A smoothed representation (based on natural exponential and logarithmic functions) for the canonical piecewise-linear model, is presented. The result is a completely differentiable formulation that exhibits interesting properties, like preserving the parameters of the original piecewise-linear model in such a way that they can be directly inherited to the smooth model in order to determine their parameters, the capability of controlling not only the smoothness grade, but also the approximation accuracy at specific breakpoint locations, a lower or equal overshooting for high order derivatives in comparison with other approaches, and the additional advantage of being expressed in a reduced mathematical form with only two types of inverse functions (logarithmic and exponential). By numerical simulation examples, this proposal is verified and well-illustrated.

Low-reflectance fiber Bragg gratings (FBGs) can be interrogated in real time with a high-resolution optical time-domain reflectometry (OTDR) technology. The technique allows interrogation of a series of FBGs with the intensity change based on the OTDR pulse spectral characteristics and the FBG reflection. Experimental results are presented for multiplexing of dual-wavelength FBG sensors to produce referencing calibration in sensor measurement. With this structure, the influence of the source power fluctuations and fiber bend losses can be greatly reduced. This scheme can be applied to the practical measurement of distributed temperature or strain. © 2003 Society of Photo-Optical Instrumentation Engineers.

It has been recently shown that application of Michelson interferometry, is suitable for monitoring of oxide layers growing in metallic structures during preliminary states of oxidation processes in aqueous solutions, without any physical contact with the sample. The qualitative and quantitative interpretation of the observed interferograms allows evaluation of important physical parameters related to specific corrosion processes [1]. Although the using of aluminum samples with surfaces polished to certain optical quality is a necessary requirement to obtain well-built interferograms, it complicates further applications for diffused surfaces typical of industrial conditions. In this work we present preliminary qualitative results obtained by using a simple experimental setup based on Digital Speckle Pattern Interferometry (DSPI) [2], as a proposal to solve this difficulty and on the other hand, to use the benefits of certain powerful tools like low-coherence optical techniques for further applications on monitoring of corrosion through turbid media.