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Dufresne, Eric; Grier, David G; Spalding (December 2000), "Computer-Generated
Holographic Optical Tweezer Arrays",
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1222:
705:
1257:
1462:
818:
1012:{\displaystyle {\bar {A}}^{f}e^{i\phi _{n}^{f}}{\xrightarrow {iFFT}}{\bar {A}}_{n}^{k}e^{i\phi _{n}^{k}}.}
51:), which derives from a group of adaptive (input-output) algorithms, can be used. The AA algorithm is an
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against the convergence requirements. If the requirements are not met then mix the transformed
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69:(k space). This can be done when given the phase’s known counterparts, usually an observed
153:
Mix transformed amplitude with desired output amplitude and combine with transformed phase
8:
1409:
Röbel, Axel (2006), "Adaptive
Additive Modeling With Continuous Parameter Trajectories",
1231:
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607:{\displaystyle \varepsilon ={\sqrt {\left(I_{n}^{f}\right)^{2}-\left(I_{0}\right)^{2}}}.}
386:
183:
86:
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375:{\displaystyle A_{0}e^{i\phi _{n}^{k}}{\xrightarrow {FFT}}A_{n}^{f}e^{i\phi _{n}^{f}}}
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Compare transformed amplitude/intensity to desired output amplitude/intensity
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66:
40:
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uses error conversion, or the error between the desired and the theoretical
35:, and diffractive optical elements (DOEs) it is often important to know the
102:
The adaptive-additive algorithm was originally created to reconstruct the
1365:
1338:
118:
113:. Since then, the AA algorithm has been adapted to work in the fields of
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191:
82:
74:
70:
55:
52:
941:
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Presentation on optical tweezers and fabrication of AA algorithm.
62:
to calculate an unknown part of a propagating wave, normally the
39:
phase of an observed wave source. In order to reconstruct this
1472:
Iterative
Methods for Diffractive Optical Elements Computation
1506:
1411:
IEEE Transactions on Audio, Speech, and
Language Processing
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516:{\displaystyle I_{n}^{f}=\left(A_{n}^{f}\right)^{2},}
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1501:
Adaptive
Additive Synthesis for Non Stationary Sound
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162:Combine new phase with original input amplitude
867:is a percentage, defined on the interval 0 ≤
1470:Soifer, V. Kotlyar; Doskolovich, L. (1997),
109:of light intensity in the study of stellar
1447:
1364:
798:{\displaystyle {\bar {A}}_{n}^{f}=\left,}
73:(position space) and an assumed starting
1301:{\displaystyle {\bar {A}}_{n}^{k}=A_{0}}
144:Separate transformed amplitude and phase
138:Define input amplitude and random phase
1518:
194:and the starting phase of the wave in
174:For the problem of reconstructing the
165:Loop back to Forward Fourier Transform
1474:, Bristol, PA: Taylor & Francis,
1408:
1397:
852:{\displaystyle A^{f}={\sqrt {I_{0}}}}
1440:Adaptive-Additive Synthesis of Sound
159:Separate new amplitude and new phase
1510:University of Maryland College Park
1398:Grier, David G (October 10, 2000),
13:
1221:then the AA algorithm becomes the
1056:{\displaystyle {\bar {A}}_{n}^{k}}
14:
1542:
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1437:
874:Combine mixed amplitude with the
1353:Review of Scientific Instruments
92:
77:(k space). To find the correct
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757:
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1:
1344:
1147:{\displaystyle \phi _{n}^{k}}
1088:{\displaystyle \phi _{n}^{k}}
385:Then compare the transformed
250:{\displaystyle \phi _{n}^{k}}
630:{\displaystyle \varepsilon }
150:Check convergence conditions
132:
7:
1401:Adaptive-Additive Algorithm
1312:
420:with the desired intensity
45:Adaptive-Additive Algorithm
10:
1547:
1319:Gerchberg–Saxton algorithm
1223:Gerchberg–Saxton algorithm
169:
97:
1526:Digital signal processing
1189:
880:inverse Fourier transform
665:{\displaystyle A_{n}^{f}}
445:{\displaystyle I_{0}^{f}}
413:{\displaystyle I_{n}^{f}}
156:Inverse Fourier Transform
141:Forward Fourier Transform
1461:: CS1 maint: location (
1179:{\displaystyle n\to n+1}
117:by Soifer and Dr. Hill,
1423:10.1109/TSA.2005.858529
1154:. Increase loop by one
672:with desired amplitude
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190:-space). Assume the
186:in the image plane (
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1214:{\displaystyle a=1}
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125:by Dr. Grier, and
58:that utilizes the
16:In the studies of
1495:David Grier's Lab
1481:978-0-7484-0634-0
1383:10.1063/1.1344176
1271:
1039:
967:
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878:-space phase and
847:
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259:Fourier transform
176:spatial frequency
104:spatial frequency
64:spatial frequency
60:Fourier Transform
37:spatial frequency
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1417:(4): 1440–1453,
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123:optical tweezers
33:optical tweezers
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1535:
1531:Physical optics
1516:
1515:
1503:Dr. Axel Röbel.
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1339:Sound Synthesis
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1489:External links
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1486:
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1467:
1449:10.1.1.27.7602
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1406:
1395:
1346:
1343:
1342:
1341:
1336:
1334:Interferometry
1331:
1326:
1324:Fourier optics
1321:
1314:
1311:
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115:Fourier Optics
111:interferometry
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29:interferometry
18:Fourier optics
9:
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1445:
1442:, ICMC 1999,
1441:
1438:Röbel, Axel,
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93:The algorithm
90:
88:
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72:
68:
65:
61:
57:
54:
50:
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38:
34:
30:
27:
23:
19:
1509:
1471:
1439:
1414:
1410:
1400:
1356:
1352:
1186:and repeat.
1095:and combine
1021:
875:
873:
868:
864:
862:
809:
807:
616:
384:
266:
262:
261:the wave in
195:
187:
179:
173:
101:
49:AA algorithm
48:
44:
15:
1359:(3): 1810,
119:soft matter
87:intensities
1520:Categories
1345:References
1329:Holography
863:Note that
265:-space to
198:-space is
129:by Röbel.
1507:Hill Labs
1444:CiteSeerX
1269:¯
1165:→
1131:ϕ
1072:ϕ
1037:¯
1022:Separate
991:ϕ
965:¯
921:ϕ
900:¯
764:−
717:¯
639:amplitude
625:ε
572:−
534:ε
387:intensity
357:ϕ
299:ϕ
234:ϕ
192:amplitude
184:intensity
133:Algorithm
83:algorithm
75:amplitude
71:amplitude
56:algorithm
53:iterative
1457:citation
1391:14064547
1313:See also
939:→
452:, where
317:→
1371:Bibcode
269:space.
178:phase (
170:Example
98:History
26:stellar
1478:
1446:
1429:
1389:
1190:Limits
808:where
617:Check
1431:73476
1427:S2CID
1387:S2CID
1361:arXiv
1254:then
1122:with
871:≤ 1.
107:phase
79:phase
67:phase
41:phase
1476:ISBN
1463:link
1063:and
225:and
121:and
81:the
47:(or
43:the
1419:doi
1379:doi
1228:If
1195:If
1522::
1512:.]
1459:}}
1455:{{
1425:,
1415:14
1413:,
1385:,
1377:,
1369:,
1357:72
1355:,
882:.
699:.
89:.
31:,
24:,
20:,
1465:)
1434:.
1421::
1405:.
1394:.
1381::
1373::
1363::
1308:.
1294:0
1290:A
1286:=
1281:k
1276:n
1266:A
1242:0
1239:=
1236:a
1225:.
1209:1
1206:=
1203:a
1174:1
1171:+
1168:n
1162:n
1140:k
1135:n
1108:0
1104:A
1081:k
1076:n
1049:k
1044:n
1034:A
1007:.
1000:k
995:n
987:i
983:e
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972:n
962:A
952:T
949:F
946:F
943:i
930:f
925:n
917:i
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907:f
897:A
876:x
869:a
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859:.
843:0
839:I
833:=
828:f
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810:a
793:,
789:]
783:f
778:n
774:A
770:)
767:a
761:1
758:(
755:+
750:f
746:A
742:a
738:[
734:=
729:f
724:n
714:A
685:f
681:A
658:f
653:n
649:A
602:.
595:2
590:)
585:0
581:I
577:(
567:2
562:)
557:f
552:n
548:I
544:(
537:=
511:,
506:2
501:)
496:f
491:n
487:A
483:(
478:=
473:f
468:n
464:I
438:f
433:0
429:I
406:f
401:n
397:I
366:f
361:n
353:i
349:e
343:f
338:n
334:A
327:T
324:F
321:F
308:k
303:n
295:i
291:e
285:0
281:A
267:x
263:k
243:k
238:n
211:0
207:A
196:k
188:x
180:k
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