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Hybrid correlation holography with a single pixel detector
Abstract
Correlation holography reconstructs three-dimensional
(3D) objects as a distribution of two-point correlations
of the random field detected by two-dimensional detector
arrays. Here, we describe a hybrid method, a combination
of optical and computational channels, to reconstruct the
objects from only a single pixel detector. An experimental
arrangement is proposed as a first step to realizing the technique;
we have simulated the experimental model for both
scalar and vectorial objects. The proposed technique provides
depth focusing and 3D reconstruction with digital
suppression of unwanted frequency spectrum.
... While the above scenario is evident, during the past decade, many prominent imaging scientists have been leading a radically different research direction of introducing chaos into imaging systems and exploiting the behavior to perform advanced imaging [4][5][6][7][8][9][10][11][12]. As a matter of fact, the above researchers have set a new research direction in imaging, which has been followed by many researchers across the world, resulting in flooding of leading research journals by articles on chaos-inspired imaging technologies (CI 2 -Tech). ...
... Another interesting direction of partially coherent lightbased quantitative phase imaging was demonstrated by Lee and Park [5]. A radical approach on correlation holography based on van Cittert-Zernike theorem and the Hanbury Brown-Twiss (HBT) has been proposed recently by the research group of Singh for imaging through scattering layers [11]. This method uses an interferometric approach to record the complex coherence function and retrieves the object information from the second-order correlation. ...
... Issue of imaging from the random light can be broadly categorized into two. First is a situation where the random light is by choice or desired such as in the correlation holography, speckle-field digital holography, and ghost imaging [11,85,[91][92][93]. The second category covers examples, where desired information is spatially scrambled due to propagation of light through a random scattering medium and examples are imaging through atmospheric turbulence, scattering wall, shower-curtain effect, etc. [17,88,94,95]. ...
In recent years, rapid developments in imaging concepts and computational methods have given rise to a new generation of imaging technologies based on chaos. These chaos-inspired imaging technologies (CI2-Tech) consist of two directions: non-invasive and invasive. Non-invasive imaging, a much older research direction with a goal of imaging through scattering layers, has reached faster, smarter, and sharper imaging capabilities in recent years. The invasive imaging direction is based on exploiting the chaos to achieve imaging characteristics and increase dimensionalities beyond the limits of conventional imagers. In this roadmap, the current and future challenges in invasive and non-invasive imaging technologies are presented.
... experimental implementation and also require flexible control over the reference field to get the interference fringes in the cross-covariance function at the array detectors plane. On the other hand, significant attempts have been made to develop computational imaging techniques such as single-pixel imaging with random and structured field illumination over the past few years [34][35][36][37][38][39][40][41][42][43] . In contrast to using conventional cameras and two-dimensional array detectors, single-pixel techniques make use of projection of light patterns onto a sample while a single-pixel detector measures the light intensity collected for each pattern. ...
... Single-pixel imaging techniques have brought advantages such as use of a non-visible wavelength or precise time resolution, which can be costly and practically challenging to realize as a pixilated imaging device. Recently, a combination of optical and computation channels has been developed for the reconstruction of the three-dimensional (3D) amplitude object from a single-pixel detector, and technique is called hybrid correlation holography (HCH) 41 . This technique makes use of cross-covariance of the intensity and is derived from the connection between complex coherence function and intensity correlation for Gaussian random field. ...
The coherence holography offers an unconventional way to reconstruct the hologram where an incoherent light illumination is used for reconstruction purposes, and object encoded into the hologram is reconstructed as the distribution of the complex coherence function. Measurement of the coherence function usually requires an interferometric setup and array detectors. This paper presents an entirely new idea of reconstruction of the complex coherence function in the coherence holography without an interferometric setup. This is realized by structured pattern projections on the incoherent source structure and implementing measurement of the cross-covariance of the intensities by a single-pixel detector. This technique, named structured transmittance illumination coherence holography (STICH), helps to reconstruct the complex coherence from the intensity measurement in a single-pixel detector without an interferometric setup and also keeps advantages of the intensity correlations. A simple experimental setup is presented as a first step to realize the technique, and results based on the computer modeling of the experimental setup are presented to show validation of the idea.
... On the other hand, significant attempts have been made to develop computational imaging techniques such as single-pixel imaging with random and structured field illumination over the past few years [33][34][35][36][37][38][39][40][41] . In contrast to using conventional cameras and two-dimensional array detectors, single-pixel techniques make use of projection of light patterns onto a sample while a single-pixel detector measures the light intensity collected for each pattern. ...
... Single-pixel imaging techniques have brought advantages such as use of a non-visible wavelength or precise time resolution, which can be costly and practically challenging to realize as a pixilated imaging device. Recently, a combination of optical and computation channels has been developed for the reconstruction of the three-dimensional (3D) amplitude object from a single-pixel detector, and technique is called hybrid correlation holography (HCH) 40 . This technique makes use of cross-covariance of the intensity and is derived from the connection between complex coherence function and intensity correlation for Gaussian random field. ...
The coherence holography offers an unconventional way to reconstruct the hologram where an incoherent light illumination is used for reconstruction purposes, and object encoded into the hologram is reconstructed as the distribution of the complex coherence function. Measurement of the coherence function usually requires an interferometric setup and array detectors. This paper presents an entirely new idea of reconstruction of the complex coherence function in the coherence holography without an interferometric setup. This is realized by structured pattern projections on the incoherent source structure and implementing measurement of the cross-covariance of the intensities by a single-pixel detector. This technique, named structured transmittance illumination coherence holography (STICH), helps to reconstruct the complex coherence from the intensity measurement in a single-pixel detector without an interferometric setup and also keeps advantages of the intensity correlations. A simple experimental setup is presented as a first step to realize the technique, and results based on the computer modeling of the experimental setup are presented to show validation of the idea.
... where I(r) ¼ U * (r)U(r) is the intensity of the speckle pattern. The phase curvature outside the integral in Eq. (109) is canceled out in the intensity correlation and this helps to achieve a stationary source at any arbitrary plane z (Singh, 2017). The speckle pattern at the observation plane is the combination of two independent fields which follow Gaussian statistics. ...
... In contrast, the Hanbury Brown-Twiss (HBT) approach along with the holographic approach is utilized in recent years to resolve the phase loss problem in the speckle correlation [26]. In a series of communications, we have reported different techniques for imaging through diffuser using the HBT approach [36,37,38,39,40]. ...
The wavefront is scrambled when coherent light propagates through a random scattering medium and which makes direct use of the conventional optical methods ineffective. In this paper, we propose and demonstrate a structured light illumination for imaging through an opaque scattering layer. Proposed technique is reference free and capable to recover the complex field from intensities of the speckle patterns. This is realized by making use of the phase-shifting in the structured light illumination and applying spatial averaging of the speckle pattern in the intensity correlation measurement. An experimental design is presented and simulated results based on the experimental design are shown to demonstrate imaging of different complex-valued objects through scattering layer.
... The technological advancements and the introduction of spatial light modulators further expands the applied domains of ghost schemes to computational with only the execution of a single detector by replacing g the high-resolution detector with a calculable pattern in the computer 28 . Such attempts have also been made in the correlation holography with a single pixel detector and a SLM to realize a thermal light source 29,30 . Majority of the developed ghost schemes require a large set of sampling data with time sequential recording or detection for the high-quality image recovery, which limits the execution of the approach in tracking and imaging of dynamic objects in a real-time scenario. ...
... Recently, to remedy the limited availability of image-sensors in the invisible wavelength regime, single-pixel cameras have been employed for holographic imaging [21,22]. From intensity-correlation measurements, single-pixel cameras provide only intensity images using a single photodiode [23,24]. ...
We propose and experimentally demonstrate a method of polarization-sensitive quantitative phase imaging using two photodetectors and a digital micromirror device. Instead of recording wide-field interference patterns, finding the modulation patterns maximizing focused intensities in terms of the polarization states enables polarization-dependent quantitative phase imaging without the need for a reference beam and an image sensor. The feasibility of the present method is experimentally validated by reconstructing Jones matrices of several samples including a polystyrene microsphere, a maize starch granule, and a mouse retinal nerve fiber layer. Since the present method is simple and sufficiently general, we expect that it may offer solutions for quantitative phase imaging of birefringent materials. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.
... It should be emphasized that the present approach is fundamentally different from previously reported methods using single-pixel cameras in interferometry [22][23][24][25][26][27][28][29]. Conventional single-pixel cameras can measure only intensity images from intensity-correlation measurements. ...
One of the fundamental limitations in photonics is the lack of a bidirectional transducer that can convert optical information into electronic signals or vice versa. In acoustics or at microwave frequencies, wave signals can be simultaneously measured and modulated by a single transducer. In optics, however, optical fields are generally measured via reference-based interferometry or holography using silicone-based image sensors, whereas they are modulated using spatial light modulators. Here, we propose a scheme for an optical bidirectional transducer using a spatial light modulator. By exploiting the principle of time-reversal symmetry of light scattering, two-dimensional reference-free measurement and modulation of optical fields are realized. We experimentally demonstrate the optical bidirectional transducer for optical information consisting of 128×128 spatial modes at visible and short-wave infrared wavelengths.
Feedback-based wavefront shaping has been proposed to modulate the speckle field generated by coherent light transmitting through scattering media. Different from a monochromatic light, a colorful speckle pattern is generated when polychromatic light transmits through scattering media. Although single-position spectrum modulation has been realized, multiple-position spectrum modulation is a much more complicated problem. Based on non-dominated sorting genetic algorithm II (NSGA2), we design a step-by-step strategy to solve this problem. The results show that modulated spectra in two spatial positions with controllable spectral shape, range and magnitude can be achieved. This research is expected to be applied in the field of adaptive spectral control ranging from advanced spectral filtering to optical fiber dispersion and multi-spectral imaging.
We propose a new scheme for the recovery of complex-valued objects in a single-pixel hybrid correlation holography. The idea is to generate an intensity correlation hologram from the correlation of intensity fluctuations obtained over two channels, namely an optical channel equipped with a single pixel detector and a digital channel. The scheme has a theoretical basis which is described to reconstruct the objects from a single pixel detector. An experimental arrangement is proposed and as a first step towards realizing/implementing the technique, simulation of the experimental model was carried to image three complex objects.
The word 'holography' means a drawing that contains all of the information for light - both amplitude and wavefront. However, because of the insufficient bandwidth of current electronics, the direct measurement of the wavefront of light has not yet been achieved. Though reference-field-assisted interferometric methods have been utilized in numerous applications, introducing a reference field raises several fundamental and practical issues. Here we demonstrate a reference-free holographic image sensor. To achieve this, we propose a speckle-correlation scattering matrix approach; light-field information passing through a thin disordered layer is recorded and retrieved from a single-shot recording of speckle intensity patterns. Self-interference via diffusive scattering enables access to impinging light-field information, when light transport in the diffusive layer is precisely calibrated. As a proof-of-concept, we demonstrate direct holographic measurements of three-dimensional optical fields using a compact device consisting of a regular image sensor and a diffusor.
We present a coherent optical method for wavelength-resolution imaging of moving objects hidden within thick randomly scattering media. Spatial speckle intensity correlations as a function of object position are shown to provide access to the spatially dependent dielectric constant of the moving object. This speckle correlation imaging method yields field-based information previously inaccessible in heavily scattering environments. Proof of concept experimental results show excellent agreement with the theory. This new imaging approach will be valuable in high resolution imaging in tissue and other scattering environments where natural motion occurs or the object position can be controlled.
Classical statistical optics is revisited with the aim of introducing the concept of spatial statistical optics that places particular focus and special emphasis on spatial statistics of the optical field, rather than on their temporal statistics. The principles of emerging technology of statistical correlation holography based on spatial statistical optics are reviewed, and their unique capabilities for coherence and polarization shaping as well as synthesizing stochastic optical fields with desired statistical properties are introduced.
We propose and experimentally demonstrate a technique for the recovery of the wavefront from spatially fluctuating fields using the two point intensity correlation, i.e., fourth order correlation. Assuming spatial ergodicity and Gaussian statistics for the speckle field, we connect the fourth order correlation to the modulus of the corresponding second order correlation. The idea is to retrieve the complex coherence function and consequently the wavefront using the off-axis holography. Application of this technique is demonstrated in the reconstruction of complex field of the object lying behind a weak scatterer. Experimental results of recovery of the complex field of phase objects “vortices” with three values of topological charges are presented.
Since its discovery, the "ghost" diffraction phenomenon has emerged as a
non-conventional technique for optical imaging with very promising advantages.
However, extracting intensity and phase information of a structured and
realistic object remains a challenge. Here, we show that a "ghost" hologram can
be recorded with a single-pixel configuration by adapting concepts from
standard digital holography. The presented homodyne scheme enables phase
imaging with nanometric depth resolution, three-dimensional focusing ability,
and shows high signal-to-noise ratio.
Cheap Pix
Three-dimensional (3D) images can be captured by, for example, holographic imaging or stereoimaging techniques. To avoid using expensive optical components that are limited to specialized bands of wavelengths, Sun et al. (p. 844 ; see the Perspective by Faccio and Leach ) projected pulses of randomly textured light onto an object. They were able to reconstruct an image of the 3D object by detecting the reflected light with several photodetectors without any need for lenses. The patterned light beams can thus in principle be substituted for light sources of any wavelength.
The ideas of incoherent holography were conceived after the invention of coherent-light holography and their concepts seems indirectly related to it. In this work, we adopt an approach based on statistical optics to describe the process of recording of an incoherent-object hologram as a complex spatial coherence function. A Sagnac radial shearing interferometer is used for the correlation of optical fields and a Pockels cell is used to phase shift the interfering fields with the objective to quantify and to retrieve the spatial coherence function.
Ghost imaging with classical incoherent light by third-order correlation is investigated. We discuss the similarities and the differences between ghost imaging by third-order correlation and by second-order correlation, and analyze the effect from each correlation part of the third-order correlation function on the imaging process. It is shown that the third-order correlated imaging includes richer correlated imaging effects than the second-order correlated one, while the imaging information originates mainly from the correlation of the intensity fluctuations between the test detector and each reference detector, as does ghost imaging by second-order correlation.
Extension of coherence holography to vectorial regime is investigated. A technique for controlling and synthesizing optical fields with desired elements of coherence-polarization matrix is proposed and experimentally demonstrated. The technique uses two separate coherence holograms, each of which is assigned to one of the orthogonal polarization components of the vectorial fields.
Unconventional holography called photon correlation holography is proposed and experimentally demonstrated. Using photon correlation, i.e. intensity correlation or fourth order correlation of optical field, a 3-D image of the object recorded in a hologram is reconstructed stochastically with illumination through a random phase screen. Two different schemes for realizing photon correlation holography are examined by numerical simulations, and the experiment was performed for one of the reconstruction schemes suitable for the experimental proof of the principle. The technique of photon correlation holography provides a new insight into how the information is embedded in the spatial as well as temporal correlation of photons in the stochastic pseudo thermal light.
We demonstrate that unspeckled images of coherently illuminated, diffuse objects can be formed from measurements of backscattered laser-speckle intensity. The theoretical basis for this imaging technique is outlined, and results of computer experiments that successfully construct images from digitally simulated laser-speckle measurements are presented.
We present what we believe to be a new digital holographic imaging method that is able to determine simultaneously the distributions of intensity, phase, and polarization state at the surface of a specimen on the basis of a single image acquisition. Two reference waves with orthogonal polarization states interfere with the object wave to create a hologram that is recorded on a CCD camera. Two wave fronts, one for each perpendicular polarization state, are numerically reconstructed in intensity and phase. Combining the intensity and the phase distributions of these two wave fronts permits the determination of all the components of the Jones vector of the object-wave front. We show that this method can be used to image and measure the distribution of the polarization state at the surface of a specimen, and the obtained results indicate that precise quantitative measurements of the polarization state can be achieved. An application of the method to image the birefringence of a stressed polymethyl methacrylate sample is presented.
A scheme for coherent imaging that exploits the classical correlation of two beams obtained by splitting incoherent thermal radiation is considered. The analysis is performed simultaneously with the configuration based on two entangled beams, which are produced by parametric down-conversion (PDC). The possibility of using classical beams from thermal radiation for ghost imaging schemes in the way as entangled beams are used, is also discussed. The results show that it is possible to perform coherent imaging without spatial coherence.
We present a new method for recording digital holograms under incoherent illumination. Light is reflected from a 3D object, propagates through a diffractive optical element (DOE), and is recorded by a digital camera. Three holograms are recorded sequentially, each for a different phase factor of the DOE. The three holograms are superposed in the computer, such that the result is a complex-valued Fresnel hologram. When this hologram is reconstructed in the computer, the 3D properties of the object are revealed.
Propagation of a coherent light through an anisotropic random medium generates randomly
polarized field, known as polarization speckle. In this paper, an experimental technique is proposed
and demonstrated to recover the transmittance of a polarized object from polarization speckle.
Recovery of the polarized object from polarization speckle is made possible by combining the
far-field intensity correlation of the object speckle with off-axis holography to determine the
complex coherence function of the speckle. The desired object speckle which is uniformly
polarized is filtered from the polarization speckle using a polarizer. The results are compared with
the case where the complex coherence function is determined in the absence of the polarizer.
Ghost-imaging experiments correlate the outputs from two photodetectors: a high-spatial-resolution (scanning pinhole or CCD array) detector that measures a field that has not interacted with the object to be imaged, and a bucket (singlepixel) detector that collects a field that has interacted with the object.We give a comprehensive review of ghost imaging-within a unified Gaussian-state framework-presenting detailed analyses of its resolution, field of view, image contrast, and signal-to-noise ratio behavior. We consider three classes of illumination: thermal-state (classical), biphoton-state (quantum), and classicalstate phase-sensitive light. The first two have been employed in a variety of ghost-imaging demonstrations. The third is the classical Gaussian state that produces ghost images that most closely mimic those obtained from biphoton illumination. The insights we develop lead naturally to a new, single-beam approach to ghost imaging, called computational ghost imaging, in which only the bucket detector is required. We provide quantitative results while simultaneously emphasizing the underlying physics of ghost imaging. The key to developing the latter understanding lies in the coherence behavior of a pair of Gaussian-state light beams with either phase-insensitive or phase-sensitive cross correlation.
Imaging with optical resolution through and inside complex samples is a
difficult challenge with important applications in many fields. The fundamental
problem is that inhomogeneous samples, such as biological tissues, randomly
scatter and diffuse light, impeding conventional image formation. Despite many
advancements, no current method enables to noninvasively image in real-time
using diffused light. Here, we show that owing to the memory-effect for speckle
correlations, a single image of the scattered light, captured with a standard
high-resolution camera, encodes all the information that is required to image
through the medium or around a corner. We experimentally demonstrate
single-shot imaging through scattering media and around corners using
incoherent light and various samples, from white paint to dynamic biological
samples. Our lensless technique is simple, does not require laser sources,
wavefront-shaping, nor time-gated detection, and is realized here using a
camera-phone. It has the potential to enable imaging in currently inaccessible
scenarios.
Ghost imaging has been receiving increasing interest for possible use as a remote-sensing system. There has been little comparison, however, between ghost imaging and the imaging laser radars with which it would be competing. Toward that end, this paper presents a performance comparison between a pulsed, computational ghost imager and a pulsed, floodlight-illumination imaging laser radar. Both are considered for range-resolving (three-dimensional) imaging of a collection of rough-surfaced objects at standoff ranges in the presence of atmospheric turbulence. Their spatial resolutions and signal-to-noise ratios are evaluated as functions of the system parameters, and these results are used to assess each system's performance tradeoffs. Scenarios in which a reflective ghost-imaging system has advantages over a laser radar are identified.
An imaging approach, based on ghost imaging, is reported to recover a pure-phase object or a complexvalued
object. Our analytical results, which are backed up by numerical simulations, demonstrate that both the
complex-valued object and its amplitude-dependent part can be separately and nonlocally reconstructed using
this approach. Both effects influencing the quality of reconstructed images and methods to further improve the
imaging quality are also discussed.
Non-invasive optical imaging techniques, such as optical coherence tomography, are essential diagnostic tools in many disciplines, from the life sciences to nanotechnology. However, present methods are not able to image through opaque layers that scatter all the incident light. Even a very thin layer of a scattering material can appear opaque and hide any objects behind it. Although great progress has been made recently with methods such as ghost imaging and wavefront shaping, present procedures are still invasive because they require either a detector or a nonlinear material to be placed behind the scattering layer. Here we report an optical method that allows non-invasive imaging of a fluorescent object that is completely hidden behind an opaque scattering layer. We illuminate the object with laser light that has passed through the scattering layer. We scan the angle of incidence of the laser beam and detect the total fluorescence of the object from the front. From the detected signal, we obtain the image of the hidden object using an iterative algorithm. As a proof of concept, we retrieve a detailed image of a fluorescent object, comparable in size (50 micrometres) to a typical human cell, hidden 6 millimetres behind an opaque optical diffuser, and an image of a complex biological sample enclosed between two opaque screens. This approach to non-invasive imaging through strongly scattering media can be generalized to other contrast mechanisms and geometries.
We describe a method for image transmission through an aberrating medium by means of a modified configuration for conventional ghost diffraction with classical incoherent beams. On the basis of optical coherence theory, we show that the effects of phase disturbances, be they deterministic or random, can be canceled out in our method and the squared modulus of the Fourier transform of the object is obtained in terms of intensity-correlation measurements. From the measurement data, the object can be reconstructed using standard phase retrieval algorithms.
A new technique, referred to as Stokes holography, is proposed and experimentally demonstrated for controlled synthesis of generalized Stokes parameters in 3D space using Stokes fringes. Stokes fringes are polarization fringes which permit to record and reconstruct complete wavefront. Full use of Stokes fringes in a single step is realized by scattering complex field and subsequently reconstructing using spatial averaging of the randomly scattered field. Mathematical formulations are derived and supported by experimental results of 3D object reconstruction in generalized Stokes parameters.
The principle of unconventional holography, called coherence holography, is proposed and experimentally demonstrated for the first time. An object recorded in a hologram is reconstructed as the three-dimensional distribution of a complex spatial coherence function, rather than as the complex amplitude distribution of the optical field itself that usually represents the reconstructed image in conventional holography. A simple optical geometry for the direct visualization of the reconstructed coherence image is proposed, along with the experimental results validating the proposed principle. Coherence holography is shown to be applicable to optical coherence tomography and profilometry.
We experimentally demonstrate pseudothermal ghost imaging and ghost
diffraction using only a single single-pixel detector. We achieve this by
replacing the high resolution detector of the reference beam with a computation
of the propagating field, following a recent proposal by Shapiro [J. H.
Shapiro, arXiv:0807.2614 (2008)]. Since only a single detector is used, this
provides an experimental evidence that pseudothermal ghost imaging does not
rely on non-local quantum correlations. In addition, we show the
depth-resolving capability of this ghost imaging technique.
We report the results of experiments about the inversion of ghost diffraction with pseudothermal light. A complete retrieval of the complex transmission function of planar transparencies, illuminated by spatially incoherent, quasimonochromatic light, is achieved. This is obtained by measuring the field (instead of the intensity) correlation function. In particular, the determination of the phase of the correlation function is made particularly easy and robust by the use of a suitably modified Young interferometer. The presented results refer to the cases of a clear slit and a phase step.
Due to the turbulent atmosphere the resolution of conventional astrophotography is limited to ~1 sec of arc. However, the speckle-masking method can yield diffraction-limited resolution, i.e., 0.03 sec of arc with a 3.6-m telescope. Speckle masking yields true images of general astronomical objects. No point source is required in the isoplanatic field of the object. We present the theory of speckle masking; it makes use of triple correlations and their Fourier counterparts, the bispectra. We show algorithms for the recovery of the object from genuine astronomical bispectra data.
Ghost-imaging experiments correlate the outputs from two photodetectors: a high spatial-resolution (scanning pinhole or CCD camera) detector that measures a field which has not interacted with the object to be imaged, and a bucket (single-pixel) detector that collects a field that has interacted with the object. We describe a computational ghost-imaging arrangement that uses only a single-pixel detector. This configuration affords background-free imagery in the narrowband limit and a 3D sectioning capability. It clearly indicates the classical nature of ghost-image formation. Comment: 4 pages, 3 figures
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