The geometry of the Moiré Effect in one, two, and three dimensions: by Vladimir Saveljev
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| Format: | Book |
| Language: | English |
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Newcastle upon Tyne
Cambridge Scholars Publishing
2023
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| Online Access: | Inhaltsverzeichnis |
| Item Description: | This book first published 2022. The present binding first published 2023. |
| Physical Description: | xxvii, 251 Seiten Illustrationen, Diagramme |
| ISBN: | 9781527599994 |
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MARC
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| 245 | 1 | 0 | |a The geometry of the Moiré Effect in one, two, and three dimensions |b by Vladimir Saveljev |
| 246 | 1 | 3 | |a The geometry of the Moiré Effect in 1, 2, and 3 dimensions |
| 264 | 1 | |a Newcastle upon Tyne |b Cambridge Scholars Publishing |c 2023 | |
| 300 | |a xxvii, 251 Seiten |b Illustrationen, Diagramme | ||
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| 500 | |a This book first published 2022. The present binding first published 2023. | ||
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Table of contents Acknowledgements. x Preface.xi Introduction. xiv Necessary conditions. xxii Definition. xxiii List of Abbreviations. xxviii Chapter 1. 1 One-Dimensional Moiré 1.1. Moiré Effect in Functions of One Variable. 1 a) Linear arrays. 1 b) Sinusoidal signals. 6 c) Sinusoidal optical arrays. 10 d) Binary optical arrays (gratings). 12 e) Examples of ID moiré effect. 16 Aliasing. 16 Stroboscopic effect . 17 Modulation/demodulation of
signals. 19 1.2. Additional Characteristics of ID Moiré Patterns. 21 a) Profile of ID moiré patterns. 21 b) Magnitude as a function of duty cycle .25 Chapter 2.30 Two-Dimensional Moiré 2.1. Classic Moiré Effect in Coplanar Images. 31 Phase. 38 2.2. Dot Arrays and Superpositions of Line Gratings . 39 2.3. 2D Spectra. 44 2.4. Magnitude of 2D Moiré Patterns. 52 a) Function of twist angle between gratings. 53 b) Function of opening ratio. 61
viii Table of Contents Chapter 3.65 Three-Dimensional Moiré 3.1. Introductory Note. 65 a) Generalized cylindrical surface (GCS). 66 b) Model of camera . 67 3.2. Projected Period. 69 a) Projected period of GCS. 70 b) Rule of incidence angles. 73 c) Projected period of planar facet. 74 d) Facets on circular cylinder. 79 e) Projected period of cylinder. 82 3.3. Moiré Effect in GCS with Planar Facets. 91 a) Parallel planes (parallelepiped) orthogonal to axis of camera. 94 Phase.100 b) Inclined parallelepiped. 107 c) Crossed planes (wedge). 109 Symmetric wedge. 109 Asymmetric
wedge. Ill d) Practical examples of the 3D moiré effect . 112 Fence. 112 Bridge. 114 Prism (wedge).115 3.4. Moiré Effect in Symmetric Curved GCS . 116 a) Single-layered cylinder. 116 b) Coaxial (double-layered) cylinders. 118 3.5. Moiré Effect in GCS with Perpendicular Wavevector. 129 a) Wedge. 130 b) Single-layered cylinder. 132 3.6. Moiré Effect in GCS with Arbitrary Oriented Wavevectors. 135 a) Asymmetric (chiral) single-layered cylinder. 137 b) Sphere. 145 c) 3D array (cube). 147 Chapter 4. 153 Time and Moiré Effect 4.1. Static Moiré Patterns in Moving Grids. 154 a) Condition of constant
phase.156 b) Static directions in unmoved coplanar grids. 157 Gratings and regular grids themselves. 157 Overlapped gratings and grids. 162 c) Static moiré patterns in sliding coplanar grids.165
The Geometry of the Moiré Effect in One, Two, and Three Dimensions ix d) Static moiré patterns in sliding non-coplanar grids. 169 4.2. Spectral Trajectories. 172 a) Spectral peaks of gratings themselves. 172 b) Spectral peaks of overlapped gratings and grids.174 c) Movement of spectral peaks. 177 d) Centres and lines. 180 e) Spectral trajectories 2D. 184 f) Spectral trajectories 3D. 189 4.3. Regular Polygons in Spectrum and Their Spatial Equivalents . 189 a) Square.190 b) Octagon.192 c) Quast-periodic moiré patterns. 195 Chapter 5. 197 Moiré Effect under Control 5.1. Probability of Moiré Effect. 197 5.2. Extreme Conditions of Moiré Effect. 200 a) Minimum (image quality). 200 b) Maximum
(display). 205 2D moiré display. 206 3D moiré display.209 5.3. Incomplete Moiré (Other Physical Effects Similar to Moiré) . 212 a) Overlap only (without averaging). 212 Beats . 212 Vernier scale.215 b) Averaging only (but no overlap). 216 Text rivers. 216 Martian canali.217 Conclusion. 219 Appendix. “Flattest” Function in Cylinder. 220 Al. Concave Cylinders. 220 A2. Convex Cylinders.224 Glossary. 227 Bibliography. 232
Index.247 |
| adam_txt |
Table of contents Acknowledgements. x Preface.xi Introduction. xiv Necessary conditions. xxii Definition. xxiii List of Abbreviations. xxviii Chapter 1. 1 One-Dimensional Moiré 1.1. Moiré Effect in Functions of One Variable. 1 a) Linear arrays. 1 b) Sinusoidal signals. 6 c) Sinusoidal optical arrays. 10 d) Binary optical arrays (gratings). 12 e) Examples of ID moiré effect. 16 Aliasing. 16 Stroboscopic effect . 17 Modulation/demodulation of
signals. 19 1.2. Additional Characteristics of ID Moiré Patterns. 21 a) Profile of ID moiré patterns. 21 b) Magnitude as a function of duty cycle .25 Chapter 2.30 Two-Dimensional Moiré 2.1. Classic Moiré Effect in Coplanar Images. 31 Phase. 38 2.2. Dot Arrays and Superpositions of Line Gratings . 39 2.3. 2D Spectra. 44 2.4. Magnitude of 2D Moiré Patterns. 52 a) Function of twist angle between gratings. 53 b) Function of opening ratio. 61
viii Table of Contents Chapter 3.65 Three-Dimensional Moiré 3.1. Introductory Note. 65 a) Generalized cylindrical surface (GCS). 66 b) Model of camera . 67 3.2. Projected Period. 69 a) Projected period of GCS. 70 b) Rule of incidence angles. 73 c) Projected period of planar facet. 74 d) Facets on circular cylinder. 79 e) Projected period of cylinder. 82 3.3. Moiré Effect in GCS with Planar Facets. 91 a) Parallel planes (parallelepiped) orthogonal to axis of camera. 94 Phase.100 b) Inclined parallelepiped. 107 c) Crossed planes (wedge). 109 Symmetric wedge. 109 Asymmetric
wedge. Ill d) Practical examples of the 3D moiré effect . 112 Fence. 112 Bridge. 114 Prism (wedge).115 3.4. Moiré Effect in Symmetric Curved GCS . 116 a) Single-layered cylinder. 116 b) Coaxial (double-layered) cylinders. 118 3.5. Moiré Effect in GCS with Perpendicular Wavevector. 129 a) Wedge. 130 b) Single-layered cylinder. 132 3.6. Moiré Effect in GCS with Arbitrary Oriented Wavevectors. 135 a) Asymmetric (chiral) single-layered cylinder. 137 b) Sphere. 145 c) 3D array (cube). 147 Chapter 4. 153 Time and Moiré Effect 4.1. Static Moiré Patterns in Moving Grids. 154 a) Condition of constant
phase.156 b) Static directions in unmoved coplanar grids. 157 Gratings and regular grids themselves. 157 Overlapped gratings and grids. 162 c) Static moiré patterns in sliding coplanar grids.165
The Geometry of the Moiré Effect in One, Two, and Three Dimensions ix d) Static moiré patterns in sliding non-coplanar grids. 169 4.2. Spectral Trajectories. 172 a) Spectral peaks of gratings themselves. 172 b) Spectral peaks of overlapped gratings and grids.174 c) Movement of spectral peaks. 177 d) Centres and lines. 180 e) Spectral trajectories 2D. 184 f) Spectral trajectories 3D. 189 4.3. Regular Polygons in Spectrum and Their Spatial Equivalents . 189 a) Square.190 b) Octagon.192 c) Quast-periodic moiré patterns. 195 Chapter 5. 197 Moiré Effect under Control 5.1. Probability of Moiré Effect. 197 5.2. Extreme Conditions of Moiré Effect. 200 a) Minimum (image quality). 200 b) Maximum
(display). 205 2D moiré display. 206 3D moiré display.209 5.3. Incomplete Moiré (Other Physical Effects Similar to Moiré) . 212 a) Overlap only (without averaging). 212 Beats . 212 Vernier scale.215 b) Averaging only (but no overlap). 216 Text rivers. 216 Martian canali.217 Conclusion. 219 Appendix. “Flattest” Function in Cylinder. 220 Al. Concave Cylinders. 220 A2. Convex Cylinders.224 Glossary. 227 Bibliography. 232
Index.247 |
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| spelling | Saveljev, Vladimir Verfasser aut The geometry of the Moiré Effect in one, two, and three dimensions by Vladimir Saveljev The geometry of the Moiré Effect in 1, 2, and 3 dimensions Newcastle upon Tyne Cambridge Scholars Publishing 2023 xxvii, 251 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier This book first published 2022. The present binding first published 2023. Moiré-Streifen (DE-588)4170359-5 gnd rswk-swf Moiré-Streifen (DE-588)4170359-5 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034949180&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Saveljev, Vladimir The geometry of the Moiré Effect in one, two, and three dimensions by Vladimir Saveljev Moiré-Streifen (DE-588)4170359-5 gnd |
| subject_GND | (DE-588)4170359-5 |
| title | The geometry of the Moiré Effect in one, two, and three dimensions by Vladimir Saveljev |
| title_alt | The geometry of the Moiré Effect in 1, 2, and 3 dimensions |
| title_auth | The geometry of the Moiré Effect in one, two, and three dimensions by Vladimir Saveljev |
| title_exact_search | The geometry of the Moiré Effect in one, two, and three dimensions by Vladimir Saveljev |
| title_exact_search_txtP | The geometry of the Moiré Effect in one, two, and three dimensions by Vladimir Saveljev |
| title_full | The geometry of the Moiré Effect in one, two, and three dimensions by Vladimir Saveljev |
| title_fullStr | The geometry of the Moiré Effect in one, two, and three dimensions by Vladimir Saveljev |
| title_full_unstemmed | The geometry of the Moiré Effect in one, two, and three dimensions by Vladimir Saveljev |
| title_short | The geometry of the Moiré Effect in one, two, and three dimensions |
| title_sort | the geometry of the moire effect in one two and three dimensions by vladimir saveljev |
| title_sub | by Vladimir Saveljev |
| topic | Moiré-Streifen (DE-588)4170359-5 gnd |
| topic_facet | Moiré-Streifen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034949180&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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