# Initial Structure Design and Optimization of an Automotive Remote Head-Up Display
## 1 Introduction  
With the development of the automobile industry, head-up display (HUD) technology has gradually been applied to car driving. It can project driving information as images to the front of the windshield of the car and provide drivers with real-time driving information, thus improving driving safety and comfort [1; 2].  
Augmented reality head-up displays (AR-HUDs) are a research hotspot that has arisen in recent years. Compared with traditional HUDs, AR-HUDs can achieve a longer projection distance and a larger field of view angle, superimpose virtual prompts in the real world, and describe and perceive information intuitively and clearly to achieve a friendly and natural interactive interface [3; 4; 5]. Aiming at the AR-HUD structure design, [PERSON] [6] et al. designed an optical path structure with a virtual image visual distance of 7.5 m and a virtual image field of view angle of \(9.8^{\circ}\times 5.5^{\circ}\) by using a free-form surface and off-axis reflected optical path structure and analyzed the tolerance of the system. [PERSON] et al. [7] designed a virtual image display light path with a virtual visual distance of 10 m and a field of view angle of \(10^{\circ}\times 5^{\circ}\) by using two free-form surfaces and an off-axis double reflection system and conducted simulation analysis on light damage. Finally, the display effect was simulated by UI images. However, the above design only analyzes the design index and results and lacks a detailed demonstration and derivation for the construction of the initial structure. In terms of initial HUD structure design, [PERSON] et al. [8] proposed a HUD initial structure design method based on off-axis triple inversion and analyzed HUD structural constraints and optimization strategies. [PERSON] et al. [9] conducted an initial design of a HUD optical system based on a seed curve expansion algorithm, verified the results, and analyzed the tolerance of thesystem. However, the above initial structure design method is only used for short-distance projection head-up display systems, and there is no mature design method suitable for long-distance display systems currently.  
Existing methods lack a detailed demonstration and derivation for the construction of the initial AR-HUD structure. Inspired by the theory of the [PERSON] rotation formula, we propose a method to design the initial AR-HUD structure. To overcome the difficulty of structural occlusion, we take the example of an off-axis triple inverse structure.  
Our contributions are as follows:  
1. The design index is proposed according to the current industry AR-HUD standard.
2. A method of initial AR-HUD structure design based on the [PERSON] rotation formula is proposed, and combined with the characteristics of the off-axis triple inverse structure, the problem of structural occlusion in the optimization process is solved.
3. We design an example according to the above method and analyze the design results.  
This article is organized as follows: Section 2 presents the basic theory and design objective, and Section 3 describes the proposed initial structure design based on the [PERSON] rotation formula and anti-occlusion optimization method. In Section 4, we design an example and discuss the experimental results. In Section 5, we summarize the content of this paper.