Using the previously developed optimization method for an extended light source [Byzov EV, Kravchenko SV, Moiseev MA, Bezus EA, Doskolovich LL. Optimization method for designing double-surface refractive optical elements for an extended light source. Opt Express 2020; 28(17): 24431-24443. DOI: 10.1364/OE.400609], we designed a compact refractive optical ele-ment (the ratio of the element height to the light source size being 1.55) providing a uniform illu-minance distribution in a shifted rectangular region. An application of the optimization method for calculating the so-called TIR-elements, exploiting the phenomenon of the total internal reflection of rays, is considered. For an extended light source, compact TIR-elements with freeform exit sur-faces that generate uniform illuminance distributions in a rectangular region are designed. The re-sults of the work show promise for a wide class of problems of designing compact optical ele-ments for light-emitting diodes

Some of the intended fusion experiments and promising technological applications require sources of microwaves with powers of about 200–1000 kW in the continuous-wave regime at frequencies of 300 GHz and higher. In the process of project accomplishment, we studied the interaction of a helical electron beam with the high-frequency field in the cavities of several design versions of such gyrotrons for operation in the continuous-wave regime. Main issues have been identified and possible solutions have been considered.

The design of a freeform mirror generating a uniform illuminance distribution in a rectangular region with angular dimensions of 30°x15° is presented. The design method is based on the formulation of the problem of calculating the "ray-mapping" as a Monge-Kantorovich mass transportation problem and its subsequent reducing to a linear assignment problem. We describe a mirror fabrication process with the use of milling technology and present results of experimental measurements of the light distribution generated by the mirror. The experimental results are in good agreement with the results of numerical simulations and thus confirm the manufacturability of mirrors designed by the method proposed.

A method for designing an optical element with two free-form surfaces generating a prescribed illuminance distribution in the case of an extended light source is considered. The method is based on the representation of the optical element surfaces by bicubic splines and on the subsequent optimization of their parameters using a quasi-Newton method implemented in the Matlab software. To calculate the merit function, a version of the ray tracing method is proposed. Using the proposed method, an optical element with record characteristics was designed: the ratio of the element height to the source size is 1.6; luminous efficiency is 89.1 %; uniformity of the generated distribution (the ratio of the minimum and average illuminance) in a given square region is 0.92.

We propose a novel technique for designing double-surface axisymmetric refractive optical elements with minimized Fresnel losses and maximized lighting efficiency. The design of the optical element is reduced to the integration of three explicit ordinary differential equations. Minimization of the Fresnel losses is provided by ensuring equal refraction angles on both “working” surfaces of the optical element. To demonstrate high performance of the method, we designed axisymmetric double-surface optical elements generating uniform illuminance distributions both in the far (angular size of 50°) and in the near (angular size of 90°) field. The lighting efficiency exceeds 87.8% for both point and extended light sources. Besides, we demonstrated that optical surfaces designed using the proposed method can serve as an excellent initial approximation in the case of a large extended light source. In the considered example with the ratio of the element height to the source diameter of only 2.2, the lighting efficiency of the optimized element exceeds 89.5%, whereas the uniformity of the resulting illuminance distribution exceeds 96%.

We propose a method for designing optical elements with two freeform refracting surfaces generating prescribed non-axisymmetric irradiance distributions in the case of an extended light source. The method is based on the representation of the optical surfaces as bicubic splines and on the subsequent optimization of their parameters using a quasi-Newton method. For the fast calculation of the merit function, we propose an efficient version of the ray tracing method. Using the proposed approach, we design optical elements generating uniform square-shaped irradiance distributions in the far- and near-field. The designed elements are very compact (the height-to-source ratio is only 1.6) and, while providing a high lighting efficiency of 89%, generate highly uniform distributions (the ratio between minimum and average irradiance values in the prescribed square-shaped region exceeds 0.9).

We consider a method for designing freeform mirrors generating prescribed irradiance distributions in the far field. The method is based on the formulation of the problem of calculating a ray mapping as a Monge-Kantorovich mass transportation problem and on the reduction of the latter problem to a linear assignment problem. As examples, we design freeform mirrors generating a uniform irradiance distribution in a rectangular region and a complex chessboard-shaped distribution. The mirror generating a rectangular irradiance distribution is fabricated and experimentally investigated. The experimental results are in good agreement with the numerical simulations and confirm the manufacturability of the mirrors designed using the considered method.

We discuss the use of variational principles for solving the phase problem in optics. In this paper, we consider the connection between four fundamental problems: the phase problem in optics, the inverse problem of focusing coherent radiation, the Monge – Kantorovich optimal mass transport problem, and the variational methods for solving the equation of a modified Monge – Ampere equation. It is shown that the solution of the phase problem in optics within the framework of the asymptotic approach is closely related to the solution of the problem of optimal mass transport with a nonquadratic cost function.

The development of LED secondary optics for road illumination is quite a challenging problem. Optical elements developed for this kind of application should have maximal efficiency, provide high luminance and illuminance uniformity, and meet many other specific requirements. Here, we demonstrate that the usage of the supporting quadric method modification enables generating free-form optical solution satisfying all these requirements perfectly. As an example, two optical elements for different roadway types are computed, manufactured by injection molding, and then measured in a photometry bench. Experimental data demonstrate that the obtained light distributions meet ME1 class requirements of EN 13201 standard. The obtained directivity patterns are universal and provide high performance with different configurations of luminaires' arrangement: the ratio of pole altitude to distance can vary from 2.5 up to 3.6.

A new method for the design of extruded optical elements with two refractive surfaces is presented. The method is based on the developed fast ray-tracing procedure, in which optical surfaces are approximated by a set of planes. High efficiency of the proposed method is illustrated by the examples of designed extruded optical elements for generating uniform intensity and illuminance distributions. The luminous efficacy of the optical element is shown to be over 89 %, whereas the relative root-mean-square error of the generated irradiance distribution is under 2 %.

The supporting quadric method (SQM) is a versatile method for the design of a wide class of freeform optical elements. In the present work, a novel SQM-based approach for the computation of total internal reflection (TIR) optical elements generating arbitrary narrow-angle light distributions is proposed. High performance of the presented method is confirmed by two designed optical elements: the first one forms an illuminance distribution in a square region with angular size of 17°, and the second one generates a bat-shaped uniformly illuminated area with an angular size of 43.6° x 22.6°. The lighting efficiencies in both cases exceed 90%, and the relative root-mean-square deviations of the generated light distributions from the required ones are less than 6%.

A new source-target mapping for the design of mirrors generating prescribed 2D intensity distributions is proposed. The surface of the mirror implementing the obtained mapping is expressed in an analytical form. Presented simulation results demonstrate high performance of the proposed method. In the case of generation of rectangular and elliptical intensity distributions with angular dimensions from 80° x 20° to 40° x 20°, relative standard error does not exceed 8.5%. The method can be extended to the calculation of refractive optical elements.

A technique for controlling and optimizing injection molding parameters by numerical simulation is proposed. Using this method for an optical element designed for roadway lighting, multilens molding quality criteria have been defined. Optimal parameters for lens manufacturing have been determined. Based on these parameters, a polycarbonate multilens has been made with an absolute tolerance equal to 0.01 mm.

A novel method for the design of total internal reflection based (TIR) optical elements generating complex two-dimensional narrow-angle light distributions is presented. The method consists of two parts: computation of a piecewise smooth solution and its subsequent approximation by a spline surface. Examples of TIR optical elements designed using the proposed approach are discussed. The simulation results demonstrate high performance of the proposed method: the luminous efficacy of the optical elements is 91.8% and the relative root-mean-square error is less than 8.6%.

A new optical surface reconstruction technique in the source-target mapping method is proposed. The technique is based on the representation of the surface as an envelope of a parametric family of paraboloids (ellipsoids). Using such a representation, the calculation of the optical surface is reduced to solving a complete differential equation without regard for the coordinate system. By way of illustration, mirrors that generate uniform intensity distributions in a square region are designed. Simulation of the design examples shows high performance of the proposed technique: it allows us to obtain good-quality intensity distributions even with violation of the integrability condition.

Design development of continuous-wave 240 GHz gyrotron and 300 GHz gyrotrons with output power about 200–1000 kW for fusion research at advanced plasmas with intense magnetic field is presented. Main goal of such gyrotrons is application for EC complexes of IGNITOR and DEMO tokamaks. This paper includes task motivation and existing technical basis, results of calculation, design, technical requirements and pre-prototype experimental tests for main subsystems of gyrotron.

The problem of focusing light flux into an arbitrary curve in 3D space arises in the design of different laser or illumination systems. Using a diaphragm with a curved hole is not efficient and does not work for any 3D pattern. In this study, we propose a numerical analytical approach for designing reflective surfaces that efficiently produces the prescribed intensity distribution on the arbitrary curve in 3D space. The method consists of two steps: computation of the eikonal function on the curve and reconstruction of the reflective surface using the precomputed eikonal function. In the first step, we use the iterative technique for obtaining the eikonal function in the set of points on the curve. After that, we compute the continuous eikonal function by interpolation of the obtained values of the eikonal in points and reconstruct the reflective surface using continuous eikonal distribution. As examples, the reflectors generating spiral lines on the inclined plane and illumination system module are computed and simulated. Simulation data show the high quality of the produced illuminance distributions.

To improve the optical performance of LED-based lighting devices, refractive optical elements are usually used. We propose a novel technique for the computation of free-form optical elements with two refractive surfaces generating the required illuminance or intensity distribution. The proposed approach makes it possible to control the balance of deflection angles between the inner and outer surfaces of the optical element. It has been proved that for the point light source, the maximal efficiency is obtained when each refractive surface performs exactly the half of the required ray deflection. As an example, a set of optical elements producing a uniformly illuminated square region is computed. Simulation of the computed designs with extended sources has shown that the most tolerant solutions to the size of the light source are obtained in the case when the inner surface performs 60-80% of the ray deflection, and the outer surface performs the remaining 20-40%. The influence of deflection balance on the size of the optical element is discussed.

A modification of the Monte-Carlo ray tracing procedure for axisymmetric surfaces is proposed. The main idea consists in the approximation of optical surfaces by truncated cones and the use of an unconventional k-d tree. The simulation results show high performance of the proposed method, with the ray tracing procedure working 3-12 times faster than conventional algorithms based on a triangle approximation.