This study concerns the determination of the diameter of an optical fiber by analysis of a 2D measured diffraction pattern relative to this linear object, falling within the scope of the Fraunhofer approximation. In this approach, when considering a small line-shaped aperture, with a radius α, or a diffractive object placed at the y-axis, an amplitude of the in-line Fraunhofer hologram can be achieved by a mathematical expression, for a given wavelength of the illuminating light λ and a distance z between the particle and the recording plane. The interferometric signal depends on an Airy curve expressed by a Sinc function whose determination of the zeros makes it possible to deduce an argument giving the radius of the fiber. The measurement is carried out for an object-CCD distance equal to <i>z</i> = 60 mm, with a wavelength of illumination λ = 635<i>nm</i>. The zeros of the Airy function appearing in the analytic expression of the interferometric signal allows us to achieve the value of the measured diameter. Knowing that the fiber radius is α = 62.5 <i>μm</i>, the measured value is acquired with an error of 1.7%.
The work developed and presented in this communication, relates to the restitution of frequency chirp of an interferometric signal deduced from a measured diffraction pattern relating to a spherical micro-particle. For this purpose, analysis were achieved by implementing a parametric method with a sliding window. These frequencies allows us to reconstruct the axial position of the corresponding object. The study, achieved in the far field approximation, allows us to validate preceding methods based on simulation results. The principle consists to generate optically in-line diffraction patterns of a spherical particle with radii of 39μm and measured with a microscope ZEISS. The collimated coherent light was generated from a He-Ne laser that the wavelength is λ = 632.8 nm. The generated diffraction pattern was recorded by using a 2D-CCD camera Ophir having 1024 x768 pixels with a pitch of 4.65 μm connected to a computer. Since the variation of the chirp frequency is linear, the knowledge of its variation slop, resulting from a linear fit, enables us to deduce the z-position of the particle. This is achieved with a resolution of 1.2 %.
An autoregressive method to analyze the fringe pattern observed in holographic interferometry is reported. Considering the impact of a 30 dB signal-to-noise ratio, we have shown that the reconstruction of the simulated symmetric profiles with 3, 4, and 5 fringes produces a maximum error of 0.300, 0.520, and 1.015 rad, respectively. The reconstruction of an asymmetric profile gives a larger error. The method was also applied to a recent fringe pattern. Our results are in qualitative agreement with those obtained using other methods.