Ghost imaging with incoherent and partially coherent light radiation

Depth of focus and intensity distribution of a lensacon illuminated by a partially coherent Gaussian Schell vortex beam

Using the extended Huygens-Fresnel principle, a cross-spectral density formula was developed for a Gaussian Schell model vortex (PCGSMV) beam diffracted through a lensacon (lens with an axicon). The intensity and depth of focus (DOF) shaped by the lensacon were calculated. Our numerical results show the relationship between the intensity distribution and depth of focus with the beam waist width as well as the spatial correlation of the coherence length. Furthermore, the relationship between the beam spot size and propagation distance was investigated. In the case of the lensacon tandem, the maximum intensity was greater than that attained by the axicon alone for the same beam parameters, and the DOF was smaller than that of the axicon alone. The vortex structure canceled out the low value of the spatial degree of coherence length. Our numerical model exhibited high-intensity values and high-quality Bessel rings along the DOF, which are critical for various applications.

Magnified x ray ghost imaging with tapered polycapillary optics free of the penumbra effect

X ray ghost imaging (XGI) offers both radiation dose-reduction potential and cost-effective benefits owing to the utilization of a single-pixel detector. Most XGI schemes with laboratory x ray sources require a mechanically moving mask for either structured illumination or structured detection. In either configuration, however, its resolution remains limited by the source size and the unit size of the mask. Upon propagation, the details of the object can actually be magnified by the divergence of x rays, but at the same time, the penumbra effect produced by the finite source size is dramatically intensified, which ultimately leads to a degradation of image quality in XGI. To address these limitations, this work proposes a magnified XGI scheme using structured detection equipped with tapered polycapillary optics, which can efficiently suppress the object's penumbra as well as resolve the magnified details of the object. In general, the resolution of this scheme is no longer affected by the source size but by the microcapillary size of polycapillary. Our work fundamentally achieves cancellation of penumbra effect-induced aberration, thus paving the way for high-resolution magnified XGI.

Evolution properties of a complex coherent square Gaussian-Schell-model beam in a uniaxial crystal orthogonal to the optical axis

The analytical formulas for spectral density, degree of coherence, and effective beam widths of complex coherent square Gaussian-Schell-model (GSM) beams in a uniaxial crystal orthogonal to the optical axis are derived. Based on these analytical formulas, the evolution properties are investigated by a set of numerical examples. It is demonstrated that the complex coherent square GSM beams spread at different rates in the directions parallel and orthogonal to the optical axis due to the anisotropic crystal, but the self-shift effect of the light field is almost unaffected by the fact that the uniaxial crystal is anisotropic. The effect of anisotropy of the uniaxial crystal on the effective width of the beam in the x direction and that in the y direction is completely opposite. The results provide a way for the modulation of the complex coherent square GSM beams and enrich the propagation theory of uniaxial crystal.

Rotating anisotropic rectangular hollow Gaussian array

A new class of partially coherent sources that can produce stable rotating anisotropic rectangular hollow Gaussian array profiles in the far field is presented. The cross-spectral density function and the spectral density of this kind of source on the propagation are derived, and its propagation characteristics, which are quite different from twisted Gaussian Schell-model beams, are discussed. The results show that each hollow lobe in the array tends to rotate around the axis during propagation. In addition, the dimension of the array, the distance between the lobes of the array, and the number of rows and columns of the rectangular array can be flexibly manipulated by adjusting the source parameters. Our work may provide a method to generate rotating anisotropic array beams with hollow lobes, which could have certain reference values in optical manipulation.

Matrix treatment for the correlation between intensity fluctuations of light waves on weak scattering from a collection of particles with L types

We report a new approach to the correlation between intensity fluctuations (CIF) of light waves on weak scattering from a collection of particles with L types. Two L×L matrices called a pair-potential matrix (PPM) and a pair-structure matrix (PSM) are introduced to jointly formulate the CIF of the scattered field for the first time. We show that the CIF equals the squared modulus of the trace of the product of the PSM and the transpose of the PPM, and thus these two matrices provide sufficient amount of information to determine the CIF of the scattered field. Based on this, we further analyze the normalized version of the CIF of the scattered field. It is found that the expression of the normalized CIF can have pretty compact and profound forms in three special cases: (I) the spatial distributions of the scattering potentials of particles of different types are similar (II) the spatial distributions of the densities of particles of different types are similar (III) both the scattering potentials and the densities of particles of different types are similarly distributed in space. Finally, the effects of the off-diagonal elements of the PPM and the PSM on the normalized CIF of the scattered field are illustrated by two examples. The results show that the non-zero cross correlation between particles of different types can induce intense changes in the normalized CIF of the scattered field.

Effect of optical spatial coherence on localized spin angular momentum density in tightly focused light [Invited]

Optical coherence is one of the most fundamental characteristics of light and has been viewed as a powerful tool for governing the spatial, spectral, and temporal statistical properties of optical fields during light-matter interactions. In this work, we use the optical coherence theory developed by Emil Wolf as well as the Richards-Wolf's vectorial diffraction method to numerically study the effect of optical coherence on the localized spin density of a tightly focused partially coherent vector beam. We find that both the transverse spin and longitudinal spin, with the former induced by the out-of-phase longitudinal field generated during strong light focusing and the latter induced by the vortex phase in the incident beam, are closely related to the optical coherence of the incident beam, i.e., with the decrease of the transverse spatial coherence width of the incident beam, the magnitude of the spin density components decreases as well. The numerical findings are interpreted well with the two-dimensional degrees of polarization between any two of the three orthogonal field components of the tightly focused field. We also explore the roles of the topological charge of the vortex phase on enhancing the spin density for the partially coherent tightly focused field. The effect of the incident beam's initial polarization state is also discussed.

Degree of paraxiality of a twist electromagnetic Gaussian Schell-model beam

The definition of the degree of paraxiality (DOP) for a stochastic electromagnetic field is applied to a twist stochastic electromagnetic field. As an illustrative example, DOP for a wide class of model stochastic fields, i.e., twist electromagnetic Gaussian Schell-model (TEGSM) fields, is discussed. The dependence of the DOP of the light source on its properties is also studied in detail. The numerical results show that the DOP of a TEGSM beam is determined by the rms widths of auto-correlation functions and the twist factor as well as by the degree of polarization. To explain the behavior of DOP, the far-field divergence angle of this beam source is also discussed.

High-performance scanning-mode polarization based computational ghost imaging (SPCGI)

Computational ghost imaging (CGI) uses preset patterns and single-pixel detection, breaking through the traditional form of point-to-point imaging. In this paper, based on the Monte Carlo model, a reflective polarization based CGI (PCGI) system has been proposed and constructed under the foggy environments. And the imaging performances of the PCGI at different optical distances have been investigated and analyzed quantitatively. When the targets and the background have a small difference in reflectivity, the difference of polarization characteristics between the targets and the background can help the CGI to remove the interference of scattering light and improve the imaging contrast. Besides, in order to further improve imaging efficiency, a scanning-mode polarization based CGI (SPCGI) has also been proposed, in which the combination of polarization characteristics and the scanning-mode plays an important role to improve the CGI's imaging efficiency and imaging quality.

On z-coherence of beams radiated by Schell-model sources with Gaussian profile

The degree of coherence and the intensity distribution on the axis of the beam radiated by a planar partially coherent source of the Schell-model type are investigated. We present an expression for the on-axis cross-spectral density which is valid for a very general Schell-model source, with the only constraint that the intensity distribution across the source is Gaussian. Furthermore, we show that such an expression takes very simple analytical forms for several commonly used degrees of coherence of the source.

Dark-field ghost imaging

Ghost imaging is a promising technique for shape reconstruction using two spatially correlated beams: one beam interacts with a target and is collected with a bucket detector, and the other beam is measured with a pixelated detector. However, orthodox ghost imaging always provides unsatisfactory results for unstained samples, phase objects, or highly transparent objects. Here we present a dark-field ghost imaging technique that can work well for these "bad" targets. The only difference from orthodox ghost imaging is that the bucket signals rule out the target's unscattered beam. As experimental proof, we demonstrate images of fine copper wires, quartz fibers, scratched and damaged glass plates, a pure phase object, and biospecimens.

Hollow rectangular multi-Gaussian Schell-model source

We introduced a new class of a partially coherent source that can generate a field with a hollow rectangular profile, named the hollow rectangular multi-Gaussian Schell-mode source. The dependence of distribution of far-zone spectral density on the properties of the proposed source was analyzed. The results show that one can control the distribution properties of the far-zone intensity profile, including the thickness of the hollow edge, the shape of the hollow, the size of the hollow, and the orientation of the hollow, by adjusting the corresponding structural parameters of the source.

Ghost polarimetry using Stokes correlations

We present here a novel ghost polarimeter based on Stokes parameter correlations and a spatially incoherent classical source with adjustable polarization state and Gaussian statistics. The setup enables extracting the four amplitudes and three phase differences related to the spectral $ 2 \times 2 $2×2 complex Jones matrix of any transmissive polarization-sensitive object. Our work extends the ghost imaging methods from the traditional intensity correlation measurements to the detection of polarization state correlations.

Evolution properties of the radially polarized Laguerre-Gaussian-correlated Schell-model beams propagating in uniaxial crystals

In this paper, we discuss, both analytically and numerically, the paraxial propagation of the radially polarized Laguerre-Gaussian-correlated Schell-model (LGCSM) beams orthogonal to the optical axis in uniaxial crystals. The analytical expression for the cross-spectral density function and the second-order moments of the radially polarized LGCSM beams are derived, and the evolution properties of the normalized intensity distribution, the spectral degree of the coherence (SDOC), and the spectral degree of the polarization (SDOP) in uniaxial crystals are elucidated by numerical examples. It is found that the intensity distribution of the radially polarized LGCSM beams evolves from a doughnut shape into a solid shape and finally converts into an elliptical symmetric hollow-ring profile in uniaxial crystals due to the combined effect of special correlation functions and the anisotropy effect of the uniaxial crystals. The evolution of the SDOC and SDOP for the radially polarized LGCSM beams is quite different from that of the radially polarized Gaussian-Schell-model beams. In addition, the propagation properties of the radially polarized LGCSM beams are closely related to the spatial coherence length, the mode order, and the ratio of extraordinary and ordinary reflective indices. The results show that the uniaxial crystals could modulate the evolution properties of the radially polarized LGCSM beams.

Fast calculation of tightly focused random electromagnetic beams: controlling the focal field by spatial coherence

Focusing of a vectorial (electromagnetic) optical beam through a high numerical aperture can be investigated by means of the Richards-Wolf diffraction integral. However, such an integral extends from two-dimensional to four-dimensional, greatly increasing the computation time and therefore limiting the applicability, when light with decreased spatial coherence is considered. Here, we advance an effective protocol for the fast calculation of the statistical properties of a tightly focused field produced by a random electromagnetic beam with arbitrary state of spatial coherence and polarization. The novel method relies on a vectorial pseudo-mode representation and a fast algorithm of the wave-vector space Fourier transform. The procedure is demonstrated for several types of radially (fully) polarized but spatially partially coherent Schell-model beams. The simulations show that the computation time for obtaining the focal spectral density distribution with 512 × 512 spatial points for a low coherence beam is less than 100 seconds, while with the conventional quadruple Richards-Wolf integral more than 100 hours is required. The results further indicate that spatial coherence can be viewed as an effective degree of freedom to govern both the transverse and longitudinal components of a tightly focused field with potential applications in reverse shaping of focal fields and optical trapping control.

Characterization of the electromagnetic Gaussian Schell-model beam using first-order interference

We propose a method for the characterization of electromagnetic Gaussian Schell-model (EMGSM) beams. This method utilizes the first-order interference consisting of polarization-state projections along with the two-point (generalized) Stokes parameters. The second-order field correlations employed in this method enable us to determine both the magnitude and the argument of the complex degree of electromagnetic coherence. We experimentally demonstrate this method by characterizing an EMGSM beam, which is synthesized using a laser beam passing through a rotating ground glass diffuser. This beam-characterization method is expected to be potentially useful for probing the partially coherent and partially polarized beams, and have tremendous applications in broad areas of optical communication and beam propagation.

Radiation forces on a Rayleigh particle produced by partially coherent circular Airy beams

In this work, the radiation force on a Rayleigh dielectric particle induced by the partially coherent circular Airy beam (PCCAB) is investigated. Our numerical results show that the PCCAB can be used to trap and manipulate particles. The radiation force distribution and trapping stability have been analyzed under different coherent lengths. It is found that, with the increase of the spatial coherent length, the radiation force is increased and the particle can be stably trapped at more points. Therefore, the radiation force as well as the depth of potential well can be effectively modulated by controlling the spatial coherent length in optical micromanipulation. The trapping properties of PCCAB have also been studied under other different parameters, including the scale factor and initial radius.

Ghost Imaging with a Partially Coherent Beam Carrying Twist Phase in a Turbulent Ocean: A Numerical Approach

Ghost imaging (GI) is an indirect imaging approach that can retrieve an object’s image even in a harsh environment through measuring the fourth-order correlation function (FOCF) between the signal and idle optical paths. In this paper, we study lensless GI with a partially coherent beam carrying twist phase, i.e., twisted Gaussian Schell-model (TGSM) beam, in the presence of oceanic turbulence. Explicit expression of the FOCF is derived based on the optical coherence theory and Rytov approximation, and the effects of the twist phase and the oceanic turbulence on the quality and visibility of image are investigated in detail through numerical examples. Our results show that the simulated oceanic turbulence strongly affects the GI. The quality of image decreases monotonously with an increase of the strength of turbulence whereas the visibility increases. When the illumination light carries a twist phase, the visibility of the image is improved while the quality of the image is reduced in contrast to those without a twist phase. By properly selecting the strength of the twist phase, the image can still be maintained at an acceptable level of quality with high visibility. Furthermore, it is found that the quality and visibility of the ghost image are less affected by the oceanic turbulence using a TGSM beam with larger twist factor. Our findings will be useful for the application of GI in an oceanic turbulent environment.

Generation and Propagation of a Hermite-Gaussian Correlated Schell-Model LG0l Beam

A partially coherent beam under the combined action of a Hermite-Gaussian correlated function and vortex phase, named the HGCSMLG0l beam has been explored both theoretically and experimentally. The statistical properties, such as the intensity and distribution of the degree of coherence (DOC) on propagation are analyzed in detail, based on the deduced equations. We find that the intensity is determined dominantly by the non-conventional correlated function when the coherence length is comparatively small and by vortex phase when the coherence length is large. The modulus of the DOC is not vulnerable to coherence width, rather, it is affected by both non-conventional correlated function and vortex phase. Our results are verified well by the experiment results.

Interaction-free ghost-imaging of structured objects

Quantum - or classically correlated - light can be employed in various ways to improve resolution and measurement sensitivity. In an "interaction-free" measurement, a single photon can be used to reveal the presence of an object placed within one arm of an interferometer without being absorbed by it. With a technique known as "ghost-imaging", entangled photon pairs are used for detecting an opaque object with significantly improved signal-to-noise ratio while preventing over-illumination. Here, we integrate these two methods to obtain a new imaging technique which we term "interaction-free ghost-imaging" (IFGI). With this new technique, we reduce photon illumination on the object by up to 26.5% while still maintaining at least the same image quality of conventional ghost-imaging. Alternatively, IFGI can improve image signal-to-noise ratio by 18% when given the same number of interacting photons as in standard ghost-imaging. IFGI is also sensitive to phase and polarisation changes of the photons introduced by a structured object. These advantages make IFGI superior for probing light-sensitive materials and biological tissues.

X-ray computational ghost imaging with single-pixel detector

We demonstrate computational ghost imaging at X-ray wavelengths with only one single-pixel detector. We show that, by using a known designed mask as a diffuser that induces intensity fluctuations in the probe beam, it is possible to compute the propagation of the electromagnetic field in the absence of the investigated object. We correlate these calculations with the measured data when the object is present in order to reconstruct the images of 50 μm and 80 μm slits. Our results open the possibilities for X-ray high-resolution imaging with partially coherent X-ray sources and can lead to a powerful tool for X-ray three-dimensional imaging.

Evolution properties of the radially polarized multi-Gaussian Schell-model beam in uniaxial crystals

The evolution properties of the normalized intensity distribution, the spectral degree of coherence (SDOC), and the spectral degree of polarization (SDOP) of the radially polarized multi-Gaussian Schell-model (MGSM) beam in uniaxial crystals are illustrated. Numerical results show that the intensity distribution of the radially polarized MGSM beam gradually evolves from a doughnut shape into an elliptical symmetric flattop shape and retains its elliptical flattop shape on further propagation in anisotropic crystals. The evolution behavior of the SDOC and SDOP for the radially polarized MGSM beam is quite different from that of the linearly polarized one. In addition, the influences of the spatial coherence length δ₀, beam index M, and the ratio of the extraordinary refractive index to the ordinary refractive index n_e/n_o of the uniaxial crystals on the evolution properties of the normalized intensity distribution, the SDOC, and the SDOP of the radially polarized MGSM beam are discussed in detail.

Discrimination of incoherent vortex states of light

Coherence vortex (CV) states provide a new way for optical manipulation and communication. As a promising option for increasing the data-transmission capacity, CV multiplexing warrants investigation. However, few studies have focused on discriminating and sorting CV states with different topological charges. In this work, we examine the cross-spectral density (CSD) of a CV state embedded in an incoherent light field and so-called incoherent vortex (ICV). Given a multiplexed ICV, we propose a method to recognize the constituting single ICVs therein. Our analytical results, which are derived according to the coherence theory and the paraxial propagation law and are given in analytical forms, show that the CSD can reveal the topological charge spectrum of a multiplexed incoherent Laguerre-Gaussian mode. This proposal can be used for free-space communication and remote sensing where light fields with low coherence are preferable to completely coherent beams.

Super-resolution imaging by anticorrelation of optical intensities

Photon bunching, a feature of classical thermal fields, has been widely exploited to implement ghost imaging. Here we show that spatial photon antibunching can be experimentally observed via low-pass filtering of the intensities of the two thermal light beams from a beamsplitter correlation system. Through suitable choice of the filter thresholds, the minimum of the measured normalized anti-correlation function, i.e., antibunching dip, can be lower than 0.2, while its full-width-at-half-maximum can be much narrower than that of the corresponding positive correlation peak. Based on this anti-correlation effect, a super-resolution negative ghost image is achieved in a lensless scheme, in which the spatial resolution can exceed the Rayleigh diffraction limit by more than a factor of two. The setup is quite simple and easy to implement, which is an advantage for practical applications.

Decoherence of fiber supercontinuum light source for speckle-free imaging

Speckle-free imaging is attractive in laser-illuminated imaging systems. The evolutionary process of supercontinuum decoherence in extra-large mode area step-index multimode fiber is analyzed to provide high-quality broadband light source for speckle-free imaging. It is found that spectral bandwidth, number of spatial transverse modes, and decoherence among different modes all greatly contribute to speckle reduction. The combination of supercontinuum and extra-large mode area step-index multimode fiber can considerably increase the efficiency of decoherence process for speckle-free imaging. This work may enrich the research of speckle-free imaging and also provide guidance on speckle-free imaging using fiber-optics based light source.

Effects of Atmospheric Turbulence on Lensless Ghost Imaging with Partially Coherent Light

Ghost imaging with partially coherent light through two kinds of atmospheric turbulences: monostatic turbulence and bistatic turbulence, is studied, both theoretically and experimentally. Based on the optical coherence theory and the extended Huygens–Fresnel integral, the analytical imaging formulae in two kinds of turbulence have been derived with the help of a tensor method. The visibility and quality of the ghost image in two different atmospheric turbulences are discussed in detail. Our results reveal that in bistatic turbulence, the visibility and quality of the image decrease with the increase of the turbulence strength, while in monostatic turbulence, the image quality remains invariant when turbulence strength changes in a certain range, only the visibility decreases with the increase of the strength of turbulence. Furthermore, we carry out experimental demonstration of lensless ghost imaging through monostatic and bistatic turbulences in the laboratory, respectively. The experiment results agree well with the theoretical predictions. Our results solve the controversy about the influence of atmospheric turbulence on ghost imaging.

High frame-rate computational ghost imaging system using an optical fiber phased array and a low-pixel APD array

To obtain a high imaging frame rate, a computational ghost imaging system scheme is proposed based on optical fiber phased array (OFPA). Through high-speed electro-optic modulators, the randomly modulated OFPA can provide much faster speckle projection, which can be precomputed according to the geometry of the fiber array and the known phases for modulation. Receiving the signal light with a low-pixel APD array can effectively decrease the requirement on sampling quantity and computation complexity owing to the reduced data dimensionality while avoiding the image aliasing due to the spatial periodicity of the speckles. The results of analysis and simulation show that the frame rate of the proposed imaging system can be significantly improved compared with traditional systems.

Sub-Rayleigh resolution ghost imaging by spatial low-pass filtering

A sub-Rayleigh resolution ghost imaging experiment is performed via post-detection spatial low-pass filtering of the instantaneous intensity. A super-resolution reconstructed image has been achieved, in which the spatial resolution can exceed the Rayleigh diffraction limit by more than a factor of two. The resolution depends on the filter threshold, and the Rayleigh limit can be exceeded for a wide choice of threshold values. The setup is simple and easy to implement, which is an advantage for practical applications.

Efficient tensor approach for simulating paraxial propagation of arbitrary partially coherent beams

Complicated partially coherent beams (PCBs) are useful in many applications, such as free-space optical communications, particle trapping and optical imaging, while usually it is hard to derive analytical propagation formulae for such beams, and one has to fall back on numerical methods. The conventional numerical methods have some intrinsic drawbacks. In this paper, we introduce an efficient tensor approach (ETA) for simulating paraxial propagation of arbitrary PCBs. The ETA is a direct reconstruction of the propagated PCB without aliasing and rippling problems, and the algorithm is simple and robust with a tensor/matrix multiplication as the main calculation. The validity of ETA is verified through comparing simulation results with analytical results, numerical integration results and experimental results, respectively. The ETA provides a fast and reliable way for simulating paraxial propagation of arbitrary PCBs.

Complex Gaussian representations of partially coherent beams with nonconventional degrees of coherence

We adopt the recently introduced complex Gaussian function to expand the partially coherent beams with nonconventional degrees of coherence, and derive detailed representations of Hermite-Gaussian correlated Schell-model beam, elliptical Laguerre-Gaussian correlated Schell-model beam, and multi-Gaussian correlated Schell-model beam. Complex Gaussian representation of a partially coherent beam provides a convenient way for treating its propagation. As an application example, we explore the self-splitting properties of a Hermite-Gaussian correlated Schell-model beam propagating in a uniaxial crystal with the help of the complex Gaussian representation, and it is found that the uniaxial crystal can be used to control the splitting properties.

Single-pixel computational ghost imaging with helicity-dependent metasurface hologram

Different optical imaging techniques are based on different characteristics of light. By controlling the abrupt phase discontinuities with different polarized incident light, a metasurface can host a phase-only and helicity-dependent hologram. In contrast, ghost imaging (GI) is an indirect imaging modality to retrieve the object information from the correlation of the light intensity fluctuations. We report single-pixel computational GI with a high-efficiency reflective metasurface in both simulations and experiments. Playing a fascinating role in switching the GI target with different polarized light, the metasurface hologram generates helicity-dependent reconstructed ghost images and successfully introduces an additional security lock in a proposed optical encryption scheme based on the GI. The robustness of our encryption scheme is further verified with the vulnerability test. Building the first bridge between the metasurface hologram and the GI, our work paves the way to integrate their applications in the fields of optical communications, imaging technology, and security.

Studying fermionic ghost imaging with independent photons

Ghost imaging with thermal fermions is calculated via two-particle interference based on the superposition principle for different alternatives in Feynman's path integral theory. It is found that ghost imaging with fully polarized thermal fermions can be simulated by ghost imaging with fully polarized thermal bosons and classical particles. Photons in pseudothermal light are employed to experimentally study fermionic ghost imaging. Ghost imaging with thermal bosons and fermions is discussed based on the point-to-point (spot) correlation between the object and image planes. The employed method offers an efficient guidance for future ghost imaging with real thermal fermions, which may also be generalized to study other second-order interference phenomena with fermions.

Point-spread function in ghost imaging system with thermal light

The point-spread function (PSF) is fundamental importance in estimating the imaging resolution in optical imaging systems. By using the Collins formula, a analytical imaging formula for ghost imaging system is obtained. The intensity fluctuation correlation function can be viewed as the convolution of the original object and a PSF. The imaging resolution is determined by the width of PSF. Based on the optical transfer matrix theory, we present the analytical formula describing the width of the PSF, by which one can estimate imaging resolution of a new-designed imaging scheme when compared with that of the existing imaging system. Several typical ghost imaging systems are chosen to verify experimentally our theoretical results.

Experimental X-Ray Ghost Imaging

We report an experimental proof of principle for ghost imaging in the hard-x-ray energy range. We use a synchrotron x-ray beam that is split using a thin crystal in Laue diffraction geometry. With an ultrafast imaging camera, we are able to image x rays generated by isolated electron bunches. At this time scale, the shot noise of the synchrotron emission process is measurable as speckles, leading to speckle correlation between the two beams. The integrated transmitted intensity from a sample located in the first beam is correlated with the spatially resolved intensity measured in the second, empty, beam to retrieve the shadow of the sample. The demonstration of ghost imaging with hard x rays may open the way to protocols to reduce radiation damage in medical imaging and in nondestructive structural characterization using free electron lasers.

Orbital angular moment of an electromagnetic Gaussian Schell-model beam with a twist phase

We derive the analytical formula for the orbital angular momentum (OAM) flux of a stochastic electromagnetic beam carrying twist phase [i.e., twisted electromagnetic Gaussian Schell-model (TEGSM) beam] in the source plane with the help of the Wigner distribution function. Furthermore, we derive the general expression of the OAM flux of a TEGSM beam on propagation with the help of a tensor method. As numerical examples, we explore the evolution properties of the OAM flux of a TEGSM beam propagating through a cylindrical thin lens or a uniaxial crystal. It is found that the OAM flux of a TEGSM beam closely depends on its twist factors and degree of polarization in the source plane, and one can modulate the OAM flux of a TEGSM beam by a cylindrical thin lens or a uniaxial crystal. Our results may be useful in some applications, such as particle manipulation and free-space optical communications, where light beam with OAM is preferred.

Experimental demonstration of ghost imaging with an electromagnetic Gaussian Schell-model beam

Recently, there has been a controversy about the dependence of the visibility of the ghost image on the degree of polarization (DOP) of a stochastic electromagnetic beam because of different definitions of the visibility. In this paper, we revisit ghost imaging with an electromagnetic Gaussian Schell-model (EGSM) beam. Through numerical examples based on the conventional definition of the visibility, we find that the visibility of the ghost image indeed increases or decreases with the increase of the DOP the beam source under certain conditions. We solve the controversy between literatures and the present paper through analyzing the r.m.s. widths of auto-correlation functions of the x component of the field and of the y component of the field. Furthermore, we carry out experimental demonstration of ghost imaging with an EGSM beam. Our experimental results verify the theoretical predictions.

High quality computational ghost imaging using multi-fluorescent screen

An alternative scheme for improvement of computational ghost imaging (GI) features is proposed based on a three-color fluorescent screen. While a monochrome fluorescent screen does not enhance the quality of ghost images in comparison with the ordinary GI technique, employment of a multi-fluorescent screen can be very effective. It is shown that the visibility, signal to noise ratio (SNR), and contrast to noise ratio (CNR) of the resultant ghost images are improved when a multi-fluorescent screen is used. In particular, the results prove 65%, 36%, and 95% improvement for visibility, SNR, and CNR over 2000 shots, respectively. Also shown is the possibility of reconstructing ghost images over a reduced number of shots (as small as 25) by increasing the number of colors on the screen, whereas ordinary GI is not possible with such a small number of shots. The results from simulations are checked with conducted experiments, and a good agreement between them is observed.

Statistical properties in Young's interference pattern formed with a radially polarized beam with controllable spatial coherence

Experimental generation of a radially polarized (RP) beam with controllable spatial coherence (i.e., partially coherent RP beam) was reported recently [Appl. Phys. Lett. 100, 051108 (2012)]. In this paper, we carry out theoretical and experimental studies of the statistical properties in Young's two-slit interference pattern formed with a partially coherent RP beam. An approximate analytical expression for the cross-spectral density matrix of a partially coherent RP beam in the observation plane is obtained, and it is found that the statistical properties, such as the intensity, the degree of coherence and the degree of polarization, are strongly affected by the spatial coherence of the incident beam. Our experimental results are consistent with the theoretical predictions, and may be useful in some applications, where light field with special statistical properties are required.

Iterative denoising of ghost imaging

We present a new technique to denoise ghost imaging (GI) in which conventional intensity correlation GI and an iteration process have been combined to give an accurate estimate of the actual noise affecting image quality. The blurring influence of the speckle areas in the beam is reduced in the iteration by setting a threshold. It is shown that with an appropriate choice of threshold value, the quality of the iterative GI reconstructed image is much better than that of differential GI for the same number of measurements. This denoising method thus offers a very effective approach to promote the implementation of GI in real applications.

Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function (WDF), we have studied the relative root-mean-square (rms) angular width and the propagation factor of cosine-Gaussian-correlated Schell-model (CGSM) beams propagating in non-Kolmogorov turbulence. It has been found that the CGSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation, and this advantage will be more obvious for the beams with larger parameter n and spatial coherence δ or under the condition of stronger fluctuation of turbulence. The CGSM beam with larger parameter n or smaller spatial coherence δ will be less affected by the turbulence. In addition, the effects of the slope-parameter α, inner and outer scale and the refractive-index structure constant of the non-Kolmogorov's power spectrum on the propagation factor are also analyzed in detailed.

An improved algorithm to reduce noise in high-order thermal ghost imaging

A modified Nth-order correlation function is derived that can effectively remove the noise background encountered in high-order thermal light ghost imaging (GI). Based on this, the quality of the reconstructed images in an Nth-order lensless GI setup has been greatly enhanced compared to former high-order schemes for the same sampling number. In addition, the dependence of the visibility and signal-to-noise ratio for different high-order images on the sampling number has been measured and compared.

Generation and propagation of partially coherent beams with nonconventional correlation functions: a review [invited]

Partially coherent beams with nonconventional correlation functions have displayed many extraordinary properties, such as self-focusing and self-splitting, which are totally different from those of partially coherent beams with conventional Gaussian correlated Schell-model functions and are useful in many applications, such as optical trapping, free-space optical communications, and material thermal processing. In this paper, we present a review of recent developments on generation and propagation of partially coherent beams with nonconventional correlation functions.

Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam

We analyze the intensity of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam focused by a thin lens near the focal region, and it is found that a controllable optical cage can be formed through varying the initial spatial coherence width. Furthermore, we carry out experimental measurement of the intensity of a focused LGCSM beam, and we observe that the optical cage is indeed formed in experiment. Our results will be useful for trapping particles or atoms.

Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere

Laguerre-Gaussian Schell-model (LGSM) beam was proposed in theory [Opt. Lett.38, 91 (2013 Opt. Lett.38, 1814 (2013)] just recently. In this paper, we study the propagation of a LGSM beam in turbulent atmosphere. Analytical expressions for the cross-spectral density and the second-order moments of the Wigner distribution function of a LGSM beam in turbulent atmosphere are derived. The statistical properties, such as the degree of coherence and the propagation factor, of a LGSM beam in turbulent atmosphere are studied in detail. It is found that a LGSM beam with larger mode order n is less affected by turbulence than a LGSM beam with smaller mode order n or a GSM beam under certain condition, which will be useful in free-space optical communications.

Reduction or annihilation of aberrations of an optical system by balancing ghost-imaging technique and optimal imaging of a pure weak phase object

It is shown, using ghost-imaging techniques, that it is possible to reduce or even to annihilate the influence of aberrations connected with an arbitrary optical system. To this end, we consider a ghost-imaging setup, which consists of two arms, each containing an optical system. The reduction cancellation of the aberrations of the total imaging system is achieved by manipulating the values of the aberrations in one arm of the optical system. The technique is then applied for the optimal reconstruction of a weak phase object, manipulating the values of the defocusing such that the "Scherzer defocus condition" is obtained.

Role of intensity fluctuations in third-order correlation double-slit interference of thermal light

A third-order double-slit interference experiment with a pseudothermal light source in the high-intensity limit has been performed by actually recording the intensities in three optical paths. It is shown that not only can the visibility be dramatically enhanced compared to the second-order case as previously theoretically predicted and shown experimentally, but also that the higher visibility is a consequence of the contribution of third-order correlation interaction terms, which is equal to the sum of all contributions from second-order correlation. It is interesting that, when the two reference detectors are scanned in opposite directions, negative values for the third-order correlation term of the intensity fluctuations may appear. The phenomenon can be completely explained by the theory of classical statistical optics and is the first concrete demonstration of the influence of the third-order correlation terms.

Optical coherenscopy based on phase-space tomography

Partially coherent light provides attractive benefits in imaging, beam shaping, free-space communications, random medium monitoring, among other applications. However, the experimental characterization of the spatial coherence is a difficult problem involving second-order statistics represented by four-dimensional functions that cannot be directly measured and analyzed. In addition, real-world applications usually require quantitative characterization of the local spatial coherence of a beam in the absence of a priori information, together with fast acquisition and processing of the experimental data. Here we propose and experimentally demonstrate a technique that solves this problem. It comprises an optical setup developed for automatized video-rate measurement and a method -phase-space tomographic coherenscopy- allowing parallel data acquisition, processing, and analysis. This technique significantly simplifies the spatial coherence analysis and opens up new perspectives for the development of tools exploiting the degrees of freedom hidden into light coherence.

Ghost imaging without discord

Ragy and Adesso argue that quantum discord is involved in the formation of a pseudothermal ghost image. We show that quantum discord plays no role in spatial light modulator ghost imaging, i.e., ghost-image formation based on structured illumination realized with laser light that has undergone spatial light modulation by the output from a pseudorandom number generator. Our analysis thus casts doubt on the degree to which quantum discord is necessary for ghost imaging.

Properties of high-order ghost imaging with natural light

We discuss theoretically the visibility and contrast-to-noise ratio (CNR) of high-order thermal ghost imaging with natural light. Five cases of an object beam and a reference beam with different polarized light are analyzed. Theoretical calculations show that a higher-order N can optimize the ghost imaging in both visibility and CNR in all five cases.