An analytical approach is developed for calculating a phase diffraction axicon with angularly variable spatial frequency that generates a prescribed light curve without iteratively solving an inverse design problem: the axicon frequency function is obtained directly from the polar equation of the target curve. When the axicon is combined with a lens, the intended curve is formed in the focal plane (Fraunhofer region), whereas in the Fresnel zone the intensity pattern is closely related to the curve’s evolute. We systematize this correspondence for rings, ellipses, spirals and polygonal curves, and derive analytical parameter bounds associated with the appearance of inflection points that qualitatively reshape both the evolute and the diffracted field (including hybrid curve–evolute patterns and “rose”-type contours). The qualitative outcome depends on the curve class/type. For a convex curve without inflections the expected curve is formed in in the far field (or in the focal plane), whereas the Fresnel intensity envelope follows the evolute. If the curve has peculiarities, especially inflection points with unbounded evolute branches, hybrid curve–evolute structure appears, and the focal pattern may itself resemble the evolute. For ellipses and polygonal families we analytically identify parameter intervals that mark this transition. The approach is verified experimentally for polygonal axicons, with attention to fabrication tolerances and to matching camera planes with the simulated propagation distances. Measured intensity distribution patterns agree with the corresponding simulations for both convex contours and curves that contain inflection points. The results are of fundamental interest and of practical value for optical trapping and laser surface structuring, where a compact phase element should deliver a controlled bright contour at a chosen working distance.

Diffractive optical elements (DOEs) represent a revolutionary advancement in modern optics, offering unparalleled versatility and efficiency in various applications. Their significance lies in their ability to manipulate light waves with intricate patterns, enabling functionalities beyond what traditional refractive optics can achieve. DOEs find widespread use in fields such as laser beam shaping, holography, optical communications, and imaging systems. By precisely controlling the phase and amplitude of light, DOEs can generate complex optical structures, correct aberrations, and enhance the performance of optical systems. Moreover, their compact size, lightweight nature, and potential for mass production make them indispensable in designing compact and efficient optical devices for diverse industrial and scientific applications. From improving the performance of laser systems to enabling innovative display technologies, DOEs continue to drive advancements in modern optics, promising even more exciting possibilities in the future. In this review, the critical importance of DOEs is illuminated and explore their profound implications in the contemporary era.

Hyperspectral imaging serves as a powerful tool for environmental studies, enabling the capture of significant properties in the objects being analyzed. These hidden properties may not be discernible through traditional RGB analysis, thus enhancing the distinguishability of target classes. Machine learning (ML) algorithms are widely utilized for processing hyperspectral data in tasks such as image classification or segmentation. Despite the rich hyperspectral feature space, ML-based approaches often struggle with the challenges posed by varying outdoor lighting conditions, leading to instability in the developed solutions. Furthermore, traditional segmentation methods designed for RGB images need to be adapted to ensure robust performance when applied to hyperspectral images (HSI). This work proposes a robust method for the classification of HSI in the outdoor environment under varying lighting conditions. A calibration procedure for hyperspectral sensor sensitivity has been proposed, ensuring improved quality of input data and, consequently, enhanced performance of models in solving hyperspectral image classification tasks. The paper also proposes a novel architecture, the Deep Spectral Spatial Transformer (DSST), which is employed as the classifier. This architecture leverages a deeper feature extractor to ensure robustness in various lightning conditions. Among these, standardization within individual channels yielded the best results. The applicability of the proposed approach is validated in the weed detection task in an agricultural field. The data collected were captured using a pushbroom hyperspectral sensor. A series of comparative experiments were conducted on a range of classification algorithms, encompassing both traditional ML algorithms and contemporary neural network architectures developed in recent years. The proposed DSST architecture demonstrated superior performance metrics, with values of 0.911 and 0.907 on F1-Score and Accuracy, respectively.

We propose a method for designing diffractive optical elements (DOEs) with a smooth phase function generalizing harmonic diffractive lenses and intended for generating a prescribed intensity distribution at several harmonic wavelengths. In this method, the phase function is represented as an expansion over a certain set of smooth and differentiable functions. The expansion coefficients are considered as optimization parameters and are calculated using a gradient method from the condition of minimizing an error function describing the deviation of the generated intensity distribution from the prescribed one. We present examples of calculating harmonic DOEs with phase functions modulo 2πM, M>1 represented as a sum of B-splines. We show that in order to obtain good performance of a harmonic DOE, the error function has to take into account not only the intensity distribution generated at the central wavelength but also the distributions formed at the other harmonic wavelengths of interest. The obtained theoretical results are confirmed by the results of an experimental investigation, including the fabrication of the designed harmonic DOE using the direct laser writing technique and measurement of the generated intensity distributions.

This article proposes an approach to the analysis of high-resolution hyperspectral images in the applied problem of analyzing the state of river waters. This method allows you to detect blooming or contamination of water by foreign substances. High-resolution hyperspectral images were obtained using a hyperspectrometer mounted on a small unmanned aerial vehicle. The difference between the spectra of river areas with different intensity of algal blooms is demonstrated. Samples of river water were taken, chemical analysis was carried out, which confirmed the different content of magnesium and calcium in all samples, corresponding to the intensity of algal blooms in the water. The effectiveness of using machine learning algorithms and the construction of index images for the classification of water areas with different intensity of algal blooms is shown.

The paper presents studies on the correctness of the application of the simplified Boer formula for estimating the components of the angular velocity vector of the spacecraft using the example of the small ISOI spacecraft (SXC3-219). The simplification consists in neglecting the total derivative of the induction vector of the Earth's magnetic field in time compared to the local derivative. This is due to the fact that measurements are carried out quite often. Therefore, the magnetic induction vector in two adjacent dimensions can be considered unchanged. The aim of the work is to estimate the error in determining the angular velocity due to this simplification. The presented results show the admissibility of neglecting the full derivative, provided that the measurement frequency is sufficient. Reference metrological tests were carried out, in which a gyroscopic angular velocity vector meter was selected as the reference measuring instrument. The errors in the estimates of micro-accelerations and the control moment, which are a consequence of the error in determining the angular velocity, are calculated.

A short wave infrared range (SWIR) imaging system using a lens, rotating substrate with applied Walsh matrices, single photodiode and a 10-bit ADC has been proposed. The possibility of using the Walsh function for encoding and restoring an optical signal is shown. A description of the design of the developed system is presented. The parameters of the structure of an encoding disk suitable for production at a circular laser recording station have been calculated. The quality of image restoration was assessed, according to which the structural similarity of the original image and the restored one is quite high, which indicates that the both images are almost identical.

We study the transformation of the analyzed object by a variety of spatial filters including bandpass, differential, radial filters, various types of vortex filters, and Hilbert filters. Advantages and disadvantages of different filters in terms of clarity and direction-invariance of edge extraction, as well as the energy efficiency are numerically demonstrated. Based on the results obtained, multi-order optical spatial vortex filters with different parameters are developed for simultaneously extracting contours of various object parts. We show that a multi-order filter makes it possible to form a set of images in one plane with a clearly defined contour, object corners and various parts of the contour. Numerical and experimental testing of 4- and 5-channel spatial vortex filters of various types was applied for test objects. A possibility of using the proposed filters to simultaneously highlight the edges of the entire image and various parts of the image in order to extract more features from the analyzed image is shown.

The paper investigates the accuracy of the angular velocity estimation based on measurements of the components of the induction vector of the Earth's magnetic field. A comparative analysis of angular velocity estimates using the Boer formula, the derivative of the induction vector of the Earth's magnetic field and direct measurements of the components of the angular velocity vector using a gyroscopic sensor for the ISOI small spacecraft (SXC3-219) is carried out. The results obtained make it possible to investigate the accuracy of estimates of the angular velocity of a small spacecraft in various ways to improve the quality of its target tasks.

This paper presents findings from a spaceborne Earth observation experiment utilizing a novel, ultra-compact hyperspectral imaging camera aboard a 3U CubeSat. Leveraging the Offner optical scheme, the camera’s hyperspectrometer captures hyperspectral images of terrestrial regions with a 200 m spatial resolution and 12 nanometer spectral resolution across a 400 to 1000 nanometer wavelength range, covering 150 channels in the visible and near-infrared spectrums. The hyperspectrometer is specifically designed for deployment on a 3U CubeSat nanosatellite platform, featuring a robust all-metal cylindrical body of the hyperspectrometer, and a coaxial arrangement of the optical elements ensures optimal compactness and vibration stability. The performance of the imaging hyperspectrometer was rigorously evaluated through numerical simulations prior to construction. Analysis of hyperspectral data acquired over a year-long orbital operation demonstrates the 3U CubeSat’s ability to produce various vegetation indices, including the normalized difference vegetation index (NDVI). A comparative study with the European Space Agency’s Sentinel-2 L2A data shows a strong agreement at critical points, confirming the 3U CubeSat’s suitability for hyperspectral imaging in the visible and near-infrared spectrums. Notably, the ISOI 3U CubeSat can generate unique index images beyond the reach of Sentinel-2 L2A, underscoring its potential for advancing remote sensing applications.

Artificial intelligence (AI) is transforming diffractive optics development through its advanced capabilities in design optimization, pattern generation, fabrication enhancement, performance forecasting, and customization. Utilizing AI algorithms like machine learning, generative models, and transformers, researchers can analyze extensive datasets to refine the design of diffractive optical elements (DOEs) tailored to specific applications and performance requirements. AI-driven pattern generation methods enable the creation of intricate and efficient optical structures that manipulate light with exceptional precision. Furthermore, AI optimizes manufacturing processes by fine-tuning fabrication parameters, resulting in higher quality and productivity. AI models also simulate diffractive optics behavior, accelerating design iterations and facilitating rapid prototyping. This integration of AI into diffractive optics holds tremendous potential to revolutionize optical technology applications across diverse sectors, spanning from imaging and sensing to telecommunications and beyond.

A family of 2D light fields consisting of the product of three Airy functions with linear arguments has been studied theoretically and experimentally. These fields, called three-Airy beams, feature a parameter shift and have a cubic phase and a super-Gaussian circular intensity in the far zone. Transformations of three-Airy beams in the Fresnel zone have been studied using theoretical, numerical, and experimental means. It has been shown that the autofocusing plane of a three-Airy beam is similar to the square root of the shift parameter. We also introduce generalized three-Airy beams containing nine free parameters, and obtain their Fourier transform in a closed form.

Photonic neural networks (PNNs), utilizing light-based technologies, show immense potential in artificial intelligence (AI) and computing. Compared to traditional electronic neural networks, they offer faster processing speeds, lower energy usage, and improved parallelism. Leveraging light's properties for information processing could revolutionize diverse applications, including complex calculations and advanced machine learning (ML). Furthermore, these networks could address scalability and efficiency challenges in large-scale AI systems, potentially reshaping the future of computing and AI research. In this comprehensive review, we provide current, cutting-edge insights into diverse types of PNNs crafted for both imaging and computing purposes. Additionally, we delve into the intricate challenges they encounter during implementation, while also illuminating the promising perspectives they introduce to the field.

The paper proposes approaches for the classification of high-resolution hyperspectral images in the problem of classification of soil species classification. A spectral-spatial convolutional neural network with compensation for illumination variations is used as a classifier. The effectiveness of the proposed approach in the problem of classification of hyperspectral images of soils obtained by a scanning type hyperspectrometer is shown. A multiclass neural network is compared with an ensemble in which the results of a multiclass neural network are refined by several binary classifiers. It is shown that the use of normalization of illumination inhomogeneity and the use of an ensemble of convolutional spatial-spectral neural networks can significantly increase the accuracy of soil type classification.

In this paper, we present a hybrid refractive-diffractive lens that, when paired with a deep neural network-based image reconstruction, produces high-quality, real-world images with minimal artifacts, reaching a PSNR of 28 dB on the test set. Our diffractive element compensates for the off-axis aberrations of a single refractive element and has reduced chromatic aberrations across the visible light spectrum. We also describe our training set augmentation and novel quality criteria called "false edge level" (FEL), which validates that the neural network produces visually appealing images without artifacts under a wide range of ISO and exposure settings. Our quality criteria (FEL) enabled us to include real scene images without a corresponding ground truth in the training process.

Detailed automated analysis of crop images is critical to the development of smart agriculture and can significantly improve the quantity and quality of agricultural products. A hyperspectral camera potentially allows to extract more information about the observed object than a conventional one, so its use can help in solving problems that are difficult to solve with conventional methods. Often, predictive models that solve such problems require a large dataset for training. However, sufficiently large datasets of hyperspectral images of agricultural plants are not currently publicly available. Therefore, we present a new dataset of hyperspectral images of plants in this paper. This dataset can be accessed via URL https://pypi.org/project/HSI-Dataset-API/. It contains 385 hyperspectral images with a spatial resolution of 512 by 512 pixels and spectral resolution of 237 spectral bands. The images were captured in the summer of 2021 in Samara and Novocherkassk (Russia) using Offner based Imaging Hyperspectrometer of our own production. The article demonstrates the work of some basic approaches to the analysis of hyperspectral images using the dataset and states problems for further solving.

Blood vessel visualization technology allows nursing staff to transition from traditional palpation or touch to locate the subcutaneous blood vessels to visualized localization by providing a clear visual aid for performing various medical procedures accurately and efficiently involving blood vessels; this can further improve the first-attempt puncture success rate for nursing staff and reduce the pain of patients. We propose a novel technique for hyperspectral visualization of blood vessels in human skin. An experiment with six participants with different skin types, race, and nationality backgrounds is described. A mere separation of spectral layers for different skin types is shown to be insufficient. The use of three-wavelength indices in imaging has shown a significant improvement in the quality of results compared to using only two-wavelength indices. This improvement can be attributed to an increase in the contrast ratio, which can be as high as 25%. We propose and implement a technique for finding new index formulae based on an exhaustive search and a binary blood-vessel image obtained through an expert assessment. As a result of the search, a novel index formula was deduced, allowing high-contrast blood vessel images to be generated for any skin type.

The possibility of essentially reducing the weight and production cost of computer vision systems has led to the publication of a large number of research works dealing with the development of new imaging systems based on diffractive optics. This study proposes a new imaging system composed of three diffractive lenses, with each forming a separate channel of the color RGB image. This approach allows us to significantly narrow the spectral range of each lens, thus significantly reducing the image distortion caused by chromatic aberration inherent in diffractive optics. It shows that this scheme allows us to perform the neural network-aided image reconstruction, providing a significantly improved resulting image quality. The study proposes a false edge level criterion (FEL) for evaluating the neural network-aided reconstruction.

The paper presents the results of a study of the method of classification of vegetation types based on hyperspectral survey data. A hyperspectrometer based on the Offner scheme was used as a shooting equipment. The spatial-spectral architecture of a convolutional neural network is used as a classifier. The experiments performed show the effectiveness of the proposed approach for the classification of vegetation types.

The paper presents a study of various approaches to the classification of soil covers based on neural network algorithms using hyperspectral remote and proximal sensing of the Earth. The spectral distributions were recorded in the laboratory using an Offner imaging scanning hyperspectrometer. Spectral-spatial characteristics of nine soil samples from various parts of a farming land in the Samara region were experimentally studied. Using a method of energy dispersion microanalysis, the correspondence between the hyperspectral data and the chemical composition of the samples taken was established. Based on the data obtained, a neural network-aided classification of soil samples was implemented depending on the content of constituent elements such as carbon and calcium. A normalized spectral-spatial convolutional neural network was used as a classifier. As a result of the work, an approach to the classification of high-resolution hyper-spectral images based on the refinement of a multiclass convolutional neural network using an ensemble of binary classifiers is proposed. It is shown that the classification of soil samples by carbon and calcium content is carried out with an accuracy of 0.96.