Fig. 1: Principle of VsLFM.

a, Principle of VsLFM using a physics-based deep neural network (Vs-Net) to extract the high-frequency information from the frequency aliasing in traditional LFM induced by diffraction of a small microlens aperture and low spatial sampling density. Such a process can be viewed as a virtual-scanning process to increase the spatial sampling density. b, Schematic diagram of the optical system and processing pipeline of VsLFM. In sLFM, a 2D scanning galvo shifts the image plane by 3 × 3 times physically to increase the sampling rate of angular views, which is limited by the physical size of each microlens in LFM. For a VsLFM system without a scanning galvo system, the microlens array (MLA) is placed at the back focal plane of the tube lens, and the length of the whole optical path is shortened. VsLFM uses a supervised-learning network (Vs-Net) including the extraction, interaction, fusion and upsampling of multiple spatial–angular features to realize the scanning process virtually. High-resolution angular measurements obtained by sLFM serve as the ground truth during network training to learn the physical prior between the phase-correlated low-resolution angular measurements. Finally, iterative tomography with DAO is implemented on multiple angular views obtained by Vs-Net to reconstruct 3D high-resolution volumes. Scale bars, 10 μm (spatial domain) and 1 μm⁻¹ (Fourier domain) (a).