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Tomography has had an important impact on the physical, biological, and medical sciences. To date, most tomographic applications have been focused on 3D scalar reconstructions. However, in some crucial applications, vector tomography is required to reconstruct 3D vector fields such as the electric and magnetic fields. Over the years, several vector tomography methods have been developed. Here, we present the mathematical foundation and algorithmic implementation of REal Space Iterative REconstruction for Vector tomography, termed RESIRE-V. RESIRE-V uses multiple tilt series of projections and iterates between the projections and a 3D reconstruction. Each iteration consists of a forward step using the Radon transform and a backward step using its transpose, then updates the object via gradient descent. Incorporating with a 3D support constraint, the algorithm iteratively minimizes an error metric, defined as the difference between the measured and calculated projections. The algorithm can also be used to refine the tilt angles and further improve the 3D reconstruction. To validate RESIRE-V, we first apply it to a simulated data set of the 3D magnetization vector field, consisting of two orthogonal tilt series, each with a missing wedge. Our quantitative analysis shows that the three components of the reconstructed magnetization vector field agree well with the ground-truth counterparts. We then use RESIRE-V to reconstruct the 3D magnetization vector field of a ferromagnetic meta-lattice consisting of three tilt series. Our 3D vector reconstruction reveals the existence of topological magnetic defects with positive and negative charges. We expect that RESIRE-V can be incorporated into different imaging modalities as a general vector tomography method. To make the algorithm accessible to a broad user community, we have made our RESIRE-V MATLAB source codes and the data freely available at https://github.com/minhpham0309/RESIRE-V .

The intensity distributions and statistics of partially coherent light fields with random fluctuations have proven to be more robust than for coherent light. However, its full potential in practical applications has not been realized due to the lack of four-dimensional optical field measurement. Here, a general incoherent modal decomposition method of partially coherent light field is proposed and demonstrated experimentally. The decomposed random modes can be used to, but not limited to, reconstruct average intensity, cross-spectral density, and orthogonal decomposition properties of the partially coherent light fields. The versatility and flexibility of this method allows it to reveal the invariance of light fields and to retrieve embedded information after propagation through complex media. The Gaussian-shell-model beam and partially coherent Gaussian array are used as examples to demonstrate the reconstruction and even prediction of second-order statistics. This method is expected to pave the way for applications of partially coherent light in optical imaging, optical encryption, and antiturbulence optical communication.

As an indispensable complement to an integer vortex beam, the fractional vortex beam has unique physical properties such as radially notched intensity distribution, complex phase structure consisting of alternating charge vortex chains, and more sophisticated orbital angular momentum modulation dimension. In recent years, we have noticed that the fractional vortex beam was widely used for complex micro-particle manipulation in optical tweezers, improving communication capacity, controllable edge enhancement of image and quantum entanglement. Moreover, this has stimulated extensive research interest, including the deep digging of the phenomenon and physics based on different advanced beam sources and has led to a new research boom in micro/nano-optical devices. Here, we review the recent advances leading to theoretical models, propagation, generation, measurement, and applications of fractional vortex beams and consider the possible directions and challenges in the future.

(1) Background: Small objects in Unmanned Aerial Vehicle (UAV) images are often scattered throughout various regions of the image, such as the corners, and may be blocked by larger objects, as well as susceptible to image noise. Moreover, due to their small size, these objects occupy a limited area in the image, resulting in a scarcity of effective features for detection. (2) Methods: To address the detection of small objects in UAV imagery, we introduce a novel algorithm called High-Resolution Feature Pyramid Network Mamba-Based YOLO (HRMamba-YOLO). This algorithm leverages the strengths of a High-Resolution Network (HRNet), EfficientVMamba, and YOLOv8, integrating a Double Spatial Pyramid Pooling (Double SPP) module, an Efficient Mamba Module (EMM), and a Fusion Mamba Module (FMM) to enhance feature extraction and capture contextual information. Additionally, a new Multi-Scale Feature Fusion Network, High-Resolution Feature Pyramid Network (HRFPN), and FMM improved feature interactions and enhanced the performance of small object detection. (3) Results: For the VisDroneDET dataset, the proposed algorithm achieved a 4.4% higher Mean Average Precision (mAP) compared to YOLOv8-m. The experimental results showed that HRMamba achieved a mAP of 37.1%, surpassing YOLOv8-m by 3.8% (Dota1.5 dataset). For the UCAS_AOD dataset and the DIOR dataset, our model had a mAP 1.5% and 0.3% higher than the YOLOv8-m model, respectively. To be fair, all the models were trained without a pre-trained model. (4) Conclusions: This study not only highlights the exceptional performance and efficiency of HRMamba-YOLO in small object detection tasks but also provides innovative solutions and valuable insights for future research. [ABSTRACT FROM AUTHOR]

In the recent decade, the rotational Doppler effect has garnered considerable attention for stimulating the development of applications such as rotational Doppler velocity and topological charge measurements. Previous studies performed measurements under sources with one or multiple amplitude, phase, and polarization modulations. However, the applicability of these schemes is limited by the crucial factor of alignment between the source and object, especially if the magnitude of the source is greater than the object size. Therefore, this study proposes a partially coherent angular velocity measurement model that allows the rotational axes of targets to deviate from the source center and is even less susceptible to external jitters. Accordingly, a proof‐of‐principle experiment to determine the angular velocity under arbitrary alignment conditions is conducted. Tracing the rotational motion by rotating the coherent structure of the source results in a frequency shift—red shift for the same rotation and blue shift for a reverse rotation. The angular velocity vectors (both magnitude and direction) of two anisotropic sub‐Rayleigh objects are successfully measured with ultrahigh precision. The lowest angular velocity is 0.001 r s−1. The average relative error is less than 0.05% with sufficient sampling. Thus, the present findings can be applied to velocity metrology and micromanipulation. [ABSTRACT FROM AUTHOR]

A new power-exponent-phase vortex beam with nonlinear phase winding has shown flexible control freedom compared with conventional vortex beams. In order to further enrich the modulation freedom and expand the ability of self-healing to meet current application requirements, we conducted a detailed study on the characteristics of the Airy transform of the new power-exponent-phase vortex beam. The influences of the Airy function, the power exponent, and the topological charge on normalized intensity and phase distributions are investigated theoretically and experimentally. More importantly, the self-healing properties of the new power-exponent-phase vortex beam with and without the Airy transform are compared. This shows that the new power-exponent-phase vortex beam with the Airy transform exhibits better self-healing ability when obstructed by obstacles. This study has potential applications in optical trapping and free-space optical communication. [ABSTRACT FROM AUTHOR]