%0 Journal Article %T In-line particle holography with an astigmatic beam: set-up self-calibration using an "inverse problems" approach %+ Laboratoire Hubert Curien (LHC) %+ Laboratoire de Mecanique des Fluides et d'Acoustique (LMFA) %A Verrier, Nicolas %A Fournier, Corinne %A Méès, Loïc %A Fournel, Thierry %Z Projet MORIN (3D Optical Measurements for Research and INdustry), financé par le gouvernement francais par l'intermédiaire de l' "Agence Nationale de la Recherche" (ANR) et du "Programme Avenir Lyon-Saint Etienne" (PAL-SE). %Z 11 pages %< avec comité de lecture %@ 1559-128X %J Applied optics %I Optical Society of America %V 53 %N 27 %P G147-G156 %8 2014-08-11 %D 2014 %R 10.1364/AO.53.00G147 %K Digital holography %K Image processing %K Inverse problems %K Image reconstruction techniques %K Metrology %Z OCIS : 090.1995, 100.3190, 100.3010,120.3940 %Z Computer Science [cs]/Image Processing [eess.IV]Journal articles %X The use of digital in-line holography for the characterization of confined flows in cylindrical geometry confinements (e.g. cylindrical pipe or cylindrical capillaries) is discussed. Due to cylindrical geometry of the walls, the illuminating laser wave can be strongly astigmatic, which renders the use of classical reconstruction techniques impossible. Contrary to plane wave holography set-up, the diffraction pattern of the particles strongly depends on the axial distance of the latter to the entry face of the confinement structure. To address this reconstruction issue, we propose to use an "inverse problems" approach. This approach amounts to finding the best match (least squares solution) between a diffraction pattern model and the captured hologram. For this purpose, a direct imaging model for astigmatic holograms, based on the use of transfer matrices is presented and validated by comparing experimental and simulated holograms. The accuracy of the "inverse problems" reconstruction is then used to calibrate the experimental set-up adjustable parameters. Finally, the approach is tested through experimental astigmatic hologram reconstruction, thus paving the way to its use in pipe flow studies. %G English %2 https://ujm.hal.science/ujm-00994307v2/document %2 https://ujm.hal.science/ujm-00994307v2/file/2014_AO_VERRIER_ConfinedInverseApproach.pdf %L ujm-00994307 %U https://ujm.hal.science/ujm-00994307 %~ UNIV-ST-ETIENNE %~ IOGS %~ CNRS %~ UNIV-LYON1 %~ INSA-LYON %~ EC-LYON %~ LAHC %~ PARISTECH %~ LMFA %~ INSA-GROUPE %~ UDL %~ UNIV-LYON %~ EC_LYON_STRICT