We propose a technique for ray tracing, based in the propagation of a Gaussian shape invariant under the Fresnel diffraction integral. The technique uses two driving independent terms to direct the ray and is based on the fact that at any arbitrary distance, the center of the propagated Gaussian beam corresponds to the geometrical projection of the center of the incident beam. We present computer simulations as examples of the use of the technique consisting in the calculation of rays through lenses and optical media where the index of refraction varies as a function of position.
The simultaneous surface and internal measurements from a chemically modified cortical bovine bone suffering a plastic range deformation are presented. Since the bone is an anisotropic structure, its mechanical response could be modified if its organic or inorganic phases change. The latter could result in high plastic deformations, where the interferometrical signal from an optical analysis is easily de-correlated. In this work, digital holography interferometry (DHI) and Fourier domain optical coherence tomography (FD-OCT) are used to analyze the plastic range deformation of the bone under compression. The simultaneous use of these two optical methods gives information even when one of them de-correlates. The surface results retrieved with DHI show the high anisotropy of the bone as a continuously increasing displacement field map. Meanwhile, the internal information obtained with FD-OCT records larger deformations at different depths. Due to the optical phase, it is possible to complement the measurements of these two methods during the plastic deformation.
A three-beam scanning optical interferometric microscopic technique applied to roughness characterization of optical flats is described. The technique is based on the heterodinization of three coherent optical beams. One of the beams, the probe beam, is focused on the surface under test. A second beam is obtained after being reflected by a reference surface. Finally, the last beam consists of one of the first orders of diffraction that emerges of a Bragg-cell. The three beams are coherently added at the sensitive surface of a photodetector that integrates the overall intensity of the beams. We show analytically that, the electrical signal at the output of the photodetector, is a time-varying signal whose amplitude is proportional to the surface local vertical height. We characterize experimentally the frequency response of the system by measuring the profile of three different gratings. We show measurements of the roughness of an optical flat processed by means of the frequency response of the system.
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