Designing double freeform optical surfaces for controlling both irradiance and wavefront.

We propose an improved double freeform-optical-surface design method for shaping a prescribed irradiance distribution whilst forming a desired wavefront from a given incident beam. This method generalizes our previous work [Opt. Exp. 21, 14728-14735 (2013)] to tackle non-separable beam irradiances. We firstly compute a proper ray mapping using an adaptive mesh method in the framework of the L2 Monge-Kantorovich mass transfer problem. Then, we construct the two freeform optical surfaces according to this mapping using a modified simultaneous point-by-point procedure which is aimed to minimize the surface errors. For the first surface, the modified procedure works by firstly approximating a value to the next point by only using the slope of the current point and then improving it by utilizing both slopes of the two points based on Snell's law. Its corresponding point on the second surface can be computed using the constant optical path length condition. A design example of producing a challenging irradiance distribution and a non-ideal wavefront demonstrates the effectiveness of the method.

[1]  Vladimir Oliker,et al.  Optical Design of Two-reflector Systems, the Monge-Kantorovich Mass Transfer Problem and Fermat's Principle , 2003 .

[2]  Jannick P Rolland,et al.  Fast freeform reflector generation usingsource-target maps. , 2010, Optics express.

[3]  Jacob Rubinstein,et al.  Intensity control with a free-form lens. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  David G. Pelka,et al.  Free-form illumination lenses designed by a pseudo-rectangular lawnmower algorithm , 2006, SPIE Optics + Photonics.

[5]  Vladimir Oliker,et al.  Designing Freeform Lenses for Intensity and Phase Control of Coherent Light with Help from Geometry and Mass Transport , 2011 .

[6]  Lei Zhu,et al.  Optimal Mass Transport for Registration and Warping , 2004, International Journal of Computer Vision.

[7]  Julio Chaves,et al.  Simultaneous multiple surface optical design method in three dimensions , 2004 .

[8]  Mali Gong,et al.  Beam shaping system design using double freeform optical surfaces. , 2013, Optics express.

[9]  Vladimir Oliker.  Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties , 2005, SPIE Optics + Photonics.

[10]  William A. Parkyn,et al.  Illumination lenses designed by extrinsic differential geometry , 1998, Other Conferences.

[11]  Harald Ries,et al.  Laser beam shaping by double tailoring , 2005, SPIE Optics + Photonics.

[12]  J. F. Williams,et al.  An efficient approach for the numerical solution of the Monge-Ampère equation , 2011 .

[13]  Yi Luo,et al.  Discontinuous free-form lens design for prescribed irradiance. , 2007, Applied optics.

[14]  D Michaelis,et al.  Cartesian oval representation of freeform optics in illumination systems. , 2011, Optics letters.

[15]  Harald Ries,et al.  Tailored freeform optical surfaces. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  R. Rockafellar.  Characterization of the subdifferentials of convex functions , 1966 .

[17]  Yann Brenier,et al.  A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem , 2000, Numerische Mathematik.

[18]  Jochen Stollenwerk,et al.  Algorithm for irradiance tailoring using multiple freeform optical surfaces. , 2012, Optics express.

[19]  R. McCann.  Existence and uniqueness of monotone measure-preserving maps , 1995 .

[20]  Xu Liu,et al.  Freeform illumination design: a nonlinear boundary problem for the elliptic Monge-Ampére equation. , 2013, Optics letters.

[21]  Jacob Rubinstein,et al.  Ray mapping and illumination control , 2013 .

[22]  Yi Luo,et al.  Design of compact and smooth free-form optical system with uniform illuminance for LED source. , 2010, Optics express.

[23]  Xu Liu,et al.  Freeform LED lens for uniform illumination. , 2008, Optics express.