This work was supported by JSPS KAKENHI, grant numbers JP16K17988 and JP16K05996, and by the Cross-Ministerial Strategic Innovation Promotion Program, Unit D66, Innovative Measurement and Analysis for Structural Materials (SIP-IMASM), operated by the cabinet office. The authors are also grateful to Drs. Satoshi Kishimoto and Kimiyoshi Naito at NIMS for their CFRP material.

1. Confirmation of the Micro/Nano-scale Grid on the Specimen
<ol>
	<li>Machining of the Specimen
	<ol>
		<li>Cut the specimen to the size required by the specific loading device used under a microscope (e.g., 1 x 5 x 30 mm3), making the surface to be observed 1.5x greater than the region of interest.</li>
		<li>Polish the specimen surface to be observed (e.g., 1 x 30 mm2), successively using coarse and fine sand paper on an automatic polishing machine (e.g., use SiC foil #320 for 3 min and then #800 for 1 min at 150 rpm and 30 N). Clean the specimen using water after each polishing step.</li>
		<li>Polish the same specimen surface, successively using coarse and fine polishing solutions on the automatic polishing machine (e.g., use DP-Spray P 15 &#181;m for 5 min, P 1 &#181;m for 8 min, and P 0.25 &#181;m for 10 min at 150 rpm and 30 N). Clean the specimen using water after each polishing step.</li>
	</ol>
	</li>
	<li>Fabrication of the Micro/Nano-scale Grid If No Periodic Pattern Exists on the Specimen 
	NOTE: This step can be omitted if a natural periodic pattern exists on the micro/nano scale on the specimen surface. Choose the grid fabrication method from the following: ultraviolet (UV) or heating nanoimprint lithography (NIL)26, electron beam lithography (EBL)2, and focused ion beam (FIB) milling6. 
	NOTE: The grid fabrication process is introduced here, with UV NIL as an example.
	<ol>
		<li>Drop 2 mL of UV resist on the specimen surface using a pipette.</li>
		<li>Coat the resist on the specimen surface using a spin coater at 1,500 rpm for 60 s.</li>
		<li>Press a nanoimprint mold to the resist layer at a pressure of 0.2 MPa. Expose the resist to UV with a wavelength of 375 nm for 30 s.</li>
		<li>Separate the nanoimprint mold from the specimen surface.</li>
	</ol>
	</li>
	<li>Observation of the Grid on the Specimen Using a Microscope
	<ol>
		<li>Coat a platinum or gold layer with a thickness of 3-10 nm on the grid surface using an ion coater (e.g., coating for 30 s at 3 Pa with a sputtering current of 30 mA).</li>
		<li>Put the specimen under a laser scanning microscope (LSM)23. 
		NOTE: Other microscopes can also be used, such as a transmission electron microscope (TEM)5, an atomic force microscope (AFM)12, or a scanning electron microscope (SEM)7.</li>
		<li>Adjust the focus and save one grid image using the microscope by clicking &#34;Capture&#34; and &#34;File | Export | Image File&#34; in the image recording software of the microscope.</li>
	</ol>
	</li>
	<li>Calculation of the Grid Pitch (nm or &#181;m) of the Specimen from the Grid Image
	<ol>
		<li>Calculate the average value of more than 10 grid pitches in the central area of the grid image to avoid the potential influence of the scanning or lens distortion. 
		NOTE: The grid on the specimen can be saved for several days at room temperature.</li>
	</ol>
	</li>
</ol>
2. Acquisition of Grid Images in the Loading Test
<ol>
	<li>Preparation of the Loading Test Under the Microscope
	<ol>
		<li>Fix the specimen to a loading device, such as a tensile, compressive, heating, or electrical loading device, under the microscope. 
		NOTE: If the grid pitch is less than 20 nm, a TEM or AFM should be used. If the grid pitch is 20 nm to 10 &#181;m, an SEM can be used. If the grid pitch is greater than 400 nm, an LSM can be used.</li>
		<li>Set the load speed (e.g.,0.01 mm/s) and the load or displacement incremental step (e.g., 0.5 N/step or 0.024 mm/step) according to the specific requirements. Preset both the load and displacement to zero.</li>
		<li>Make the grid surface in the observation plane. Choose an area of interest under a low magnification by moving or rotating the sample stage of the microscope.</li>
		<li>Select an appropriate magnification by making the grid pitch in the image greater than 1.8&#215; one pixel size. 
		NOTE: Usually, it is better to make the grid pitch in the image greater than 2 pixels. The more pixels one grid pitch corresponds, the higher the accuracy of the deformation measurement, but the smaller the field of view of the measurement.</li>
	</ol>
	</li>
	<li>Collection of Grid Images in the Loading Test
	<ol>
		<li>Save a grid image of the area of interest before loading by clicking &#34;Capture&#34; and &#34;File | Export | Image File&#34; in the image recording software of the microscope.</li>
		<li>Begin to load the specimen in situ onto the microscope by exerting the first load step (e.g., 0.5 N or 0.024 mm) using the operating software of the loading device.</li>
		<li>Record a grid image of the area of interest after the first load step (e.g., at 0.5 N or 0.024 mm) by clicking &#34;Capture&#34; and &#34;File | Export | Image File&#34; in the image recording software of the microscope. Ensure that the magnification and working distance of the microscope remain unchanged.</li>
		<li>Continue to load the specimen by exerting each load step using the loading device. Record the grid image after each load step until the specimen is broken or until a certain value is attained (e.g., load 19 times and record 19 grid images at 1 N, 1.5 N, 2.0 N, &#8230;, 10 N, at intervals of 0.5 N; or at 0.048 mm, 0.072 mm, 0.096 mm, &#8230;, 0.48 mm, at intervals of 0.024 mm). Make sure that the magnification and working distance of the microscope remains unchanged. 
		NOTE: The grid images can be saved for an arbitrarily long period of time.</li>
	</ol>
	</li>
</ol>
3. Generation of Sampling Moir&#233; Fringes before and after Deformation
<ol>
	<li>Estimation of Grid Pitches (pixel) in the Grid Images
	<ol>
		<li>Estimate the grid pitch (unit: pixel) in the grid image before loading by measuring the distance between the centers of two adjacent grid dots in an image processing software (e.g., Microsoft Paint).</li>
		<li>Estimate the grid pitch in the grid image at the maximum load.</li>
	</ol>
	</li>
	<li>Determination of Sampling Pitch (pixel)
	<ol>
		<li>Move to step 3.2.2 when the grid pitches before and after deformation are between 1.8 and 2.5 pixels. Skip to step 3.2.3 when the grid pitches before and after deformation are between 2.4 and 3.6 pixels. Skip to step 3.2.4 when the grid pitches before and after deformation are greater than 3.2 pixels.</li>
		<li>Set the sampling pitch to T = 2 pixels. Skip to step 3.3.</li>
		<li>Set the sampling pitch to T = 3 pixels. Skip to step 3.3.</li>
		<li>Set the sampling pitch T to a positive integer within 0.75x and 1.25x the grid pitches before and after deformation, determined from abundant simulation results22. 
		NOTE: If there are 2 positive integers that meet the requirements in steps 3.2.1 and 3.2.4, it is better to choose the greater integer as the sampling pitch. If there are 3 or more positive integers that meet the requirements, it is better to choose the middle integer, as long as it is a little bit greater than the sampling pitch.</li>
	</ol>
	</li>
	<li>Generation of Sampling Moir&#233; Fringes Before Deformation
	<ol>
		<li>Open the grid image before deformation. Assuming that the x direction is horizontally rightward, the y direction is vertically downward, and the coordinate (0, 0) is at the top-left corner, calculate the image width W in the x direction and the image height H in the y direction. 
		NOTE: The y direction can also be defined as vertically upward.</li>
		<li>Move to step 3.3.3 to generate moir&#233; fringes in the y direction. Skip to step 3.3.7 to generate moir&#233; fringes in the x direction.</li>
		<li>Process the grid image to a grating image using a low-pass filter (LPF). For example, use an FT algorithm to suppress the grating, with a principal direction of x, where the principal direction is defined as the direction perpendicular to the grating lines. Set the filter size to be close to the grid pitch.</li>
		<li>Thin out the grid image by only extracting the gray values in several horizontal lines, with the spacing of the sampling pitch T (T &#8805;2) from y = k pixels (k = 0) (Figure 1) (i.e., only keep the gray values in sampling lines of y = k pixels, y = k+T pixels, &#8230; , y = k + iT pixels, where i is a positive integer). Make the coordinate of the last sampling line, k + iT, less than the image height H.</li>
		<li>Generate a sampling moir&#233; pattern in the y direction by performing full-field intensity interpolation (linear or B-spline) of the image with horizontal sampling lines.</li>
		<li>Generate other T-1 sampling moir&#233; patterns in the y direction by repeating steps 3.3.4 and 3.3.5 T-1 times by changing k at the incremental step of 1 pixel (i.e., shifting the starting point of thinning out to y = k pixels; k = 1, &#8230;, T-1).</li>
		<li>Use the same procedures in steps 3.3.3-3.3.6 to generate T-step spatial phase-shifting sampling moir&#233; patterns in the x direction by changing x to y in step 3.3.3, changing the image height H to the image width W, and changing y to x in steps 3.3.4-3.3.6. 
		NOTE: The sampling pitch in the x direction can be different from that in the y direction.</li>
	</ol>
	</li>
	<li>Generation of Sampling Moir&#233; Fringes After Deformation
	<ol>
		<li>Open all grid images at different loads. Suppose the number of grid images is N.</li>
		<li>Generate N groups of T-step spatial phase-shifting moir&#233; fringes in the y direction by repeating steps 3.3.3-3.3.6 N times.</li>
		<li>Generate N groups of T-step spatial phase-shifting moir&#233; fringes in the x direction by repeating step 3.3.7 N times.</li>
	</ol>
	</li>
</ol>
4. Deformation Measurement of the Specimen in the Loading Test
<ol>
	<li>Determination of the Intensities of Moir&#233; Fringes Before and After Deformation
	<ol>
		<li>Extract the intensities of the T-step moir&#233; fringes before deformation in the y direction in steps 3.3.5 and 3.3.6; determine those moir&#233; intensities in the x direction in step 3.3.7. Describe the T-step (T &#8805;2) moir&#233; intensities before deformation in the j (j = x, y) direction using the following equation23: 
		<img alt="Equation 1" src="/files/ftp_upload/55739/image001.jpg" /> (1) 
		where pj is the grid pitch before deformation in the j (j = x, y) direction, A is the modulated amplitude, and D includes the background and the higher-frequency intensities.</li>
		<li>Extract the intensities of the T-step moir&#233; fringes after deformation in the y direction in step 3.4.2 and determine those moir&#233; intensities in the x direction in step 3.4.3. Describe the T-step (T &#8805; 2) moir&#233; intensities after deformation in the j (j = x, y) direction using the same equation as above (Equation 1) by changing Im,j(k), pj, A, and D to I&#39;m,j(k), p&#39;j, A&#39;, and D&#39;, respectively, where the superscript single quote means after deformation. 
		NOTE: If the sampling pitch is T &#8805; 3 pixels, ignore this step and skip to step 4.3.</li>
	</ol>
	</li>
	<li>&#160;
	<ol>
		<li>Reconstruct multiplication moir&#233; fringes from the multiplicative interference between the two-step sampling moir&#233; intensities (Figure 1a) before deformation using the following equation23 
		<img alt="Equation 2" src="/files/ftp_upload/55739/image002.jpg" /> (2) 
		where Imulti,j stands for the intensity of the reconstructed multiplication moir&#233; fringes in the j ( j = x, y) direction before deformation.</li>
		<li>Process the reconstructed multiplication moir&#233; fringes before deformation using the fringe centering technique24. Assign consecutive integers and half integers fj = [1, 1.5, 2, 2.5, &#8230;] to the fringe orders at the center lines of the reconstructed multiplication moir&#233;. 
		NOTE: If the multiplication moir&#233; fringes are too dense, the fringe orders of the two-step sampling moir&#233; can be determined first (i.e., fj(0) = [1, 0, 2, 0, 3, 0, &#8230;] and fj(1) = [0, 1.5, 0, 2.5, 0, 3.5, &#8230;]). The fringe order of the multiplication moir&#233; fringes will be fj = fj(0) + fj(1) = [1, 1.5, 2, 2.5, 3, 3.5, &#8230;]. The rigid-body displacement will not affect the strain result.</li>
		<li>Measure the relative strain of the specimen before deformation relative to the sampling pitch using the following equations23 
		<img alt="Equation 3" src="/files/ftp_upload/55739/image003.jpg" /> (3) 
		<img alt="Equation 4" src="/files/ftp_upload/55739/image004.jpg" /> (4) 
		where uj_rela and &#949;j_rela represent the relative displacement and the relative strain of the specimen before deformation in the j (j = x, y) direction, respectively, and &#947;xy_rela expresses the relative shear strain before deformation.</li>
		<li>Repeat steps 4.2.1-4.2.3 to determine the relative strains of the specimen after deformation in the x and y directions for N times, changing Imulti,j, Im,j(0), Im,j(1), pj, A, D, uj_rela (j = x, y), &#949;j_rela, and &#947;xy_rela in equations (2)-(4) to I&#39;multi,j, I&#39;m,j(0), I&#39;m,j(1), p&#39;j, A&#39;, D&#39;, u&#39;j_rela (j = x, y), &#949;&#39;j_rela, and &#947;&#39;xy_rela, respectively, where the superscript single quote means after deformation.</li>
		<li>Determine the actual normal strain &#949;j in the j (j = x, y) direction, which is the relative change of the grid pitch and the shear strain, &#947;xy, which is the absolute variation of the grid angle of the specimen caused by the load from the relative strains before and after deformation20. 
		<img alt="Equation 5" src="/files/ftp_upload/55739/image005.jpg" /> (5) 
		<img alt="Equation 6" src="/files/ftp_upload/55739/image006.jpg" /> (6)</li>
	</ol>
	</li>
	<li>Deformation Measurement When the Sampling Pitch is T &#8805; 3 pixels
	<ol>
		<li>Calculate the phase of the sampling moir&#233; fringes in the j (j = x, y) direction before deformation when k = 0 (Figure 1b) using the spatial phase-shifting technique21 
		<img alt="Equation 7" src="/files/ftp_upload/55739/image007.jpg" /> (7)</li>
		<li>Obtain the phase of the sampling moir&#233; fringes in the j (j = x, y) direction after deformation when k =0 by replacing &#966;m,j and Im,j(k) in equation (7) with &#966;&#39;m,j and I&#39;m,j(k), respectively, where the superscript single quote means after deformation. Repeat N times for N loads. 
		NOTE: If there is too much random noise in the phase distributions in steps 4.3.1 and 4.3.2, a sin/cos filter25 can be used to smooth the phases.</li>
		<li>Determine the phase difference of the sampling moir&#233; fringes in the j (j = x, y) direction before and after deformation (i.e.,&#916;&#966;m,j=&#966;&#39;m,j-&#966;m,j).</li>
		<li>Measure the distributions of displacement uj, normal strain &#949;j in the j (j = x, y) direction, and the shear strain &#947;xy of the specimen caused by the load. Use the following equations6,21 
		<img alt="Equation 8" src="/files/ftp_upload/55739/image008.jpg" /> (8) 
		<img alt="Equation 9" src="/files/ftp_upload/55739/image009.jpg" /> (9) 
		<img alt="Equation 10" src="/files/ftp_upload/55739/image010.jpg" /> (10) 
		NOTE: If there is too much noise in the strain distributions, an average smoothing filter can be used, with a filter size smaller than 2 grid pitches.</li>
	</ol>
	</li>
	<li>Result Storage
	<ol>
		<li>Save the data of the moir&#233; fringes, phases (when the sampling pitch is T &#8805;3 pixels), displacements, and strains in the forms of images, such as .tif or .bmp files, and text, such as .txt or .csv files.</li>
	</ol>
	</li>
</ol>

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Opt. 51 (16), 3214-3223 (2012).</li><li>Wang, Q., Ri, S., Tsuda, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Digital+sampling+Moir&#233;+as+a+substitute+for+microscope+scanning+Moir&#233;+for+high-sensitivity+and+full-field+deformation+measurement+at+micron/nano+scales.">Digital sampling Moir&#233; as a substitute for microscope scanning Moir&#233; for high-sensitivity and full-field deformation measurement at micron/nano scales.</a> Appl. Opt. 55 (25), 6858-6865 (2016).</li><li>Dai, F., Wang, Z. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Automatic+fringe+patterns+analysis+using+digital+processing+tehniques:+I+fringe+center+method.">Automatic fringe patterns analysis using digital processing tehniques: I fringe center method.</a> Acta Photonica Sinica. 28, 700-706 (1999).</li><li>Gutmann, B., Weber, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Phase-shifter+calibration+and+error+detection+in+phase-shifting+applications:+a+new+method.">Phase-shifter calibration and error detection in phase-shifting applications: a new method.</a> Appl. Opt. 37 (32), 7624-7631 (1998).</li><li>Wang, Q., Kishimoto, S., Tanaka, Y., Kagawa, Y. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Micro/submicro+grating+fabrication+on+metals+for+deformation+measurement+based+on+ultraviolet+nanoimprint+lithography.">Micro/submicro grating fabrication on metals for deformation measurement based on ultraviolet nanoimprint lithography.</a> Opt. Lasers Eng. 51 (7), 944-948 (2013).</li><li>Min-Jin, T., Hui-Min, X., Yan-Jie, L., Xiao-Jun, L., Dan, W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+new+grating+fabrication+technique+on+metal+films+using+UV-nanoimprint+lithography.">A new grating fabrication technique on metal films using UV-nanoimprint lithography.</a> Chin. Phys. Lett. 29 (9), 098101 (2012).</li></ol>

The authors have nothing to disclose.

In the described technique, one challenging step is the micro/nano-scale grid or grating (abbreviated as grid) fabrication26 if no periodic pattern exists on the specimen. The grid pitch should be uniform before deformation because it is an important parameter for the deformation measurement. If the material is a metal, a metal alloy, or a ceramic, UV or heating nanoimprint lithography (NIL)27, electron beam lithography (EBL)2, focused ion beam (FIB)...

Micro/nano-scale deformation measurements are vitally essential for evaluating the mechanical properties, instability behaviors, residual stresses, and crack occurrences of advanced materials. Since optical techniques are non-contact, full-field, and non-destructive, various optical methods have been developed for deformation measurement during the last few decades. In recent years, the micro/nano-scale deformation measurement techniques mainly include the moir&#233; methods1,2,3,4, geometric phase analysis (GPA)5,6, Fourier transformation (FT), digital image correlation (DIC), and electronic speckle pattern interferometry (ESPI). Among these techniques, GPA and FT are not well suited for complex deformation measurements because multiple frequencies exist. The DIC method is simple but powerless against noise because the deformation carrier is random speckle. Finally, ESPI is strongly sensitive to vibration.
Among micro/nano-scale moir&#233; methods, the most commonly used methods at present are the microscope scanning moir&#233; methods, such as electron scanning moir&#233;7,8,9, laser scanning moir&#233;10,11, and atomic force microscope (AFM) moir&#233;12, and some microscope-based moir&#233; methods, such as the digital/overlapping moir&#233;13,14,15 method and the multiplication/fractional moir&#233; method16,17. The scanning moir&#233; method has many advantages, such as a wide field of view, high resolution, and insensitivity to random noise. However, the traditional scanning moir&#233; method is inconvenient for 2D strain measurements because it is necessary to rotate the sample stage or the scanning direction by 90&#176; and to scan twice to generate moir&#233; fringes in two directions18. Rotation and the dual scanning processes introduce rotation error and take a long time, seriously influencing the measurement accuracy of the 2D strain, especially for the shear strain. Although the temporal phase-shifting technique19,20 can improve the deformation measurement accuracy, it requires time and a special phase-shift device unsuitable for dynamic tests.
The sampling moir&#233; method21,22 has a high accuracy in displacement measurements and is now mainly used for deflection measurements on bridges when automobiles pass. To extend the sampling moir&#233; method to micro/nano-scale 2D strain measurements, a reconstructed multiplication moir&#233; method has been newly developed23 from 2-pixel sampling moir&#233; fringes, in which the measurements are twice as sensitive and the wide field of view of the scanning moir&#233; method is kept. Moreover, the spatial phase-shifting sampling moir&#233; method is also developed from multi-pixel sampling moir&#233; fringes, allowing for high-accuracy strain measurements. This protocol will introduce the detailed strain measurement procedure and is expected to help researchers and engineers learn how to measure deformation, improving the manufacturing processes of materials and products.

<table><tbody><tr><td>Automatic Polishing Machine</td><td>Marumoto Struers K.K.</td><td>LaboPol-30, Labor Force-100</td><td></td></tr><tr><td>Carbon Fiber Reinforced Plastic</td><td>Mitsubishi Plastics, Inc.&amp;nbsp;</td><td>HYEJ16M95DHX1</td><td></td></tr><tr><td>Computer</td><td>DELL Japan</td><td>VOSTRO</td><td>Can be replaced with another computer with C++ programming language</td></tr><tr><td>Image Recording Software</td><td>Lasertec Corporation</td><td>LMEYE7</td><td>Installed in a laser scanning microscope</td></tr><tr><td>Ion Coater</td><td>Japan Electron Optics Laboratory Ltd.</td><td>JEC3000F</td><td></td></tr><tr><td>Laser Scanning Microscope</td><td>Lasertec Corporation</td><td>OPTELICS HYBRID</td><td></td></tr><tr><td>Nanoimprint Device</td><td>Japan Laser Corporation&amp;nbsp;</td><td>EUN-4200</td><td>Can be replaced with a electron beam lithography device or a focused ion beam milling device</td></tr><tr><td>Nanoimprint Mold</td><td>SCIVAX Corporation</td><td>3.0&amp;mu;m pitch</td><td>Customized</td></tr><tr><td>Nanoimprint Resist</td><td>Toyo Gosei Co., Ltd&amp;nbsp;</td><td>PAK01</td><td></td></tr><tr><td>Polishing Solution</td><td>Marumoto Struers K.K.</td><td>DP-Spray P 15&amp;mu;m, 1&amp;mu;m, 0.25&amp;mu;m</td><td>Use from coarse to fine</td></tr><tr><td>Pipet</td><td>AS ONE Corporation</td><td>10mL</td><td></td></tr><tr><td>Sand Paper</td><td>Marumoto Struers K.K.</td><td>SiC Foil #320, #800</td><td>Use from coarse to fine</td></tr><tr><td>Spin Coater</td><td>MIKASA Corporation</td><td>MS-A100</td><td></td></tr></tbody></table>

micro/nano-scale strain distribution measurement from sampling moir&#233; fringes

This work describes the measurement procedure and principles of a sampling moir&#233; technique for full-field micro/nano-scale deformation measurements. The developed technique can be performed in two ways: using the reconstructed multiplication moir&#233; method or the spatial phase-shifting sampling moir&#233; method. When the specimen grid pitch is around 2 pixels, 2-pixel sampling moir&#233; fringes are generated to reconstruct a multiplication moir&#233; pattern for a deformation measurement. Both the displacement and strain sensitivities are twice as high as in the traditional scanning moir&#233; method in the same wide field of view. When the specimen grid pitch is around or greater than 3 pixels, multi-pixel sampling moir&#233; fringes are generated, and a spatial phase-shifting technique is combined for a full-field deformation measurement. The strain measurement accuracy is significantly improved, and automatic batch measurement is easily achievable. Both methods can measure the two-dimensional (2D) strain distributions from a single-shot grid image without rotating the specimen or scanning lines, as in traditional moir&#233; techniques. As examples, the 2D displacement and strain distributions, including the shear strains of two carbon fiber-reinforced plastic specimens, were measured in three-point bending tests. The proposed technique is expected to play an important role in the non-destructive quantitative evaluations of mechanical properties, crack occurrences, and residual stresses of a variety of materials.

The 2D displacement and strain distributions of two carbon fiber-reinforced plastic (CFRP) specimens (#1 and #2) were measured according to the moir&#233; formation principle23 and the measurement process (Figure 1). The CFRP specimens were made up of 10-11 &#181;m-diameter K13D carbon fibers and epoxy resins. The deformation of CFRP #1 was determined using the reconstructed multiplication moir&#233; method from two-step sampling moir&...

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Micro/Nano-scale Strain Distribution Measurement from Sampling Moir&#233; Fringes

A sampling moir&#233; technique featuring 2-pixel and multi-pixel sampling methods for high-accuracy strain distribution measurements at the micro/nano-scale is presented here.

This work describes the measurement procedure and principles of a sampling moir&#233; technique for full-field micro/nano-scale deformation measurements. ...

micronano-scale-strain-distribution-measurement-from-sampling-moir

Research

JoVE Journal

Engineering

12.2K Views.  National Institute of Advanced Industrial Science and Technology (AIST). A sampling moiré technique featuring 2-pixel and multi-pixel sampling methods for high-accuracy strain distribution measurements at the micro/nano-scale is presented here.

Video: Micro/Nano-scale Strain Distribution Measurement from Sampling Moiré Fringes

Measuring Material Microstructure Under Flow Using 1-2 Plane Flow-Small Angle Neutron Scattering

A new small-angle neutron scattering (SANS) sample environment optimized for studying the microstructure of complex fluids under simple shear flow is presented. The SANS shear cell consists of a concentric cylinder Couette geometry that is sealed and rotating about a horizontal axis so that the vorticity direction of the flow field is aligned with the neutron beam enabling scattering from the 1-2 plane of shear (velocity-velocity gradient, respectively). This approach is an advance over previous shear cell sample environments as there is a strong coupling between the bulk rheology and microstructural features in the 1-2 plane of shear. Flow-instabilities, such as shear banding, can also be studied by spatially resolved measurements. This is accomplished in this sample environment by using a narrow aperture for the neutron beam and scanning along the velocity gradient direction. Time resolved experiments, such as flow start-ups and large amplitude oscillatory shear flow are also possible by synchronization of the shear motion and time-resolved detection of scattered neutrons. Representative results using the methods outlined here demonstrate the useful nature of spatial resolution for measuring the microstructure of a wormlike micelle solution that exhibits shear banding, a phenomenon that can only be investigated by resolving the structure along the velocity gradient direction. Finally, potential improvements to the current design are discussed along with suggestions for supplementary experiments as motivation for future experiments on a broad range of complex fluids in a variety of shear motions.

A shear cell is developed for small-angle neutron scattering measurements in the velocity-velocity gradient plane of shear and is used to characterize complex fluids. Spatially resolved measurements in the velocity gradient direction are possible for studying shear-banding materials. Applications include investigations of colloidal dispersions, polymer solutions, and self-assembled structures.

A new small-angle neutron scattering (SANS) sample environment optimized for studying the microstructure of complex fluids under simple shear flow is ...

Implementation of a Reference Interferometer for Nanodetection

A thermally and mechanically stabilized fiber interferometer suited for examining ultra-high quality factor microcavities is fashioned. After assessing its free spectral range (FSR), the module is put in parallel with a fiber taper-microcavity system and then calibrated through isolating and eliminating random shifts in the laser frequency (i.e. laser jitter noise). To realize the taper-microcavity junction and to maximize the optical power that is transferred to the resonator, a single-mode optical fiber waveguide is pulled. Solutions containing polystyrene nanobeads are then prepared and flown to the microcavity in order to demonstrate the system&#8217;s ability to sense binding to the surface of the microcavity. Data is post-processed via adaptive curve fitting, which allows for high-resolution measurements of the quality factor as well as the plotting of time-dependent parameters, such as resonant wavelength and split frequency shifts. By carefully inspecting steps in the time-domain response and shifting in the frequency-domain response, this instrument can quantify discrete binding events.

A reference interferometer technique, which is designed to remove undesirable laser jitter noise for nanodetection, is utilized for probing an ultra-high quality factor microcavity. Instructions for assembly, setup, and data acquisition are provided, alongside the measurement process for specifying the cavity quality factor.

A thermally and mechanically stabilized fiber interferometer suited for examining ultra-high quality factor microcavities is fashioned. After assessing ...

Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction

We report detailed procedures for performing compression experiments on rocks and mineral aggregates within a multi-anvil deformation apparatus (D-DIA) coupled with synchrotron X-radiation. A cube-shaped sample assembly is prepared and compressed, at room temperature, by a set of four X-ray transparent sintered diamond anvils and two tungsten carbide anvils, in the lateral and the vertical planes, respectively. All six anvils are housed within a 250-ton hydraulic press and driven inward simultaneously by two wedged guide blocks. A horizontal energy dispersive X-ray beam is projected through and diffracted by the sample assembly. The beam is commonly in the mode of either white or monochromatic X-ray. In the case of white X-ray, the diffracted X-rays are detected by a solid-state detector array that collects the resulting energy dispersive diffraction pattern. In the case of monochromatic X-ray, the diffracted pattern is recorded using a two-dimensional (2-D) detector, such as an imaging plate or a charge-coupled device (CCD) detector. The 2-D diffraction patterns are analyzed to derive lattice spacings. The elastic strains of the sample are derived from the atomic lattice spacing within grains. The stress is then calculated using the predetermined elastic modulus and the elastic strain. Furthermore, the stress distribution in two-dimensions allow for understanding how stress is distributed in different orientations. In addition, a scintillator in the X-ray path yields a visible light image of the sample environment, which allows for the precise measurement of sample length changes during the experiment, yielding a direct measurement of volume strain on the sample. This type of experiment can quantify the stress distribution within geomaterials, which can ultimately shed light on the mechanism responsible for compaction. Such knowledge has the potential to significantly improve our understanding of key processes in rock mechanics, geotechnical engineering, mineral physics, and material science applications where compactive processes are important.

We report detailed procedures for compression experiments on rocks and mineral aggregates within a multi-anvil deformation apparatus coupled with synchrotron X-radiation. Such experiments allow quantification of the stress distribution within samples, that ultimately sheds light on compaction processes in geomaterials.

We report detailed procedures for performing compression experiments on rocks and mineral aggregates within a multi-anvil deformation apparatus (D-DIA) ...

Environment

Observing and Quantifying Fibroblast-mediated Fibrin Gel Compaction

Cells embedded in collagen and fibrin gels attach and exert traction forces on the fibers of the gel. These forces can lead to local and global reorganization and realignment of the gel microstructure. This process proceeds in a complex manner that is dependent in part on the interplay between the location of the cells, the geometry of the gel, and the mechanical constraints on the gel. To better understand how these variables produce global fiber alignment patterns, we use time-lapse differential interference contrast (DIC) microscopy coupled with an environmentally controlled bioreactor to observe the compaction process between geometrically spaced explants (clusters of fibroblasts). The images are then analyzed with a custom image processing algorithm to obtain maps of the strain. The information obtained from this technique can be used to probe the mechanobiology of various cell-matrix interactions, which has important implications for understanding processes in wound healing, disease development, and tissue engineering applications.

Time-lapse microscopy and image processing techniques were used to observe and analyze fibroblast-mediated gel compaction and fibrin fiber realignment in an environmentally controlled bioreactor over a 48 hr&#160;period.

Cells embedded in collagen and fibrin gels attach and exert traction forces on the fibers of the gel. These forces can lead to local and global ...

Bioengineering

Synchrotron X-ray Microdiffraction and Fluorescence Imaging of Mineral and Rock Samples

In this report, we describe a detailed procedure for acquiring and processing&#160;x-ray microfluorescence (&#956;XRF), and Laue and powder microdiffraction two-dimensional (2D) maps at beamline 12.3.2 of the Advanced Light Source (ALS), Lawrence Berkeley National Laboratory. Measurements can be performed on any sample that is less than 10 cm x 10 cm x 5 cm, with a flat exposed surface. The experimental geometry is calibrated using standard materials (elemental standards for XRF, and crystalline samples such as Si, quartz, or Al2O3 for diffraction). Samples are aligned to the focal point of the x-ray microbeam, and raster scans are performed, where each pixel of a map corresponds to one measurement, e.g., one XRF spectrum or one diffraction pattern. The data are then processed using the in-house developed software XMAS, which outputs text files, where each row corresponds to a pixel position. Representative data from moissanite and an olive snail shell are presented to demonstrate data quality, collection, and analysis strategies.

We describe a beamline setup meant to carry out rapid two-dimensional x-ray fluorescence and x-ray microdiffraction mapping of single crystal or powder samples using either Laue (polychromatic radiation) or powder (monochromatic radiation) diffraction. The resulting maps give information about strain, orientation, phase distribution, and plastic deformation.

In this report, we describe a detailed procedure for acquiring and processing&#160;x-ray microfluorescence (&#956;XRF), and Laue and powder ...

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method

A novel measurement approach is used to reveal the cumulative deformation field at a sub-grain level and to study the influence of microstructure on the growth of microstructurally small fatigue cracks. The proposed strain field analysis methodology is based on the use of a unique pattering technique with a characteristic speckle size of approximately 10 &#181;m. The developed methodology is applied to study the small fatigue crack behavior in body centered cubic (bcc) Fe-Cr ferritic stainless steel with a relatively large grain size allowing a high spatial measurement accuracy at the sub-grain level. This methodology allows the measurement of small fatigue crack growth retardation events and associated intermittent shear strain localization zones ahead of the crack tip. In addition, this can be correlated with the grain orientation and size. Thus, the developed methodology can provide a deeper fundamental understanding of the small fatigue crack growth behavior, required for the development of robust theoretical models for the small fatigue crack&#160;propagation in polycrystalline materials.

Microstructurally small fatigue crack growth behavior is investigated using a novel methodological approach combining crack growth rate measurement and strain-field analysis to reveal the cumulative deformation field at sub-grain level.

A novel measurement approach is used to reveal the cumulative deformation field at a sub-grain level and to study the influence of microstructure on the ...

Spectral and Angle-Resolved Magneto-Optical Characterization of Photonic Nanostructures

Photonic crystals are periodic nanostructures that can support a variety of confined electromagnetic modes. Such confined modes are usually accompanied by local enhancement of electric field intensity that strengthens light-matter interactions, enabling applications such as surface-enhanced Raman scattering (SERS) and surface plasmon enhanced sensing. In the presence of magneto-optically active materials, the local field enhancement gives rise to anomalous magneto-optical activity. Typically, the confined modes of a given photonic crystal depend strongly on the wavelength and incidence angle of the incident electromagnetic radiation. Thus, spectral and angular-resolved measurements are needed to fully identify them as well as to establish their relationship with the magneto-optical activity of the crystal. In this article, we describe how to use a Fourier-plane (back focal plane) microscope to characterize magneto-optically active samples. As a model system, here we use a plasmonic grating built out of magneto-optically active Au/Co/Au multilayer. In the experiments, we apply a magnetic field on the grating in situ and measure its reciprocal space response, obtaining the magneto-optical response of the grating over a range of wavelengths and incident angles. This information enables us to build a complete map of the plasmonic band structure of the grating and the angle and wavelength dependent magneto-optical activity. These two images allow us to pinpoint the effect that the plasmon resonances have on the magneto-optical response of the grating. The relatively small magnitude of magneto-optical effects requires a careful treatment of the acquired optical signals. To this end, an image processing protocol for obtaining magneto-optical response from the acquired raw data is laid out.

Photonic band structure enables understanding how confined electromagnetic modes propagate within a photonic crystal. In photonic crystals that incorporate magnetic elements, such confined and resonant optical modes are accompanied by enhanced and modified magneto-optical activity. We describe a measurement procedure to extract the magneto-optical band structure by Fourier space microscopy.

Photonic crystals are periodic nanostructures that can support a variety of confined electromagnetic modes. Such confined modes are usually accompanied by ...

Production of a Strain-Measuring Device with an Improved 3D Printer

A traditional strain measurement sensor needs to be electrified and is susceptible to electromagnetic interference. In order to solve the fluctuations in the analog electrical signal in a traditional strain gauge operation, a new strain measurement method is presented here. It uses a photographic technique to display the strain change by amplifying the change of the pointer displacement of the mechanism. A visual polydimethylsiloxane (PDMS) lens with a focal length of 7.16 mm was added to a smartphone camera to generate a lens group acting as a microscope to capture images. It had an equivalent focal length of 5.74 mm. Acrylonitrile butadiene styrene (ABS) and nylon amplifiers were used to test the influence of different materials on the sensor performance. The production of the amplifiers and PDMS lens is based on improved 3D printing technology. The data obtained were compared with the results from finite element analysis (FEA) to verify their validity. The sensitivity of the ABS amplifier was 36.03 &plusmn; 1.34 &#181;&epsilon;/&#181;m, and the sensitivity of the nylon amplifier was 36.55 &plusmn; 0.53 &#181;&epsilon;/&#181;m.

This work presents a strain measurement sensor consisting of an amplification mechanism and a polydimethylsiloxane microscope manufactured using an improved 3D printer.

A traditional strain measurement sensor needs to be electrified and is susceptible to electromagnetic interference. In order to solve the fluctuations in ...

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Adsorption of surface-active molecules to fluid-fluid interfaces is ubiquitous in nature. Characterizing these interfaces requires measuring surfactant adsorption rates, evaluating equilibrium surface tensions as a function of bulk surfactant concentration, and relating how surface tension changes with changes in the interfacial area following equilibration. Simultaneous visualization of the interface using fluorescence imaging with a high-speed confocal microscope allows the direct evaluation of structure-function relationships. In the capillary pressure microtensiometer (CPM), a hemispherical air bubble is pinned at the end of the capillary in a 1 mL volume liquid reservoir. The capillary pressure across the bubble interface is controlled via a commercial microfluidic flow controller that allows for model-based pressure, bubble curvature, or bubble area control based on the Laplace equation. Compared to previous techniques such as the Langmuir trough and pendant drop, the measurement and control precision and response time are greatly enhanced; capillary pressure variations can be applied and controlled in milliseconds. The dynamic response of the bubble interface is visualized via a second optical lens as the bubble expands and contracts. The bubble contour is fit to a circular profile to determine the bubble curvature radius, R, as well as any deviations from circularity that would invalidate the results. The Laplace equation is used to determine the dynamic surface tension of the interface. Following equilibration, small pressure oscillations can be imposed by the computer-controlled microfluidic pump to oscillate the bubble radius (frequencies of 0.001-100 cycles/min) to determine the dilatational modulus The overall dimensions of the system are sufficiently small that the microtensiometer fits under the lens of a high-speed confocal microscope allowing fluorescently tagged chemical species to be quantitatively tracked with submicron lateral resolution.

This manuscript describes the design and operation of a microtensiometer/confocal microscope to do simultaneous measurements of interfacial tension and surface dilatational rheology while visualizing the interfacial morphology. This provides the real-time construction of structure-property relationships of interfaces important in technology and physiology.

Adsorption of surface-active molecules to fluid-fluid interfaces is ubiquitous in nature. Characterizing these interfaces requires measuring surfactant ...

Controlled Strain of 3D Hydrogels under Live Microscopy Imaging

External forces are an important factor in tissue formation, development, and maintenance. The effects of these forces are often studied using specialized in vitro stretching methods. Various available systems use 2D substrate-based stretchers, while the accessibility of 3D techniques to strain soft hydrogels, is more restricted. Here, we describe a method that allows external stretching of soft hydrogels from their circumference, using an elastic silicone strip as the sample carrier. The stretching system utilized in this protocol is constructed from 3D-printed parts and low-cost electronics, making it simple and easy to replicate in other labs. The experimental process begins with polymerizing thick (&#62;100 &#956;m) soft fibrin hydrogels (Elastic Modulus of ~100 Pa) in a cut-out at the center of a silicone strip. Silicone-gel constructs are then attached to the printed-stretching device and placed on the confocal microscope stage. Under live microscopy the stretching device is activated, and the gels are imaged at various stretch magnitudes. Image processing is then used to quantify the resulting gel deformations, demonstrating relatively homogenous strains and fiber alignment throughout the gel&#8217;s 3D thickness (Z-axis). Advantages of this method include the ability to strain extremely soft hydrogels in 3D while executing in situ microscopy, and the freedom to manipulate the geometry and size of the sample according to the user&#8217;s needs. Additionally, with proper adaptation, this method can be used to stretch other types of hydrogels (e.g., collagen, polyacrylamide or polyethylene glycol) and can allow for analysis of cells and tissue response to external forces under more biomimetic 3D conditions.

The presented method involves uniaxial stretching of 3D soft hydrogels embedded in silicone rubber while allowing live confocal microscopy. Characterization of the external and internal hydrogel strains as well as fiber alignment are demonstrated. The device and protocol developed can assess the response of cells to various strain regimes.

External forces are an important factor in tissue formation, development, and maintenance. The effects of these forces are often studied using specialized ...

Micro/Nano-scale Strain Distribution Measurement from Sampling Moiré Fringes

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