An efficient wave-optics framework for partially coherent pink X-ray beam simulation and analysis

The advent of fourth-generation synchrotron radiation sources has enabled advanced coherent X-ray techniques. However, high-flux pink-beam operation introduces significant computational challenges for wave-optics-based coherence analysis. Conventional approaches, such as Monte Carlo sampling of the electron beam or direct diagonalization of the cross-spectral density, become computationally prohibitive when extended to broadband spectra. In this work, we develop an integrated computational framework that combines Monte Carlo brightness convolution for efficient wavefront matrix construction, hierarchical incremental singular value decomposition to overcome memory bottlenecks in coherent mode decomposition, and spectral-spatial decomposition to extract a global orthogonal basis for rapid broadband propagation. The reliability of the proposed method is validated through comparison with Synchrotron Radiation Workshop (SRW) simulations and experimental measurements performed at the HEPS Hard X-ray Coherent Scattering (HXCS) beamline. Furthermore, the framework is applied to analyze chromatic aberrations in compound refractive lens focusing systems, quantitatively evaluating focal-spot broadening and coherence degradation inherent to pink-beam operation. The proposed framework provides a practical and scalable tool for the design and optimization of high-flux pink-beam coherent experiments at modern synchrotron facilities.