| Preface to the Second Edition |
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xv | |
| From the Preface to the First Edition |
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xvii | |
| Colour Plates |
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xix | |
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1 | (8) |
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1 | (1) |
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A brief historical background |
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2 | (1) |
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The scope of the present book |
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3 | (2) |
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Overview of the following chapters |
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5 | (2) |
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About the exercises and the moire demonstration samples |
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7 | (2) |
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Background and basic notions |
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9 | (50) |
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9 | (1) |
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The spectral approach; images and their spectra |
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10 | (5) |
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Superposition of two cosinusoidal gratings |
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15 | (3) |
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Superposition of three or more cosinusoidal gratings |
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18 | (3) |
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Binary square waves and their spectra |
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21 | (2) |
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Superposition of binary gratings; higher order moires |
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23 | (7) |
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The impulse indexing notation |
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30 | (3) |
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The notational system for superposition moires |
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33 | (2) |
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Singular moire states; stable vs. unstable moire-free superpositions |
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35 | (3) |
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The intensity profile of the moire and its perceptual contrast |
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38 | (2) |
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Square grids and their superpositions |
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40 | (4) |
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Dot-screens and their superpositions |
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44 | (4) |
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Sampling moires; moires as aliasing phenomena |
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48 | (3) |
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Advantages of the spectral approach |
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51 | (8) |
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52 | (7) |
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59 | (22) |
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59 | (1) |
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Colour separation and halftoning |
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60 | (2) |
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The challenge of moire minimization in colour printing |
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62 | (2) |
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Navigation in the moire parameter space |
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64 | (7) |
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The case of two superposed screens |
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65 | (3) |
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The case of three superposed screens |
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68 | (3) |
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Finding moire-free screen combinations for colour printing |
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71 | (4) |
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75 | (6) |
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77 | (4) |
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The moire profile form and intensity levels |
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81 | (28) |
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81 | (1) |
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Extraction of the profile of a moire between superposed line-gratings |
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82 | (7) |
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Extension of the moire extraction to the 2D case of superposed screens |
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89 | (7) |
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The special case of the (1,0,-1,0)-moire |
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96 | (6) |
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Shape of the intensity profile of the moire cells |
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97 | (4) |
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Orientation and size of the moire cells |
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101 | (1) |
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The case of more complex and higher order moires |
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102 | (7) |
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103 | (6) |
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The algebraic foundation of the spectrum properties |
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109 | (40) |
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109 | (1) |
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The support of a spectrum; lattices and modules |
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109 | (5) |
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Lattices and modules in Rn |
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110 | (3) |
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Application to the frequency spectrum |
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113 | (1) |
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The mapping between the impulse indices and their geometric locations |
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114 | (1) |
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A short reminder from linear algebra |
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115 | (3) |
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The image and the kernel of a linear transformation |
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115 | (1) |
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Partition of a vector space into equivalence classes |
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116 | (1) |
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The partition of V into equivalence classes induced by Φ |
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117 | (1) |
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The application of these results to our continuous case |
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118 | (1) |
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The discrete mapping Ψ vs. the continuous mapping Φ |
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118 | (3) |
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The algebraic interpretation of the impulse locations in the spectrum support |
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121 | (5) |
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The global spectrum support |
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121 | (2) |
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The individual impulse-clusters |
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123 | (2) |
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The spread-out clusters slightly off the singular state |
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125 | (1) |
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126 | (17) |
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143 | (6) |
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146 | (3) |
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Fourier-based interpretation of the algebraic spectrum properties |
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149 | (16) |
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149 | (1) |
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Image domain interpretation of the algebraic structure of the spectrum support |
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149 | (2) |
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Image domain interpretation of the impulse-clusters in the spectrum |
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151 | (1) |
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The amplitude of the collapsed impulse-clusters in a singular state |
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152 | (1) |
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The exponential Fourier expression for two-grating superpositions |
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153 | (2) |
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Two-grating superpositions and their singular states |
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155 | (3) |
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Two gratings with identical frequencies |
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155 | (2) |
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Two gratings with different frequencies |
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157 | (1) |
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Two-screen superpositions and their singular states |
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158 | (3) |
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The general superposition of m layers and its singular states |
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161 | (4) |
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163 | (2) |
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165 | (26) |
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165 | (1) |
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The phase of a periodic function |
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166 | (2) |
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The phase terminology for periodic functions in the 1D case |
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168 | (1) |
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The phase terminology for 1-fold periodic functions in the 2D case |
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169 | (2) |
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The phase terminology for the general 2D case: 2-fold periodic functions |
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171 | (5) |
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Using the period-vector notation |
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172 | (1) |
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Using the step-vector notation |
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173 | (3) |
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Moire phases in the superposition of periodic layers |
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176 | (3) |
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The influence of layer shifts on the overall superposition |
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179 | (12) |
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186 | (5) |
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Macro- and microstructures in the superposition |
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191 | (42) |
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191 | (3) |
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Rosettes in singular states |
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194 | (4) |
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Rosettes in periodic singular states |
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194 | (1) |
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Rosettes in almost-periodic singular states |
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195 | (3) |
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The influence of layer shifts on the rosettes in singular states |
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198 | (2) |
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The microstructure slightly off the singular state; the relationship between macro- and microstructures |
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200 | (1) |
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The microstructure in stable moire-free superpositions |
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201 | (3) |
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Rational vs. irrational screen superpositions; rational approximants |
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204 | (6) |
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210 | (8) |
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The microstructure of the conventional 3-screen superposition |
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218 | (5) |
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Variance or invariance of the microstructure under layer shifts |
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223 | (3) |
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Period-coordinates and period-shifts in the Fourier decomposition |
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226 | (7) |
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231 | (2) |
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Polychromatic moire effects |
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233 | (16) |
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233 | (1) |
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Some basic notions from colour theory |
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234 | (2) |
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Physical aspects of colour |
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234 | (1) |
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Physiological aspects of colour |
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235 | (1) |
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Extension of the spectral approach to the polychromatic case |
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236 | (5) |
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The representation of images and image superpositions |
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236 | (4) |
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The influence of the human visual system |
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240 | (1) |
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The Fourier-spectrum convolution and the superposition moires |
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241 | (1) |
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Extraction of the moire intensity profiles |
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241 | (1) |
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The (1,-1)-moire between two colour line-gratings |
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242 | (3) |
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The (1,0,-1,0)-moire between two colour dot-screens |
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245 | (1) |
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The case of more complex and higher-order moires |
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246 | (3) |
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246 | (3) |
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Moires between repetitive, non-periodic layers |
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249 | (104) |
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249 | (1) |
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Repetitive, non-periodic layers |
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250 | (8) |
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The influence of a coordinate change on the spectrum |
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258 | (6) |
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Curvilinear cosinusoidal gratings and their different types of spectra |
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264 | (8) |
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Gradual transitions between cosinusoidal gratings of different types |
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268 | (4) |
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The Fourier decomposition of curved, repetitive structures |
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272 | (3) |
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The Fourier decomposition of curvilinear gratings |
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272 | (2) |
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The Fourier decomposition of curved line-grids and dot-screens |
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274 | (1) |
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The spectrum of curved, repetitive structures |
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275 | (4) |
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The spectrum of curvilinear gratings |
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275 | (3) |
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The spectrum of curved line-grids and dot-screens |
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278 | (1) |
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The superposition of curved, repetitive layers |
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279 | (44) |
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Moires in the superposition of curved, repetitive layers |
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279 | (3) |
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Image domain vs. spectral domain investigation of the superposition |
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282 | (1) |
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The superposition of a parabolic grating and a periodic straight grating |
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283 | (7) |
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The superposition of two parabolic gratings |
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290 | (7) |
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The superposition of a circular grating and a periodic straight grating |
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297 | (9) |
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The superposition of two circular gratings |
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306 | (5) |
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The superposition of a zone grating and a periodic straight grating |
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311 | (8) |
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The superposition of two circular zone gratings |
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319 | (4) |
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Periodic moires in the superposition of non-periodic layers |
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323 | (6) |
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Moire analysis and synthesis in the superposition of curved, repetitive layers |
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329 | (14) |
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The case of curvilinear gratings |
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329 | (8) |
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The case of curved dot-screens |
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337 | (6) |
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Local frequencies and singular states in curved, repetitive layers |
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343 | (4) |
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Moires in the superposition of screen gradations |
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347 | (1) |
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348 | (5) |
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349 | (4) |
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Other possible approaches for moire analysis |
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353 | (150) |
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353 | (1) |
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The indicial equations method |
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353 | (7) |
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358 | (1) |
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Comparison with the spectral approach |
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359 | (1) |
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Approximation using the first harmonic |
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360 | (3) |
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362 | (1) |
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The local frequency method |
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363 | (6) |
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368 | (1) |
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Comparison with the spectral approach |
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369 | (1) |
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369 | (6) |
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370 | (5) |
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Periodic functions and their spectra |
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375 | (20) |
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375 | (1) |
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Periodic functions, their Fourier series and their spectra in the 1D case |
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375 | (3) |
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Periodic functions, their Fourier series and their spectra in the 2D case |
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378 | (1) |
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1-fold periodic functions in the x or y direction |
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378 | (1) |
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2-fold periodic functions in the x and y directions |
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378 | (2) |
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1-fold periodic functions in an arbitrary direction |
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380 | (1) |
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2-fold periodic functions in arbitrary directions (skew-periodic functions) |
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381 | (5) |
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The period-lattice and the frequency-lattice (=spectrum support) |
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386 | (3) |
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The matrix notation, its appeal, and its limitations for our needs |
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389 | (3) |
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The period-vectors Pi vs. the step-vectors Ti |
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392 | (3) |
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Almost-periodic functions and their spectra |
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395 | (14) |
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395 | (1) |
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A simple illustrative example |
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395 | (1) |
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Definitions and main properties |
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396 | (3) |
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The spectrum of almost-periodic functions |
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399 | (2) |
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The different classes of almost-periodic functions and their spectra |
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401 | (3) |
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Characterization of functions according to their spectrum support |
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404 | (2) |
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Almost-periodic functions in two variables |
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406 | (3) |
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Miscellaneous issues and derivations |
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409 | (76) |
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Derivation of the classical moire formula (2.9) of Sec. 2.4 |
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409 | (1) |
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Derivation of the first part of Proposition 2.1 of Sec. 2.5 |
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410 | (1) |
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Invariance of the impulse amplitudes under rotations and x, y scalings |
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411 | (1) |
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Invariance of the 2D Fourier transform under rotations |
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411 | (1) |
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Invariance of the impulse amplitudes under x, y scalings |
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411 | (1) |
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412 | (1) |
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412 | (2) |
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The particular case of periodic functions |
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414 | (1) |
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The phase of a periodic function: the φ and the Ø notations |
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415 | (2) |
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The function Rc(u) converges to δ(u) as a→0 |
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417 | (1) |
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The 2D spectrum of a cosinusoidal zone grating |
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418 | (1) |
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The convolution of two orthogonal line-impulses |
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419 | (1) |
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The compound line-impulse of the singular (k1, k2)-line-impulse cluster |
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420 | (3) |
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The 1D Fourier transform of the chirp cos(ax2 + b) |
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423 | (1) |
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The 2D Fourier transform of the 2D chirp cos(ax2 + by2 + c) |
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424 | (1) |
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The spectrum of screen gradations |
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425 | (4) |
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Convergence issues related to Fourier series |
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429 | (1) |
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On the convergence of Fourier series |
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429 | (1) |
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Multiplication of infinite series |
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430 | (2) |
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Moire effects in image reproduction |
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432 | (1) |
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Hybrid (1,-1)-moire effects whose moire bands have 2D intensity profiles |
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433 | (1) |
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Preliminary considerations |
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433 | (3) |
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The Fourier-based approach |
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436 | (13) |
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Generalization to curvilinear gratings |
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449 | (4) |
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Synthesis of hybrid (1,-1)-moire effects |
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453 | (11) |
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Moire effects between general 2-fold periodic layers |
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464 | (1) |
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Examples of general 2-fold periodic layers |
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465 | (4) |
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Adaptation of results from
Chapter 10 to our particular case |
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469 | (1) |
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The (1,0,-1,0)-moire between two regular screens or grids |
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470 | (4) |
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The (1,0,-1,0)-moire between two hexagonal screens or grids |
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474 | (2) |
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The (1,0,-1,0)-moire between two general 2-fold periodic screens or grids |
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476 | (1) |
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Allowing for layer shifts |
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476 | (4) |
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The order of the superposed layers |
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480 | (2) |
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Layer normalization issues |
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482 | (3) |
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Glossary of the main terms |
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485 | (18) |
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485 | (1) |
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Terms in the image domain |
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486 | (4) |
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Terms in the spectral domain |
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490 | (4) |
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494 | (2) |
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Terms related to light and colour |
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496 | (2) |
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498 | (5) |
| List of notations and symbols |
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503 | (4) |
| List of abbreviations |
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507 | (2) |
| References |
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509 | (10) |
| Index |
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519 | |
Lisainfo e-raamatute kohta