ABSTRACT
We propose a method for designing a refractive optical element with two working surfaces transforming an incident beam with a plane wavefront into an output beam with prescribed irradiance distribution and a non-planar wavefront. The presented method generalizes the supporting quadric method [Opt. Express28, 22642 (2020)10.1364/OE.398990] proposed for collimated beam shaping to the case of a non-planar output wavefront. The method is simple to implement and is based on just a few main equations. We present several examples of designing optical elements (including elements with piecewise-smooth optical surfaces) generating light beams with prescribed irradiance distributions and wavefronts (spherical and aspherical). The examples demonstrate high performance of the method.
ABSTRACT
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.
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 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
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.
