Tailoring electron vortex beams with customizable intensity patterns by electron diffraction holography

An electron vortex beam(EVB) carrying orbital angular momentum(OAM) plays a key role in a series of fundamental scientific researches, such as chiral energy-loss spectroscopy and magnetic dichroism spectroscopy. So far, almost all the experimentally created EVBs manifest isotropic doughnut intensity patterns. Here, based on the correlation between local divergence angle of electron beam and phase gradient along azimuthal direction, we show that free electrons can be tailored to EVBs with customizable intensity patterns independent of the carried OAM. As proof-of-concept, by using computer generated hologram and designing phase masks to shape the incident free electrons in the transmission electron microscope, three structured EVBs carrying identical OAM are tailored to exhibit completely different intensity patterns. Furthermore, through the modal decomposition, we quantitatively investigate their OAM spectral distributions and reveal that structured EVBs present a superposition of a series of different eigenstates induced by the locally varied geometries. These results not only generalize the concept of EVB, but also demonstrate an extra highly controllable degree of freedom for electron beam manipulation in addition to OAM.

Bessel–Gaussian beam-based orbital angular momentum holography

Orbital angular momentum(OAM), as a new degree of freedom, has recently been applied in holography technology.Due to the infinite helical mode index of OAM mode, a large number of holographic images can be reconstructed from an OAM-multiplexing hologram. However, the traditional design of an OAM hologram is constrained by the helical mode index of the selected OAM mode, for a larger helical mode index OAM mode has a bigger sampling distance, and the crosstalk is produced for different sampling distances for different OAM modes. In this paper, we present the design of the OAM hologram based on a Bessel–Gaussian beam, which is non-diffractive and has a self-healing property during its propagation. The Fourier transform of the Bessel–Gaussian beam is the perfect vortex mode that has the fixed ring radius for different OAM modes. The results of simulation and experiment have demonstrated the feasibility of the generation of the OAM hologram with the Bessel–Gaussian beam. The quality of the reconstructed holographic image is increased, and the security is enhanced. Additionally, the anti-interference property is improved owing to its self-healing property of the Bessel-OAM holography.

4K-DMDNet:diffraction model-driven network for 4K computer-generated holography

Deep learning offers a novel opportunity to achieve both high-quality and high-speed computer-generated holography(CGH).Current data-driven deep learning algorithms face the challenge that the labeled training datasets limit the training performance and generalization.The model-driven deep learning introduces the diffraction model into the neural network.It eliminates the need for the labeled training dataset and has been extensively applied to hologram generation.However,the existing model-driven deep learning algorithms face the problem of insufficient constraints.In this study,we propose a model-driven neural network capable of high-fidelity 4K computer-generated hologram generation,called 4K Diffraction Model-driven Network(4K-DMDNet).The constraint of the reconstructed images in the frequency domain is strengthened.And a network structure that combines the residual method and sub-pixel convolution method is built,which effectively enhances the fitting ability of the network for inverse problems.The generalization of the 4K-DMDNet is demonstrated with binary,grayscale and 3D images.High-quality full-color optical reconstructions of the 4K holograms have been achieved at the wavelengths of 450 nm,520 nm,and 638 nm.

Method for eliminating zero-order image in digital holography

For eliminating the zero-order image in digital holography, a new method using the differential of the hologram intensity instead of the hologram itself for numerical reconstruction is proposed. This method is based on digital image processing. By analyzing the spatial spectrum of the off-axis digital hologram, it theoretically proves that the zero-order image can be effectively eliminated by differential before reconstruction. Then, the detected hologram is processed in the program with differential and reconstruction. Both the theoretical analysis and digital reconstruction results show that it can effectively eliminate the large bright spot in the center of the reconstructed image caused by the zero-order image, improve the image quality significantly, and render a better contrast of the reconstructed image. This method is very simple and convenient due to no superfluous optical elements and requiring only one time record.

An encryption scheme based on phase-shifting digital holography and amplitude-phase disturbance

In this paper, we propose an encryption scheme based on phase-shifting digital interferometry. According to the original system framework, we add a random amplitude mask and replace the Fourier transform by the Fresnel transform. We develop a mathematical model and give a discrete formula based on the scheme, which makes it easy to implement the scheme in computer programming. The experimental results show that the improved system has a better performance in security than the original encryption method. Moreover, it demonstrates a good capability of anti-noise and anti-shear robustness.

Interface charges boosted ultrafast lithiation in Li_4Ti_5O_12 revealed by in-situ electron holography

It is still a great challenge at present to combine the high rate capability of the electrochemical capacitor with the high electrochemical capacity feature of rechargeable battery in energy storage and transport devices. By studying the lithiation mechanism of Li_4Ti_5O_12 （LTO） using in-situ electron holography, we find that double charge layers are formed at the interface of the insulating Li_4Ti_5O_12 （Li_4） phase and the semiconducting Li_7Ti_5O_12 （Li_7） phase, and can greatly boost the lithiation kinetics. The electron wave phase of the LTO particle is found to gradually shrink with the interface movement, leaving a positive electric field from Li_7 to Li_4 phase. Once the capacitive interface charges are formed, the lithiation of the core/shell particle could be established within 10 s. The ultrafast kinetics is attributed to the built-in interface potential and the mixed Ti3＋/Ti4＋ sites at the interface that could be maximally lowering the thermodynamic barrier for Li ion migration.

Phase-shifting digital holography in image reconstruction

A phase-shifting digital holography scheme developed to investigate internal defects in artworks is described. Phase-shifting is utilized to obtain a clear reconstructed object wave from a rough surface texture. A reverse-transform algorithm is employed to reconstruct the object wave on its original position of unknown distance or the imaging position from the object wave information on the holographic plane. To get the clearest reconstruction the exact registration of the unknown distance is determined by applying the intensity sum as the auto-focusing function, The spatial resolution of the reconstruction image is also investigated for a variety of affecting factors. Laboratory results of reconstruction images under deformation are presented.

RECONSTRUCTION STABILITY OF NEARFIELD ACOUSTIC HOLOGRAPHY

The distributed source boundary point method （DSBPM） is used as the spatial transform algorithm for realizing nearfield acoustic holography （NAH）, the sensitivity of the reconstructed solution to the measurement errors is analyzed, and the regularization method is proposed to stabilize the reconstruction process, control the influence of the measurement errors and get a better approximate solution. An oscillating sphere is investigated as a numerical example, the influence of the measurement errors on the reconstruction solution is demonstrated, and the feasibility and validity of the regularization method are validated. Key words： Acoustic holography Boundary point method Inverse problem Regularization

Optical encryption of multiple three-dimensional objects based on multiple interferences and single-pixel digital holography

We present an optical encryption method of multiple three-dimensional objects based on multiple interferences and single-pixel digital holography. By modifying the Mach-Zehnder interferometer, the interference of the multiple objects beams and the one reference beam is used to simultaneously encrypt multiple objects into a ciphertext. During decryption, each three-dimensional object can be decrypted independently without having to decrypt other objects. Since the single- pixel digital holography based on compressive sensing theory is introduced, the encrypted data of this method is effectively reduced. In addition, recording fewer encrypted data can greatly reduce the bandwidth of network transmission. Moreover, the compressive sensing essentially serves as a secret key that makes an intruder attack invalid, which means that the system is more secure than the conventional encryption method. Simulation results demonstrate the feasibility of the proposed method and show that the system has good security performance.

Compensation of body shake errors in terahertz beam scanning single frequency holography for standoff personnel screening

In the terahertz（THz） band, the inherent shake of the human body may strongly impair the image quality of a beam scanning single frequency holography system for personnel screening. To realize accurate shake compensation in imaging processing, it is quite necessary to develop a high-precision measure system. However, in many cases, different parts of a human body may shake to different extents, resulting in greatly increasing the difficulty in conducting a reasonable measurement of body shake errors for image reconstruction. In this paper, a body shake error compensation algorithm based on the raw data is proposed. To analyze the effect of the body shake on the raw data, a model of echoed signal is rebuilt with considering both the beam scanning mode and the body shake. According to the rebuilt signal model, we derive the body shake error estimated method to compensate for the phase error. Simulation on the reconstruction of point targets with shake errors and proof-of-principle experiments on the human body in the 0.2-THz band are both performed to confirm the effectiveness of the body shake compensation algorithm proposed.

A new method of aperture synthetizing in digital holography

This paper proposes a new method of aperture synthetizing in digital holography based on the principle of holography.In the new method aperture synthetizing is achieved by reconstructing each sub-hologram respectively,firstly,moving each reconstructed wave field referred to the benchmark reconstructed wave field according to the relationship between spacial motion and frequency shift,and finally splicing them by using superposition. Two different recording ways,using plane wave to record and using spherical wave to record,are analyzed,and their moving formula is deduced,too.Simulation and experiment are done. The results show that in comparison with the traditional method of aperture synthetizing in digital holography,the new method can decrease calculation and save reconstructed time obviously which has better applicability.

Detection of the spatiotemporal field of a single-shot terahertz pulse based on spectral holography

According to electro-optical sampling theory, we propose a new method to detect the spatiotemporal field of a single- shot terahertz pulse by spectral holography for the first time. The single-shot terahertz pulse is coupled into a broadened chirped femtosecond pulse according to electro-optical sampling theory in the detecting system. Then the reference wave and the signal wave are split by Dammann grating and spread into the interference band-pass filter. The filtered sub-waves are at different central-frequencies because of the different incident angles. These sub-waves at different central-frequencies interfere to form sub-holograms, which are recorded in a single frame of a charge coupled device （CCD）. The sub-holograms are numerically processed, and the spatiotemporal field distribution of the original terahertz pulse is reconstructed. The computer simulations verify the feasibility of the proposed method.

100 Hertz frame-rate switching threedimensional orbital angular momentum multiplexing holography via cross convolution

The orbital angular momentum(OAM)of light has been implemented as an information carrier in OAM holography.Holographic information can be multiplexed in theoretical unbounded OAM channels,promoting the applications of optically addressable dynamic display and high-security optical encryption.However,the frame-rate of the dynamic extraction of the information reconstruction process in OAM holography is physically determined by the switching speed of the incident OAM states,which is currently below 30 Hz limited by refreshing rate of the phase-modulation spatial light modulator(SLM).Here,based on a cross convolution with the spatial frequency of the OAM-multiplexing hologram,the spatial frequencies of an elaborately-designed amplitude distribution,namely amplitude decoding key,has been adopted for the extraction of three-dimensional holographic information encoded in a specific OAM information channel.We experimentally demonstrated a dynamic extraction frame rate of 100 Hz from an OAM multiplexing hologram with 10 information channels indicated by individual OAM values from-50 to 50.The new concept of cross convolution theorem can even provide the potential of parallel reproduction and distribution of information encoded in many OAM channels at various positions which boosts the capacity of information processing far beyond the traditional decoding methods.Thus,our results provide a holographic paradigm for high-speed 3D information processing,paving an unprecedented way to achieve the high-capacity short-range optical communication system.

Possibility to break through limitation of measurement range in dual-wavelength digital holography

By using the beat frequency technique,the dual-wavelength digital holography(DWDH)can greatly increase the measurement range of the system.However,the beat frequency technique has a limitation in measurement range.The measurement range is not larger than a synthetic wavelength.Here,to break through this limitation,we propose a novel DWDH method based on the constrained underdetermined equations,which consists of three parts:(i)prove that the constrained underdetermined equation has a unique integer solution,(ii)design an algorithm to search for the unique integer solution,(iii)introduce a third wavelength into the DWDH system,and design a corresponding algorithm to enhance the anti-noise performance of DWDH.As far as we know,it is the first time that we have discovered that the problem of DWDH can belong in a problem of contained underdetermined equations,and it is also the first time that we have given the mathematical proof for breaking through the limitation of the measurement range.A series of results is shown to test the theory and the corresponding algorithms.More importantly,since the principle of proposed DWDH is based on basic mathematical principles,it can be further extended to various fields,such as dual-wavelength microwave imaging and dual-wavelength coherent diffraction imaging.

NEAR-FIELD ACOUSTIC HOLOGRAPHY FOR SEMI-FREE ACOUSTIC FIELD BASED ON WAVE SUPERPOSITION APPROACH

In the semi-free acoustic field, the actual acoustic pressure at any point is composed of two parts： The direct acoustic pressure and the reflected acoustic pressure. The general acoustic holographic theories and algorithms request that there is only the direct acoustic pressure contained in the pressure at any point on the hologram surface, consequently, they cannot be used to reconstruct acoustic source and predict acoustic field directly. To take the reflected pressure into consideration, near-field acoustic holography for semi-free acoustic field based on wave superposition approach is proposed to realize the holographic reconstruction and prediction of the semi-free acoustic field, and the wave superposition approach is adopted as a holographic transform algorithm. The proposed theory and algorithm are realized and verified with a numerical example, and the drawbacks of the general theories and algorithms in the holographic reconstruction and prediction of the semi-free acoustic field are also demonstrated by this numerical example.

Linear polarization holography

Polarization holography is a newly researched field,that has gained traction with the development of tensor theory.It primarily focuses on the interaction between polarization waves and photosensitive materials.The extraordinary capabil-ities in modulating the amplitude,phase,and polarization of light have resulted in several new applications,such as holo-graphic storage technology,multichannel polarization multiplexing,vector beams,and optical functional devices.In this paper,fundamental research on polarization holography with linear polarized wave,a component of the theory of polariz-ation holography,has been reviewed.Primarily,the effect of various polarization changes on the linear and nonlinear po-larization characteristics of reconstructed wave under continuous exposure and during holographic recording and recon-struction have been focused upon.The polarization modulation realized using these polarization characteristics exhibits unusual functionalities,rendering polarization holography as an attractive research topic in many fields of applications.This paper aims to provide readers with new insights and broaden the application of polarization holography in more sci-entific and technological research fields.

Study of structure-property relationship of semiconductor nanomaterials by off-axis electron holography

As the scaling down of semiconductor devices, it would be necessary to discover the structure-property relationship of semiconductor nanomaterials at nanometer scale. In this review, the quantitative characterization technique off-axis electron holography is introduced in details, followed by its applications in various semiconductor nanomaterials including group IV, compound and two-dimensional semiconductor nanostructures in static states as well as under various stimuli. The advantages and disadvantages of off-axis electron holography in material analysis are discussed, the challenges facing in-situ electron holographic study of semiconductor devices at working conditions are presented, and all the possible influencing factors need to be considered to achieve the final goal of fulfilling quantitative characterization of the structure-property relationship of semiconductor devices at their working conditions.

Wide-Field Vibrational Phase Contrast Imaging Based on Coherent Anti-Stokes Raman Scattering Holography

We propose and implement a wide-field vibrational phase contrast detection to obtain imaging of imaginary components of third-order nonlinear susceptibility in a coherent anti-Stokes Raman scattering （CARS） microscope with full suppression of the non-resonant background. This technique is based on the unique ability of recovering the phase of the generated CARS signal based on holographic recording. By capturing the phase distributions of the generated CARS field from the sample and from the environment under resonant illumination, we demonstrate the retrieval of imaginary components in the CARS microscope and achieve background free coherent Raman imaging.

Speckle reduction by selective spatial-domain mask in digital holography

An improved method of using a selective spatial-domain mask to reduce speckle noise in digital holography is proposed.The sub-holograms are obtained from the original hologram filtered by the binary masks including a shifting aperture for being reconstructed. Normally, the speckle patterns of these sub-reconstructed images are different. The speckle intensity of the final reconstructed image is suppressed by averaging the favorable sub-reconstructed images which are selected based on the most optimal pixel intensity sub-range in the sub-holograms. Compared with the conventional spatial-domain mask method, the proposed method not only reduces the speckle noise more effectively with fewer sub-reconstructed images,but also reduces the redundant information used in the reconstruction process.

Novel Method for Selection of Regularization Parameter in the Near-field Acoustic Holography

Because of the ill-posedness of the near-field acoustic holography（NAH）,the regularization method is required to stabilize the computational process of NAH.The regularization effect is related to how to select the parameter correctly and effectively.However the L-curve method commonly used for the selection of regularization parameters has the disadvantages of wrong selection and incorrect selection,which influences the application of NAH.For the purpose of solving the problems existed in the L-curve method,the （？）-curve method is introduced into the field of NAH,and the performance applied to NAH directly is analyzed on the basis of equivalent source method-based NAH.However,it is found out via investigations that the（？）-curve method in NAH also has the problem of wrong selection and is unable to choose the regularization parameter correctly.In order to select the parameter correctly and effectively,a novel method for selecting regularization parameters is proposed based on the original（？）-curve method,which can be called improved （？）-curve method.In the proposed method the regularization parameters are discretized linearly between the largest singular value and the smallest singular value,and the solution norm and the residual norm corresponding to these regularization parameters are also described in a linear coordinate instead of in a lg-lg coordinate,which are the two main differences compared with the L-curve and with the original（？）-curve method.In linear coordinate and using the linearly discretized regularization parameters,the solution norm is a monotonically decreasing function of the residual norm as the increase of the regularization parameter,moreover the curve is convex everywhere.So the regularization parameters can be selected correctly and effectively based on the improved（？）-curve method.Then a numerical simulation is done with a simply supported plate to verify the validity of the proposed method.Experiments with two actual sources,a clamped plate and the double speakers,are carried out to do a further demonstration.The simulation result as well as the experimental result shows that the improved（？）-curve method is efficacious and has some advantages over the L-curve method and the original（？）-curve method.The proposed novel method is able to avoid the problem of wrong selection and to select the regularization parameter correctly even if the curve is smooth.