# Initial Structure Design and Optimization of an Automotive Remote Head-Up Display
## 2 Basic Theory and Design Objective
### Design Parameter Analysis  
In the process of AR-HUD design, the main design parameters include virtual image visual distance, field of view angle, eyebox size, source image size, and image quality requirements.  
In the AR-HUD projection process, the projected image needs to be combined with the real scene. Considering driving comfort, the virtual visual distance of the AR-HUD required in the industry is between 7.5 m and 20 m [10]. This paper adopts the 7.5 m virtual visual distance commonly used in the industry as the design objective.  
The field of view angle refers to the angle between the edge of the observed object and the center of the observation point, and in the head-up display system, it is just the angle between the edge of the formed virtual image and the center of the pupil of the human eye. The current industry standard for AR-HUD generally sets the field of view angle to about 10\({}^{\circ}\)\(\times\) 5\({}^{\circ}\).  
Figure 1: Virtual image schematic diagram.  
As shown in Figure 2 below, eyebox refers to the range through which the driver's eyes can adjust during driving without affecting the sharpness of the virtual image. This data is an empirical statistical value, which is usually set according to relevant research and the demands of automobile manufacturers. In this paper, the empirical value is set at 130 mm \(\times\) 50 mm.  
As shown in Figure 3 below, the visual distance of the virtual image is 7.5 m, and the field of view angle is set to \(10^{\circ}\times 5^{\circ}\). The horizontal imaging size \(X\) can be calculated as  
\[X=2d\cdot\tan\frac{10^{\circ}}{2}=1312.33\ \mathrm{mm}. \tag{1}\]  
Similarly, the imaging size in the vertical direction can be calculated as 654.91 mm.  
The typical resolution of the human eye is \(1^{\prime}\). When the field of view angle is \(10^{\circ}\times 5^{\circ}\), in order for the driver to clearly observe the virtual image generated by the HUD system, the image resolution is required to be greater than 600 \(\times\) 300 pixels. In this paper, the DLP5530S-Q1 automotive digital micromirror device (DMD), produced by Texas Instruments, is selected as the source image module with a resolution of 1152 \(\times\) 576 pixels, which can achieve a high-performance augmented reality HUD, gaining a wider field of view and greater driver eye movement range.  
Based on the virtual image resolution of 1152 \(\times\) 576 pixels, the size of each pixel of the horizontal virtual image \(\mu\) can be calculated as  
\[\mu=\frac{X}{R_{x}}, \tag{2}\]  
where \(X\) is the horizontal imaging size and \(R_{x}\) is the virtual image resolution at x direction. It can be calculated at about 1.14 mm.  
Figure 3: Virtual image size calculation diagram.  
Figure 2: Eyebox.  
To obtain the analytical modulation transfer function (_MTF_) value [6] of the optical transfer function, according to [PERSON]'s sampling theorem, the resolution of the optical system in the virtual image space \(MTF_{vis}\) is at least  
\[MTF_{vis}=\frac{1}{2\mu}\approx 0.44 lp/\mathrm{mm}. \tag{3}\]  
According to the analysis of the above technical indicators, considering the compact HUD structure, the machinability of a free-form surface in the later stage, and optimizing the layout, the specific parameters and indicators of the HUD system in this paper are shown in Table 1 below: