Adjoint-Assisted Shape Optimization of Microlenses for CMOS Image Sensors

Recently, there have been significant developments in the designs of CMOS image sensors to achieve high-resolution sensing capabilities. One of the fundamental factors determining the sensor's ability to capture high-resolution images is its efficiency in focusing the visible light onto the photosensitive region of the submicron scale. In most CMOS imaging technologies, this is typically achieved through microlenses. Light collection under diverse conditions can be significantly improved through the efficient design of microlenses. While the optimization of microlenses appears to be imperative, achieving efficient designs of microlenses for high-density pixels under various conditions remains a significant challenge. Therefore, a systematic optimization approach is required to accelerate the development of efficient microlenses with enhanced optical performance. In this paper, we present an approach to optimize the shape of CMOS microlenses through adjoint sensitivity analysis (ASA). A novel figure of merit (FOM) is developed and incorporated into the optimization process to enhance the light collection. The gradient of the FOM is computed iteratively using two field simulations only. The functionality and robustness of the optimization framework are thoroughly evaluated. Furthermore, the performance of the optimized CMOS microlenses is compared to that of the conventional microlenses. The adjoint-assisted optimization framework presented here can be further used to develop efficient optical devices that perform optical manipulation such as concentrating, bending, or dispersing light in compact imaging systems.