自由曲面照明设计方法的研究
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摘要
自由曲面照明是一种显著区别于常规曲面照明的新型照明方式,具有灵活的空间布局和极高的设计自由度。采用自由曲面不仅可极大简化照明系统的结构,还可以有效控制光束分布,轻松实现复杂的照明。自由曲面照明取代常规曲面照明将进一步促进新的照明应用领域的开拓,实现绿色照明及安全照明,并有望成为非成像光学的一次重大变革。
本论文致力于自由曲面照明的核心问题—自由曲面照明设计方法的研究,旨在建立一套有效的连续自由曲面照明的设计理论,为自由曲面照明提供了一套可靠的光学解决方案。针对现有自由曲面照明设计方法的不足,论文经历了三个主要研究阶段,最终提出了一种有效的连续自由曲面照明的设计方法,并建立了自由曲面照明的数学模型。
论文第一阶段针对平行光照明,从Snell定律和能量守恒定律出发,将自由曲面照明设计转化成一阶偏微分方程组,通过数值求解方程组得到自由曲面的离散数据点。并借助一个具体的激光整形应用,验证了该设计方法的有效性。然而,由该方法得到的自由曲面的连续性取决于映射关系的可积性。针对自由曲面激光光束整形,为获得连续的自由曲面,提出了一种透镜阵列思想,保证了透镜单元自由曲面的连续性。随后,针对现有连续自由曲面构造方法的不足,论文提出了一种采用数据点单位切矢作为约束条件的连续自由曲面构造方法,提高了曲面构造的准确性,以较少的数据点获得了更好的光学性能。
为建立一种更为通用的连续自由曲面照明设计方法,论文第二阶段基于最优化思想,提出了一种基于光线定位的连续自由曲面照明优化设计方法。该方法包含两个优化步骤,优化第一步骤基于序列光线追迹方法,采用光线在目标面上落点的实际位置与预定位置的坐标偏差构建评价函数,用于获取大致的光斑形状；优化第二步骤基于非序列光线追迹方法,采用照明区域的照度平均标准偏差和系统的效率构建评价函数,用于进一步改善照明光斑的性能。鉴于优化第二步骤设计效率偏低,论文随后针对第二步骤提出了一种改进思想,采用了一种新的照度评价方式,使该步骤仅采用序列光线追迹方法即可显著改善光斑的照度均匀性。改进后的设计方法优化效率较高,并通过理论模拟、实际加工和实验分析验证了该优化方法的有效性。然而,该方法的优化结果过于依赖初始结构,且只能实现简单的连续自由曲面照明。
论文第三阶段从自由曲面照明的本质入手,提出了一种基于Monge-Ampere方程的连续自由曲面照明设计方法,该方法将自由曲面照明问题转化成一个带非线性边界条件的Monge-Ampere方程。分别针对平行光和点光源照明,建立了相应的自由曲面照明数学模型,并给出了该类数学模型详细的求解算法。采用该设计方法解决了复杂的激光光束整形和LED照明问题,获得了连续的自由曲面面型,并通过实际加工和实验分析验证了该设计方法的有效性。该方法具有极好的普适性及较高的设计自由度,取得了自2002年之后自由曲面照明设计方法的一大突破,为自由曲面照明提供了一套有效的光学解决方案。
Freeform surface illumination is an elegant way of lighting, which is remarkably different from the conventional surface illumination, due to its flexible spatial layout and high degrees of design freedom. With optical freeform surfaces in an illumination system, the structure of the system could be significantly simplified, the incident beams of the light source could be well controlled and some special illuminations could be easily produced. Moreover, some new illumination applications would be further explored, and both green lighting and healthy lighting could be achieved by using the freeform surface illumination. The freeform surface illumination could be a major breakthrough of nonimaging optics.
This paper focuses on studying the design methods of freeform surface illumination, and aims to establish an effective theory and optical strategy for designing smooth freeform illumination. Based on the shortcomings of the existing design methods, this work goes through three main research phases, and finally proposes an effective design method for solving the problem of smooth freeform surface illumination, and establishes a mathematical model for the freeform surface illumination.
In the first research phase, a method is proposed for design freeform surface for solving the illumination problem of collimated light. With this method, the inverse problem of freeform illumination design is converted into first-order partial differential equations, and a set of discrete data points of the freeform surface are obtained by mathematically solving these partial differential equations. A specific application of laser beam shaping is given to verify the feasibility of this design method. The continuity of the freeform surface designed by this method is strongly determined by the integrability of the mapping. Then, a design strategy of freeform lens arrays is proposed to obtain smooth freeform surface for laser beam shaping. With this design strategy, the continuity of the freeform surface in each freeform lens unit is ensured. Since freeform optical surfaces are often constructed only to pass though data points in most current CAD software packages and the given normal at the prescribed point can not be ensured, this paper also proposes a novel method to construct smooth freeform optical surfaces using unit tangent vectors of feature data points as constraints. Beams are controlled well with this new construction method, and better results can be obtained with fewer feature data points.
In order to establish a more effective approach, an optimization method is employed in designing smooth freeform surface illumination using ray targeting in the second phase. Two main optimization steps are contained in this method. Based on the sequence ray tracing, the merit function of the first optimization step is constructed with the position deviation on the target plane for each ray to ensure the shape of the illumination pattern. The second optimization step employs the non-sequence ray tracing, and construct the merit function with the relative standard deviation of irradiance and the transmission efficiency of the illumination system to improve the optical performance of the illumination pattern. Due to the low design efficiency of the second step, an efficient evaluation method is introduced in this step to further improve the irradiance uniformity. With this new evaluation method, the irradiance uniformity can be significantly improved just by tracing several hundred rays based on the sequence ray tracing. The modified optimization design method is more efficient, and feasibility of this method is verified by theoretical simulation, manufacturing and experimental test. But, the results of this method are strongly determined by the initial design, and only some simple illumination tasks can be tackled by using this method.
A design theory is established in the third research phase to deal with the problem of smooth freeform surface illumination design without assuming any symmetry based on the concept that this problem is similar to the problem of optimal mass transport. With this method, the freeform design is converted into a nonlinear boundary problem for the elliptic Monge-Ampere equation. For collimated beam and compact light source, a corresponding mathematical model is established for the freeform illumination, and a numerical method is given for solving this kind of mathematical model. Complex illumination tasks for laser beam shaping and LED illumination are easily tackled with this method, and smooth freeform surfaces are obtained. Also, feasibility of this method is verified by theoretical simulation, manufacturing and experimental test. This design method is more effective than other methods reported within the last ten years to the best of our knowledge, for tackling the problem of freeform illumination design.
本论文致力于自由曲面照明的核心问题—自由曲面照明设计方法的研究,旨在建立一套有效的连续自由曲面照明的设计理论,为自由曲面照明提供了一套可靠的光学解决方案。针对现有自由曲面照明设计方法的不足,论文经历了三个主要研究阶段,最终提出了一种有效的连续自由曲面照明的设计方法,并建立了自由曲面照明的数学模型。
论文第一阶段针对平行光照明,从Snell定律和能量守恒定律出发,将自由曲面照明设计转化成一阶偏微分方程组,通过数值求解方程组得到自由曲面的离散数据点。并借助一个具体的激光整形应用,验证了该设计方法的有效性。然而,由该方法得到的自由曲面的连续性取决于映射关系的可积性。针对自由曲面激光光束整形,为获得连续的自由曲面,提出了一种透镜阵列思想,保证了透镜单元自由曲面的连续性。随后,针对现有连续自由曲面构造方法的不足,论文提出了一种采用数据点单位切矢作为约束条件的连续自由曲面构造方法,提高了曲面构造的准确性,以较少的数据点获得了更好的光学性能。
为建立一种更为通用的连续自由曲面照明设计方法,论文第二阶段基于最优化思想,提出了一种基于光线定位的连续自由曲面照明优化设计方法。该方法包含两个优化步骤,优化第一步骤基于序列光线追迹方法,采用光线在目标面上落点的实际位置与预定位置的坐标偏差构建评价函数,用于获取大致的光斑形状；优化第二步骤基于非序列光线追迹方法,采用照明区域的照度平均标准偏差和系统的效率构建评价函数,用于进一步改善照明光斑的性能。鉴于优化第二步骤设计效率偏低,论文随后针对第二步骤提出了一种改进思想,采用了一种新的照度评价方式,使该步骤仅采用序列光线追迹方法即可显著改善光斑的照度均匀性。改进后的设计方法优化效率较高,并通过理论模拟、实际加工和实验分析验证了该优化方法的有效性。然而,该方法的优化结果过于依赖初始结构,且只能实现简单的连续自由曲面照明。
论文第三阶段从自由曲面照明的本质入手,提出了一种基于Monge-Ampere方程的连续自由曲面照明设计方法,该方法将自由曲面照明问题转化成一个带非线性边界条件的Monge-Ampere方程。分别针对平行光和点光源照明,建立了相应的自由曲面照明数学模型,并给出了该类数学模型详细的求解算法。采用该设计方法解决了复杂的激光光束整形和LED照明问题,获得了连续的自由曲面面型,并通过实际加工和实验分析验证了该设计方法的有效性。该方法具有极好的普适性及较高的设计自由度,取得了自2002年之后自由曲面照明设计方法的一大突破,为自由曲面照明提供了一套有效的光学解决方案。
Freeform surface illumination is an elegant way of lighting, which is remarkably different from the conventional surface illumination, due to its flexible spatial layout and high degrees of design freedom. With optical freeform surfaces in an illumination system, the structure of the system could be significantly simplified, the incident beams of the light source could be well controlled and some special illuminations could be easily produced. Moreover, some new illumination applications would be further explored, and both green lighting and healthy lighting could be achieved by using the freeform surface illumination. The freeform surface illumination could be a major breakthrough of nonimaging optics.
This paper focuses on studying the design methods of freeform surface illumination, and aims to establish an effective theory and optical strategy for designing smooth freeform illumination. Based on the shortcomings of the existing design methods, this work goes through three main research phases, and finally proposes an effective design method for solving the problem of smooth freeform surface illumination, and establishes a mathematical model for the freeform surface illumination.
In the first research phase, a method is proposed for design freeform surface for solving the illumination problem of collimated light. With this method, the inverse problem of freeform illumination design is converted into first-order partial differential equations, and a set of discrete data points of the freeform surface are obtained by mathematically solving these partial differential equations. A specific application of laser beam shaping is given to verify the feasibility of this design method. The continuity of the freeform surface designed by this method is strongly determined by the integrability of the mapping. Then, a design strategy of freeform lens arrays is proposed to obtain smooth freeform surface for laser beam shaping. With this design strategy, the continuity of the freeform surface in each freeform lens unit is ensured. Since freeform optical surfaces are often constructed only to pass though data points in most current CAD software packages and the given normal at the prescribed point can not be ensured, this paper also proposes a novel method to construct smooth freeform optical surfaces using unit tangent vectors of feature data points as constraints. Beams are controlled well with this new construction method, and better results can be obtained with fewer feature data points.
In order to establish a more effective approach, an optimization method is employed in designing smooth freeform surface illumination using ray targeting in the second phase. Two main optimization steps are contained in this method. Based on the sequence ray tracing, the merit function of the first optimization step is constructed with the position deviation on the target plane for each ray to ensure the shape of the illumination pattern. The second optimization step employs the non-sequence ray tracing, and construct the merit function with the relative standard deviation of irradiance and the transmission efficiency of the illumination system to improve the optical performance of the illumination pattern. Due to the low design efficiency of the second step, an efficient evaluation method is introduced in this step to further improve the irradiance uniformity. With this new evaluation method, the irradiance uniformity can be significantly improved just by tracing several hundred rays based on the sequence ray tracing. The modified optimization design method is more efficient, and feasibility of this method is verified by theoretical simulation, manufacturing and experimental test. But, the results of this method are strongly determined by the initial design, and only some simple illumination tasks can be tackled by using this method.
A design theory is established in the third research phase to deal with the problem of smooth freeform surface illumination design without assuming any symmetry based on the concept that this problem is similar to the problem of optimal mass transport. With this method, the freeform design is converted into a nonlinear boundary problem for the elliptic Monge-Ampere equation. For collimated beam and compact light source, a corresponding mathematical model is established for the freeform illumination, and a numerical method is given for solving this kind of mathematical model. Complex illumination tasks for laser beam shaping and LED illumination are easily tackled with this method, and smooth freeform surfaces are obtained. Also, feasibility of this method is verified by theoretical simulation, manufacturing and experimental test. This design method is more effective than other methods reported within the last ten years to the best of our knowledge, for tackling the problem of freeform illumination design.
引文
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[2]刘旭,李海峰,现代投影显示技术,浙江大学出版社,2009,213-316.
[3]Xing Zhao, Zhi-liang Fang, Ji-cheng Cui, Xin Zhang, and Guo-guang Mu, "Illumination system using LED sources for pocket-size projectors," Appl. Opt.2007,46,522-526.
[4]I. Moreno, M. Avendano-Alejo, and R. I. Tzonchev, "Designing light-emitting diode arrays for uniform near-field irradiance," Appl. Opt.2006,45,2265-2272.
[5]K. Wang, D. Wu, Z. Qin, F. Chen, X. B. Luo, and S. Liu, "New reversing design method for LED uniform illumination," Opt. Express 2011.19, A830-A840.
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