Ghost imaging (GI) exploits the second-order correlation of two photons to reconstruct an image [1,2], which is different from the conventional imaging methods that are based on the first-order interference and typically use lenses to construct images. Its imaging architecture possesses several advantages such as less sensitivity to optical turbulence [3,4], high detection sensitivity [5,6], lensless imaging capability [7], non-invasive imaging through strong scattering media [8], and being able to easily adapt to various scenarios [9–11]. During the past two decades, there is a growing body of research studies on GI, invoking a lot of potential applications in various fields ranging from optical imaging [12–15], X-ray imaging [16–18], atomic sensing [19,20], biological diagnostics [21], and feature extraction without image reconstruction [22,23] to physical encryption [24–26].

Recent research studies showed that GI has the ability of imaging under weak illumination [6,18], which suggested that GI has a great capability in high-speed imaging [6,27]. However, the traditional GI methods rely on the precise information of the illumination patterns on objects, which has become an obstacle to the realization of high-speed GI. It is because high technology is required for fabricating an illumination source to produce a sequence of preset or predictable patterns at a very high modulation rate. Meanwhile, the high speed raises the difficulty in synchronizing a sent-out pattern with its corresponding bucket detection. Although a GI technique with more than 1 MHz frame rate has been proposed, its resolution is limited [6], narrowing the scope in applications.

OPAs have been considered a promising technology for light detection and ranging (LiDAR) [28–31], where OPAs act as high-speed beam-steering components. OPAs are also key components for high-speed ghost imaging, since an OPA exploits the interference of a few antennas to generate complicated speckle patterns without sacrificing the modulation speed. Recently, OPA-based GI has been proposed [32]. Since 2017, on-chip OPAs has been used to experimentally implement ghost imaging [33–36]. OPA-based GI does not exploit beam steering. Instead, an OPA generates random speckle patterns in the far field. Compared with the beam-steering-based OPA method, OPA-based GI has several advantages: 1) the requirement of precise phase control is highly mitigated; 2) it does not limit the separation of the adjacent antennas, allowing high-power applications with large antennas’ separation; and 3) it does not need a repetitive phase-lock cycle via a specific algorithm throughout the measurement [37]. Instead, OPA-based GI only needs a simple calibration to record speckle patterns right before the measurement [34]. However, the calibration is indispensable since GI requires knowing the speckle patterns on an object, raising a challenge for a realistic application of OPA-based GI. First, due to phase drifts caused by thermal and acoustic noises, the calibration needs to be periodically performed to mitigate the dephasing. The calibration time is proportional to the pixel number of the imaging. Second, along with the increasing antennas’ separation, which is required for high power and high resolution, the phase drifts will become much more severe and the dephasing occurs much more frequently. How to predict or measure and compensate the phase drifts is one of the keys for OPA-based GI. Another way is to remove the requirement of knowing speckle patterns for GI.

Recently, Wang and Zheng proposed a scheme called naked-eye ghost imaging (NEGI) [38,39], which implements the correlation via an optical process in place of the traditional electronic process. During the whole process, the system neither needs to measure or predict the illumination patterns on the object nor requires the synchronization between the illumination patterns and their corresponding bucket detections. The optical correlation can directly display the image on human eyes or a camera. This paves a way to high-speed imaging for OPA-based GI. We built an optical phased array of 30 antennas, each of which is a waveguide-type electro-optic phase modulator (EOPM). The phases of the antennas were randomly modulated at a 5 MHz rate. The interference of the fields emitted from the EOPMs constructed random-like patterns on the object plane at the same rate. Since the thermal effect or vibration will cause an unpredictable phase drift on an EOM, the phases of the antennas are unpredictable, resulting in undeterminable illumination patterns. However, the proposed ghost-imaging system is able to directly display images at a frame rate of 1 kHz with the help of NEGI.

The experimental setup is sketched in Figure 1. The laser is a 100 mW continuous wave fiber laser, whose wavelength is 1,064 nm with a line width of 100 kHz. The OPA consists of a light splitter (LS), 30 EOPMs, a controller, and a light combiner (LC). LS is a fiber splitter that splits the input laser beam into 30 sub-beams each of which is input into an EOPM. The intensity difference among the sub-beams is less than 2 dB. The input and output of each EOPM are single-mode fibers at 1,064 nm. The half-wave voltage of each EOPM is ∼ 2.4 V . Its maximum response bandwidth is more than 300 MHz. The voltage added on each EOPM is individually manipulated by the controller, which consists of a field-programmable gate array (FPGA) and 30 digital-to-analog converters (DACs). The controller can load a set of preset voltages onto the EOPMs which append corresponding phases to the 30 passing light fields. This process can run at a speed as high as 100 MHz. The other ends (fiber tips) of the EOPMs are randomly stacked in a 4 mm × 4 mm plane, constructing the OPA’s antenna array. Figure 2 shows the arrangement of the fiber tips (the antennas). The light fields emitting out from the fiber tips interfere together and construct a speckle-like pattern on the object plane, as shown in Figure 1.

Before the experiment, we generated 5000 sets of random numbers. Each set contains 30 random integer numbers ranging in [0, 15]. All these numbers were stored in the FPGA in advance. In the experiment, the controller took one set of random numbers (denoted as {d _j }), each of which was sent to its corresponding DAC. The jth DAC generates a voltage of {d _j *0.2V} to drive the jth EOPM, making the passing light field acquire a random phase. Such an operation was repeated every 200 ns. The interference of the light fields from the antennas constructed a time-varying random pattern at the rate of 5 MHz. The fields were incident onto an artifact removal system (which will be described in the following sections) and propagated toward the scene. Eventually, an object was illuminated by a random speckle pattern that changed every 200 ns.

The light reflected back from the object was received by a bucket detector, which was made of a high-speed avalanche photodiode detector (APD) and has a bandwidth of ∼ 150 MHz. The signal from the bucket detector was amplified using an amplifier. Figure 3 shows how the amplified bucket signal changed when the controller refreshed the speckle pattern. Each green pulse indicates when the controller refreshed the applied voltages on the EOPMs. The clock of the FPGA was 50 MHz, namely, that it finished the refreshing within 20 ns. The bucket signal correspondingly rushed to a new level within this time, as we can see the rising or falling curves within the green pulses in Figure 3. The amplified bucket signal was then used to drive an electro-optic amplitude modulator (AM), which linearly changed the input light intensity into the OPA. Therefore, each illumination pattern on the object has a total power proportional to the bucket detection called an “adaptive-power pattern.”A beam splitter (BS) is used to take a copy of those adaptive-power patterns and project them onto a camera (OSG030-815UM), which can run at a frame rate of 815@640*480, 1000@560*400, or 2000@280*200. The exposure time of the camera was set to 1 ms, during which the camera superposed 5000 adaptive-power patterns, directly yielding an image of the object. This process is equivalent to making a correlation between the illumination patterns and the bucket detections (see the following section for theoretical analysis). While the object (four numbers of “2 3 4 5” on a plate) was sliding by a screen, the camera captured a sequence of frames and stored each frame as a file. We picked frames every 10 ms and built a video at 100 fps (see the Supplementary Material S1). Figure 4 exhibits five of the frames. On the first row are the original captured images, while on the second row, there are the images after cutting off their backgrounds.

Since the number of antennas is only 30, it is insufficient to sample the spatial frequencies of the object, causing repetitive visual artifacts in the reconstructed image [40,41]. To eliminate those artifacts, we employed a rotating ground glass to scramble the artifacts by focusing the emitted fields on GG with Len1 which was then collimated toward the scene with Len2. This caused the pattern of the artifact changing at a rate more than 40,000 Hz (the revolutions per minute of the GG was 40, and the focus spot was 45 mm off the axis). Therefore, within the exposure time of the camera, more than 40 different artifact patterns were averaged. The artifact was flattened out in a certain extend. Then, the image could be directly observed on the camera. On the other hand, the average of the artifact patterns causes a higher noisy background, as shown in the first row of Figure 4. By simply cutting out a certain background of each image, the contrast of the image is increased, as shown in the second row of Figures 4D–F. However, this process does not effectively flat out the artifact. They might be sufficiently eliminated using a neural network [41] or the “CLEAN” algorithm [40].

One drawback of GI is the trade-off between the resolution (the number of pixels) and the contrast. When an object occupies more pixels (a pixel size is an average size of a speckle), the signal-to-background ratio proportionally decreases, reducing the image contrast. In this system, the background is uneven. When the background rises up, the artifacts will become much obvious in the image, bringing much more difficulty in cutting the background without dramatically losing the information of the image. We therefore used a pinhole of 300 μm as an object to test the system. We used a CCD of Stingray F125BC and set a resolution of 1,024 × 768. It is important to note that the focus spot on GG was ∼ 1.5 m m , and the distance between GG and Len2 was ∼ 300 m m . Thus, a resolution cell of the speckle pattern has a size of λ*300mm/1.5 mm ≈ 200 μm. We manually moved the pinhole up and down with various moving speeds, while the CCD captured a video. For such a simple object, the background can be removed relatively thoroughly, and clean images were obtained as shown in Figure 5. The full video is given in Supplementary Material S2 “Pinhole.mp4.”

We demonstrated a high-speed ghost imaging with an optical phased array. The OPA generated time-varying speckle patterns at 5 MHz. We did not measure or predict the patterns. Based on the scheme of naked-eye ghost imaging, the image of a moving object is directly displayed on a CCD camera with the optical computation of the correlation simply with a beam splitter copying the light patterns on the object plane to the CCD plane. The image of the object is constructed on the CCD every ∼ 1 m s .

Wave-guide electro-optic modulators are not stable. When the field transmits through an EOPM, there is an additional phase drift appended to the field. This phase fluctuates at a rate around 0.1s ∼ 1s depending on the temperature fluctuation and vibration of the environment. If the environment is noisier, the phase fluctuates more quickly. Since the phase drift is unknown, it is hard to determine the interference pattern of the fields from the EOPMs. Typically, an OPA is designed for high-speed beam steering. In addition to trying to obtain the real-time steering angle, people have also been seeking a way to manipulate the beam shape in order to maintain a narrow main lobe but remove the side lobes. However, these are still the major problems due to the current state of the art. Although we used an OPA as a light source, we did not use it in a normal way. In this work, we used the OPA in an opposite way: we neither tried to manipulate the beam of the OPA nor did we measure or predict the beam shape; instead, the OPA randomly generated speckle patterns. Since ghost imaging can reconstruct images without knowing the illumination patterns with the help of optical computation of the correlation, the OPA brought us a high-speed ghost-image method. Here, we made use of the high-speed modulation feature of the OPA and its unpredictable phase change with time. In the experiment, we intentionally increased the environment noise by adding vibration in order to make the phase change more random. This method might be a candidate way of using OPAs.

On the other hand, this method uses a CCD to record a dynamic image. Although the frame rate of the system is merely determined by the CCD, the exposure time of a frame can be much shorter than the time interval of two adjacent frames, which, for example, can be less than 1 m. A short exposure time is suitable for a high-speed motion scenario. Second, GI has an advantage in imaging under low illumination [6,18], which is suitable not only for a biomedical scenario that requires weak light exposure but also for a long-distance imaging scenario. In contrast, the traditional imaging method (a CCD and lenses) hardly reaches such scenarios.

The experimental results still contain apparent artifacts. We have provided an analytical analysis and numerical simulations to investigate the causes. In addition to using a low-speed rotating ground glass to average the artifacts to a certain extent, for a better result, a suitable algorithm such as the SDDAN network [41] or the modified “CLEAN” algorithm [40] may be needed to give a clear image. Another way is increasing the number of antennas. Since this way raises the cost and highly adds to the manufacturing complexity, looking for an optimal number of antennas is the next key research objective. A comprehensive study needs to be carried out in the future on investigating the relationship between the number of antennas and the signal-to-noise ratio of images.