Learnable fractional Fourier transform for high-quality computer-generated holography

Deep learning-based computer-generated holography is a promising method for achieving high-quality holographic displays. However, most existing methods are restricted to extracting features from fixed spatial or frequency domains for generating phase-only holograms (POHs), resulting in the loss of finer details in holographic imaging. To overcome this limitation, we propose a complex-valued fractional Fourier network (CFrFNet) that integrates the fractional Fourier transform (FrFT) within a unified spatial-frequency framework to produce high-fidelity POHs. A fractional Fourier neural module (FrFNM) is designed to access arbitrary fractional domains between the spatial and frequency domains after a FrFT. To accommodate the characteristics of the fractional domain, a multiscale feature extraction block (MFEB) is proposed to extract rich spatial-frequency joint features. We also introduced a learnable strategy to adaptively optimize the fractional order of the FrFT during the training process. Both simulations and experiments validate the effectiveness of our approach, highlighting its potential to significantly enhance the quality of holographic imaging.