Creating unconventional geometric beams with large depth of field using double freeform-surface optics

Abstract

We consider here creation of an unconventional flattop beam with a large depth of field by employing double freeform optical surfaces. The output beam is designed with continuous variations from the flattop to almost zero near the edges to resist the influence of diffraction on its propagation. We solve this challenging problem by naturally incorporating an optimal transport map computation scheme for unconventional boundary conditions with a simultaneous point-by-point double surface construction procedure. We demonstrate experimentally the generation of a long-range propagated triangular beam through a plano-freeform lens pair fabricated by a diamond-tuning machine.

Design of Freeform Illumination Optics

“…This allows us to deal with the design of freeform illumination optics from a mathematical point of view and establish a universal mathematical design model. Laser beam shaping is an important application of freeform optics and has been widely studied . In the illumination design for a point‐like source, the current work focuses mainly on on‐axis illumination design with one single surface.…”

“…Laser beam shaping is an important application of freeform optics and has been widely studied. [110,127] In the illumination design for a point-like source, the current work focuses mainly on on-axis illumination design with one single surface. One more freeform surface can offer more degrees of design freedom and most importantly can significantly improve the energy efficiency.…”

Designing double freeform surfaces for collimated beam shaping with optimal mass transportation and linear assignment problems

“…The considered problem can also be addressed by using another, mathematically less rigorous approach based on the so-called ray-mapping methods [9][10][11]. In this case, the ray mapping, i.e.…”

“…the mapping between the coordinates of the rays on the wavefronts of the incident and the output beams is found by solving a standard Monge-Ampère (MA) equation. The MA equation is solved either using the above-mentioned finite-difference method based on reducing the task to the solution of a system of nonlinear equations, or using an explicit finite-difference method based on the replacement of the original equation by the non-stationary parabolic Monge-Ampère equation [10,11]. The optical surfaces are calculated on the basis of the computed ray mapping using numerical integration.…”

“…In contrast, the calculation of such a mapping using finite-difference methods for the solution of a PDE of Monge-Ampère type requires solving a system of 143 2 = 20449 nonlinear equations and is by several orders of magnitude slower [16]. Besides, the computation of the ray mapping by solving a mass transportation problem makes it possible to design elements with piecewise-smooth continuous optical surfaces, as distinct from smooth optical surfaces resulting from the solution of an elliptic nonlinear PDE [6][7][8][9][10][11]. It widens the range of the problems that can be solved, in particular, enabling the generation of uniform irradiance distributions in complex domains with non-smooth boundaries.…”