# Initial Structure Design and Optimization of an Automotive Remote Head-Up Display
## 4 Simulation Design and Results
### Image Quality Analysis  
Imaging optical design must correct the aberration of the optical system, and the determination of aberration tolerance can effectively guide the optical design. In the process of HUD design, spot diagrams, optical modulation transfer functions, and distortion are usually used to evaluate the image quality. Figure 10: Ray tracing map. \begin{table}
\begin{tabular}{c c c c c} \hline
**Surface** & **Radius (mm)** & **Interval (mm)** & **Tilt x (\({}^{\circ}\))** & **Tilt y (\({}^{\circ}\))** \\ \hline M\({}_{1}\) & \(-\)12,494.98 & \(-\)140.64 & \(-\)39.229 & 0.223 \\ M\({}_{2}\) & \(-\)106.487 & \(-\)154.320 & \(-\)12.525 & 3.225 \\ Windshield & \(-\)7526.66 & 286.972 & 61.836 & \(-\)6.956 \\ \hline \end{tabular}
\end{table} 
Table 3: Optical path structure parameters. Figure 9: Optical path of the AR-HUD virtual image display. Spot diagrams are tools that describe the image quality of an optical system, which refers to the distribution of the image obtained by imaging a point light source in the image plane. The size and shape distribution of the spot are directly related to the aberration of the optical system. The smaller the distribution area of the spots is, the smaller the aberration is. In addition, the more concentrated the spots are, the better the image quality of the system is. The pupil of the human eye is regarded as the aperture stop of the system, and the diameter of the pupil of the human eye is usually between 1 and 4 mm. In this paper, the diameter of the entrance pupil is set at 4 mm. The spot diagram distribution of each field of view on the image plane is shown in Figure 11 below. The RMS radius of the center field of view is 16.407 \(\upmu\)m, and the maximum RMS radius of the edge field of view is only 89.011 \(\upmu\)m, which is less than the experience value of AR-HUD design (100 \(\upmu\)m). The distribution of visible light spots in the nine fields of view shows that they are all within Airy spots, the shape of the spots is relatively regular, and they are concentrated near the center of the circle, indicating that the whole system has small aberrations and good imaging quality. In optical systems, the modulation transfer function (MTF) can be used to describe factors such as image quality, contrast, resolution, and sharpness. The specific calculation process can be referred to in [14]. In general, the MTF curve is expressed as the response to the spatial frequency of the input signal, with a value between 0 and 1, indicating the ability of the system to transmit a certain spatial frequency component. High-quality optical systems typically have high MTF values, which means that they can efficiently transmit signals with a high spatial frequency component, thus providing higher resolution and better image quality. The MTF curve of the AR-HUD system designed in this paper in the image square space is shown in Figure 12 below. The MTF curve of the full field of view is basically greater than 0.5 at the maximum Nyquist frequency of 0.44 lp/mm, and the performance of the entire curve is close to the diffraction limit, indicating that the overall imaging quality is good. Figure 13a-d below are the distortion maps obtained by the system in the scanning mode of +y, +x, -y, and -x respectively. The distortion values of the system in the four scanning directions are 0.3110%, 0.3111%, 0.3617%, and 0.3342%, which are far less than the set standard value of 2%, indicating that the distortion of the system is small. The results meet the design requirements. The image simulation tool provided by Zemax software (OpticStudio 19.4 Premium) is used to simulate and analyze the imaging performance of the system, and the original optical position image is compared with the simulation image to reflect the effect of the system in actual imaging. The specific effect is shown in Figure 14 below. It can be seen from the grid simulation diagram that the system has a slight tilt to the left during imaging, and some image details are missing. However, in the actual navigation image simulation,