# Tailoring the V-Model for Optics: A Methodology for Optomechatronic Systems
## 3 Concretization of the V-Model for High Resolution Lighting Systems
Inefficient preliminary designs are characterized by an Etendue factor of significantly greater \((E_{F}>1)\) or less \((E_{F}<1)\) than one. However, since both an efficient and inefficient preliminary design cannot be considered equivalent to the fulfillment or non-fulfillment of photometric requirements, a so-called luminous flux factor \((L_{F})\) is also defined. * **Calculate luminous flux factor:** The luminous flux factor is used to ensure the preliminary design with regard to the feasibility of photometric requirements and is described by the ratio of actual to target luminous flux on the active area of the modulator. The target luminous flux is determined using the required luminous flux in the light distribution based on assumptions about the efficiency of the subsystem for projection as well as the illumination overfill of the active area of the modulator. The actual luminous flux is determined using the Etendue and thus the usable portion of the luminous flux from the light source to illuminate the active area of the modulator, as well as assumptions about the efficiency of the subsystem used for illumination. For preliminary designs indicated by a luminous flux factor of approximately and greater than one \((L_{F}\approx 1,L_{F}>1)\), the photometric requirements can be realized. Preliminary designs indicated by a luminous flux factor of significantly less than one \((L_{F}<1)\), the photometric requirements cannot be met. * **Case analysis:** Within the scope of the case analysis shown in Figure 7, the developed preliminary designs are evaluated with regard to the conservation of Etendue and the fulfillment of photometric requirements. The occurring cases can be divided into the following three categories:* Category 1 is associated with cases \([(E_{F}\
eq 1\wedge L_{F}\
eq 1)\vee(E_{F}=1\wedge L_{F}\
eq 1)\), where the photometric requirements cannot be realized due to a too low luminous flux factor;
* For preliminary designs of category 2 \([(E_{F}\
eq 1\wedge L_{F}\approx 1]\), the photometric requirements are met, but due to an Etendue factor considerably differing from one, these designs are characterized by inefficiency. Consequently, either the light source or the light modulator is oversized;
* If the photometric requirements and simultaneously the Etendue conservation are fulfilled, then the preliminary designs are of category \(3\)\([(E_{F}\approx 1\wedge L_{F}\approx 1]\), allowing to proceed directly to the last design step of the method. For category 1 and 2 designs, loops are provided within the method to return to specific design steps for targeted optimization. An explanation of when to return to which design step can be found in [17]. * **Create beam model:** In the final step, a beam model is created for the preliminary design of the high-resolution lighting system, which serves as the basis for the domain-specific detailed design of the optical system. The beam path of the high-resolution lighting system is designed from the light source on the object side to the projection area on the image side. Furthermore, the beam model can be used to identify system configurations in which, for example, individual optical elements or the subsystems for illumination and for projection collide. Occurring collisions can be resolved via loops within the method to the steps \"Determine system architecture\" and \"Specify light generation\", which is explained in more detail in [17]. As a result of the method, various preliminary designs of the high-resolution lighting system are thus available in terms of beam models. For each beam model, in addition to the modulation technology to be used and the number and size of the light modulator as well as the light source(s), the type and number of beam shaping and deflecting optical elements as well as their spatial arrangement in the system are known. Furthermore, the focal length and the image scale are known. The beam model describes a possible implementation of the optical system, taking into account the concept-defining requirements.