Designing double freeform optical surfaces for controlling both irradiance and wavefront

Abstract

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.

Enhanced performance of refractive laser beam shapers through additional phase control at focus

“…However, detailed design procedures have been reported mainly for collimated laser beam shaping with plane wavefronts. [15][16][17][18][19][20][21][22][23][24] There is work 25 which can be used to generate a freeform wavefront; however, the irradiance is defined in the case at a plane close to the wavefront rather than on the wavefront itself. In our case, we have defined both the irradiance and the phase at the same plane, so that the design has a good accuracy even when the beam is strongly focused.…”

“…To evaluate the shaping quality, the difference between the actual irradiance and the expected one can be quantified by the relative root-mean-squared error (RRMSE) 25,28 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 2 7 ; 3 2 6 ; 4 2 1…”

Direct design of aspherical lenses for extended non-Lambertian sources in three-dimensional rotational geometry

“…Generally, the illumination design algorithms can be divided into two groups: zero-étendue algorithms [2][3][4][5][6][7][8][9] and algorithms for extended sources [10][11][12][13]. For a zero-étendue algorithm, the light source is assumed as an ideal source (a point source or a parallel beam), in which there is only one single ray passing through each point on the optical surface, as shown in Fig.…”

“…1(a). This simplistic assumption allows us to easily achieve a predefined deflection of the optical surface for each incident ray [6,9]. Since the étendue of an actual light source usually cannot be zero in practical applications, these zero-étendue algorithms are invalid in a compact design where the influence of the size or the angular extent of the extended source on the performance of an illumination system cannot be ignored.…”

Simultaneous control on the intensity and phase profile of laser beam with Monge-Ampère equation method

“…Even so, the simultaneous control on both the intensity and phase profile is still a real challenge of laser beam shaping. There are several reports which have addressed this challenging issue [9][10][11][12][13] . Rubinstein employed a freeform lens integrated with two freeform surfaces to control the intensity and phase profile of laser beam [9] .…”