Digital in-line holography for the characterization of flowing particles in astigmatic optical systems

An extended Generalized Fresnel Transform (GFT) is proposed to account for the astigmatism introduced by optical elements described, in the paraxial approximation, with a ray transfer matrix analysis. Generalized impulse response and generalized Fresnel transfer function propagators as well as sampling conditions are derived to properly implement this transformation. As a test case, the near-field diffraction patterns and in-line holograms produced by droplets flowing in a tube with cylindrical interfaces have been simulated. A best fitting approach is introduced to retrieve, from the propagated holograms, the 3D position and size of the droplets. Several hologram focusing indicators based on the analysis of droplets focus region are also proposed to further improve the estimation of the droplets position along the optical axis. Numerical simulations and experimental results confirm the applicability and accuracy of the proposed methods. •A model to simulate holograms in astigmatic optical system is proposed.•A generalized convolution method allows reconstructing particle holograms.•A best fitting approach allows particles positions and diameters assessment.•Particle position along the optical axis is improved by localizing the focus region.•The method is validated on a cylindrical liquid/liquid extracting device.