Cesar A. Sciammarella

Frequency modulation interpretation of fringes and computation of strains

Phase modulation is a traditional model for the interpretation of fringe patterns that provide displacement information, moiré, holographic interferometry, and speckle techniques. An alternative interpretation of the fringes is to consider them as frequency modulated signals. This change of interpretation has profound practical consequences if the space-frequency representation of signals is applied. The utilization of the energy representation of a signal in the coordinates-frequency space provides powerful procedures to retrieve strains distributions directly, from fringe patterns without resorting to differentiation of the displacements. This approach also simplifies the determination of displacements replacing unwrapping procedures by integration of the strains, a robust operation in the presence of noise. The Gabor transform, wavelet transforms, and quadratic representations of the energy of signals are tools that are available to carry out the practical implementation of this approach to fringe processing. This paper extends to two dimensions the methodology developed for one dimension in a previous paper.

High-accuracy contouring using projection moiré

Shadow and projection moire are the oldest forms of moire to be used in actual technical applications. In spite of this fact and the extensive number of papers that have been published on this topic, the use of shadow moire as an accurate tool that can compete with alternative devices poses very many problems that go to the very essence of the mathematical models used to obtain contour information from fringe pattern data. In this paper some recent developments on the projection moire method are presented. Comparisons between the results obtained with the projection method and the results obtained by mechanical devices that operate with contact probes are presented. These results show that the use of projection moire makes it possible to achieve the same accuracy that current mechanical touch probe devices can provide.

General model for moiré contouring, part 2: applications

Applications are presented of the general shadow-projection moire model described in the companion paper, A general model for moire contouring, part 1: theory. Two examples are discussed in detail. One example deals with the deflection of a large-size thin panel subjected to bending. The other example analyzes the accuracy that can be achieved in laser lithography rapid prototyping. The first example illustrates some theoretical aspects of the general contouring model proposed in this research and explains the reasons for differences between theoretical predictions and experimental results. In the second example, the whole process of data gathering and merging using geometric primitives and optimization techniques is demonstrated practically. Finally, a clear relationship between the measured standard deviations and moire sensitivity values is obtained. The results show that the proposed methodologies lead to a quasi-quadratic correlation.

Strain measurements in the nanometer range in a particulate composite using computer-aided moiré

When using metals and polymers in structural applications the macroscopic behavior depends on events taking place at levels in micrometer and nanometer ranges. At this range, material behavior, phenomena such as plasticity and fracture are size-dependent. We discuss these phenomena with regards to the case analyzed in this paper. Continuum mechanics flow theory of plasticity cannot explain the failure behavior of a particle-reinforced aluminum composite. An experimental study of the strain field in the micrometer range provides an explanation of the earlier than expected failure of the composite. We give a detailed description of the optical technique used to make the experimental mechanics measurements.

General model for moiré contouring, part 1: theory

In the current moire literature, techniques to determine displacements, strains, and techniques to get geometrical parameters of surfaces using the shadow-projection moire method are considered two separated branches of moire. We have formulated a mathematical model that shows a deeper commonality between the two moire applications: strain fields and surfaces are tensors of the second order. A direct consequence of this property is that a system of orthogonal grids is required in both cases when Cartesian tensors are utilized. The two systems of lines projected on a surface to get its contour are assimilated to parametric lines used in differential geometry to describe a surface. The classical moire equations of projection and observation from infinity are extended to more general conditions of projection and observation. The use of four projectors (i.e., two groups of two projectors) in a mutually orthogonal system with one camera is shown to provide the necessary means to implement the model for high-accuracy contouring. Geometrical primitives are introduced to provide a simple and direct procedure to reduce all the measured values to a preselected coordinate system. Different views of the same surface are merged to the selected coordinate system directly without the need to introduce markers on the surface or utilize correlation methods to identify identical regions. Examples of the application of the new model of contouring to practical cases are presented in the companion paper “A general model for moire contouring, part 2: applications.”

Measurement of deflections experienced by electronic chips during soldering

Electronic chips may experience, during the soldering process to a circuit board, out-of-plane displacements whose magnitude is not compatible with technological requirements on good bonding. This paper presents an experimental procedure based on the projection computer-aided moiré (PCAM) system in order to contour the distorted shape of electronic chips undergoing a thermal cycle which simulates the soldering process. The PCAM system is an integrated system where a pattern of fringes is transformed via software into a continuous phase distribution from which the distorted shape of the chip can be recovered. In this study, a number of chips have been heated at different temperatures ranging between 120 and 220°C in order to reproduce conditions that may occur during the real soldering process. Since measurements are carried out when the thermal field has become uniform, the chip deforms in the fashion of a quadric surface (i.e. a hyperboloid). Analysis of the chips deformed shape reveals that the largest displacement gradients experienced by the chips tested in this study are such that requirements on good bonding of the welded assembly are met. This finding, together with the fact that handling and investigation of electronic chips usually require special care, supports the conclusion that the PCAM approach may be successfully applied in the industry for the non-destructive testing of delicate components.

Fracture of Turbine Blades under Self-Exciting Modes

Failure of blades of a turbo-compressor occurred during operation. Three different typical failure geometries were observed repeatedly. One mode was clearly identifiable as the first bending mode. The other two (Figs. 1–2) could not be directly identified.

Fringe pattern information retrieval using wavelets

Two-dimensional phase modulation is currently the basic model used in the interpretation of fringe patterns that contain displacement information, moire, holographic interferometry, speckle techniques. Another way to look to these two-dimensional signals is to consider them as frequency modulated signals. This alternative interpretation has practical implications similar to those that exist in radio engineering for handling frequency modulated signals. Utilizing this model it is possible to obtain frequency information by using the energy approach introduced by Ville in 1944. A natural complementary tool of this process is the wavelet methodology. The use of wavelet makes it possible to obtain the local values of the frequency in a one or two dimensional domain without the need of previous phase retrieval and differentiation. Furthermore from the properties of wavelets it is also possible to obtain at the same time the phase of the signal with the advantage of a better noise removal capabilities and the possibility of developing simpler algorithms for phase unwrapping due to the availability of the derivative of the phase.

Nano-Holographic Interferometry for In-Vivo Observations

This chapter highlights the recently developed technique of nano-holographic interferometry via far-field microscopy. The main difference between conventional lens holography of phase objects and the methodology presented in this chapter is that the observations are made well beyond the classical limits of optical resolution. Going beyond the resolution limits becomes feasible by the use of evanescent wavefronts as a source of illumination. The objects to be analyzed enter an excited state that produces pseudo-nondiffracting wavefronts. These wavefronts can travel well beyond the traditional limits and enable the observations via a far-field microscope. The first portion of this chapter is dedicated to the theoretical explanation of this observed phenomenon. The second portion presents previous work carried out with this methodology in which nanocrystals were resolved to within a 3.7xa0nm standard deviation. Finally, some future applications will be discussed to show that it is possible to perform in vivo observations with-off-the shelf equipment.