3D imaging and microscopy by a single-pixel correlation holography

We propose a new holography technique using an incoherent source and apply it to three-dimensional imaging and microscopy. This is implemented by recording an incoherent object hologram as a distribution of a complex coherence function and reconstructing it using a single-pixel intensity correlation measurement in an inline geometry, and without an interferometer. Here, structured illumination with a Fourier basis is applied for inline reconstruction of a hologram, and a complex field is recovered using three-phase-shifted structured patterns at each frequency and a phase-shifting relation. Intensity correlation is evaluated by temporal averaging of the detected signals by a single-pixel detector. Further, we extend our work by retrieving incoherently illuminated objects at different depths from the recovered complex coherence. We also demonstrated the application of the proposed technique in microscopy, enabling a new computational microscopic method with incoherent illumination.