onto hidden targets for enhanced echo. In this approach, the polarization and wavefront of the laser spot are intelligently optimized via a feedback algorithm to form a near-perfect focusing pattern through a random scattering wall. By raster scanning the focusing spot across the object’s surface within the optical-memory-effect range of the wall, we obtain nearly diffraction-limited NLOS imaging with an enhanced signal-to-noise ratio. Our experimental results demonstrate a resolution of 0.40 mm at a distance of 0.35 m, reaching the diffraction limit of the system. Furthermore, we demonstrate that the proposed method is feasible for various complex NLOS scenarios. Our methods may open an avenue for active imaging, communication, and laser wireless power transfer.

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Keywords

Non-line-of-sight imaging / Vectorial digitelligent optics / Spatial light modulator / Digital optics / Wavefront shaping / Metasurface

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Yinghui Guo, Yunsong Lei, Mingbo Pu, Fei Zhang, Qi Zhang, Xiaoyin Li, Runzhe Zhang, Zhibin Zhao, Rui Zhou, Yulong Fan, Xiangang Luo. Vectorial Digitelligent Optics for High-Resolution Non-Line-of-Sight Imaging. Engineering, 2025, 45(2): 76-84 DOI:10.1016/j.eng.2024.11.013

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1. Introduction

With rapid developments in detection technology and significant improvements in computational power, the use of intelligent algorithms and digital optical elements—such as digital micromirror devices (DMDs), spatial light modulators (SLMs), and metasurfaces—in computational imaging has become increasingly widespread [1], [2], [3]. These significant advances in digital optics, which feature binary micro/nano microstructures, local optical field manipulation, and complementary metal oxide semiconductor (CMOS)-compatible fabrication [4], [5], are pushing engineering optics into a new development stage, dubbed Engineering Optics 2.0 [6]. Among these advances is the rapidly emerging hot research topic of non-line-of-sight (NLOS) imaging [7], [8], [9], [10], a method that transmits the image information of a target to an observer indirectly via relay walls. Currently, NLOS imaging techniques fall into two main categories: The first type relies on the time of flight (TOF) of photons for the image reconstruction of the object [11], [12], [13], [14], while the second category employs a wavefront shaping technique to rectify the distortion induced by scattering from intermediate surfaces [15], [16], focusing on the object and enhancing the signal-to-noise ratio (SNR) of the echo signal for efficient imaging. For photon TOF-based NLOS imaging technology, attaining millimeter-level resolution requires the time resolution of the detector to be at the picosecond level, placing significant technical demands on the pulse laser and detector [17]. In comparison, wavefront-shaping-based NLOS imaging demands less from the experimental setup; it can achieve a diffraction-limited focus spot through wavefront shaping optimized by intelligent algorithms, initiating scanning imaging. The system resolution is determined by the size of the focused spot, and the imaging contrast ratio depends on the SNR of the echo signal.

In practical NLOS imaging applications, the echo signal undergoes multiple reflections off the target object and relay surfaces, which inherently scrambles its polarization state. Thus, multiple reflections ultimately lead to a “depolarized” speckles and a reduced SNR, which are extremely detrimental for diffraction-limited imaging and three-dimensional (3D) imaging [18]. Despite the remarkable achievements that have been made in refocusing techniques, traditional wavefront shaping techniques only optimize the phase modulation and ignore the influence of polarization [19]; thus, they cannot ensure optimal modulation, especially for inclined illumination in NLOS imaging.

In recent years, vector optical field (VOF)-shaping technology, which pre-compensates for phase distortions and optimizes the incident polarization, has made significant advancements in areas such as imaging through scattering media, communication, precision measurement, and laser manufacturing [20], [21], [22], [23], [24], [25], [26], [27], [28]. The integration of VOF shaping with metasurfaces, which are nanoscale structures capable of manipulating incident light waves in complex ways, is playing a significant role in the field of nonlinear optics, where metasurfaces are particularly important due to their exceptional ability to control the interaction between light and matter [29], [30]. The design flexibility of metasurfaces in terms of geometric shape and material composition enables them to effectively modulate the phase and polarization of nonlinear signals. This capability showcases the tremendous potential of metasurfaces in various areas such as tensorial phase control [31] and infrared upconversion imaging [32]. The integration of VOF shaping with digital and intelligent (digitelligent) metasurfaces demonstrates remarkable potential for VOF shaping and computational imaging, laying a solid foundation for the development of vectorial digitelligent optics (VDO) [33], [34], [35], [36], [37], [38]. However, designing a system that is both flexible and efficient in generating a VOF and integrating it successfully with an NLOS imaging system remains a considerable challenge, necessitating further research and technological advancement.

In this study, we propose a concept of VDO for high-resolution NLOS imaging. As illustrated in Fig. 1, the proposed system offers precise and flexible control over the light beam’s polarization state, phase, and amplitude in a digital manner. The achievable abundant VOF in VDO, summarized in the higher-order Poincaré sphere (HOPS), is the localized linear polarization at the HOPS equator. Thanks to its reconfigurable polarization and wavefront generated by intelligent feedback with a guide star, the system achieves diffraction-limited spatial resolution and a high SNR even under harsh conditions such as low light, turbulence distortion, and polarization-sensitive screens. The proposed approach not only offers new strategies for overcoming NLOS imaging challenges but also significantly broadens the application prospects of VOF shaping technology in optical imaging and detection, promoting the development of VDO.

2. Methods

An illustration of the VDO-empowered NLOS imaging system is shown in Fig. 1. Our goal is to use the digital optical elements to project an engineered vector wavefront that can counter the spatially varying polarization and phase shift induced by the relay wall. The system performs a global search using digital optical elements, such as an active metasurface or an SLM, in conjunction with deep learning algorithms. It controls the wavefront and polarization of the incident light to adjust the polarization states along the equatorial plane of the HOPS. Consequently, our system possesses two degrees of freedom in scanning: the angle of incidence of the light beam

θ_{1}

and the polarization angle

θ_{2}

. This can be explained by Fresnel’s equations under the assumption of incoming light with an angle of incidence

θ_{1}

and polarization angle

θ_{2}

, which can be expressed by the following formula:

(1)

I_{R} = I_{s} R_{s θ_{1}} + I_{p} R_{p θ_{1}} = I \sin θ_{2} R_{s θ_{1}} + I \cos θ_{2} R_{p θ_{1}}

where I_R represents the intensity of the reflected light, which can be decomposed into S-polarized and P-polarized light, with corresponding intensities I_s and I_p, respectively.

I

represents the intensity of the incident light, while

R_{s}

and

R_{p}

denote the reflection coefficients for the S-polarized wave and P-polarized wave, respectively. For a given object under testing, the angle of incidence

θ_{1}

is fixed. Consequently, a specific polarization angle

θ_{2}

exists at which the intensity of the reflected light is maximized. Therefore, by controlling the polarization angle

θ_{2}

through intelligent feedback, the intensity of the echo signal can be significantly enhanced, improving the overall SNR.

In the coherent polarization beam synthesis method, two orthogonal polarization states are exploited to generate a VOF [39], [40], [41], [42], [43], [44], [45]. By imparting independently controlled phases to two beams with orthogonal polarization states, such as one with left-handed circular polarization (LCP) and another with right-handed circular polarization (RCP), a VOF beam can be created. The mathematical expression for the generated VOF is as follows:

(2)

E_{o} = \frac{1}{\sqrt{2}} [\begin{matrix} 1 \\ - i \end{matrix}] e^{i ϕ_{L} (x, y)} + \frac{1}{\sqrt{2}} [\begin{matrix} 1 \\ i \end{matrix}] e^{i ϕ_{R} (x, y)} = \frac{2}{\sqrt{2}} [\begin{matrix} \cos \frac{ϕ_{L} (x, y) - ϕ_{R} (x, y)}{2} \\ \sin \frac{ϕ_{L} (x, y) - ϕ_{R} (x, y)}{2} \end{matrix}] e^{i \frac{ϕ_{L} (x, y) + ϕ_{R} (x, y)}{2}}

where E_o represents the VOF, i denotes the imaginary unit,

ϕ_{L} (x, y)

and

ϕ_{R} (x, y)

represent the phase profiles imparted by the left and right parts of the digital optical elements, respectively. This equation indicates that the tunable linear polarization state and the phase at each spatial point can be independently controlled to meet specific imaging requirements. A conceptual sketch of the experimental setup for generating the VOF is shown in Fig. 2(a), where an SLM is purposely divided into two parts to independently modulate two previously split beams. As required by the polarization-sensitive SLM, the polarization of the two incident beams is adjusted to align with the S-polarization direction. After passing through the SLM, the polarization of one beam is tuned to P-polarization by a half-wave plate (HWP). Subsequently, the two orthogonally polarized beams are transformed into LCP and RCP through a quarter-wave plate (QWP). After the combination, a VOF beam is successfully generated. An example is presented in Figs. 2(b) and (c), where the former represents a laser spot before impinging on the SLM with the phase profile shown in Fig. 2(c). The results shown in Figs. 2(d)–(f) preliminarily demonstrate the system’s effectiveness in generating a radial cylindrical vector light, showcasing its fundamental capability in VOF generation. Detailed experimental results and analyses are provided in Appendix A Section S1, while Section S2 in Appendix A provides a detailed description of the operational procedures for wavefront shaping and scanning.

3. Results

The experimental setup (Fig. 3) utilizes a 532 nm picosecond fiber laser as the light source (Yb-Doped Single-Pass SHG Fiber Laser 532 nm, Precilasers, China). Initially, a 4f system (where f is the focal length of lens; Fig. 3, lenses 1 and 2) is used to expand the laser beam to the required spot size, approximately 3 mm in diameter. We employ an SLM (SLM-210, Santec, Japan) as a digital optical element for experimental verification. An HWP aligns the beam’s polarization to P-polarization, matching the response of the SLM. Subsequently, a beam splitter divides the beam into two paths, which are directed by mirrors to the left and right regions of the SLM for phase modulations. Before combining, another HWP is used to change the polarization of one beam from P-polarization to S-polarization. The two beams are combined using a polarization beam splitter (PBS) and subsequently transformed into LCP and RCP through a QWP. Next, a second 4f system (Fig. 3, lenses 3 and 4) images the SLM-modulated beam onto a wall surface. The light, modulated by the SLM and reflected from the wall, illuminates the object. For simplicity in the experiment, a diffusive reflection mirror (DG10-1500-P01, Thorlabs, USA) substitutes for the wall. The light reflected from the object is captured by a single-photon avalanche diode (SPAD; FastGated-SPAD, MPD, Italy) using a lens (lens 5).

3.1. Single-object NLOS imaging

We utilized reflective tape stuck on cardboard as the object, which was surrounded by black diffusive tape to enhance the contrast ratio of the echo signal. The spot before and after VDO optimization are respectively shown in Figs. 4(a) and (b). The corresponding phase profile for wavefront shaping is shown in Fig. 4(c). Subsequently, a scan of the target object was conducted by adding a tilted phase to the pattern on the SLM. In this experiment, the object was placed 0.25 m from the wall. Meanwhile, an SPAD was positioned 0.1 m from the wall. It is important to note that an obstacle obstructed the direct line of sight between the object and the SPAD.

In this experiment, the focal spot size on the object possessed a full width at half maximum (FWHM) of 0.42 mm, which was acquired by replacing the object with a camera. This measurement closely aligns with the theoretical diffraction-limited spot size of approximately 0.36 mm in our setup, indicating that VDO can indeed provide close to diffraction-limited focusing. Figs. 4(d)–(f) show a schematic of the imaging objects. The results shown in Figs. 4(g)–(l) clearly indicate that our VDO technique can achieve near-perfect focusing. The imaging results shown in Figs. 4(j)–(l) exhibit a clear target profile. For assessing the imaging quality, the peak signal-to-noise ratio (PSNR) was used as an evaluation metric, as shown in Fig. 4(m). The results indicate that the scanning performance improved significantly after the VDO. Using the PSNR as a reference, the improvement was 7.9-fold for the parallelogram, 7.3-fold for the trapezoid, and 5.4-fold for the letter L; the average improvement was 6.9-fold, highlighting the potential of our technology for enhancing imaging accuracy.

3.2. Multi-object NLOS imaging

To further validate the imaging capabilities, an experimental demonstration involving multiple objects was conducted. Since our experimental setup utilized a pulsed laser and an SPAD, the 3D information of objects could be reconstructed based on the TOF. Since the refreshing frequency of the SLM was much lower than the response time of the SPAD, the echo signal from the SPAD at each position was recorded before each scanning refresh. During each refresh of the SLM, the SPAD received a marker signal. Using this marker signal, we were able to accurately extract the SPAD signal corresponding to each pixel and determine the TOF by analyzing the first-bounced and second-bounced photons, thereby obtaining the axial information. As shown in Figs. 5(a) and (b), two objects were placed at different locations and imaged in a front-and-back arrangement. The obtained imaging results are displayed in Fig. 5.

In this experiment, the axial distance between the two objects was approximately 2.5 cm. Using the TOF method, the actual axial distance was calculated to be 2.08 cm, indicating a relative error of about 16.8%. The system’s axial resolution is primarily limited by the overall timing jitter, with a time resolution of approximately 100 ps, as measured by the instrumental response function [46]. This corresponds to an error in the total photon flight distance of approximately 3 cm. By calculating the difference between these two total distances and dividing by two, we can determine the axial distance between the objects to be 1.5 cm. Fig. 5(c) displays the spatial position of the reconstructed object, with the color of each point representing its intensity. The central point exhibits a higher intensity, whereas the edge points have weaker intensities. This pattern aligns with the optical memory effect, where the light intensity varies with focus movement. Despite this variation, the overall reconstruction of the object’s information remains unaffected, allowing for accurate reconstruction of its spatial distribution, as illustrated in Fig. 5(d).

3.3. Polarization-selected NLOS imaging

In NLOS imaging technology, the polarization characteristics are crucial for target recognition. Utilizing the polarization information can significantly enhance the target contrast in complex scenes, improving the imaging quality. Particularly in urban or natural environments, where light undergoes multiple reflections, refractions, and scattering, leveraging the polarization characteristics makes it possible to effectively distinguish between direct and indirect reflections, enhancing imaging accuracy and reliability. Moreover, for targets with polarization selectivity, detecting with an appropriate polarization state can reduce the background noise and further enhance the visibility of the target signal [47], [48].

To verify the impact of the incident polarization state on the echo signal strength, a specific experiment was designed. In this experiment, upon obtaining a focused spot on the object, a phase difference was actively introduced in the left and right areas of the SLM according to Eq. (2). This method alters the incident polarization state without affecting the wavefront distribution. The experimental setup involved a low-power laser and large angle-of-incidence conditions, using a near-Lambertian surface as the test object. The projected light was isotropically scattered via the near-Lambertian surfaces, allowing the influence of the angle of the Lambertian scattering to be ignored. The relationship between the echo signal intensity and the incident polarization state was examined, and scanning imaging was conducted under conditions both before and after polarization selection. The Pearson correlation coefficient (PCC) was included as an evaluation criterion. The experimental results are illustrated in Fig. 6.

From Figs. 6(a) and (b), it is evident that selecting the polarization state of the incident light caused the number of photons in the echo signal to increase significantly, with an 11.38% improvement in the SNR. This enhancement is also evident in the scanning imaging results, as illustrated in Figs. 6(c) and (f). Prior to polarization selection, the scanned images exhibited significant information loss at the edges of the objects, as depicted in Figs. 6(d) and (g). Following polarization selection, the images demonstrated enhanced contrast and more accurately restored the details of the objects, as shown in Figs. 6(e) and (h). Moreover, the PSNR increased by 37.67% and 10.01% and the PCC by 30.12% and 9.87%, respectively, as shown in Fig. 6(i). Due to the method's polarization selectivity, we discuss its application of vectorial adaptive optics in Appendix A Section S3, and more experimental data is provided in Appendix A Section S4.

4. Discussion and conclusions

We have demonstrated an innovative NLOS imaging technique based on VDO. In our approach, light reflected off a rough surface is initially focused onto a point using wavefront shaping technology. Then, the polarization state of the incident light is actively modulated to maximize the detectable echo signal. Furthermore, by exploiting the optical memory effect, this focal point can be moved to scan and image objects within the NLOS area. In this method, the imaging resolution is determined by the size of the focused spot, which can be optimized to the diffraction limit. Moreover, the ability to actively control the incident polarization state allows for high SNR echo signals and high-quality object imaging, even under low laser power illumination conditions. Most importantly, as the echo signal contains TOF information, this technique also enables the 3D reconstruction of objects.

Although our current research has not yet achieved direct focusing of the light scattered by the wall onto the test object based on the echo signal while optimizing the polarization state of the incident light, the primary reason is the technical challenge of real-time signal reading from an SPAD. To address this issue, we are considering the future use of photomultiplier tubes as detectors and exploring the combined use of DMDs with SLMs [16]. Additionally, our current VOF is generated by an SLM. However, recent advances in metasurface-based VOF manipulation technology have shown significant progress, offering more streamlined and compact system designs [36], [49], [50]. This enhanced precision in VOF manipulation enables the feasibility of laser wireless power transmission. Furthermore, metasurfaces have demonstrated a stronger optical memory effect [51]. In the field of biomedical applications, the polarization control properties of meta-optics have significantly enhanced the performance of various biological imaging techniques [52]. Moreover, meta-processors utilizing meta-optics offer the advantages of low power consumption and high-speed processing for optical simulation image processing [53]. Through the combination of metasurface technology with recent NLOS imaging technologies, such as deep learning and end-to-end design [54], [55], [56], [57], further enhancement of imaging speed and quality is expected. Our future research may involve delving deeper into these technologies, with the aim of comprehensively addressing the challenges of NLOS imaging and achieving further breakthroughs in the field.

Acknowledgments

This research was supported by the National Key Research and Development Program of China (2023YFB2805800 and 2021YFA1401003) and the National Natural Science Foundation of China (62222513).

Compliance with ethics guidelines

Yinghui Guo, Yunsong Lei, Mingbo Pu, Fei Zhang, Qi Zhang, Xiaoyin Li, Runzhe Zhang, Zhibin Zhao, Rui Zhou, Yulong Fan, and Xiangang Luo declare that they have no conflict of interest or financial conflicts to disclose.

Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2024.11.013.

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