Compound eye inspired flat lensless imaging with spatially-coded Voronoi-Fresnel phase

Lensless cameras are a class of imaging devices that shrink the physical dimensions to the very close vicinity of the image sensor by integrating flat optics and computational algorithms. Here we report a flat lensless camera with spatially-coded Voronoi-Fresnel phase, partly inspired by biological apposition compound eye, to achieve superior image quality. We propose a design principle of maximizing the information in optics to facilitate the computational reconstruction. By introducing a Fourier domain metric, Modulation Transfer Function volume (MTFv), we devise an optimization framework to guide the optimal design of the optical element. The resulting Voronoi-Fresnel phase features an irregular array of quasi-Centroidal Voronoi cells containing a base first-order Fresnel phase function. We demonstrate and verify the imaging performance with a prototype Voronoi-Fresnel lensless camera on a 1.6-megapixel image sensor in various illumination conditions. The proposed design could benefit the development of compact imaging systems working in extreme physical conditions.