Introduction

The direct analysis of diffraction fringes can resort to different methods of digital restitution, for example inverse Fresnel transformation.

This method prevents us for finding the shape of the object back when the coding beam is astigmatic: curvature radiuses in two orthogonal axes x and y are different and nothing can invites us to choose different quadratic phases in Fresnel core.

Besides, fractional Fourier Transforms enable us to choose different quadratic phases following both axes.

The intensity distributions of a diffracted field by objects (fibers, particles, etc.) recorded on a quadratic medium in in-line-holography will involve different linear frequency drifts along the axes (x, y) of the image.

Nevertheless, we consider here that the beam is flat and has no aberration. This section offers a method to analyze fiber holograms by fractional Fourier transforms. The approach within fractional TF metrology is first to define the intensity distribution in the quadratic sensor plane and, secondly, to identify the functions having linear frequency drifts to analyze them using fractional FTs.