# A Study of High-Efficiency Laser Headlight Design Using Gradient-Index Lens and Liquid Lens
## 3 Simulation and Analysis of the Headlight Optical System
Secondly, we find some fiber files from LightTools database. They are files with all fixed data so these are not able to be optimized. If laser diode is determined like in Figure 7B, fiber will be selected in order to achieve best performance according to light efficiency, basically like in Figure 7C. Generally speaking, fiber and laser diode both are selected before optimization procedure in order to match of optical components each other's, which is nothing to do with later optimization. The parameters of optimization with regard to this system are following:  
1. ROD variables: total length; width and height in order to reach best light efficiency in Figure 7D. 2. GRIN optics variables: GRIN index from polar coordinates on optical axis and its thickness. In order to reach uniformity in Figure 7E. 3. Freeform optics variables: Radius and off-axis X and Y coefficients in order to achieve best results inclusive of light efficiency, uniformity and the most important, match the safety requirement ECE R-112 in Figures 8 and 9. Figure 6: Assembly schematic of the 3D digital optical headlight system, with laser source numbering. 2, 3, 4, 5, 6, 7, 8, e, f, total nine diodes are designed and optimized for low beam; compared to low beam, eight (a, b, c, d, e, f, g, h) is designed and optimized for high beam. More laser diodes is employed for low beam is due to light path of low beam suffer much more vignetting effect than high beam ones and low beam’s projection area is slightly larger than high beam’s. In addition, this set of laser diode array was designed for further upgrade of smart active laser headlight system with digital signal processing so that there must be more room for wide projection of low beam. Figure 7: **(A)** Ray trace analysis of the optical system. Each chart indicates the different light source distribution at various image planes, **(B)** The output light pattern of laser beam, **(C)** the selected output light pattern from various optical fibers. If laser diode is selected, fiber must match this laser diode to reach maximum light efficiency, **(D)** The output light of ROD, **(E)** the optimized output light pattern of GRIN lens (also check Figure 2a,b). Next, the diffused laser beam entered the liquid lens to enable switching between the high and low beams, wherein the liquid lens curvature and optical axis were changed. The freeform lens was made of Kopp Sharp CutRed 2424 glass. Due to effect of complicated annealing process during freeform manufacture, only very few optical glass in the current market is feasible for this project. CutRed 2424 glass is always strongly recommended for this kind of project. It has a curved surface shape, which was constructed by Equation (1). Adjusting the parameters to values that satisfy the regulations is time consuming and labor intensive. Therefore, we employed an automated program, in which the Monte Carlo method was used as the optimization engine to iteratively optimize surface parameters. Figure 10 shows the automated optimization process. First, the initial values of the parameters in Equation (1) were set, and the range of parameter value intervals was given. Then, the surface position and illuminance values detected according to the regulations were set as the optimization target values. The Monte Carlo method employed by LightTools for the basic theory of ray tracking was used to conduct an iterative operation using an automatic random sampling technique to determine optimal surface parameters, which could be obtained with a certain number of iterations [25]. In this experiment, the high-beam system had eight laser sources (a, b, c, d, e, f, g, h) turned on, with a total power of 6.4 W for high beam after reduction of system light loss due to not perfection of light efficiency. The experimental data of the high-beam detection points are shown in Figure 8b. The maximum illumination was 55.2 lux, as shown in Figure 8a, which satisfies the high-beam regulation requirements.