# Tailoring the V-Model for Optics: A Methodology for Optomechatronic Systems
## 3 Concretization of the V-Model for High Resolution Lighting Systems
Depending on the defined technologies for light modulation and generation as well as on the elicited requirements, different system architectures are feasible. Using a light modulator, the optical system of a high-resolution lighting system can be divided into a subsystem to illuminate the light modulator and a subsystem to project it into the application area. Both subsystems are functionally as well as spatially interdependent. Functional dependence arises from the strategy to illuminate the active area of the modulator (cf. paragraph Define illumination strategy) and the lighting of the projection area (cf. paragraph Adjust distortion). The spatial dependence derives from the chosen technology for light modulation, which at the same time affects the Etendue of the system. For example, when using a DMD to implement a non-telecentric system architecture, higher angles are required to illuminate the light modulator in order to achieve sufficient separation of the incident light from the illumination system and the light reflected into the projection system than with a telecentric system architecture. As the illumination angle increases, the seemingly illuminated area of the light modulator is reduced, thus reducing the Etendue of the DMD. Figure 7: Method for the preliminary design of high-resolution lighting systems according to [16]. * **Define illumination strategy:** Strategies to illuminate the active area of the modulator can be differentiated primarily into imaging and non-imaging and secondarily into homogeneous and inhomogeneous [31; 57]. According to photometric regulations for headlamps, which are specified in various ECE regulations, an inhomogeneous distribution of illuminance within the traffic area is required [58; 59; 60]. Therefore, it seems to be obvious to use an inhomogeneous strategy to illuminate the active area of the modulator. However, an inhomogeneous illuminance distribution of the active area of the modulator, regardless of whether it is generated imaging or non-imaging, can lead to a damage of individual micromirrors or of the entire light modulator due to the irregular heat input in case of insufficient cooling. Using imaging illumination strategies, a precise illumination of the active area of the modulator is possible given appropriate manufacturing and assembly tolerances of the optical and mechanical components. Luminous flux losses, which occur when using non-imaging illumination strategies due to illumination overfill of the active area of the modulator [61; 62], are therefore reduced. However, as a result of the functional dependence between the illumination and projection optics, the overall efficiency of high-resolution lighting systems for vehicle front illumination can be increased using a distortion of the projection system adjusted to the inhomogeneous illumination strategy [63]. * **Adjust distortion:** In order to meet the photometric requirements, a distortion of the projection optics is determined that is adjusted to the illumination strategy, taking into account the subsystem that illuminates the active area of the modulator. Usually an aberration in optical systems, distortion does not lead to blur but to a distortion of the projected image and thus to a positionally variant image scale [64; 65]. For example, anamorphic distortion can be used to change the image scale in horizontal and/or vertical direction. Thus, the geometry of the illuminated area can be decoupled from the aspect ratio of the light modulator [12; 63]. In addition to a variable pixel size, a pincushion distortion also enables a redistribution of the illuminance, which benefits the application as a headlamp [66; 67]. * **Calculate Etendue factor:** To evaluate the Etendue conservation and thus the efficiency of the high-resolution lighting system, the so-called Etendue factor \((E_{F})\) is defined. Defined as the ratio of the Etendue of the light source to the Etendue of the light modulator [68], efficient preliminary designs are indicated by an Etendue factor of approximately one \((E_{F}\approx 1)\).