The adaptive BRDF display method utilizing multiple light ray projections (ABDM-MLRP) offers promising capabilities for replicating real-world materiality. This adaptive approach allows for BRDF display on arbitrarily shaped surfaces without the need for geometrical calibration. While initially proposed for materiality reproduction of BRDF, its applications extend to scientific simulations, product design, and the fusion of virtual and real-world environments in the emerging metaverse. However, ABDM-MLRP has challenges in accurately representing matte materiality due to a limited number of cast light rays. To address this, we propose employing light ray diffusion. This paper presents a precise model of light ray diffusion, demonstrating how the diffuser expands the numeric aperture of incident light rays to address glossiness issues in matte BRDF representation. However, the straightforward introduction of diffuser plate utilization blurs display results and clears away the color gradation of structural color and specular reflections. To mitigate this, we propose introducing pre-compensation on BRDF data. Our results show that the proposed method effectively resolves these issues, enhancing materiality representation, including structural color and glossiness, across various shapes and transparent objects.