Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left"> </td><td class="align_center">N-LUT</td><td class="align_center">Proposed algorithm</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">Multiplicative computational complexity</td><td class="align_center"><span style="width: 15.994ptpx;"><svg height="11.7978pt" id="M87" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 15.994 11.7978" width="15.994pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="839" vert-adv-y="839" xpluscharwidth="10.907"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.91,-5.741)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="15.34168539"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 48.2547ptpx;"><svg height="11.7978pt" id="M88" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 48.2547 11.7978" width="48.2547pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480" xpluscharwidth="6.24"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480" xpluscharwidth="12.48"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.48,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480" xpluscharwidth="18.72"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,21.696,0)"><path d="M471 153C471 170 463 194 452 212C400 220 373 229 322 255C373 281 400 290 452 298C463 316 471 339 471 357C456 366 431 371 410 370C377 329 356 310 308 279C311 336 317 364 336 413C326 432 310 451 294 459C279 451 262 432 252 413C271 364 277 336 280 279C232 310 211 329 178 370C157 371 132 367 117 357C117 340 125 316 136 298C188 290 215 281 266 255C215 229 188 220 136 212C125 194 117 171 117 153C132 144 157 139 178 140C211 181 232 200 280 231C277 174 271 146 252 97C262 78 278 59 294 51C309 59 326 78 336 97C317 146 311 174 308 231C356 200 377 181 410 140C431 139 456 143 471 153Z" id="g113-43"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587" xpluscharwidth="29.327"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,32.232,0)"><path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="839" vert-adv-y="839" xpluscharwidth="43.138999999999996"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,43.142,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="47.57368539"></glyph.data></g></svg></span></td></tr><tr><td class="align_left">Additive computational complexity</td><td class="align_center"><span style="width: 15.994ptpx;"><svg height="11.7978pt" id="M89" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 15.994 11.7978" width="15.994pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="839" vert-adv-y="839" xpluscharwidth="10.907"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.91,-5.741)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="15.34168539"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 15.994ptpx;"><svg height="11.7978pt" id="M90" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.5914 15.994 11.7978" width="15.994pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="839" vert-adv-y="839" xpluscharwidth="10.907"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.91,-5.741)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="15.34168539"></glyph.data></g></svg></span></td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Computational complexity for a grayscale image.

Mathematical Problems in Engineering

tab3

Table 3

Table 3: Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms 