We previously proposed an iterative wavefront tailoring (IWT) method [Optics Letters 44(9): 2274-2277] to solve the freeform lens design problem for irradiance tailoring, where the entrance surface can be predefined as a spherical, aspherical or freeform surface. Here, this method is adapted to address a more challenging design problem where the exit surface is predefined. We design a freeform lens with a fixed aspherical exit surface to demonstrate the effectiveness of the modified method.
High-precision phase reconstruction is crucial for beam analysis and control. In a previous work, we proposed a phase retrieval method based on the Monge-Ampère equation (MAE). Similar to the commonly-used transport of intensity equation (TIE), the MAE is also a partial differential equation (PDE) that describes the relationship between irradiance and phase. However, in the framework of geometric optics, the MAE could be a more accurate and general method for solving the phase retrieval problem compared to the TIE. In this paper, we apply the MAE to reconstruct the field of a laser beam. By capturing two irradiance distributions at two different planes that are perpedicular to the propagation direction, the complex amplitude distribution at the first plane can be retrieved based on the MAE method. The angular spectrum method is employed to determine the complex amplitude distributions at different positions along the beam propagation direction. The factor of the laser beam is calculated based on the reconstructed beam field. Results show that the factor values computed based on the MAE method have small deviations from that tested with a commercial beam profiler.
We previously optimized the freeform surfaces using extended polynomials in stereographic projection coordinates based on an automated workflow linking the optimization engine, 3D modeling software and ray tracing software [Optics Express 29(9), 13469–13485 (2021)]. However, this method is time consuming as it needs thousands of irradiance evaluations. Here, we speed up the optimization of spherical-freeform lenses for uniform illumination based on differentiable ray tracing. The freeform surface is still parameterized with the ‘uv’ extended polynomials under stereographic projection coordinates, which is suitable for generating simple illumination patterns. We implement differentiable ray tracing based on computation graph in MindSpore framework, which is efficient and effective by calculating derivatives of the surface parameters during a single backpropagation. We provide two design examples for generating uniform irradiance distributions with a point-like source and an extended light source, respectively.
Compared with traditional optical surfaces, freeform surfaces provide much more degrees of freedom to tailor the irradiance distributions of light sources, forming previously unimaginable illumination optical systems. However, the complexity of freeform surfaces presents a huge challenge to the design process, especially when the light source size is assignable. We achieved fast irradiance evaluation of freeform illumination lens based on deep learning methods, preparing for a rapid optimization for the lens design. These learned simulation results are similar to those of LightTools, while the computation time is greatly reduced. The representation of freeform surfaces, the generation of datasets, and the selection of neural network structures are introduced in this paper. In the future, we will further improve the neural network performance and use the back-propagation of the neural network to realize a rapid optimization of the freeform lens.
Freeform lens design for LED beam shaping is a difficult inverse problem which generally doesn’t have a unique solution. Under point source approximation, we have proposed an iterative wavefront tailoring (IWT) method [Opt. Lett. 44, 2274-2277 (2019)] for manipulating the irradiance distribution on a planar or curved target. This method has the ability to generate a variety of freeform lens structures including plano-freeform, spherical freeform and double freeform lenses with high accuracy. However, such a point-source design method becomes less valid for a compact design where the LED size is no longer negligible. We integrate the IWT method with an adaptive over compensation to reduce the irradiance deformations caused by the extended LED source. The IWT designs are iteratively modified to approach the prescribed irradiance distributions with the help of an over compensation coefficients. The new composite method combines the advantages of both the IWT method and the over compensation method.
KEYWORDS: Ray tracing, Freeform optics, Light emitting diodes, Lens design, Computer simulations, 3D modeling, Optimization (mathematics), MATLAB, Monte Carlo methods, Data modeling
Most of the freeform lens optimization methods for LED beam shaping are focused on producing rectangular illumination patterns. Here we demonstrate the generation of non-rectangular irradiance distributions by optimizing the 'uv'-polynomial freeform surface, where (u,v) are stereographic coordinates. An initial freeform surface is designed with an optimal transport ray mapping method that is suitable for unconventional boundaries. Simulated annealing is then used to optimize the polynomial coefficients based on an automated workflow that links Matlab (central platform and optimization engine), Rhinoceros (3D molding) and LightTools (Ray tracing).
Ray mapping method can greatly simplify the freeform illumination lens design. However, the result obtained by the ray mapping method sometimes deviates much from the design target. Therefore, we present a construction of double freeform surfaces based on nonlinear least squares and non-uniform rational B-spline surfaces (NURBS) to minimize the deviations. By this way, we can get a smooth double-freeform-surface lens with good optical performance.
Compared with light emitting diodes (LEDs), laser diodes (LDs) are attractive for applications in which size and radiance matter. The elliptical, highly divergent, and astigmatic beam characteristics make LD beams difficult to handle. Compare with conventional techniques, freeform optics can precisely control the LD beam. However, freeform optics design for LD beam shaping is a very difficult inverse problem. A simple and efficient method is provided to iteratively construct freeform surfaces for achieving difficult LD beam shaping tasks.
KEYWORDS: Light sources and illumination, Roads, Freeform optics, Light emitting diodes, Ray tracing, Lens design, Monte Carlo methods, Computer simulations, Energy efficiency, Lamps
Road lighting can benefit strongly from LEDs and freeform lenses. However, freeform lenses design for road lighting applications is complicated and difficult when balancing energy efficiency and lighting quality. In addition, the asymmetric properties of the required light distributions and non-neglectable sizes of LEDs make the design more challenging. Currently, we prefer an efficient design strategy with two steps: light distribution optimization and freeform lens construction. In the first step, we employ a modified polynomial representation of the illuminance distribution and perform constrained optimization. In the second step, we construct the freeform lens with double freeform surfaces to realize the optimized light distribution using the ray mapping method associated with over compensation.
In this paper, we propose a new composite ray mapping method to design freeform total internal reflective (TIR) optics for LED illumination. We sample the ray intensity distribution into rectangular grids which have the best topological match to those rectangular grids on the target surface. With the multiple-to-one mapping relationships between the source intensity distribution and target irradiance distribution, we can construct the freeform TIR surfaces and freeform refractive surface using Snell’s law. Compared to our previous design using uv-θϕ composite ray mapping method, this design approach is expected to have much less surface error and improve the illumination uniformity further because of the better topological match. In addition, due to the overlapping mechanism by multiple-to-one (composite) ray mapping, the method could lead to a more robust freeform optics compared to traditional freeform optics designs.
We propose a new method to design freeform reflectors by nonuniformly sampling the source intensity distribution in double pole coordinate system. In double pole coordinate system, there is no pole for the whole hemisphere because both poles of the spherical coordinate system are moved to southernmost point of the sphere and overlapped together. With symmetric definition of both angular coordinates in the modified double pole coordinate system, a better match between the source intensity distribution and target irradiance distribution can be achieved for reflectors with large acceptance solid angle, leading to higher light efficiency and better uniformity on the target surface. With non-uniform sampling of the source intensity, we can design circular freeform reflector to obtain uniform rectangular illumination pattern. Aided by the feedback optimization, the freeform reflector can achieve the collection efficiency for ideal point source over 0.7 and relative standard deviation (RSD) less than 0.1.
We propose a novel method for designing reflectors with large-size spherical surface sources. The center portion of the reflector is designed using the edge-ray principle, while the rim portion is designed based on the variable-separation mapping method. Step discontinuities are introduced during rim surface construction to control the deviation caused by error in normal vectors, and a feedback modification is adopted to compensate for the illuminance deviation produced by the large size of sources. As an example, a streetlamp with a desired rectangular illuminance distribution on the road is designed using a spherical surface source (10 cm diam) and a compact reflector. It has an illuminance uniformity of 60.2% and utilance of 66.9%, considerably improved from the traditional values of 35 and 40%, respectively.
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