160:
reported by Waters whose major assumption originated with Rogers who recognized that a
Fresnel zone plate could be considered a special case of the hologram proposed by Gabor. But, as far as most of the object points were non-zero, the computational complexity of the point-source concept was much higher than in the Fourier transformation concept. Some researchers tried to overcome this drawback by predefining and storing all the possible elementary holograms using special data storage techniques because of the huge capacity that is needed in this case, others by using special hardware.
144:
images. Brown and
Lohmann introduced a technique to calculate computer generated holograms of 3D objects. Calculation of the light propagation from three-dimensional objects is performed according to the usual parabolic approximation to the Fresnel-Kirchhoff diffraction integral. The wavefront to be reconstructed by the hologram is, therefore, the superposition of the Fourier transforms of each object plane in depth, modified by a quadratic phase factor.
115:
equipment, real-time computation is tricky. There are many different methods for calculating the interference pattern for a CGH. In the following 25 years, many methods for computer-generated holograms were proposed in the fields of holographic information and computational reduction as well as in computational and quantization techniques. The algorithms can be categorized in two main concepts: Fourier transform holograms and point source holograms.
187:(SLM), abusing this term to include not only LCD displays or similar devices, but also films and masks. Basically, there are different types of SLMs available: Pure phase modulators (retarding the illuminating wave), pure amplitude modulators (blocking the illumination light), polarization modulators (influencing the polarization state of light) and SLMs which have the capability of combined phase/amplitude modulation.
203:
reasonable. So far two different approaches for amplitude-phase-modulation have been implemented. One is based on phase-only or amplitude-only modulation and consecutive spatial filtering, the other one is based on polarization holograms with variable orientation and magnitude of local birefringence. Holograms with a constraint, such as phase-only or amplitude-only, may be computed via algorithms such as the
271:
75:(1900–1979) to improve the resolving power on electron microscopes. An object is illuminated with a coherent (usually monochromatic) light beam; the scattered light is brought to interference with a reference beam of the same source, recording the interference pattern. CGH as defined in the introduction has broadly three tasks:
153:
171:. Ray tracing is perhaps the simplest method of computer generated holography to visualize. Essentially, the path length difference between the distance a virtual "reference beam" and a virtual "object beam" have to travel is calculated; this will give the relative phase of the scattered object beam.
159:
The second computational strategy is based on the point source concept, where the object is broken down in self-luminous points. An elementary hologram is calculated for every point source and the final hologram is synthesized by superimposing all the elementary holograms. This concept has been first
331:
Recently computer-generated holography has been extended in its usage beyond light optics, and applied in generating structured electron wavefunctions with a desired amplitude and phase profile. The computer generated holograms are designed by the interference of a target wave with a reference wave,
220:
exposure. Holographic displays are currently yet a challenge (as of 2008), although successful prototypes have been built. An ideal display for computer generated holograms would consist of pixels smaller than a wavelength of light with adjustable phase and brightness. Such displays have been called
130:
In the first one, the
Fourier transformation is used to simulate the propagation of each plane of depth of the object to the hologram plane. The Fourier transformation concept was first introduced by Byron R. Brown and Adolf W. Lohmann with the detour phase method leading to cell oriented holograms.
202:
Even if a fully complex phase/amplitude modulation would be ideal, a pure phase or pure amplitude solution is normally preferred because it is much easier to implement technologically. Nevertheless, for the creation of complicated light distribution simultaneous modulation of amplitude and phase is
143:
for reconstruction. So there are two steps in this process: computing the light field in the far observer plane, and then
Fourier transforming this field back to the lens plane. These holograms are called Fourier Based Holograms. First CGHs based on the Fourier transform could reconstruct only 2D
174:
Over the last three decades, both concepts have made remarkable progress improving computational speed and image quality. However, some technical restraints, like computation and storage capacity, still burden digital holography which makes real-time applications almost impossible with current
163:
In the point-source concept the major problem is the trade-off between data storage capacity and computational speed. In particular, algorithms that increase computational speed usually have much greater data storage requirements while algorithms that reduce data storage requirements have high
114:
Unfortunately, the researchers soon realized that there are noticeable lower and upper bounds in terms of computational speed and image quality and fidelity respectively. Wavefront calculations are computationally very intensive; even with modern mathematical techniques and high-end computing
34:. A computer-generated hologram can be displayed on a dynamic holographic display, or it can be printed onto a mask or film using lithography. When a hologram is printed onto a mask or film, it is then illuminated by a coherent light source to display the holographic images.
190:
In the case of pure phase or amplitude modulation, clearly quality losses are unavoidable. Early forms of pure amplitude holograms were simply printed in black and white, meaning that the amplitude had to be encoded with one bit of depth only. Similarly, the
215:
The third (technical) issue is beam modulation and actual wavefront reconstruction. Masks may be printed, resulting often in a grained pattern structure since most printers can make only dots (although very small ones). Films may be developed by
110:
Computer generated holograms offer important advantages over optical holograms since there is no need for a real object. Because of this breakthrough, a three-dimensional display was expected when the first algorithms were reported at 1966.
44:
Compared to classical holograms, computer-generated holograms have the advantage that the objects that one wants to show do not have to possess any physical reality, and can be completely synthetically generated.
332:
which could be, e.g. a plane-like wave slightly tilted in one direction. The holographic diffractive optical elements used are usually constructed out of thin membranes of materials such as silicon nitride.
781:
Clark, Matthew (1 September 1999). "Two-dimensional, three-dimensional, and gray-scale images reconstructed from computer-generated holograms designed by use of a direct-search method".
41:
suitable for observation. If holographic data of existing objects is generated optically and recorded and processed digitally, and subsequently displayed, this is termed CGH as well.
1703:
Ekberg M., Larsson M., Hård S. (1990). "Multilevel Phase
Holograms Manufactured by Electron-Beam Lithography". Opt. Lett. (OSA) 15 (10): 568-569. 0146-9592/90/100568-02$ 2.00/0
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1315:
M. Nakajima; H. Komatsu; Y. Mitsuhashi; T. Morikawa (1976). "Computer generated polarization holograms: phase recording by polarization effect in photodichroic materials".
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A coding technique suggested by Burch replaced the cell oriented holograms by point holograms and made this kind of computer generated holograms more attractive. In a
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Memmolo, Pasquale; Miccio, Lisa; Merola, Francesco; Paciello, Antonio; Embrione, Valerio; Fusco, Sabato; Ferraro, Pietro; Antonio Netti, Paolo (2014-01-01).
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Yaraş, Fahri; Kang, Hoonjong; Onural, Levent (29 September 2009). "Real-time phase-only color holographic video display system using LED illumination".
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Note that it is not always justified to make a strict distinction between these steps; however it helps the discussion to structure it in this way.
241:
VividQ provides software for real-time CGH devices, allowing for the generation of images with over 200 depth layers using standard computing power
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or more general optimisation algorithms such as direct search, simulated annealing or stochastic gradient descent using, for example, TensorFlow.
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P. J. Christopher; A. Kadis; G. S. D. Gordon; T. D. Wilkinson (2022). "HoloGen: An open-source toolbox for high-speed hologram generation".
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The term "computer-generated holography" has become used to denote the whole process chain of synthetically preparing holographic light
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H. Yang; E. S. Kim (1996). "Waveform-decomposition-based algorithm for horizontal parallax-only-display computer-generated holograms".
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1195:
J. L. Juárez-Peréz; A. Olivares- Peréz & L. R. Berriel-Valdos (1997). "Nonredundant calculations for creating
Fresnel holograms".
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the interference pattern onto a coherent light beam by technological means, to transport it to the user observing the hologram.
31:
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F. Wyrowski; R. Hauck & O. Bryngdahl (1987). "Computer-generated holography: hologram repetition and phase manipulation".
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Ultimately, computer-generated holography might expand upon all the roles of current computer-generated imagery. Holographic
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Cortical Cafe CGH Kit is a CGH related hobbyist site with instructions, source code, and a web-application for CGH creation.
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Once it is known what the scattered wavefront of the object looks like or how it may be computed, it must be fixed on a
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738:
D. Leseberg & C. Frère (1988). "Computer-generated holograms of 3-D objects composed of tilted planar segments".
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Ch. Slinger; C. Cameron; M. Stanley (Aug 2005), "Computer-Generated
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H. Yoshikawa; S. Iwase & T. Oneda (2001). "Fast
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1416:"Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulators"
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Currently, several companies and university departments are researching on the field of CGH devices:
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One of the more prevalent methods that can be used to generate phase-only holograms is the
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912:
J.J. Burch (1967). "A Computer
Algorithm for the Synthesis of Spatial Frequency Filters".
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Brown, Byron R.; Lohmann, Adolf W. (1966). "Complex spatial filtering with binary masks".
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M. Lucente (1993). "Interactive computation of holograms using a look-up table".
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D. Leseberg & O. Bryngdahl (1984). "Computer-generated rainbow holograms".
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W.H. Lee (1970). "Sampled
Fourier Transform Hologram Generated by Computer".
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139:. This is usually achieved by using the Fourier transforming properties of a
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Sahin, Erdem; Stoykova, Elena; Mäkinen, Jani; Gotchev, Atanas (2020-03-20).
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1022:"Gabor diffraction microscopy: the hologram as a generalized zone-plate"
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displays might be used for a wide range of applications, for example
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1465:"Full phase and amplitude control in computer-generated holography"
826:"Investigation on specific solutions of Gerchberg–Saxton algorithm"
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computational complexity (though some optimizations are possible).
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1267:"Computer-generated holograms: A simplified ray-tracing approach"
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989:"Holographic Image synthesis utilizing theoretical methods"
26:) is a technique that uses computer algorithms to generate
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Another concept which leads to point source CGHs is the
351:"Computer-Generated Holograms for 3D Imaging: A Survey"
135:
hologram the reconstruction of the image occurs in the
1414:
V. Arrizon; G. Mendez; D. Sanchez-de-La-Llave (2005).
1385:"The Kinoform: A New Wavefront Reconstruction Device"
1383:
L. B. Lesem; P. M. Hirsch; J. A. Jordan, Jr. (1969).
585:"The Kinοform: A New Wavefront Reconstruction Device"
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2012:
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Thick-film dielectric electroluminescent technology
1911:
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583:L.B. Lesem; P.M. Hirsch & J.A. Jordan (1969).
542:L.B. Lesem; P.M. Hirsch & J.A. Jordan (1968).
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492:
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2286:Comparison of CRT, LCD, plasma, and OLED displays
544:"Computer synthesis of holograms for 3-D display"
1265:A. D. Stein; Z. Wang; J. S. Leigh, Jr. (1992).
871:Liu, Shujian; Takaki, Yasuhiro (January 2020).
1722:
8:
88:the wavefront data, preparing it for display
1940:Surface-conduction electron-emitter display
299:. Unsourced material may be challenged and
1851:Active-Matrix Organic light-emitting diode
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1612:Molecular Speculations on Global Abundance
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1463:M. Fratz; P. Fischer; D. M. Giel (2009).
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319:Learn how and when to remove this message
247:has developed the "Holovideo" CGH display
1389:IBM Journal of Research and Development
948:IBM Journal of Research and Development
592:IBM Journal of Research and Development
341:
1582:gsdgordon/hologramGenerationTensorflow
939:B.R. Brown & A.W. Lohmann (1969).
67:is a technique originally invented by
56:(CAD), gaming, and holographic video.
941:"Computer-generated Binary Holograms"
195:is a pure-phase encoding invented at
30:. It involves generating holographic
7:
1987:Ferroelectric liquid crystal display
1688:"CorticalCafe Free Desktop Software"
1670:"The Holovideo Page by Mark Lucente"
297:adding citations to reliable sources
2061:Light-emitting electrochemical cell
16:Three-dimensional imaging technique
2260:Large-screen television technology
82:of the virtual scattered wavefront
14:
1934:Organic light-emitting transistor
2297:Comparison of display technology
830:Optics and Lasers in Engineering
269:
1928:Electroluminescent Quantum Dots
1520:Computer Physics Communications
1358:W. Lauterborn; T. Kurz (2002).
850:10.1016/j.optlaseng.2013.06.008
120:Gerchberg-Saxton (GS) algorithm
1999:Laser-powered phosphor display
1579:G. S. D. Gordon (2020-04-21),
1:
2265:Optimum HDTV viewing distance
2255:History of display technology
2143:Computer-generated holography
1074:Journal of Electronic Imaging
253:have prototyped a CGH display
20:Computer-generated holography
1845:Organic light-emitting diode
1839:Light-emitting diode display
1139:10.1016/0010-4655(95)00125-5
175:standard computer hardware.
229:is required to build them.
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2055:Vacuum fluorescent display
1779:Electroluminescent display
1362:(2nd ed.). Springer.
205:Gerchberg-Saxton algorithm
199:in the early days of CGH.
2294:
1902:Liquid crystal on silicon
1550:10.1016/j.cpc.2021.108139
1252:10.1007/s10043-001-0331-y
548:Communications of the ACM
2093:Fourteen-segment display
1896:Digital Light Processing
1608:. In BC Crandall (ed.).
126:Fourier transform method
2099:Sixteen-segment display
1785:Rear-projection display
914:Proceedings of the IEEE
185:spatial light modulator
1946:Field-emission display
1861:Liquid-crystal display
1441:10.1364/opex.13.007913
926:10.1109/PROC.1967.5620
725:10.1364/JOSAA.4.000694
225:. Further progress in
156:
148:Point source holograms
2083:Eight-segment display
2077:Seven-segment display
1606:"Phased Array Optics"
561:10.1145/364096.364111
358:ACM Computing Surveys
155:
106:Wavefront computation
54:computer-aided design
32:interference patterns
2205:Display capabilities
2088:Nine-segment display
1790:Plasma display panel
1489:10.1364/ol.34.003659
1337:10.1364/ao.15.001030
1271:Computers in Physics
1209:10.1364/AO.36.007437
1174:10.1364/OL.21.000510
1119:Comput. Phys. Commun
1020:G.L. Rogers (1950).
803:10.1364/ao.38.005331
760:10.1364/AO.27.003020
682:10.1364/AO.23.002441
455:10.1364/AO.48.000H48
293:improve this section
251:SeeReal Technologies
179:Generated Holography
2234:See-through display
2138:Holographic display
1816:Quantum dot display
1542:2022CoPhC.27008139C
1481:2009OptL...34.3659F
1432:2005OExpr..13.7913A
1401:10.1147/rd.132.0150
1329:1976ApOpt..15.1030N
1283:1992ComPh...6..389S
1244:2001OptRv...8..331Y
1166:1996OptL...21..510Y
1131:1996CoPhC..93...13I
1086:1993JEI.....2...28L
1038:1950Natur.166..237R
987:J.P.Waters (1968).
960:10.1147/rd.132.0160
890:10.3390/app10124283
842:2014OptLE..52..206M
795:1999ApOpt..38.5331C
752:1988ApOpt..27.3020L
717:1987JOSAA...4..694W
674:1984ApOpt..23.2441L
631:10.1364/AO.9.000639
604:10.1147/rd.132.0150
521:10.1364/AO.5.000967
513:1966ApOpt...5..967B
447:2009ApOpt..48H..48Y
413:10.1109/mc.2005.260
223:phased array optics
2276:Color Light Output
2270:High Dynamic Range
2072:Dot-matrix display
2067:Lightguide display
1738:Display technology
1526:(108139): 108139.
705:J. Opt. Soc. Am. A
261:In electron optics
169:ray tracing method
157:
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2229:Always-on display
2020:Electromechanical
2008:
2007:
1631:978-0-262-03237-7
1475:(23): 3659–3661.
1426:(20): 7913–7927.
1369:978-3-540-43933-2
1203:(29): 7437–7443.
1104:10.1117/12.133376
1006:10.1063/1.1754630
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746:(14): 3020–3024.
668:(14): 2441–2447.
364:(2): 32:1–32:35.
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133:Fourier Transform
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2281:Flexible display
2243:Related articles
2123:Autostereoscopic
1822:Electronic paper
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1238:(5): 331–335.
1232:Optical Review
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1095:10.1.1.51.4513
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954:(2): 160–168.
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783:Applied Optics
773:
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711:(4): 694–698.
695:
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625:(3): 639–643.
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598:(2): 150–155.
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501:Applied Optics
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441:(34): H48-53.
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1652:"VividQ Home"
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969:on 2012-02-24
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278:This section
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245:MIT Media Lab
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141:positive lens
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2191:Transparency
2164:Static media
2142:
2118:Stereoscopic
1691:
1682:
1673:
1664:
1655:
1646:
1635:. Retrieved
1611:
1596:
1586:, retrieved
1581:
1574:
1523:
1519:
1513:
1472:
1468:
1458:
1423:
1420:Opt. Express
1419:
1409:
1392:
1388:
1378:
1359:
1353:
1320:
1316:
1310:
1299:. Retrieved
1295:the original
1274:
1270:
1260:
1235:
1231:
1225:
1200:
1196:
1190:
1157:
1153:
1147:
1125:(1): 13–20.
1122:
1118:
1112:
1077:
1073:
1029:
1025:
1015:
996:
992:
982:
971:. Retrieved
964:the original
951:
947:
934:
917:
913:
907:
883:(12): 4283.
880:
876:
866:
833:
829:
819:
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776:
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708:
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612:
595:
591:
578:
551:
547:
537:
507:(6): 967–9.
504:
500:
438:
434:
428:
407:(8): 46–53,
404:
400:
394:
361:
357:
344:
330:
315:
306:
291:Please help
279:
236:
233:Applications
214:
201:
189:
182:
173:
168:
166:
162:
158:
129:
117:
113:
109:
101:
95:
91:
85:
79:
73:Dennis Gabor
63:
47:
43:
36:
23:
19:
18:
2155:Fog display
2128:Multiscopic
2045:Fiber-optic
1957:Quantum dot
1656:vivid-q.com
1620:. pp.
836:: 206–211.
464:11693/22545
80:Computation
2316:Holography
2196:Laser beam
2150:Volumetric
2110:3D display
2050:Nixie tube
2030:Split-flap
1915:generation
1889:Blue Phase
1809:generation
1756:generation
1637:2007-02-18
1588:2024-01-20
1533:2008.12214
1301:2010-09-14
973:2009-06-17
336:References
96:Modulating
71:physicist
65:Holography
39:wavefronts
2250:Scan line
2224:DisplayID
2181:Neon sign
2171:Monoscope
2013:Non-video
1774:Jumbotron
1618:MIT Press
1566:221340546
1558:0010-4655
1469:Opt. Lett
1317:Appl. Opt
1197:Appl. Opt
1154:Opt. Lett
1090:CiteSeerX
1080:: 28–34.
899:2076-3417
858:0143-8166
740:Appl. Opt
662:Appl. Opt
619:Appl. Opt
386:215854874
378:0360-0300
280:does not
137:far field
69:Hungarian
28:holograms
2310:Category
2133:Hologram
2040:Eggcrate
2025:Flip-dot
1971:display
1952:Laser TV
1923:microLED
1853:(AMOLED)
1807:Current
1763:Eidophor
1604:(1996).
1497:19953153
1450:19498821
1345:20165114
1217:18264254
1182:19865455
1056:15439257
811:18324035
768:20531880
690:18213016
647:15902468
639:20076253
570:18707299
529:20048989
473:19956301
401:Computer
193:kinoform
86:Encoding
60:Overview
50:computer
2217:CEA-861
1847:(OLED)
1832:Gyricon
1674:mit.edu
1622:147–160
1538:Bibcode
1505:5726900
1477:Bibcode
1428:Bibcode
1325:Bibcode
1279:Bibcode
1240:Bibcode
1162:Bibcode
1127:Bibcode
1082:Bibcode
1034:Bibcode
838:Bibcode
791:Bibcode
748:Bibcode
713:Bibcode
670:Bibcode
509:Bibcode
481:5890199
443:Bibcode
421:7394380
301:removed
286:sources
2101:(SISD)
1995:(TDEL)
1989:(FLCD)
1936:(OLET)
1904:(LCoS)
1863:(LCD)
1841:(LED)
1818:(QLED)
1792:(PDP)
1628:
1602:Wowk B
1564:
1556:
1503:
1495:
1448:
1366:
1343:
1215:
1180:
1092:
1054:
1026:Nature
897:
856:
809:
766:
688:
645:
637:
568:
527:
479:
471:
419:
384:
376:
2272:(HDR)
2095:(FSD)
2079:(SSD)
2063:(LEC)
2057:(VFD)
2001:(LPD)
1948:(FED)
1942:(SED)
1913:Next
1898:(DLP)
1827:E Ink
1781:(ELD)
1770:(CRT)
1562:S2CID
1528:arXiv
1501:S2CID
967:(PDF)
944:(PDF)
643:S2CID
588:(PDF)
566:S2CID
477:S2CID
417:S2CID
382:S2CID
354:(PDF)
218:laser
2212:EDID
2034:Vane
1980:TMOS
1975:IMoD
1969:MEMS
1796:ALiS
1754:Past
1626:ISBN
1554:ISSN
1493:PMID
1446:PMID
1364:ISBN
1341:PMID
1213:PMID
1178:PMID
1052:PMID
895:ISSN
854:ISSN
807:PMID
764:PMID
686:PMID
635:PMID
525:PMID
469:PMID
374:ISSN
284:any
282:cite
1884:LED
1877:IPS
1867:TFT
1546:doi
1524:270
1485:doi
1436:doi
1397:doi
1333:doi
1287:doi
1248:doi
1205:doi
1170:doi
1135:doi
1100:doi
1042:doi
1030:166
1001:doi
956:doi
922:doi
885:doi
846:doi
799:doi
756:doi
721:doi
678:doi
627:doi
600:doi
556:doi
517:doi
459:hdl
451:doi
409:doi
366:doi
295:by
197:IBM
24:CGH
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
