## 3 Results
### 2D-EPE Simulation and Optimization Results  
The optical parameters of HMD, such as FOV, chromatic aberration, color uniformity, brightness uniformity, and light efficiency, need to be considered during the design phase. Sufficiently flexible parameter settings can help the evaluation function quickly escape from local minima. The optimization variables are determined based on the shape and microstructure of the input and output coupling gratings, while the evaluation function is determined according to the specified targets. Iterative optimization of the variables is conducted using software like Zemax OpticStudio [26; 27]. In this paper, a diffractive waveguide system was simulated, using a volume holographic grating as the input coupling grating and a 2D grating as the output coupling grating, as shown in Figure 11a. By partitioning the output coupling grating, the multi-order diffraction efficiency of different sub-regions was set as the optimization variable while keeping the shape of the input and output coupling gratings unchanged.  
Figure 10: Diffractive waveguide system: (**a**) central field of view design; (**b**) the diffractive waveguide couples out the k-vector parallel component ((**a**) is a schematic diagram of the direction of light. The explanation of the arrows and their colors in (**b**) is completely consistent with Figure 2).  
The output coupling grating region is shown in Figure 11b. The output coupling grating was partitioned into hexagonal sub-regions. Each hexagonal 2D grating has a uniform periodicity but a different surface profile, causing the same angle of deflection for incident light rays but different diffraction efficiency distributions, which are collectively combined to form a honeycomb-like array of the output coupling grating. Through software simulations, we established 22 optimization variables and employed brightness uniformity and light energy utilization evaluation as the objective functions for our optimization process. The (\(-\)1,1), (1,1), (0,0), and (0,2) diffraction orders of regions 4, 5, 6, 7, and 8, as well as the corresponding diffraction orders of other regions, were set as optimization variables for further optimization. As shown in Figure 12, when the output coupling grating was not partitioned, the standard deviation of the detector grid illuminance data was 0.00189, while the light efficiency was 0.73%. When the output coupling grating was partitioned, the standard deviation of the illuminance data increased to 0.00274 but the light efficiency increased to 1.9%. This resulted in a significant increase in display brightness with high uniformity maintained. Compared to the nonoptimized model, the light efficiency was significantly improved.  
The experimental results of tracing the 2D grating DLL diffraction function optimized using Monte Carlo ray tracing are shown in Figure 13. After adopting probabilistic splitting, the simulation time was reduced from 11.852 min to 1.744 min per iteration. The time difference in ray tracing consumption increases as the number of traced rays increases, with typically millions of rays required for nonsequential simulation of optical systems. As  
Figure 11: (**a**) The 2D-EPE of diffractive waveguide system; (**b**) outcoupling grating array (In order to mark to distinguish each area. Due to historical version reasons, 1–3 are not used as marks).  
Figure 12: (**a**) Exit pupil illumination before optimization; (**b**) exit pupil illumination after optimization. Incoherent irradiance unit: watt/cm\({}^{2}\), co-ordinate unit: mm.  
the complexity of the optical system increases, such as in diffractive waveguides where multiple traces of the same object are required, the superiority of the probabilistic splitting DLL optimized by Monte Carlo ray tracing in this study will gradually emerge.