Abstract

Abstract: A 3D SEM Moiré Method (SMM) is proposed in this investigation for the first time for 3D shape measurement with nano-scale sensitivity. The geometric model of the 3D SMM has been theoretically established, combining the stereovision technology in an SEM with the existing principles of in-plane SMM. The Virtual Projection Fringe (VPF) generated under different conditions has been analyzed for 3D reconstructions. Two typical applications have been used to experimentally validate the theoretical model. Experimental results, with the height measurement sensitivity less than 10nm, agree well with the theoretical model we proposed. The uncertainty analysis for the method has also been performed by other auxiliary measurements.

© 2013 OSA

1. Introduction

Moiré measurement methods, including the geometric Moiré and the Moiré interferometry, have been widely used in macroscopical measurement [13].Due to the formation mechanism of Moiré fringes, large field of view to be observed is feasible when the measurement is conducted, considered to be the most attractive characteristic of this age old method. Despite the distinct measurement principles of the above mentioned two methods, one similarity of the two could be found, namely the disability in the measurement at micro-/nano-scales. To overcome this shortcoming, with the wide use of advanced microscopes with ultrahigh resolution such as a Scanning Electron Microscopy (SEM) and a Scanning Probe Microscopy (SPM)and the recent technique of nano-scale grating manufacturing, micro-/nano-Moiré methods were developed [49].Based on the imaging manners (mostly the scanning manner) of these microscopes, it is generally recognized that the Moiré pattern formed in electron microscopes results from the geometric interference between the electronic scanning lines and the gratings (or grids) on the surface of tested objects, as shown in Fig. 1. SEM Moiré Method(SMM), developed from the electron Moiré method [1012], has been investigated by many researchers during the past 20 years, being efficient in measurement for mechanical properties [7,11,1317] and in inversion for objects with periodic structure [16,18]. However, deformation as well as the surface appearance of actual micro-/nano-objects is mostly three-dimensional, which has been usually simplified into two-dimensional measurements. No article has been found in studying 3D measurement with SMM. This is because the complexity of the imaging mechanism of an SEM and the variety of the factors influencing on the Moiré formation to some extent limit the development of3D SMM. Of extraordinary interest is the study by Yasuhiko Arai et al. [19] who proposed a 3D measurement method in an SEM, by machining a micro grating through which the electrons can pass to form the shadow Moiré when electrons emitted from the pole piece of an SEM and scattered from the specimen pass through the grating. Nevertheless, it is difficult to operate in an SEM for the procedures, not only because of the requirement for the special gratings but also of the grating positioning manipulations.

 

Fig. 1 Mechanism of fringe generation: when specimen grating (on the sample surface) varies ((a) rotation; (b) compressing or stretching), there appears fringes containing the information of displacement and strain of the sample.

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In this study, a novel method used in 3D measurement of micro-/nano-objects with 3D SMM is proposed. The 3D geometric model is established by combing the stereophotography technology of the SEM with traditional in-plane SMM. The Virtual Projection Fringes (VPF) under different conditions is analyzed. Two examples are adopted to experimentally validate the proposed method.

2. Theoretical model of the 3D SMM

2.1. Basic principles

Although the imaging mechanism of an SEM is quite different from that of an optical system, the pinhole imaging model is used to approximately describe the imaging system in an SEM. It is comprehensible that the electrons beam is compared to the light beam, on which the SEM stereophotography technology has been mainly based. The signal electrons (such as secondary electrons and backscattered electrons) are collected by a detector, recognized as a key device for imaging. It may be easier to understand that the imaging plane is pictured beneath the sample plane, as pictorialized in Fig. 2(a) and 2(b). Hence, the 3D model of the SEM stereophotography can be established based on the conventional optical model geometrically. Due to this analogy, images on the imaging plane vary with the tilting angle change of the sample plane. Capturing two images at different angles, the acquired image pair can be processed to reconstruct the 3D appearance of the measured object. The well-established geometric model of an SEM can be described mathematically in Eq. (1) which gives the relationship between the height of the sample surface and the projective 2D parallax shift (shown in the SEM monitor) [20]. Accordingly, by acquiring the 2D parallax shift value of the sample surface projected onto the imaging plane, the height (surface shape) of the object is obtained [21].

h=y1y22Msinφ+y1y2M2Rcosφ1+y1y2(MR)2+y1y22MRcotφtanφ
wherey1andy2are the distances to the tilt spindle in the SEM monitor at angle 1 (before the tilt) and angle 2 (after the tilt) respectively;Mis the magnification factor;Ris the fictitious projection distance, an instrumental parameter related to the experimental condition;φis the angular variation between two observing tilt angles. These geometric parameters are also shown in Fig. 2(a).Specifically, Eq. (1) can be simplified into Eq. (2) considering the infinitesimal ofy1,y2relative to the geometric parameterRand that1tanφ1when the tilting angleφis small (less than 10°).This is more obvious in an SEM at high magnifications, at which the fictitious projection distanceRis much larger than the working distanced.

 

Fig. 2 (a) Imaging principle of an SEM; (b) Geometric location change fromy1toy2after the tilt of the sample plane.

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h=1My1y22sinφ

Inspired by the above principle, grid/grating methods for in-plane deformation measurement can be extended into 3D measurement [22].Images of Objects with Gratings on the Surface (OGSs) under the SEM at different tilt angles are captured and processed to calculate the surface profile value of the OGS, i.e. the 3D shape. Nevertheless, the method from Ref [22]. has an intrinsic shortcoming. At large magnifications, the area that can be observed in the field of view is limited to a relatively small part of the OGS. However, this limitation can be overcome by means of Moiré methods, which can enhance the field of view almost by one order in dimension compared to that achieved by means of the grid/grating methods under the same resolution. Considering the feasibility of 3D measurement in an SEM based on the grid/grating processing technology, SMM is investigated here for its application in 3D shape measurement.

As previously mentioned, the fundamentals, experimental validations of the in-plane SMM have been fully discussed by many other researchers [918]. Here, only some indispensable knowledge, concerning the research in this study, is given. The theoretical model and formulas of traditional geometric Moiré method are available for SMM. The in-plane displacement can be conveniently calculated with expressions of geometric Moiré method.

u=Nxpr
and
v=Nypr
whereuandvare the displacement whileNxandNyare the Moiré fringe order number in thexandydirection, respectively;pris the spatial frequency of the reference grating.

2.2. Virtual projection fringes in an SEM

For the in-plane SMM, the scanning lines of the SEM are recognized as the reference gratings. Regarding the scanning lines of the SEM as stationary lines (here the term stationary implies the frequency invariance of the reference grating), the Moiré fringes, if there is any, change their pattern styles when the sample stage moves vertically (either out-of-plane translation or tilt). This variation of the fringe patterns simply results from the rigid body displacement of the specimen, causing the shortening or the lengthening of the projection image of the OGSs, instead of the real deformation, which can be defined as Virtual Projection Fringes (VPF).As the definition suggests, the appeared Moiré fringes in the SMM may be as a consequence partly of the real deformation, partly of the stage movement. Accordingly, to define the Moiré Fringes is of great significance. The following two cases are discussed in detail.

A. Out-of-plane translation

Sample stage translating slightly up and down may result in remarkable variations in the Moiré Fringes style. As depicted in Fig. 3(a), compared to the initial location of the sample stage, upper and lower location of the sample may influence the imaging in the SEM. Specifically, when the sample stage translates upward with Δd, the edge part of the scanning area would be lost in the field of view. In the meantime, the specimen grating becomes sparser. Hence it can be regarded as a virtual stretching deformation. Similarly, when the sample stage translates downward with Δd, the specimen grating becomes denser, which is defined as the virtual compression deformation, depicted in Fig. 3(b).Nevertheless, the working distance couples with other parameters of the SEM such as magnification and scanning angle. Besides, tiny adjustment and the self-regulation for the working distance always exist in the SEM when operators attempt to bring the observed sample into focus. Therefore, it is fairly difficult to precisely control the working distance as we are willing to. Fortunately, the change of the working distance has little influence on the generation of VPF, compared to the other factor which is discussed in the following section.

 

Fig. 3 Generation of the VPF by out-of-plane translation: (a) equivalent optical system; (b) imaging variation in the monitor.

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B. Tilting the stage

Tilting the sample stage can be regarded as a main factor that leads to generate the VPF without any actual deformation. This kind of VPF is more significant, compared with the case we mentioned in section A, for the 3D analysis in an SEM, since the whole SEM stereophotography principle is based on the variation of the SEM images under the tilting manipulation. Figure 4is the schematic for the generation of the VPF by tilting the sample stage. Simulation, as shown in Fig. 4(a), illustrated the formation of the VPF. It is obvious that the projection of the observed object onto the imaging plane has always been compressed whatever the tilt direction is clockwise or anticlockwise. Consequently, unlike the translation case, the tilting manipulation generating the VPF always results in the compressive virtual strain. The above conclusion has great significance, not only for the analysis in the VPF style, but also for the following discussion of the 3D reconstructions.

 

Fig. 4 Schematic of the VPF: (a) simulation of the VPF; (b) geometric description of the VPF generation by tilting the sample stage.

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To quantify the influence of the tilt manipulation on the generation of the VPF, some simple but important geometric deductions are given as follows. The tilting angleφis a variable which determines the virtual strain, as shown in Fig. 4(b). With the geometric relations, it can be deduced as:

ΔL=L(1cosφ)
whereLis the original width of the sample in the field of view (before tilting), ΔLis the virtual compressive displacement in the field of view. More generally analyzing, each point on the sample stage has a corresponding parallax shift when the stage tilts and the parallax shift can be expressed according to Eq. (5).The parallax shift signifies the projection change onto the imaging plane in the equivalent optical system, which can be clearly displayed in the SEM monitor. According to the analysis in 2.1, ΔLcan be expressed in the form of the Moiré fringes as:

Nxxpr=sinφtanφ2

Here, it is notable that the directionxin Eq. (6) is perpendicular to the spindle of the SEM sample stage. Obviously, the VPF order number caused by tilting the sample stage is a one-to-one correspondence with the tilting angle, which is demonstrated in the following chapters with designed experiments. In 2.1, we have referred the classical geometric 3D model of the SEM that applies the parallax shift to calculate the height of a random point on the surface of the tested object, achieving the 3D reconstruction. This method, if neglecting other subordinate influencing factors, can be promoted further into a new technique combined with the SMM, namely the 3D SMM.

2.3. The model of the 3DSMM and the height measurement sensitivity

For the realization of the shape measurement in an SEM, which differs from the deformation measurement, the parallax shift in the monitor is the main measured value according to Eq. (1) or Eq. (2). In other words, any 3D measurement based on optics methods is ultimately processed with2D calculation. The logic of the 3D SMM method can be described as follows: Tilting the sample stage generates the VPF, representing the in-plane parallax shift. To process the VPF, the parallax shift can be obtained, which is next substituted into the 3D model Eq. (Eq. (1) or Eq. (2)). The 3D reconstruction is consequently achieved. Combining the Moiré expression (Eq. (3) and Eq. (4)) with Eq. (1) and Eq. (2) respectively, the height expressions can be obtained as:

h=N2pr2R(MMcosφ)2-Npr2Msinφ1+N2pr2cosφ[MR(1-cosφ)]2-Npr2MRcotφtanφ
and

h=1MNpr2sinφ

The parameters in Eq. (7) and Eq. (8) areas previously defined. Furthermore, according to Eq. (8), the relation between the magnification of the SEM and the spatial frequency of the reference gratings is linear, which has been calibrated in the experiments, expressed as:

fr=1pr=3.42M

LetM=350,N=1,φ=10and pr=830nm, the case that a 1200lines/mm grating has been selected, the height valuehcalculated with Eq. (8) is approximately 6.8nmand the height resolution is 1.1nmwhen a 3000lines/mm grating is used. Hence we know that the theoretical sensitivity of the method we proposed reaches to the scale less than10nm. Theoretically, the increase of the spatial frequency of the specimen grating can further enhance the sensitivity of the method. This enhancement depends heavily on the development of advanced micro fabrication technologies for high frequency gratings. Although, logically, it is reasonable for the above derivation, the calculation from Eq. (7) to Eq. (9) should be under one important assumption that the tilting manipulation must be eucentric tilting, which can be satisfied in most new-style SEMs [23]. Another key point is that, like any other Moiré method, the formation of Moiré fringes is conditioned geometrically. When the tilting angle is not as large as it should be, there will not be any VPFs. Some discussion, therefore, has been requisite, given in the following section.

Assume that the minimum parallax shiftΔuis 1 pixel, (only larger than this minimum value, will there be the Moiré fringes), expressed asΔumin=L(1cosφ)=pr=1pixel. Let the lateral resolution of the SEM monitor be 1024 pixels, and obviously the minimum level of the VPF is that the distance between two fringes is 1024 pixels. The minimum tilting angle is obtained by the following Eq.:

Δφmin=arccos(ΔL1ΔL)Δφmin|ΔL=1024pixels2.53

Therefore, the tilting angle should be larger than 2.53°to form the least Moiré fringes. Similarly, there also exists a maximal tilting angle, below which the generated VPF can be used in the measurement. According to Ref [22], an empirical value of 10 degree is commonly adopted.

2.4. The order number of the fringes

The acquisition for the displacement field, according to Eq. (3) and Eq. (4) relates to the order number of the Moiré fringes using any Moiré methods. The Moiré fringes, essentially the isolines of displacement, denotes the larger displacement of the varying (either real deformation or the virtual deformation) OGSs with the increase of the fringe order. In the 3D SMM model of the SEM, defining the fringe order facilitates the 3D reconstruction. Considering the tilting manipulations, the order of the fringe farthest from the eucentric tilting spindle is selected asN=0. Distinct from the traditional geometric Moiré methods, the definition proposed here for the fringe order number does not represent the position with zero displacement physically. The fringe with the order numberN=0is defined as a datum fringe. The displacement values of other fringes have been calculated by contrasting with this datum fringe.

Besides, it is notable that the displacement value obtained before tilting the stage is generated by the mismatch between the reference grating (scanning lines) and the sample grating. This means that the displacement is not the consequent of a true movement or deformation. This initial displacement is usually defined as a carrier wave displacement used in the following calculation for surface height of a tested object.

3. Experimental analysis

To fully demonstrate the method, two cases were analyzed experimentally, in which different materials and loads were applied. The optimized nanoimprint lithography [24] was applied to fabricate the gratings on the tested object surface. Before any experimental validation, the calibration for the spatial frequency of the reference grating (the scanning lines of the SEM) has been performed, shown in Fig. 5.All the experiments were performed using an FEI Quanta 450SEM.

 

Fig. 5 Calibration curve for the spatial frequency of the reference grating in the SEM.

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The first task is to validate the VPF theory we proposed in the above sections. Standard gratings fabricated using photolithography technique with the spatial frequencies of 3000lines/mm and 1200lines/mm were selected in the experiment. Figure 6shows the VPF formed by tilting the sample stage with the tilting angle of 6 degree. In Figs. 6(a) and 6(b), two standard gratings with various spatial frequencies are tested. The distance variation between the two fringes results from the tilting, which is coupled with the tilting angle according to Eq. (5) and Eq. (6). By calculating the displacement variation, the tilting angle can be obtained,L(cosφ2cosφ1)=|LL'|=ΔL, whereφ1andφ2are the angles relative to the horizontal plane at the first position (before the tilt) and the second one (after the tilt) of the sample stage, respectively. The lengthLandLhave both been marked in Fig. 6. By calculating with the above equations, the angle has been determined to be, approximately, the value of6.3°, which is consistent with the actual value (6°).Achieving the 3D reconstruction depends not only on the theory model, but also on the calculational software packages such as MATLAB to process the Moiré fringe images and to solve the equations. The fringe processing methodology has been seen in a series of articles [2529], which is not discussed here in detail.

 

Fig. 6 VPF formed by tilting the sample stage with (a) 1200lines/mm sample and (b) 3000lines/mm sample.

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To validate the theory model we proposed in the previous sections, some applications are given in the following sections.

3.1. The 3D shape measurement for a polydimethylsiloxane (PDMS)sheet(sample 1)

A PDMS sheet with nano-scale gratings on the surface was prepared in our experiments, combing the optimized nanoimprint lithography. The PDMS sheet was solidified in a 2000lines/mm nanoimprint stamper. Then the PDMS sheet plate was compressed by a mechanical clamp to generate a 3D deformation. Figure 7 shows the PDMS sample. It can be noticed that there appears the Moiré fringes on the surface of the PDMS sheet at the tilt angle of 0°.This is due to the in-plane deformation, which can be neglected when 3D shape reconstruction becomes the main purpose of the measurement. This is, to some extent, difficult to comprehend physically. Actually, initial fringes have always been arising even though the reference grating (scanning lines) fits the specimen grating very well. It is acceptable that the initial fringes exist, since the variation of the fringes parallax shift between the two different tilting angles is the decisive factor to the 3D reconstruction. Consequently, the initial 2D Moiré fringes can be recognized as the carrier wave displacement field. To apply the previously mentioned 3D SMM model in the experiment, some calculations are indispensable using MATLAB software package. The 3D reconstruction with the calculation was depicted in Fig. 8.

 

Fig. 7 Optical and SEM image ((a) and (b) respectively) of the PDMS sheet at tilt angle of (c) 0°and (d) 6°, showing the parallax shift change of the Moiré fringes with respect to the tilt.

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Fig. 8 Calculation: (a) different displacement field obtained at different tilt angles; (b) profile of the tested area.

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3.2. Deformation of the grating sample (sample 2)

Gratings fabricated with lithography may deform when they were in humid environments for a long time, since the residual developing liquid reacts with metal films. The 3D shape of the deformed gratings used in our experiment is the blister shape, as shown in Figs. 9(a) and 9(b). The scanning Moiré fringes have been shown in Figs. 9(c) and 9(d). Different tilting directions may generate different styles of fringes. The displacement distribution can be obtained at angle 1 and angle 2, respectively, as shown in Fig. 9(e).

 

Fig. 9 Blister shape deformation of the grating: (a) image under an optical microscopy; (b) 3D shape obtained by a 3D digital microscopy (Keyence VHX-500F); (c)scanning Moiré image of the sample at tilt angle of 0° and (d) at ± 10°; (e)calculation of the displacement field at different tilting angles.

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4. Results discussion

As presented in the previous paragraph, two typical experiments were conducted. Both of the samples have been measured using the 3D SMM, by which the 3D shape can be obtained. To experimentally validate the feasibility and the correctness as well as analyze the error of the results, a Laser Scanning Confocal Microscope (LSCM) and a 3D digital microscopy were used. The LSCM and the 3D microscopy used in our experiments are made by Lasertec Corporation and Keyence Corporation, respectively. The measurements of the samples have been listed in Table1 and Table2, depicted in Fig. 10 and Fig. 11. The measured profile of the samples used in the first experiment (sample 1) and the second experiment (sample 2) are marked in Fig. 8 and Fig. 9(a) with section lineAB (the purple dotted line).

Tables Icon

Table 1. The height values of sample 1 obtained by different equipment.

Tables Icon

Table 2. The height values of sample 2 obtained by different equipment.

 

Fig. 10 Profile of sample 1 measured by different methods.

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Fig. 11 Profile of sample 2 measured by different methods.

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According to the results, the measurement obtained by 3D SMM coincides, in the shape trend, with that by the LSCM and the 3D digital microscopy. It can also be determined quantitatively that the average relative uncertainty of 3D SMM, based on the result data, to the results by LSCM and 3D digital microscopy are less than, 7.5% and 16.7%, respectively. The accuracy of the LSCM measurement is higher than that of the 3D digital microscopy. Hence the former relative uncertainty, namely 7.5%, is more receivable.

It is noted that the experimental uncertainty is influenced by various factors. The most significant one is that the scanning lines of the SEM are not geometrically perfect. The non-linearity of the scanning lines induces image distortion and the minor change of the frequency of the reference grating, which may limit the accuracy and the extensive application of the proposed 3D SMM. The distortion elimination in SMM will play an important role in improvement of the measurement accuracy, and the scanning lines/rasters calibration can be performed according to distortion elimination principle of SEM images reported in [30, 31].

5. Conclusion

We have, for the first time, proposed a 3D shape measurement method for micro- or nano-objects. The technology combines the SEM stereophotography technique with the in-plane SEM Moiré method. By analyzing the virtual projection fringes formed in the tilting manipulation of the sample stage, the 3D geometrical model of the SEM Moiré method can be established. Experiments for different samples validate the feasibility of the method in 3D shape measurement. Commercial measuring devices are used in our study to obtain data compared with the results by the proposed method. It has been proved that the relative uncertainty of the method was no more than 7.5%.

Acknowledgments

The authors are grateful to the financial support from the National Basic Research Program of China (“973” Project) (Grant No.2010CB631005, 2011CB606105), the National Natural Science Foundation of China (Grant Nos. 11232008, 91216301, 11227801, 11172151, 11072033), Tsinghua University Initiative Scientific Research Program, Program for New Century Excellent Talents in University (Grant No.NCET-12-0036), Natural Science Foundation of Beijing, China (Grant No. 3122027).

References and links

1. D. Post, B. Han, and P. Ifju, High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials (Springer-Verlag, 1994), Chap.4.

2. O. Bryngdahl, “Moiré: Formation and interpretation,” J. Opt. Soc. Am. 64(10), 1287–1294 (1974). [CrossRef]  

3. I. Amidror, The Theory of the Moiré Phenomenon (Springer-Verlag, 2009).

4. J. W. Dally and D. T. Read, “Electron beam moiré,” Exp. Mech. 33(4), 270–277 (1993). [CrossRef]  

5. B. Pan, H. M. Xie, S. Kishimoto, and Y. Xing, “Experimental study of moiré method in laser scanning confocal microscopy,” Rev. Sci. Instrum. 77(4), 043101 (2006). [CrossRef]  

6. H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech. 24(1), 31–32 (2000).

7. S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993). [CrossRef]  

8. C. M. Liu, L. W. Chen, and C. C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology 17(17), 4359–4366 (2006). [CrossRef]  

9. F. Silly, “Moiré pattern induced by the electronic coupling between 1-octanol self-assembled monolayers and graphite surface,” Nanotechnology 23(22), 225603 (2012). [CrossRef]   [PubMed]  

10. S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mat. Sci. 40(452), 637–641 (1991). [CrossRef]  

11. Z. W. Zhong, “Thermal strain analysis of IC packages using various Moiré methods,” Microelectron. Int. 21(3), 25–28 (2004). [CrossRef]  

12. H. Chen and D. Liu, “Advances in scanning electron microscope Moiré,” Exp. Mech. 41(2), 165–173 (2001). [CrossRef]  

13. Y. M. Xing, Y. Tanaka, S. Kishimoto, and N. Shinya, “Determining interfacial thermal residual stress in SiC/Ti-15-3 composites,” Scr. Mater. 48(6), 701–706 (2003). [CrossRef]  

14. H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng. 45(12), 1157–1169 (2007). [CrossRef]  

15. Y. J. Li, H. M. Xie, B. Q. Guo, Q. Luo, C. Z. Gu, and M. Q. Xu, “Fabrication of high-frequency moiré gratings for microscopic deformation measurement using focused ion beam milling,” J. Micromech. Microeng. 20(5), 055037 (2010). [CrossRef]  

16. Z. W. Liu, X. F. Huang, H. M. Xie, X. H. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol. 22(12), 125702 (2011). [CrossRef]  

17. Z. X. Hu, H. Xie, J. Lu, Z. Liu, and Q. Wang, “A new method for the reconstruction of micro- and nanoscale planar periodic structures,” Ultramicroscopy 110(9), 1223–1230 (2010). [CrossRef]   [PubMed]  

18. H. M. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy Moiré method and its application in the structure of butterfly wing,” J. Appl. Phys. 101(10), 103511 (2007). [CrossRef]  

19. Y. Arai, M. Ando, S. Kanameishi, and S. Yokozeki, “Micro 3D measurement method using SEM,” Mapan 26(1), 69–78 (2011). [CrossRef]  

20. G. Piazzesi, “Photogrammetry with the scanning electron microscope,” J. Phys. E Sci. Instrum. 6(4), 392–396 (1973). [CrossRef]  

21. G. S. Lane, “The application of stereographic techniques to the scanning electron microscope,” J. Phys. E Sci. Instrum. 2(7), 565–569 (1969). [CrossRef]  

22. C. W. Li, Z. W. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol. 24(4), 045401 (2013). [CrossRef]  

23. F. Marinello, P. Bariani, E. Savio, A. Horsewell, and L. De Chiffre, “Critical factors in SEM 3D stereo microscopy,” Meas. Sci. Technol. 19(6), 065705 (2008). [CrossRef]  

24. M. J. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of Moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express 20(3), 2942–2955 (2012). [CrossRef]   [PubMed]  

25. G. A. Mastin and D. C. Ghiglia, “Digital extraction of interference fringe contours,” Appl. Opt. 24(12), 1727–1728 (1985). [CrossRef]   [PubMed]  

26. T. Y. Chen and C. E. Taylor, “Computerized fringe analysis in photomechanics,” Exp. Mech. 29(3), 323–329 (1989). [CrossRef]  

27. Y. Morimoto, “Digital image processing,” In: Kobayashi A. eds., Handbook on Experimental Mechanics. 2nd edition. SEM, (1994).

28. W. W. Macy Jr and W. William, “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22(23), 3898–3901 (1983). [CrossRef]   [PubMed]  

29. G. Lai and T. Yatagai, “Generalized phase-shifting interferometry,” JOSA A. 8(5), 822–827 (1991). [CrossRef]  

30. M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol. 17(10), 2613–2622 (2006). [CrossRef]  

31. T. Zhu, M. A. Sutton, N. Li, J. J. Orteu, N. Cornille, X. Li, and A. P. Reynolds, “Quantitative stereovision in a scanning electron microscope,” Exp. Mech. 51(1), 97–109 (2011). [CrossRef]  

References

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  1. D. Post, B. Han, and P. Ifju, High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials (Springer-Verlag, 1994), Chap.4.
  2. O. Bryngdahl, “Moiré: Formation and interpretation,” J. Opt. Soc. Am.64(10), 1287–1294 (1974).
    [CrossRef]
  3. I. Amidror, The Theory of the Moiré Phenomenon (Springer-Verlag, 2009).
  4. J. W. Dally and D. T. Read, “Electron beam moiré,” Exp. Mech.33(4), 270–277 (1993).
    [CrossRef]
  5. B. Pan, H. M. Xie, S. Kishimoto, and Y. Xing, “Experimental study of moiré method in laser scanning confocal microscopy,” Rev. Sci. Instrum.77(4), 043101 (2006).
    [CrossRef]
  6. H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech.24(1), 31–32 (2000).
  7. S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng.32(3), 522–526 (1993).
    [CrossRef]
  8. C. M. Liu, L. W. Chen, and C. C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology17(17), 4359–4366 (2006).
    [CrossRef]
  9. F. Silly, “Moiré pattern induced by the electronic coupling between 1-octanol self-assembled monolayers and graphite surface,” Nanotechnology23(22), 225603 (2012).
    [CrossRef] [PubMed]
  10. S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mat. Sci.40(452), 637–641 (1991).
    [CrossRef]
  11. Z. W. Zhong, “Thermal strain analysis of IC packages using various Moiré methods,” Microelectron. Int.21(3), 25–28 (2004).
    [CrossRef]
  12. H. Chen and D. Liu, “Advances in scanning electron microscope Moiré,” Exp. Mech.41(2), 165–173 (2001).
    [CrossRef]
  13. Y. M. Xing, Y. Tanaka, S. Kishimoto, and N. Shinya, “Determining interfacial thermal residual stress in SiC/Ti-15-3 composites,” Scr. Mater.48(6), 701–706 (2003).
    [CrossRef]
  14. H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng.45(12), 1157–1169 (2007).
    [CrossRef]
  15. Y. J. Li, H. M. Xie, B. Q. Guo, Q. Luo, C. Z. Gu, and M. Q. Xu, “Fabrication of high-frequency moiré gratings for microscopic deformation measurement using focused ion beam milling,” J. Micromech. Microeng.20(5), 055037 (2010).
    [CrossRef]
  16. Z. W. Liu, X. F. Huang, H. M. Xie, X. H. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol.22(12), 125702 (2011).
    [CrossRef]
  17. Z. X. Hu, H. Xie, J. Lu, Z. Liu, and Q. Wang, “A new method for the reconstruction of micro- and nanoscale planar periodic structures,” Ultramicroscopy110(9), 1223–1230 (2010).
    [CrossRef] [PubMed]
  18. H. M. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy Moiré method and its application in the structure of butterfly wing,” J. Appl. Phys.101(10), 103511 (2007).
    [CrossRef]
  19. Y. Arai, M. Ando, S. Kanameishi, and S. Yokozeki, “Micro 3D measurement method using SEM,” Mapan26(1), 69–78 (2011).
    [CrossRef]
  20. G. Piazzesi, “Photogrammetry with the scanning electron microscope,” J. Phys. E Sci. Instrum.6(4), 392–396 (1973).
    [CrossRef]
  21. G. S. Lane, “The application of stereographic techniques to the scanning electron microscope,” J. Phys. E Sci. Instrum.2(7), 565–569 (1969).
    [CrossRef]
  22. C. W. Li, Z. W. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol.24(4), 045401 (2013).
    [CrossRef]
  23. F. Marinello, P. Bariani, E. Savio, A. Horsewell, and L. De Chiffre, “Critical factors in SEM 3D stereo microscopy,” Meas. Sci. Technol.19(6), 065705 (2008).
    [CrossRef]
  24. M. J. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of Moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express20(3), 2942–2955 (2012).
    [CrossRef] [PubMed]
  25. G. A. Mastin and D. C. Ghiglia, “Digital extraction of interference fringe contours,” Appl. Opt.24(12), 1727–1728 (1985).
    [CrossRef] [PubMed]
  26. T. Y. Chen and C. E. Taylor, “Computerized fringe analysis in photomechanics,” Exp. Mech.29(3), 323–329 (1989).
    [CrossRef]
  27. Y. Morimoto, “Digital image processing,” In: Kobayashi A. eds., Handbook on Experimental Mechanics. 2nd edition. SEM, (1994).
  28. W. W. Macy and W. William, “Two-dimensional fringe-pattern analysis,” Appl. Opt.22(23), 3898–3901 (1983).
    [CrossRef] [PubMed]
  29. G. Lai and T. Yatagai, “Generalized phase-shifting interferometry,” JOSA A.8(5), 822–827 (1991).
    [CrossRef]
  30. M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol.17(10), 2613–2622 (2006).
    [CrossRef]
  31. T. Zhu, M. A. Sutton, N. Li, J. J. Orteu, N. Cornille, X. Li, and A. P. Reynolds, “Quantitative stereovision in a scanning electron microscope,” Exp. Mech.51(1), 97–109 (2011).
    [CrossRef]

2013 (1)

C. W. Li, Z. W. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol.24(4), 045401 (2013).
[CrossRef]

2012 (2)

M. J. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of Moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express20(3), 2942–2955 (2012).
[CrossRef] [PubMed]

F. Silly, “Moiré pattern induced by the electronic coupling between 1-octanol self-assembled monolayers and graphite surface,” Nanotechnology23(22), 225603 (2012).
[CrossRef] [PubMed]

2011 (3)

Z. W. Liu, X. F. Huang, H. M. Xie, X. H. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol.22(12), 125702 (2011).
[CrossRef]

Y. Arai, M. Ando, S. Kanameishi, and S. Yokozeki, “Micro 3D measurement method using SEM,” Mapan26(1), 69–78 (2011).
[CrossRef]

T. Zhu, M. A. Sutton, N. Li, J. J. Orteu, N. Cornille, X. Li, and A. P. Reynolds, “Quantitative stereovision in a scanning electron microscope,” Exp. Mech.51(1), 97–109 (2011).
[CrossRef]

2010 (2)

Z. X. Hu, H. Xie, J. Lu, Z. Liu, and Q. Wang, “A new method for the reconstruction of micro- and nanoscale planar periodic structures,” Ultramicroscopy110(9), 1223–1230 (2010).
[CrossRef] [PubMed]

Y. J. Li, H. M. Xie, B. Q. Guo, Q. Luo, C. Z. Gu, and M. Q. Xu, “Fabrication of high-frequency moiré gratings for microscopic deformation measurement using focused ion beam milling,” J. Micromech. Microeng.20(5), 055037 (2010).
[CrossRef]

2008 (1)

F. Marinello, P. Bariani, E. Savio, A. Horsewell, and L. De Chiffre, “Critical factors in SEM 3D stereo microscopy,” Meas. Sci. Technol.19(6), 065705 (2008).
[CrossRef]

2007 (2)

H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng.45(12), 1157–1169 (2007).
[CrossRef]

H. M. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy Moiré method and its application in the structure of butterfly wing,” J. Appl. Phys.101(10), 103511 (2007).
[CrossRef]

2006 (3)

C. M. Liu, L. W. Chen, and C. C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology17(17), 4359–4366 (2006).
[CrossRef]

B. Pan, H. M. Xie, S. Kishimoto, and Y. Xing, “Experimental study of moiré method in laser scanning confocal microscopy,” Rev. Sci. Instrum.77(4), 043101 (2006).
[CrossRef]

M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol.17(10), 2613–2622 (2006).
[CrossRef]

2004 (1)

Z. W. Zhong, “Thermal strain analysis of IC packages using various Moiré methods,” Microelectron. Int.21(3), 25–28 (2004).
[CrossRef]

2003 (1)

Y. M. Xing, Y. Tanaka, S. Kishimoto, and N. Shinya, “Determining interfacial thermal residual stress in SiC/Ti-15-3 composites,” Scr. Mater.48(6), 701–706 (2003).
[CrossRef]

2001 (1)

H. Chen and D. Liu, “Advances in scanning electron microscope Moiré,” Exp. Mech.41(2), 165–173 (2001).
[CrossRef]

2000 (1)

H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech.24(1), 31–32 (2000).

1993 (2)

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng.32(3), 522–526 (1993).
[CrossRef]

J. W. Dally and D. T. Read, “Electron beam moiré,” Exp. Mech.33(4), 270–277 (1993).
[CrossRef]

1991 (2)

S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mat. Sci.40(452), 637–641 (1991).
[CrossRef]

G. Lai and T. Yatagai, “Generalized phase-shifting interferometry,” JOSA A.8(5), 822–827 (1991).
[CrossRef]

1989 (1)

T. Y. Chen and C. E. Taylor, “Computerized fringe analysis in photomechanics,” Exp. Mech.29(3), 323–329 (1989).
[CrossRef]

1985 (1)

1983 (1)

1974 (1)

1973 (1)

G. Piazzesi, “Photogrammetry with the scanning electron microscope,” J. Phys. E Sci. Instrum.6(4), 392–396 (1973).
[CrossRef]

1969 (1)

G. S. Lane, “The application of stereographic techniques to the scanning electron microscope,” J. Phys. E Sci. Instrum.2(7), 565–569 (1969).
[CrossRef]

Ando, M.

Y. Arai, M. Ando, S. Kanameishi, and S. Yokozeki, “Micro 3D measurement method using SEM,” Mapan26(1), 69–78 (2011).
[CrossRef]

Arai, Y.

Y. Arai, M. Ando, S. Kanameishi, and S. Yokozeki, “Micro 3D measurement method using SEM,” Mapan26(1), 69–78 (2011).
[CrossRef]

Bariani, P.

F. Marinello, P. Bariani, E. Savio, A. Horsewell, and L. De Chiffre, “Critical factors in SEM 3D stereo microscopy,” Meas. Sci. Technol.19(6), 065705 (2008).
[CrossRef]

Bryngdahl, O.

Chen, H.

H. Chen and D. Liu, “Advances in scanning electron microscope Moiré,” Exp. Mech.41(2), 165–173 (2001).
[CrossRef]

H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech.24(1), 31–32 (2000).

Chen, L. W.

C. M. Liu, L. W. Chen, and C. C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology17(17), 4359–4366 (2006).
[CrossRef]

Chen, T. Y.

T. Y. Chen and C. E. Taylor, “Computerized fringe analysis in photomechanics,” Exp. Mech.29(3), 323–329 (1989).
[CrossRef]

Cornille, N.

T. Zhu, M. A. Sutton, N. Li, J. J. Orteu, N. Cornille, X. Li, and A. P. Reynolds, “Quantitative stereovision in a scanning electron microscope,” Exp. Mech.51(1), 97–109 (2011).
[CrossRef]

M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol.17(10), 2613–2622 (2006).
[CrossRef]

Dai, F.

H. M. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy Moiré method and its application in the structure of butterfly wing,” J. Appl. Phys.101(10), 103511 (2007).
[CrossRef]

Dally, J. W.

J. W. Dally and D. T. Read, “Electron beam moiré,” Exp. Mech.33(4), 270–277 (1993).
[CrossRef]

De Chiffre, L.

F. Marinello, P. Bariani, E. Savio, A. Horsewell, and L. De Chiffre, “Critical factors in SEM 3D stereo microscopy,” Meas. Sci. Technol.19(6), 065705 (2008).
[CrossRef]

Du, H.

Z. W. Liu, X. F. Huang, H. M. Xie, X. H. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol.22(12), 125702 (2011).
[CrossRef]

H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng.45(12), 1157–1169 (2007).
[CrossRef]

Egashira, M.

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng.32(3), 522–526 (1993).
[CrossRef]

S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mat. Sci.40(452), 637–641 (1991).
[CrossRef]

Garcia, D.

M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol.17(10), 2613–2622 (2006).
[CrossRef]

Ghiglia, D. C.

Gu, C.

H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng.45(12), 1157–1169 (2007).
[CrossRef]

Gu, C. Z.

Y. J. Li, H. M. Xie, B. Q. Guo, Q. Luo, C. Z. Gu, and M. Q. Xu, “Fabrication of high-frequency moiré gratings for microscopic deformation measurement using focused ion beam milling,” J. Micromech. Microeng.20(5), 055037 (2010).
[CrossRef]

Guo, B. Q.

Y. J. Li, H. M. Xie, B. Q. Guo, Q. Luo, C. Z. Gu, and M. Q. Xu, “Fabrication of high-frequency moiré gratings for microscopic deformation measurement using focused ion beam milling,” J. Micromech. Microeng.20(5), 055037 (2010).
[CrossRef]

Guo, Z.

H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng.45(12), 1157–1169 (2007).
[CrossRef]

Horsewell, A.

F. Marinello, P. Bariani, E. Savio, A. Horsewell, and L. De Chiffre, “Critical factors in SEM 3D stereo microscopy,” Meas. Sci. Technol.19(6), 065705 (2008).
[CrossRef]

Hu, Z. X.

Z. X. Hu, H. Xie, J. Lu, Z. Liu, and Q. Wang, “A new method for the reconstruction of micro- and nanoscale planar periodic structures,” Ultramicroscopy110(9), 1223–1230 (2010).
[CrossRef] [PubMed]

Huang, X. F.

Z. W. Liu, X. F. Huang, H. M. Xie, X. H. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol.22(12), 125702 (2011).
[CrossRef]

Jiang, H.

H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng.45(12), 1157–1169 (2007).
[CrossRef]

Kanameishi, S.

Y. Arai, M. Ando, S. Kanameishi, and S. Yokozeki, “Micro 3D measurement method using SEM,” Mapan26(1), 69–78 (2011).
[CrossRef]

Kishimoto, S.

H. M. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy Moiré method and its application in the structure of butterfly wing,” J. Appl. Phys.101(10), 103511 (2007).
[CrossRef]

B. Pan, H. M. Xie, S. Kishimoto, and Y. Xing, “Experimental study of moiré method in laser scanning confocal microscopy,” Rev. Sci. Instrum.77(4), 043101 (2006).
[CrossRef]

Y. M. Xing, Y. Tanaka, S. Kishimoto, and N. Shinya, “Determining interfacial thermal residual stress in SiC/Ti-15-3 composites,” Scr. Mater.48(6), 701–706 (2003).
[CrossRef]

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng.32(3), 522–526 (1993).
[CrossRef]

S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mat. Sci.40(452), 637–641 (1991).
[CrossRef]

Lai, G.

G. Lai and T. Yatagai, “Generalized phase-shifting interferometry,” JOSA A.8(5), 822–827 (1991).
[CrossRef]

Lane, G. S.

G. S. Lane, “The application of stereographic techniques to the scanning electron microscope,” J. Phys. E Sci. Instrum.2(7), 565–569 (1969).
[CrossRef]

Lee, A.

H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech.24(1), 31–32 (2000).

Li, C. W.

C. W. Li, Z. W. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol.24(4), 045401 (2013).
[CrossRef]

Li, N.

T. Zhu, M. A. Sutton, N. Li, J. J. Orteu, N. Cornille, X. Li, and A. P. Reynolds, “Quantitative stereovision in a scanning electron microscope,” Exp. Mech.51(1), 97–109 (2011).
[CrossRef]

M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol.17(10), 2613–2622 (2006).
[CrossRef]

Li, X.

M. J. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of Moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express20(3), 2942–2955 (2012).
[CrossRef] [PubMed]

T. Zhu, M. A. Sutton, N. Li, J. J. Orteu, N. Cornille, X. Li, and A. P. Reynolds, “Quantitative stereovision in a scanning electron microscope,” Exp. Mech.51(1), 97–109 (2011).
[CrossRef]

Li, X. D.

M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol.17(10), 2613–2622 (2006).
[CrossRef]

Li, Y.

Li, Y. J.

Y. J. Li, H. M. Xie, B. Q. Guo, Q. Luo, C. Z. Gu, and M. Q. Xu, “Fabrication of high-frequency moiré gratings for microscopic deformation measurement using focused ion beam milling,” J. Micromech. Microeng.20(5), 055037 (2010).
[CrossRef]

Liu, C. M.

C. M. Liu, L. W. Chen, and C. C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology17(17), 4359–4366 (2006).
[CrossRef]

Liu, D.

H. Chen and D. Liu, “Advances in scanning electron microscope Moiré,” Exp. Mech.41(2), 165–173 (2001).
[CrossRef]

H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech.24(1), 31–32 (2000).

Liu, Z.

Z. X. Hu, H. Xie, J. Lu, Z. Liu, and Q. Wang, “A new method for the reconstruction of micro- and nanoscale planar periodic structures,” Ultramicroscopy110(9), 1223–1230 (2010).
[CrossRef] [PubMed]

Liu, Z. W.

C. W. Li, Z. W. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol.24(4), 045401 (2013).
[CrossRef]

Z. W. Liu, X. F. Huang, H. M. Xie, X. H. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol.22(12), 125702 (2011).
[CrossRef]

Lou, X. H.

Z. W. Liu, X. F. Huang, H. M. Xie, X. H. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol.22(12), 125702 (2011).
[CrossRef]

Lu, J.

Z. X. Hu, H. Xie, J. Lu, Z. Liu, and Q. Wang, “A new method for the reconstruction of micro- and nanoscale planar periodic structures,” Ultramicroscopy110(9), 1223–1230 (2010).
[CrossRef] [PubMed]

Luo, Q.

Y. J. Li, H. M. Xie, B. Q. Guo, Q. Luo, C. Z. Gu, and M. Q. Xu, “Fabrication of high-frequency moiré gratings for microscopic deformation measurement using focused ion beam milling,” J. Micromech. Microeng.20(5), 055037 (2010).
[CrossRef]

H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng.45(12), 1157–1169 (2007).
[CrossRef]

Macy, W. W.

Marinello, F.

F. Marinello, P. Bariani, E. Savio, A. Horsewell, and L. De Chiffre, “Critical factors in SEM 3D stereo microscopy,” Meas. Sci. Technol.19(6), 065705 (2008).
[CrossRef]

Mastin, G. A.

Mcneill, S. R.

M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol.17(10), 2613–2622 (2006).
[CrossRef]

Orteu, J. J.

T. Zhu, M. A. Sutton, N. Li, J. J. Orteu, N. Cornille, X. Li, and A. P. Reynolds, “Quantitative stereovision in a scanning electron microscope,” Exp. Mech.51(1), 97–109 (2011).
[CrossRef]

M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol.17(10), 2613–2622 (2006).
[CrossRef]

Pan, B.

H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng.45(12), 1157–1169 (2007).
[CrossRef]

B. Pan, H. M. Xie, S. Kishimoto, and Y. Xing, “Experimental study of moiré method in laser scanning confocal microscopy,” Rev. Sci. Instrum.77(4), 043101 (2006).
[CrossRef]

Piazzesi, G.

G. Piazzesi, “Photogrammetry with the scanning electron microscope,” J. Phys. E Sci. Instrum.6(4), 392–396 (1973).
[CrossRef]

Read, D. T.

J. W. Dally and D. T. Read, “Electron beam moiré,” Exp. Mech.33(4), 270–277 (1993).
[CrossRef]

Reynolds, A. P.

T. Zhu, M. A. Sutton, N. Li, J. J. Orteu, N. Cornille, X. Li, and A. P. Reynolds, “Quantitative stereovision in a scanning electron microscope,” Exp. Mech.51(1), 97–109 (2011).
[CrossRef]

Rong, L.

H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng.45(12), 1157–1169 (2007).
[CrossRef]

Savio, E.

F. Marinello, P. Bariani, E. Savio, A. Horsewell, and L. De Chiffre, “Critical factors in SEM 3D stereo microscopy,” Meas. Sci. Technol.19(6), 065705 (2008).
[CrossRef]

Schreier, H. W.

M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol.17(10), 2613–2622 (2006).
[CrossRef]

Shinya, N.

Y. M. Xing, Y. Tanaka, S. Kishimoto, and N. Shinya, “Determining interfacial thermal residual stress in SiC/Ti-15-3 composites,” Scr. Mater.48(6), 701–706 (2003).
[CrossRef]

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng.32(3), 522–526 (1993).
[CrossRef]

S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mat. Sci.40(452), 637–641 (1991).
[CrossRef]

Silly, F.

F. Silly, “Moiré pattern induced by the electronic coupling between 1-octanol self-assembled monolayers and graphite surface,” Nanotechnology23(22), 225603 (2012).
[CrossRef] [PubMed]

Sutton, M. A.

T. Zhu, M. A. Sutton, N. Li, J. J. Orteu, N. Cornille, X. Li, and A. P. Reynolds, “Quantitative stereovision in a scanning electron microscope,” Exp. Mech.51(1), 97–109 (2011).
[CrossRef]

M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol.17(10), 2613–2622 (2006).
[CrossRef]

Tanaka, Y.

Y. M. Xing, Y. Tanaka, S. Kishimoto, and N. Shinya, “Determining interfacial thermal residual stress in SiC/Ti-15-3 composites,” Scr. Mater.48(6), 701–706 (2003).
[CrossRef]

Tang, M. J.

Taylor, C. E.

T. Y. Chen and C. E. Taylor, “Computerized fringe analysis in photomechanics,” Exp. Mech.29(3), 323–329 (1989).
[CrossRef]

Wang, C. C.

C. M. Liu, L. W. Chen, and C. C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology17(17), 4359–4366 (2006).
[CrossRef]

Wang, Q.

Z. X. Hu, H. Xie, J. Lu, Z. Liu, and Q. Wang, “A new method for the reconstruction of micro- and nanoscale planar periodic structures,” Ultramicroscopy110(9), 1223–1230 (2010).
[CrossRef] [PubMed]

H. M. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy Moiré method and its application in the structure of butterfly wing,” J. Appl. Phys.101(10), 103511 (2007).
[CrossRef]

William, W.

Xie, H.

C. W. Li, Z. W. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol.24(4), 045401 (2013).
[CrossRef]

M. J. Tang, H. Xie, J. Zhu, X. Li, and Y. Li, “Study of Moiré grating fabrication on metal samples using nanoimprint lithography,” Opt. Express20(3), 2942–2955 (2012).
[CrossRef] [PubMed]

Z. X. Hu, H. Xie, J. Lu, Z. Liu, and Q. Wang, “A new method for the reconstruction of micro- and nanoscale planar periodic structures,” Ultramicroscopy110(9), 1223–1230 (2010).
[CrossRef] [PubMed]

H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng.45(12), 1157–1169 (2007).
[CrossRef]

Xie, H. M.

Z. W. Liu, X. F. Huang, H. M. Xie, X. H. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol.22(12), 125702 (2011).
[CrossRef]

Y. J. Li, H. M. Xie, B. Q. Guo, Q. Luo, C. Z. Gu, and M. Q. Xu, “Fabrication of high-frequency moiré gratings for microscopic deformation measurement using focused ion beam milling,” J. Micromech. Microeng.20(5), 055037 (2010).
[CrossRef]

H. M. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy Moiré method and its application in the structure of butterfly wing,” J. Appl. Phys.101(10), 103511 (2007).
[CrossRef]

B. Pan, H. M. Xie, S. Kishimoto, and Y. Xing, “Experimental study of moiré method in laser scanning confocal microscopy,” Rev. Sci. Instrum.77(4), 043101 (2006).
[CrossRef]

Xing, Y.

B. Pan, H. M. Xie, S. Kishimoto, and Y. Xing, “Experimental study of moiré method in laser scanning confocal microscopy,” Rev. Sci. Instrum.77(4), 043101 (2006).
[CrossRef]

Xing, Y. M.

Y. M. Xing, Y. Tanaka, S. Kishimoto, and N. Shinya, “Determining interfacial thermal residual stress in SiC/Ti-15-3 composites,” Scr. Mater.48(6), 701–706 (2003).
[CrossRef]

Xu, M. Q.

Y. J. Li, H. M. Xie, B. Q. Guo, Q. Luo, C. Z. Gu, and M. Q. Xu, “Fabrication of high-frequency moiré gratings for microscopic deformation measurement using focused ion beam milling,” J. Micromech. Microeng.20(5), 055037 (2010).
[CrossRef]

Yatagai, T.

G. Lai and T. Yatagai, “Generalized phase-shifting interferometry,” JOSA A.8(5), 822–827 (1991).
[CrossRef]

Yokozeki, S.

Y. Arai, M. Ando, S. Kanameishi, and S. Yokozeki, “Micro 3D measurement method using SEM,” Mapan26(1), 69–78 (2011).
[CrossRef]

Zhong, Z. W.

Z. W. Zhong, “Thermal strain analysis of IC packages using various Moiré methods,” Microelectron. Int.21(3), 25–28 (2004).
[CrossRef]

Zhu, J.

Zhu, T.

T. Zhu, M. A. Sutton, N. Li, J. J. Orteu, N. Cornille, X. Li, and A. P. Reynolds, “Quantitative stereovision in a scanning electron microscope,” Exp. Mech.51(1), 97–109 (2011).
[CrossRef]

Appl. Opt. (2)

Exp. Mech. (5)

T. Zhu, M. A. Sutton, N. Li, J. J. Orteu, N. Cornille, X. Li, and A. P. Reynolds, “Quantitative stereovision in a scanning electron microscope,” Exp. Mech.51(1), 97–109 (2011).
[CrossRef]

T. Y. Chen and C. E. Taylor, “Computerized fringe analysis in photomechanics,” Exp. Mech.29(3), 323–329 (1989).
[CrossRef]

J. W. Dally and D. T. Read, “Electron beam moiré,” Exp. Mech.33(4), 270–277 (1993).
[CrossRef]

H. Chen, D. Liu, and A. Lee, “Moiré in atomic force microscope,” Exp. Mech.24(1), 31–32 (2000).

H. Chen and D. Liu, “Advances in scanning electron microscope Moiré,” Exp. Mech.41(2), 165–173 (2001).
[CrossRef]

J. Appl. Phys. (1)

H. M. Xie, Q. Wang, S. Kishimoto, and F. Dai, “Characterization of planar periodic structure using inverse laser scanning confocal microscopy Moiré method and its application in the structure of butterfly wing,” J. Appl. Phys.101(10), 103511 (2007).
[CrossRef]

J. Micromech. Microeng. (1)

Y. J. Li, H. M. Xie, B. Q. Guo, Q. Luo, C. Z. Gu, and M. Q. Xu, “Fabrication of high-frequency moiré gratings for microscopic deformation measurement using focused ion beam milling,” J. Micromech. Microeng.20(5), 055037 (2010).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. E Sci. Instrum. (2)

G. Piazzesi, “Photogrammetry with the scanning electron microscope,” J. Phys. E Sci. Instrum.6(4), 392–396 (1973).
[CrossRef]

G. S. Lane, “The application of stereographic techniques to the scanning electron microscope,” J. Phys. E Sci. Instrum.2(7), 565–569 (1969).
[CrossRef]

J. Soc. Mat. Sci. (1)

S. Kishimoto, M. Egashira, and N. Shinya, “Observation of micro-deformation by moiré method using a scanning electron microscope,” J. Soc. Mat. Sci.40(452), 637–641 (1991).
[CrossRef]

JOSA A. (1)

G. Lai and T. Yatagai, “Generalized phase-shifting interferometry,” JOSA A.8(5), 822–827 (1991).
[CrossRef]

Mapan (1)

Y. Arai, M. Ando, S. Kanameishi, and S. Yokozeki, “Micro 3D measurement method using SEM,” Mapan26(1), 69–78 (2011).
[CrossRef]

Meas. Sci. Technol. (4)

Z. W. Liu, X. F. Huang, H. M. Xie, X. H. Lou, and H. Du, “The artificial periodic lattice phase analysis method applied to deformation evaluation of TiNi shape memory alloy in micro scale,” Meas. Sci. Technol.22(12), 125702 (2011).
[CrossRef]

M. A. Sutton, N. Li, D. Garcia, N. Cornille, J. J. Orteu, S. R. Mcneill, H. W. Schreier, and X. D. Li, “Metrology in a scanning electron microscope: theoretical developments and experimental validation,” Meas. Sci. Technol.17(10), 2613–2622 (2006).
[CrossRef]

C. W. Li, Z. W. Liu, and H. Xie, “A measurement method for micro 3D shape based on grids-processing and stereovision technology,” Meas. Sci. Technol.24(4), 045401 (2013).
[CrossRef]

F. Marinello, P. Bariani, E. Savio, A. Horsewell, and L. De Chiffre, “Critical factors in SEM 3D stereo microscopy,” Meas. Sci. Technol.19(6), 065705 (2008).
[CrossRef]

Microelectron. Int. (1)

Z. W. Zhong, “Thermal strain analysis of IC packages using various Moiré methods,” Microelectron. Int.21(3), 25–28 (2004).
[CrossRef]

Nanotechnology (2)

C. M. Liu, L. W. Chen, and C. C. Wang, “Nanoscale displacement measurement by a digital nano-moire method with wavelet transformation,” Nanotechnology17(17), 4359–4366 (2006).
[CrossRef]

F. Silly, “Moiré pattern induced by the electronic coupling between 1-octanol self-assembled monolayers and graphite surface,” Nanotechnology23(22), 225603 (2012).
[CrossRef] [PubMed]

Opt. Eng. (1)

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng.32(3), 522–526 (1993).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

H. Du, H. Xie, Z. Guo, B. Pan, Q. Luo, C. Gu, H. Jiang, and L. Rong, “Large-deformation analysis in microscopic area using micro- Moiré methods with a focused ion beam milling grating,” Opt. Lasers Eng.45(12), 1157–1169 (2007).
[CrossRef]

Rev. Sci. Instrum. (1)

B. Pan, H. M. Xie, S. Kishimoto, and Y. Xing, “Experimental study of moiré method in laser scanning confocal microscopy,” Rev. Sci. Instrum.77(4), 043101 (2006).
[CrossRef]

Scr. Mater. (1)

Y. M. Xing, Y. Tanaka, S. Kishimoto, and N. Shinya, “Determining interfacial thermal residual stress in SiC/Ti-15-3 composites,” Scr. Mater.48(6), 701–706 (2003).
[CrossRef]

Ultramicroscopy (1)

Z. X. Hu, H. Xie, J. Lu, Z. Liu, and Q. Wang, “A new method for the reconstruction of micro- and nanoscale planar periodic structures,” Ultramicroscopy110(9), 1223–1230 (2010).
[CrossRef] [PubMed]

Other (3)

I. Amidror, The Theory of the Moiré Phenomenon (Springer-Verlag, 2009).

D. Post, B. Han, and P. Ifju, High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials (Springer-Verlag, 1994), Chap.4.

Y. Morimoto, “Digital image processing,” In: Kobayashi A. eds., Handbook on Experimental Mechanics. 2nd edition. SEM, (1994).

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Figures (11)

Fig. 1
Fig. 1

Mechanism of fringe generation: when specimen grating (on the sample surface) varies ((a) rotation; (b) compressing or stretching), there appears fringes containing the information of displacement and strain of the sample.

Fig. 2
Fig. 2

(a) Imaging principle of an SEM; (b) Geometric location change from y 1 to y 2 after the tilt of the sample plane.

Fig. 3
Fig. 3

Generation of the VPF by out-of-plane translation: (a) equivalent optical system; (b) imaging variation in the monitor.

Fig. 4
Fig. 4

Schematic of the VPF: (a) simulation of the VPF; (b) geometric description of the VPF generation by tilting the sample stage.

Fig. 5
Fig. 5

Calibration curve for the spatial frequency of the reference grating in the SEM.

Fig. 6
Fig. 6

VPF formed by tilting the sample stage with (a) 1200lines/mm sample and (b) 3000lines/mm sample.

Fig. 7
Fig. 7

Optical and SEM image ((a) and (b) respectively) of the PDMS sheet at tilt angle of (c) 0°and (d) 6°, showing the parallax shift change of the Moiré fringes with respect to the tilt.

Fig. 8
Fig. 8

Calculation: (a) different displacement field obtained at different tilt angles; (b) profile of the tested area.

Fig. 9
Fig. 9

Blister shape deformation of the grating: (a) image under an optical microscopy; (b) 3D shape obtained by a 3D digital microscopy (Keyence VHX-500F); (c)scanning Moiré image of the sample at tilt angle of 0° and (d) at ± 10°; (e)calculation of the displacement field at different tilting angles.

Fig. 10
Fig. 10

Profile of sample 1 measured by different methods.

Fig. 11
Fig. 11

Profile of sample 2 measured by different methods.

Tables (2)

Tables Icon

Table 1 The height values of sample 1 obtained by different equipment.

Tables Icon

Table 2 The height values of sample 2 obtained by different equipment.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

h= y 1 y 2 2Msinφ + y 1 y 2 M 2 Rcosφ 1+ y 1 y 2 (MR) 2 + y 1 y 2 2MR cotφtanφ
h= 1 M y 1 y 2 2sinφ
u= N x p r
v= N y p r
ΔL=L(1cosφ)
N x x p r =sinφtan φ 2
h = N 2 p r 2 R (MMcosφ) 2 - N p r 2Msinφ 1+ N 2 p r 2 cosφ [MR(1-cosφ)] 2 - N p r 2MR cotφtanφ
h= 1 M N p r 2sinφ
f r = 1 p r =3.42M
Δ φ min =arccos( ΔL1 ΔL ) Δ φ min | ΔL=1024pixels 2.53

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