# Tailoring the V-Model for Optics: A Methodology for Optomechatronic Systems
## 3 Concretization of the V-Model for High Resolution Lighting Systems
This is predominantly due to the fact that, in addition to specific design steps arising from the challenges mentioned in Section 1.2, the Etendue must also be considered a conservation quantity. The Etendue can be used to describe the spatial and angular propagation of light through an optical system [55]. Within an ideal optical system, the Etendue can be preserved. However, due to diffusion, scattering, aberration and diffraction at imperfect optical elements, the Etendue increases under real conditions [56]. A lossless reduction of the Etendue is not possible. Furthermore, in each optical system there exists an element with the lowest Etendue, which thus limits the light propagation. With this knowledge, statements can be made about the theoretical maximum efficiency of optical systems. Since the spatial light modulator is usually the Etendue-limiting element in high-resolution lighting systems, the first step is to select the light modulator for the preliminary design. Based on the Etendue of the selected light modulator, the light generation must then be specified. If another component has the lowest Etendue, this element must be considered accordingly. Taking into account functional dependencies between the subsystem to illuminate the light modulator and to project it into the traffic area (see Section 1.2), the system architecture is determined by positioning the two subsystems with respect to each other. In the subsequent design steps \"Define illumination strategy\" and \"Adjust distortion\", the conflict of objectives between high optical efficiency and image quality is analyzed on the basis of the system architecture. Since different solution principles to implement high-resolution lighting systems are possible in each design step, the preliminary designs are checked using a so-called Etendue factor and a luminous flux factor. The luminous flux factor is used to check the preliminary design with regard to the fulfillment of the photometric requirements, and the Etendue factor is used to evaluate the efficiency (cf. Figure 7). Finally, a beam model of the optical path is created, which serves as the basis for the detailed design, which is carried out within the framework of the domain-specific design. * **Select spatial light modulator:** For the preliminary design of a high-resolution lighting system, we first need to define the Etendue-limiting component, which in this case is the light modulator. If no specific technology for light modulation (e.g., LCD or DMD) has been defined within the scope of the requirements elicitation; this is carried out in this step. Criteria for selecting a suitable technology may include resolution, contrast or efficiency. Furthermore, the aspect ratio and the number of light modulators to be used must be defined. Based on the luminous flux in the light distribution to be generated and an initially assumed efficiency of the subsystem used for projection into the traffic area, the minimum required Etendue of the light modulator can be determined. Since the functional principle of the modulator determines its acceptance angle, the active area required for modulation can be determined accordingly. * **Specify light generation:** For the illumination of the active area of the selected light modulator, a suitable technology for light generation (discharge lamp, electroluminescent emitter, etc.) has to be specified, if not already done in the requirements elicitation. Then, based on the Etendue of the light modulator, the number of light sources to be used and the size of the emission areas need to be determined. Neglecting Fresnel reflections and scattering in the optical system, an efficient light system can be assumed if the Etendue of light source and light modulator are equivalent. * **Determine system architecture:** When determining the architecture of the high-resolution lighting system, not only the type and number of optical elements to be used for beam shaping and deflection are specified, but also the spatial arrangement of these elements required for implementation.