2bd0ecd34ed6557e729442ab6c786f0f crystals_a2022m9v12n9p1212.pdf 16ac1585604d28b04ed8c457f762896ab968a872 crystals_a2022m9v12n9p1212.pdf 2838d523b6182a1606055a31b795e59e4753a5050c890f87d4523577c7339be3 crystals_a2022m9v12n9p1212.pdf Title: Comparison of Brillouin Light Scattering and Density of States in a Supported Layer: Analytical and Experimental Study Subject: We provide a detailed analytical calculation of the Brillouin light scattering (BLS) intensity of a layer on a substrate, taking into account both photoelastic and moving boundary (ripple effect) mechanisms, and give a comparison between BLS intensity and density of states (DOS) to determine the dispersion curves of longitudinal guided modes in the supported layer. In particular, in the case where the mismatch between the elastic parameters of the substrate and the adsorbed layer is high, such as in a PMMA layer on a Si substrate, we derive closed-form expressions of BLS and DOS and demonstrate a simple relationship between these two quantities. A very good agreement between experimental and theoretical BLS spectra was found and compared to theoretical DOS spectra. In particular, we show that while the peaks in the DOS present a uniform behavior, the BLS spectra follows a sine cardinal (sinc) function shape around a given frequency fixed by the chosen laser wavelength. The theoretical calculation is performed within the framework of the Green’s function approach. Keywords: Brillouin light scattering; density of states; supported layer; Green’s function Author: Ossama El Abouti, John Cuffe, El Houssaine El Boudouti, Clivia M. Sotomayor Torres, Emigdio Chavez-Angel, Bahram Djafari-Rouhani and Francesc Alzina Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Sat Sep 3 08:29:42 2022 CEST ModDate: Sat Sep 3 08:46:53 2022 CEST Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 15 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 3499068 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- OMJKBH+VnURWPalladioL Type 1 Custom yes yes no 10 0 FVJESE+URWPalladioL-Bold Type 1 Custom yes yes no 15 0 NFTIUB+URWPalladioL-Roma Type 1 Custom yes yes no 20 0 AOXPWA+URWPalladioL-Ital Type 1 Custom yes yes no 24 0 INEITC+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 43 0 SECYHN+EURM10 Type 1 Builtin yes yes no 65 0 SNYHYX+PazoMath-Italic Type 1 Builtin yes yes no 73 0 OZOQRG+CMSY10 Type 1 Builtin yes yes no 77 0 SOSTRQ+CMR10 Type 1 Builtin yes yes no 81 0 BCDEEE+PalatinoLinotype-Bold TrueType WinAnsi yes yes no 89 0 BCDFEE+PalatinoLinotype-Roman TrueType WinAnsi yes yes no 93 0 BCDGEE+PalatinoLinotype-Italic TrueType WinAnsi yes yes no 97 0 BCDHEE+PalatinoLinotype-Roman CID TrueType Identity-H yes yes yes 101 0 BCDJEE+CambriaMath CID TrueType Identity-H yes yes yes 108 0 BCDKEE+Cambria CID TrueType Identity-H yes yes yes 115 0 XXXWGO+CMEX10 Type 1 Builtin yes yes no 127 0 SMMDOS+SFRM1000 Type 1 Custom yes yes no 134 0 VUQMPS+PazoMath Type 1 Builtin yes yes no 142 0 SPAJTN+URWPalladioL-BoldItal Type 1 Custom yes yes no 149 0 BCDEEE+PalatinoLinotype-Bold TrueType WinAnsi yes yes no 164 0 Arial-BoldMT TrueType WinAnsi no no no 168 0 Arial-ItalicMT TrueType WinAnsi no no no 171 0 ArialMT TrueType WinAnsi no no no 174 0 BCDFEE+PalatinoLinotype-Roman TrueType WinAnsi yes yes no 177 0 BCDGEE+PalatinoLinotype-Italic TrueType WinAnsi yes yes no 181 0 BCDJEE+CambriaMath CID TrueType Identity-H yes yes yes 185 0 ABCDEE+Palatino Linotype,Bold TrueType WinAnsi yes yes no 218 0 Arial,Bold TrueType WinAnsi no no no 222 0 Arial TrueType WinAnsi no no no 225 0 ABCDEE+Palatino Linotype TrueType WinAnsi yes yes no 228 0 ABCDEE+Palatino Linotype,Italic TrueType WinAnsi yes yes no 232 0 ABCDEE+Cambria Math CID TrueType Identity-H yes yes yes 236 0 BCDEEE+PalatinoLinotype-Bold TrueType WinAnsi yes yes no 276 0 Arial-BoldMT TrueType WinAnsi no no no 280 0 ArialMT TrueType WinAnsi no no no 283 0 BCDFEE+PalatinoLinotype-Roman TrueType WinAnsi yes yes no 286 0 BCDGEE+PalatinoLinotype-Italic TrueType WinAnsi yes yes no 290 0 BCDJEE+CambriaMath CID TrueType Identity-H yes yes yes 294 0 RLYTRW+CMMI10 Type 1 Builtin yes yes no 318 0 DDZECJ+EURM7 Type 1 Builtin yes yes no 322 0 BCDEEE+PalatinoLinotype-Bold TrueType WinAnsi yes yes no 330 0 BCDFEE+PalatinoLinotype-Roman TrueType WinAnsi yes yes no 334 0 BCDGEE+PalatinoLinotype-Italic TrueType WinAnsi yes yes no 338 0 BCDJEE+CambriaMath CID TrueType Identity-H yes yes yes 342 0 Arial-BoldMT TrueType WinAnsi no no no 350 0 ArialMT TrueType WinAnsi no no no 353 0 BCDEEE+PalatinoLinotype-Bold TrueType WinAnsi yes yes no 365 0 BCDFEE+PalatinoLinotype-Roman TrueType WinAnsi yes yes no 369 0 BCDGEE+PalatinoLinotype-Italic TrueType WinAnsi yes yes no 373 0 BCDHEE+PalatinoLinotype-Roman CID TrueType Identity-H yes yes yes 377 0 BCDJEE+CambriaMath CID TrueType Identity-H yes yes yes 384 0 Arial-BoldMT TrueType WinAnsi no no no 392 0 ArialMT TrueType WinAnsi no no no 395 0 BCDEEE+PalatinoLinotype-Bold TrueType WinAnsi yes yes no 406 0 ArialMT TrueType WinAnsi no no no 410 0 BCDFEE+PalatinoLinotype-Roman TrueType WinAnsi yes yes no 413 0 BCDGEE+PalatinoLinotype-Italic TrueType WinAnsi yes yes no 417 0 BCDHEE+PalatinoLinotype-Roman CID TrueType Identity-H yes yes yes 421 0 BCDJEE+CambriaMath CID TrueType Identity-H yes yes yes 428 0 Arial-BoldMT TrueType WinAnsi no no no 437 0 ArialMT TrueType WinAnsi no no no 440 0 Jhove (Rel. 1.22.1, 2019-04-17) Date: 2023-05-13 02:40:03 CEST RepresentationInformation: crystals_a2022m9v12n9p1212.pdf ReportingModule: PDF-hul, Rel. 1.12.1 (2019-04-17) LastModified: 2023-05-12 13:19:15 CEST Size: 3499068 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 642 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@44c8afef Item: Title: Analytical Results Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@7b69c6ba Children: Item: Title: Scattering Intensity in a Supported Layer Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@46daef40 Item: Title: Density of States and Reflection Delay Time Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@12f41634 Item: Title: Particular Case of a Soft Layer on a Hard Substrate Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@13c27452 Item: Title: Numerical and Experimental Results Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@262b2c86 Children: Item: Title: Experimental Setup Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@371a67ec Item: Title: Results and Discussion Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@5ed828d Item: Title: Conclusions Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@50d0686 Item: Title: Appendix A Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@7a3d45bd Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@1e7c7811 Info: Title: Comparison of Brillouin Light Scattering and Density of States in a Supported Layer: Analytical and Experimental Study Author: Ossama El Abouti, John Cuffe, El Houssaine El Boudouti, Clivia M. Sotomayor Torres, Emigdio Chavez-Angel, Bahram Djafari-Rouhani and Francesc Alzina Subject: We provide a detailed analytical calculation of the Brillouin light scattering (BLS) intensity of a layer on a substrate, taking into account both photoelastic and moving boundary (ripple effect) mechanisms, and give a comparison between BLS intensity and density of states (DOS) to determine the dispersion curves of longitudinal guided modes in the supported layer. In particular, in the case where the mismatch between the elastic parameters of the substrate and the adsorbed layer is high, such as in a PMMA layer on a Si substrate, we derive closed-form expressions of BLS and DOS and demonstrate a simple relationship between these two quantities. A very good agreement between experimental and theoretical BLS spectra was found and compared to theoretical DOS spectra. In particular, we show that while the peaks in the DOS present a uniform behavior, the BLS spectra follows a sine cardinal (sinc) function shape around a given frequency fixed by the chosen laser wavelength. The theoretical calculation is performed within the framework of the Green’s function approach. Keywords: Brillouin light scattering; density of states; supported layer; Green’s function Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Sat Sep 03 08:29:42 CEST 2022 ModDate: Sat Sep 03 08:46:53 CEST 2022 ID: 0x8e2a4a0bc39163c73bf86c1e185efccf, 0x8e2a4a0bc39163c73bf86c1e185efccf Filters: FilterPipeline: FlateDecode Fonts: Type1: Font: BaseFont: SECYHN+EURM10 FontSubset: true FirstChar: 11 LastChar: 28 FontDescriptor: FontName: SECYHN+EURM10 Flags: Symbolic FontBBox: -32, -243, 1060, 720 FontFile: true Font: BaseFont: DDZECJ+EURM7 FontSubset: true FirstChar: 33 LastChar: 33 FontDescriptor: FontName: DDZECJ+EURM7 Flags: Symbolic FontBBox: -5, -243, 1229, 720 FontFile: true Font: BaseFont: SMMDOS+SFRM1000 FontSubset: true FirstChar: 163 LastChar: 163 FontDescriptor: FontName: SMMDOS+SFRM1000 Flags: Symbolic FontBBox: -189, -321, 1456, 937 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: SNYHYX+PazoMath-Italic FontSubset: true FirstChar: 35 LastChar: 182 FontDescriptor: FontName: SNYHYX+PazoMath-Italic Flags: Symbolic FontBBox: -70, -277, 902, 733 FontFile: true Font: BaseFont: OMJKBH+VnURWPalladioL FontSubset: true FirstChar: 178 LastChar: 182 FontDescriptor: FontName: OMJKBH+VnURWPalladioL Flags: Symbolic FontBBox: -166, -283, 1021, 943 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: OZOQRG+CMSY10 FontSubset: true FirstChar: 0 LastChar: 106 FontDescriptor: FontName: OZOQRG+CMSY10 Flags: Symbolic FontBBox: -29, -960, 1116, 775 FontFile: true Font: BaseFont: VUQMPS+PazoMath FontSubset: true FirstChar: 68 LastChar: 181 FontDescriptor: FontName: VUQMPS+PazoMath Flags: Symbolic FontBBox: -40, -283, 878, 946 FontFile: true Font: BaseFont: FVJESE+URWPalladioL-Bold FontSubset: true FirstChar: 3 LastChar: 122 FontDescriptor: FontName: FVJESE+URWPalladioL-Bold Flags: Symbolic FontBBox: -152, -301, 1000, 935 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: SOSTRQ+CMR10 FontSubset: true FirstChar: 40 LastChar: 93 FontDescriptor: FontName: SOSTRQ+CMR10 Flags: Symbolic FontBBox: -40, -250, 1009, 750 FontFile: true Font: BaseFont: NFTIUB+URWPalladioL-Roma FontSubset: true FirstChar: 2 LastChar: 252 FontDescriptor: FontName: NFTIUB+URWPalladioL-Roma Flags: Symbolic FontBBox: -166, -283, 1021, 943 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: SPAJTN+URWPalladioL-BoldItal FontSubset: true FirstChar: 110 LastChar: 118 FontDescriptor: FontName: SPAJTN+URWPalladioL-BoldItal Flags: Symbolic FontBBox: -170, -300, 1073, 935 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: AOXPWA+URWPalladioL-Ital FontSubset: true FirstChar: 3 LastChar: 121 FontDescriptor: FontName: AOXPWA+URWPalladioL-Ital Flags: Symbolic FontBBox: -170, -305, 1010, 941 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: RLYTRW+CMMI10 FontSubset: true FirstChar: 60 LastChar: 60 FontDescriptor: FontName: RLYTRW+CMMI10 Flags: Symbolic FontBBox: -32, -250, 1048, 750 FontFile: true Font: BaseFont: XXXWGO+CMEX10 FontSubset: true FirstChar: 0 LastChar: 111 FontDescriptor: FontName: XXXWGO+CMEX10 Flags: Symbolic FontBBox: -24, -2960, 1454, 772 FontFile: true Pages: Page: Sequence: 1 Annotations: Annotation: Subtype: Link Rect: 54, 323, 152, 332 Annotation: Subtype: Link Rect: 34, 311, 79, 320 Annotation: Subtype: Link Rect: 34, 164, 96, 186 Annotation: Subtype: Link Rect: 126, 90, 154, 99 Annotation: Subtype: Link Rect: 34, 78, 147, 87 Annotation: Subtype: Link Rect: 34, 756, 153, 792 Annotation: Subtype: Link Rect: 515, 756, 560, 792 Annotation: Subtype: Link Rect: 327, 660, 338, 674 Annotation: Subtype: Link Rect: 480, 660, 491, 674 Annotation: Subtype: Link Rect: 147, 648, 158, 661 Annotation: Subtype: Link Rect: 281, 648, 292, 661 Annotation: Subtype: Link Rect: 391, 648, 402, 661 Annotation: Subtype: Link Rect: 514, 284, 521, 293 ActionDest: 398 Annotation: Subtype: Link Rect: 205, 246, 212, 255 ActionDest: 398 Annotation: Subtype: Link Rect: 215, 246, 227, 255 ActionDest: 442 Annotation: Subtype: Link Rect: 289, 234, 301, 242 ActionDest: 442 Annotation: Subtype: Link Rect: 304, 233, 316, 242 ActionDest: 442 Annotation: Subtype: Link Rect: 548, 221, 555, 230 ActionDest: 398 Annotation: Subtype: Link Rect: 308, 208, 315, 217 ActionDest: 442 Annotation: Subtype: Link Rect: 380, 208, 387, 217 ActionDest: 442 Annotation: Subtype: Link Rect: 454, 208, 466, 217 ActionDest: 442 Annotation: Subtype: Link Rect: 511, 208, 523, 217 ActionDest: 442 Annotation: Subtype: Link Rect: 489, 196, 501, 205 ActionDest: 442 Annotation: Subtype: Link Rect: 370, 171, 382, 180 ActionDest: 442 Annotation: Subtype: Link Rect: 544, 121, 556, 129 ActionDest: 442 Annotation: Subtype: Link Rect: 115, 17, 257, 28 Annotation: Subtype: Link Rect: 409, 17, 560, 28 Annotation: Subtype: Link Rect: 34, 432, 87, 451 Page: Sequence: 2 Annotations: Annotation: Subtype: Link Rect: 478, 736, 490, 744 ActionDest: 442 Annotation: Subtype: Link Rect: 490, 735, 502, 744 ActionDest: 442 Annotation: Subtype: Link Rect: 392, 673, 404, 682 ActionDest: 442 Annotation: Subtype: Link Rect: 407, 673, 419, 682 ActionDest: 442 Annotation: Subtype: Link Rect: 425, 647, 437, 657 ActionDest: 442 Annotation: Subtype: Link Rect: 440, 647, 452, 657 ActionDest: 442 Annotation: Subtype: Link Rect: 252, 635, 264, 644 ActionDest: 445 Annotation: Subtype: Link Rect: 267, 635, 279, 644 ActionDest: 445 Annotation: Subtype: Link Rect: 358, 635, 370, 644 ActionDest: 445 Annotation: Subtype: Link Rect: 432, 635, 444, 644 ActionDest: 445 Annotation: Subtype: Link Rect: 444, 635, 456, 644 ActionDest: 445 Annotation: Subtype: Link Rect: 227, 597, 239, 606 ActionDest: 445 Annotation: Subtype: Link Rect: 242, 597, 254, 606 ActionDest: 445 Annotation: Subtype: Link Rect: 382, 535, 394, 544 ActionDest: 445 Annotation: Subtype: Link Rect: 491, 535, 503, 544 ActionDest: 445 Annotation: Subtype: Link Rect: 213, 472, 225, 481 ActionDest: 445 Annotation: Subtype: Link Rect: 211, 447, 223, 456 ActionDest: 445 Annotation: Subtype: Link Rect: 500, 447, 512, 456 ActionDest: 445 Annotation: Subtype: Link Rect: 527, 434, 534, 443 ActionDest: 398 Annotation: Subtype: Link Rect: 535, 434, 546, 443 ActionDest: 442 Annotation: Subtype: Link Rect: 355, 371, 366, 380 ActionDest: 445 Annotation: Subtype: Link Rect: 246, 346, 257, 355 ActionDest: 445 Annotation: Subtype: Link Rect: 305, 334, 317, 343 ActionDest: 445 Annotation: Subtype: Link Rect: 282, 321, 293, 330 ActionDest: 445 Annotation: Subtype: Link Rect: 198, 296, 210, 305 ActionDest: 442 Annotation: Subtype: Link Rect: 211, 296, 222, 305 ActionDest: 442 Annotation: Subtype: Link Rect: 223, 296, 235, 305 ActionDest: 445 Annotation: Subtype: Link Rect: 235, 296, 247, 305 ActionDest: 445 Annotation: Subtype: Link Rect: 250, 296, 262, 305 ActionDest: 445 Annotation: Subtype: Link Rect: 500, 271, 512, 280 ActionDest: 442 Annotation: Subtype: Link Rect: 513, 271, 524, 280 ActionDest: 442 Annotation: Subtype: Link Rect: 332, 246, 344, 255 ActionDest: 442 Annotation: Subtype: Link Rect: 345, 246, 356, 255 ActionDest: 442 Annotation: Subtype: Link Rect: 357, 246, 368, 255 ActionDest: 442 Annotation: Subtype: Link Rect: 369, 246, 381, 255 ActionDest: 445 Annotation: Subtype: Link Rect: 381, 246, 393, 255 ActionDest: 445 Page: Sequence: 3 Annotations: Annotation: Subtype: Link Rect: 387, 733, 394, 745 ActionDest: 69 Annotation: Subtype: Link Rect: 206, 710, 218, 719 ActionDest: 442 Annotation: Subtype: Link Rect: 262, 708, 269, 720 ActionDest: 146 Annotation: Subtype: Link Rect: 481, 695, 488, 707 ActionDest: 357 Annotation: Subtype: Link Rect: 280, 631, 287, 643 ActionDest: 69 Page: Sequence: 4 Annotations: Annotation: Subtype: Link Rect: 496, 669, 508, 678 ActionDest: 445 Annotation: Subtype: Link Rect: 326, 605, 337, 614 ActionDest: 445 Annotation: Subtype: Link Rect: 276, 516, 283, 529 ActionDest: 69 Annotation: Subtype: Link Rect: 274, 491, 286, 500 ActionDest: 445 Annotation: Subtype: Link Rect: 543, 374, 555, 383 ActionDest: 445 Page: Sequence: 5 Page: Sequence: 6 Annotations: Annotation: Subtype: Link Rect: 218, 405, 225, 414 ActionDest: 398 Page: Sequence: 7 Annotations: Annotation: Subtype: Link Rect: 401, 708, 416, 720 ActionDest: 153 Annotation: Subtype: Link Rect: 218, 683, 233, 695 ActionDest: 153 Annotation: Subtype: Link Rect: 473, 670, 480, 682 ActionDest: 146 Page: Sequence: 8 Annotations: Annotation: Subtype: Link Rect: 289, 698, 301, 707 ActionDest: 445 Annotation: Subtype: Link Rect: 195, 519, 202, 531 ActionDest: 156 Annotation: Subtype: Link Rect: 459, 326, 466, 338 ActionDest: 156 Annotation: Subtype: Link Rect: 207, 263, 214, 275 ActionDest: 156 Annotation: Subtype: Link Rect: 297, 238, 304, 250 ActionDest: 146 Annotation: Subtype: Link Rect: 308, 241, 320, 250 ActionDest: 445 Annotation: Subtype: Link Rect: 320, 241, 332, 250 ActionDest: 445 Annotation: Subtype: Link Rect: 333, 241, 345, 250 ActionDest: 445 Annotation: Subtype: Link Rect: 242, 200, 249, 212 ActionDest: 156 Annotation: Subtype: Link Rect: 196, 175, 211, 187 ActionDest: 398 Annotation: Subtype: Link Rect: 286, 175, 295, 187 ActionDest: 398 Annotation: Subtype: Link Rect: 219, 163, 226, 175 ActionDest: 156 Annotation: Subtype: Link Rect: 362, 138, 369, 150 ActionDest: 156 Annotation: Subtype: Link Rect: 241, 87, 248, 99 ActionDest: 156 Annotation: Subtype: Link Rect: 329, 62, 336, 74 ActionDest: 146 Page: Sequence: 9 Annotations: Annotation: Subtype: Link Rect: 378, 708, 385, 720 ActionDest: 156 Annotation: Subtype: Link Rect: 217, 695, 224, 707 ActionDest: 210 Annotation: Subtype: Link Rect: 361, 645, 368, 657 ActionDest: 210 Page: Sequence: 10 Annotations: Annotation: Subtype: Link Rect: 326, 450, 333, 470 ActionDest: 210 Annotation: Subtype: Link Rect: 491, 416, 498, 432 ActionDest: 210 Annotation: Subtype: Link Rect: 420, 393, 426, 405 ActionDest: 210 Annotation: Subtype: Link Rect: 362, 320, 374, 329 ActionDest: 445 Annotation: Subtype: Link Rect: 497, 307, 509, 316 ActionDest: 445 Page: Sequence: 11 Annotations: Annotation: Subtype: Link Rect: 196, 720, 203, 732 ActionDest: 314 Annotation: Subtype: Link Rect: 464, 279, 476, 288 ActionDest: 442 Annotation: Subtype: Link Rect: 477, 278, 489, 288 ActionDest: 445 Annotation: Subtype: Link Rect: 548, 257, 555, 277 ActionDest: 357 Annotation: Subtype: Link Rect: 450, 221, 457, 233 ActionDest: 314 Annotation: Subtype: Link Rect: 539, 183, 546, 195 ActionDest: 357 Annotation: Subtype: Link Rect: 275, 133, 282, 145 ActionDest: 357 Annotation: Subtype: Link Rect: 448, 95, 455, 107 ActionDest: 210 Page: Sequence: 12 Annotations: Annotation: Subtype: Link Rect: 283, 311, 290, 325 ActionDest: 314 Page: Sequence: 13 Annotations: Annotation: Subtype: Link Rect: 536, 733, 560, 744 Annotation: Subtype: Link Rect: 165, 721, 380, 732 Annotation: Subtype: Link Rect: 229, 521, 244, 533 ActionDest: 398 Annotation: Subtype: Link Rect: 236, 144, 273, 155 Annotation: Subtype: Link Rect: 456, 133, 493, 144 Annotation: Subtype: Link Rect: 493, 121, 531, 132 Annotation: Subtype: Link Rect: 353, 98, 390, 109 Annotation: Subtype: Link Rect: 397, 98, 433, 109 Annotation: Subtype: Link Rect: 353, 75, 390, 86 Page: Sequence: 14 Annotations: Annotation: Subtype: Link Rect: 484, 722, 521, 733 Annotation: Subtype: Link Rect: 116, 699, 154, 710 Annotation: Subtype: Link Rect: 231, 676, 268, 687 Annotation: Subtype: Link Rect: 59, 642, 96, 652 Annotation: Subtype: Link Rect: 424, 618, 461, 629 Annotation: Subtype: Link Rect: 519, 595, 557, 606 Annotation: Subtype: Link Rect: 59, 584, 95, 594 Annotation: Subtype: Link Rect: 519, 560, 557, 571 Annotation: Subtype: Link Rect: 59, 550, 95, 560 Annotation: Subtype: Link Rect: 187, 526, 225, 537 Annotation: Subtype: Link Rect: 503, 503, 541, 514 Annotation: Subtype: Link Rect: 458, 480, 495, 491 Annotation: Subtype: Link Rect: 273, 457, 310, 468 Annotation: Subtype: Link Rect: 500, 445, 537, 456 Annotation: Subtype: Link Rect: 314, 422, 351, 433 Annotation: Subtype: Link Rect: 175, 400, 212, 410 Annotation: Subtype: Link Rect: 115, 377, 153, 387 Annotation: Subtype: Link Rect: 284, 353, 322, 364 Annotation: Subtype: Link Rect: 326, 330, 364, 341 Annotation: Subtype: Link Rect: 127, 308, 164, 318 Annotation: Subtype: Link Rect: 192, 284, 229, 295 Annotation: Subtype: Link Rect: 127, 262, 164, 272 Annotation: Subtype: Link Rect: 458, 238, 495, 249 Annotation: Subtype: Link Rect: 129, 216, 166, 226 Annotation: Subtype: Link Rect: 240, 192, 278, 203 Annotation: Subtype: Link Rect: 145, 158, 183, 169 Annotation: Subtype: Link Rect: 350, 135, 387, 146 Annotation: Subtype: Link Rect: 231, 112, 268, 123 Annotation: Subtype: Link Rect: 329, 89, 367, 100 Annotation: Subtype: Link Rect: 275, 66, 313, 77 Page: Sequence: 15 Annotations: Annotation: Subtype: Link Rect: 273, 722, 310, 733 Annotation: Subtype: Link Rect: 192, 699, 229, 710 Annotation: Subtype: Link Rect: 485, 687, 522, 698 Annotation: Subtype: Link Rect: 451, 676, 489, 687 Annotation: Subtype: Link Rect: 95, 653, 133, 664 Annotation: Subtype: Link Rect: 237, 630, 275, 640 Annotation: Subtype: Link Rect: 210, 606, 248, 617 Annotation: Subtype: Link Rect: 409, 583, 446, 594 Annotation: Subtype: Link Rect: 452, 583, 488, 594 Annotation: Subtype: Link Rect: 393, 560, 430, 571 Annotation: Subtype: Link Rect: 437, 560, 473, 571 Annotation: Subtype: Link Rect: 131, 527, 168, 537 Annotation: Subtype: Link Rect: 175, 527, 211, 537 Annotation: Subtype: Link Rect: 303, 503, 341, 514 Annotation: Subtype: Link Rect: 59, 481, 96, 491 Annotation: Subtype: Link Rect: 501, 457, 539, 468 Annotation: Subtype: Link Rect: 410, 434, 448, 445 Annotation: Subtype: Link Rect: 476, 399, 514, 410 Annotation: Subtype: Link Rect: 286, 353, 324, 364 Annotation: Subtype: Link Rect: 266, 330, 303, 341 Annotation: Subtype: Link Rect: 273, 307, 311, 318 Annotation: Subtype: Link Rect: 175, 284, 213, 295 Annotation: Subtype: Link Rect: 457, 273, 494, 284 Annotation: Subtype: Link Rect: 324, 204, 361, 215 Annotation: Subtype: Link Rect: 367, 204, 403, 215 Annotation: Subtype: Link Rect: 95, 182, 133, 192 Annotation: Subtype: Link Rect: 125, 159, 162, 169 Annotation: Subtype: Link Rect: 519, 135, 557, 146 Annotation: Subtype: Link Rect: 399, 112, 437, 123 Checksum: a5d72189 Type: CRC32 Checksum: 2bd0ecd34ed6557e729442ab6c786f0f Type: MD5 Checksum: 16ac1585604d28b04ed8c457f762896ab968a872 Type: SHA-1