Reconstruction of the rose of directions from a digital micro-hologram of fibers

Loïc Denis (1) , Thierry Fournel (1) , Corinne Fournier (1) , Dominique Jeulin (2)

1 LHC - Laboratoire Hubert Curien
2 CMM - Centre de Morphologie Mathématique

Digital holography makes it possible to acquire quickly the interference patterns of objects spread in a volume. The digital processing of the fringes is still too slow to achieve on line analysis of the holograms. We describe a new approach to obtain information on the direction of illuminated objects. The key idea is to avoid reconstruction of the volume followed by classical three-dimensional image processing. The hologram is processed using a global analysis based on autocorrelation. A fundamental property of diffraction patterns leads to an estimate of the mean geometric-covariogram (MGC) of the objects projections. The rose of directions is connected with the MGC through an inverse problem. In the general case, only the 2D rose of the object projections can be reconstructed. The further assumption of unique-size objects gives access with the knowledge of this size to the 3D direction information. An iterative scheme is suggested to reconstruct the 3D rose in this special case. Results are provided on holograms of paper fibers.

Mots clés: covariogram inversion; digital holography; mean geometric covariogram; rose of directions; stereology

Domaines: Traitement du signal et de l'image [eess.SP]; Optique [physics.optics]; Traitement du signal et de l'image [eess.SP]

Loïc Denis, Thierry Fournel, Corinne Fournier, Dominique Jeulin. Reconstruction of the rose of directions from a digital micro-hologram of fibers. Journal of Microscopy, 2007, 225 (3), pp.283-292. ⟨10.1111/j.1365-2818.2007.01744.x⟩. ⟨ujm-00116998v1⟩