ABSTRACT
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).
ABSTRACT
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.
ABSTRACT
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%.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
A new iterative technique for calculating the eikonal function of a light field providing the focusing into a set of points is introduced. This technique is a modification of the supporting quadric method widely used for design of reflecting and refracting optical surfaces for generating prescribed illuminance distributions at given discrete set of points. As an example, we design a refractive optical element which focuses an incident beam into a set of points with energy pattern forming an image of a keyboard of a calculator. It is shown that the proposed technique is well-suited for the design of diffractive optical elements producing continuous intensity distributions within the scalar theory of diffraction. It is also shown that the calculated eikonal function is a good initial guess when designing diffractive optical elements using the iterative Gerchberg-Saxton algorithm.
ABSTRACT
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.
ABSTRACT
We calculate a refractive surface to generate a one-parameter intensity distribution described by a vector function of one argument from an incident beam with a plane wavefront. The calculation of the refractive surface is reduced to the solution of two explicit ordinary differential equations of the first order. An approach to solving the problem of the existence of solutions for various one-parameter intensity distributions is proposed. Optical elements that form a variety of intensity distributions (a line, a circular arc, and a double-arc) are designed. The results of numerical simulations of the designed optical elements demonstrate the high quality of the generated line-shaped patterns.
ABSTRACT
Most LED illumination applications require generation of complex light patterns for which the secondary optics with two free-form surfaces needs to be used. We present a novel optimization method for computing such type of optical elements. An analytical solution for the generation of the initial surfaces is proposed. To accelerate the optimization process, a specific surface representation is used, that eliminates the need to run a time-expensive raytracing procedure. As an example, an optical element generating uniformly illuminated rectangular area with size of 60° by 40° is computed. Lighting efficacy for the extended Lambertian source 1x1 mm is 88.5% and nonuniformity is less than 8.5%.
ABSTRACT
A method is proposed for designing refractive optical elements focusing a collimated incident beam into a curve with specified shape. A general relationship for the freeform surface of the optical element is derived as an envelope of a parametric family of hyperboloids of revolution that focuses the incident beam into the points on the curve. Using the thin optical element approximation, the calculation of the hyperboloid parameters providing required irradiance distribution along the curve is reduced to the solution of an explicit first order differential equation. Optical elements generating line segment focus and circular arc focus are designed. The simulation results demonstrate generation of high-quality curves.
ABSTRACT
An LED optical element is proposed as an alternative to cold-cathode fluorescent lamps. The optical element generates two symmetric uniformly illuminated line segments on the diffuse reflector. The illuminated segments then act as secondary linear light sources. The calculation of the optical element is reduced to the integration of the system of two explicit ordinary differential equations. The results of the simulation of an illumination system module consisting of a set of optical elements generating a set of line segments on the surface of the diffuse reflector are presented. The elements are located directly on the surface of the reflector. The simulation results demonstrate the uniform illumination of a rectangular area at a distance of 30-40 mm from the light source plane. The lighting efficiency of the designed system exceeds 83%.
ABSTRACT
We present the method for computation of highly effective total internal reflection (TIR) optics for LED-based illumination systems. The computation problem is reduced to the integration of several explicit independent first-order differential equations. Two designs of TIR optics are considered and compared: with flat and with aspherical upper surface. The dependence of nonuniformity of generated irradiance distribution on the size of the light source is studied for both designs numerically. It is shown that point source approximation is acceptable in cases when the size of the light source is 5 (or more) times less than the distance to the inner surface of the optical element.
ABSTRACT
We propose a compact optical system made up of a thin collimator and a free-form lens array to provide the uniform illumination of various-shape regions. Analytical formulas to design the lens array are derived. The simulation results for the designed optical elements demonstrate the high-level illumination uniformity of various regions in the form of a rectangle, a cross, a flag-shaped region, a line segment, and a set of line segments.
ABSTRACT
We propose a method for the design of an optical element generating the required irradiance distribution in a rectangular area with a large aspect ratio. Application fields include streetlights, the illumination of halls or corridors, and so forth. The design assumes that the optical element has a complex form and contains two refractive surfaces. The first one converts a spherical beam from the light source to a cylindrical beam. The second one transforms an incident cylindrical beam and generates the required irradiance distribution in the target plane. Two optical elements producing a uniform irradiance distribution from a Cree® XLamp® source in rectangular regions of 17 m × 4 m and 17 m × 2 m are designed. The light efficiency of the designed optical element is larger than 83%, whereas the irradiance nonuniformity is less than 9%.
