|
Tolerance analysis is an integral part of the design process that saves time and money while improving the product quality. Nevertheless, tolerancing of illumination optics is often glossed over by the current industry. Consequently, there is a need to understand and establish tolerancing in illumination optics.
This research focuses on single surface deformation. In the process referred to as surface perturbation, the surface is perturbed by a known amount. Then, the changes on the irradiance target are evaluated.
A localized surface perturbation, like a bump or hole, results in either a local increase in irradiance with an annulus dip around the elevated irradiance or a local decrease in irradiance with an annulus increase around the decreased irradiance. Such an outcome is a result of flux conservation.
The ratio between the height and the surface area (referred to as the size) of the localized surface perturbation has an approximately linear relationship to the largest irradiance change. Once the linearity of the relationship is understood for the localized surface perturbation of a particular size, the tolerance range can be estimated for other localized surface perturbations sizes.
Within the optics’ tolerancing range, the Laplacian of the surface perturbation predicts the irradiance change. As long as the ray-mapping between the surface and the target is known, the Laplacian of the surface change can be mapped onto the target. The surface change also perturbs the ray-mapping. Thus, taking the perturbed ray-mapping into account enables prediction with greater accuracy. Using this method, expected surface deformation from the manufacturing process can guide estimating irradiance changes, providing a first-order method to tolerance illumination optics.
|
