Advances in scanning electron microscope moiré

The scanning electron microscope (SEM) moiré method for microscopic measurements based on electron beam lithography and an SEM has been well developed. Although it has been a reliable method, some drawbacks exist: reinforcement effects, complicated processing and low sensitivity. To improve the SEM moiré method, new grating-casting techniques and a fringe-viewing technique must be developed. In this study, a carbonaceous grating technique and a total imaging technique are introduced. Accordingly, there are two techniques available for grating-casting (i.e., the carbonaceous grating technique and the existing lithography grating technique) and three techniques available for fringe viewing (i.e., the total imaging technique, the existing, monitor viewing technique and the existing photographic viewing technique). A total of six new imaging techniques of SEM moiré methods are available for microscopic measurements by combining one technique from each of the two groups. This study demonstrates the feasibility of the individual techniques and discusses the characteristics and limitations of each. Based on the presented total imaging technique, the sensitivity of the moiré method is only dependent on the frequency of specimen grating. Because it can be made as high as 10,000 lines/mm, the SEM moiré method can achieve sensitivity as high as 0.01 percent.     

A new application of isodensitometry in the moiré technique

Some years ago, isodensitometry was introduced into the moiré technique in order to improve the sensitivity of this method. The application of the Sabattier effect gives now a new possibility to produce more lines of equal displacement. The obtained experimental data are the additional lines and the moiré fringes of full or half order. This method is applied on a beam under pure bending and a circular ring loaded diametrically. It will be shown in this paper that the calibration of the displacement curves can be accomplished by a calibration bar or by ‘self calibration’ which will be done on the same model to be studied. Further, the photographic process can be influenced in a way that different lines of equal displacement can be produced for a given system of moiré fringes. The additional lines are shifted here by choosing different times of exposure.     

Hologram projection on curved image planes

Holography allows in-focus projection of images on three-dimensional focal planes of arbitrary shape. Potential application of the method lies in photoetching reference grids for moiré-pattern strain analysis using a green-sensitive photoresist with an argon-ion laser. The method is demonstrated using photographic film and an estimate of focussing errors and aberrations is made.     

Experimental analysis of the deformation of convex cylindrical surfaces

The described method is based on the moiré technque. By applying a special stripping film with a copied grid to a convex cylindrical surface, it is possible to express the equations of the deformed as well as the undeformed grid. By using the double-exposure photographic technique, a field of moiré fringes will be obtained, which gives information of the component perpendicular to the direction of observation of the deformation vector in the plane perpendicular to the axis of revolution. By observing two different directions α₁ and α₂, the experimental data yield the calculation of the displacement vector. The application of the derived method and its reliability will be demonstrated by several examples. The method does not require highly expensive laboratory equipment and is especially useful for engineers in consulting and structural design.     

The moiré method—A review

The paper focuses on the moiré phenomenon as a tool of experimental mechanics. The properties of moiré patterns are outlined. The application of these properties to the measurement of displacements of the points of a surface (intrinsic moiré), contours or deflections (projection moiré) and slopes (reflection moiré) is discussed. Observation methods, recording methods, data-processing techniques are outlined and practical aspects are stressed. Sensitivities and precisions that have been achieved are reviewed. Finally, some typical applications to problems in areas of interest are briefly described.     

A new optical system for moiré methods

A new optical system for moiré methods is proposed in which the light path from the model grating and that from the master grating are diffent. They are combined by mirrors to form moiré patterns. Its application to Ligtenberg's reflective moiré method extends the method to dynamic problems and also facilitates the use of linearmismatch fringes. It can also be applied to in-plane moiré method in cases where deformation is large and diect contact with model grating is to be avoided.     

The micro-connection of the second-order moiré fringes and its order determination,and the determination of the boundary strains

The micro-connection method for determining the centre lines of second-order moiré fringes presented in this paper can enhance the accuracy in measuring strain fields, and generally can determine the absolute order of the second-order moiré fringes. The strain data obtained from curved beam experiment are in good accordance with theory. The relationship between the second-order moiré fringe and the strains at the specific points of the specimen is derived. Hence a reciprocate shift method is presented for determining strain distributions in the non-overlapping region of the shifted moiré patterns, (usually in the region of specimen where no second-order moiré fringes occur is the boundary region).     

The governing equations for moiré interferometry and their identity to equations of geometrical moiré

The equations prescribing the gradient and inclination of fringes in moiré interferometry are derived from the basic laws of diffraction and interference. A vectorial representation of three-dimensional diffraction employs incidence and emergence vectors in the plane of the grating; the representation is especially well suited for this type of analysis. The corresponding equations for geometrical moiré are derived by a remarkably direct vectorial method. The analyses prove that the patterns of moiré interferometry and geometrical moiré are governed by identical relationships. Paper was presented at 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14, 1985.     

An electron moiré method for a common SEM

In the electron moiré method, a high-frequency grating is used to measure microscopic deformation, which promises significant potential applications for the method in the microscopic analysis of materials. However, a special beam scanning control device is required to produce a grating and generate a moiré fringe pattern for the scanning electron microscope (SEM). Because only a few SEMs used in the material science studies are equipped with this device, the use of the electron moiré method is limited. In this study, an electron moiré method for a common SEM without the beam control device is presented. A grating based on a multi-scanning concept is fabricated in any observing mode. A real-time moiré pattern can also be generated in the SEM or an optical filtering system. Without the beam control device being a prerequisite, the electron moiré method can be more widely used. The experimental results from three different types of SEMs show that high quality gratings with uniform lines and less pitch error can be fabricated by this method, and moiré patterns can also be correctly generated.The project supported by the National Natural Science Foundation of China (10662005) and JSPS fellowship in Japan. The English text was polished by Keren Wang.     

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.     

Biomechanical research of joint III. An experimental biomechanical research on the Femur's articular surface of knee of pongidae

In this paper, moiré contour fringes is applied to study the femur's articular surface of the knee of Pongidae. The preliminary division of the femur's articular surface of knee into three types is proposed. The moiré contour fringes ofthe medial condyle is taken as a mark according to the references. Owing to the fact that the moiré contour fringes obtained from experiments after the 2nd order of fringe basically follow a certain rule, an investigation is made on the distribution of the angle α which is defined as the angle of the major axis of the 2nd order's near-oval shaped moiré contour fringe on the medial condyle with the horizontal axis. Preliminary distribution graphs are given in the paper.     

A multilevel treatment of moiré fringe data using finite elements

Finite element procedures are applied to the modeling, analysis and visualization of experimental moiré data. Smoothing elements are introduced and evaluated with respect to data sparseness and error. A one-dimensional smoothing element is uniquely coupled with the method of principal curves to extract moiré fringe centers. A two-dimensional smoothing element is then used to produce a full-field representation given the fringe locations. The moiré technique is applied to the four-point bend experiment, and the surface-modeling technique is used to obtain displacement and gradient (strain) information.     

Scanning moiré at high magnification using optical methods

Methods of employing scanning moiré at high magnification are developed and demonstrated. Modern lithographic techniques for producing custom moiré gratings with a frequency up to 250l/mm are described. On a probing station equipped with a video system, pseudo-color moiré fringes are produced using the scannning lines of the color charge-coupled-device (CCD) camera. Fringe multiplication from 1 to 5 is possible with correct combinations of magnification and grating pitch. An analysis is given to show that strain sensitivity depends only on the number of scanning lines used to record the image. The grating pitch and the magnification are important because they reduce the gage length of the strain measurement. The high-magnification scanning moiré was used to study plastic- strain fields in an aluminum tensile specimen. Local disturbances in the strain field were observed at 2 to 2.5 percent applied strain. These discontinuities became more significant at higher levels of applied strain.     

Log-art as a means of humanization

Log-art is an “artistic” science. By selection and sometimes by deliberate combination of records, methods used to study nature scientifically permit the expression of an artistic feeling. Usually the data are obtained in the form of photographs covering the range of astronomy to electron microscopy. In this paper, particular emphasis will be put on photographic records obtained by experimental stress analysts using photoelasticity, moiré and holography. It is believed that log-art may develop into a powerful means of humanizing scientists by calling their attention to the fact that their scientific records can be looked at other ways than from the scientific point of view.     

Surface and interior strain fileds measured by multiple-embedded-grid moiré and strain gages

Surface and interior straini fields in thick specimens of polycarbonate have been measured by an embedded-multiple-grid moiré method. Interior gratings are photographed through intervening gratings. Coherent optical processing of grating records creates moiré fringe pattern. A correction procedure was developed to eliminate moiré errors caused by strain-induced gradients of refractive index. This procedure utilizes the refraction distribution as obtained from observation of a grating from opposite sides of a specimen. No measurements other than the normal moiré observations are required in order to find actual strains. The correction technique should be useful in refining the results obtained when other optical methods are used in three-dimensional situations. The method is utilized to determine strains on the surfaces and at the mid-and quarter-planes of thick compact tension specimens. Results obtained, after correction, agree with measurements made with embedded strain gages. Maximum tensile strain occurs on the midplane. The findings are rationalized by consideration of thickness and proximity to the crack tip.     

Accuracy of the Sampling Moiré Method and its Application to Deflection Measurements of Large-Scale Structures

Measuring accurate displacement distributions for large-scale structures is an important issue and a very challenging task. Recently, a simple and accurate phase measurement technique called sampling moiré method [Exp Mech 50–4:501–508, (2010)] has been developed for small-displacement distribution measurements. In this method, the phase distribution of moiré fringes can be analyzed from a single grating image by simultaneously performing down-sampling image processing and intensity-interpolation to generate multiple phase-shifted moiré fringe images. In addition, the phase of the original grating can also be obtained from the phase of the moiré fringe by adding the phase of the sampling grating. In this study, the measurement accuracy of the sampling moiré method was analyzed through computer simulations and a displacement measurement experiment. Four factors of the sampling moiré method were investigated, including the sampling pitch, the order of the intensity-interpolation, random noise, and the form of grating. The results show that determining the optimal sampling pitch is an important factor for obtaining better results but it is not critical. In addition, a practical application of the sampling moiré method is presented that involves a deflection measurement on a 10-meter-long crane. The experimental results demonstrate that submillimeter deflections of the crane can be successfully detected.     

The magic of carrier fringes in moiré interferometry

Practical applications in which carrier fringes are used with moiré interferometry for strain measurements are presented. Examples illustrate how moiré carrier fringes are applied to obtain the desired data in complex laminated composite specimens. In many cases, carrier fringes permit extraction of much more detailed information, with procedures that are easier and more accurate than those using loadinduced fringes alone. The fringe vector for carrier fringes is introduced and its application to the interpretation of fringe patterns is explained. In moiré interferometry, the carrier fringes are produced easily by adjustments of optical elements that control the virtual reference grating.     

Rapid interpretation of moiré photographs

The paper describes the possibilities of rapidly and conveniently obtaining results by means of the reflection moiré method. The moiré photographs are produced with the aid of a screen provided with a finely ruled grid. The contrast of the photographs is increased by optical means. By displacement of two equal moiré photographs, moiré fringes of second order for the curvature or the twist are obtained. It is shown how charts can be produced which indicate:

1. The distribution of the bending moments
2. The distribution of the bending moments for which the reinforcement should be designed
3. The distribution of the shear forces and the magnitude of the bearing reactions.