Establishment and verification of diffraction BRDF model for scratched material surface

•The analysis of incoherent reflectance based on wave optics is presented, and a diffraction BRDF model for scratched material surface is proposed.•We mainly consider the wave-optical effect and accounts for diffraction and source coherence effects for scratch under arbitrary viewing and lighting conditions.•A novel BRDF measurement with fast and efficient performance is used.•The theoretical model is verified by experimental data and the results can provide theoretical basis for proposing detection scheme for scratches of different standards