# Design of Dual-Focal-Plane AR-HUD Optical System Based on a Single Picture Generation Unit and Two Freeform Mirrors

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## Abstract

**:**

## 1. Introduction

## 2. Dual-Focal-Plane AR-HUD Structure and Principle

## 3. AR-HUD Optical System Design

#### 3.1. Design Considerations

_{v max}is the maximum value of the vertical FOV; F

_{v min}is the minimum value of the vertical FOV; and F

_{H}is the size of the horizontal FOV. According to Equations (1) and (2), the far-field VID size of this system is 2.278 m × 0.698 m, and the near-field VID size is 0.797 m × 0.086 m, which is enough to display rich AR interactive information, and the near-field VID area will not be too large to cause field of view obstruction. In conclusion, the parameter is reasonable.

#### 3.2. Optical Design Optimization

_{ij}is the coefficient of the x–y term in the XY polynomial, c is the base curvature of the surface at the vertex, and k is the conic constant. During the design, the whole optical system is asymmetric, and the range of the FOV is rectangular. Therefore, it is necessary to sample the entire rectangular field of view. The near-field and far-field image plane configurations of the FOV sampling method for this paper are shown in Figure 3.

_{i}is the coordinate of the ith FOV on the ideal image plane, and P

_{i}′ is the coordinate of the ith FOV on the real image plane. To constrain the distortion, we controlled the distance between Pi and Pi′, and the distortion value R of Pi′ is shown in Equation (4):

_{2}~P

_{9}corresponding to F2~F9 and the real image plane coordinates P

_{2′}~P

_{9′}.

_{10}~P

_{21}corresponding to F10~F21, and the real image plane coordinates P

_{10′}~P

_{21′}were increased for constraints so that the distortion values of the whole FOV were optimized to within the range of human eyes.

#### 3.3. Performance Analysis

## 4. Projection Lens Design and Overall Evaluation

## 5. Discussion of Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Schematic diagram of dual-focal-plane AR-HUD parameters. (

**a**) Schematic of the field of view setup; (

**b**) schematic of the eye pupil and eyebox.

**Figure 3.**Optimization process field of view settings. (

**a**) Pre- and mid-optimization; (

**b**) post-optimization.

**Figure 7.**Enlarged view of dashed box in Figure 6.

**Figure 8.**Performance analysis of the eye pupil at the eyebox center position of the AR-HUD. (

**a**) Far-field configuration spot diagram; (

**b**) far-field configuration MTF curve; (

**c**) far-field configuration aberration grid diagram; (

**d**) near-field configuration spot diagram; (

**e**) near-field configuration MTF curve; (

**f**) near-field configuration aberration grid diagram.

**Figure 11.**Imaging performance in the entire eyebox. (

**a**) Minimum MTF value for the full FOV at each eye-pupil position in the far-field configuration; (

**b**) maximum distortion value for each eye pupil position in the far-field configuration; (

**c**) minimum MTF value for the full FOV at each eye-pupil position in the near-field configuration; (

**d**) minimum distortion value for each eye pupil position in the far-field configuration.

**Figure 12.**Binocular divergence parallax analysis results. (

**a**) Results of far-field image analysis when both eyes are at E1 and E2 positions, respectively; (

**b**) results of near-field image analysis when both eyes are at positions E1 and E2, respectively; (

**c**) results of far-field image analysis when both eyes are at positions E3 and E4, respectively; (

**d**) results of near-field image analysis when both eyes are at positions E3 and E4, respectively.

**Figure 13.**Image simulation results. (

**a**) Eye pupil at the leftmost side of the eyebox; (

**b**) eye pupil at the center of the eyebox; (

**c**) eye pupil at the rightmost side of the eyebox.

**Figure 18.**The results of the projection lens performance analysis. (

**a**) Far-field configuration MTF curve; (

**b**) far-field configuration distortion grid; (

**c**) near-field configuration MTF curve; (

**d**) far-field configuration distortion grid.

Parameter | Value |
---|---|

FOV | Far: 13° × 4° Near: 13° × 1.4° |

VID | Far: 10 m Near: 3.5 m |

Eyebox size | 130 mm × 60 mm |

Distortion | <5% |

Pupil diameter | 6 mm |

Modulation transfer function (MTF) @ Nyquist frequency | >0.3 lp/mm |

x^{m}y^{n} Item | PM | SM |
---|---|---|

x | / | −3.690 × 10^{−5} |

y | / | −9.107 × 10^{−17} |

x^{2} | −7.694 × 10^{−5} | −4.278 × 10^{−4} |

xy | 2.114 × 10^{−5} | −2.338 × 10^{−5} |

y^{2} | 2.352 × 10^{−4} | −3.614 × 10^{−5} |

x^{3} | −3.691 × 10^{−8} | −1.816 × 10^{−7} |

x^{2}y | 1.411 × 10^{−7} | 1.261 × 10^{−6} |

xy^{2} | −4.745 × 10^{−8} | −9.538 × 10^{−8} |

y^{3} | 2.666 × 10^{−7} | −9.404 × 10^{−7} |

x^{4} | −1.047 × 10^{−10} | 1.749 × 10^{−10} |

x^{3}y | −3.501 × 10^{−12} | 2.898 × 10^{−10} |

x^{2}y^{2} | 2.373 × 10^{−10} | 1.284 × 10^{−10} |

x^{2}y^{3} | 9.535 × 10^{−10} | 3.851 × 10^{−9} |

y^{4} | 4.867 × 10^{−9} | 1.407 × 10^{−8} |

Qin’s [21] | Shi’s [20] | Volkswagen ID4′s [32] | Ours | |
---|---|---|---|---|

FOV | Far: 10° × 3° Near: 6° × 2° | Far: 10° × 5° Near: 5° × 1° | Far: 9° × 4° Near: 7° × 1° | Far: 13° × 4° Near: 13° × 1.4° |

VID | Far: 9 m Near: 2.5 m | Far: 7.8 m Near: 2.7 m | Far: 10 m Near: 3 m | Far: 10 m Near: 3.5 m |

Eyebox size | 120 mm × 60 mm | 150 mm × 80 mm | / | 130 mm × 60 mm |

Volume | 8.5 L | 30 L | 14 L | 16 L |

PGU | Single LCD | Two LCDs | Two LCDs | Single DLP |

Distortion | <3.05% | <3.60% | / | <3.58% |

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**MDPI and ACS Style**

Fan, C.; Kong, L.; Yang, B.; Wan, X.
Design of Dual-Focal-Plane AR-HUD Optical System Based on a Single Picture Generation Unit and Two Freeform Mirrors. *Photonics* **2023**, *10*, 1192.
https://doi.org/10.3390/photonics10111192

**AMA Style**

Fan C, Kong L, Yang B, Wan X.
Design of Dual-Focal-Plane AR-HUD Optical System Based on a Single Picture Generation Unit and Two Freeform Mirrors. *Photonics*. 2023; 10(11):1192.
https://doi.org/10.3390/photonics10111192

**Chicago/Turabian Style**

Fan, Chengxiang, Lingbao Kong, Bo Yang, and Xinjun Wan.
2023. "Design of Dual-Focal-Plane AR-HUD Optical System Based on a Single Picture Generation Unit and Two Freeform Mirrors" *Photonics* 10, no. 11: 1192.
https://doi.org/10.3390/photonics10111192