Ghost imaging is a fascinating process, where light interacting with an
object is recorded without resolution, but the shape of the object is
nevertheless retrieved, thanks to quantum or classical correlations of this
interacting light with either a computed or detected random signal. Recently,
ghost imaging has been extended to a time object, by using several thousands
copies of this periodic object. Here, we present a very simple device, inspired
by computational ghost imaging, that allows the retrieval of a single
non-reproducible, periodic or non-periodic, temporal signal. The reconstruction
is performed by a single shot, spatially multiplexed, measurement of the
spatial intensity correlations between computer-generated random images and the
images, modulated by a temporal signal, recorded and summed on a chip CMOS
camera used with no temporal resolution. Our device allows the reconstruction
of either a single temporal signal with monochrome images or
wavelength-multiplexed signals with color images

Denis, Severine

Devaux, Fabrice

Lantz, Eric

Moreau, Paul-Antoine

English

arXiv

International audienceGhost imaging is a fascinating process in which light interacting with an object is recorded without resolution, but the shape of the object is nevertheless retrieved, thanks to quantum or classical correlations of this interacting light with either a computed or detected random signal. Recently, ghost imaging has been extended to a time object, by using several thousand copies of this periodic object. Here, we present a very simple device, inspired by computational ghost imaging, that allows the retrieval of a single nonreproducible, periodic, or nonperiodic, temporal signal. The reconstruction is performed by a single-shot spatially multiplexed measurement of the spatial intensity correlations between computer-generated random images and the images, modulated by a temporal signal, recorded, and summed on a chip CMOS camera used with no temporal resolution. Our device allows the reconstruction of either a single temporal signal with monochrome images or wavelength-multiplexed signals with color images

Archive Ouverte en Sciences de l'Information et de la Communication

Computational temporal ghost imaging

Ghost imaging is a fascinating process in which light interacting with an object is recorded without resolution, but the shape of the object is nevertheless retrieved, thanks to quantum or classical correlations of this interacting light with either a computed or detected random signal. Recently, ghost imaging has been extended to a time object, by using several thousand copies of this periodic object. Here, we present a very simple device, inspired by computational ghost imaging, that allows the retrieval of a single nonreproducible, periodic, or nonperiodic, temporal signal. The reconstruction is performed by a single-shot spatially multiplexed measurement of the spatial intensity correlations between computer-generated random images and the images, modulated by a temporal signal, recorded, and summed on a chip CMOS camera used with no temporal resolution. Our device allows the reconstruction of either a single temporal signal with monochrome images or wavelength-multiplexed signals with color images

Denis, Séverine

Enlighten

Enlighten: Publications

Fabrice Devaux

Paul-Antoine Moreau

Séverine Denis

Eric Lantz

Crossref

Optica

HAL - Université de Franche-Comté

We present a very simple device, inspired by computational ghost imaging, that allows the re-trieval of a single non-reproducible, periodic or non-periodic, temporal signal. The reconstruction is performed by a single shot, spatially multiplexed, measurement of the spatial intensity correlations between computer-generated random images and the images modulated by the temporal signal, recorded and summed on a chip CMOS camera used with no temporal resolution

Explore Bristol Research

                          Devaux, F., Moreau, P-A., Denis, S., & Lantz, E. (2016). Computationaltemporal ghost imaging. Optica, 3(7), 698-701. DOI:10.1364/OPTICA.3.000698Peer reviewed versionLicense (if available):CC BY-NCLink to published version (if available):10.1364/OPTICA.3.000698Link to publication record in Explore Bristol ResearchPDF-documentThis is the author accepted manuscript (AAM). The final published version (version of record) is available onlinevia OSA at https://www.osapublishing.org/optica/abstract.cfm?uri=optica-3-7-698. Please refer to any applicableterms of use of the publisher.University of Bristol - Explore Bristol ResearchGeneral rightsThis document is made available in accordance with publisher policies. Please cite only the publishedversion using the reference above. Full terms of use are available:http://www.bristol.ac.uk/pure/about/ebr-terms.htmlComputational temporal ghost imagingFabrice Devaux1∗, Paul-Antoine Moreau2, Se´verine Denis1 and Eric Lantz11 Institut FEMTO-ST,De´partement d’Optique P. M. Duffieux, UMR 6174 CNRSUniversite´ Bourgogne Franche-Comte´,15b Avenue des Montboucons, 25030 Besanc¸on - France2 Centre for Quantum Photonics, H. H. WillsPhysics Laboratory and Department of Electrical and Electronic EngineeringUniversity of Bristol, Merchant Venturers Building,Woodland Road, Bristol BS8 1UB, United KingdomWe present a very simple device, inspired by computational ghost imaging, that allows the re-trieval of a single non-reproducible, periodic or non-periodic, temporal signal. The reconstruction isperformed by a single shot, spatially multiplexed, measurement of the spatial intensity correlationsbetween computer-generated random images and the images modulated by the temporal signal,recorded and summed on a chip CMOS camera used with no temporal resolution.I. INTRODUCTIONExploitation of the statistical properties of classical or non classical light sources is the cause of fascinating newapplications. For the two last decades, ghost imaging has emerged as a way to form images of an object with aSingle Point Detector (SPD) that does not have spatial resolution. The initial works used the quantum nature ofentanglement of a two-photons state, where photons of a pair are spatially correlated, to detect temporal coincidences[1]. While one of the photons passing through the object was detected by a photon counter with no spatial resolution,its twin photon was detected with spatial resolution by scanning the transverse plane with a single detector[1], orrecently by an intensified charge-coupled device (ICCD) [2].Later, ghost imaging exploiting the temporal correlations of the intensity fluctuations of pseudothermal light wasproposed. With a two-detector setup [3], a ghost image of the object was obtained by correlating the pseudothermalfield measured by a CCD with the intensity measured with a SPD. More recently, computational ghost imaging andghost diffraction were performed with only one SPD [4, 5]: the object was illuminated by a pseudothermal light beam,generated with a Spatial Light Modulator (SLM) addressed with random phase masks. Then, the transmitted lightwas detected with the SPD. The image or the Fourier transform of the object was reconstructed by correlating thetemporal fluctuations of the calculated field patterns with the measured intensities. With the same principle, ghostimaging with wavelength-multiplexing has been performed [6].By taking into account space-time duality in optics, the extension of the results of spatial ghost imaging to thetime domain has been investigated theoretically, numerically and recently experimentally either with a classical non-stationary light source [7, 8], bi-photon states [9], a chaotic laser [10] or a multimode laser source [11]. In all cases,the light emitted by the sources was split into two arms, called ”reference” and ”test” arms. While in the test armthe light was transmitted through a ”time object” and detected with a slow SPD which can not properly resolvethe time object, in the reference arm the light, that did not interact with the temporal object, was detected witha fast SPD. As for spatial ghost imaging, the temporal object was reconstructed by measuring the correlations ofthe temporal intensity fluctuations or the temporal coincidences between the two arms. In [11], measurements overseveral thousands copies of the temporal signal were necessary to retrieve an embedded binary signal with a goodsignal-to-noise ratio [12].The extension of spatial ghost imaging to the time domain looks attractive for dynamic imaging of ultra-fastwaveforms with high resolution. However, the currently proposed solutions require many realizations of the sametemporal signal, limiting the current applications to the detection of synchronized and reproducible signals [12]. Thisis in contrast with spatial ghost imaging, where the object is unique, but multiplied in the time domain by a randommodulation, different from one pixel to another, leading to multiplexing in this time domain. In the present paperwe propose an original and completely different scheme which is the exact space-time transposition of computationalghost imaging [5]: a single shot acquisition of a non-reproducible time object is performed by multiplying it withcomputer-generated random images, ensuring spatial multiplexing of temporal intensity correlations before detectionof the time integrated images with a camera that has no temporal resolution.arXiv:1603.04647v1  [physics.optics]  15 Mar 20162FIG. 1: Experimental setup : (P) linear polarizer (WP) liquid crystal variable wave plate. Images of random patterns displayedon a LCD screen are acquired with a CMOS camera. The transmission of the imaging system is modulated by a temporalsignal that drives the WP placed in front of the polarizer.II. RESULTSFig. 1 depicts the set-up. First, a stack of K independent random binary patterns X, with a large number ofpixels, are generated and displayed on a LCD (Liquid Crystal Display) screen. In these binary patterns, a pixel takesthe value 1 with probability p and the value 0 with probability 1 − p, hence verifies the statistical properties of aBernouilli distribution (〈X〉 = p, σ2X = p(1− p)). Images of the patterns are acquired with a compact CMOS USB2.0camera (IDS UI-1640C, 1280×1024 pixels) on a 8 bits grey scale. Since the light emitted by the LCD screen is linearlypolarised at 45◦, the energy transmission of the imaging system can be linearly modulated by a temporal signal duringthe exposure time of the camera, by means of a liquid crystal variable wave plate (WP, Thorlabs LCC1113-A) placedbefore a linear polariser (P) in front of the camera objective.At first, each pattern Xk of the stack (k denotes the rank of the pattern in the stack) is recorded individually withthe same exposure time. The retardation of the WP and the direction of the polariser are adjusted to maximise theenergy transmission of the imaging system, that will be considered in the following as a level of 100% (T = 1). Then,the mean and the variance of each image X ′k are measured. Since the displayed patterns are binary, the sharp edgesof the original pixels are blurred in the recorded images because of the modulation transfer function (MTF) of theobjective. Consequently, as the recorded images are encoded over 255 grey levels, they do no longer verify the initialstatistical properties. Several experiments were conducted to optimize all the setup parameters (focus, numericalaperture and magnification of the objective, number of independent pixels in patterns, probability p) such as thestatistical properties of intensity fluctuations in the recorded images are the closest of those of the computed patterns(see supplement).In a second experiment, the patterns of the stack are displayed successively on the LCD screen, imaged with atransmission coefficient given by the driving temporal signal (0 ≤ T (t) ≤ 1), and summed on the camera during along exposure time (5 to 10 s). In that case, the recorded image S corresponds to the time integrated image of thedisplayed patterns such as the level of a pixel Sij of coordinates (i, j) is given by :Sij =K∑k=1T (k)X ′k,ij (1)where T (k) is the value of the transmission at the time when the kth pattern is displayed. Fig. 2 shows a selectedregion of interest (ROI) in images of the displayed patterns. Fig. 2a corresponds to the image of a single pattern andFig. 2b corresponds to the image of the time integrated patterns of the stack where a temporal object is embedded.Because the circular aperture of the WP limits the field of view of the imaging system and induces deterministicfluctuations for pixels close to the border, we selected the larger ROI of N ×N pixels (N = 700) in images where thegray level of a lighted pixel is almost constant. In the subsequent calculations, residual covariances between images oftwo independent binary patterns, due to these deterministic intensity fluctuations, are removed by filtering numericallythe recorded images. Because of the magnification of the imaging system, the image size of an independent pixel ofthe displayed patterns is larger than the size of a pixel of the camera. Then, the number of effective independentpixels in an image is smaller than the number of pixels in the selected ROI.3  100 200 300 400 500 600 700100200300400500600700 246810121416Sij(a)X’k,ij  100 200 300 400 500 600 700100200300400500600700304050607080(b)FIG. 2: (a) Image of a single random pattern where p = 0.5. (b) Image of the time integrated pattern’s stack with a temporalobject embedded. The measurements are performed inside a ROI of 700× 700 pixels.As for other methods of ghost imaging, the temporal signal is reconstructed by calculating the intensity correlationsbetween the time integrated image S and the images X ′ of the K random patterns. The value of T (k0) at the ”time”k0 is estimated by (a hat means ”estimator of”):Tˆ (k0) =γN∑i=1N∑j=1(Sij − S) (X ′k0,ij −X′k0)N∑i=1N∑j=1(X ′k0,ij −X′k0)2 (2)where S and X′k0 are the arithmetic mean levels of the related images. γ is a normalization coefficient correspondingto the ratio between the exposure time of the camera for the acquisition of the individual images X ′k and the displaytime of the random patterns during the acquisition of S. It can be shown (see supplement) that the noise in themeasurement is minimized when p = 0.5. Then, the signal-to-noise ratio (SNR) is given by:SNR[T (k0)] =T (k0)σT (k0)=NeffT (k0)√K∑k=1,k 6=k0T 2(k)≥ Neff√K − 1T (k0) (3)where N2eff represents the total number of effective independent pixels in recorded images. With a ROI of 700× 700pixels, N2eff has been estimated as 153 × 153 independent pixels. Fig. 3 shows ghost images of different temporalsignals (analogic or binary and periodic or non periodic). Each ghost image corresponds to a single shot measurementwhich is performed with images of 700×700 pixels (where Neff = 153), the same stack of 20 random patterns (wherep = 0.5) and a long camera exposure time between 6 s and 8 s. For periodic signals (figures 3a to Fig. 3c), the WPcontroller is driven in a linear regime by 0.5 Hz periodic signals with different shapes (square, sinus and ramp) whichare depicted by the green curves (only phases of these curves are adusted to fit the experimental data representedby the blue stars). Error bars are deduced from the measured SNR. Voltage amplitude of these signals are fixedsuch as the transmission of the imaging system is in the range 0.4 ≤ T (t) ≤ 0.9. These low and high transmissionlevels are depicted in Fig. 3a-c by the horizontal black dotted lines. Fig. 3d corresponds to the ghost image of arandom binary word of 20 bits formed with a mechanical shutter ensuring T = 0 when closed, but T < 1 when openbecause opening is not synchronized with the display of the random patterns on the LCD screen. These results clearlyshow that our device is able to reconstruct, with a single shot measurement and with a very good accuracy, varioustemporal analogic or binary signals. We emphasize that thanks to the single shot measurement, our device allowsnon reproducible and non synchronizable signals to be recorded.In order to measure the SNR, several single shot measurements were performed with the same experimentalparameters and the WP controller driven by different continuous voltages such as the transmission coefficient is set asconstants during the acquisition time of the ghost images (T =0.4, 0.9 and 1). The measured values are 0.38± 0.03,0.90± 0.06 and 0.99± 0.08, respectively. Using Eq. 3, it corresponds to SNRs of 26± 8, 28± 6 and 26± 8, which arein rather good agreement with the theoretical SNR : 153√19= 35.41 2 3 400.511 2 3 41 2 3 400.510 2 4 6 8(d)Time (s)T(t)1  0  0   0  0   1  0   0  0   0  1   0  0  0   0  0  0   0  0  0  00.5100.51Time (s)Time (s)Time (s)T(t)T(t)T(t)(c)(a) (b)Experimental data Temporal signalFIG. 3: Ghost images of different temporal signals. 3 kind of 0.5 Hz periodic signals: (a) square, (b) sinus, (c) ramp. (d)corresponds to the single shot measurement of a binary word of 20 bits. Each acquisition is performed with the same stack of20 random patterns. Blue stars correspond to experimental data and the green curves show the original temporal signals. Errorbars are deduced from the measured SNR. For periodic signals, horizontal black dotted lines show the effective amplitude ofthe transmission levels of the imaging system.III. CONCLUSIONTo summarize, these experiments represent the first demonstration of ghost imaging of a single, non-reproducibletime object. They are performed by multiplying this object with computer-generated random images, ensuringthe exact space-time transposition of computational ghost imaging. With a very simple device we were able toreconstruct with a very good accuracy different kinds of temporal signals. When compared to the recent experimentaldemonstration of temporal ghost imaging [11], the main advantage of our system consists in no need of multiple(thousands) synchronized copies of the temporal signal and the use of a single detector (the camera) that has notemporal resolution. In the present form of the set-up, its obvious drawback is the slowness which was imposed bythe simple and low cost devices used to display the random patterns and to generate the temporal signals. Thegeneration rate of random patterns with a large number of independent spatial modes can be easily increased by usingeither a fast digital micromirror device to display the random patterns up to tens of kHz [13] or spatial multiplexingof modulated light sources in multimode fibers to generate random patterns with a rate up to 100 MHz. Moreprospectively, exact space-time transposition of ghost imaging with thermal light [3] can be suggested where singleshot acquisition of a temporal signal with sub-picosecond resolution could be obtained. First, patterns due to fastspatial fluctuations of a thermal-like light source are divided in two arms with a beam splitter. In the fist arm, spatialfluctuations of pattens are resolved with a high-speed photography device (a motion-picture camera with 4.4 × 1012frames per second is reported in [14]), while in the second arm the same patterns are transmitted through a ”timeobject” and integrated with a classical slow camera.Authors contributionsF. Devaux and E. Lantz wrote the manuscript text. P.A. Moreau had the original idea of the experiment. F.Devaux designed the experimental setup and performed the experiments. E. Lantz developed the theoretical model.S. Denis participated to the experiments.5FundingThis work was supported by the Labex ACTION program (ANR-11-LABX-0001-01).[1] T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, ”Optical imaging by means of two-photon quantumentanglement,” Phys. Rev. A 52, R3429 (1995)[2] P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M. J. Padgett, ”Imaging with a small number of photons,”Nat. Commun. 6, 5913 (2015)[3] R. S. Bennink, S. J. Bentley, and R. W. Boyd, ”Two-Photon coincidence imaging with a classical source,” Phys. Rev. Lett.89, 113601 (2002)[4] J. H. Shapiro, ”Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008)[5] Y. Bromberg, O. Katz, and Y. Silberberg, ”Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009)[6] D.-J. Zhang, H.-G. Li, Q.-L. Zhao, S. Wang, H.-B. Wang, J. Xiong, and K. Wang, ”Wavelength-multiplexing ghostimaging,” Phys. Rev. A 92, 013823 (2015)[7] T. Shirai, T. Seta¨la¨, and A. T. Friberg, ”Temporal ghost imaging with classical non-stationary pulsed light,” JOSA B 27,2549 (2010)[8] T. Seta¨la¨, T. Shirai, and A. T. Friberg, ”Fractional Fourier transform in temporal ghost imaging with classical light,”Phys. Rev. A 82, 043813 (2010)[9] K. Cho and J. Noh, ”Temporal ghost imaging of a time object, dispersion cancelation, and nonlocal time lens with bi-photonstate,” Optics Communications 285, 1275 (2012)[10] Z. Chen, H. Li, Y. Li, J. Shi, and G. Zeng, ”Temporal ghost imaging with a chaotic laser,” Opt. Eng 5, 076103 (2013)[11] P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, ”Ghost imaging in the time domain,” Nat Photon10, 167 (2016)[12] D. Faccio, ”Optical communications: Temporal ghost imaging,” Nature Photonics 10, 150 (2016)[13] C. Gu, D. Zhang, Y. Chang, and S.-C. Chen, ”Digital micromirror device-based ultrafast pulse shaping for femtosecondlaser,” Optics Letters 40, 2870 (2015)[14] K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda,et al., ”Sequentially timed all-optical mapping photography (STAMP),” Nat. Photon. 8, 695 (2014)

Computational temporal ghost imaging

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