Neural network-based design of freeform off-axis three-mirror telescopes for space applications

This work explores the development of an innovative Neural Network-based framework to automate the design of freeform off-axis three-mirror imaging systems. These optical systems, consisting of three freeform optical components arranged in a non-collinear manner, have enormous potential in fields such as space exploration and astronomy, due to their compactness and superior imaging capabilities. Starting with a comprehensive overview of freeform optics, this thesis provides an in-depth explanation of the mathematical representations, fabrication, and metrology of freeform surfaces. The challenges of realizing complex optical systems are highlighted, emphasizing the need for efficient designs. Furthermore, we analyze the advantages of freeform off-axis three-mirror imaging systems in space exploration when compared to conventional designs, providing valuable context for the developed framework. In this thesis, we propose a methodology based on Neural Networks to generate effective starting points in the design process. The framework comprises several significant phases. To begin with, we identify the key parameters of the representative system which include the Field of View, F-number, and Entrance Pupil Diameter. Next, we establish the System Parameter Space (SPS) by taking into account the design requirements and the parameters involved in the system. Then, we create a dataset through systematic sampling within the SPS, using a system evolution approach to derive the corresponding surface parameters that can fully describe the location and shape of the surfaces. The Feed-Forward Neural Network (FFNN) is trained rigorously with the given dataset. Once it is validated and proven effective, the trained FFNN can quickly produce the corresponding surface parameters when specific system parameter combinations are provided. As a result, it serves as an optimal starting point for subsequent optimizations, significantly reducing the amount of manual effort required during the design process. This novel framework represents a step forward in the fusion of advanced machine learning techniques with optical design principles. By automating and streamlining the design process, this framework sets the stage for a new era in the creation of high-performance optical systems, paving the way for future advancements in space exploration, astronomy, and various other domains.