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[Resolution Improvement of DPC Microscopy_R1_ preprint.pdf](https://mdr.nims.go.jp/filesets/be65dbc9-f11b-46f7-9805-12bb6b215a61/download)

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[Kazutaka Mitsuishi](https://orcid.org/0000-0002-9361-4057), Fumiaki Ichihashi, Yoshio Takahashi, [Katsuaki Nakazawa](https://orcid.org/0000-0002-6056-5615), [Masaki Takeguchi](https://orcid.org/0000-0002-0282-6020), [Ayako Hashimoto](https://orcid.org/0000-0002-1985-7667), Toshiaki Tanigaki

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[Resolution improvement of differential phase-contrast microscopy via tilt-series acquisition for environmental cell application](https://mdr.nims.go.jp/datasets/ba4806b0-53da-4d95-b0b4-fb9e7831d047)

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1 Resolution Improvement of Differential Phase-Contrast Microscopy via Tilt-Series 1 Acquisition for Environmental Cell Application 2 Kazutaka Mitsuishi1*, Fumiaki Ichihashi2, Yoshio Takahashi2, Katsuaki Nakazawa1, Masaki 3 Takeguchi1, Ayako Hashimoto1, and Toshiaki Tanigaki2 4  5 1National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki, 305-0047, Japan, 6 2Research and Development Group, Hitachi, Ltd., 2520 Akanuma, Hatoyama, Saitama, 350-7 0395, Japan 8  9 *Correspondence should be addressed to 10 Kazutaka Mitsuishi, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki, 11 305-0047, Japan  12 Phone: +81-29-863-5474 13 E-mail: MITSUISHI.Kazutaka@nims.go.jp  14 Running title: Resolution Improvement of DPC Microscopy 15 Keywords: differential phase contrast, environmental cell, in situ transmission electron 16 microscopy 17 Total Number of Pages: 19 18 Number of Figures: 5  19 2 Abstract 20 A simple method that improves the resolution of the phase measurement of differential phase-21 contrast (DPC) scanning transmission electron microscopy for closed-type environmental cell 22 applications was developed and tested using a model sample simulating environmental cell 23 observations. Because the top and bottom membranes of an environmental cell are typically 24 far apart, the images from these membranes are shifted widely by tilt-series acquisition, and 25 averaging the images after alignment can effectively eliminate undesired signals from the 26 membranes while improving the signal from the object of interest. It was demonstrated that a 27 phase precision of 2π/100 rad is well achievable using the proposed method for the sample in 28 an environmental cell. 29  30 Abbreviations 31 DPC: differential phase-contrast  32 3 Introduction 33 With growing environmental problems, the demand for improving the properties of functional 34 materials is rapidly increasing. For example, catalytic nanoparticles are used for various 35 purposes, such as CO oxidation, NOx gas purification, selective oxidation, selective 36 hydrogenation, and photocatalytic reactions [1], and improving their performance is strongly 37 desired. Electron microscopy is an ideal method for analyzing these systems, and charge-state 38 characterization correlated with catalytic activity has recently been realized using electron 39 holography [2, 3], showing that the charge amount of nanoparticle catalysis is related to 40 lattice distortion. To further understand the mechanism, it is important to observe these 41 materials under actual operating conditions, such as liquid or gas atmospheres. In such in situ 42 observations, closed-type environmental holders that employ electron transparent membranes 43 to confine liquids or gases are widely used [4-8], but high-resolution observation is generally 44 difficult because the contrasts from these membranes are superimposed on the obtained 45 image. For example, Hyllested and Beleggia studied phase measurements using electron 46 holography in gas environmental cell holders and reported a phase resolution of 47 approximately 0.35 rad, stating that the degradation of phase resolution caused by the 48 membrane is more significant than the type and pressure of gas in the environmental cell. [9] 49 Differential phase-contrast (DPC) scanning transmission electron microscopy (STEM) [10, 50 11] measures electronic and/or magnetic fields by measuring the deflection of the transmitted 51 4 disk. It has been applied to a wide range of materials [12, 13], and in contrast to electron 52 holography, it does not require a reference vacuum area, which is necessary to create an 53 interference pattern with the electron waves that pass through the sample. This is particularly 54 beneficial for the observation of environmental cells in which a reference area is extremely 55 difficult—if not impossible—to obtain. 56 Herein, we propose a simple method that increases the phase measurement precision for an 57 object in a closed-type in situ observation holder by averaging tilt-series DPC center of mass 58 (CoM) images. Tilt-series DPC is a well-established technique that was developed to suppress 59 diffraction contrast [14, 15] and extract electric [13] or magnetic [16] information. We used it 60 to discriminate the information of the membranes at different heights from the region of 61 interest. 62 The achievable phase measurement precision [17] is expressed as 63 𝜑𝜑𝜎𝜎 = 𝑅𝑅𝜎𝜎𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑2𝜋𝜋𝜆𝜆,                                    (1) 64 where 𝑅𝑅 represents the spatial resolution, 𝜎𝜎𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 represents the standard deviation of the 65 CoM that corresponds to the precision of the detectable deflection angle, and 𝜆𝜆 represents 66 the wavelength of incident electrons. The relationship between the electron dose and field 67 resolution [18] is expressed as  68 𝜎𝜎𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝜃𝜃𝑘𝑘0 �12�𝑁𝑁𝑒𝑒12�𝑁𝑁𝑒𝑒�,                                  (2) 69 5 where 𝜃𝜃 represents the convergence semi-angle of the probe, 𝑘𝑘0 represents the 70 wavenumber, and 𝑁𝑁𝑒𝑒 represents the number of electrons in the diffraction pattern. This is a 71 surprisingly simple function implying that the field resolution is solely dependent on the 72 electron dose and convergence angle and is not dependent on the camera length. This relation 73 was derived under the assumption of statical noise, providing the theoretical lower limit of the 74 achievable phase resolution. In the case of the observation using a cell with membranes, the 75 phase noise due to the membrane is superimposed, and those cannot be eliminated even with 76 infinite dose. The objective of this research is to eliminate those with tilt series acquisition. In 77 reality, however, because DPC is a scanning technique, the position of the transmitted disk is 78 also affected by the parallelism of the beam during the scan and how accurately the detector is 79 electro-optically placed in the diffraction plane. Since, the previous studies only confirmed it 80 through numerical simulation [18], we first experimentally verified the precision of the phase 81 measurement (Eq. (2)) by measuring the standard deviation of the CoM as a function of the 82 electron dose. The achievable phase precision was evaluated by assuming a spatial resolution 83 𝑅𝑅 with the value expected from the convergence angle. Next, tilt-series acquisitions were 84 applied to a model sample in which PtPd nanoparticles were deposited on a Si pillar placed 85 between a pair of SiN membranes. Here, the field resolution was evaluated using the tilt-86 averaged standard deviation of the CoM of the membrane-only region, and the spatial 87 resolution was evaluated using the Young’s fringe technique with a pair of partially averaged 88 6 images [19]. 89  90 Experimental 91 An aberration-corrected microscope (JEOL JEM-ARM200F) equipped with a high-speed 92 pixelated STEM detector (JEOL 4DCanvas) was used at 200 kV for DPC measurement. 93 Convergence semi-angles of 4 mrad and 22.5 μrad were used, which corresponded to the 94 objective lens ON and OFF conditions, respectively, for measuring the relationship between 95 dose and phase resolution. To maximize the angular resolution, each diffraction pattern was 96 obtained with a maximum of 264 × 264 pixels, and the CoM at each scan point was calculated 97 from these patterns. The camera lengths were adjusted such that the size of the transmitted 98 disk (Ronchigram) was approximately 70% of the detector’s field of view. Prior to data 99 acquisition, the deflector balance for the parallel-beam scan and intermediate lens focus was 100 carefully adjusted such that the Ronchigram did not move along with the scan. For the 101 evaluation of the relationship between electron dose and standard deviations, the experiments 102 were conducted in a vacuum region without any sample. For the model sample measurement, 103 only the 4-mrad convergence semi-angle was used, because the structure was too small for a 104 smaller convergence angle. The 4-mrad convergence semi-angle was selected considering the 105 balance between the spatial and phase resolutions, along with the size of the model structure. 106 The model structure, which imitated environmental cells, was fabricated on a selectively 107 7 etched Si window-supported SiN (50 nm thick) film as a lower membrane. A Si pillar was 108 placed over it, fabricated using a focused ion beam (FIB), and the upper membrane was 109 placed on top of the Si pillar, sliced from another area of the grid by the FIB. A schematic and 110 transmission electron microscopy (TEM) images are shown in Figs. 1(a) and (b), respectively. 111 To separate the films homogeneously around the pillar, a square wall was created via C 112 deposition before placing the upper membrane. The distance between the films and the height 113 of the edge of the Si pillar were measured via TEM by using the Fourier transform of 114 amorphous membrane contrast (diffractogram), and the inter-membrane and pillar–membrane 115 distances were 2.6 and 1.3 μm, respectively. The Si pillar was coated with PtPd nanoparticles 116 that imitated catalytic particles, and these particles were used as markers for tilt-series image 117 alignment. 118 [Insert Figure 1 here] 119 Tilt-series acquisitions were performed using originally developed acquisition software, 120 which controls the microscope deflectors and aperture positions. It controls the aperture 121 positions to pre-specified positions to tilt the incident direction and moves the transmitted 122 beam to the detector position by controlling the deflector after the sample. Six sets of data 123 were acquired consisting of 10 tilt directions with 1.6-mrad steps with the pillar placed 124 between the membranes as the pivot point. A 264 × 264 pixel diffraction pattern was aquired 125 for each of the 128 × 128 scan points. The tilt direction was parallel to the edge of the Si 126 8 pillar. These steps and angles were selected so that the aperture positions were well within the 127 corrected region of the Ronchigram, which was approximately 24 mrad.  128  129 Results 130 Relationship between phase resolution and dose 131 To determine the achievable phase resolution, the relationship between the dose and the 132 standard deviation of the CoM was evaluated. As stated previously, the phase resolution 133 depends only on the electron dose and the convergence semi-angle of the probe. However, 134 because the probe is scanned, the position of the transmitted disk is affected by the parallelism 135 of the beam and a slight deviation of the detector from the back focal position. Considering 136 the expected resolution of each convergence semi-angle, the data were acquired at 137 magnifications of 4M and 8M for 4 mrad and 200k for 22.5 μrad, with 128 × 128 scan points. 138 The results are summarized in Fig. 2. 139  [Insert Figure 2 here] 140 To clearly observe the effect of the scan width, the standard deviations derived from the data 141 were separately plotted for the entire scan area, center 1/4 area, and center 1/8 area. The solid 142 blue and orange lines in Fig. 2 correspond to the theoretical predictions (Eq. (2)). Considering 143 that the lines indicate the theoretical lower limit of the resolution, it can be concluded that the 144 result agrees well with the prediction. For the 4-mrad convergence semi-angle, because the 145 9 magnification is high and the phase resolution is low, the phase resolution does not strongly 146 depend on the magnification or the scan area. Panel (b) presents a magnified image of the 147 enclosed area in (a), which shows that it indeed depends on the scan area but is almost 148 negligible. The green and red horizontal dotted lines represent the standard-deviation values 149 that correspond to 2𝜋𝜋 100⁄  rad, assuming a diffraction-limited resolution of 0.38 nm. The 150 plot indicates that 2𝜋𝜋 100⁄  rad can be attained using an electron dose of >1000 (e-/pattern).  151 For the smaller convergence semi-angle of 22.5 μm, the effect of the scan is obvious. This is 152 due to the (two orders of magnitude) higher phase resolution, and the wider scan is due to the 153 low magnification of 200k. A phase resolution better than 2𝜋𝜋 100⁄  rad is still achievable 154 using more than 1000 e-/patterns; however, resolution improvements along the dose are 155 hindered by the effect of the scan. When the scan area was narrowed to 1/4 and 1/8, the plot 156 approached the theoretical limit. However, the 1/8 scan area corresponds to a magnification of 157 1.6 M, in which the field of view is approximately 130 nm. Because the expected spatial 158 resolution of 22.5 μrad is approximately 68 nm, using such a high magnification is not so 159 useful in practice. However, because the parallelism of the scan is reproducible under the 160 same scan conditions, the effect can be compensated for using reference data obtained without 161 a sample. 162  163 Resolution improvements via tilt-series acquisition for model sample 164 10 To improve the resolution of the environmental cell phase measurement, tilt-series acquisition 165 was performed for the model sample, as shown in Fig. 1. According to the results discussed in 166 the previous section, the electron currents were adjusted to approximately 4000 e-/pattern on 167 average in the membrane-only region; thus, each pattern in the tilt series was expected to have 168 a base resolution better than 2π/100 rad. 169 The membrane is amorphous in structure and is observed as a granular contrast, and since the 170 tilt angles are still very small, the granular contrast of the films does not change much. 171 However, because the upper and lower membranes are far from the pivot point, tilting around 172 a Pt particle as a pivot results in a significant relative shift in opposite directions. After 173 aligning the tilt series images with the Pt particles and superimposing them, the membrane 174 images overlap with shifted granular contrast images, resulting in an overall reduction in 175 contrast. On the other hand, by correcting the positions of the obtained images with pillar 176 region and summing them, the random noise components present in each image of the tilt 177 series are averaged and thus reduced, which improves contrast. Additionally, summing 178 multiple images is equivalent to effectively increasing the dose. Therefore, averaging the 179 images after aligning the position with the PtPd particles on the pillar blured the image from 180 the membrane while improving the signal from the pillar. 181 Fig. 3 shows examples of the (a) first and (b) last images of a tilt series and (c) the image after 182 averaging. Averaging was performed after aligning the tilt-series images by using the PtPd 183 11 particles on the Si pillar as position markers. The upper half of the image corresponds to the 184 pillar region, and the lower half corresponds to vacuum (only membranes). The standard 185 deviation in the lower region (only membranes) before averaging in (a) is 0.07 mrad. As 186 shown in (c), after tilt-series averaging, the smoothing effect in the membrane region is 187 evident, where the granular contrast of the membranes observed in (a) and (b) is almost 188 completely eliminated, while the PtPd particle contrast is improved. The membrane contrasts 189 also overlapped in the pillar region, but these contrasts moved far more upon tilting relative to 190 the PtPd contrast on the pillar; thus, they were effectively smoothed by the averaging 191 procedure. The standard-deviation value for the membrane region after averaging is improved 192 to 0.03 mrad in (c).  193 [Insert Figure 3 here] 194  195 Spatial-resolution- evaluation of tilt-series averaged image 196 To evaluate the phase precision attainable via DPC, it is necessary to measure not only the 197 standard deviation of the CoM but also the spatial resolution. Young’s fringe resolution 198 evaluation [18] was performed to evaluate the spatial resolution of the DPC images after tilt-199 series averaging. Regarding the photographs in the tilt-series datasets, the first half were 200 aligned with the first image, and the remaining half were aligned with the last image, resulting 201 in pairs of averaged images with slight shifts relative to each other. These pairs of images 202 12 were superimposed and used for the Young’s fringe evaluation. Fig. 4 presents example 203 images for the CoM of the x direction (a, b), and the CoM of the y direction (d, e). The spatial 204 resolution was evaluated as 0.79 nm for this case. Here, the x and y directions correspond to 205 the directions of the detector, and because they are rotated approximately 45 degrees from the 206 direction of the sample edge on the diffraction plane, edge contrast appears in both the CoMx 207 and CoMy images.  208 The resolution evaluation results using just two images (the first and last) were shown in Fig. 209 4 (c) and (f) for CoMx, and CoMy respectively. In comparison to the evaluations performed 210 after aligning and summing five images shown in Fig. 4(b) and (e), the Young's fringe images 211 created with just two images exhibit poorer contrast. Specifically, there is a slight degradation 212 in the x direction and a more pronounced degradation in the y direction. This indicates that, 213 due to the small tilt angle increment of 1.6 mrad and a total tilt of only 16 mrad which is well 214 within the aberration corrected phase flat area of around 15 mrad (semi-angle), the changes of 215 the aberrations between individual images are minimal when acquiring the tilt series.  216 Consequently, the improvement in the signal-to-noise ratio from summing the images leads to 217 an overall enhancement in resolution, outweighing any degradation in resolution from 218 overlaying different images. 219 [Insert Figure 4 here] 220 The evaluated spatial resolutions for all the datasets are presented in Fig. 5, together with the 221 13 standard deviation of the CoM of the vacuum (membranes only) regions (lower part of the 222 tilt-series averaged image). As indicated by Eq. (1), the achievable phase resolution can be 223 determined using a pair of spatial resolutions and the standard deviations of the CoM. The 224 dotted line indicates the boundary below which the resolution of 2π/100 rad is achieved. As 225 shown, most of the datasets are well within the range, suggesting that the phase resolution of 226 2π/100 rad can be achieved using the proposed tilt-series acquisition method by minimizing 227 the film contrast for the sample in an environmental cell.  228 [Insert Figure 5 here] 229  230 Discussion 231 Here, we discuss the comparison between the proposed method and the method of using a 232 large convergence angle to improve depth resolution. Assuming the angle range typically 233 correctable by an aberration corrector is 30 mrad, the depth obtained as the FWHM (Full 234 Width at Half Maximum) of the probe intensity is Δz = 1.77 λ/α², which is approximately 5 235 nm, providing sufficient resolution to clearly resolve the center of the environmental cell. 236 Furthermore, with a convergence angle of 30 mrad, the probe spread at the position of the 237 membrane, which is 1.3 μm away from the focal point, is 1.3μm × 0.03 rad = 39 nm in 238 radius, or 78 nm in diameter. This means that the influence of the amorphous structure within 239 this range will be averaged out, thus significantly reducing the membrane contrast. However, 240 14 increasing the convergence angle in DPC reduces the resolution of the detected deflection 241 angle changes. As shown by Equation (2), when the dose is kept constant, the standard 242 deviation increases proportionally with the convergence angle making it difficult to detect 243 small deflection angles, such as those caused by the potential distributions around catalyst 244 nanoparticles. Therefore, it is necessary to choose an appropriate convergence angle 245 according to the target to be measured. On the contrary, reducing the influence of the 246 membrane by acquiring a tilt series can be done independently of the choice of convergence 247 angle, allowing the convergence angle to be freely chosen according to the target of 248 observation. 249 Conclusion 250 A simple technique to improve the resolution of the phase measurement of DPC for 251 environmental cell applications was developed and tested using a model sample simulating 252 environmental cell observations. The relationship between the dose and the attainable CoM 253 precision was tested for two convergent semi-angles that coincided well with theoretical 254 predictions. The pairs of spatial resolutions and standard deviation of the CoM were evaluated 255 for the images obtained via tilt-series acquisition, and the results indicated that 2π/100 rad is 256 well achievable using the proposed tilt-series acquisition method for the sample in an 257 environmental cell. 258  259 15 Funding 260 This work was supported by the Innovative Science and Technology Initiative for Security, 261 Acquisition, Technology, and Logistics Agency, Japan [grant number JPJ004596]. 262  263 Conflict of interest 264 The authors declare that they have no conflict of interest. 265  266 Acknowledgement 267 We would like to thank Editage (www.editage.jp) for English language editing. 268   269 16 References 270 1. Liu, L. and A. Corma, Metal Catalysts for Heterogeneous Catalysis: From Single Atoms to 271 Nanoclusters and Nanoparticles. Chem Rev, 2018. 118(10): p. 4981-5079. 272 2. Aso, R., et al., Direct identification of the charge state in a single platinum nanoparticle on 273 titanium oxide. Science, 2022. 378(6616): p. 202-206. 274 3. Aso, R., et al., High-precision charge analysis in a catalytic nanoparticle by electron 275 holography. Microscopy (Oxf), 2024. 276 4. Williamson, M.J., et al., Dynamic microscopy of nanoscale cluster growth at the solid-liquid 277 interface. Nat Mater, 2003. 2(8): p. 532-6. 278 5. Ring, E.A. and N. de Jonge, Microfluidic system for transmission electron microscopy. Microsc 279 Microanal, 2010. 16(5): p. 622-9. 280 6. Ye, F., et al., In Situ TEM Studies of Catalysts Using Windowed Gas Cells. Catalysts, 2020. 281 10(7). 282 7. Qu, J., M. Sui, and R. Li, Recent advances in in-situ transmission electron microscopy 283 techniques for heterogeneous catalysis. iScience, 2023. 26(7): p. 107072. 284 8. Yaguchi, T., et al., In-situ TEM study from the perspective of holders. Microscopy (Oxf), 2024. 285 73(2): p. 117-132. 286 9. Hyllested, J.A.E. and M. Beleggia, Investigation of gas-electron interactions with electron 287 holography. Ultramicroscopy, 2021. 221: p. 113178. 288 10. Shibata, N., et al., Direct Visualization of Local Electromagnetic Field Structures by Scanning 289 Transmission Electron Microscopy. Acc Chem Res, 2017. 50(7): p. 1502-1512. 290 11. Shibata, N., et al., Differential phase-contrast microscopy at atomic resolution. Nature Physics, 291 2012. 8(8): p. 611-615. 292 12. Kohno, Y., et al., Real-space visualization of intrinsic magnetic fields of an antiferromagnet. 293 Nature, 2022. 602(7896): p. 234-239. 294 13. Toyama, S., et al., Real-space observation of a two-dimensional electron gas at semiconductor 295 heterointerfaces. Nat Nanotech, 2023. 18(5): p. 521-528. 296 14. Nakamura, A., et al., Differential Phase Contrast Imaging with Reduced Dynamical Diffraction 297 Effect. Microscopy and Microanalysis, 2017. 23(S1): p. 1412-1413. 298 15. Kohno, Y., et al., Development of tilt-scan system for differential phase contrast scanning 299 transmission electron microscopy. Microscopy (Oxf), 2022. 71(2): p. 111-116. 300 16. Murakami, Y.O., et al., Magnetic-structure imaging in polycrystalline materials by specimen-301 tilt series averaged DPC STEM. Microscopy (Oxf), 2020. 69(5): p. 312-320. 302 17. Ishikawa, R., et al., Spatial and phase resolution in electron microscopy. Microscopy (Oxf), 303 2023. 72(2): p. 78-96. 304 17 18. Pollath, S., F. Schwarzhuber, and J. Zweck, The differential phase contrast uncertainty relation: 305 Connection between electron dose and field resolution. Ultramicroscopy, 2021. 228: p. 113342. 306 19. Weiss, F.Z.K., Young's interference fringes in electron microscopy revisited. Ultramicroscopy, 307 1993. 50(50): p. 123. 308 Figure Legends 309 Fig. 1 (a) Schematic of the model sample structure and tilt-series acquisition; (b) TEM image 310 of a model sample. 311 Fig. 2 (a) Relationship between the electron dose and the standard deviation of the CoM for 312 convergence semi-angles of 4 mrad and 22.5 μrad. (b) Magnified image of the enclosed 313 region in (a). The solid lines represent theoretical predictions, and the dotted lines represent 314 standard deviations that correspond to the phase precision of 2𝜋𝜋/100 rad, assuming 315 diffraction-limited spatial resolutions.  316 Fig. 3 Example images of tilt-series acquisition of the Si pillar edge region of the model 317 sample. The upper half of the image corresponds to the pillar region, and the lower half of the 318 image corresponds to the vacuum (only membranes). (a) First and (b) last images of a tilt-319 series and (c) the image after averaging. The averaging was performed after aligning tilt-320 series images by using PtPd particles on the Si pillar as position markers. 321 Fig. 4 Example images for Young’s fringe spatial resolution evaluation of tilt-series 322 acquisition of the Si pillar edge region of the model sample. Regarding the photographs in tilt-323 series datasets, the first half were aligned with the first image, and the remaining half were 324 aligned with the last image. The resultant pair of images were superimposed and used for 325 18 Young’s fringe evaluation. (a) Resultant averaged image of CoMx; (b) Fourier transform of 326 (a); (d) CoMy; (f) Fourier transform of (d). (c) and (f) are the Young’s fringe evaluation result 327 using just two images (the first and last) for CoMx, and CoMy, respectively. 328 Fig. 5 Plot of the spatial resolution versus the standard deviation of the CoM, showing the 329 achievable phase resolution. The dotted line indicates the boundary below which the 330 resolution of 2π/100 rad is achieved. 331   332 19  333  334 Figure 1 335   336 20  337 Figure 2 338   339 21  340 Figure 3 341   342 22  343 Figure 4 344   345 23  346 Figure 5 347