Inverse mask design for interference lithography using automatic differentiable wave propagation

Interference lithography (IL) is powerful for fabricating high-resolution periodic nanostructures, but designing masks to produce non-periodic patterns remains challenging. We introduce a gradient-based optimization framework for binary IL mask design using automatic differentiation. The forward model is implemented using the differentiable angular spectrum method (ASM). The inverse mask design is formulated as an optimization problem, where the mask logits are updated through backpropagation of the loss between the simulated field amplitude and the target pattern. We optimize a mask that reproduces a target pattern with only 0.1% isolated pixel-level defects, resolving features at half the mask pixel pitch. To scale mask optimization, we employ the shifted ASM, which partitions the mask into patches that are propagated independently and summed at the image plane. For a 3.84 mm$\times$3.84 mm mask, shifted ASM with 16 patches reduces peak GPU memory by 3.8$\times$ at only 1.3$\times$ runtime cost relative to standard ASM. With gradient checkpointing, peak memory is reduced by 7.4$\times$ at 2$\times$ runtime. Distributing across multiple GPUs further accelerates the optimization. This work establishes a physics-informed, machine learning-driven approach for IL mask design, moving a step further towards complex, non-periodic patterns. The source code is available at https://github.com/chuntian236/holography-optimization.git .