Quantitative Interpretation Of Holograms And Specklegrams

ABSTRACT Fundamentals of laser hologram interferometry and speckle metrology are reviewed with special emphasis on principles governing formation of fringe patterns and dependence of this phenomenon on object's motion and/or deformation. Processes relating to recording and reconstruction of holograms and specklegrams are discussed and are followed by presentation of procedures for their quantitative interpretation based on the method of projection matrices. Since there is a unique projection matrix for each hologram, or specklegram recorded from a different direction, each of the matrix equations relates the fringe parameters and recording geometry to the unknown deformation. Therefore, the resulting system of matrix equations can be solved for the unknown displacements, rotations, and strains. 1. INTRODUCTION Interpretation of experimental data is, in general, not easy1 . Frequently, using conventional experimental techniques, the system's characteristics may be altered as a result of probes that are used, so that the user is not certain about the effect that has been measured. However, recent advances in the laser methods offer the advantage, over the conventional experimental methods, that when properly executed they do not disturb the system being investigated. Also, the laser methods give rapid, full field, three dimensional information ranging from qualitative studies of the overall behavior of the system to precise measurement of its critical parameters2"4. Furthermore, the laser methods provide data which are computer compatible in terms of acquisition, storage, and processing, and yield results that have high accuracy and precision.Today, the laser methods, employing either CW (continuous-wave) or pulsed lasers, are developed to the degree where static, dynamic, as well as transient characteristics of systems can be studied. These techniques utilize the transmitted, reflected, and/or backscattered light. As such, they can be used in a number of applications involving opaque and transparent media.The problem of quantification of holograms and specklegrams, however, is not trivial5 . As a result of this, there is not yet a general method available that can be used reliably to interpret fringe patterns obtain information on displacements and/or deformations of arbitrary objects.All approaches to quantification of holograms and specklegrams rely on mathematical relationships that govern conversion of the data, encoded within an image, to results that can be meaningful to the user. Recent advances in quantitative interpretation of images, however, show that most of the relationships between the involved parameters can best be described by matrix transformations. These transformations map fields of the three- dimensional vectors in one space into corresponding fields of vectors in another space. That is, they allow conversion of the data from image space into the results that can be understood by the user. Furthermore, solution of the resulting equations, to obtain quantitative results, can be achieved in a straightforward manner following established computational procedures for "manipulation" of matrix equations6.