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) milling6, or the grid duplicate method26 can be used. If the material contains a weak polymer, EBL and FIB milling are not suggested. When a component of the material is not heat-resisting, heating NIL cannot be used. If the specimen is a thin film, the grid duplicate method is difficult to apply because it is not easy to separate the specimen.
The critical step for the strain measurement of the grid image before and after deformation using the proposed technique is the generation of sampling moir&#233; fringes22, the principle of which is different from the formation principle of conventional interference moir&#233; fringes. To generate distinct sampling moir&#233; fringes, a low-pass filter, such as an FT algorithm, is suggested to suppress unwanted lines or dots. If the sampling moir&#233; fringes are indistinct after down-sampling (i.e., thinning out the grid image) and linear-intensity interpolation, a smoothing filter, such as an average filter, can be adopted before down-sampling. A second- or even third-order B-spline interpolation algorithm can be used for the intensity interpolation to generate distinct sampling moir&#233; fringes.
Compared with the traditional moir&#233; methods, the proposed sampling moir&#233; technique for strain distribution measurement has the advantage of being a simple 2D strain measurement and having simple processing, high speed, high deformation sensitivity, and high measurement accuracy23. The 2D strain measurement can be easily performed without rotating the sample stage or the scanning lines of the microscope, which is necessary in conventional methods. In addition, dynamic deformation can be measured, as the required information is only a single-shot grid image at each load. This cannot be done with the temporal phase-shifting moir&#233; method because several grid or moir&#233; images are needed, along with time at each load.
Although the described technique allows for easy 2D strain measurements at the micro/nano scales, it has its own limitations23, as does any other technique. The grid pitch in a recorded image should be greater than 1.8 pixels to generate 2-pixel or multi-pixel sampling moir&#233; fringes. If the grid pitch in the image is around 2 pixels, the 2-pixel sampling moir&#233; fringes can serve as the substitute for the microscope scanning moir&#233; fringes, with the same field of view at the same magnification. However, if the grid pitch in an image is around 1 pixel at the highest scanning resolution of the microscope when distinct scanning moir&#233; fringes are directly observable, sampling moir&#233; fringes will be unable to form at the same magnification. Although sampling moir&#233; fringes can be generated when increasing the microscope magnification, the field of view for the deformation measurement will decrease. Fortunately, the scanning resolutions of commercial microscopes are improving, and sampling moir&#233; fringes can be generated in most cases. The higher the scanning resolution, the bigger the pixel number of one grid pitch, and the higher the strain measurement accuracy.
As opposed to the reconstructed multiplication moir&#233; method from 2-pixel sampling moir&#233; fringes, the spatial phase-shifting sampling moir&#233; method from multi-pixel sampling moir&#233; fringes has a higher processing speed and a higher measurement accuracy but a smaller field of view. The choice of method depends on the pixel number of the specimen grid pitch, or on the required measurement accuracy and field of view if the pixel number of the specimen grid pitch is controllable. Both methods are useful for taking nondestructive deformation measurements and making quantitative evaluations of mechanical properties, crack occurrence and growth, residual stresses, defect detection, structural characterization, etc.

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&#233; fringes, and that of CFRP #2 was measured using the spatial phase-shifting sampling moir&#233; method from three-step sampling moir&#233; fringes.
A) Deformation Measurement of CFRP #1
The thickness, length, and width of CFRP #1 were 1 mm, 22 mm, and 4 mm, respectively (Figure 2a). The length direction of all fibers was perpendicular to the 1 &#215; 22 mm2 surface, which was polished using sand papers and polishing solutions. A grid with a pitch of 3.0 &#181;m was fabricated on the polished surface using UV nanoimprint lithography (Figure 2b). A strain gauge was pasted on the bottom 4 &#215; 22 mm2 surface to monitor the greatest tensile strain.
A three-point bending test was carried out on CFRP #1 using a loading jig, with a support span of 16 mm, under a laser scanning microscope. The span-to-depth ratio was 16 according to the American Society for Testing and Materials (ASTM) standards. The grid images when the strain-gauge values were 0 and 0.00533 (Figure 2b) were recorded. The magnification of the objective lens of the microscope was 5&#215;, and the scanning resolution was 1,024 x 1,024. The x direction is horizontally rightward and the y direction is vertically upward.
Since the grid pitches on CFRP #1 in both the x and y directions were around 2 pixels in the recorded image, the down-sampling pitches in the two directions were set to be T = 2 pixels for the deformation measurement. To avoid the potential influence of scanning distortion, a central area with size of 1.26 x 0.53 mm2 was chosen as the area of interest. From 2-pixel down-sampling and equation (2), 2-step sampling moir&#233; patterns and the reconstructed multiplication moir&#233; pattern were generated after deformation (Figure 2c). Using equations (3) and (4), the deformation relative to the sampling pitch when the strain gauge value was 0.00533 was calculated. Similarly, the relative deformation when the strain gauge value was 0 was also obtained. Finally, the actual deformation distributions, including the 2D displacements (Figure 2d), the 2D normal strains, and the shear strain (Figure 2e), were measured using equations (5) and (6).
From the displacement distributions (Figure 2d), the x-direction displacement is positive at the upper-left and lower-right corners, but negative at the other two corners. The y-direction displacement is negative in the whole area and at a minimum in the central area. This agrees well with the deformation features of a bending specimen. From the strain distributions (Figure 2e), the upper area bears compressive strain in the x direction but tensile strain in the y direction, and the lower area bears tensile strain in the x direction but compressive strain in the y direction, demonstrating an interesting deformation characteristic. The shear strain is negative in the left area and positive in the right area, conforming to the bending property.
B) Deformation Measurement of CFRP #2
The thickness, length, and width of the laminated CFRP #2 were 1 mm, 30 mm and 5 mm, respectively (Figure 3a). There were 8 layers, and the thickness of each layer was 0.13 mm. The length direction of all fibers was perpendicular to the 1 x 30 mm2 surface, which was polished using sand papers and polishing solutions. A grid with pitch of 3.7 &#181;m was then fabricated on the polished surface using UV nanoimprint lithography (Figure 3b).
A three-point bending test was carried out using a loading jig, with support span of 16 mm, under a laser scanning microscope. The span-to-depth ratio was also 16. The grid image at the 0.2 N preload was first recorded. When the load was 10.8 N and the deflection was -200 &#181;m, the deformed grid image was also recorded (Figure 3b). The magnification of the objective lens of the microscope was 5x, the imaging zoom was 120%, and the scanning resolution was 1,024 x 1,024 pixels. The x direction is horizontally rightward and the y direction is vertically upward.
Since the grid pitches on CFRP #2 in both the x and y directions were around 3 pixels in the recorded image, the down-sampling pitches in the two directions were set to be T = 3 pixels for the deformation measurement. To avoid the potential influence of the scanning distortion, a central area with a size of 1.15 x 0.49 mm2 was chosen as the area of interest. Using the method described in step 4.3, the moir&#233; phase distributions at 0.2 N and 10.8 N in both the x and y directions were obtained (Figure 3c). The distributions of the 2D in-plane displacements (Figure 3d), the 2D normal strains, and the shear strain (Figure 3e) were determined.
The displacement distribution (Figure 3d) features of CFRP #2 are similar to those of CFRP #1 (Figure 2d), except that the y-direction displacement is slightly different. The features of the x-direction strain and the shear strain of CFRP #2 (Figure 3e) are also similar to those of CFRP #1 (Figure 2e), agreeing with the deformation features of a bending specimen. However, the y-direction strain of CFRP #2 (Figure 3e) is different than that of CFRP #1 because CFRP #2 is a laminated specimen. Several layers can be observed from the distribution of the y-direction strain, which is almost negative in the whole area.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/55739/55739fig1.jpg" /> 
Figure 1: Sampling moir&#233; formation principle and measurement process. (a) Generation principle of reconstructed moir&#233; from 2-pixel sampling moir&#233; fringes when the sampling pitch is T = 2 pixels. (b) Formation principle of multi-step phase-shifting sampling moir&#233; fringes and the measurement process for the moir&#233; phase when the sampling pitch is T &#8805;3 pixels. <a href="https://cloudflare-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/55739/55739fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/55739/55739fig2.jpg" /> 
Figure 2: Deformation measurement results of CFRP #1. (a) Experimental setup of the three-point bending test under a laser microscope and the specimen diagram. (b) The observed surface of CFRP #1 with a micro grid. (c) Two-step sampling moir&#233; patterns and the reconstructed multiplication moir&#233; pattern when the strain gauge value was 0.00533. (d) The measured displacement distributions in the x and y directions. (e) The measured distributions of the x direction, y direction, and shear strains of CFRP #1. <a href="https://cloudflare-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/55739/55739fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/55739/55739fig3.jpg" /> 
Figure 3: Deformation measurement results of laminated CFRP #2. (a) Diagram of the three-point bending test under a laser microscope. (b) The observed surface of CFRP #2 with a micro grid. (c) The wrapped phase (range: -&#960;~&#960;) distributions of the sampling moir&#233; fringes at the 0.2 N preload and 10.8 N load in the x and y directions. (d) The measured displacement distributions in the x and y directions, where the deflection (-200 &#181;m) in the y direction was not displayed. (e) The measured distributions of the x direction, y direction, and shear strains of CFRP #2. <a href="https://cloudflare-jove-com.remotexs.ntu.edu.sg/files/ftp_upload/55739/55739fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

Watch this Scientific Journal Video about Micro/Nano-scale Strain Distribution Measurement from Sampling MoirÃ© Fringes at JoVE.com

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

Nanyang Technological University

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

Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

Slow light has been one of the hot topics in the photonics community in the past decade, generating great interest both from a fundamental point of view and for its considerable potential for practical applications. Slow light photonic crystal waveguides, in particular, have played a major part and have been successfully employed for delaying optical signals1-4 and the enhancement of both linear5-7 and nonlinear devices.8-11
Photonic crystal cavities achieve similar effects to that of slow light waveguides, but over a reduced band-width. These cavities offer high Q-factor/volume ratio, for the realization of optically12 and electrically13 pumped ultra-low threshold lasers and the enhancement of nonlinear effects.14-16 Furthermore, passive filters17 and modulators18-19 have been demonstrated, exhibiting ultra-narrow line-width, high free-spectral range and record values of low energy consumption.
To attain these exciting results, a robust repeatable fabrication protocol must be developed. In this paper we take an in-depth look at our fabrication protocol which employs electron-beam lithography for the definition of photonic crystal patterns and uses wet and dry etching techniques. Our optimised fabrication recipe results in photonic crystals that do not suffer from vertical asymmetry and exhibit very good edge-wall roughness. We discuss the results of varying the etching parameters and the detrimental effects that they can have on a device, leading to a diagnostic route that can be taken to identify and eliminate similar issues.
The key to evaluating slow light waveguides is the passive characterization of transmission and group index spectra. Various methods have been reported, most notably resolving the Fabry-Perot fringes of the transmission spectrum20-21 and interferometric techniques.22-25 Here, we describe a direct, broadband measurement technique combining spectral interferometry with Fourier transform analysis.26 Our method stands out for its simplicity and power, as we can characterise a bare photonic crystal with access waveguides, without need for on-chip interference components, and the setup only consists of a Mach-Zehnder interferometer, with no need for moving parts and delay scans.
When characterising photonic crystal cavities, techniques involving internal sources21 or external waveguides directly coupled to the cavity27 impact on the performance of the cavity itself, thereby distorting the measurement. Here, we describe a novel and non-intrusive technique that makes use of a cross-polarised probe beam and is known as resonant scattering (RS), where the probe is coupled out-of plane into the cavity through an objective. The technique was first demonstrated by McCutcheon et al.28 and further developed by Galli et al.29

Use of photonic crystal slow light waveguides and cavities has been widely adopted by the photonics community in many differing applications. Therefore fabrication and characterization of these devices are of great interest. This paper outlines our fabrication technique and two optical characterization methods, namely: interferometric (waveguides) and resonant scattering (cavities).

Slow light has been one of the hot topics in the photonics community in the past decade, generating great interest both from a fundamental point of view ...

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 ...

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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 ...

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

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Last year, not only saturation, but also reverse saturation of scattering in an isolated plasmonic particle was demonstrated for the first time. The results showed that saturable scattering exhibits clear wavelength dependence, which seems to be directly linked to the localized surface plasmon resonance (LSPR). Combined with the intensity-dependent measurements, the results suggest the possibility of a common mechanism underlying the nonlinear behaviors of scattering and absorption. These nonlinearities of scattering from a single gold nanosphere (GNS) are widely applicable, including in super-resolution microscopy and optical switches. 
In this paper, it is described in detail how to measure nonlinearity of scattering in a single GNP and how to employ the super-resolution technique to enhance the optical imaging resolution based on saturable scattering. This discovery features the first super-resolution microscopy based on nonlinear scattering, which is a novel non-bleaching contrast method that can achieve a resolution as low as l/8 and will potentially be useful in biomedicine and material studies.

Saturable and reverse saturable scattering were discovered in isolated plasmonic particles and adopted as a novel non-bleaching contrast method in super-resolution microscopy. Here the experimental procedures of detecting and extracting nonlinear scattering are explained in detail, as well as how to enhance resolution with the aid of saturated excitation microscopy.

Plasmonics, which are based on the collective oscillation of electrons due to light excitation, involve strongly enhanced local electric fields and thus ...

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Stimuli-sensitive poly(N-isopropylacrylamide) (PNIPAM) microgels have various prospective practical applications and uses in fundamental research. In this work, we use single particle tracking of fluorescently labeled PNIPAM microgels as a showcase for tuning microgel size by a rapid non-stirred precipitation polymerization procedure. This approach is well suited for prototyping new reaction compositions and conditions or for applications that do not require large amounts of product. Microgel synthesis, particle size and structure determination by dynamic and static light scattering are detailed in the protocol. It is shown that the addition of functional comonomers can have a large influence on the particle nucleation and structure. Single particle tracking by wide-field fluorescence microscopy allows for an investigation of the diffusion of labeled tracer microgels in a concentrated matrix of non-labeled microgels, a system not easily investigated by other methods such as dynamic light scattering.

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels

Non-stirred precipitation polymerization provides a rapid, reproducible prototyping approach to the synthesis of stimuli-sensitive poly(N-isopropylacrylamide) microgels of narrow size distribution. In this protocol synthesis, light scattering characterization and single particle fluorescence tracking of these microgels in a wide-field microscopy setup are demonstrated.

Stimuli-sensitive poly(N-isopropylacrylamide) (PNIPAM) microgels have various prospective practical applications and uses in fundamental research. In this ...

Chemistry

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy

A protocol for measuring polydispersity of concentrated polymer solutions using dynamic light scattering is described. Dynamic light scattering is a technique used to measure the size distribution of polymer solutions or colloidal particles. Although this technique is widely used for the assessment of polymer solutions, it is difficult to measure the particle size in concentrated solutions due to the multiple scattering effect or strong light absorption. Therefore, the concentrated solutions should be diluted before measurement. Implementation of the confocal optical component in a dynamic light scattering microscope1 helps to overcome this barrier. Using such a microscopic system, both transparent and turbid systems can be analyzed under the same experimental setup without a dilution. As a representative example, a size distribution measurement of a temperature-responsive polymer solution was performed. The sizes of the polymer chains in an aqueous solution were several tens of nanometers at a temperature below the lower critical solution temperature (LCST). In contrast, the sizes increased to more than 1.0 &#181;m when above the LCST. This result is consistent with the observation that the solution turned turbid above the LCST.

A protocol for the direct measurement of particle size distribution in concentrated solutions using dynamic light scattering microscopy is presented.

A protocol for measuring polydispersity of concentrated polymer solutions using dynamic light scattering is described. Dynamic light scattering is a ...

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit manipulation, and integrated single-photon detectors. Here, we present the key aspects of preparing and testing a silicon photonic quantum chip with an integrated photon source and two-photon interferometer. The most important aspect of an integrated quantum circuit is minimizing loss so that all of the generated photons are detected with the highest possible fidelity. Here, we describe how to perform low-loss edge coupling by using an ultra-high numerical aperture fiber to closely match the mode of the silicon waveguides. By using an optimized fusion splicing recipe, the UHNA fiber is seamlessly interfaced with a standard single-mode fiber. This low-loss coupling allows the measurement of high-fidelity photon production in an integrated silicon ring resonator and the subsequent two-photon interference of the produced photons in a closely integrated Mach-Zehnder interferometer. This paper describes the essential procedures for the preparation and characterization of high-performance and scalable silicon quantum photonic circuits.

Silicon photonic chips have the potential to realize complex integrated quantum systems. Presented here is a method for preparing and testing a silicon photonic chip for quantum measurements.

Silicon photonic chips have the potential to realize complex integrated quantum information processing circuits, including photon sources, qubit ...

Construction and Operation of a Light-driven Gold Nanorod Rotary Motor System

The possibility to generate and measure rotation and torque at the nanoscale is of fundamental interest to the study and application of biological and artificial nanomotors and may provide new routes towards single cell analysis, studies of non-equilibrium thermodynamics, and mechanical actuation of nanoscale systems. A facile way to drive rotation is to use focused circularly polarized laser light in optical tweezers. Using this approach, metallic nanoparticles can be operated as highly efficient scattering-driven rotary motors spinning at unprecedented rotation frequencies in water.
In this protocol, we outline the construction and operation of circularly-polarized optical tweezers for nanoparticle rotation and describe the instrumentation needed for recording the Brownian dynamics and Rayleigh scattering of the trapped particle. The rotational motion and the scattering spectra provides independent information on the properties of the nanoparticle and its immediate environment. The experimental platform has proven useful as a nanoscopic gauge of viscosity and local temperature, for tracking morphological changes of nanorods and molecular coatings, and as a transducer and probe of photothermal and thermodynamic processes.

Plasmonic gold nanorods can be trapped in liquids and rotated at kHz frequencies using circularly-polarized optical tweezers. Introducing tools for Brownian dynamics analysis and light scatteringspectroscopy leads to a powerful system for research and application in numerous fields of science.

The possibility to generate and measure rotation and torque at the nanoscale is of fundamental interest to the study and application of biological and ...

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 ...

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

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