Reconstruction of the rose of directions from a digital microhologram of fibres

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 of the objects projections. The rose of directions is connected with the mean geometric covariogram through an inverse problem. In the general case, only the two‐dimensional 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 three‐dimensional direction information. An iterative scheme is suggested to reconstruct the three‐dimensional rose in this special case. Results are provided on holograms of paper fibres.

[1]  Dietrich Stoyan,et al.  Anisotropy analysis for particle systems , 1991 .

[2]  William H. Richardson,et al.  Bayesian-Based Iterative Method of Image Restoration , 1972 .

[3]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[4]  H. Lantéri,et al.  Penalized maximum likelihood image restoration with positivity constraints:multiplicative algorithms , 2002 .

[5]  L. Onural,et al.  Diffraction from a wavelet point of view. , 1993, Optics letters.

[6]  M. Daube-Witherspoon,et al.  An Iterative Image Space Reconstruction Algorthm Suitable for Volume ECT , 1986, IEEE Transactions on Medical Imaging.

[7]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.

[8]  E. Saff,et al.  Minimal Discrete Energy on the Sphere , 1994 .

[9]  Ting-Chung Poon,et al.  Digital holography--coherent optics of the 21st century: introduction , 2006 .

[10]  M. Kiderlen,et al.  Algorithms to estimate the rose of directions of a spatial fibre system , 2005, Journal of microscopy.

[11]  Eric Thiebaut,et al.  Optimization issues in blind deconvolution algorithms , 2002, SPIE Astronomical Telescopes + Instrumentation.

[12]  H Royer,et al.  An application of high-speed microholography: the mertology of fogs , 1974 .

[13]  J. Goodman.  Introduction to Fourier optics , 1969 .

[14]  L. Lucy.  An iterative technique for the rectification of observed distributions , 1974 .

[15]  Christophe Ducottet,et al.  Direct extraction of the mean particle size from a digital hologram. , 2006, Applied optics.

[16]  L. Shepp,et al.  Maximum Likelihood Reconstruction for Emission Tomography , 1983, IEEE Transactions on Medical Imaging.