Three-dimensional measurement of a particle field using phase retrieval digital holography

Digital inline holography (DIH) has long been used to measure the three-dimensional (3D) distribution of micrometer particles in suspensions. However, DIH experiences a virtual image problem that limits the particle density and the placement of the hologram plane relative to the sample volume. Here, we apply virtual-image-free phase retrieval digital holography (PRDH) to detect opaque particles in 3D volumes that exceed $ 2000\;{\rm particles}/{{\rm mm}^3} $2000particles/mm³. PRDH is based on recording two holograms whose planes are displaced along the optical axis, and then reconstructing the complete optical waves estimated by the iterative phase retrieval algorithm. Both numerical and experimental tests are performed, and results show that PRDH recovers the original 3D particle distributions even when the hologram planes are within the particle suspensions. Moreover, compared to single-hologram-based DIH, PRDH is proved to have better particle detection qualities. The uncertainty in the localization of particle centers is reduced to less than one particle diameter.