添付資料 - TOKYO TECH OCW

6.4.2 䝩䝻䜾䝷䝣䜱䞊䛾グ㘓䛸෌⏕
Hologram
Reconstructing
illumination
Reference beam
ග⏬ീᕤᏛ
Optical imaging and image processing
(XIII)
Object
Object beam
Recording
Reconstructed
light
Virtual image
Reconstruction
• Reconstructing wavefront of light wave
• ග䛾䛂Ἴ㠃䛃䜢෌⏕
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5
6.4 䝩䝻䜾䝷䝣䜱䞊
Reconstruction of real image
6.4.1 䝩䝻䜾䝷䝣䜱䞊䛸䛿
• Ἴ㠃䛾グ㘓䞉෌⌧
Reference
beam
– ❧యീ䛾グ㘓䞉⾲♧
– ගィ Reconstructed
light
• ග䛾㐍⾜᪉ྥ䚸䝡䞊䝮ᙧ≧➼䜢ไᚚ
– ᅇᢡගᏛ⣲Ꮚ
– ග᝟ሗฎ⌮
• Ἴ㛗ศᩓ䚸Ἴ㛗㑅ᢥ
object
– ගᏛ⣲Ꮚ
– ⓑⰍග෌⏕❧యീ⾲♧
Object
beam
• 㧗ᐦᗘグ㘓䞉෕㛗ᛶ
– ග䝯䝰䝸
Recording
Real image
Conjugate wave
with respect to reference beam
Reconstruction
• ୖグ≉ᚩ䛾⤌䜏ྜ䜟䛫
– 䝉䜻䝳䝸䝔䜱䞊༳ๅ䠄ഇ㐀㜵Ṇ䠅
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Reconstruction of hologram
ᖹ㠃Ἴྠኈ䛾ᖸ΅䛸ᅇᢡ
•
• m=1䛾Ἴ㠃䠖O䛸ྠ䛨Ἴ㠃
Reconstructing wave U(r) = UR(r) TA
= t1 UR(r) T0 + t1 UR(r) {| US(r) |2 + | UR(r) |2 }
+ t1 US(r) | UR(r) |2
+ t1 US(r)* UR(r)2
= U0'(r) + UD'(r) + UC'(r)
UD'(r) = t1 US(r) | UR(r) |2
→
O
= t1 B2 US(r)
Object wave is reconstructed (Virtual image)
• Conjugate image reconstruction
R
-1
C
U(r) = UR(r)* TA
= U0"(r) + UC"(r) + UD"(r)
0
O’
グ㘓
෌⏕
UD"(r) = t1 US(r)* | UR(r) |2
= t1 B2 US(r) = t1 B2 A(r) exp { j I(r) }
1
→
(188)
Conjugate wave is reconstructed (Real image)
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6.4.3 䝩䝻䜾䝷䝣䜱䞊䛾Ṕྐ
Recording of hologram
• Interference of two wavefronts
I(r) = < | USc(r, t) + URc(r, t) |2 >
• Complex amplitude
– Object wave US(r) = A(r) exp { j I(r) }
– Reference wave UR(r) = B exp { j k x sinT }
• For coherent light
I(r) = | US(r) + UR(r)
|2
1948
䝩䝻䜾䝷䝣䜱䞊䛾Ⓨ᫂ (Dennis Gabor)
䜲䞁䝷䜲䞁ᆺ䠈㟁Ꮚ㢧ᚤ㙾䛾᪂䛧䛔ཎ⌮
1960
ୡ⏺ึ䛾䝺䞊䝄䞊Ⓨ᣺ (T. Maiman)
䠄Ruby Laser, 䝩䝻䜾䝷䝣䜱䞊䛾Ⓨᒎ䜈䛾
ዎᶵ䠅
1962
1963
䜸䝣䜰䜽䝅䝇ᆺ䝩䝻䜾䝷䝮 (E. Leith and J.
Upatnieks)
㏻ಙ⌮ㄽ䛾ᑟධ
䝺䞊䝄䞊෌⏕䛻䜘䜛❧యീ⾲♧
1963
཯ᑕయ✚ᆺ䝩䝻䜾䝷䝮 (Y. N. Denisyuk)
ⓑⰍග෌⏕཯ᑕᆺ
1964
ගᏛⓗ䝬䝑䝏䝖䝣䜱䝹䝍䝸䞁䜾 (A. Vander-Lugt)
ග᝟ሗฎ⌮䛻䜘䜛䝟䝍䞊䞁䝬䝑䝏䞁䜾
1966
䝩䝻䜾䝷䝮䛾䝔䝺䝡ఏ㏦ (L. H. Enloe et. al.)
㟼Ṇ⏬ᩥᏐ䝟䝍䞊䞁䛾䝩䝻䜾䝷䝮ఏ㏦
1967
ィ⟬ᶵྜᡂ䝩䝻䜾䝷䝮 (A. W. Lohmann and D. P. 䝥䝻䝑䝍䞊䛷ฟຊ䛧䛯䜒䛾䜢෗┿⦰ᑠ
Paris)
1968
䝩䝻䜾䝷䝣䜱䝑䜽䞉䝇䝔䝺䜸䜾䝷䝮 (J. T.
McCrickerd and N. George)
1969
䝺䜲䞁䝪䜴䝩䝻䜾䝷䝮 (S. A. Benton)
ⓑⰍග෌⏕㏱㐣ᆺ䠄Ỉᖹ᪉ྥどᕪ䛾䜏䠅
1973
䝬䝹䝏䝥䝺䝑䜽䝇䝩䝻䜾䝷䝮 (L. Cross)
ⓑⰍග෌⏕෇⟄ᆺ䝩䝻䜾䝷䝣䜱䝑䜽䝇䝔䝺
䜸䜾䝷䝮
1975
䜶䞁䝪䝇䝩䝻䜾䝷䝮ᐇ⏝໬ (F. Iwata)
㔞⏘ᆺ䝩䝻䜾䝷䝮ᢏ⾡䛾☜❧
1976
Museum of Holography 㛤タ
New York, 1992 㛢㤋
1990
䝩䝻䜾䝷䝣䜱䝑䜽䞉䝡䝕䜸 (P. St.-Hilaire, et. al.)
㡢㡪ගᏛኚㄪჾ䜢⏝䛔䛯㟁Ꮚ䝩䝻䜾䝷
䝣䜱䞊
= | US(r) |2 + | UR(r) |2 + US(r) UR(r)* + US(r)* UR(r)
= A(r) 2 + B 2 + A(r) B exp { j ( I (r) kx sin T ) }
+ A(r) B exp { j ( I (r) kx sin T ) }
• Amplitude transmittance of recording medium
– When it is linear to exposed light energy
TA = T0 + t1 I( r )
8
䝺䞊䝄䞊෌⏕䛻䜘䜛ከどⅬ⏬ീ䛾䝩䝻䜾
䝷䝮
11
䝩䝻䜾䝷䝮䛾ᅇᢡຠ⋡
6.4.4 䝩䝻䜾䝷䝣䜱䞊䛾ᇶᮏᢏ⾡
•
䝩䝻䜾䝷䝮䛾✀㢮
ᅇᢡຠ⋡
K = Io / Ii
Kd • ᣺ᖜ䝩䝻䜾䝷䝮
• ≀య䛸䛾఩⨨㛵ಀ䠖䜲䝯䞊䝆ᆺ䚸䝣䝺䝛䝹ᆺ䚸䝣䞊䝸䜶ኚ
᥮䝩䝻䜾䝷䝮
• ኚㄪ᪉ᘧ䠖᣺ᖜᆺ䚸఩┦ᆺ䚸」ྜᆺ
• ங๣䛾ཌ䛥
• ほᐹ᪉ᘧ䠖཯ᑕᆺ䚸㏱㐣ᆺ
• ෌⏕᪉ᘧ䠖䝺䞊䝄෌⏕䚸ⓑⰍග෌⏕
• 䝩䝻䜾䝷䝣䜱䝑䜽䞉䝇䝔䝺䜸䜾䝷䝮
• ィ⟬ᶵྜᡂ䝩䝻䜾䝷䝮䠄CGH䠅
Kd ఩┦࣍ࣟࢢ࣒ࣛ
• ཌ࠸఩┦࣍ࣟࢢ࣒ࣛ
Ka
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≀య䛸䛾఩⨨㛵ಀ
ཌ䛔䝩䝻䜾䝷䝮
• Ἴ㛗㑅ᢥᛶ
Bragg䛾᮲௳
• 䜲䝯䞊䝆ᆺ䝩䝻䜾䝷䝮
• ゅᗘ㑅ᢥᛶ
• 䝣䝺䝛䝹ᆺ䝩䝻䜾䝷䝮
• 䝣䞊䝸䜶ኚ᥮䝩䝻䜾䝷䝮
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グ㘓䠄཯ᑕᆺ䠅
෌⏕
19
䝕䜱䝇䝥䝺䜲⏝䝩䝻䜾䝷䝮
䝩䝻䜾䝷䝮䛾」〇
• 䝺䞊䝄෌⏕䝩䝻䜾䝷䝮
– 䝣䝺䝛䝹䝩䝻䜾䝷䝮
• ⓑⰍග෌⏕䝩䝻䜾䝷䝮
1.
䜶䞁䝪䝇ᆺ䝩䝻䜾䝷䝮
2.
䝁䞁䝍䜽䝖䝁䝢䞊
1. 䜲䝯䞊䝆䝩䝻䜾䝷䝮
2. 䝺䜲䞁䝪䜴䝩䝻䜾䝷䝮
• 1-step䚸2-step
3. 䝸䝑䝥䝬䞁䝩䝻䜾䝷䝮䠄Denisyuk 䝩䝻䜾䝷䝮䠅
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Applications of holography
䜹䝷䞊䝩䝻䜾䝷䝮
• 3D display
– Publishing, Security, Package, Interior, Advertisement, Education
– Printing of 3D image data, Medical 3D displays
1. 䝺䞊䝄෌⏕ᆺ
2. ⓑⰍග෌⏕ᆺ
• Security Printing
– Banknote (10k, 5k bills), Credit card, Package of digital media
• Optical measurement
– 2.1 䝺䜲䞁䝪䜴ᆺ
– 2.2 ཯ᑕయ✚ᆺ䠄䝕䝙䝅䝳䞊䜽ᆺ䚸䝸䝑䝥䝬䞁ᆺ䠅
– Holographic interferometer
– Shape, Motion, Vibration, Refractive index, birefrengence
– Digital holography (using CCD cameras instead of photographic recording
media)
3. 䜹䝷䞊䞉䝩䝻䜾䝷䝣䜱䝑䜽䞉䝇䝔䝺䜸䜾䝷䝮
– 2.1 䝺䜲䞁䝪䜴ᆺ
– 2.2 ཯ᑕయ✚ᆺ䠄䝕䝙䝅䝳䞊䜽ᆺ䚸䝸䝑䝥䝬䞁ᆺ䠅
• Optical information processing, Optical memory
– Holographic matched filter, Holographic memory
• Holographic Optical Element (HOE)
– Lens, Mirror, Diffuser, HUD, Projector, LCD
– Screen, Dispersion element, Optical interconnection
– Optical pickup, Scanner, Bar-code reader, Laser–beam printer, Beam shaping
• Imaging (Microscopy)
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– Electron holography, X-ray holography
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䝩䝻䜾䝷䝣䜱䛾≉ᚩ
䝕䜱䝇䝥䝺䜲䝩䝻䜾䝷䝮ᢏ⾡
• Ἴ㠃䛾グ㘓䞉෌⏕
䠏ḟඖ᝟ሗ䛾ྲྀᚓ
఩┦᝟ሗ䛾ྲྀᚓ
• ග⥺ไᚚᶵ⬟
• ീ෌⏕ᶵ⬟
• Ἴ㠃ไᚚᶵ⬟
• 㧗⢭ᗘ
• ⷧ䛔
• ㏱᫂
• Ⰽ䛾ศ㞳䞉ྜᡂ
• ⓑⰍග෌⏕
– 䝺䜲䞁䝪䜴ᆺ䚸䝸䝑䝥䝬䞁ᆺ䚸䜲䝯䞊䝆ᆺ
• ᯫ✵≀య䚸ィ⟬ᶵ䛸䛾⼥ྜ
– 䝩䝻䜾䝷䝣䜱䝑䜽䞉䝇䝔䝺䜸䜾䝷䝮䚸CGH
• 㟁Ꮚ䝩䝻䜾䝷䝣䜱䞊
– AO⣲Ꮚ䚸ᾮᬗ䝟䝛䝹➼䜢⏝䛔䛯ື⏬䝩䝻䜾䝷䝣䜱䞊
• 䝁䝢䞊
– 䜶䞁䝪䝇䝩䝻䜾䝷䝮䚸䝩䝻䜾䝷䝮䝁䝢䞊ᢏ⾡
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3-D image
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䝕䜱䝇䝥䝺䜲䝩䝻䜾䝷䝮䛾ᛂ⏝
Different colors
•
•
•
•
•
•
•
Hologram
Hologram
• ↷᫂ 䠉䜶䝑䝆䝸䝑䝖
• ᧜ᙳ 䠉 䝩䝻䜾䝷䝣䜱䞊䜹䝯䝷
• 䜹䝷䞊໬
(a)
(c)
ฟ∧
䝉䜻䝳䝸䝔䜱
䝟䝑䜿䞊䝆
䜲䞁䝔䝸䜰䚸⿦㣭䚸ᗈ࿌
ᩍ⫱
3ḟඖ⏬ീ䛾䝥䝸䞁䝍
་⏝⏬ീ䛾❧య⾲♧
illumination
Hologram
Hologram
(b)
(d)
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䠉ⱁ⾡䠉
ᮾᕤ኱䛸䝩䝻䜾䝷䝣䜱䞊
Setsuko Ishii’s work has debuted as permanent
installation at Tokyo Institute of Technology
Centennial Hall at Tokyo Institute of Technology,
Ookayama Campus (Tokyo, Japan)
Lobby
Murmur of Aqueus, 1995
Multicolor rainbow hologram, Glass, Stainless steel mirror, water
Hologram size ~ 3m㽢2m (1m㽢2m 㽢 3)
Opening Ceremony : 23 January 2003
→1/21
䠉ᮾᕤ኱༤≀㤋䠉
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䝩䝻䜾䝷䝣䜱䞊ᖸ΅ィ ᅜෆእ䛾䝩䝻䜾䝷䝣䜱䞊䛾཰㞟䞉ಖᏑ䞉ᒎ♧䜢⾜䛖
•
•
•
•
ኚ఩ィ ᣺ືィ ᙧ≧ィ ᒅᢡ⋡ศᕸィ 䠎㔜㟢ගἲ
ᐇ᫬㛫ἲ
᫬㛫ᖹᆒἲ
䝇䝖䝻䝪ἲ
఩┦䝅䝣䝖ᖸ΅⣔
஧Ἴ㛗ἲ
㠀◚ቯ᳨ᰝ
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ᾮᬗ䝥䝻䝆䜵䜽䝍ගᏛ⣔
䝩䝻䜾䝷䝣䜱䝑䜽ගᏛ⣲Ꮚ
• ≉ᚩ
Holographic Optical Element (HOE)
– Ἴ㛗ศᩓ→Ⰽ䛾⏕ᡂ䚸㧗ຠ⋡໬
– య✚ᆺ䝩䝻䜾䝷䝮→㧗ᅇᢡຠ⋡
– ගἼไᚚ䠄䝺䞁䝈ᶵ⬟䠅→ගᏛ⣔䛾⡆༢໬
• 䝺䞁䝈䞉䝭䝷䞊
• ཯ᑕᯈ
• ௦᭰ᢏ⾡
– HUD䚸ᾮᬗ䝥䝻䝆䜵䜽䝍䚸཯ᑕᆺLCD➼
– Ⰽ䝣䜱䝹䝍䚸䝬䜲䜽䝻䝺䞁䝈䜰䝺䜲
• 䝥䝻䝆䜵䜽䝍⏝䝇䜽䝸䞊䞁
• ศග⣲Ꮚ
• ග䜲䞁䝍䞊䝁䝛䜽䝖
White light source
Field lens
Projection lens
– 䝏䝑䝥㛫ග᥋⥆䚸ග䝢䝑䜽䜰䝑䝥
• 䝇䜻䝱䝘
HOE
– 䝞䞊䝁䞊䝗䝸䞊䝎䚸䝺䞊䝄䝥䝸䞁䝍
• 䝡䞊䝮ᩚᙧ ➼
LCD panel
Screen
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ᦠᖏ㟁ヰ䞉PDA
HUD(Head-up display)
• ཯ᑕᯈ
• ≉ᚩ
– どᇦゅไ㝈→㧗㍤ᗘ
– Ἴ㛗㑅ᢥᛶ→Ⰽ
Virtual image
• ㏱᫂䠄఩┦ᆺ䝩䝻䜾䝷䝮䠅䠖
• 䝞䝑䜽䝷䜲䝖䛿㏱㐣
• ௦᭰ᢏ⾡
• Features
– ᣑᩓᯈ
– Virtual image formation
– Only the light of specific wavelength is reflected, others are
transmitted. (High-transmittance)
– Thin device (Sandwich between glasses)
• Substitution of concave half-mirror, Fresnel lens, and
Dichroic mirror
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