Daniel Post

Developments In Moire Interferometry

Recent progress in high-sensitivity moire interferometry is reviewed. Interference patterns reveal full-field contour maps of in-plane displacements. Sensitivity corresponds to moire with 1200 lines/mm (30,480 //in.) for most examples, but approaches the theoretical limit of X/2 displacement per fringe in one demonstration. Techniques for producing cross-line phase gratings on specimens are described, as well as use of real and virtual reference gratings. Carrier patterns and optical filtering are used to cancel initial or no-load patterns. Diverse applications are illustrated.

Moiré interferometry at VPI & SU

A relatively easy technique for producing high-frequency gratings on specimens extends moiré techniques into the high-sensitivity domain. Whole-field patterns of inplane displacement components are obtained with grating frequencies of 1200, 2400 and 4000 l/mm (30,480, 60,960 and 101,600 l/in.). Moiré interferometry is a case of two-beam interference, characterized by extensive range, excellent fringe contrast and fringe localization on the specimen surface. It is a reflection technique, compatible with opaque specimens and live observation of deformation.

Sharpening and multiplication of moiré fringes

Moiré fringe sharpening is produced when the widths of clear and opaque bands in a pair of super-imposed screens are complementary. Fringe multiplication is produced when the frequency of lines in the reference screen exceeds the frequency in the specimen screen by an integral factor. The number of moiré fringes then formed corresponds to the greater frequency.The conditions of formation of these moiré patterns are presented and demonstrated. Intensity distribution across projected images of moiré fringes is discussed.

Moiré Methods for Engineering and Science — Moiré Interferometry and Shadow Moiré

Moire interferometry and shadow moire are extraordinarily versatile and effective methods for determining in-plane and out-of-plane displacement fields, respectively. The basic concepts are reviewed for both methods, topics on practice and analysis are addressed, and numerous examples of important applications are presented.

Moiré interferometry: Advances and applications

Recent applications of moiré interferometry at VPI & SU and related developments of laboratory techniques are reviewed. The applications are studies of composite bodies, including micromechanics and macromechanics of composites, thermal strains and residual strains. The techniques section discusses steady-state thermal strain measurements, carrier fringes, and advances in methods for producing specimen gratings. With its high sensitivity, high spatial resolution and extensive displacement range, moiré interferometry has matured into a powerful technique for measuring inplane deformations of complex materials and structures.

The moiré grid-analyzer method for strain analysis

The complete state of strain throughout an extended field can be determined from a single photograph by the moiré grid-analyzer method. Grids are used for the active, or specimen screen, and for the rigid analyzer screen. Hence, two families of moiré fringes appear simultaneously, providing displacements inx andy directions throughout the field.Interweaving of moiré fringes so as to disguise the identity of each family is prevented by use of an initial pattern. The initial pattern also eliminates uncertainties in assignment of moiré fringe orders throughout the field, and it provides numerous data points in any local region for reliable evaluation of fringe gradients. A rigorous derivation is presented for interpretation of such patterns in terms of strains.Errors in computed shear strains caused by analyzer misalignment are automatically canceled. The effects of rigid-body rotation of elements within the specimen are routinely eliminated in strain computations. Since calculated strains are independent of analyzer orientation, no fine control of analyzer alignment is required, and small shifts of analyzer position during the experiment are permissible. Accordingly, the moiré grid-analyzer method not only makes possible analysis of problems that previously could not be approached, but also offers vast simplifications for all extended-field moiré analyses.

Free Edge Strain Concentrations in Real Composite Laminates: Experimental-Theoretical Correlation

The magnitude of the maximum shear strain at the free edge of axially loaded theta (2)/-theta(2)(s) and (+ or - theta(2) (s) composite laminates was investigated experimentally and numerically to ascertain the actual value of strain concentration in resin matrix laminates and to determine the accuracy of finite element results. Experimental results using moire interferometry show large, but finite, shear strain concentrations at the free edge of graphite-epoxy and graphite-polyimide laminates. Comparison of the experimental results with those obtained using several different finite element representations showed that a four node isoparametric finite element provided the best and most trouble free numerical results. The results indicate that the ratio of maxium shear strain at the free edge to applied axial strain varies with fiber orientation and does not exceed nine for the most critical angle which is 15 deg.

Analysis of Moiré Fringe Multiplication Phenomena

Sensitivity and accuracy of measurements made by the moiré effect can be increased by a fringe multiplication factor. For a given displacement or deformation, the number of fringes that cross the field is increased by this factor. Multiplications as high as thirty are demonstrated. High sensitivity measurements are possible with coarse active gratings. With two amplitude gratings of equal nominal frequencies multiplication patterns exhibiting pure two-beam interference are produced when transmittance is 0.5. With gratings in which frequencies are dissimilar by integral factor beta, multiplication by bbeta is achieved, where b is an integer. Guilds theory of moiré fringes is extended to this case of grossly dissimilar grating frequencies. The combination of a symmetrical double-order blazed reference grating with a coarse bar-and-space active grating appears most attractive for many metrological applications.

An interpretation of Moiré interferometry from wavefront interference theory

Abstract The process of moire interferometry is given mathematical description in terms of the classical theory of optical interference. The governing relationship between displacement and fringe order is derived, and the analysis is extended to cover carrier patterns, double exposure methods, and initial fringe pattern elimination. Various processes for obtaining patterns of displacement derivatives are also described mathematically.

New optical methods of moiré fringe multiplication

Photographs or other replicas of relatively coarse specimen screens can be analyzed with sensitivities corresponding to screens of many thousands of lines per inch (lpi). Moiré fringe multiplication is accomplished by collecting specific groups of diffracted beams emanating from two moiré screens in series. Three methods are described and multiplication by factors as high as 30 are demonstrated. Sensitivity and accuracy are increased by the fringe-multiplication factor. Usefulness of full-field mechanical differentiation techniques is extended to cases of correspondingly lower strains. These fringe-multiplication methods apply to both bar-and-space screens and transparent diffraction gratings.