Design of freeform microlens arrays with prescribed luminance distributions for MicroLED optical packaging

Non-uniform angular luminance distribution and limited viewing-angle control remain key challenges in MicroLED display modules. In this paper, we propose an optical packaging structure and a design method based on a freeform microlens array (MLA) to achieve prescribed angular luminance distributions. While freeform optics have been extensively studied for general illumination, their application in MicroLED packaging for directional luminance control has been rarely explored. Here, we extend an integrable ray mapping framework into the luminance domain and apply it to the design of MicroLED packaging optics, enabling compact, high-efficiency, and high-uniformity beam shaping. A lossless energy transformation strategy is first employed to convert the target luminance distribution into a uniformly sampled angular domain, addressing sampling imbalances at large viewing angles. An extended integrable ray mapping method is then used to compute a mapping between the MicroLED source domain and the angular domain, from which manufacturable single-surface freeform lenses and MLAs are derived. Two design examples-under symmetric and non-rotationally symmetric viewing conditions-are presented to validate the proposed approach. Simulation results demonstrate that the method achieves accurate angular luminance control and high uniformity across the desired viewing cone, confirming its practicality for real-world MicroLED display applications.