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.

A problem of optimizing the subwavelength microrelief of a binary cylindrical transmissive diffractive lens (DL) with a 300-mm focal length for a wavelength of λ=141 μm was considered. High-resistivity silicon was chosen as the DL substrate material. The angle of incidence of the illuminating beam was taken to be π/6. The optimization parameters were the height of the DL profile and the fill factor of the groove. The main goal of optimizing the design was to increase the diffraction efficiency of the lens. The DL diffraction efficiency was calculated using a Fourier mod method. The DL was fabricated by plasma-chemical etching (Bosch process) of the surface of a silicon substrate. The diffraction efficiency of the calculated lens was estimated to be 70%. However, a full-scale experiment showed the real efficiency to be much lower. These differences are related to both errors in the manufacturing process of the DL and non-ideal thickness parameters of the silicon wafers.

Launched in March 2021, the 3U CubeSat nanosatellite was the first ever to use an ultra-lightweight harmonic diffractive lens for Earth remote sensing. We describe the CubeSat platform we used; our 10 mm diameter and 70 mm focal length lens synthesis, design, and manufacturing; a custom 3D-printed camera housing built from a zero-thermal-expansion metal alloy; and the on-Earth image post-processing with a convolutional neural network resulting in images comparable in quality to classical refractive optics used for remote sensing before.

We propose a method for calculating the so-called multi-wavelength diffractive lenses (MWDLs) intended for separating and focusing the radiation of L given wavelengths to L given points located in a certain plane perpendicular to the optical axis. The method is based on minimizing the objective function characterizing the deviation of the complex transmission functions of the MWDL from the complex transmission functions of diffractive lenses focusing the design wavelengths to the given points. In the method, the MWDL calculation is reduced to a set of independent pointwise optimization problems, each of which describes the calculation of the MWDL microrelief at one point. The presented results of the numerical simulation of the designed MWDLs confirm high performance of the proposed method. The numerical simulation results are confirmed by the results of experimental investigations, including the fabrication of MWDLs using the direct laser writing technique and the study of the MWDL operation in an optical experiment.

Subject of study. The simplest scheme comprising two harmonic lenses is considered, which allows the formation of an image with higher quality than that obtained using each of these lenses individually owing to the accurate selection of the heights of their microreliefs. Method. Two harmonic lenses with coupled microrelief heights are fabricated using the direct laser writing method on the photoresist. An experiment is conducted on the formation of images by the system comprising two harmonic lenses and an individual harmonic lens. Main results. A "HarmLens" software for modeling of the systems comprising harmonic and diffractive lenses is designed. Modeling is performed within the geometric optic approximation using the ray tracing method. The possibility of obtaining a significant reduction in the displacement of the primary focal plane in comparison with the individual harmonic lens case is demonstrated by the specific selection of the microrelief height in this system. The system of two harmonic lenses is demonstrated to form an image with an average contrast exceeding the average contrast of the image formed by the individual harmonic lens by 1.4 times. The point spread function of the system comprising two harmonic lenses is experimentally demonstrated to be 1.6 times narrower than that of the individual harmonic lens with an equivalent focal length. Practical significance. The system of two harmonic lenses proposed in this work allows a sharper image than the image formed by an individual harmonic lens to be obtained. The system of two harmonic lenses can be adopted in machine vision systems where the compact arrangement of the objective's elements is more important than the high quality of the formed image. (C) 2022 Optica Publishing Group

The simplest lens, consisting of the refractive and diffractive lenses, in which the main geometric aberrations are compensated due to the shape of the diffractive lens, is considered. It is considered the way of calculation of this system based on minimization of a chromatic aberration. The results of the experiment, in which a frequency–contrast characteristic of a hybrid lens was directly determined, are presented.

Hybrid methods combining the geometrical-optics and diffraction-theory methods enable designing diffractive optical elements (DOEs) with high performance due to the suppression of stray light and speckles and, at the same time, with a regular and fabrication-friendly microrelief. Here, we propose a geometrical-optics method for calculating the eikonal function of the light field providing the generation of a required irradiance distribution. In the method, the problem of calculating the eikonal function is formulated in a semi-discrete form as a problem of maximizing a concave function. For solving the maximization problem, a gradient method is used, with analytical expressions obtained for the gradient. In contrast to geometrical-optics approaches based on solving the Monge-Ampére equation using finite difference methods, the proposed method enables generating irradiance distributions defined on disconnected regions with non-smooth boundaries. As an example, we calculate an eikonal function, which provides the generation of a "discontinuous" irradiance distribution in the form of a hexagram. It is shown that the utilization of the hybrid approach, in which the obtained geometrical-optics solution is used as a starting point in iterative Fourier transform algorithms, enables designing DOEs with a quasi-regular or piecewise-smooth microrelief structure. The calculation results are confirmed by the results of experimental investigations of a DOE generating a hexagram-shaped irradiance distribution.

A schematic diagram of a RoF radio-optic system with vortex signals is presented, in which the radio frequency is determined by the difference between the wavelengths of two lasers. It is assumed that the generation of a vortex signal can be performed through a vortex fiber-optic periodic structure, which can be obtained using a technology similar to the manufacture of long-period fiber Bragg gratings. The parameters of the grating are modeled assuming that the fundamental light-guide mode (LP01) is applied to the specified vortex element, and the higher-order mode (LP11) is reflected. It was found that the distortion of the vortex signal can be reduced by introducing apodization and chirping of this periodic structure. The following optimal parameters have been estimated: the apodization and chirp multiplier functions, at which the distortions of the amplitude and phase of the vortex signal, as well as the appearance of an unwanted angle distortion, will be minimal. It is shown that such gratings can be exploited in addressed sensors systems using the orbital angular momentum (OAM) of a lightwave as a unique sensor address.

Diffractive optical elements for the formation of laser beams with intensity distributions in the form of ring light traps with zero total orbital angular momentum are considered and studied by means of a computational experiment. The beams are formed as a superposition of two vortex beams with the same magnitude but different sign orbital angular momentum by encoding multilevel diffractive optical elements (256 quantization levels) in polar angle. The considered elements form an intensity distribution in the form of spots located in the same places where the light rings are located in the initial vortex beams. Such beams can possess all the properties of vortex beams when propagating in the atmosphere, for example, increased stability to aerosol noise.

This paper examines the spectral properties of a spiral phase plate (SPP) generating orbital angular momentum (OAM) beams. A simple method is proposed for calculating the resulting OAM by measuring only two maximum expansion coefficients. A comparative numerical simulation of the proposed and traditional methods is performed. An SPP is fabricated for generation of an OAM with integer values at infrared and visible wavelengths. Qualitative experimental studies of the changes in a generated OAM with a change in the operating wavelength are performed using the spatial filtering method. The experimental results are found to agree with the results of numerical simulation. Beams with integer and fractional OAM values are obtained experimentally by changing the wavelength.

The paper presents results of the experimental investigation of "spectral" diffractive lenses the same focus position for several given wavelengths. Two spectral diffractive lenses designed to focus radiation of three and five specified wavelengths in the visible spectrum were investigated. Using a method of direct laser writing in photoresist with iterative correction of writing parameters, we fabricated a diffractive microrelief of the spectral lenses with the height deviation from the designed relief of less than 30 nm. Using a pinhole located at the focus of the fabricated lenses, we estimated the operation wavelengths. The point spread functions of the spectral lenses at the designed wavelengths were measured with the use of a tunable laser. The imaging properties of the spectral lenses were illustrated by the images of a reference color table.

In this study, a configuration of a compact imaging objective based on a reflecting annular harmonic lens was proposed. Light propagation through the proposed optical system was comprehensively modeled using a dedicated special program and the ZEMAX software, with the latter used to derive the point spread function (PSF). Several relationships were used to describe the connection between key parameters of the objective, including its focal length, field of view, and thickness. We demonstrated that it was possible to design a compact imaging objective whose overall length could be one to two orders of magnitude smaller than its focal length. Using direct laser writing, a reflecting annular harmonic lens was fabricated and used in the proposed objective scheme. The performance of the objective was experimentally studied by imaging a light source and a test pattern. The performance of the compact imaging objective based on a reflecting annular harmonic lens was verified in principle. A PSF value of approximately 16 microns was experimentally obtained, for a lens with a diameter of 25 mm with a focal length of 100 mm.

The characteristics (modulation transfer functions) of harmonic lenses made by direct laser patterning of resist are experimentally studied. The influence of technological errors in the manufacture of lenses on the formation of the point spread function is modelled for harmonic lenses with 32 and 256 quantisation levels. Direct laser writing is used to produce lenses with these numbers of levels. It is experimentally shown that the modulation transfer function of the harmonic lens with 32 quantisation levels is significantly greater at high spatial frequencies (50 mm(-1)).

We propose a method for designing diffractive lenses having a fixed-position focus at several prescribed wavelengths, which we refer to as spectral diffractive lenses (SDLs). The method is based on minimizing an objective function describing the deviation of the complex transmission functions of the spectral lens at the operating wavelengths from the complex transmission functions of diffractive lenses calculated separately for each of these wavelengths. As examples, SDLs operating at three, five, and seven different wavelengths are designed. The simulation results of the calculated lenses confirm high efficiency of the proposed method. For experimental verification of the design method, we fabricate using direct laser writing and experimentally investigate an SDL operating at five wavelengths. The presented experimental results confirm the efficiency of the proposed method in practical problems of designing SDLs. The obtained results may find applications in the design and fabrication of novel flat diffractive lenses with reduced chromatic effects.

We described an experiment on passing Bessel beams through the atmosphere with heat-trolled flows. We showed that at small distances, while passing through the region with a hot air flow, the Bessel beam can be distorted to a complete loss of the structure, but with further propagation over large distances it completely restores its structure. We also described an experiment with the passage of superpositions of vortex beams through the atmosphere with heat flows and aerosols.

We present a new type of diffractive optical elements (DOE) – hybrid axicons. The process of formation of identical intensity distributions in focus by different hybrid axicons on the example of Bessel beams is shown. The beams order is determined by the sum of the topological charges of the phase plate (structure charge) and the spiral axicon (zone charge). The results of mathematical modeling of light diffraction on hybrid axicons are presented.

We consider the possibility of using generalized lenses in imaging optical systems. We propose using two generalized lenses in a system similar to a Fourier-correlator to obtain a point-to-point mapping, where the second lens is set so that a plane wave is also formed at the output of the system when the incident wave is plane. We show that for generalized lenses with a small deviation of their degree from 2, such a system forms a fairly high-quality image. We use a standard radial photographic chart to test the system, which allows us to determine its key optical characteristics.

A new method for forming hypergeometric beams, based on addition of topological charges of the axicon structure with a logarithmic arrangement of bands and topological charges of bands themselves is proposed. The results of a natural experiment confirming the effect of addition of topological charges are presented.

We proposed and modeleda modified direct laser photoresist recording method. The method is based on using a planar-parallel plate to shift the writing beam. We carried out an experimental study on the recording of radially symmetric structures by a beam with a shifted focusing.

A method for fabrication of mechanical elements (microturbines) that receive torque from vortex optical beams is proposed. Experimental results on fabrication of multiple microturbines are presented. Shapes of the microturbines are measured using an optical microscope, ZYGO white-light interferometer, and electron microscope.