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ABSTRACT Compressed ultrafast photography (CUP), a computational imaging technique, is synchronized with short-pulsed laser illumination to enable dynamic three-dimensional (3D) imaging. By

leveraging the time-of-flight (ToF) information of pulsed light backscattered by the object, ToF-CUP can reconstruct a volumetric image from a single camera snapshot. In addition, the

approach unites the encryption of depth data with the compressed acquisition of 3D data in a single snapshot measurement, thereby allowing efficient and secure data storage and transmission.

We demonstrated high-speed 3D videography of moving objects at up to 75 volumes per second. The ToF-CUP camera was applied to track the 3D position of a live comet goldfish. We have also

imaged a moving object obscured by a scattering medium. SIMILAR CONTENT BEING VIEWED BY OTHERS SINGLE-SHOT STEREO-POLARIMETRIC COMPRESSED ULTRAFAST PHOTOGRAPHY FOR LIGHT-SPEED OBSERVATION OF

HIGH-DIMENSIONAL OPTICAL TRANSIENTS WITH PICOSECOND RESOLUTION Article Open access 16 October 2020 SINGLE-SHOT ULTRAFAST TERAHERTZ PHOTOGRAPHY Article Open access 27 March 2023 SINGLE-PIXEL

IMAGING OF DYNAMIC OBJECTS USING MULTI-FRAME MOTION ESTIMATION Article Open access 08 April 2021 INTRODUCTION Three-dimensional (3D) imaging technologies have been extensively studied for

many years, going back to the “mirror stereoscope” invented by Sir Charles Wheatstone in 18381. Since then, 3D imaging techniques have been used in many applications, including remote

sensing, biology and entertainment2,3,4. In the past decade, they have also been widely employed in the safety and national security communities5, in applications such as biometrics6,7,

under-vehicle inspection8,9 and battlefield evaluation10,11. These applications impose demanding requirements—the 3D images must be captured and transmitted to users in a secure and fast

manner. The scattered photons from the object carry a variety of tags, such as emittance angle and time-of-flight (ToF), which convey the 3D surface information. Using these photon tags,

numerous 3D imaging techniques have been developed, including structured-illumination12,13, holography14, streak imaging15,16, integral imaging17, multiple camera or multiple single-pixel

detector photogrammetry18,19 and ToF detection20. Among these techniques, holography has demonstrated secure 3D surface imaging. Holography-based encryption is optically performed by using

the diffraction pattern of a pseudo-random phase or amplitude mask14. This mask acts as the decryption key in reconstructing images of the 3D object from different viewing angles. However,

as an interference-based approach, holographic imaging system is sensitive to motion during the relatively long exposure, which can severely degrade image quality. ToF detection is another

commonly used approach for 3D imaging. By measuring the ToF of a light signal between the object and the detector, the depth of the 3D object can be quantified. Among developed ToF detectors

are the Microsoft KinectTM sensor21 for Xbox One and the single photon avalanche diode detector22. Although having largely improved the detection sensitivity, these ToF detectors acquire 3D

images through multiple measurements, which limits applications for imaging fast-moving 3D objects. To mitigate motion distortion in 3D images, single-shot ToF detection is an attractive

approach. Among developed techniques21,22,23,24,25,26,27, the 3D Flash LIDAR camera26 has gained the most attention. This device can collect the entire spatiotemporal datacube within a

single camera exposure, with an imaging speed up to 30 Hz26. However, the best achievable depth resolution is limited to ~10 cm27. In addition, the 3D images are first recorded on the

sensor, followed by data compression and encryption for transmission28. Therefore, the sensor itself suffers from a heavy data load. In addition, the separate recording, compressing and

encrypting processes create a security loophole in the system. To overcome these limitations, we present single-shot encrypted 3D imaging using compressed ultrafast photography (CUP). As a

novel ultrafast imaging technique, CUP captures transient events with picosecond temporal resolution in a single snapshot29. Herein, we integrated CUP with active illumination and

constructed a new ToF-CUP camera for snapshot volumetric imaging. Compared with previous techniques30,31,32,33, our system has three major advantages. First, the united process incorporating

the encryption of depth data with the compressed acquisition of 3D data protects the security of private content. Second, each volumetric image is stored as a 2D snapshot in the

measurement, which significantly reduces the data acquisition load on the sensor and therefore allows faster data communication to users. Third, the ToF-CUP camera can capture 3D images with

a rate up to 75 volumes per second with a 1-cm depth resolution, outperforming the state-of-the-art single-shot 3D cameras. In the following, we will describe the principle of our approach,

present the system prototype and demonstrate encrypted 3D videography by imaging various moving 3D objects. OPERATION PRINCIPLE The principle of CUP has been detailed in our recent

publication29. Here, we provide CUP with active illumination to detect photons backscattered from a 3D object. For collocated illumination and detection, the round-trip ToF signal carries

information about the depth, _z_, relative to the point of light incidence on the object’s surface, which can be recovered by where is the ToF of received photons and _c_ is the speed of

light. The factor of two in the denominator on the right side of Eq. 1 accounts for the round-trip flight of photons. A collimated laser beam illuminates the 3D object having intensity

reflectivity _R_(_x_, _y_, _z_). The backscattered light signal from this 3D object, , enters the ToF-CUP system. The depth information of the 3D object is conveyed as the ToF of the

backscattered light signal. Mathematically, this process can be described by where _P_ is a linear operator for light illumination and backscattering. Considering that the scattering is a

linear process, is linearly proportional to _R_(_x_, _y_, _z_). Our system then images this 3D object in three steps. First, the collected photons are spatially encrypted with a

pseudo-random binary pattern, in which each pixel is set to either on or off. This pattern also acts as the decryption key to unlock and retrieve the image of the 3D object. Second, a streak

camera temporally shears the ToF signal along the vertical direction. Third, the encrypted and sheared image is recorded on a CCD sensor in the streak camera via pixel-wise spatiotemporal

integration. The optical energy measured at pixel on the CCD, , is related to the original 3D light intensity reflectivity, _R_(_x_, _y_, _z_), by Here, _T_, _S_ and _C_ are linear operators

that represent spatiotemporal integration, temporal shearing and spatial encryption, respectively. Equation 3 shows that the encryption process is inherently embedded in ToF-CUP. Image

decryption can be computationally performed by users who are granted the decryption key. If the 3D object is spatiotemporally sparse, can be reasonably estimated by solving the inverse

problem of Eq. 3 using compressed-sensing algorithms34,35,36,37,38,39. In our study, we choose the two-step iterative shrinkage/thresholding (TwIST) algorithm34, which minimizes a convex

objective function given by Here, denotes the total-variation (TV) regularizer that encourages sparsity in the gradient domain during reconstruction40. The TwIST algorithm is initialized

with a pseudo-random matrix of the discretized form of _P__R_ and then converged to a solution by minimizing the objective function in Eq. 4. The regularization parameter λ, which controls

the weight of the TV regularizer, is adjusted empirically to provide the best for a given physical reality. Finally, can be recovered given the linear relation between the backscattered

light signal and the intensity reflectivity of the object. Further, in continuous shooting mode, the evolution of the 3D images over the “slow time”, , , can be recovered by decrypting

sequential snapshots. Here, the “slow time”, _t__s_, relative to , is defined as the time of capture of the imaged volume. SYSTEM CONFIGURATION The system schematic is shown in Fig. 1. A

solid-state pulsed laser (532 nm wavelength, 7 ps pulse duration) is the light source. The laser beam passes through an engineered diffuser (ED) and illuminates a 3D object. The object is

first imaged by a camera zoom lens (focal length 18–55 mm). Following the intermediate image plane, a beam splitter reflects half of the light to an external CCD camera (CCD 1 in Fig. 1),

hereinafter called the reference camera, which records a reference 2D image of the 3D object. The other half of the light is transmitted through the beam splitter and passed to a digital

micromirror device (DMD) by a 4-_f_ imaging system consisting of a tube lens and a microscope objective (focal length 45 mm, numerical aperture 0.16). The total demagnification of the

imaging system from the object to the DMD is ~46 ×. To encrypt the input image, a pseudo-random binary pattern is generated by the host as the key and displayed on the DMD. Each encoded

pixel in the binary pattern contains 3 × 3 DMD pixels (21.6 μm × 21.6 μm). The encrypted image is retro-reflected through the same 4-_f_ system, reflected by the beam splitter and imaged

onto the fully opened entrance slit (~5 mm wide) of a streak camera. Deflected by a time-varying sweeping voltage, , the light signal lands at various spatial locations on the _y’_ axis

according to its ToF. This temporally sheared image is recorded by an internal CCD sensor (CCD 2 in Fig. 1) in a single snapshot. This CCD sensor has 672 × 512 binned pixels (2 × 2 binning)

and each encoded pixel is imaged by 3 × 3 binned CCD pixels. Finally, the encrypted data is transmitted to the user who decrypts the image with the key provided by the host. The external CCD

camera (CCD 1 in Fig. 1) is synchronized with the streak camera for each snapshot. An USAF resolution target is used to co-register images acquired by these two devices. Used as an

intensity mask, the reference image is overlaid with the reconstructed 3D image to enhance the image quality. For each snapshot, the reconstructed 3D datacube contains _N__x_ × _N__y_ 

×_N__z_ = 150 × 150 × 350 voxels along the _x, y,_ and _z_ axes, respectively. In the _x-y_ plane, this size gives a maximum imaging field-of-view (FOV) of . Given the collocated

illumination and detection, the depth, , can be calculated by where _n__z_ is the pixel index along the _z_ axis, _d_ is the CCD’s binned pixel size along the _y’_ axis and _v_ is the

shearing velocity of the streak camera. In our experiments, , and _v_ is set to 0.66 mm/ns. Therefore, the maximum depth range is . RESULTS To quantify the system’s depth resolution, we

imaged a 3D target with fins of varying heights (Fig. 2a). This target (100 mm × 50 mm along the _x_ and _y_ axes) was fabricated in-house using a 3D printer (Form 1+, Formlabs). Along the

_x_ axis, each fin has a width of 5 mm and the height of the fins ascends from 2.5 mm to 25 mm, in steps of 2.5 mm. The imaging system was placed perpendicular to the target and collected

the backscattered photons from the surface. Image reconstruction retrieved the ToF 2D images (Fig. 2b) and the corresponding movie of the ToF snapshots of the _x-y_ light distributions is in

Supplementary Video 1, which reveals the arrival sequence of photons backscattered by these fins. Three representative temporal frames at  = 120, 200 and 280 ps are shown in Fig. 2c. In

each frame, five fins are observed, indicating that the system’s depth resolution is approximately 10 mm. To demonstrate ToF-CUP’s 3D imaging capability, we first imaged static objects (Fig.

3). Specifically, two letters, “W” and “U”, were placed with a depth separation of 40 mm (Supplementary Fig. 1a). The streak camera acquired a spatially-encrypted, temporally-sheared image

of this 3D target in a single snapshot. The reference camera also directly imaged the same 3D target without temporal shearing to acquire a reference (Supplementary Fig. 1b). Using Eq. 5,

the ToF signal was converted into depth information and ToF-CUP reconstructed 3D _x, y, z_ image of the target. For each pixel in the _x-y_ plane, we found the maximum intensity in the _z_

axis and recorded that coordinate to build a depth map. We color-encoded this depth map and overlaid it with the reference image to produce a depth-encoded image (Fig. 3a). For this object,

the depth distance between the two letters was measured to be ~40 mm, which agreed with the true value. In addition, we imaged two additional static objects, a wooden mannequin and a human

hand (Supplementary Fig. 1c,d). In both cases, we could successfully retrieve the depth information of the object using ToF-CUP (Fig. 3b,c). It is worth noting that the lateral resolution of

the reconstructed datacube is ~0.1 line pairs per mm and the reference images taken by the external CCD camera have a higher lateral resolution (~0.8 line pairs per mm). Because the

depth-encoded image is produced by overlaying the depth map with the reference image, it has a lateral resolution limited by the reconstructed datacube. To verify the system’s encryption

capability, we compared the image quality of the 3D datacubes reconstructed under two types of decryption attacks. The static 3D object “WU” was used in these tests. First, we imitated a

brute force attack28, which attempted to guess the decryption key without any prior information. 50 pseudo-random binary masks were generated as invalid decryption keys. For each invalid

key, we calculated its percentage of resemblance to the correct key. After the reconstruction, the cross correlations41 between the 3D datacubes based on these invalid keys and the one based

on the correct key were calculated to quantify the reconstructed image quality (Fig. 4a). Without the valid decryption key, the reconstructed image quality is largely degraded, as reflected

in the decreased correlation coefficients. For direct comparison, we show the reconstructed 3D datacube of the “WU” target produced by the valid and invalid keys (Fig. 4b,c). With the

correct decryption key, the reconstructed image well resembles the object. The invalid decryption key, on the contrary, yields no useful information. In each attack, the reconstruction using

the invalid key failed to retrieve the depth information, which demonstrated that our system is resistant to brute force attacks. In addition, we tested the system’s performance when part

of encryption key was known, but its position with respect to the encrypted image was unknown. To imitate this situation, a subarea (40 × 40 encoded pixels in the _x_ and _y_ axes) was

selected from the full encryption key (50 × 50 encoded pixels in the _x_ and _y_ axes) as the decryption key (Fig. 4d inset). This decryption key was horizontally shifted by various numbers

of the encoded pixels. For each shift, the reconstructed 3D datacube was compared with the correct reconstruction result to calculate the cross-correlation coefficient (Fig. 4d). The

comparison shows that the reconstruction quality is sensitive to the relative position between the decryption key and the encrypted data (Fig. 4e), demonstrating that our system can protect

the information in the 3D datacube even when part of the encryption key is leaked. We note that reconstructed datacubes from invalid decryption keys contain randomly distributed artifacts,

some of which may have high intensity. These artifacts could affect the cross-correlation calculation. However, as shown in Fig. 4c,e, even with seemingly high cross-correlation

coefficients, the reconstruction using invalid encryption keys does not resemble the original 3D object. To demonstrate ToF-CUP’s dynamic 3D imaging capability, we imaged a rotating object

in real time (Fig. 5a). In the experiment, a foam ball with a diameter of 50.8 mm was rotated by a motorized stage at ~150 revolutions per minute. Two “mountains” and a “crater” were added

as features on this object. Another foam ball, 25.4 mm in diameter, was placed 63.5 mm from the larger foam ball and rotated concentrically at the same angular speed. The ToF-CUP camera

captured the rotation of this two-ball system by sequentially acquiring images at 75 volumes per second. Once each image was reconstructed to a 3D _x, y, z_ datacube, these datacubes formed

a time-lapse 4D _x, y, z, t__s_ datacube. Figure 5b shows representative depth-encoded images at six different slow-time points, which reveals the relative depth positions of these two

balls. The experimental setup of this moving 3D object and a reconstructed movie of its full-cycle rotation are shown in Supplementary Video 2. To apply ToF-CUP’s dynamic 3D imaging

capability to biological applications, we imaged a swimming comet goldfish (_Carassius auratus_). The ToF-CUP camera acquired 3D images at two volumes per second to capture the fish’s

relatively slow movement over a sufficiently long time. Figure 5c shows six representative depth-encoded images of the fish. By tracing the centroid of each reconstructed datacube, we

demonstrated 3D spatial position tracking of the fish (Fig. 5d). In this representative example, the ToF-CUP camera reveals that the fish first stayed at the rear lower left corner and then

moved toward the right, after which it started to move toward the front wall of the fish tank. Supplementary Video 3 shows its full motion. In dynamic 3D imaging experiments, the external

CCD camera was operated at a relatively long exposure time to tolerate relatively weak backscattered light. As a result, the movement of objects blurred the reference image. In contrast,

because the exposure time of the streak camera is on the nanosecond level, the movement of the object did not noticeably affect the reconstructed datacube. Hence, the lateral and depth

resolutions in the reconstructed images are not degraded. To explore ToF-CUP’s imaging capability in a real-world environment, we imaged an object moving behind a scattering medium that was

composed by adding various concentrations of milk to water in a tank. The experimental setup is illustrated in Fig. 6a. Specifically, the incident laser beam was first de-expanded to ~2 mm

in diameter. A beam sampler reflected a small fraction of the energy of the beam toward the tank. After propagating through the scattering medium, the transmitted beam passed through an iris

(~2 mm in diameter). Then, the transmitted beam was measured by a photodiode detector to quantify the scattering level in the medium, which is presented as the equivalent scattering

thickness in units of the mean free path (). The rest of the incident laser beam was sent through the beam sampler and reflected by a mirror to an engineered diffuser (ED in Fig. 1), which

generated wide-field illumination of a moving airplane-model target behind the scattering medium. This manually operated airplane-model target moved in a curved trajectory illustrated in

Fig. 6a. The ToF-CUP camera imaged this moving object through the scattering medium with various scattering thicknesses. To quantitatively compare the image quality, we selected a

representative reconstructed 3D _x, y, z_, image at a single slow-time point for each scattering thickness and summed over the 3D image voxels along the _z_ axis. The resultant projected

images are shown in Fig. 6b. In addition, the intensity profile of a cross section of the airplane wing is plotted under these conditions in Fig. 6c. The image contrast decreases with

increased scattering in the medium and finally vanishes when the scattering thickness reaches 2.2_l__t_. Figure 6d,e show representative images of this moving airplane target at five

different slow-time points with two scattering thicknesses (1.0_l__t_ in d and 2.1_l__t_ in e), which record that the airplane-model target moved from the lower left to the upper right, as

well as toward the ToF-CUP camera in the depth direction. Although scattering causes loss of contrast and features in the image, the depth can still be perceived. The corresponding movie is

Supplementary Video 4. Due to the manual operation, the speed of the airplane-model target was slightly different in each experiment. As a result, the recorded movies with two scattering

thicknesses (1.0_l__t_ and 2.1_l__t_) have different lengths and so have the selected representative images in Fig. 6d,e. DISCUSSION Besides security, ToF-CUP offers the advantage of more

efficient information storage and transmission because data is compressed during acquisition. ToF-CUP compresses a 3D datacube with voxels to a 2D encrypted image with pixels. The data

compression ratio can therefore be calculated as . With the current setup . Therefore, ToF-CUP can potentially improve the data transmission rate by over two orders of magnitude. However,

compared with optical bandwidth-limited images, the implementation of ToF-CUP degrades the spatial resolutions by factors of 1.8 and 2.2 along the _x_ and _y_ axes29. In addition, the depth

resolution is degraded by 3.3 along the _z_ axis, compared to the streak camera’s native resolution in resolving a ToF signal. Thus, regarding actual information content, we can estimate the

data compression ratio by . For the current system, . Currently, the ToF-CUP camera’s performance is mainly restricted by the speed of the imaging devices and the illumination laser pulse

energy. First, the streak camera’s sweeping repetition frequency and the CCD sensor’s readout speed limit the volume rate of the ToF-CUP camera. The current ORCA-R2 CCD42 in the streak

camera has a full frame rate of 28 Hz, much lower than the streak camera’s sweeping repetition frequency of up to 1000 Hz43. Binning pixels or using a sub-array of the sensor could increase

the readout rate at the expense of image resolution or FOV. Replacing the current CCD with an advanced high-speed CMOS sensor44 could largely increase the frame rate. In addition, ToF-CUP’s

image reconstruction requires the DMD mask to be resolved in each encoded image at a given depth with a sufficient contrast-to-noise ratio (CNR). In our experiments, the minimal value of the

required CNR was empirically determined to be a value which yielded reliable reconstruction results. To provide enough illumination intensity, the maximal FOV at the object was limited to

approximately with the full laser energy (96.4 μJ per pulse). In addition, the maximum shearing velocity was held at 0.66 mm/ns in the streak camera, which corresponded to a spatial sampling

interval of 3 mm along the _z_ axis. With the current illumination intensity, a greater shearing velocity would reduce the number of collected photons per camera pixel and might result in

an insufficient CNR. The ToF-CUP camera can be potentially linked to a variety of future applications. For example, in terrestrial transportation, fog, haze and dust pose severe potential

threats to traffic safety. By integrating ToF-CUP with automobiles and aircraft, we could simultaneously track 3D positions of multiple objects in real time to avoid collisions caused by low

visibility. CONCLUSIONS In summary, we demonstrated encrypted 3D dynamic imaging using ToF-CUP. As a new type of ToF camera, ToF-CUP integrates the encryption of depth data with the

compressed acquisition of 3D data in a single snapshot measurement, significantly enhancing information security and transmission efficiency. Our experiments demonstrated that the image of

an original 3D object can be recovered only by users granted the decryption key. Moreover, from sequential image acquisition, we can track the 3D position of moving objects in real time.

Finally, we demonstrated that ToF-CUP can image 3D moving objects obscured by a scattering medium. In the future, we plan to use a higher pulse-energy laser and a faster streak camera to

further increase the imaging speed, FOV and depth resolution. ADDITIONAL INFORMATION HOW TO CITE THIS ARTICLE: Liang, J. _et al._ Encrypted Three-dimensional Dynamic Imaging using Snapshot

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K.K., _ORCA-Flash4.0 V2_, http://www.hamamatsu.com/resources/pdf/sys/SCAS0081E_C11440-22CU.pdf Accessed at: 8/22/2015. Download references ACKNOWLEDGEMENTS The authors thank Liren Zhu for

experimental assistance and Prof. James Ballard for close reading of the manuscript. A patent on this prototype is currently pending. This work was supported in part by National Institutes

of Health grants DP1 EB016986 (NIH Director’s Pioneer Award) and R01 CA186567 (NIH Director’s Transformative Research Award). AUTHOR INFORMATION Author notes * Liang Jinyang and Gao Liang

contributed equally to this work. AUTHORS AND AFFILIATIONS * Department of Biomedical Engineering, Optical Imaging Laboratory, Washington University in St. Louis, Campus Box 1097, One

Brookings Drive, St. Louis, 63130, Missouri, USA Jinyang Liang, Pengfei Hai, Chiye Li & Lihong V. Wang * Department of Electrical and Computer Engineering, University of Illinois at

Urbana-Champaign, 405 North Mathews Avenue, Urbana, 61801, Illinois, USA Liang Gao Authors * Jinyang Liang View author publications You can also search for this author inPubMed Google

Scholar * Liang Gao View author publications You can also search for this author inPubMed Google Scholar * Pengfei Hai View author publications You can also search for this author inPubMed 

Google Scholar * Chiye Li View author publications You can also search for this author inPubMed Google Scholar * Lihong V. Wang View author publications You can also search for this author

inPubMed Google Scholar CONTRIBUTIONS J.L. and L.G. designed and built the system. J.L. performed all experiments and analysed the data. L.G. and P.H. performed some experiments and analysed

the data. C.L. prepared samples and performed some experiments. L.V.W. contributed the conceptual system and provided supervision. All authors were involved in preparing and revising the

manuscript. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. ELECTRONIC SUPPLEMENTARY MATERIAL SUPPLEMENTARY VIDEO 1 SUPPLEMENTARY VIDEO 2

SUPPLEMENTARY VIDEO 3 SUPPLEMENTARY VIDEO 4 SUPPLEMENTARY INFORMATION RIGHTS AND PERMISSIONS This work is licensed under a Creative Commons Attribution 4.0 International License. The images

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Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit

http://creativecommons.org/licenses/by/4.0/ Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Liang, J., Gao, L., Hai, P. _et al._ Encrypted Three-dimensional Dynamic Imaging

using Snapshot Time-of-flight Compressed Ultrafast Photography. _Sci Rep_ 5, 15504 (2015). https://doi.org/10.1038/srep15504 Download citation * Received: 25 June 2015 * Accepted: 29

September 2015 * Published: 27 October 2015 * DOI: https://doi.org/10.1038/srep15504 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get

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