Over the past decade, researchers have worked on developing non-line-of-sight (NLOS) imaging technologies to overcome the limitations of traditional line-of-sight (LOS) cameras, offering great potential for applications in autonomous driving, robotic vision, and medical imaging^[1].

In active optical methods, imaging hidden scenes around obstacles relies on analyzing the time-of-flight (TOF) of light returned via different scattering paths on the relay surface to calculate the shape and reflectance of hidden objects. In 2012, Velten et al. demonstrated NLOS imaging using the filtered back projection (FBP) algorithm, with a femtosecond pulsed laser and a streak camera^[2]. In 2015, Buttafava et al. proposed a NLOS imaging system based on single-photon avalanche diodes (SPADs), which reduced the system’s cost^[3]. Many works of optical techniques for NLOS imaging emerged, such as transient imaging^[2–5], confocal imaging^[6,7], wave-propagation transformation^[8–11], and Fermat paths^[12].

Despite this remarkable progress in this field, NLOS imaging still requires thousands of scans, which is time-consuming and significantly affects the real-time performance. To address this issue, in 2017, Chan et al. obtained the position of hidden targets through a few scans by analyzing the probability density distribution of the hidden space^[13,14]. Caramazza et al. used a SPAD array and an artificial neural network (ANN) to locate hidden targets^[15]. In 2021, Ye et al. reduced the number of scans using compressed sensing and convex optimization methods^[16]. In the same year, Nam et al. proposed a method to improve the real-time performance with a small SPAD array and a fast-scanning galvanometer^[17]. In 2024, Li et al. proposed a rectangular-based 2D size detection method to reduce the number of scans and avoid extensive scanning^[18]. Additionally, researchers explored methods for detecting target signals with low signal-to-noise ratio (SNR) in NLOS detection^[19] to reduce the acquisition time per frame and improve real-time performance.

In general, the above research takes only one measurement per detecting period and the period depends on the repetition frequency of the system. In LiDAR imaging, researchers proposed solutions by multiplexing to improve the efficiency in each detection period, including frequency-division multiplexing^[20], a combined wavelength-division multiplexing and time-division multiplexing^[21], and time-multiplexing at the receiving end^[22]. In 2024, Zheng et al. tracked a NLOS target by employing a time-multiplexing method at the transmitting end, which reduced the number of scans^[23]. However, to date, this time-multiplexing method has not been further applied to NLOS imaging.

Herein, we propose a time-multiplexing NLOS imaging scheme and experimentally demonstrate the feasibility of this approach, which can reduce the scans on the relay surface by half. Specifically, at the transmitted end, we divide the emitted pulse laser into two beams and introduce extra delays in one beam by multi-reflections. Then, the two beams with different delays are recombined by passing through a beam splitter and sent to the relay surface via the galvanometer, achieving twice the measurements at each measurement for NLOS imaging. Ultimately, we conduct a proof-of-concept demonstration of this method, achieving NLOS reconstruction based on time-multiplexing and reducing the number of scans by half. This study provides a multiplexing strategy to enhance the efficiency of NLOS imaging.

The optical NLOS imaging setup, shown in Fig. 1(a), utilizes two beam splitters to generate two laser pulses in each one, detecting a period. First, we divide the emitted pulse laser (VisIR) with a 1531 nm peak wavelength, a 40 MHz repetition frequency, a 70 ps pulse width, and a 375 mW average power into two beams using a beam splitter (Thorlabs), as illustrated with the yellow and red arrows in the left part of Fig. 1(a). One beam directly enters the second beam splitter (Thorlabs), while the other beam goes through a convex lens, two mirrors, and a telescope, and finally enters into the second beam splitter, where the mirrors in the path are used to change direction and the convex lens, and the telescope are used to overcome the beam divergence. A beam dump is used to collect the photons at the other end of the beam splitter. Before the beams are sent to the galvanometer, the direct beam and the delayed beam are recombined by the second beam splitter with a tiny difference in angle. Then, the galvanometer sends the recombined beam to two different sampling positions and scans the relay surface sequentially.

At the receiving end, an imaging lens with a 50 mm focal length captures the returning photons at the sensing spots on the relay surface. These photons are filtered through a bandpass filter ($1530\mathrm{nm}\pm 2.4\mathrm{nm}$) before being directed to a superconducting nanowire single photon detector (SNSPD, Single Quantum), where the detection efficiency is between 70% and 80%, the time jitter is 77–79 ps, the deadtime is less than 30 ns, and the dark count rate is less than 300 Hz. The SNSPD is integrated with a time-correlated single-photon counting (TCSPC) module (qutools-quTAG) with a time jitter of less than 10 ps and a time resolution of 1 ps. The photograph of the setup is shown in Fig. 1(b). Due to the manufactured delay, during each period, the echoes arrive at different time ranges, thus increasing the utilization.

In the experimental scenario, as shown in Fig. 1(a), the prototype is placed approximately 2 m from the relay surface. We split the emitted laser beam and add a time delay of 10 ns by multi-time reflections, corresponding to a route of 3 m at the transmitting end. The galvanometer sent out the recombined beam to two sampling positions of a scanning area ($60\mathrm{cm}\times 60\mathrm{cm}$) on the relay surface, where the vertical difference is 1.5 cm between the two positions, and the horizontal difference is zero. The dimensions of the targets are as follows: number “5” ($28\mathrm{cm}\times 43\mathrm{cm}$), letter “T” ($34\mathrm{cm}\times 30\mathrm{cm}$), and letter “L” ($28\mathrm{cm}\times 34\mathrm{cm}$). To detect two scans during the period of 25 ns (depending on the laser repetition frequency), the hidden target should be placed less than 1 m from the relay surface, taking into account the width of the echo. The exposure time is 5 s for the reduction of the laser power, where the emitted beam passes through the beam splitter twice, and the practical laser power is $\sim 93.75\mathrm{mW}$. The number of galvanometer scans is $64\times 32=2048$, and the total number of sampling points is 4096 because the galvanometer can detect two sampling points at a time.

With the setup described above, we acquired 4096 sampling points on the relay surface by 2048 scans and obtained the counts histogram. The histogram contains the first bounces returned from laser points L1 and L2 and then the third bounces returned via laser points L1 and L2, as shown in Fig. 2(a), respectively. For each histogram, we subtract the pre-collected background from the histograms, as well as smooth them appropriately using a mean filter. Second, the histogram is clipped and divided into two parts. The first peaks are shifted to the origin of the coordination, regarded as the “start” time, as shown in Fig. 2(b). Ultimately, in Fig. 3, we reconstruct the three targets, the number “5”, the letter “T”, and the letter “L,” with half the number of scans through filtered back-projection (FBP) method^[2], demonstrating the feasibility of the time-multiplexing scheme for NLOS imaging. In the implementation, the filter is a $3\times 3\times 3$ Laplacian of Gaussian (LoG) filter^[24]. In Fig. 3, the quality of the reconstruction is limited by the output power and lower SNR. In the reconstructions, the FBP images suffer from the relatively low SNR of the echoes, which mainly contributes to two main factors. One is the echo intensity that varies with the distance between the laser point and detection point on the relay surface (non-confocal). The other reason is the reduction in laser energy (down to one-fourth of the original power) combined with additional losses in the optical path. During the FBP accumulation process, each voxel receives relatively small contributions from all pixels. Alternatively, the second beam splitter can be replaced by a perforated mirror to combine the two beams, which allows a higher intensity of the emitted laser. In addition, the FBP method is commonly used in non-confocal NLOS imaging. Alternatively, using normal moveout (NMO) and dip moveout (DMO) corrections, we can obtain a confocal approximation of the dataset, which allows us to further apply confocal-based NLOS imaging algorithms. In addition, using a pulse laser with a lower repetition rate, its longer period (i.e., the inverse of the repetition rate) allows for more times of time-multiplexing, thereby further reducing the number of required scans for NLOS imaging.

The single-pixel single-photon detector accumulates the flight times of returning photons to generate a histogram of photon arrival times, which represents the probability distribution of the target distance. Since this histogram is a one-dimensional signal, spatial information of the image must be obtained through a scanning process. A single-photon detector array can collect echoes simultaneously, but the detection efficiency of the array is lower than that of a single-pixel single-photon detector, and it is also more expensive. Thus, single-channel single-photon detectors or small array detectors are still the primary detection methods, which require point-by-point scanning to obtain spatial information from the relay surface, which is inherently time-consuming. Due to these limitations, imaging requires multiplexing techniques to reduce the number of scans. In the following sections, we will analyze the method of time-multiplexing for NLOS imaging.

In NLOS scenarios, the laser pulse first scatters at the relay surface and illuminates the hidden scene. Due to scattering, the laser intensity rapidly attenuates, which limits the effective detection range for each measurement. Usually, hidden objects can be detected up to 2–2.5 m behind the relay surface, corresponding to echo delays of approximately 13.3 to 16.7 ns for the first bounce and third bounce. The laser repetition frequencies typically used in NLOS imaging range from 100 kHz to 40 MHz, corresponding to time ranges of 25 ns to 10 ms. This implies that, especially when using lower repetition rate lasers, the effective detection distance occupies only a small portion of the total detection interval. Therefore, the remaining time ranges can be exploited to receive extra information. To fully utilize the remaining time range, the echoes should arrive at the unoccupied time range, which requires the echoes to have different flight times. As illustrated in Fig. 4(a), the emitted laser beam is split by a beam splitter, and the delay of one beam is added through multiple reflections, as proposed by the previous work^[23].

In this case, we simulate four pulses with distinct delays and send them to points L1 to L4 on the relay surface, as shown in Fig. 4(a). The pulses scatter at the relay surface and reach the objects in the hidden scene. Specifically, the pulse passing through point L1 reaches the hidden target first, with the shortest delay time. It scatters off the hidden object, returns to the relay surface, and finally enters the detector via the sensor point $s$. The pulses passing through L2, L3, and L4 follow in sequence. Based on the arrival times of the pulses, a simulated histogram can be recorded, as shown in Fig. 4(b). To avoid causing overlapping of the echoes, we need to ensure that the delay is sufficient, as in Eqs. (1) and (2). $$d_n=|o-l_n|+|l_n-p|+|p-s|+|s-d|+c\mathrm{\Delta }t,$$(1)$$d_{\text{delay}}>d_n,$$(2)where $d_n$ is the distance between the first bounce and the third bounce, which is relevant to the pointed laser position; $c$ is the speed of light; $\mathrm{\Delta }t$ is the width of the third echoes, which is relevant to the target size and detector jitter; and $d_{\text{delay}}$ is the required delay of the laser pulse at the transmitting end. The maximum number $N$ of time-multiplexing follows Eq. (3), $$N=c/(f_L·d_{\mathrm{delay}}).$$(3)

Further, this method can be applied to non-confocal NLOS imaging to increase real-time performance. For example, in Ref. [17], researchers used a pulsed laser with a wavelength of 532 nm and a repetition frequency of 5 MHz for the demonstration, corresponding to a period of 200 ns for each detection. The maximum distance between the hidden target and the relay surface is up to 3 m, which implies that the time interval from the first bounce to the third bounce is less than 25 ns. In this way, the period of 200 ns can be divided into 8 parts for multiplexing, thus significantly reducing the number of scans.

In the second simulation, we modeled a scenario to evaluate the performance with and without splitting the emitted laser beam. It is assumed that splitting the laser beam twice reduces its power to one-fourth of its initial value. The target is a resolution Siemens star pattern consisting of 18 petals, with an angle of 10 deg.

The target size is set to $0.25\mathrm{m}\times 0.25\mathrm{m}$, and the scanning area is $2.5\mathrm{m}\times 2.5\mathrm{m}$ on the relay surface. As shown in Fig. 5, it is observed that there is a trade-off that when the laser power is relatively low, splitting the beam into two paths weakens the reconstruction due to reduced intensity. When the laser power is sufficiently high, splitting it into two paths can indeed improve imaging quality due to the extra spatial information provided by the increased number of sampling points on the visible wall. In general, the method is suitable for sufficient laser power and should be avoided in low-power conditions.

Single-photon detector arrays are expensive and have lower detection efficiency compared to single-pixel single-photon detectors. As a result, the combination of single-pixel single-photon detectors with pulsed laser scanning has been widely adopted^[25]. However, current NLOS imaging still requires thousands of scans, which are extremely time-consuming and significantly impact imaging real-time performance, becoming a major limitation for the application of NLOS imaging. Multiplexing is an effective method for improving the efficiency of a single measurement. Even if single-photon detector arrays become widely used in the future, multiplexing techniques will continue to play an important role.

In this work, we address the issue of the large number of scans required by the galvanometer by proposing an NLOS imaging scheme based on time-multiplexing. This approach significantly reduces the number of scans on the relay surface. Specifically, we introduce a delay at the transmitting end and send the two laser pulses with different delays to two positions on the relay surface within each period. A single-pixel single-photon detector receives the returned pulses with different delay times and decouples these echoes based on the added delay to construct a complete transient measurement, thereby enabling the simultaneous acquisition of multiple sampling points on the relay surface. We conducted proof-of-concept experiments to demonstrate the provided method for time-multiplexing NLOS imaging, which reduced the number of scans by half. Additionally, images of the hidden objects were successfully reconstructed, validating the feasibility of this approach. This study presents a time-multiplexing-based NLOS imaging scheme, which significantly reduces the number of scans on the relay surface and shows considerable potential. It is anticipated that this approach could be applied to real-time NLOS imaging systems in the future.

Furthermore, our future direction will focus on several aspects, including introducing delays at the transmitting end through external excitation, reducing the laser repetition frequency while further increasing the multiplexing times, and integrating small single-photon detector arrays to further enhance imaging efficiency.