## 4 Validation of Homogenization Principle
### Prototype Demonstration  
A desktop prototype is set up to investigate the performance of the homogenizer. Three RGB laser diodes (450 nm, 520 nm, 638 nm) are used as the light source with respective collimators and beam expanders for rough pre-shaping, as mentioned in Section 4.1. A dichroic prism is used afterward for the beam combination. Once the laser beams are combined into one joint beam, it goes into the homogenizer. Both the beam expander and the homogenizer components used in the demonstrator are manufactured by an IMES five-Axis milling machine and made of PMMA. After the homogenizer  
Figure 5: Simulation model of a LA homogenizer with the distibutions of the radiation intensity of the incident light and the target plane. locates the twisted nematic LCoS detailed in Table 1 with a PBS (Polarizing Beam Splitter), which is commonly used in display applications with the LCoS. Finally, a projection lens group projects the light from the LCoS to a measurement screen. Figure 6 shows the demonstrator setup schematic and the manufactured LA. For the evaluation of the homogeneity, the ANSI uniformity standard for evaluating projectors is applied. The whole illumination area is divided into nine parts on average. The center point of each part is the measuring point in terms of the illuminance. In addition, four more measuring points on the corner are taken into account. They are defined as 10% of the distance from the corner to the center point of the entire illumination area. The sampled measuring points are shown in Figure 7. The homogeneity is defined by \(Ur+\) and \(Ur-\), which are the maximum deviation from the average measurements [24]. \(Ur+\) and \(Ur-\) can be calculated while using following equations [24; 25]:  
\[Ur+=\left(\frac{\text{Maximum}\left[E_{i}\right]_{i=10,11,12,13}}{\text{ Average}\left[E_{i}\right]_{i=12,\ldots,9}}-1\right)\times 100\% \tag{5}\]  
\[Ur-=\left(\frac{\text{Minimum}\left[E_{i}\right]_{i=10,11,12,13}}{\text{ Average}\left[E_{i}\right]_{i=12,\ldots,9}}-1\right)\times 100\% \tag{6}\]  
where \(\text{Maximum}[E_{i}]_{i=10,11,12,13}\) and \(\text{Minimum}[E_{i}]_{i=10,11,12,13}\) mean the maximum and the minimum illuminance values among points 10-13, respectively. \(\text{Average}[E_{i}]_{i=1,2,\ldots,9}\) means the average illuminance value among points 1-9. A lux meter measures the illuminance of these thirteen points, and these values are used to calculate the homogeneity deviations. Besides the illuminance measurement, an LMK color five CCD camera collects the luminance information of the entire illumination area as a reference, so that human eyes can directly observe the illumination result. The measuring setup is also presented in Figure 7.  
The \(Ur+\) and \(Ur-\) values according to Equations (5) and (6) are calculated from the measured illuminance data by the lux meter, which are +5.76 %/\(-\)6.51 %. This result is fully acceptable for illumination from practical experiences, and human eyes can hardly perceive the inhomogeneity. Thus, using LAs as the homogenizer for high-resolution headlamp systems is promising. The measured luminance image from the luminous camera and the photographed projection picture is shown in Figure 8 as a reference. Because of the coherence laser light sources, the illumination on the measuring surface shows an apparent speckle pattern, which also affects the whole homogeneity. Figure 6: Demonstrator setup and manufactured LA. (**a**) Demonstrator schematic for the performance investigation; (**b**) The manufactured LA. When directly using laser beams as the light source in headlamp systems, a further investigation of whether the laser speckle impacts the illumination performance should be made. When necessary, additional optics or vibrators can be considered as complementary elements to the LAs to cope with the speckle pattern [26; 27]. Besides the laser speckle, the projection homogeneity is affected by the aperture ratio of the LCoS as well. An LCoS has inter-pixel dead zones, although its aperture ratio is relatively high.