Applications are presented of the general shadow-projection moiré model described in the companion paper, “A general model for moiré 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 moiré sensitivity values is obtained. The results show that the proposed methodologies lead to a quasi-quadratic correlation.
In the current moiré literature, techniques to determine displacements, strains, and techniques to get geometrical parameters of surfaces using the shadow-projection moiré method are considered two separated branches of moiré. We have formulated a mathematical model that shows a deeper commonality between the two moiré 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 moiré 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 moiré contouring, part 2: applications.”
Optical techniques that are used to measure displacements utilize a carrier. When a load is applied the displacement field modulates the carrier. The accuracy of the information that can be recovered from the modulated carrier is limited by a number of factors. In this paper these factors are analyzed and conclusions concerning the limitations in information recovery are illustrated with examples taken from experimental data.
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.
Shadow and projection moiré are the oldest forms of moiré 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 moiré 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 moiré 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 moiré makes it possible to achieve the same accuracy that current mechanical touch probe devices can provide.
The basic theory behind microscopic electronic holographic moire is presented. Conditions of observation are discussed, and optimal parameters are established. An application is presented as an example where experimental result are statistically analyzed and successfully correlated with an independent method of measurement of the same quantity.
The process of encoding displacement information in electronic Holographic Interferometry is reviewed. Procedures to extend the applicability of this technique to large deformations are given. The proposed techniques are applied and results from these experiments are compared with results obtained by other means. The similarity between the two sets of results illustrates the validity for the new techniques.
The process of fringe formation under simultaneous illumination in two orthogonal directions is analyzed. Procedures to extend the applicability of this technique to large deformation and high density of fringes are introduced. The proposed techniques are applied to a number of technical problems. Good agreement is obtained when the experimental results are compared with results obtained by other methods.
The determination of pressures along the surface of a wind tunnel proves difficult with methods that must introduce devices into the flow stream. This paper presents a sensor that is part of the wall. A special interferometric reflection moire technique is developed and used to produce signals that measures pressure both in static and dynamic settings. The sensor developed is an intelligent sensor that combines optics and electronics to analyze the pressure patterns. The sensor provides the input to a control system that is capable of modifying the shape of the wall and preserve the stability of the flow.
The practical application of electronic holography requires the use of fiber optics. The need of employing coherent fiber optics imposes restrictions in the efficient use of laser light. This paper proposes a new solution to this problem. The proposed method increases the efficiency in the use of the laser light and simplifies the interface between the laser source and the fiber optics. This paper will present the theory behind the proposed method. A discussion of the effect of the different parameters that influence the formation of interference fringes is presented. Limitations and results that can be achieved are given. An example of application is presented.
A new reflection moire technique is introduced in this paper. The basic equations that relate the measurement of slopes to the basic geometric and optical parameters of the system are derived. The sensitivity and accuracy of the method are discussed. Examples of application to the study of silicon wafers and electronic chips are given.
The difference between theoretical and experimental strength of solids, leads to the assumption that the presence of defects under the form of cracks is responsible for this difference. The classical work of Griffith on glass provided the foundations for the generalization ofthis model to explain the process of fracture of materials. The fracture of materials is then associated with the presence of very large stress and strain gradients in a small region, the crack tip. To experimentally verify the theoretical results of fracture mechanics, it is necessary to make observations at different levels of spatial resolutions depending of the actual physical size of the corresponding cracks. The actual level of resolution selected depends on the actual physical size of the crystal defect that one wants to observe. If one wants to observe individual dislocations, the level of the resolution is of the order of 10'°m to 105m. if one wants to observegrain domains, the level of resolution is iø8 to 104m, and if one wants to analyze composites, the level of resolution is 10 to 102m. Eight orders of magnitude are required to observe the different levels. To make observations at these different levels, different type of radiations are required depending on the resolution. Using conventional optics, one can make observations from 10m up. To proceed to make observations one must use a mathematical model, the most commonly used model is the continuum mechanics model. In this model, it is assumed that the deformations of a body can be represented by analytical functions with continuous derivatives up to the third order. This model implies to ignore the discrete nature of matter and replace it by an ideal medium, the continuum. In this model the deformations of the body are characterized by combinations of the derivatives of the displacement function. This model is used at all the levels of resolutions that we have referred to, from few atomic distances in the case of dislocations, to sizes of the order of 102m in concrete structures with large aggregates. If one looks at a given problem, for example concrete with large aggregates, one can look to the displacement field in a given region at the level of 102m, and go on observing the same field at the different levels of resolution that we have mentioned. One will observe different details of the same field with increasing resolutions. The situation is similar to that of fractal geometry, the deeper one looks the more detail appears. But unlike the simple rule of self-similitude existing in fractal geometry, the different levels are related by more complicated rules. If one considers the displacements, both in direction and magnitude, the displacements between two points are the average of the displacements of the points that appear between these two points at higher levels of resolution. In the case of fracture mechanics, the level of observation depends of how deep one wants to look in the chain leading to fracture. If one wants to look at the level used by the continuum mechanics approach that analyzes the elasto-plastic singular field, one should select a spatial resolution such that the statistical fluctuation caused by the presence of individual grains are smoothed out.
The measurement of strains at high temperatures has become a very important field of research. Advanced technology applications such as structures for high speed aircraft and high efficiency thermal engines are examples of areas requiring measurements of strains at temperatures well above the capability of present day strain gage technology. In a recent paper by one of the authors1 references on the application of optical techniques to field measurement of strains at high temperatures are given. Of the different techniques that are used, speckle and holographic interferometry are of particular interest. Both techniques are remote sensing and do not require elaborate preparation of the surfaces being investigated. From the view of practical applications the use of TV cameras for recording purposes and electro-optical data manipulation and processing are of great interest. Simplicity in handling the recording process, speedy data collection, and automatic data processing are the main advantages of using electro-optical methods. Some more developments in this field can be found in Reference 2-6. Reference 4 contains quantitative results proving the feasibility of making accurate measurements at temperatures up to 1000°C.
A portable holographic interferometer that can be used to measure displacements and strains in all kinds of mechanical components and structures is described. The holostrain system captures images on a TV camera that detects interference patterns produced by laser illumination. The video signals are digitized. The digitized interferograms are processed by a fast processing system. The output of the system are the strains or the stresses of the observed mechanical component or structure.
Strain measurement using interferometry requires an efficient way to extract the desired information from interferometric fringes. Availability of digital image processing systems makes it possible to use digital techniques for the analysis of fringes. In the past, there have been several developments in the area of one dimensional and two dimensional fringe analysis techniques, including the carrier fringe method (spatial heterodyning) and the phase stepping (quasi-heterodyning) technique. This paper presents some new developments in the area of two dimensional fringe analysis, including a phase stepping technique supplemented by the carrier fringe method and a two dimensional Fourier transform method to obtain the strain directly from the discontinuous phase contour map.
The paper presents the analysis of the strain distribution of turbines blades. The holographic moiré technique is used in conjunction with computer analysis of the fringes. The application of computer fringe analysis techniques reduces the number of holograms to be recorded to two. Stroboscopic illumination is used to record the patterns. Strains and stresses are computed.
This paper presents a high resolution computer assisted moiré technique for the measurement of displacements and strains at the microscopic level. The detection of micro-displacements using a moiré grid and the problem associated with the recovery of displacement field from the sampled values of the grid intensity are discussed. A two dimensional Fourier transform method for the extraction of displacements from the image of the moiré grid is outlined. An example of application of the technique to the measurement of strains and stresses in the vicinity of the crack tip in a compact tension specimen is given.
The paper presents a system that may be used in a wide range of biomedical fields. The system can be applied in conjunction with different optical techniques: (a) holography, (b) moire method, (c) speckle techniques, (d) photoelasticity. The system has been built in such a way that an operator with average skills will be able to use it; data acquisition and processing are fast and almost automatic. A brief description of the system, its main components and the basic theory behind it, are given. The use of the system is illustrated with examples in orthopedics and in the cardio-vascular area.
The use of a TV camera as a recording medium and the observation of whole field displacements in real time makes holographic TV a very interesting and powerful tool in a variety of areas from NDE to research and development. The paper presents new developments in the field that add to the versatility of the technique by introducing portability and methods to obtain accurate quantitative results. Examples of applications are given to the measurement of strains both at room and at high temperatures and strain measurements at the microscopic level. 1.