Cost optimization of optical designs

High-performance devices can be produced by choosing only the best materials and most accurate manufacturing processes. However, they often do not generate large sales volumes because of excessive pricing. If lower-cost materials and processes are used instead, production costs decrease, but this is usually followed by performance degradation.

The term ‘design for manufacturability’¹ is generally used to describe product design for a particular manufacturing process in order to minimize costs. Several different technologies can be employed to fabricate precision components for use in optics modules or systems. Optical designers can also realize the requisite optical functions by employing a large variety of different designs. This freedom of choice enables one to find several alternative solutions to a single problem, but it also complicates the selection of a suitable manufacturing method for cost optimization.

Cost modeling can be used effectively to find the right balance among the multiple variables involved in designing an optics product. Models can simulate the effects of design variations on manufacturing costs in a similar way as optical-design software is used to simulate performance differences. By employing both tools concurrently, designers can transition from partial to true module- or system-level optimization.²

We have developed a tool to calculate optics production costs under the aegis of the European Commission-sponsored project Production 4μ.^3,4 We can obtain a detailed cost analysis of the complete process chain of three main optical-component production methods, including glass grinding, glass molding, and plastic injection molding (see Figure 1).

Figure 1. Process chain for the production of lenses by precision glass molding.

To show the potential of our cost-calculation tool, we created a set of 11 imaging-lens designs⁵ that all had the same specifications, e.g., for size, field of view (150^°), and imaging area (1/4in sensor). The main idea was to create a set of hybrid designs characterized by different manufacturing requirements and quality levels. The range of manufacturing methods drove the lens production costs in separate directions. Their performance varied as we fitted the materials and surface shapes to the relevant production-method characteristics.

Figure 2 shows ray-trace drawings of the best and worst six-element designs and their modulation-transfer-function graphs (which indicate the achievable resolution). The worst-performing design contained one ground glass and five injection-molded plastic elements. The best design included five ground glass and only one plastic element. The performance difference between both examples is clear. The first design could be used only with a low-resolution camera (with a pixel size of ~10μm), while the second can produce sharp images even for a camera sensor with small, ~2μm pixels.

Figure 2. Ray-trace drawings and modulation-transfer-function (MTF) graphs of the worst (left) and best (right) lenses among our example designs. OTF: Optical transfer function. G, P: Glass, plastic. TS: Tangential and sagittal (referring to the two ray-intersection directions used to calculate the MTFs in the optical-design software).

Figure 3 shows the total costs for the two example hybrid-lens designs. The setup with a majority of plastic components (1gg0mg5p) starts from a cost level of 920€/lens for a production volume of 100 and ends up at approximately 12€/lens for a volume of 1,000,000. The design with mostly ground glass components (5gg0mg1p) starts at 450€/lens and reaches about 24€/lens for the same volumes.

Figure 3. Total optical-element costs of the two example hybrid-lens designs for different manufacturing volumes.

We can draw several important conclusions by combining the results of our performance and cost analyses. Our low-performance design nicely matches that of in-car rear-view-camera (RVC) systems, which have only a small, low-resolution display on the dashboard. RVC systems must be very inexpensive at high volumes, and our results show that the lens can be manufactured at about half the cost of the higher-performance alternative. Our high-performance design has sufficiently high resolution that it could be used in tandem with a large 50in full high-definition liquid-crystal display in surveillance systems in which the higher cost can easily be rationalized by the requirement for high-resolution imaging. Surveillance systems are not high-volume products and, therefore, the cost-reduction trend at the low-volume boundary is of particular interest for this application.

The main benefit of the calculation methodology and software tools created as part of the Production 4μ project is that they enable cost calculations with a high level of detail for only a small effort. Our example calculations were done for the European production environment, but such tools could also be used for comparative calculations between different global production locations. If the input parameters are adjusted to reflect the conditions of a low-labor-cost country like China, the results will obviously be different.

One additional use of cost-calculation tools could be in assessing tolerancing costs. Both qualitative and quantitative analyses can be performed with a parameterized model. Separate analysis of each variable in the cost model reveals the most sensitive parameters in both the design and manufacturing processes. A Monte Carlo analysis with estimated variable distributions can provide the cost probability distribution. These kinds of simulations could make cost risk management a little easier. We will continue to add more machines and tools to our software database to create an extensive expert system for optics production-cost calculations.