Freeform Lens Design for Uniform Rectangular Illumination

Light flux from LED must be redistributed to meet the needs of lighting in most cases, a new method is proposed for its secondary optic design. Based on refractive equation and energy conservation, a set of first-order partial differential equations which represent the characters of LED source and desired illumination were presented. The freeform lens was constructed by solving these equations numerically. The numerical results showed that we can get a freeform lens for the illumination of uniformity near to 90%, with considerable high computation speed. This method can shorten the designing time of the freeform lens with high accepted tolerance.

Design of double freeform-surface lens for LED uniform illumination with minimum Fresnel losses

An optimization method is proposed for designing an LED freeform lens which produces a uniform circular pattern with high energy efficiency. This method is composed of three main aspects: design of the initial guess, parameterization of the freeform surface, and construction of the merit function. The initial guess is created by solving an ordinary differential equation numerically. An approach of selecting optimization points is introduced for parameterization of the freeform surface. The merit function is constructed by use of the irradiance uniformity and the efficiency of the lens. Design examples are given, and the results show that the irradiance distribution is well controlled with a maximum uniformity (the relative standard deviation of irradiance, RSD) of 0.0122 and a maximum efficiency of 93.88%. This optimization method can be generalized to design freeform lenses with different lighting patterns or without rotational symmetry.

This paper presents a three dimensional lens shaping method for dual-LED packaging module using silicon micromachined substrate. The technology utilizes flower-typed structure and silicone dispensing process to fabricate a 3-D freeform encapsulation lens for achieving uniform illumination and specific light pattern. Based on the experimental results, with the size of 2×4 mm2 of the flower-typed island, the freeform lens is formed with a sag height of 2.7 mm when the dispensing volume is 15 mm3. On the measurement, the projected light pattern is obvious that the light distribution is similar to a rectangular shape, with a good uniformity.

In high power laser system, such as laser forming, the requirement for the intensity distribution of the focused laser profile must be top head, steep edge, low side lobe and concentrated high power performance in the main lobe. Such uniform illumination can be realized by the Diffractive Optical Element (DOE), because the DOE has many advantages, such as high light efficiency of pure phase modulation, strong flexibility of phase distribution design and so on. In some application field, uniform illumination is needed on the plane non-perpendicular to the optical axis and the DOE designed by conventional method which only involves the focal plane is difficult to realize such uniform illumination on the planes which are at angles of 30 degree(s), 45 degree(s), 55 degree(s) with the optical axis. To obtain good illumination uniformity on the inclined plane, based on the method of designing a DOE with long focal depth, an indirect design principle is proposed to realize such uniform illumination, by designing the phase distribution of the DOE to make uniform illumination on three planes at right angles with the optical axis, then the uniform illuminations on the incline planes are assured. A hybrid algorithm based on hill-climbing and simulated annealing is utilized for phase design which exploits the ability of strong convergence of the hill-climbing and the global optimization potential of the simulated annealing sufficiently. Simulated results show the non-uniformity on the incline planes at angles of 30 degree(s), 45 degree(s), 55 degree(s) with the optical axis are 5.91%, 4.00%, 3.38%, respectively.

Optical design for an integrated light source is currently a hot topic, but it is also difficult due to the complexity of the calculations. In this paper, based on the edge-ray principle and the grid division method, two types of lenses for creating a 3:1 uniformly illuminated rectangular spot and 1:1 uniformly illuminated square spot are designed. Research results show that when the ratio of the size of the LED light source to the lens height is 1:10 and 1:5, i.e. it is equivalent to a point source, the uniformity of illuminance on the target surface is as high as 90%, and the system energy utilisation is 88%. When the ratio of the size of the LED source to the lens height is 1:3.3, 1:2.5 or 1:2.0, i.e. the equivalent of an extended source, the uniformity of illuminance on the target surface is more than 80% and the system energy utilisation is about 88%. This means the lenses can maintain the high energy efficiency and illuminance uniformity for an extended source. Tolerance analyses were also conducted. It seems that the illumination uniformity is sensitive to light source installation errors, but when the offset of the LED from the lens is less than 0.2 mm, illumination uniformity is maintained at a high level.

Recent energy efficient illumination advancements have capitalized on using light-emitting diodes (LEDs) in combination with freeform lenses. However, the available freeform lens design methods are application specific. In addition, manufacturing of this class of optics is challenging. In this work, considering manufacturing constraints, we apply a customized algorithm to design freeform lenses for (1) transforming LED radiation into a uniform rectangular illumination pattern and (2) shaping collimated LED light beams into complex image target irradiance distributions. The algorithm is based on a numerical solution of the elliptic Monge–Ampere equation. Then, we proposed manufacturing these lenses using a modified ink-jet 3D printing technology called Printoptical technology. The demonstrated optical performance of printed lenses, exhibiting surface roughness of $\textrm {RMS} = 10\pm 2$RMS=10±2 nm, is in good agreement with the simulation. We also explored an industrial application of the 3D-printed lens matrix for low-cost illumination of a paper milling machine.

Nonuniform illumination caused by extended source is one of the challenging points for high power Light-emitting diodes (LEDs) especially for LED array applications. A new design method to improve the uniformity of illuminance of extended source is presented. To obtain high uniformity at target plane, a feedback optimization method is introduced including target plane girds, light source girds and target plane and light source girds optimization algorithms. Monte Carlo ray tracing simulation results demonstrate that our feedback optimization algorithms are able to obviously increase the uniformity of illuminance at target plane. The uniformity increases from 0.53 to 0.9, 0.77 and 0.88 by our three different optimization algorithms respectively. This method would be a potential way in improving the uniformity of illuminance at target plane with little light pattern expansion.

Freeform lenses play a critical role in LED packaging due to their beam-shaping capabilities. However, existing packaging designs commonly neglect the Fresnel loss effect at multi-interface boundaries. Addressing this gap, this study establishes a synergistic freeform lens design methodology based on a multi-objective optimization framework, achieving breakthroughs in both high light extraction efficiency and optical quality control. Leveraging the Fresnel equations, a multi-interface energy transmission model is constructed to quantitatively characterize the coupled mechanism of total internal reflection and refraction losses. A triobjective optimization scheme was implemented, targeting flux loss minimization, surface curvature regularization, and illuminance uniformity enhancement. Pareto-optimal solutions were generated via the NSGA-II algorithm, balancing Snell's law compliance, differential geometry constraints, and ray-mapping optimization. Experimental validation demonstrated reduced total flux loss from 8.98 to 4.41 lm, suppressed peak surface curvature from 25.4 to 2.42, and improved illuminance uniformity from 0.84 to 0.91. The proposed methodology provides a systematic approach for designing high-efficiency freeform optics with balanced photometric performance.

The collimating lens used for uniform illumination has been widely used in lighting engineering as the LED secondary optics. A novel lens structure including four freeform surfaces is designed in this paper, the freeform surfaces can be constructed by an iterative process, which is based on nonimaging optics and geometrical optics. This method can be used not only for Lambertian-type LED source, but also for near-Lambertian-type LED source. Since the LED source is regarded as a point source during the design process, in order to verify the feasibility of the design method, an LED chip whose size is 1 mm *1 mm is used in the simulation. Three lens models with different initial parameters are established for optical simulation. The simulation results show that the total optical efficiency is greater than 87%, the uniformity is greater than 0.93, and the full width at half maxima (FWHM) is approximately 2 * 2 degrees. The performance difference of the three models is small, which indicates that the initial parameters have little effect on the lens performance under certain conditions.

Energy mappings of edge rays are required in design of a freeform lens for LED illumination. The mappings dominate the outcome of the lens design and the final distribution of the LED light illumination. Smoothness of the mappings is critical to assure the edge-ray principle hold. Design of energy mappings with good smoothness for circular distribution of uniform luminance is known, but the design for non-circular distribution is not well discussed in the literature yet. In this paper, a design method of smooth energy mappings for rectangular distribution of uniform luminance is proposed. It will be demonstrated by the Monte Carlo ray tracing simulations that the proposed mappings can generate luminance distribution with a clear-cut horizon and a 15° slope.

Freeform lenses can be designed for diverse illumination profiles with good uniformity. However, most of the previous studies formulated for a single point source and the lens to design has a spherical bottom. In this study, the formulation is extended for multiple point sources and for lenses with a flat bottom in favor of prototyping and manufacturing. The extended formulation requires only a freeform surface to design. However, it could be over determined if the light rays emitted from the multiple point sources overlap at the near field. The weighted least-square method is introduced to solve the over-determined problem. A weighting function correlated with the emitting intensities of the sources is proposed to design for illumination profile fit and uniformity in trade-off. The adequacy of the extended formulation is demonstrated by simulation. Circular and rectangular illuminations of multiple point sources in different layouts are illustrated. The simulation results show that profile fit and uniformity could be significantly affected by a source offset. With the offset taken into account in the extended formulation, the effects can be properly collimated.

Large aperture continuous phase diffractive optical element to realize uniform focal spot

Design of a novel, alignment-free, ultra-thin multi-layered diffuser film for mini-LED backlight unit and other LED general lighting applications is presented. The ultra-thin diffuser film is inserted between the blue mini-LED array and the QD film for the backlight application. The diffuser film consists of two optical elements, a diffractive layer (DOE or a microprism-array) faced on the mini-LED side and a dielectric multi-layer stack faced on the QD film side. The diffractive layer optimally adjusts the incident angle of the lights emitted out of the mini-LED and the dielectric multi-layer stack acts as an angle-selective filter. The innovative combination of the two optical elements realizes distinct improvement of lighting efficiency and illuminance uniformity without alignment of the diffuser film with the mini-LED array. We also demonstrate the optimal design of the diffuser film using Pareto solution analysis. This method is flexibly applicable to optimally designing not only mini-LED backlight units but also various general lighting applications.

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.