SIGGRAPH Asia 2020 勉強会 "Computational Holography"

$PNQVUBUJPOBM)PMPHSBQIZ 4*((3"1)"TJB5FDIOJDBM1BQFST

3 %JTUSJCVUJPOPG5PEBZT1SFTFOUBUJPO /FVSBM)PMPHSBQIZ -FBSOFE)BSEXBSFJOUIFMPPQ )0& 3FOEFSJOH4QFDLMF

/FVSBM)PMPHSBQIZXJUI$BNFSBJOUIFMPPQ 5SBJOJOH%JTQMBZT :*'"/1&/( 46:&0/$)0* /*5*4)1"%."/"#"/ (03%0/8&5;45&*/ 4UBOGPSE6OJWFSTJUZ

લఏ஌ࣝͷڞ༗

6 • ޫͷճંɾׯবʹΑͬͯɼ̏࣍ݩʹݟ͑Δޫͷ࠶ੜɾอଘٕज़ʢྫɿࠨਤʣ • Ұൠతʹ͸ӈਤͷΑ͏ʹϨʔβʔޫΛࡱӨΦϒδΣΫτͱه࿥༻ͷϓϨʔτʹ౰ͯͯࡱ૾͢Δ લఏ஌ࣝ ϗϩάϥϜͬͯͳΜͰ͔͢ʁ https://www.litiholo.com/hologram-kits.html ʢൃද࣌লུʣ

7 • ۭؒޫมௐثʢ4-.ʣͱݺ͹ΕΔӷথ੍ޚػࡐͷൃలʹΑΓɼػցతʹϗϩάϥϜΛ࡞੒ɾ੍ޚ͢Δ͜ͱ͕Մೳͱͳͬͯ ͖͍ͯΔ • ݴͬͯ͠·͑͹ɼ4-.ͱ͍͏֎෦σΟεϓϨΠʹͳΜΒ͔ͷύλʔϯΛදࣔ͢Δͱ ̏࣍ݩը૾ΛදࣔͰ͖Δͱ͍͏͜ͱ • Αͬͯɼ͜ͷ4-.ʹͲΜͳύλʔϯΛදࣔ͢Δ͔Λܭࢉ͢Δ͜ͱ͕ͱͯ΋ॏཁʂʂ ࠷ۙͷϗϩάϥϜࣄ৘
લఏ஌ࣝ ʢൃද࣌লུʣ ʢൃද࣌লུʣ

8 • ࠷΋؆୯ͳ࠷దԽͷྫɿ̎࣍ؔ਺ͷ࠷খ஋୳ࡧ ࠷దԽͬͯͳΜͰ͔͢ʁ https://www.youtube.com/watch?v=_Q4QJO8SEsY લఏ஌ࣝ ʢൃද࣌লུʣ

9 • ࠷΋؆୯ͳ࠷దԽͷྫɿ̎࣍ؔ਺ͷ࠷খ஋୳ࡧ • ࠷దԽ໰୊ͱͯ͠هड़͢Δͱ ࠷దԽͬͯͳΜͰ͔͢ʁ https://www.youtube.com/watch?v=_Q4QJO8SEsY લఏ஌ࣝ ʢൃද࣌লུʣ

10 • Ͳ͏΍ͬͯ࠷খ஋ΛͱΔYΛ୳ࡧ͢Δ͔ʁ • ࠷΋جຊతͳख๏͸ɼ܏͖Λ࢖ͬͯ୳ࡧ͢Δख๏ • ͱ͋Δ఺ʹ͓͚Δޯ഑ͷٯํ޲ ʹਐΉͱ࠷খ஋ʹ޲͔͏ •
ӈਤͰ͍͏ͱɼ੺ͷ઀ઓͷ܏͖͸ϚΠφεʢԾʹͱ͢Δʣ • XΛ ͷํ޲΁ͣΒ͢ʢX X ʣ • ͢Δͱ࠷খ஋ΛͱΔXʹۙͮ͘ • ඍ෼Λͯ͠܏͖ʢޯ഑ʣΛऔಘ͢Δ͜ͱ͕࠷దԽʹ͸ඞਢ ࠷దԽʹඞཁͳޯ഑ લఏ஌ࣝ

11 • ̎࣍ؔ਺ͷΑ͏ͳ؆୯ͳؔ਺ͳΒී௨ʹඍ෼ͯ͠΋ྑ͍͕ɼ࣮ࡍͷ໰୊Ͱѻ͏ํఔࣜ͸΋ͬͱෳࡶ • Ұൠతʹɼ͜Ε·Ͱ̏ͭͷख๏͕ଟ͔ͬͨ • खܭࢉ • ਺஋ඍ෼ •
γϯϘϦοΫඍ෼ • ۙ೥ɼػցֶशʢಛʹ/FVSBM/FUXPSLʣʹ͓͚Δ όοΫϓϩύήʔγϣϯͷ࣮૷ʹ୅ද͞ΕΔࣗಈඍ෼͕ ྲྀߦ Ͳ͏΍ͬͯඍ෼ʢޯ഑ʣΛܭࢉ͢Δ͔ʁ લఏ஌ࣝ "Automatic Differentiation in Machine Learning: a Survey" (2018) https://jmlr.org/papers/v18/17-468.html

12 • ΊͬͪΌΊͪΌࡶʹݴ͏ͱʮඍ෼ΛϓϩάϥϜͰ؆୯ʹ΍ͬͯ͘ΕΔ΍ͭʯ • ܭࢉաఔΛϓϩάϥϜʹ͢Δͱ͍͏͜ͱ͸ɼԼਤͷΑ͏ʹجຊతͳܭࢉͷ૊Έ߹ΘͤͰ࣮૷͢Δ͜ͱ • ̍ͭ̍ͭͷܭࢉ͸୯७ͳͷͰɼ̍ͭ̍ͭͷඍ෼͸ܭࢉ͠΍͍͢ • ͜ͷ̍ͭ̍ͭͷඍ෼Λ࢖ͬͯɼ໨తؔ਺ͷඍ෼ʢޯ഑ʣΛܭࢉ͢Δ •
େࣄͳ͜ͱ͸ɼ࣮૷Ͱ͖Ε͹ඍ෼͕ՄೳʹͳΔʹޯ഑͕ٻΊΒΕΔͱ͍͏͜ͱ • ʔʼ࠷దԽʹ࢖͑Δʂʂʂ ࣗಈඍ෼ͬͯͳΜͰ͔͢ʁ લఏ஌ࣝ

13 • ϗϩάϥϜ͕Ͳ͏͍͏΋ͷ͔ͷ঺հ • ࠷దԽʹ͍ͭͯͷجຊతͳ঺հ • ࣗಈඍ෼ͱ͍͏ٕज़ʹؔ͢Δجຊతͳ঺հ લఏ஌ࣝͷ੔ཧ ѻͬͨ಺༰ ʢൃද࣌লུʣ

ຊ࿦จͷ঺հ

16 • ࣗಈඍ෼Λ༻͍ͨ࠷దԽ͕͜Ε·Ͱͷશͯͷ࠷దԽख๏Λ্ճΔਫ਼౓Λୡ੒ͨ͠ͱ͍͏'JOEJOHT • $BNFSBJOUIFMPPQΛߏஙͯ͠ϗϩάϥϜΛ͞Βʹ࠷దԽ • ϦΞϧλΠϜॲཧͷͨΊͷ/FVSBM/FUXPSLߏங ಋೖ ౰࿦จͷίϯτϦϏϡʔγϣϯ ,FZXPSETࣗಈඍ෼ɾ࠷దԽɾ*OGFBTJCMF.PEFM%JGGFSFOUJBUJPO
0QUJNJ[BUJPO ɾ999JOUIFMPPQ

ίϯτϦϏϡʔγϣϯ̍ɿ ࣗಈඍ෼Λ༻͍ͨϗϩάϥϜ࠷దԽ

18 • ͳΜΒ͔ͷύλʔϯПΛ4-.ʹදࣔ͢Δͱɼ݁Ռ ͕ಘΒΕΔ • ͜ΕΛ໨ඪͱͷࠩ෼͕࠷΋খ͘͞ͳΔΑ͏ʹʢ ʣ͢Δͷ͕ຊ࿦จͰͷ࠷దԽ • ࠷దԽͷߋ৽ʹ͋ͨͬͯ͸ɼࣗಈඍ෼ʹΑͬͯٻΊΒΕΔޯ഑Λ׆༻ ̂
f(ϕ) ̂ f(ϕ) − Atarget = 0 ຊ࿦จʹ͓͚Δ໰୊ͷఆࣜԽ ຊ࿦จʹ͓͚Δ࠷దԽ໰୊ ೖྗɿП ඍ෼Մೳ γϛϡϨʔγϣϯ ̂ f ग़ྗɿ ̂ f(ϕ)

19 • ·ͣ͸ӈଆͷάϥϑͷΈʹ஫໨ • 4(%͕ఏҊख๏Ͱɼ8)ɾ(4͕طଘख๏ • ಛʹTUBUFPGUIFBSUͷख๏Ͱ͋Δ8)Λ্ճΔͷ͸ڻ͖ ίϯτϦϏϡʔγϣϯ̍ ࣗಈඍ෼Λ༻͍ͨ࠷దԽ

20 • ͜ͷࣸਅͩͱຊ౰ʹେ͖͘վળ͍ͯ͠Δ͔͸֬ೝͮ͠Β͍͕ɼ14/3ɾ44*.஋͸࠷΋ߴ͍݁ՌΛ͍ࣔͯ͠Δ • ࣮૷ָ͕ͱ͍͏ͷ΋ඇৗʹخ͍͠ϙΠϯτ • ຊ࿦จ͸1ZUPSDIͰ࣮૷͞Εɼࣗಈඍ෼Λ༻͍ͯޯ഑ܭࢉ͕ͳ͞Ε͍ͯΔ ίϯτϦϏϡʔγϣϯ̍ ࣗಈඍ෼Λ༻͍ͨ࠷దԽ

21 • ࠓݟͨख๏ͱ͍͏ͷ͸ࡢࠓͷඍ෼ՄೳͳγϛϡϨʔγϣϯͱಉ͡ϫʔΫϑϩʔͰ͋Δ͜ͱ͕Ӑ͑Δ • ඍ෼ՄೳϨϯμϦϯάʢFY.JUTVCBʣɾඍ෼ՄೳϓϩάϥϛϯάʢFY%JGG5BJDIJʣͳͲ • ೖྗม਺ʢPS/FVSBM/FUXPSLʣΛ࠷దԽ͢Δ໰୊ʹద༻ՄೳͰɼ ࠷దԽʹ͓͚Δޯ഑ܭࢉͷͨΊʹࣗಈඍ෼ʹରԠͨ͠ඍ෼ՄೳͳγϛϡϨʔλΛ׆༻͍ͯ͠Δ ࣗಈඍ෼ʢඍ෼ՄೳγϛϡϨʔγϣϯʣͷࡢࠓ ඍ෼ՄೳγϛϡϨʔγϣϯͷྲྀߦ
ೖྗɿП ඍ෼Մೳ γϛϡϨʔγϣϯ ̂ f ग़ྗɿ ̂ f(ϕ) ʢൃද࣌লུʣ

22 • ࣗಈඍ෼ʹରԠͨ͠ి࣓৔ܭࢉʢ'%'%๏ʣΛ࣮૷͠ɼܗঢ়࠷దԽʹద༻ͨ͠ • Լਤ͸ޫͷ೾௕ʹԠͯ͡ܦ࿏Λ੾Γସ͑Δܗঢ়࠷దԽ • ࠷దԽର৅ʢೖྗม਺ʣɿփ৭ྖҬͷܗঢ় • ඍ෼ՄೳγϛϡϨʔγϣϯɿ'%'% •
࠷దԽɿܗঢ়Λೖྗͱͯ͠'%'%γϛϡϨʔγϣϯΛ࣮ߦɽ࣮ߦ݁Ռ͔Βࣗಈඍ෼Ͱޯ഑Λಋग़͠ɼܗঢ়Λߋ৽ɽ ࣗಈඍ෼ʢඍ෼ՄೳγϛϡϨʔγϣϯʣͷࡢࠓ ۩ମྫ̍ɿ'PSXBSE.PEF%JGGFSFOUJBUJPOPG.BYXFMM`T&RVBUJPOT ॳظܗঢ় ࠷దԽܗঢ় ೖྗɿ ܗঢ় ඍ෼Մೳ γϛϡϨʔγϣϯɿ '%5%๏ ग़ྗɿ ޫͷ఻ൖܦ࿏ ʢൃද࣌লུʣ

23 • ෳ਺ͷϏϡʔϙΠϯτը૾͔Βɼ͋ΒΏΔํ޲ͷϏϡʔϙΠϯτը૾Λੜ੒Ͱ͖ΔΑ͏ʹ͢Δݚڀ • //ೖྗɿY Z [ В П •
//ग़ྗɿ3(#М • ඍ෼ՄೳγϛϡϨʔγϣϯɿ7PMVNF3FOEFSJOH • ࠷దԽɿ3FOEFSJOH݁ՌʹΑΔ-PTT͔Βඍ෼Ͱ୧͍ͬͯͬͯ//Λߋ৽ ࣗಈඍ෼ʢඍ෼ՄೳγϛϡϨʔγϣϯʣͷࡢࠓ ۩ମྫ̎ɿ/F3'3FQSFTFOUJOH4DFOFTBT/FVSBM3BEJBODF'JFMETGPS7JFX4ZOUIFTJT ೖྗɿ ࠲ඪɾํ޲ ඍ෼Մೳԋࢉɿ /FVSBM/FUXPSL 7PMVNF3FOEFSJOH ग़ྗɿ ϏϡʔϙΠϯτը૾ ʢൃද࣌লུʣ

ίϯτϦϏϡʔγϣϯ̎ɿ %JSFDUMZ*OGFBTJCMFϞσϧͷ࠷దԽ $BNFSBJOUIFMPPQ

25 • γϛϡϨʔγϣϯͰ͸΄΅ϊΠζͷͳ͍ը૾͕ੜ੒͞Ε͍ͯΔʢࣼઢࠨʣ ͕ɼ࣮ࡍͷޫֶܥΛ௨͢ͱϊΠζͷ͋Δը૾͕؍ଌ͞ΕΔʢࣼઢӈʣ • ͜Ε͸࣮ࡍͷޫֶܥʹ͸֤ޫֶܥݻ༗ͷ࿪Έ͕͋ΔͨΊ • ͜ͷ࿪ΈΛղফ͢ΔͨΊʹɼ$BNFSBJOUIFMPPQPQUJNJ[BUJPOΛ࣮૷ ίϯτϦϏϡʔγϣϯ̎ ࣮ࡍͷޫֶܥʹ͸࿪Έ͕͋Δ
Simulation Result Physical Result ݻ༗ͷ࿪Έ͋Γ

26 • ίϯτϦϏϡʔγϣϯ̍Ͱ͸ɼγϛϡϨʔγϣϯ্ͷؔ਺ ʹରͯ͠࠷దԽΛ ߦ͍ͬͯͨʢӈ্ࣜʣ • ͜Εͱಉ͡Α͏ʹ࣮ࡍͷޫֶܥʹରͯ͠΋࠷దԽΛߦ͍͍͕ͨɼ ࣮ࡍͷޫֶܥͷ఻ൖॲཧΛ௚઀ඍ෼͢Δ͜ͱ͸Ͱ͖ͳ͍ ̂ f
Ͳ͏΍࣮ͬͯޫֶܥʹ࠷దԽॲཧΛ૊ΈࠐΉ͔ʁ ίϯτϦϏϡʔγϣϯ̎ ͜Ε͸ඍ෼Ͱ͖ͳ͍ γϛϡϨʔγϣϯ্ͷ఻ൖؔ਺ɿ ࣮ࡍͷޫֶܥͰͷ఻ൖؔ਺ɿ ̂ f f

27 • ͔͠͠ɼγϛϡϨʔγϣϯϞσϧͱ࣮ޫֶܥ͸΄΅Ұக͍ͯ͠Δͱݟͳ͢͜ͱ͸Ͱ͖Δ ˠඍ෼ύʔτ͚ͩγϛϡϨʔγϣϯϕʔεʹஔ͖׵͑ͯ͠·͓͏ʂ Ͳ͏΍࣮ͬͯޫֶܥʹ࠷దԽॲཧΛ૊ΈࠐΉ͔ʁ ίϯτϦϏϡʔγϣϯ̎ ࣮ޫֶܥͷ ఻ൖɿG ग़ྗɿG П
ඍ෼ՄೳγϛϡϨʔγϣϯ Ͱ ஔ͖׵͑ͯඍ෼ ̂ f ೖྗɿП ೖྗПΛ࠷దԽ ஔ͖׵͑ ஔ͖׵͑

• ΧϝϥͰ࣮ࡍʹࡱӨͨ͠ϗϩάϥϜͷ݁ՌΛ࢖ͬͯ࠷దԽ͠Α͏ • ΧϝϥͰࡱӨͨ͠ը૾ΛMPTTؔ਺ʹ૊ΈࠐΉ ͭ·ΓɼΧϝϥը૾ͱ໨ඪը૾ͷࠩ෼ΛMPTTͱఆٛ͢Δ • ޯ഑͸γϛϡϨʔγϣϯϞσϧΛ׆༻ͯ͠ɼҐ૬Λߋ৽͠Α͏ ίϯτϦϏϡʔγϣϯ̎ Ͳ͏΍࣮ͬͯޫֶܥʹ࠷దԽॲཧΛ૊ΈࠐΉ͔ʁ Captured
Image: f(ϕk−1) SLM Phase: ϕk−1 Propagation Function: f ࣮ޫֶܥͷࡱӨ݁ՌΛ૊ΈࠐΜͩߋ৽ࣜ Χϝϥͱ໨ඪը૾ͷࠩ෼ ஔ͖׵͑ඍ෼ܭࢉ 28

29 • ϊΠζ͕ܰݮ͞Εɼ׈Β͔ͳ݁Ռ͕ಘΒΕΔΑ͏ʹͳͬͨ • ࠨɿγϛϡϨʔγϣϯ্ͷ࠷దԽͷΈɼӈɿΧϝϥࡱӨΛؚΊͨ࠷దԽ ࣮ޫֶܥͷ݁ՌΛ΋ͱʹ࠷దԽͨ݁͠Ռ ίϯτϦϏϡʔγϣϯ̎

30 • දࣔը૾̍ຕ̍ຕʹରͯ͠࠷దԽΛ͢Δඞཁ͕ൃੜ͍ͯ͠Δʢ͔͔࣌ؒΓ͗͢ʣ • ޫֶܥͷಛੑΛֶशͯ͠ɼͲΜͳදࣔը૾ʹରͯ͠΋ରԠͰ͖ΔϞσϧΛֶशͰ͖ͳ͍͔ʁ • ˠ$BNFSBJOUIFMPPQ.PEFM5SBJOJOH • ࢥ͍ͭ͘؆ܿͳख๏͸ $POWPMVUJPOBM
/FVSBM/FUXPSLΛ׆༻ͨ͠ख๏ • ͨͩ/FVSBM/FUXPSLʹ͢ΔͱͲ͏͍ͬͨཁૉ͕ىҼ͍ͯ͠Δ͔ͷ෼ੳ͕ࠔ೉ • ˠຊ࿦จͰ͸ɼ1IZTJDBMMZ#BTFE.PEFMΛߏங ୯७ͳ$BNFSBJOUIFMPPQͷ໰୊఺ ίϯτϦϏϡʔγϣϯ̎ γϛϡϨʔγϣϯ ࠷దԽҐ૬ɿϕ /FVSBM/FUXPSL *OQVU 0VUQVU ϕ ϕ′ ࣮ޫֶܥͰͷ ग़ྗɿf(ϕ′ ) NNΛֶश

31 • 1IZTJDBMMZ#BTFE.PEFM͸̐ཁૉ͔Β੒ΔʢӈԼࣜʹʣ • $POUFOU*OEFQFOEFOU4PVSDFBOE5BSHFU'JFME7BSJBUJPO • .PEFMJOH0QUJDBM1SPQBHBUJPOXJUI"CFSSBUJPOT • .PEFMJOH1IBTF/POMJOFBSJUJFT •
$POUFOUEFQFOEFOU6OEJSFDUFE-JHIU • શύϥϝʔλΛ͋ΘͤͯВͱఆٛ͠ɼͦΕΛֶश ίϯτϦϏϡʔγϣϯ̎ $BNFSBJOUIFMPPQ.PEFM5SBJOJOH มԽ ඍ෼Մೳ γϛϡϨʔγϣϯ ̂ fθ ೖྗɿ ࠷దԽҐ૬ ϞσϧύϥϝʔλВ ϕ ࣮ޫֶܥͰͷ ग़ྗɿfθ (ϕ′ ) ௨ৗͷ఻ൖࣜ ϊΠζཁૉ͕ύϥϝλϥΠζ͞Εͯ૊Έࠐ·Εͨ఻ൖࣜ

32 • $*5-0QUJNJ[BUJPO͸ϞσϧԽ͠ͳ͍Ͱը૾͝ͱʹ௚઀࠷దԽ ͢Δख๏ • $*5-DBMJCSBUFE.PEFM͕ը૾ʹґଘͤͣɼ఻ൖϞσϧΛֶश ͤͨ͞ख๏ • $*5-0QUJNJ[BUJPO͕ϕετύϑΥʔϚϯεΛൃش͢Δ͕ɼ $*5-DBMJCSBUFE.PEFM΋طଘख๏Λ্ճͬͨ
݁Ռͷൺֱ ίϯτϦϏϡʔγϣϯ̎

33 • ਓؒΛ௚઀ඍ෼͢Δ͜ͱ͸Ͱ͖ͳ͍ͷͰɼਓؒΛ͋ΔϞσϧʹஔ͖׵͑ͯʢ#MBDLCPYγεςϜͱͯ͠औΓѻͬͯʣ ࠷దԽʹ૊ΈࠐΉΑ͏ͳ࿩͕͋Δ • ྫɿ)VNBOJOUIFMPPQΛ׆༻ͨ͠ਓؒ("/ %JSFDUMZ*OGFBTJCMFϞσϧͷ࠷దԽ ඍ෼Ͱ͖ͳ͍ྫɿਓؒ BΛೖྗͱͯ͠
ར༻ ਓ͕ؒ൑அ %JTDSJNJOBUPS ग़ྗC ඍ෼ՄೳͳϞσϧͰ ਓؒΛஔ͖׵͑ɼ ޯ഑ܭࢉʹ׆༻ //͕ੜ੒ (FOFSBUPS ɿB NNΛֶश ʢൃද࣌লུʣ

ίϯτϦϏϡʔγϣϯ̏ɿ ܭࢉߴ଎ԽͷͨΊͷ/FVSBM/FUXPSLͷར༻

35 • ࠷దԽ͸جຊతʹΠςϨʔγϣϯΛඞཁͱ͢ΔͷͰ͕͔͔࣌ؒΔ • ௚઀ɼҐ૬Λܭࢉ͢ΔΑ͏ͳߴ଎ख๏͕ٻΊΒΕΔ • ຊ࿦จͰ͸)PMP/FUͱ͍͏ωοτϫʔΫΛ૊Έɼߴ଎ԽΛ࣮ݱ ίϯτϦϏϡʔγϣϯ̏ ܭࢉߴ଎Խ

36 • ΍ ͱ͍ͬͨඍ෼Մೳͳ෺ཧԋࢉΛؚΊͯMPTTܭࢉʹ׆༻͢ΔωοτϫʔΫΞʔΩςΫνϟͷ૊Έํ͕ಛ௃తʁ ʢ࠷ۙ૿͍͑ͯΔؾ͸͢Δʣ ̂ f −1 ̂ fθ
ωοτϫʔΫΞʔΩςΫνϟ ίϯτϦϏϡʔγϣϯ̏ ֶशର৅ ֶशର৅ ඍ෼Մೳԋࢉ ඍ෼Մೳԋࢉ

37 • ࠷దԽϧʔϓΛඞཁͱ͠ͳ͍ख๏ಉ࢜Ͱൺ΂ͯΈΔͱɼ طଘख๏Λ্ճ͍ͬͯΔ͜ͱ͕Θ͔Δ ݁Ռ ίϯτϦϏϡʔγϣϯ̏

39 • ίϯτϦϏϡʔγϣϯ̍ɿࣗಈඍ෼ͱඍ෼ՄೳγϛϡϨʔλͱ࠷దԽ • ࣗಈඍ෼ʹରԠͨ͠ඍ෼ՄೳγϛϡϨʔγϣϯʹΑΔ࠷దԽ͕࠷΋ྑ͍݁ՌΛ࣮ݱ • ඍ෼ՄೳγϛϡϨʔγϣϯΛ׆༻ͨ͠࠷దԽ͸ࠓޙ΋৭ʑͳ෼໺Ͱొ৔͢ΔͩΖ͏ • ίϯτϦϏϡʔγϣϯ̎ɿ%JSFDUMZ*OGFBTJCMFϞσϧͷ࠷దԽ •
࣮ޫֶܥͷΑ͏ʹ௚઀ܭࢉػͰѻ͑ͳ͍΋ͷͰ͋ͬͯ΋ɼஔ͖׵͑౳Ͱඍ෼Մೳʹ͢Δ͜ͱͰ࠷దԽॲཧͷதʹ ૊ΈࠐΉ͜ͱ͕Ͱ͖Δ • ϋʔυ΢ΣΞͷΈͳΒͣɼਓؒͷΑ͏ͳੜ෺΋ର৅ͱͳΓ͏Δߟ͑ํͰ͋Ζ͏ • ίϯτϦϏϡʔγϣϯ̏ɿ/FVSBM/FUXPSLʹΑΔߴ଎Խ • ඍ෼ՄೳͳԋࢉͰ͋Ε͹ɼ//ͷܗΛऔΒͳͯ͘΋MPTTؔ਺ʹ૊ΈࠐΜͰɼֶशʹ׆༻Ͱ͖Δ • ޻෉ͷࢪ͞Εͨ//"SDIJUFDUVSF͸ࠓޙӹʑ૿͑ΔͩΖ͏ ૯ׅ

-FBSOFE)BSEXBSFJOUIFMPPQ1IBTF3FUSJFWBMGPS )PMPHSBQIJD/FBS&ZF%JTQMBZT 1SBOFFUI$IBLSBWBSUIVMB &UIBO5TFOH 5BSVO4SJWBTUBWB )FOSZ'VDIT 'FMJY)FJEF 6/$$IBQFM)JMM 1SJODFUPO6OJWFSTJUZ

41 • ޫֶܥͷಛੑΛֶशͯ͠ɼͲΜͳදࣔը૾ʹରͯ͠΋ରԠͰ͖ΔϞσϧΛֶशͰ͖ͳ͍͔ʁ • ࢥ͍ͭ͘؆ܿͳख๏͸ $POWPMVUJPOBM /FVSBM/FUXPSLΛ׆༻ͨ͠ख๏ //Λ༻͍ͨղܾํ๏ /FVSBM)PMPHSBQIZʹ͓͚ΔఏҊ γϛϡϨʔγϣϯ
࠷దԽҐ૬ɿϕ /FVSBM/FUXPSL *OQVU 0VUQVU ϕ ϕ′ ࣮ޫֶܥͰͷ ग़ྗɿf(ϕ′ ) NNΛֶश

42 • ຊ࿦จͷఏҊख๏ͷύΠϓϥΠϯ͸Լਤ • ᶃҐ૬ 4-.໘ ͔Β఻ൖܭࢉɹᶄ఻ൖܭࢉ͞Εͨཧ૝తͳը૾Λݱ࣮ͱಉ͡ϊΠζ࠶ݱΛͰ͖Δ//ͰΞ΢τϓοτ ᶅϊΠζ࠶ݱ͞Εͨը૾ͱλʔήοτը૾ͷࠩ෼ MPTT ͔ΒɼೖྗҐ૬Їʹର͢Δޯ഑ܭࢉɹᶆҐ૬ߋ৽
࠷దԽ ΞΠσΞࣗମ͸͔ͳΓ͍ۙʢ໰୊ҙࣝ͸ҰॹʹͲ͏΍ͬͯޫֶϊΠζΛແ͔͘͢ʣ -FBSOFE)BSEXBSFJOUIFMPPQͰͷ࣮૷

43 • %JTDSJNJOBUPSͱ(FOFSBUPS͔Β੒Δ("/ͷωοτϫʔΫϞσϧͱͳ͍ͬͯΔ • ݱ࣮ͷΩϟϓνϟը૾ʹͳΔΑ͏ͳ(FOFSBUPSΛֶश্ͤͨ͞ͰɼͦͷϞσϧΛ࢖ͬͯೖྗҐ૬Їͷ࠷దԽʹҠΔ ΞΠσΞࣗମ͸͔ͳΓ͍ۙʢ໰୊ҙࣝ͸ҰॹʹͲ͏΍ͬͯޫֶϊΠζΛແ͔͘͢ʣ -FBSOFE)BSEXBSFJOUIFMPPQͰͷ࣮૷

44 ηοτΞοϓ͸ී௨ 0QUJDBM4FUVQ

45 طଘख๏ͱͷൺֱ %JTQMBZ3FTVMUT

%FTJHOBOE'BCSJDBUJPOPG'SFFGPSN)PMPHSBQIJD0QUJDBM &MFNFOUT $IBOHXPO+BOH 0MJWFS.FSDJFS ,JTFVOH#BOH (BOH-J :BOH;IBP %PVHMBT-BONBO 'BDFCPPL3FBMJUZ-BCT3FTFBSDI

47 • χΞΞΠσΟεϓϨΠʹ͓͍ͯ࠷΋ྑ͘ݟΔ)0&ͷ࢖༻ํ๏͸ɼ ϝΨωܕσόΠεͷϨϯζ෦෼ʹूޫੑೳΛ࣋ͨͤͨ)0&Λ഑ஔ͢Δͱ͍͏΋ͷ • ΑΓෳࡶͳઃܭʹ଱͑Δ΋ͷ͕ཉ͍͠ɼͱ'#3FBMJUZ -BC͕ओு͢Δͷ͸ྑ͘Θ͔Δؾ͕͢Δ 73"3σόΠεͷখܕԽʹ͸ඞਢͷޫֶૉࢠ 8IBUJT)PMPHSBQIJD0QUJDBM&MFNFOU )0&
[Maimone et al. 2017]

48 • ಠࣗͷબ୒ੑΛߟྀͨ͠ϑϦʔϑΥʔϜ)0&ͷ࠷దԽख๏ • )0&༻ͷμΠϠϞϯυટ࡟ʹΑΔϑϦʔϑΥʔϜද໘੡଄ɾͭͷ೾໘มௐΞʔϜΛඋ͑ͨϗϩάϥϑΟοΫϓϦϯλʔ ͷ࢖༻ͱ͍ͬͨɼ̎छྨͷϑϦʔϑΥʔϜ)0&੡଄ख๏ • ྆ํͷ੡଄Ξϓϩʔνʹ߹Θͤͯௐ੔͞Εͨݎ࿚ͳ೾໘෼ղΞϧΰϦζϜ • "3ΠϝʔδίϯόΠφʔɾϔουΞοϓσΟεϓϨΠɾϨϯζΞϨΠͳͲͷ
σΟεϓϨΠ͓ΑͼΠϝʔδϯάΞϓϦέʔγϣϯͷྫ • ϑϧΧϥʔ$BVTUJDT౤Ө)0&ͷσϞ ຊ࿦จͷߩݙ $POUSJCVUJPOT

49 • ʢ͢Έ·ͤΜɼ͜͜͸ਂ͘ಡΊͯ·ͤΜʣ ϑϦʔϑΥʔϜ)0&ͷ࠷దԽʢσβΠϯʣ $POUSJCVUJPO

50 • )0&͸ޫͷׯবʹΑͬͯه࿥͞ΕΔ • ఏҊख๏ͱͯ͠͸̎ͭͷΨϥεͷϑϦʔϑΥʔϜαʔϑΣεʹΑͬͯׯবͤͯ͞ɼ)0&ͷύλʔϯΛ࡞Δ Ψϥε੾࡟ʹΑΔϑϦʔϑΥʔϜαʔϑΣε $POUSJCVUJPO HOEͷম͖෇͚ ϑϦʔϑΥʔϜΨϥεද໘ͷ੾࡟

51 • 4-.ʹΑͬͯมௐ͞Εͨޫ೾͕ೋํ޲͔Β఻ൖ͖ͯͯ͠ɼͦͷׯবΛه࿥͢Δख๏ ϗϩάϥϜϓϦϯλʔʹΑΔ)0&ͷ࡞੒ $POUSJCVUJPO ϗϩάϥϜϓϦϯλʔʹΑΔHOEͷম͖෇͚

52 3FTVMUT "QQMJDBUJPOT ඇٿ໘ϨϯζHOE (a,b,c) HUDϨϯζHOE (d,e,f) Printed HUDϨϯζHOE (g,h) 
ϨϯζΞϨΠHOE (i) Caustic HOE (j,k,l)

3FOEFSJOH/FBS'JFME4QFDLMF4UBUJTUJDTJO4DBUUFSJOH .FEJB $IFO#BS *PBOOJT(LJPVMFLBT "OBU-FWJO %FQBSUNFOUPG&MFDUSJDBM&OHJOFFSJOH 5FDIOJPO *TSBFM 3PCPUJDT*OTUJUVUF $BSOFHJF.FMMPO6OJWFSTJUZ
64"

54 εϖοΫϧϊΠζͱ͸ 8IBUJTTQFDLMFOPJTFʁ ϨʔβʔͷΑ͏ͳίώʔϨϯτޫΛࢄཚഔ࣭ʹ౰ͯΔͱɼεϖοΫϧϊΠζͱݺ͹ΕΔϥϯμϜͳϊΠζ͕ൃੜ͢Δ   ʰࢄཚഔମதͷ෺ମΠϝʔδϯά͓Αͼ෺ମೝࣝʹؔ͢Δݚڀʱ(2016) ΑΓը૾Ҿ༻

55 • ͜͏ͨ͠ࢄཚഔ࣭Λ௨աͨ͠ޙͷεϖοΫϧϊΠζΛϨϯμϦϯά͢Δख๏ͷఏҊ • ʢ͢Έ·ͤΜʣ ຊݚڀͷߩݙ $POUSJCVUJPOPG5IJT3FTFBSDI

SIGGRAPH Asia 2020 勉強会 "Computational Holography"

SIGGRAPH Asia 2020 勉強会 "Computational Holography"

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