Three-dimensional coherence holography using a commercial projector for display and incoherent illumination of a coherence hologram

We propose a simple implementation of off-axis coherence holography with a commercial projector combined with a Sagnac radial shearing interferometer. The projector functions as a device for display and incoherent illumination of a coherence hologram, which permits reconstruction of the hologram with a generic spatially-incoherent quasimonochromatic thermal light source. The Sagnac radial shearing interferometer, with its inherent stability of a common-path interferometer and controllable magnification introduced by variable shear, functions as a device for correlating optical fields to detect the 3-D coherence function that represents the object recorded in the coherence hologram. A set of phase-shifted Fourier transform holograms was displayed sequentially with the projector. The coherence function was detected by applying the phase-shift technique to the Sagnac radial shearing interferometer, and the object was reconstructed as the 3-D correlation map of the fields diffracted from the hologram. The technique can be applied for dispersion-free spatial coherence tomography and profilometry.