Correlation holography uses incoherent light to reconstruct holograms. This technique reconstructs objects as distributions of two-point coherence function rather than using optical fields, as in conventional holography. The basic principle of correlation holography is derived from the van Cittert--Zernike theorem and relies on the similarity between the optical field and the coherence functions. Experimental implementation of the correlation holography techniques requires a field or intensity interferometer, and fringe analysis and cross-covariance measurement in these interferometers require a conventional camera with array detectors. With the availability of digitally controlled diffractive elements, it is possible to replace the incoherent light source, such as a rotating ground glass, with a digital source loaded with the random patterns in sequence. Such strategies ease the burden on the detector and allow for correlation holography with a single-pixel detector (SPD) to be used. This review paper discusses a close connection between digital holography and correlation holography. The principles of correlation holography with the SPD are reviewed in detail, and the advantages of using digital sources to mimic incoherent illumination in the correlation holography are examined in the context of three-dimensional and complex field imaging.

Correlation holography uses incoherent light to reconstruct holograms. This technique reconstructs objects as distributions of two-point coherence function rather than using optical fields, as in conventional holography. The basic principle of correlation holography is derived from the van Cittert--Zernike theorem and relies on the similarity between the optical field and the coherence functions. Experimental implementation of the correlation holography techniques requires a field or intensity interferometer, and fringe analysis and cross-covariance measurement in these interferometers require a conventional camera with array detectors. With the availability of digitally controlled diffractive elements, it is possible to replace the incoherent light source, such as a rotating ground glass, with a digital source loaded with the random patterns in sequence. Such strategies ease the burden on the detector and allow for correlation holography with a single-pixel detector (SPD) to be used. This review paper discusses a close connection between digital holography and correlation holography. The principles of correlation holography with the SPD are reviewed in detail, and the advantages of using digital sources to mimic incoherent illumination in the correlation holography are examined in the context of three-dimensional and complex field imaging.