Fringe Multiplication Research Articles

Flow visualization by an improved double exposure method in holography

Some optical differential interferometric techniques were investigated in order to measure the density distribution in the air jet flow of a small scale flow cell while excluding the effects of the optical distortion of its glass windows. A technique using moiré fringe formation by rotating the reference wave in one exposure of the double exposure method was found to be most suitable for this purpose. High contrast and multiplication of moiré fringes can be obtained by a moiré fringe sharpening and multiplication method.

Strain analysis of composites by moiré methods

Moire techniques were developed, adapted and applied to the determination of strain fields in filamentary composite laminates. Conventional techniques, using 1000 line-per-inch (Ipi) arrays bonded or photoprinted onto the specimen, were applied to glass-epoxy and boron-epoxy specimens with holes and cracks. Techniques for tenfold fringe multiplication were also applied to glass-epoxy and boron-epoxy laminates with holes. A reflective surface of glass-like smoothness was produced on the specimen and a 500 dot-per-inch grid photoprinted on it. A rigid distortion-free camera was used for recording replicas of the specimen grid by projection photography. These replicas were analyzed with a 200 line-per-millimeter (5080 Ipi) grating for reconstruction of moire-fringe patterns. These patterns were analyzed by graphical and mechanical differentiation using second-order moire. Strain distributions and strain-concentration factors were in very good agreement with theoretical and other experimental results.

Improvement on Moiré Technique for In-Plane Deformation Measurements

A technique to improve the sensitivity of in-plane deformation measurements on transparent and reflective specimens under tension or compression is described. The principle of this technique is that of moiré fringe multiplication. Experiments with 20-cycle/mm gratings yielded results having eighteen times the sensitivity of the conventional moiré technique. One fringe shift of each moiré fringe corresponded to an in-plane deformation of 2.7 microm.

Developments in the optical spatial filtering of superposed crossed gratings

It is shown in this paper how the whole field of displacement components and of their time and space derivatives (isothetics, isotachics and isoparagogics) can be obtained individually, as separate patterns in a simple and precise manner using spatial-filtering techniques. This result can be obtained even when crossed gratings are used on the deformed body. A method for achieving fringe multiplication in moire patterns produced by superposed, crossed gratings is also demonstrated. It is also shown that displacement components and their time and space derivatives in directions diagonal to the crossed-grating lines can be obtained by proper handling of grating transparencies and spatial-filtering techniques. Hence, the moire equivalent of a whole field of rosette-strain-gage measurements is obtained from a single photograph of a deformed crossed grating. A disk compressed between two wedges is used as an example. Important applications will be found in the fields of dynamics, nonlinear elasticity and plasticity.

Moiré Fringe Multiplication with a Nonsymmetrical Doubly Blazed Reference Grating

A fine reference grating and coarse specimen grating in series are illuminated so that two dominant diffraction sequences take symmetrical paths in the intergrating space. In this optimum configuration, observation is on or near the axis of symmetry. Moiré sensitivity is that of the reference grating and independent of the specimen grating. The contour map described by moiré fringes depicts in-plane displacements uniquely, being insensitive to thickness and taper of gap between gratings. Moiré fringes are nearly perfect two-beam interference fringes of superb contrast. Existing gratings blazed for single-order dominance can be used under conditions that produce the required double-order dominance. In experimental evaluations, coarse gratings of 200 rulings/cm were mated with various reference gratings up to 12,000 rulings/cm for fringe multiplications by factors up to 60.

Instrumentation for fringe multiplication

The paper describes commercial fringe multiplication equipment designed for rapid analysis of frozen stress slices.

Photoelastic-fringe multiplication—For tenfold increase in sensitivity

Slices from three-dimensional frozen-stress models were collected from numerous photoelastic laboratories and these diverse samples were used to demonstrate fringe multiplication. Multiplied isochromatic patterns of excellent clarity and fidelity are presented. Maximum multiplication factors of 9 or 11 are exhibited for most demonstrations, but multiplications by 17 and 25 are exhibited for special cases. Speed, accuracy and simplicity of the method are discussed, and benefits of full-field data retrieval are emphasized.

Slope-contour fringe multiplication by Fresnel diffraction

Coherent collimated monochromatic light emitted from a He−Ne laser was used to illuminate a transparent sheet specimen in plane stress. The light emerging from the specimen was concentrated by a thin positive lens on a coarse amplitude grating placed at the vicinity of the focus of the lens and projected on a ground-glass screen. The strongly coherent light of the laser was diffracted at the coarse grating. The deformed lateral surfaces of the loaded specimen worked as a thin lens of continuously variable focal length, which was interposed in the path of the beam and distorted the diffraction image. The pattern yielded the partialslope contours of the thickness variation in a direction normal to the rulings of the grating. Positioning the grating within the focal distance of the lens resulted in a predominant Fresnel diffraction of the opaque strips of the grating. Placing the grating beyond the focal plane created a Fresnel diffraction of the open slits. Both diffraction patterns yielded a high multiplication of fringes which increased considerably the accuracy of the experimental results.

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). Moire fringe multiplication is accomplished by collecting specific groups of diffracted beams emanating from two moire 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.

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. Guild's 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.

Sharpening and multiplication of moiré fringes

Moire 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 moire fringes then formed corresponds to the greater frequency.

COMPARISON OF FRINGE MULTIPLICATION AND TARDY COMPENSATION METHODS FOR A FROZEN STRESS INVESTIGATION

SummaryA practical application of the fringe multiplication method is described. Using techniques reported by Post, the method was found to be convenient and less time consuming than the normal Tardy compensation technique which was used as a comparison. For the cases studied it was found that fringe multiplications of 7x gave equivalent fringe order distributions to the Tardy technique.

FRINGE MULTIPLICATION ON A SHOE STRING

StrainVolume 3, Issue 1 p. 12-13 FRINGE MULTIPLICATION ON A SHOE STRING G. R. HINDLE, G. R. HINDLESearch for more papers by this author G. R. HINDLE, G. R. HINDLESearch for more papers by this author First published: January 1967 https://doi.org/10.1111/j.1475-1305.1967.tb00859.xCitations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article.Citing Literature Volume3, Issue1January 1967Pages 12-13 RelatedInformation

Fringe multiplication in three-dimensional photoelasticity

Isochromatic fringe multiplication by a factor of up to 17 is demonstrated for slices from three-dimensional frozen-stress models. With this method, sensitivity is increased by an order of magnitude, the taking of data is quick and easy and the interpretation of data is less subject to errors than compensation techniques.

On the accuracy of fringe multiplication with mirrored birefringent coatings

On the accuracy of fringe multiplication with mirrored birefringent coatings

The influence of grid geometry on moiré fringe properties

General equations are developed which relate the characteristics of moiré fringes to the geometry of two superposed, dissimilar grid systems. Equations are derived geometrically, assuming the rectilinear propagation of light, and the analysis is restricted to a consideration of linear, periodic, mutually inclined systems. Criteria are established for the production of first and second order fringe systems, and some particular cases of grid geometry are examined in detail. The concepts of mixed grids and hybrid grid combinations are introduced, and the principles and possible applications of fringe sharpening, fringe multiplication and dual sensitivity systems are discussed.

Fringe multiplication and thickness effects in birefringent coating

The feasibility of applying fringe-multiplication technique in birefringent-coating analysis is studied, and the conditions under which this technique can be used are discussed. The fringe-multiplication technique is then applied to birefringent-coating analysis of a plate with a central circular hole under uniaxial tension. The experimental results are then compared with Howland's analytical results for the shear-stress distribution along the minimum cross section and for normal stress distribution along the edge of the plate. Duffy's correction factors for curvatures and strain gradients are used to estimate the correction in the latter experimental results.

The Library Shelf

The first number of the sixteenth volume in this series contains eighteen papers covering the usual wide range of topics. The longest paper describes a photoelastic investigation carried out in the U.S. Naval Research Laboratory, Washington, D.C., to determine the dynamic stress distribution surrounding a running crack. Iso‐chromatics were obtained using the Schardin multiple spark technique, with the optical system modified for the method of fringe multiplication. Principal stress distributions were found by means of an optical interferometer with single spark illumination, using a number of similar models. Principal stresses were corrected to allow for the variation of stress‐optical sensitivity with time. It was found that the dynamic distribution approximates to that in a statically loaded specimen extended at its ends by a fixed displacement. The zone of stress disturbance grows in all directions proportionally to crack length. The average stress on the remaining uncracked cross section increases with length of crack to a maximum of about 1½ times the original value. Measured terminal crack velocities agreed well with calculated values. The discussion compares the results with theoretical analysis.