Application Of The Fractional Fourier Transform To The Restitution Of The Holograms Of Particles Moving

The follow-up of particles of the tracer type in the fluids constitutes a field of study rather significant and at the same time rather complex owing to the fact that the number of parameters studied and at the same time significant and concerning the random one. The use of holography as a technique of imagery for the follow-up of these particles was applied by various laboratories for a long time. With the appearance of digital holography, the application of this technique became more than of topicality owing to the fact that it became possible to record in real time a succession of holograms using a camera CCD rapid, that it will be possible to put in perspective there after in a numerical way and to try to extract information related to the movements described by these particles which will be automatically those of the studied fluids. The numerical reconstruction of digital holograms being based on the laws of fight propagation such as, the Fresnel integral and the traditional Fourier transform. The fractional Fourier Transform (FrFT) is defined as being a generalization of the traditional Fourier transform. It was proposed by Namias and was reintroduced in the optical systems by Lohmann, Mendlovic and Ozaktas. Pellat-Finet studied the relationship between (FrFT) and the Fresnel diffraction, therefore this operator also allows rebuilding the holograms. In this study we use the (FrFT) to reconstruct in line holograms of small particles plunged in a fluid. Three-dimensional information on the particles can be extracted by sweeping the fractional order.