A moiré grating is a basic optical component used in various moiré methods for deformation measurement. In this study, nanoimprint lithography (NIL) was proposed to produce high frequency moiré gratings on metal samples. A new type of NIL mold and a hot embossing system were developed to overcome the poor flatness and roughness of metal samples. This three-layer mold based on nickel grating was unbreakable, and the self-developed hot embossing system used a bellows cylinder to satisfy the parallelism requirement of grating fabrication on metal samples. In order to generate high quality moiré patterns, the grating profile of the mold was optimized. Then, 1200-3000 lines/mm frequency gratings were successfully fabricated on the different materials such as SiO2, aluminum and stainless steel. In order to evaluate the quality of the replication, the distortion in the fabricated SiO2 grating was analyzed by an inverse moiré method. As an application, the replicated grating on the aluminum sample in combination with the moiré interferometry was used to measure the tensile deformation of the sample. The successful experimental results demonstrate the feasibility and reliability of nanoimprint lithography to produce gratings on metal samples.
© 2012 OSA
Moiré methods are important grating techniques that among others are capable to measure full field deformation in experimental mechanics. Since first introduced by Weller and Shepherd  in 1948, geometric moiré has been developed into a mature and effective optical testing method for in-plane and out-of-plane deformation measurement. Usually, the geometric moiré method can only be used for measuring large deformations because the frequency of the grating utilized in this method is lower than 100 lines/mm. In the past thirty years, new experimental techniques, grating-fabrication techniques and high resolution electron microscopes have been introduced into moiré method, and they have brought two significant advances. One important advance has been the moiré interferometry method developed by Post et al. [2,3], which is now well recognized as a very powerful and accurate technique for full field strain measurement. Another important development was represented by the scanning electron microscope (SEM) moiré method, which was first developed by Kishimoto et al.  in the 1990s. Unlike the traditional geometric moiré method, the electron beam scan is utilized as a virtual reference grating, instead of the actual reference grating to interfere with the specimen grating for generating moiré patterns. A grating up to a frequency of 10 000 lines/mm can be used in SEM moiré to measure the deformation in a micro-zone, which represents a very high sensitivity. The similar principle has been utilized to form a series of other high-resolution moiré patterns, such as laser scanning confocal microscope (LSCM) moiré , atomic force microscope (AFM) moiré . The frequency of the gratings used in moiré techniques is shown in Table 1 .
Gratings are a series of straight, parallel, and equispaced grooves. Orthogonal gratings are two-dimension pillar arrays along two perpendicular directions. As a basic optical component, it can be used in various optical technologies, such as traditional moiré method, moiré interferometry and various microscopic moiré methods, to measure the surface deformation on the object. In grating techniques, the measurement sensitivity increases with the grating frequency. To accurately analyze micro-nano scale deformation, the difficulty comes from the fabrication of high frequency specimen gratings.
As a conventional grating fabrication method developed in the early 1960s, holography lithography technique  is based on the interference of two coherent beams of light and the exposure of photoresist and can usually produce grating with a frequency at 600-2400 lines/mm. However, the complex arrangement of optical components has made it very difficult to put into practice, and restrained its wide applications.
In recent years, researchers have investigated a number of microfabrication technologies to fabricate gratings, such as electron beam writing  and focus ion beam writing . Although high-resolution alignment can be created, low throughput and high cost make it impractical for commercialization.
Furthermore, researchers also developed some convenient replication methods, in which liquid adhesives, such as epoxy  or silicone rubber , are used to transfer a grating film to the specimen. However, the grating quality of replication method depends on the skills and experiences of the operator, thus the quality of the replication is uncontrollable.
Nanoimprint lithography (NIL) or hot embossing lithography (HEL), initially proposed and developed by Chou’s group in 1995 , has emerged as one of the most promising technologies for nanoscale patterning. It can create micro/nano scale patterns in a resist material with rapid-processing and high-throughput, capable of sub-micron alignment over a large area. Nanoimprint lithography based on mechanical deformation of imprint resist can break through the resolution limit of conventional photolithography. Furthermore, the mold can be used repeatedly for at least one hundred imprints, thus the cost is very low and more feasible for mass production. In general, silicon stamp has been used in hot embossing lithography, however, it has a short lifetime due to its brittleness.
The gratings fabricated by nanoimprint lithography in this study are used to generate high quality moiré patterns for deformation measurement. Different from some micromachining technologies, the fabrication technique for moiré grating do not pursue excessively small linewidth of microstructure nor focus on the details of micro/nano scale patterns. Because too high grating frequency may lead to too dense moiré fringes in a certain field size and a grating frequency of thousands lines/mm (Table 1) will meet the measurement accuracy in common mechanical properties testing. Furthermore, metal samples (such as aluminum, copper, iron, and stainless steel et al) are widely used in mechanical testing. However, it is more difficult to fabricate high frequency gratings on metal samples than on silicon substrates due to their poor flatness and roughness. This work aims to develop a simple, easy to operate, low cost and high throughput grating fabrication technique on metal substrates to popularize the moiré method.
In this paper, in order to fabricate high frequency gratings on metal substrates, a new type of NIL mold and a hot embossing system were developed. This three-layer mold based on nickel stamp and 3M film was unbreakable and can provide uniform compression. The self-developed hot embossing system used a device of bellows cylinder for parallelism, and can satisfy the need of grating fabrication on metal samples. Then, in order to create high quality moiré patterns, the grating profile of the NIL mold was optimized through computer simulations. Through a number of experiments, the process parameters in HEL process were optimized and 1200-3000 lines/mm frequency gratings were successfully fabricated on SiO2, aluminum and stainless steel substrates. In order to check the quality of the fabricated grating, the distortion in the fabricated SiO2 grating was measured by inverse moiré method. As typical application of the replicated grating, the deformation of a tensile aluminum sample with grating was measured by moiré interferometry. The successful experimental results demonstrate the feasibility of the grating fabricated on metal samples by NIL for the moiré measurement.
2. Principle of NIL and experimental devices
2.1. Principle of grating fabrication using nanoimprint lithography
As illustrated in Fig. 1 , the grating fabrication with HEL process involves an imprint step with physical deformation of a thin film of a thermoplastic polymer cast on a substrate by using a rigid mold under pressure and elevated temperature above the glass transition temperature (Tg), followed by solidification and demolding after the polymer cooled to a temperature below Tg. After the patterns were transferred to the polymer, a thin metal layer with thickness less than 100 nm was deposited before it used as a moiré grating at normal temperature. As for gratings in high temperature circumstance, post-processing techniques such as reactive ion etching (RIE) and lift-off process should be adopted.
Grating fabrication technique using NIL is a simple nanolithography process with the advantages of low cost, high throughput and high resolution.
2.2. Self-developed hot embossing system
The self-developed hot embossing system (Fig. 2(a) , THU-NIL-01 type) is a desktop thermal NIL system. It consists of an imprint chamber, a control box, a vacuum pump and a compressor. This small-sized system possesses the advantages of low cost and good operation. It can fabricate sub-micrometer structures on 100 mm wafer.
Figure 2(b) illustrates the structure of the imprint chamber which includes a bellow cylinder (Festo EB-145-60), an upper pressure plate, a lower pressure plate, samples etc. The vacuum pump was connected to the external space of the bellow cylinder, and kept the inner space under low vacuum condition. While, the air compressor injected high pressure (1-7 bar) air into the internal space of the air bag (i.e. the bellow cylinder). Because of the difference of pressure inside and outside the air bag, the air bag expanded and rose, and then propelled the lower pressure plate close to the upper one. Finally, the samples were compressed by the two pressure plates with a maximum load of 7000 N. The pressure range to the samples is 0-10 MPa. The hot wire in the lower pressure plate can increase temperature quickly from the room temperature to 200°C.
Bellow cylinder was used to ensure stamp and substrate parallel to each other, and transfer the pressure to a large area substrate effectively and uniformly. This good parallel adjustment device of bellows cylinder can overcome the poor parallelism between top and bottom surfaces of mental samples. Therefore, the system can satisfy the need of manufacture of high-frequency gratings on metal samples.
2.3. New type of mold in NIL
The mold plays an important role in the nanoimprint technique. Silicon mold has been used widely in HEL, however, it is friable and has a short lifetime due to its brittleness.
One of the greatest challenges to fabricate gratings directly on the surface of metal substrate is its poor flatness and roughness, which has great influence on the quality of the imprinted gratings and is also harmful to the silicon mold due to the non-uniform pressure. In this work, a new type of mold is developed for nanoimprint on mental samples. As shown in Fig. 3 , the mold consists of three different layers: a 0.1 mm thick nickel grating prepared by electroforming (1200-3000 lines/mm), a buffer layer of a 0.13 mm thick 3M adhesive film and a 1 mm thick silicon baseplate.
The nickel grating is duplicated from silicon stamp or PMMA stamp using electroforming technique. In this study, the microstructures of silicon stamp, PMMA stamp and nickel grating are designed in Section 3 in order to generate high quality moiré patterns. The silicon stamp and the PMMA stamp can be fabricated by electron beam writing, holography lithography technique, or even nanoimprint lithography itself. The nickel grating offers some advantages for metal substrates: (1) unbreakable; (2) low thermal expansion coefficient which leads to small distortion; (3) would not adhere to many resists and make demolding easy. (4) 0.1 mm thick nickel stamp exhibits a certain flexibility which would be beneficial to metal surface with poor flatness.
The buffer layer in this study is 3M adhesive film (heat resistant temperature 250°C) which is widely used in compression molding. It can improve the contact condition between the mold and the metal substrate and provide uniform compression in the hot embossing process. Thus, the new type of mold is unbreakable and can improve the quality of the fabricated grating on metal substrates.
The resists used in this study are mr-I 75k PMMA (micro resist technology, Germany, no adhesion promoter necessary on silicon, SiO2 or aluminum substrates) and BP-212 positive resist (made in Beijing, China). The substrates contain SiO2, aluminum and stainless steel materials.
3. Optimization design of the profiles of grating mold
In this study, the grating fabricated by nanoimprint lithography is used in moiré method to generate high quality moiré patterns. It is well known that the quality of the moiré patterns directly affect the measurement accuracy and the moiré fringe profile is determined by the profiles of composite grids. Thus, it is important to optimize the profiles of the mold and the fabricated gratings, especially the profile of the mold in NIL.
Some optimization studies based on the theory of the moiré phenomenon have been given by some researchers [12,13]. In this study, some optimization results through computer simulations are presented visually to show the variations of the moiré quality with grating parameters.
Several factors of gratings were investigated, including the grating pitch, the opening ratio, and the form of grating.
3.1 The grating pitch
The pitch (or period) of a grating is in inverse ratio of the frequency of a grating. The measurement sensitivity increases with the grating frequency in moiré techniques. However, problems will also arise when the frequency is too high. In the moiré interferometry method, a high frequency grating of 600-2400 lines/mm is usually used. The wavelength of the laser λ and the frequency of the grating f satisfy Table 1) will meet the measurement accuracy in common mechanical properties testing in microscopic moiré methods.
3.2. The opening ratio
A grating is a series of straight, parallel, and equispaced grooves. If represented by a picture (256 gray levels), it is a collection of parallel black bars separated by white bars. One period of such a grating consists of one black bar and one adjacent white bar. The opening ratio (here is expressed as τ/T) is the ratio of width of the white bar to period.
Figure 4 shows three square-wave gratings with different opening ratios, where white means 255, black means 0. Figure 5 is parallel moiré patterns generated by gratings with different opening ratios. (τ/T)s and (τ/T)r are the opening ratios of specimen grating and reference grating, respectively. And pr = 1.1 ps, here, pr and ps respectively are the reference grating pitch and the specimen grating pitch. In order to correspond to the moiré images perceived by CCD, Gaussian blur is applied in computer simulations. Every moiré image in Fig. 5 has a profile section diagram (the horizontal axis shows luminance or gray value) in the right-hand.
It can be seen that when the opening ratios of both gratings are equal to 0.5, the intensity difference (the difference between the maximum and the minimum grey values, i.e. twice the amplitude of the periodic fringe pattern) of moiré fringes is the highest, as shown in Fig. 5(a). The moiré fringes with second highest intensity difference are observed when the opening ratios of one grating is equal to 0.5, as shown in Figs. 5(d) and 5(e). The intensity difference of the moiré fringes is the lowest when the opening ratios of neither grating are equal to 0.5, as shown in Fig. 5(b), Fig. 5(c) and Fig. 5(f). Thus, gratings with identical width of the black and white bars (i.e., the opening ratios is τ/T = 0.5; see Fig. 4(a)) are most preferred to generate high quality moiré patterns.
3.3. The form of grating
The forms of grating include sine-wave, square-wave, triangle-wave, and sawtooth-wave et al. Different forms of gratings will create moiré patterns of different qualities. Figures 6(a) -6(d) are the four different forms of gratings (original gratings: 1024×1024 pixels, 20 pixels per period, crops of the original images are presented to see the grating structures clearly) and Figs. 6(e)-6(h) are the profiles of corresponding gratings. Figures 6(i)-6(l) show the moiré patterns (parallel moiré, pr = 1.1 ps) generated by gratings with different forms. Seen from the intensity profiles of the moiré (Fig. 7 ), the intensity difference of the moiré generated by four forms gratings from high to low is: square > sine > triangle > sawtooth. Thus, a square grating would be the best choice. In the intensity distribution, the profiles of the moiré generated by square and sine gratings are approximately triangle-wave and sine-wave, respectively. Because many moiré theories are based on the sinusoidal distribution, sine grating would also be a good choice.
In consequence, two types of optimized gratings (Fig. 8 ) are chosen to be the mold structures in nanoimprint lithography: a sine-wave grating and a square-wave grating, both of them have identical width of the black and white bars.
Based on the results in Fig. 8, two nickel stamps were fabricated by electroforming technique. One is a sine-wave grating stamp (Fig. 9(a) , 1200 lines/mm, cross type, 50-150 nm depth) duplicated from PMMA stamp (fabricated by holography lithography technique), the other is a square-wave grating stamp (Fig. 9(b), 2000 or 3000 lines/mm, 330 nm depth) duplicated from silicon stamp (fabricated by electron beam writing). The AFM or SEM images of the two nickel molds are shown in Figs. 9(a′) and 9(b′). Both of the two nickel stamps will be in the form of three layer molds (Fig. 3) before using as NIL molds.
4. Experimental results on SiO2 substrate and distortion measurement
4.1. Experimental results on SiO2 substrate
In this process, an thickness of 600 nm PMMA (mr-I 75k, micro resist technology, Germany) were spin-coated onto the substrate of a SiO2 wafer (about 20 mm × 20 mm), and was heated to 180°C. A three-layer mold (Fig. 3) which contained a nickel grating of 2000 lines/mm (Fig. 9(b)) was placed on the face of the PMMA under a pressure of 2 MPa. The samples were cooled to 70°C after 5 minutes, and the load was then removed. The mold was immediately peeled from the substrate. Finally, the PMMA and the SiO2 substrate were etched by RIE with an etching ratio of 1:1 and the grating structure was transferred to the SiO2 substrate. The diffraction image of the SiO2 grating fabricated by NIL was shown in Fig. 10(a) . The color region reflected the high-frequency periodical structures on the surface of the SiO2 grating. The AFM image in Fig. 11(a) shows the 3D structures of the grating, and the groove depth of the SiO2 grating analyzed by AFM (Fig. 11(b)) is 96.3 nm.
4.2. Distortion measurement using inverse moiré method for NIL
To characterize high frequency grating structure and improve product quality, distortion caused in the hot embossing lithography should be measured .
The view field in AFM is so small that it is difficult to obtain the whole structural character of the grating in a large region. In this paper, inverse LSCM moiré method  is applied to identify the distortion in the hot embossing process. This method integrates the advantages of moiré method (such as high sensitivity and large field of view), with the advantages of LSCM (high-quality images, open-air environment for operation, et al).
In this experiment, a Leica TCS SP5 type LSCM (488 nm blue argon laser) was used. To generate parallel moiré patterns in LSCM, the direction of the scanning lines of the LSCM was finely adjusted to parallel to the SiO2 grating. Figures 10(b) and 10(c) show the parallel moiré pattern obtained with the scan size (denoted by L) of 513.74 μm and the scan line number (denoted by N) of 1024. Thus the pitch of the scanning lines (i.e. reference grating) pr = L/N = 501.7 nm. Based on the principle of inverse moiré method, the fringes contour interval is equal to one pitch of reference grating. The fringe number variation between the LSCM moiré fringes (Figs. 10(b) and 10(c)) of the SiO2 grating (area 1 in Fig. 10(a), i.e., the center region) and the mold is about a fringe. That means the displacement of the specimen in the view field (513.74 μm scan size) is about one pitch (pr).Table 2 .
As we can see from Table 2, the pitch in SiO2 grating fabricated by HEL is slightly larger than the pitch of the mold. The possible reason is the thermal mismatch between nickel mold and SiO2 substrates. The nickel mold in HEL has thermal expansion due to the high temperature, especially the difference between the room temperature (20°C) to the demolding temperature (70°C). And the flow of the PMMA may also have influence on the distortion of nano scale patterns. The distortions in three areas in SiO2 grating (Fig. 10(a)) are almost equal, and the maximum distortion is less than 0.1%. The distortion in SiO2 grating is small and even, and thus the fabricated grating is suitable for the moiré measurement.
5. Experimental procedure and results on metal substrate
5.1. Parameter optimization
The imprint conditions, such as temperature (T), pressure (p), and time (t), are all considered in developing the new lithography technique. The process parameters were optimized through a number of experiments.
In this experiment, 1200 lines/mm frequency nickel mold in Fig. 9(a) and mr-I 75k PMMA with 600 nm thickness were used. The aluminum substrates (25 mm square) were polished manually to Ra<0.8 μm and then coated with the PMMA film. The patterns of the mold were successfully duplicated to the PMMA at different embossing conditions (Table 3 ). Then the PMMA gratings on the surface of aluminum substrates were analyzed by AFM in Fig. 12 .
5.2. Experimental results on metal substrates
Using the optimized embossing condition in subsection 5.1, 1200 lines/mm grating patterns were successfully duplicated to the PMMA on the surface of an aluminum tensile sample, see Fig. 13 . And an aluminum film was deposited to enhance their reflectivity in moiré interferometry.
In order to confirm the feasibility and reliability of the grating fabricated by NIL, a tensile test of an aluminum sample was performed under a moiré interferometer. Figures 14(a) and (b) are the null-field moiré fringes (X and Y directions are horizontal and vertical directions, respectively) before loading. Since the null-field moiré image has only 1-2 fringes, the initial carrier strain is small, and thus the grating is suitable for the moiré measurement.
Figures 14(c) and 14(d) are U-field moiré fringes under load of 180 N and 300 N, respectively. A load step of 60 N was exerted up to 360 N. At each load step, strain was calculated using the moiré data, while the stresses were calculated by dividing the tensile load by area of the cross-section. The strain and stress values obtained by moiré interferometry were plotted and the linear fit of data points was shown in Fig. 15 (solid line). Another tensile test of the same material using strain gauge method was carried out. The linear fit of stress-strain values obtained by the strain gauge method was the dashed line in Fig. 15. The two elastic modulus of the same material obtained by the strain gauge method and moiré interferometry based on the grating fabricated by NIL were 70.1 GPa and 71.3 GPa, respectively. Thus, the relative error was 1.7% which means that results from the grating fabricated by NIL agree well with that of strain gauge. This loading experiment indicates that the PMMA grating fabricated on aluminum samples by NIL can record and measure the deformation of a loaded sample accurately.
Experiments on substrates of different materials and different frequencies of gratings were also carried out. Figure 16 presents a stainless steel sample for three-point bend test with 1200 lines/mm grating fabricated by NIL. And mr-I 75k PMMA was used, however, the adhesion property between this PMMA and the stainless steel was poor. Thus, an adhesion promoter should be applied on the surface of stainless steel substrate. Figure 17 gives a 3000 lines/mm resist film grating on the surface of an aluminum sample. A thickness of 300 nm BP-212 positive resist was spin-coated onto the aluminum substrate and grating patterns were duplicated to its surface by NIL. The SEM image in Fig. 17 shows grating lines which are straight, parallel, and equispaced.
In this study, nanoimprint lithography (NIL) is developed to produce high frequency gratings on metal samples which are widely used in mechanical testing. Specific findings are summarized as below:
- (1) 1200-3000 lines/mm gratings were successfully fabricated on SiO2, aluminum and stainless steel substrates by nanoimprint lithography. Thus, NIL can be applied to produce high frequency moiré grating with simple operation and high efficiency. This may help to popularize the moiré method.
- (2) The new three-layer mold and the self-developed hot embossing system can satisfy the need of grating fabrication on metal samples. The three-layer mold based on nickel grating and 3M film is unbreakable and can provide uniform compression. The hot embossing system uses a bellows cylinder for parallelism. These advantages can overcome the poor flatness and roughness of metal samples.
- (3) The grating profile of the NIL mold was optimized in order to form high quality moiré patterns. The simulations present the variations of the moiré quality with the opening ratios and the forms of gratings. The results show that a sine-wave or square-wave grating with identical width of the black and white bars is beneficial to moiré quality.
- (4) The distortion in the SiO2 grating fabricated by NIL was successfully measured by inverse LSCM moiré method in a large region of several hundreds of millimeters. The distortion in this SiO2 grating is almost uniform, the maximum distortion is less than 0.1%. Thus, the fabricated SiO2 grating is of high quality.
- (5) A tensile test of an aluminum sample with the grating fabricated by NIL was performed. The deformations of the aluminum sample under different tensile loads were measured by moiré interferometry. Compared with the result of strain gauge, the fabricated grating can realize deformation measurement accurately. The successful result demonstrates the feasibility and reliability of the grating fabricated on metal samples by NIL for the moiré measurement.
The authors are grateful to financial support by the National Basic Research Program of China (“973” Project) (Grant Nos. 2010CB631005, 2011CB606105), the National Natural Science Foundation of China (Grant Nos. 11172151, 90916010), and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20090002110048). The authors are grateful to the opening funds from the State Key Laboratory of Explosion Science and Technology (KFJJ10-18Y). The authors also thank NIL Technology APS for providing the stamp.
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