Bilateral filter based orientation smoothing of EBSD data

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/44682747 Bilateral filter based orientation smoothing of EBSD data Article in Ultramicroscopy · June 2010 DOI: 10.1016/j.ultramic.2010.06.003 · Source: PubMed CITATIONS READS 3 39 2 authors: Delphic Chen Jui-Chao Kuo 20 PUBLICATIONS 119 CITATIONS 83 PUBLICATIONS 438 CITATIONS National Cheng Kung University SEE PROFILE National Cheng Kung University SEE PROFILE All content following this page was uploaded by Jui-Chao Kuo on 24 June 2015. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. Ultramicroscopy 110 (2010) 1297–1305 Contents lists available at ScienceDirect Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic Bilateral filter based orientation smoothing of EBSD data Delphic Chen, Jui-Chao Kuo n Department of Materials Science and Engineering, National Cheng Kung University, 70101 Tainan, Taiwan a r t i c l e in fo abstract Article history: Received 31 October 2009 Received in revised form 24 May 2010 Accepted 1 June 2010 Bilateral filter based orientation smoothing was implemented in this study to improve the angular precision of orientation maps for deposited and deformed structures of pure Cu obtained from electron backscattered diffraction (EBSD) measurements. Applying the method to the deformed and deposited structures, the accuracy of misorientation (or the limit of orientation noise) is enhanced from 0.71 to 0.251 and 0.071, respectively. Orientation smoothing has two features: preservation of boundary structures or deformed substructures and significant reduction in orientation noise after only one pass. & 2010 Elsevier B.V. All rights reserved. Keywords: EBSD Orientation smoothing Bilateral filter Orientation noise 1. Introduction Electron backscatter diffraction (EBSD) is widely used for the quantitative characterization of crystallographic microstructures. Boundaries of low-angle misorientations that occur during deformation are known as incidental dislocation boundaries [1]. Such misorientations in the subgrains may be in the range of 1–51, which is near the detectable angular resolution of 21 [2]. The detection of subgrain boundaries with misorientation angles below 21 is then limited by the angular resolution. According to Humphreys et al. [2], the angular resolution is affected by a number of factors, such as the microscope operating conditions, the pixels in the CCD camera, the resolution of the digitized pattern, and the accuracy of the pattern solving algorithms [3]. In subgrain boundaries the Kikuchi pattern quality becomes worse with increase in strain because of both the overlapping patterns in the vicinity of the subgrains and the increased incoherent scattering associated with higher dislocation densities. Rapid data collection using low-resolution electron backscatter patterns (EBSPs) can also reduce the Kikuchi pattern quality. This results in inaccurate orientations, which is considered the local orientation deviation or orientation spread. As the EBSD data collection rate increases, the local orientation spread, known as the ‘‘orientation noise’’ [2,4], also increases and then the angular resolution decreases. Post-processing routines are important for reducing the orientation noise and improving the angular accuracy. These n Corresponding author. Tel.: + 886 6 2757575x31130; fax: + 886 6 2754194. E-mail address: jckuo@mail.ncku.edu.tw (J.-C. Kuo). 0304-3991/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2010.06.003 routines are aimed at reducing the average orientation noise and the number of artificial errors introduced by filtering. The Kuwahara-based orientation filter was introduced by Humphreys et al. [5] to reduce the average noise level. Godfrey [6] proposed a modified Kuwahara filter to improve the edge preservation near the triple junctions. Cho et al. [7] also introduced a new orientation averaging method. The bilateral filter introduced by Tomasi and Manduchi [8] can be used to smooth out image noise and to retain the edge detail of an original image. This filter is now applied in the field of image processing to recover details from noisy signals. The bilateral filter, similar to a Gaussian filter, smoothes the pixels in a digital image [9], but it does not smooth the pixels if the color components (i.e. RGB value) are not similar. An orientation smoothing method based on a bilateral filter is used to reduce orientation noise and to preserve boundary structures. Deposited and deformed (10% tensile strain) pure Cu structures are applied to examine the performance of the bilateral-based orientation smoothing method. The paper is organized as follows: the concept of the orientation bilateral filter is presented firstly in Section 2. Then the materials and the experimental procedure are presented in Section 3. After that the performance of the orientation bilateral filter is discussed in terms of the reduction of the orientation noise and of the preservation of the grain boundaries in Sections 4 and 5, respectively. Finally, three filtering methods are compared in Section 6. 2. Orientation bilateral filter A simple Kuwahara filter, which uses the average orientation, is used to remove the orientation noise in EBSD data. A conventional 1298 D. Chen, J.-C. Kuo / Ultramicroscopy 110 (2010) 1297–1305 average orientation is obtained from the arithmetic mean value of orientation data. Many possible methods have been proposed by Lassen et al. [10], Humbert et al. [11], Humphreys et al. [5], and Cho et al. [7] to determine the average orientation. Orientation smoothing using Kuwahara filter involves replacing the central point of interest in a square grid through the average orientation with a minimum misorientation [5]. We propose a new orientation filter called ‘‘orientation bilateral filter’’, which combines the average orientation [5] and the bilateral filter [8] to preserve microstructural features and to smooth orientation noise. The difference between the Kuwahara filter and the orientation bilateral filter is that the latter uses the weighted average of misorientations and the former uses the arithmetic mean of the misorientations without considering the influence of the distance from the point of interest. The bilateral filter extends the concept of Gaussian smoothing by weighing the filter coefficients (called a spatial weight function) with their corresponding relative pixel intensities (called an intensity weight function). The weighted average is computed based on both the spatial and intensity weight functions for the misorientation. The former and latter functions measure the geometric distance and the misorientation between the center point and the sampling point, respectively. In addition to misorientations, indexing parameters, such as the confidence index (CI), fit (or maximum angular deviation), and image quality (IQ) are possible candidates for application in the intensity weight function. The parameters of CI and fit depend on the orientation of grains. Thus, it is difficult to directly compare the value of these parameters for different orientations as there exist no direct linking between the microstructure and these parameters. The image quality maps display boundary structures and features, which look like a dislocation network. The average misorientation maps, in comparison with the image quality, can also show boundary structures expressed in misorientation spreads between each orientation in a grain and the average orientation. Therefore, the average misorientation was chosen in this study to be the intensity weight function. The smoothing process requires a quick computation of the misorientation achieved using quaternion. The equation for quaternion, which was first introduced by Hamilton [12,13], is as follows: Q ¼ cosðy=2Þ, r1 sinðy=2Þ, r2 sinðy=2Þ, r3 sinðy=2Þ Fig. 2. Effect of parameters sS and sR on the number of points with a misorientation between 0.51 and 21 (orientation noise) for electrodeposited copper. ð1Þ Fig. 1. Schematic illustration of the hexagonal sampling grids used for the bilateral filtering process of a hexagonal image structure. The solid, dotted, and dashed lines represent the hexagonal grids with 7, 19, and 37 sampling points, respectively. Fig. 3. Image quality map and (a) orientation maps for the cross-section of electrodeposited copper using inverse pole figure color coding with the reference direction in the normal direction (ND): (b) without a filtering process, (c) using a hexagonal sampling grid of 7 sampling points, (d) using a hexagonal sampling grid of 19 sampling points, (e) using a hexagonal sampling grid of 37 sampling points, and (f) the inverse pole figure color coding. The black lines indicate grain boundaries with misorientation angles between 0.51 and 62.81. D. Chen, J.-C. Kuo / Ultramicroscopy 110 (2010) 1297–1305 where r¼(r1,r2,r3) is the axis with a common numerical description for both the crystal and the reference axes, and y is the rotation angle of the axis that completes the orientation specification. The average orientation for the center point, based on the orientation bilateral filter, is computed by the weight function n1 P Q ðx0 ,y0 Þ ¼ Q ðxi ,yi Þ  wðxi ,yi Þ i¼0 n1 P where Q(xi,yi) and Q(x0,y0) are the quaternions at the sampling point (xi,yi) and the center point (x0,y0), respectively. The weight function Q(xi,yi) is given by wðxi ,yi Þ ¼ wS ðxi ,yi Þ  wR ðxi ,yi Þ 2 wðxi ,yi Þ i¼0 Fig. 4. Misorientation angle histogram of electrodeposited copper for raw data and bilateral filtered data using 7, 19, and 37 sampling points. (The value of 62.8 is referred to in [17].) ð3Þ The spatial weight function wS(xi,yi) and intensity weight function wR(xi,yi) are obtained by wS ðxi ,yi Þ ¼ e½ðxi x0 Þ ð2Þ 1299 þ ðyi y0 Þ2 =2s2S ð4Þ and 2 wR ðxi ,yi Þ ¼ eðDgi0 Þ =2s2R ð5Þ where sS is a parameter in the spatial domain, sR is a parameter in the intensity domain, and Dgi0 is the misorientation between the sampling point (xi,yi) and the center point (x0,y0). The smoothing process is performed on a hexagonal grid of measured orientations. A new orientation is replaced by the averaged orientation, over a set of values at each hexagonal grid point, according to Eq. (2). The size and shape of the entire sampling region can have significant effects on the smoothing process. The shape of the orientation bilateral filter is a hexagonal grid that contains 37 points, including the central point. These points correspond to the three nearest hexagonal neighborhoods (Fig. 1). Other grid sizes such as 7 (the nearest hexagon neighbors) and 19 (two nearest hexagon neighbors) are also discussed. The orientation bilateral filter varying the values of sS and sR is applied on an EBSD data set to find the optimal values for the spatial and intensity domain parameters sS and sR,. The points with misorientations 0.5–21 are considered as the orientation noise after the smoothing process. Fig. 2 shows the effect of the parameters sS and sR on the number of the orientation noise. The orientation noise for sS ¼ 2 and 4 is smaller than that for sS ¼1 when the value of sR is in the range 0.5–5. A minimum sR was observed at 2 when sS ¼2 and 4. Based on the Fig. 5. Distribution of point-to-point misorientation angle for electrodeposited copper: (a) raw data; (b) with 7 sampling points; (c) with 19 sampling points; and (d) 37 sampling points. The Lorentz and Gauss fitting curves are shown as solid and dashed lines, respectively. 1300 D. Chen, J.-C. Kuo / Ultramicroscopy 110 (2010) 1297–1305 observations, the parameters sS and sR are selected to be 2 and 2, respectively. Gaussian and Lorentz distribution functions are chosen to fit the curve in order to investigate the distribution of misorientations 0–1.01. The Gaussian distribution is given by the formula y ¼ y0 þ 2 A 2 pffiffiffiffiffiffiffiffi e2ðxxc Þ =w w p=2 ð6Þ where y0 is the offset, A the total area under the curve, xc the mean, and w/2 the standard deviation, which is approximately 0.425 the full-width at half-maximum (FWHM). The Lorentz distribution is given as y ¼ y0 þ 2A w ð7Þ p 4ðxxc Þ2 þ w2 where y0 is the offset, A the total area under the curve, xc the mean, and w is FWHM. Fig. 6. Maximum deviation after filter passes for electrodeposited copper. 3. Materials and experimental procedure Cu film was synthesized through a pulsed electrodeposition technique from an additive-free acidic Cu electrolyte 0.5 M CuSO4. The pH value was adjusted to 1 by adding sulfuric acid. Mechanical agitation was applied to ensure the refreshment of the electrolytic solution and to prevent organic contamination. All depositions were conducted at 20 1C under a current density of 0.5 A/cm2. The pulsed current chain was composed of time-on 0.2 s and time-off 2.0 s. A pure Cu sample for the tensile test was prepared by an electric discharge machine into the specimen dimensions. A specimen was ground, polished with a 1 mm diamond paste, and electropolished in a phosphoric-based electrolyte at 20 1C under 1.5 V for 60 s. This sample was deformed by 10% through microtensile testing (Kammrath and Weiss GmbH). The deposited and deformed Cu samples were mechanically polished through a standard metallographic procedure to a final level of 0.03 mm. This was followed by electropolishing at a voltage of 1.5 V for 60 s in a phosphoric acid electrolyte. EBSD measurements were carried out using an EDAX/TSL Technology EBSD system, including a Digiview IV Detector, mounted on a field-emission scanning electron microscope (FESEM, JEOL JSM7001F). All EBSD data collection and analysis were performed using TSLs OIM Data Collection and Analysis software 5.2. The electron beam was operated at 30 kV with step sizes of 50 and 25 nm for the deposited and 10% strained Cu samples, respectively. To achieve a low orientation noise—that is, a high-quality EBSD orientation map—the exposure time for the CCD camera was set to 0.03 s for the deposited Cu and 0.05 s for the deformed Cu. The binning size for the CCD camera was set to 4  4 and 2  2 pixels, for the deposited and deformed Cu, respectively. Table 1 Fitting parameters of the average misorientation xc and the full-width at halfmaximum FWHM using Gauss and Lorentz functions for raw data and orientation bilateral filtering with 7, 19 and 37 points in the case of deposit copper. Sampling size Raw data 7 points 19 points 37 points Gauss function Lorentz function xc FWHM xc FWHM 0.32,329 0.12,388 0.07,722 0.06,069 0.43,848 0.19,318 0.12,813 0.11,281 0.31,985 0.11,737 0.07,312 0.05,857 0.5005 0.18,023 0.11,464 0.09,729 Fig. 7. (a) Image quality map of pure copper after 10% tensile strain. Orientation maps for the pure copper after 10% tensile strain using inverse pole figure color coding with the reference direction in the normal direction (ND): (b) without the filtering process, (c) using a hexagonal sampling grid of 7 sampling points, (d) using a hexagonal sampling grid of 19 sampling points, (e) using a hexagonal sampling grid of 37 sampling points, and (f) the inverse pole figure color coding. The black lines indicate grain boundaries with misorientation angles between 0.51 and 62.81. 1301 D. Chen, J.-C. Kuo / Ultramicroscopy 110 (2010) 1297–1305 4. Orientation smoothing 4.1. Deposited structure Fig. 3a shows the image quality map of a deposited structure of Cu obtained using a scanning step size of 50 nm. The inverse pole figure maps with highlighted boundaries obtained from the raw ESBD data are shown in Fig. 3b. The black represents boundaries with misorientations 0.5–62.81, which are comprised of the orientation noise of 0.5–51, low-angle grain boundaries (LAGBs) of misorientations 5–151, and high-angle grain boundaries (HAGBs) of misorientations 15–62.81 [17]. The ratio of 62,926 points, with misorientations 0.5–51, to the total measured number of 92,220 points was 68.3% (Fig. 4). Three sampling hexagonal grids containing 7, 19, and 37 points were chosen to filter the raw EBSD data during orientation smoothing (Fig. 1). The number of the orientation noise was significantly reduced from 62,926 to 10,835, 4806, and 3,660 (corresponding reductions from 68.3% to 11.7%, 5.2%, and 3.9%) for the points 7, 19, and 37, respectively (Figs. 3c and 4). As the number of sampling points increases, the number of the orientation noise decreases. The number of LAGBs and HAGBs remains unchanged after filtering (Fig. 4). The angular resolution is considered as a lower limit of misorientation between points recognized above the noise threshold. According to Humphreys et al. [2], the EBSD angular resolution, which depends on the EBSD detector, cell size, and beam conditions, approaches 11. The misorientation distribution of the raw data is displayed from 01 to 1.01 in Fig. 5a. Lorentz function gives a better fit for the range of 0.6–1.01 compared with Table 2 Fitting parameters of the average misorientation xc and the full-width at halfmaximum FWHM using Gauss and Lorentz functions for raw data and orientation bilateral filtering with 7, 19, and 37 points in the case of deformed copper. Sampling points Fig. 8. Misorientation angle histogram of pure copper after 10% tensile strain for raw data and after bilateral filtering using 7, 19, and 37 sampling points. (The value of 62.8 is referred to in [17].) Raw data 7 19 37 Gauss function Lorentz function xc FWHM xc FWHM 0.32,046 0.15,468 0.11,792 0.11,172 0.37,553 0.25,067 0.21,449 0.20,623 0.31,572 0.14,701 0.11,166 0.10,596 0.40,830 0.24,110 0.20,010 0.19,115 Fig. 9. Distribution of point-to-point misorientation angle for pure copper after 10% tensile strain: (a) raw data, (b) with 7 sampling points, (c) with 19 sampling points, and (d) with 37 sampling points. The Lorentz and Gauss fitting curves are shown as solid and dashed lines, respectively. 1302 D. Chen, J.-C. Kuo / Ultramicroscopy 110 (2010) 1297–1305 Fig. 10. Maximum deviation after filter passes for deformed copper. the Gauss function (Fig. 5a). However, both functions fail to fit the raw data in the range of 0–0.251. The computed Gaussian function fitting indicates an average misorientation of 0.3231 with an FWHM of 0.4381, while a mean misorientation of 0.3201 with an FWHM of 0.5011 is obtained using the Lorentz function (in Table 1). The value of the angular resolution here is derived by adding the mean value and two standard deviations (2s), which is approximated by 0.849  FWHM. Therefore, an angular resolution of 0.71 is achieved in the EBSD raw data without filtering. The effects of the sampling size (the number of the sampling points) and the filter pass number on the reduction of the orientation noise using the orientation bilateral filter are investigated. The limits of the orientation noise are 0.291, 0.191, and 0.161 (reducing them by factors of 2.4, 3.7, and 4.4) after one pass using 7, 19, and 37 points, respectively. The reduction factors were 4.8, 8.2, and 9.8, corresponding to the orientation noise values of 0.15, 0.08, and 0.07 after five passes using 7, 19, and 37 points, respectively (Fig. 6). The decrease in the orientation noise is not significant when the number of the sampling points is greater than 19. If the pass number is 45, the angular resolution Fig. 11. ODF sections with the constant j2 using the Bunge angular notation for electrodeposited copper: (a) without the filtering process; (b) using a hexagonal sampling grid of 7 sampling points; (c) using a hexagonal sampling grid of 19 sampling points; and (d) using a hexagonal sampling grid of 37 sampling points. The intensity scale is given in (f). D. Chen, J.-C. Kuo / Ultramicroscopy 110 (2010) 1297–1305 approaches to the limit value of 0.071, which is recognized as the angular resolution with filtering. The angular resolution after filtering is clearly improved from an initial value of 0.71 to 0.071. 4.2. Deformed substructure The image quality map taken a step size of 25 nm and having 65,008 total measured points shows the 10% tensile strained structure of pure Cu (Fig. 7a). The subgrain structure is clearly seen in the image quality map. The corresponding map using color coding in terms of an inverse pole figure is overlaid with reconstructed boundaries (Fig. 7b). The black represents boundaries with misorientations 0.5–62.81, which include the orientation noise (0.5–51), LAGBs (5–151), and HAGBs (15–62.81). Fig. 7c–e illustrates that applying this technique to the ESBD orientation data significantly reduces the amount of the orientation noise. The fraction of the orientation noise is significantly decreased to 28.7% of the total measured points after one pass using 37 points (Fig. 8). 1303 An average misorientation of 0.3201 with an FWHM of 0.3761 is determined using the Gaussian function for the raw data, while a mean misorientation of 0.3161 with an FWHM of 0.4081 is obtained using the Lorentz function (Fig. 9 and Table 2). An angular resolution of 0.71 is determined for the deformed Cu structure without filtering, based on the definition in Section 4.1. The angular resolution without filtering is 0.71 for the cases of deposited and deformed structures. A limit value of 0.71 is then considered as the angular resolution for FESEM in this study. The orientation noise limit is decreased to 0.281, 0.291, and 0.281 after orientation smoothing using 7, 19, and 37 points with one pass, respectively (Fig. 10). With five passes, the values of the orientation noise using 7, 19, and 37 points are 0.291, 0.261, and 0.251, respectively. The decrease in the orientation noise is not significant when the number of the points is greater than 19. If the pass number is 42, the angular resolution approaches to a limit value of 0.251 after filtering. The noise limit of 0.251, determined for the deformed structure in Fig. 10, is smaller than that of 0.071 for the deposited structure in Fig. 6. This observation suggests that increase in the orientation noise from 0.071 to 0.251 Fig. 12. ODF sections with a constant j2 using the Bunge angular notation for pure copper after 10% tensile strain: (a) without the filtering process; (b) using a hexagonal sampling grid of 7 sampling points; (c) using a hexagonal sampling grid of 19 sampling points; and (d) using a hexagonal sampling grid of 37 sampling points. 1304 D. Chen, J.-C. Kuo / Ultramicroscopy 110 (2010) 1297–1305 is due to the formation of subgrain structures with LAGBs during deformation. 5. Preservation of boundary structure 5.1. Deposited structure The preservation of boundary structures is now presented here after discussing the decrease in the orientation noise. The orientation distribution function (ODF) sections demonstrate the preservation of boundary structures, including LAGBs and HAGBs. These ODF sections reveal a similar orientation distribution as that obtained from the raw EBSD data after smoothing with 7, 19, and 37 points (Fig. 11). However, the maximum intensity in the ODF sections increases as the number of the points increases from 7 to 37. This observation of increase in orientation intensity results from the reduction in the orientation noise and preservation of the initial orientation (Fig. 4). The frequency of LAGBs and HAGBs after orientation smoothing is compared with the raw data in Fig. 4. The number of LAGBs and HAGBs remains unchanged after smoothing, as in the case of the raw data after smoothing. Therefore, orientation smoothing leads to a drastic reduction in the orientation noise. 5.2. Deformed substructure The 10% tensile strained structure after orientation smoothing is illustrated in Fig. 7. These ODF sections, using 7, 19, and 37 points, reveal a similar orientation distribution as the initial ODF sections in the EBSD raw data, as shown in Fig. 12. However, the maximum intensity in the ODF section increases as the number of sampling points increases from 7 to 37, showing the same trend as that of the deposited structure. The deformed structure consists of LAGBs, HAGBs, and the orientation noise (Fig. 8). The frequencies of LAGBs and HAGBs remain unchanged, similar to the raw data after smoothing. Deformed structures typically contain cells or subgrains with misorientations 0.5–31 [14–16]. The boundaries with misorientations 0.5–5.01 made up a large fraction (28%) of the deformed structure after orientation smoothing. This is larger than 4% observed for the deposited structure. Subgrain boundaries with misorientations between 0.51 and 5.01 are formed during deformation. 6. Comparison of Kuwahara filtering, orientation bilateral filtering, and cleanup processing The performances of the orientation bilateral and the Kuwahara filters are compared in terms of their orientation noise reduction and the boundary preservation of deposited and deformed structures. A symmetrical square grid of 5  5 pixels was adopted for the Kuwahara filtering and the minimum misorientation was selected as 21. A hexagonal grid containing 19 sampling points was chosen for the orientation bilateral filter, and other parameters were maintained similar to those seen in Section 2. As well, the built-in cleanup function of the TSL OIM Analysiss 5.1 for a single orientation per grain was also used as a reference. This process is called the cleanup process. The minimum misorientation angle for the cleanup process was also set to 21. The TSL OIM analysis software was used to analyze all EBSD data after Kuwahara and orientation bilateral filtering. The boundaries are classified into four groups, based on the following misorientations: 0.5–2.01 (purple), 2.0–5.01 (red), 5.0–15.01 (black), and 15.0–62.81 (green). The image quality maps Fig. 13. Image quality maps for the deposited copper: (a) without the filtering process; (b) using ‘‘single orientation per grain’’ cleanup method; (c) using Kuwahara filter; (d) using orientation bilateral filter of 19 sampling points. The purple, red, black, and green lines indicate grain boundaries with misorientation angles between 0.51 and 21, 21 and 51, 51 and 151, and 151 and 62.81, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 3 Number of boundary misorientations of 0.5–21, 2–51, 5–151, and 15–62.81 for raw data, cleanup processing, Kuwahara filtering, and orientation bilateral filtering, respectively, in the case of deposited copper. Filtering method 0.5–2o 2–5o 5–15o 15–62.8o Raw Cleanup Kuwahara Bilateral 65,529 14,438 33,105 8717 633 7765 534 436 371 372 370 372 25,902 25,903 25,902 25,904 Table 4 Number of boundary misorientations of 0.5–21, 2–51, 5–151, and 15–62.81 for raw data, cleanup processing, Kuwahara filtering, and orientation bilateral filtering, respectively, in the case of deformed copper. Filtering method 0.5–21 2–51 5–151 15–62.81 Raw Cleanup Kuwahara Bilateral 50,053 12,903 36,255 16,878 4307 8580 3953 4095 2291 7721 2450 2467 1942 1936 614 602 with boundaries are shown in Fig. 13 for the deposited Cu structure. Boundaries with misorientations 0.5–21 contain 65,529 points corresponding to 68.8% of the total measured points in the raw data (Table 3). The number of the points with misorientations 0.5–2.01 is reduced to 33,105 (35.9%), 8717 (9.4%), and 14,438 (15.7%), respectively, after one pass using Kuwahara filtering, orientation bilateral filtering, and cleanup processing (as shown in Table 3). The number of boundaries with misorientations 2.0–5.01 increases after cleanup processing (Table 4). The number of D. Chen, J.-C. Kuo / Ultramicroscopy 110 (2010) 1297–1305 1305 deposited and deformed structures. This orientation smoothing provides a simple and rapid alternative to reducing the orientation noise and preserving boundary structures after a single pass. The angular resolution of the measured EBSD data without filtering is 0.71, which is determined from the limit of the orientation noise for deposited and deformed Cu structures. The angular resolution is improved from the initial value of 0.71 to 0.071 and 0.251 after the application of the filter to deposited and deformed structures of pure Cu, respectively. Acknowledgements The authors would like to thank the National Science Council of the Republic of China under Contract no. NSC 98-2221-E-006 081 -MY2, and the Center for Micro/Nano Science and Technology for providing facilities. References Fig. 14. Image quality maps for the pure copper after 10% tensile strain: (a) without the filtering process; (b) using ‘‘single orientation per grain’’ cleanup method; (c) using Kuwahara filter; (d) using orientation bilateral filter of 19 sampling points. The purple, red, black, and green lines indicate grain boundaries with misorientation angles between 0.51 and 21, 21 and 51, 51 and 151, and 151 and 62.81, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) boundaries at 2.0–5.01, 5.0–15.01, and 15.0–62.81 remains almost the same for both Kuwahara and orientation bilateral filtering. Fig. 14 shows image quality maps with boundaries for the 10% strained pure Cu. The fraction of points with misorientations 0.5–2.01 is 77.0% (50,053 points) in the case of the raw data. This is larger than 68.8% of the deposited Cu. This could be due to the formation of subgrain boundaries during straining. The number of the points with misorientations 0.5–2.01 is reduced to 36,255 (55.7%), 16,878 (25.9%), and 12,903 (20%), respectively, after applying Kuwahara filtering, orientation bilateral filtering, and cleanup processing. 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