Machine learning-aided automatic and precise focal length estimation of multilayer Laue lenses for high-resolution hard x-ray microscopy

Multilayer Laue lenses (MLLs) are promising optics for achieving high-efficiency hard x-ray nanofocusing. A critical parameter for their application in x-ray microscopy is the focal length. Conventionally, focal length estimation involves analyzing the positions of internal reference layers (marker layers) in MLLs based on pixel intensity variations in scanning electron microscope (SEM) images. However, this approach is affected by various factors, such as marker layer orientation and image quality, leading to reduced reliability and accuracy. Here, we introduce a new approach that integrates image-processing techniques with machine-learning algorithms to automatically and precisely estimate the MLL focal length from marker layer profiles. This method overcomes conventional limitations, enhancing accuracy and reliability. Validation with MLL samples demonstrated robust performance and good agreement with x-ray measurements. This advancement improves MLL characterization and supports the development of MLL-based high-resolution hard x-ray microscopy. Additionally, this method can be adapted to analyze other multilayered structures and patterns, offering broader applicability across diverse scientific and engineering disciplines.