Complex Amplitude Distribution Research Articles

Spatially distributed low-cross talk vector beams.

A spatially distributed low-cross talk vector beam refers to a vector beam that exhibits different intensities, phases, and polarization states along the propagation direction. This type of vector beam features low-cross talk between beams on different planes and finds extensive applications in optical communications and related fields. However, current technologies face challenges such as intensity interference at different imaging planes and difficulties in the precise control of phases and polarization states, which affect beam quality. In this study, we investigated the beam propagation process and employed a global optimization strategy to precisely control the intensity and phase distribution of the beam fields. This approach ensures that the beam forms the desired complex amplitude distribution in the target region while effectively suppressing cross talk in non-target regions. We utilized the method to generate two beams with complementary intensities and phases. Subsequently, through an interference optical path, we separated these two beams and converted them into orthogonal polarization states. Finally, by superimposing these two beams, we obtained a spatially varying low-cross talk vector beam. We experimentally validated the beam's different optical characteristics and low-cross talk properties on three planes. Our work opens up new prospects, to the best of our knowledge, for holographic technology with capabilities for ultra-fine depth control and polarization multiplexing.

High-quality phase imaging by phase-shifting digital holography and deep learning

Quantitative phase imaging (QPI) technology is widely used in biomedical imaging and other fields because it can realize exact imaging for transparent phase-type samples, which is of great research significance. The complex amplitude distribution of the object wave obtained by phase-shifting digital holography (PSDH) reproduction can provide phase information for QPI, but its existence of phase wrapping and other problems limits its practical application. Although the traditional phase unwrapping algorithm provides a solution, it has problems such as low unwrapping accuracy or long time running. To solve these problems in QPI, a high-quality phase imaging (HQPI) method by PSDH and deep learning (DL) is proposed, where QPI is achieved by extracting the unknown phase shift using a generalized non-iterative phase shift extraction algorithm and unwrapping the wrapped phase by a DL network. Both numerical simulations and optical experiments verify the feasibility of the method. By comparing with the traditional phase unwrapping algorithm, it is demonstrated that the DL unwrapping method has higher unwrapping accuracy and more efficiency. The results show that the method of HQPI is capable of realizing comparatively fast and accurate QPI.

Arbitrary engineering of spatial caustics with 3D-printed metasurfaces

Caustics occur in diverse physical systems, spanning the nano-scale in electron microscopy to astronomical-scale in gravitational lensing. As envelopes of rays, optical caustics result in sharp edges or extended networks. Caustics in structured light, characterized by complex-amplitude distributions, have innovated numerous applications including particle manipulation, high-resolution imaging techniques, and optical communication. However, these applications have encountered limitations due to a major challenge in engineering caustic fields with customizable propagation trajectories and in-plane intensity profiles. Here, we introduce the “compensation phase” via 3D-printed metasurfaces to shape caustic fields with curved trajectories in free space. The in-plane caustic patterns can be preserved or morphed from one structure to another during propagation. Large-scale fabrication of these metasurfaces is enabled by the fast-prototyping and cost-effective two-photon polymerization lithography. Our optical elements with the ultra-thin profile and sub-millimeter extension offer a compact solution to generating caustic structured light for beam shaping, high-resolution microscopy, and light-matter-interaction studies.

3D fluorescence imaging through scattering medium using transport of intensity equation and iterative phase retrieval.

In this paper, we have proposed a method of three-dimensional (3D) fluorescence imaging through a scattering medium. The proposed method combines the numerical digital phase conjugation propagation after measurement of the complex amplitude distribution of scattered light waves by the transport of intensity equation (TIE) with followed iterative phase retrieval to achieve 3D fluorescence imaging through a scattering medium. In the experiment, we present the quantitative evaluation of the depth position of fluorescent beads. In addition, for time-lapse measurement, cell division of tobacco-cultured cells was observed. Numerical results presented the effective range of the phase amount in the scattering medium. From these results, the proposed method is capable of recovering images degraded by a thin scattering phase object beyond a small phase change approximation.

Cepstrum-based interferometric microscopy (CIM) for quantitative phase imaging

A universal methodology for coding-decoding the complex amplitude field of an imaged sample in coherent microscopy is presented, where no restrictions on any of the two interferometric beams are required. Thus, the imaging beam can be overlapped with, in general, any other complex amplitude distribution and, in particular, with a coherent and shifted version of itself considering two orthogonal directions. The complex field values are retrieved by a novel Cepstrum-based algorithm, named as Spatial-Shifting Cepstrum (SSC), based on a weighted subtraction of the Cepstrum transform in the cross-correlation term of the object field spectrum in addition with the generation of a complex pupil from the combination of the information retrieved from different holographic recordings (one in horizontal and one in vertical direction) where one of the interferometric beams is shifted 1 pixel. As a result, the field of view is tripled since the complex amplitudes of the three interferometric fields involved in the process are retrieved. Proof-of-concept validation of this methodology, named as Cepstrum-based Interferometric Microscopy (CIM), is provided considering an off-axis holographic configuration for retrieving the cross-correlation of the two interferometric complex amplitude fields in a compact quasi-common path Michelson interferometric configuration. Experimental results for different types of phase samples (resolution test targets for step-by-step calibration and demonstration as well as fixed biosamples) are included.

Multi-Mode Vector Light Field Generation Using Modified Off-Axis Interferometric Holography and Liquid Crystal Spatial Light Modulators

The increasing enhancement in the modulation accuracy of spatial light modulators has garnered significant attention towards real-time control technology for light fields based on these modulators. It has been demonstrated that this technology possesses a remarkable capability to generate vector beams with arbitrary complex amplitude distributions. Nevertheless, past studies indicate that the generation of only one vector beam at a time has been observed. The simultaneous generation of numerous vector light fields can give rise to several challenges, including compromised picture quality, limited single-mode operation, and intricate optical path configurations. In pursuit of this objective, we present a novel methodology that integrates the coding methodology of modified off-axis interferometric holography with the idea of optical superposition. This technique facilitates the concurrent generation of several vector beams. In this study, we present a demonstration of the simultaneous creation of twelve vector beams using a single spatial light modulator (SLM) as a proof of concept. Significantly, this technology has the ability to generate an unlimited quantity of vector light fields concurrently under the assumption that the resolution of the SLM does not impose any limitations. The findings indicate that the imaging quality achieved by this technology is of a high standard. Furthermore, it is possible to separately control the beam waist radius, topological charge, polarization order, and extra phase of each beam.

3D digital holographic polarimetry of diffuse optically anisotropic biological tissue object fields

The experimental validation of methods for the digital holographic 3D layer-by-layer reconstruction of complex amplitude distributions in different phase planes of diffuse biological tissue histological section microscopic images with a subsequent reconstruction of azimuth and ellipticity polarization maps is presented. Polarization dependencies of the integral and layer-by-layer vector structure of the laser object field azimuth and ellipticity distributions in two types of biological layer samples—the fibrous myocardium and parenchymal liver—have been investigated. Scenarios and dynamics of changes in the values of statistical moments of the first to fourth orders, which characterize the integral and layer-by-layer polarization maps of diffuse biological tissue histological section microscopic images with different morphological structures, have been determined. Criteria for selecting the polarization components of the object field that are formed by acts of scattering of different multiplicities have been identified. An example of biomedical application in cancer detection of biological tissues is provided.

In-focus quantitative phase imaging from defocused off-axis holograms: synergistic reconstruction framework.

Digital holographic microscopy (DHM) enables the three-dimensional (3D) reconstruction of quantitative phase distributions from a defocused hologram. Traditional computational algorithms follow a sequential approach in which one first reconstructs the complex amplitude distribution and later applies focusing algorithms to provide an in-focus phase map. In this work, we have developed a synergistic computational framework to compensate for the linear tilt introduced in off-axis DHM systems and autofocus the defocused holograms by minimizing a cost function, providing in-focus reconstructed phase images without phase distortions. The proposed computational tool has been validated in defocused holograms of human red blood cells and three-dimensional images of dynamic sperm cells.

Continuous-wave terahertz in-line holographic diffraction tomography with the scattering fields reconstructed by a physics-enhanced deep neural network

Diffraction tomography is a promising, quantitative, and nondestructive three-dimensional (3D) imaging method that enables us to obtain the complex refractive index distribution of a sample. The acquisition of the scattered fields under the different illumination angles is a key issue, where the complex scattered fields need to be retrieved. Presently, in order to develop terahertz (THz) diffraction tomography, the advanced acquisition of the scattered fields is desired. In this paper, a THz in-line digital holographic diffraction tomography (THz-IDHDT) is proposed with an extremely compact optical configuration and implemented for the first time, to the best of our knowledge. A learning-based phase retrieval algorithm by combining the physical model and the convolution neural networks, named the physics-enhanced deep neural network (PhysenNet), is applied to reconstruct the THz in-line digital hologram, and obtain the complex amplitude distribution of the sample with high fidelity. The advantages of the PhysenNet are that there is no need for pretraining by using a large set of labeled data, and it can also work for thick samples. Experimentally with a continuous-wave THz laser, the PhysenNet is first demonstrated by using the thin samples and exhibits superiority in terms of imaging quality. More importantly, with regard to the thick samples, PhysenNet still works well, and can offer 2D complex scattered fields for diffraction tomography. Furthermore, the 3D refractive index maps of two types of foam sphere samples are successfully reconstructed by the proposed method. For a single foam sphere, the relative error of the average refractive index value is only 0.17%, compared to the commercial THz time-domain spectroscopy system. This demonstrates the feasibility and high accuracy of the THz-IDHDT, and the idea can be applied to other wavebands as well.

Untrained network regularized by total variation in single-shot lensless holography

The optical complex-amplitude (CA) distribution of an object contains rich information, providing insights into the object’s optical characteristics such as retardation and absorption. Coaxial lensless holography (CLH) using a learning-based approach offers promise for retrieving CA maps with advantages such as compact setup and single-shot acquisition, while suffers from the laborious and time-consuming acquisition of datasets and labels required for network training. To address this challenge, we propose an untrained neural network with Lp-norm total variation regularization (LTVR-net) by integrating physical model into the learning process. The LTVR-net effectively suppresses twin-image and artifact noises in reconstructing CA images, outperforming traditional methods on quantitative metrics. Besides, the CA retrieval results at different imaging distances consistently exhibit excellent performance, indicating that LTVR-net possesses a distance-resolution-balanced characteristic. This feature holds promise for expanding the application scope of CLH, allowing for more versatile and flexible configurations in various scenarios. Furthermore, the experimental results on biological tissue demonstrate the ability of LTVR-net to reveal fine structures with clear boundaries, highlighting its superiority in biological imaging. These results collectively prove that LTVR-net is an untrained, single-shot, and distance-robust approach capable of achieving high-quality CA retrieval.

Two-step diffraction method for an optical 360° cylindrical holographic display.

We present a two-step diffraction method for an optical 360∘ cylindrical holographic display with a planar spatial light modulator (SLM) and a 45∘ conical mirror. The first step involves layered diffraction of the cylindrical object surface to obtain the complex amplitude distribution on the conical mirror, and the second step is the coordinate transformation, followed by plane-to-plane diffraction to finally obtain the hologram. Numerical simulations and optical experiments show that our proposed method offers improved accuracy in the propagation process compared with the previous method; furthermore, it enables better quality of reconstruction, particularly at large radius of object surface. We believe it is a solid step toward practicality for a cylindrical holographic display.

Multiplexed superresolution phase microscopy with transport of intensity equation

Resolving power in imaging systems, optical microscopy in particular, is limited by several factors being diffraction probably the most important one. Digital holographic microscopy (DHM) allows diffraction-limited quantitative phase imaging (QPI) with high accuracy by retrieving complex fields using interferometric recording, and a bunch of superresolution (SR) techniques have been widely reported through the past. However, there are additional ways to retrieve the complex amplitude distribution (such as the transport of intensity equation – TIE), having additional advantages over interferometric recording. We present how to increase the resolution limit in low/medium numerical aperture (NA) microscope objectives by using time and angular multiplexing while providing quantitative phase imaging (QPI) retrieved by TIE algorithm. This is, to the best of our knowledge, the first time that the resolution limit is experimentally improved in combination with TIE for phase retrieval in QPI. The proposed approach is validated in a real microscope embodiment (Olympus IX81) using resolution targets for quantitative resolution analysis and verifying a resolution gain factor of 2 from an experimental point of view.

Compressed phase coding-based optical image encryption

With the development of artificial intelligence technology, the traditional inflexible optical image encryption system has been difficult to resist security attacks such as chosen-plaintext attack and known-plaintext attack, and its security has been greatly challenged. Therefore, an optical image encryption method based on compressed phase coding is proposed, in which a spatial light modulator (SLM) is used to encode the phase of the optical system randomly, and then combined with the measurement matrix in the single pixel sampling process to build a flexible key system. In the encryption process, a phase-only SLM is firstly implemented to realize phase encoding of the original plaintext image and loading the phase key. Then the modulated reference light is implemented to further hide the complex amplitude distribution of the encrypted image. Finally, the encoded object light and reference light are coherently superimposed in the digital micromirror device (DMD), and the inner product operation is carried out with the measurement matrix to realize further encryption and collected by the single pixel detector. Both simulation and experiment proved that the proposed compressed phase coding-based image encryption system is similar to "one time one pad" cryptographic system, which greatly improves the security of the optical encryption system.

Review of development for ptychography algorithm

With the development of synchrotron radiation technology and the improvement of light source coherence, ptychography has developed rapidly. Ptychography algorithm solves the problems of slow convergence and easily falls into the local optimal solution and stagnation of the traditional coherent diffraction imaging algorithm. It has the advantages of large imaging field of view, robustness of algorithm, high tolerance to error and wide range of applications, and is becoming a hot research direction in the field of coherent diffraction imaging. Ptychography reconstructs the complex amplitude distribution and illumination light of the sample by iterative algorithms, which can theoretically reach the resolution of the diffraction limit. It has excellent applications in the fields of wavefront detection, phase imaging and optical metrology. This paper first introduces the background of the proposed ptychography algorithm and briefly describes the problem of coherent diffraction imaging algorithm and its development, and then summarizes the development of ptychography algorithm in detail, mainly including the mainstream algorithm of ptychography and its kernel. This paper then describes in detail the improvement of algorithms corresponding to the improvement of the efficiency of ptychography experiments, correction of position errors and the effect of illumination light multi-modal, and elaborates the algorithm flow. After analyzing the possible intersection of diffraction imaging and neural networks in the field of artificial intelligence, this paper introduces new algorithms with combining ptychography with artificial intelligence. New algorithms with combining ptychography with neural networks will have new potential applications in generality, accuracy and robustness. Finally, a specific parallelization implementation of the ptychography algorithm and common software packages are presented. The logic for writing the parallelization of the algorithm implementation of each package and the corresponding advantages and disadvantages of the packages are described in detail. The characteristics and performance of each package are then listed for reference. This paper helps to establish a global perspective of the algorithm itself, artificial intelligence and computational methods in the field of ptychography, and presents an important reference for systematically developing the ptychography method.

Time-Resolved Four-Channel Jones Matrix Measurement of Birefringent Materials Using an Ultrafast Laser.

A method for ultrafast time-resolved four-channel Jones matrix measurement of birefringent materials using an ultrafast laser is investigated. This facilitated the acquisition of a four-channel angular multiplexing hologram in a single shot. The Jones matrix information of a birefringent sample was retrieved from the spatial spectrum of a hologram. The feasibility of this approach was established by measuring the Jones matrix of starch granules in microfluidic chips and the complex amplitude distribution and phase delay distribution of liquid crystal cell at different voltages. Moreover, when the picosecond laser was switched to a femtosecond laser, ultrafast measurements were possible provided that the time interval between two detection pulses was larger than the pulse width.

Method for generating planar computer-generated hologram at free viewpoint from cylindrical object light

Computer-generated holography (CGH) is an ideal three-dimensional (3D) display technology, and head-mounted displays (HMDs) using CGH are expected to become the next-generation display devices without eye strain, which is called holographic HMDs (holo-HMDs). However, the CGH computational load is too much for a holo-HMD, which has limited processing power. We have devised a method that calculates the cylindrical object light on a sender, broadcasts the object light data to multiple holo-HMDs, and generates holograms matched to the planar display device on the holo-HMD. The cylindrical object light calculations, which take up most of the computational load, are performed on a high-performance computer with sufficient computational power. The cylindrical object light is transformed into an object light on the plane in accordance with the motion of the holo-HMD. The phase difference information between the complex amplitude distribution of the cylindrical object light and the object light on the plane corresponding to a free viewpoint position must be corrected. Using this method, objects placed near the center of the cylinder can be observed from a wide area, making it possible to support 3D image observation with multiple holo-HMDs. Experiments using an actual optical system demonstrated that planar transform was performed and that the computational load on a holo-HMD side was very small.

PyDHM: A Python library for applications in digital holographic microscopy.

pyDHM is an open-source Python library aimed at Digital Holographic Microscopy (DHM) applications. The pyDHM is a user-friendly library written in the robust programming language of Python that provides a set of numerical processing algorithms for reconstructing amplitude and phase images for a broad range of optical DHM configurations. The pyDHM implements phase-shifting approaches for in-line and slightly off-axis systems and enables phase compensation for telecentric and non-telecentric systems. In addition, pyDHM includes three propagation algorithms for numerical focusing complex amplitude distributions in DHM and digital holography (DH) setups. We have validated the library using numerical and experimental holograms.

37‐3: Student Paper: Method of Color Amplitude‐Only Hologram Generation for Speckle Noise Suppression

In this paper, a calculation method of color amplitude‐only computer‐generated hologram (CGH) that can suppress speckle noise is proposed. Firstly, the amplitude information of the red, green and blue channels of the object is extracted. Secondly, to reduce the speckle noise, the convolution result of the amplitude information with a constrained random phase is used as the complex amplitude distribution of the object. Then, the multi‐frame amplitude‐only CGHs for each color channel of the object are generated by using the modified double‐step Fresnel diffraction algorithm. Finally, the digital micromirror device is used to refresh the multi‐frame amplitude‐only CGHs, and the speckle noise is suppressed by using the time‐averaging method. The validity of the computational method is verified.

Optimized Iterative Algorithm to Generate Computer-Generated Holograms Based on the Intermediate Angular-Spectrum Method

The intermediate angular-spectrum method is an efficient way to calculate computer-generated holograms without zero-padding and cropping operation. In this paper, we present an optimized iteration algorithm to improve the reconstruction quality in the intermediate angular-spectrum method. The quadratic phase is multiplied with the target image as the initial complex amplitude distribution to suppresses the speckle noise and the freedom domain is introduced in the image plane to improve the reconstruction quality. Numerical simulations and optical experiments are performed to demonstrate that proposed method is an effective method for high-quality reconstruction. It is expected that proposed method could be widely applied in the holographic field in the future.

Adjusted EfficientNet for the diagnostic of orbital angular momentum spectrum.

Orbital angular momentum (OAM) is one of multiple dimensions of beams. A beam can carry multiple OAM components, and their intensity weights form the OAM spectrum. The OAM spectrum determines complex amplitude distributions of a beam and features unique characteristics. Thus, measuring the OAM spectrum is of great significance, especially for OAM-based applications. Here we employ a deep neural network combined with a phase-only diffraction optical element to measure the OAM spectrum. The diffraction optical element is designed to diffract incident beams into distinct patterns corresponding to OAM distributions. Then, the EfficientNet, a kind of deep neural network, is adjusted to adapt and analyze the diffraction pattern to calculate the OAM spectrum. The favorable experimental results show that our proposal can reconstruct the OAM spectra with high precision and speed, works well for different numbers of OAM channels, and is also robust to Gaussian noise and random zooming. This work opens a new, to the best of our knowledge, ability for OAM spectrum recognition and will find applications in a number of advanced domains including large capacity optical communications, quantum key distribution, optical trapping, rotation detection, and so on.