Complex Amplitude Distribution Research Articles

Measurement of moving objects with phase-shifting digital holography using liquid crystal retarder

We propose a phase-shifting digital holography (DH) method that uses a liquid crystal (LC) retarder for use in the measurement of moving objects. Because LCs are birefringent, they can be used as waveplates for phase-shifting operations. In addition, the phase retardation can be adjusted by varying the LC drive voltage. Mechanical operations are unnecessary in phase shifting when using LCs, but fast interference fringe measurements are possible. The proposed method can be realized by incorporating the LC retarder into a conventional interferometer and is both simple and inexpensive. We performed experiments to verify the effectiveness of the proposed method and confirmed that the method is effective for imaging of the complex amplitude distributions of moving objects.

Adaptive background interference removal for Fourier ptychographic microscopy.

Fourier ptychographic microscopy (FPM) is a recently proposed computational imaging method that achieves both high resolution (HR) and wide field of view. In the conventional FPM model, the sample is assumed to be a 2D thin layer, and a series of low-resolution images at different illumination angles is used for HR image reconstruction. However, in practice, the sample complex amplitude distribution is usually mixed with some unknown background interferences. These background interferences may result from inhomogeneous media distribution or other defocusing layers, etc. The background interference will significantly degrade FPM reconstruction results, but so far it is not considered in the conventional FPM algorithm. Here, we propose a method that adaptively separates background interferences for each illumination angle. Experimental results show that the proposed method has a faster convergence speed and better reconstruction accuracy than the conventional FPM model.

Hyperbolic accelerating beams and their relation with Hermite-Gaussian beams.

We derive the initial distributions of phase and complex amplitude of accelerating beams with arbitrary predesigned hyperbolic trajectories using the caustic-design method and explore the relation between these beams and Hermite-Gaussian beams. The results show the hyperbolic accelerating beams are a larger class of beams than Hermite-Gaussian beams. When the bending parameter is an integer, the hyperbolic accelerating beams have a similar initial complex amplitude distribution and almost the same propagating characteristics as Hermite-Gaussian beams. Through the analysis of the ray-based method, we also derive an approximate expression for the initial complex amplitude of Hermite-Gaussian beams after introducing an amplitude distribution function. Although the proposed approximate expressions of complex amplitude are more complex than the usually used Hermite-Gaussian function, they explicitly indicate the information on local amplitude, wave vector, and internal ray structure (including caustics) of these beams and thus provide us clearer geometrical insights into these beams.

Asymmetric Color Image Cryptosystem Using Detour Cylindrical-Diffraction and Phase Reservation & Truncation

Recently, color image encryption has attracted extensive research interests. However, challenging issues, such as linearity, complex-valued output, and information disclosure, remain. To address these issues, we propose an asymmetric color image cryptosystem by using detour cylindrical-diffraction and phase reservation and truncation (PRT). In this cryptosystem, a complex combination of two color components of a color image is encrypted through a detour cylindrical-diffraction process with double random phase masks, which are located on the input and intermediate surfaces. The diffraction distribution of complex amplitude is separated into phase and amplitude parts using PRT. The phase parts are saved as asymmetric keys, while the two amplitude parts are combined with another color component and saved as ciphertext, respectively. The asymmetric detour cylindrical-diffraction destroys the linearity of the proposed cryptosystem and solves the issue of information disclosure. Meanwhile, the PRT ensures that the cryptosystem is asymmetric and has amplitude-only output, which further destroys the linearity. Therefore, the three issues in color image encryption are resolved. Numerical simulation results validate the effectiveness and flexibility of the proposed cryptosystem.

Double-channel angular-multiplexing polarization holography with common-path and off-axis configuration.

We propose a double-channel angular-multiplexing polarization holographic imaging system with common-path and off-axis configurations. In the system, its input plane is spatially divided into three windows: an object window and two reference windows, and two orthogonal linear polarizers are attached, respectively, on the two reference windows; a two-dimensional cross grating is inserted between the input and output planes of the system. Thus the object beam passing through the object window and the two orthogonal polarized reference beams passing through the two reference windows can overlap each other at the output plane of the system and form a double-channel angular-multiplexing polarization hologram (DC-AM-PH). Using this system, the complex amplitude distributions of two orthogonal polarized components from an object can be recorded and reconstructed by one single-shot DC-AM-PH at the same time. Theoretical analysis and experimental results demonstrated that the system can be used to measure the Jones matrix parameters of polarization-sensitive or birefringent materials.

One-shot time-resolved holographic polarization microscopy for imaging laser-induced ultrafast phenomena

A time-resolved holographic polarization microscopy, based on angular multiplexing holographic technique, is proposed for imaging ultrafast phenomena in polarization-sensitive transparent materials. This method can retrieve and image the complex amplitude distributions of two orthogonal polarization components of two sequential vector wavefronts with ultrashort time interval by a single short recording. Some experimental results for imaging the pulse laser induced ultrafast events based on the method are given. It is demonstrated that this technique may provide a potential tool for characterizing ultrafast processes in polarization-sensitive materials, especially in the non-reproducible experiment conditions.

Multiwavelength digital holography with wavelength-multiplexed holograms and arbitrary symmetric phase shifts

We propose multiwavelength in-line digital holography with wavelength-multiplexed phase-shifted holograms and arbitrary symmetric phase shifts. We use phase-shifting interferometry selectively extracting wavelength information to reconstruct multiwavelength object waves separately from wavelength-multiplexed monochromatic images. The proposed technique obtains systems of equations for real and imaginary parts of multiwavelength object waves from the holograms by introducing arbitrary symmetric phase shifts. Then, the technique derives each complex amplitude distribution of each object wave selectively and analytically by solving the two systems of equations. We formulate the algorithm in the case of an arbitrary number of wavelengths and confirm its validity numerically and experimentally in the cases where the number of wavelengths is two and three.

Resolution and quality enhancement in terahertz in-line holography by sub-pixel sampling with double-distance reconstruction.

We demonstrate the enhancement of resolution and image quality in terahertz (THz) lens-free in-line digital holography by sub-pixel sampling with double-distance reconstruction. Multiple sub-pixel shifted low-resolution (LR) holograms recorded by a pyroelectric array detector (100 μm × 100 μm pixel pitch, 124 × 124 pixels) are aligned precisely to synthesize a high-resolution (HR) hologram. By this method, the lateral resolution is no more limited by the pixel pitch, and lateral resolution of 150 μm is obtained, which corresponds to 1.26λ with respect to the illuminating wavelength of 118.8 μm (2.52 THz). Compared with other published works, to date, this is the highest resolution in THz digital holography when considering the illuminating wavelength. In addition, to suppress the twin-image and zero-order artifacts, the complex amplitude distributions of both object and illuminaing background wave fields are reconstructed simultaneously. This is achieved by iterative phase retrieval between the double HR holograms and background images at two recording planes, which does not require any constraints on object plane or a priori knowledge of the sample.

Multilevel recording of complex amplitude data pages in a holographic data storage system using digital holography.

A holographic data storage system using digital holography is proposed to record and retrieve multilevel complex amplitude data pages. Digital holographic techniques are capable of modulating and detecting complex amplitude distribution using current electronic devices. These techniques allow the development of a simple, compact, and stable holographic storage system that mainly consists of a single phase-only spatial light modulator and an image sensor. As a proof-of-principle experiment, complex amplitude data pages with binary amplitude and four-level phase are recorded and retrieved. Experimental results show the feasibility of the proposed holographic data storage system.

Linear phase encoding for holographic data storage with a single phase-only spatial light modulator

A linear phase encoding is presented for realizing a compact and simple holographic data storage system with a single spatial light modulator (SLM). This encoding method makes it possible to modulate a complex amplitude distribution with a single phase-only SLM in a holographic storage system. In addition, an undesired light due to the imperfection of an SLM can be removed by spatial frequency filtering with a Nyquist aperture. The linear phase encoding is introduced to coaxial holographic data storage. The generation of a signal beam using linear phase encoding is experimentally verified in an interferometer. In a coaxial holographic data storage system, single data recording, shift selectivity, and shift multiplexed recording are experimentally demonstrated.

基于交替相移掩模矢量空间像的偏振像差检测方法

In the single-beam illuminating 3PIE (ptychographic iterative engine)method,the specimen is vertically illuminated without considering the influence of oblique illumination on the reconstruction result.In this paper,a dual-beam illuminating 3PIE method is proposed on the basis of the single-beam illuminating 3PIE method,and the simulation result shows that the reconstructed images are influenced by the phase inclination factor of the initial guessed illumination light beam.In the process of iterative recovery by the proposed method,two light beams are used to update the complex amplitude distribution of the same specimen area.The proposed method is demonstrated theoretically and experimentally. The results verify that the method can improve the convergence speed while weakening crosstalk between different specimen slices,and it is suitable for three-dimensional depth resolved imaging.

Dispersion of a Femtosecond Wave Packet Focused by an Axicon. A Scaling Parameter

We investigate the propagation of a femtosecond wave packet focused by an axicon in the linear medium. We introduce a scaling parameter for the problem of the Bessel–Gaussian beam formation in the femtosecond light. This parameter is based on a multiplicative representation for spatiotemporal distribution of the light-field complex amplitude. In this approach, the systematic error for estimating the wave-packet energetic parameters is determined. The approximate method presented can be used for analyzing a femtosecond laser-pulse filamentation under axicon focusing.

Simple method for generation of vector beams using a small-angle birefringent beam splitter.

A simple and practical system for generation of vector beams with arbitrary polarization and complex-amplitude distributions is proposed. The system mainly consists of a scalar computer-generated hologram (CGH), a small-angle birefringent beam splitter (BBS), and a Fourier lens with a filtering aperture (FA). The CGH is placed in front of the Fourier lens. The BBS is inserted between the CGH and the Fourier lens. When the CGH specially designed according to the method described in this Letter is illuminated by a plane beam or a Gaussian beam, a desired vector beam can be obtained through the FA placed at the back focal plane of the Fourier lens. Because no coupling element and half-wave plate are to be placed between the CGH and the BBS, the extinction ratios of both the two orthogonal polarization components for the vector beam can be better than 10(-5) and so high-quality vector beams can be generated.

Computer-generated hologram calculation for real scenes using a commercial portable plenoptic camera

This paper shows the process used to calculate a computer-generated hologram (CGH) for real scenes under natural light using a commercial portable plenoptic camera. In the CGH calculation, a light field captured with the commercial plenoptic camera is converted into a complex amplitude distribution. Then the converted complex amplitude is propagated to a CGH plane. We tested both numerical and optical reconstructions of the CGH and showed that the CGH calculation from captured data with the commercial plenoptic camera was successful.

Optical Encryption and Authentication Based on Phase Retrieval and Sparsity Constraints

Complex holographic schemes are usually required to obtain complex-valued encrypted images that are used for verification in previously proposed authentication approaches based on photon-counting imaging and double-random-phase encoding (DRPE). In this paper, we propose an optical information encryption and authentication system by integrating the classical optical DRPE with a modified iterative phase retrieval algorithm using 2-D median filtering. Only the intensity of the encrypted data needs to be recorded during the optical encryption process, and a private phase distribution is generated by combining iterative phase retrieval and 2-D median filtering. Sparse representation for the phase distribution, but not for a complex-amplitude distribution, is used for decryption and verification. Simulation results demonstrate the validity of the proposed approach.

Accelerating nondiffracting beams

We present a set of beams which combine the properties of accelerating beams and (conventional) diffraction-free beams. These beams can travel along a desired trajectory while keeping an approximately invariant transverse profile, which may be (higher-order) Bessel-, Mathieu- or parabolic-nondiffracting-like beams, depending on the initial complex amplitude distribution. A possible application of these beams presented here may be found in optical tapping field. For example, a higher-order Bessel-like beam, which has a hollow (transverse) pattern, is suitable for guiding low-refractive-index or metal particles along a curve. (C) 2015 Elsevier B.V. All rights reserved.

On the Forming of Orthogonal Beams by Planar Array Antennas

A general approach to determination of geometrical parameters of planar array antennas designed for forming of orthogonal beams steered in the nodes of a Cartesian periodic lattice specified in the space of direction cosines is proposed. The proof of orthogonality of the complex amplitude distributions and appropriate array factors for the arrays constructed according to the proposed approach is given. The role of the array element patterns in providing the beam pattern orthogonality is underlined. The issue of the number of the array elements necessary for forming of the specified number of beams is discussed. A few demonstrative examples of the beam clusters and appropriate configurations of the arrays where the number of the elements is equal to the specified number of the beams are considered.

Superresolution of interference fringes in parallel four-step phase-shifting digital holography

A superresolution method for interference fringes obtained by parallel four-step phase-shifting digital holography is proposed. A complex amplitude distribution of an object wave is derived from a recorded hologram by parallel phase-shifting interferometry using two pixels without any interpolation procedures. Multiple distributions are derived by changing one of the two pixels when conducting phase-shifting interferometry. The angular spectrum distribution of the object wave is obtained by both the Fourier transforms and synthesis of the spectrum distribution from the Fourier-transformed images in the spatial frequency domain. Available space bandwidth is extended to half of that of an image sensor.

Double-channel vector spatial light modulator for generation of arbitrary complex vector beams

We propose an approach for implementation of an arbitrary vector beam based on a vector spatial light modulator (VSLM), which is simply composed by a phase-only spatial light modulator (SLM) and a composed half-wave plate with checkerboard structure. In combination with a four-phase encoding algorithm, the VSLM can transform a linear polarized Gaussian beam or a plane wave into a vector beam with both arbitrary spatial polarization and complex amplitude distributions in two dimensions. It is demonstrated that the VSLM can directly transform pure phase values into two orthogonal polarized complex values with high-diffraction efficiency. Compared with the existing methods for generation of vector beams with SLMs, our approach is on-axis and common-path with simple structure and only involves the zero-order diffraction. The proposed structure is also easier to make an integration and design portable device since it abstains from using optical elements such as special gratings, prisms, and reflectors.

Effect of intensity quantization level in parallel phase-shifting digital holography

Parallel phase-shifting digital holography (PPSDH) enables the instantaneous recording of three-dimensional fields. The three-dimensional field can be reconstructed using a computer by numerical scalar wave propagation. In PPSDH, we record a space-division multiplexed hologram that includes the required phase retardation in the spatial distribution of the reference wave and then interpolate the data at blanked pixels for each phase retardation to obtain the complex amplitude distribution of an object wave. The recorded quality of the multiplexed hologram influences the reconstruction quality. In this study, we investigate the effect of the intensity quantization of a multiplexed hologram on the reconstruction quality. We compare the influence of intensity quantization in PPSDH with that in the conventional phase-shifting method. Random noise is also added to the multiplexed hologram. The required intensity quantization level is helpful for selecting a digital image sensor.