DMD diffraction propagation model and frequency-domain energy optimization under incoherent illumination

With the rapid advancement of projection and illumination technologies, incoherent light sources are increasingly utilized due to their low cost, high stability, and ease of system integration. Digital Micromirror Devices (DMDs), functioning as high-speed programmable spatial light modulators, are widely deployed in applications such as projection display, photolithography, and structured illumination microscopy. However, the micrometer-scale reflective structure of DMDs introduces significant diffraction effects when illuminated by incoherent or broadband sources. These effects manifest as reduced fringe contrast, enhanced background scattering, and strong wavelength-dependent variations in diffraction efficiency. Existing models are largely based on Fourier optics approximations and are generally limited to coherent, monochromatic sources, making them insufficient for accurately describing structural diffraction under incoherent illumination. To address these limitations, we propose a diffraction modeling framework for DMDs illuminated by extended incoherent sources. This model is constructed based on the spatial propagation paths of individual point emitters and their phase modulation across the micromirror array, leading to a complete formulation of the optical field superposition. The model incorporates key physical parameters, enabling accurate prediction of energy distribution and spectral response. Furthermore, frequency-domain optimization of the diffraction characteristics enables enhanced optical energy efficiency and improved contrast in projected patterns. Numerical simulations and experimental validations demonstrate that the proposed framework achieves notable improvements in system energy efficiency and image quality. This study provides a solid theoretical foundation and a generalizable modeling framework for incoherent illumination applications across fields such as microscopy, spectral imaging, and programmable light projection.