Zexin Feng

Design of compact and smooth free-form optical system with uniform illuminance for LED source

A feedback modification method based on variable separation mapping is proposed in the design of free-form optical system with uniform illuminance for LED source. In this method, the non-negligible size of LED source is taken into account, and a smooth optical system is established with single freeform surface regenerated by adding feedback to the lens design for a point light source. More rounds of feedback can improve the lens performance. As an example, a smooth free-form lens with rectangular illuminance distribution is designed, and the illuminance uniformity is improved from 18.75% to 81.08% after eight times feedback.

Design of LED freeform optical system for road lighting with high luminance/illuminance ratio

A systematic method is proposed for designing an optical system for road lighting using an LED and a freeform lens that is optimized to produce a certain luminance distribution on the road surface. The proposed design method takes account of the luminance characteristics of the road surface, the energy efficiency of the system, the glare problem of the luminaire and the effects of four adjacent luminaries illuminating a single road surface. Firstly, the road surface illuminance with a polynomial of cosine functions along the road is optimized to maximize Q (the ratio of the average luminance to the average illuminance) as well as satisfying the lighting requirements provided by CIE. Then, a smooth freeform lens with this optimized illuminance is designed based on the variable separation method and the feedback modification method. Results show that, from two typical observer positions on the 2-lane C2 class road, luminaires with these freeform lenses can provide Q values of 7.90 × 10(-2) and 8.69 × 10(-2), the overall road surface luminance uniformity of 0.55 and 0.56, the longitudinal road surface luminance uniformity of 0.72 and 0.79, and the glare factors of 10.06% and 6.73% .

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 Snells 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.

Beam shaping system design using double freeform optical surfaces

A numerical double-freeform-optical-surface design method is proposed for beam shaping applications. In this method, both the irradiance distribution and the wavefront of the output beam are taken into account. After numerically obtaining the input-output ray mapping based on Energy conservation using the variable separation method, the two freeform optical surfaces can be constructed simultaneously and point by point corresponding to the ray mapping based on Snells law and the constancy of the optical path length. The method is only applicable for separable irradiance distributions. However, such a restriction is fulfilled by many practical laser beam shaping examples. Moreover, the restriction can simplify the computation considerably. Therefore, the method may be quite useful in practice, although it is not applicable to more general cases. As an example, the method was applied to design a two-plano-freeform-lens system for transforming a collimated 20 mm Gaussian laser beam (beam waist: 5mm) into a uniform 10 × 40 mm(2) rectangular one without changing the wavefront. Simulation results show that we can obtain a dual lens beam shaping system with the relative root mean square deviation of the irradiance ranging from 0.0652 to 0.326 and the power ratio concentrated on the desired region ranging from 97.5% to 88.3% as the output beam transfers from 0mm to 1000mm.

Freeform illumination lens design using composite ray mapping

We develop a new ray mapping approach to address the surface error and hot spot issues in designing a freeform total internal reflection (TIR) lens for nonrotational uniform illumination. Our proposed ray mapping approach partitions the source intensity distribution in the peripheral regions using the traditional spherical coordinate system to design the freeform TIR surfaces and in the central regions using the modified spherical coordinate system to design the freeform refractive surface. This new design method will reduce the surface error in the current ray mapping methods, therefore improving the illumination uniformity significantly. In addition, the freeform lens designed with this approach is much more robust than the lenses designed using other ray mapping methods.

Tailoring freeform illumination optics in a double-pole coordinate system

We have developed a new method to design freeform illumination optics by introducing a double-pole coordinate system in ray mapping. This method establishes a much more accurate ray mapping by moving the two poles of the spherical coordinate system to the southernmost point of the sphere and overlapping them together. It can reduce surface error and improve illumination uniformity significantly. The residual surface error (RSE) of the freeform lens designed in the double-pole coordinate system is one magnitude smaller than that of the lens designed in the (θ,φ) coordinate system and is only 1/3 of that of the freeform surface designed in the (u,v) coordinate system.

Freeform illumination optics construction following an optimal transport map

We present a modified optimal transport (OT) ray-mapping approach for designing freeform illumination optics. After mapping the source intensity into a virtual irradiance distribution under stereographic projection, we employ an advanced OT map computation method with the ability to tackle nonstandard boundary conditions. Following the computed map, we construct the freeform optical surface directly from normal vectors by requiring that the chord between two adjacent points is perpendicular to the average of the two normal vectors at these two points and enforcing this relationship with a least squares method. Examples of designing freeform lenses for LED sources show that we can produce various uniform illumination patterns with high optical efficiencies.

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

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.

Research on the particular temperature-induced surface shape of a National Ignition Facility deformable mirror

We investigate the changes in the shape of a deformable mirror used at the National Ignition Facility caused by differences in temperature between the working environment and the mounting temperature of the mirror. In general, the temperature-induced profile change of the mirror is dominated by a few low-order aberrations, which mainly result in defocus. However, after these low-order distortions are corrected, there remain special, higher-order, surface distortions caused by the particular arrangement, construction, and mounting of the mirror actuators. This work analyzes these special aberrations, and their dependence on the particular actuator design, using the finite element method. Experiments are carried out to verify the computational results, and finally, design considerations to help minimize the temperature-induced high-order aberrations are suggested.

Reflector design for large-size spherical surface sources

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.