MIT 2.71/2.710 Optics12/07/05 wk14-b-13D OpticsMIT 2.71/2.710 Optics12/07/05 wk14-b-22D Optics3D Opticslenses gratingsLight interacts with medium on a sequence of discrete surfacesGRadient INdex optics(GRIN)VolumeHologramsLight interacts with medium throughout a volumethroughout a volumeMIT 2.71/2.710 Optics12/07/05 wk14-b-3MIT 2.71/2.710 Optics12/07/05 wk14-b-4Imaging with traditional lensesdepthoffieldlensAAimagedBBblurredimage planeMIT 2.71/2.710 Optics12/07/05 wk14-b-5Imaging with 3D lensesdepthoffield3D lensBBblockedimage planeAAimagedContrast Defocus⇔MIT 2.71/2.710 Optics12/07/05 wk14-b-6Shape recovery (“profilometry”) with 3D lensesLine scan method: 2D scanningLine scan method: 2D scanninglongitudinal + one lateral dimensionlongitudinal + one lateral dimensionraw imageson CCD camera2½D shape(“profile”)in digital formWorking distanced= 50cmLongitudinal resolution ∆z FWHM< 1mmMIT 2.71/2.710 Optics12/07/05 wk14-b-7z=0 µm z=50 µmz=200 µmz=250 µmoriginalobjectMicroturbine provided by Chee Wei Wong, Alan Epstein, MIT Object Distance = 46 cmObject Distance = 46 cmResolution accomplished Resolution accomplished ≤≤100 100 µµmmraw imagesraw imagesprofileprofilereconstructionreconstructionArnab Sinha, George BarbastathisMIT 3D Optical Systems groupOptics Express 11:3202, 2003Shape recovery (“profilometry”) with 3D lensesMIT 2.71/2.710 Optics12/07/05 wk14-b-8index ofrefractionn0+n1n0– n13D lens: plane-to-plane wave volume hologramMIT 2.71/2.710 Optics12/07/05 wk14-b-9Making the (simplest) 3D lensphotosensitivematerialreferencepoint sourceofsθplane wavesignal beamreferenceplane()()[]rkkr⋅−+=rs10cosnnnafter exposureMIT 2.71/2.710 Optics12/07/05 wk14-b-10Operating the (simplest) 3D lens3D objectobjectivelens3D lenscollectorlensdigitalcameravisiblecolumnx∆y∆z∆Lofsθxyzmm1m100~÷µLMIT 2.71/2.710 Optics12/07/05 wk14-b-11Operating a multiplex 3D lens3D objectobjectivelenscollectorlensdigitalcameravisiblecolumnsXYZXYZ3D lens(multiplex)MIT 2.71/2.710 Optics12/07/05 wk14-b-12Operating a hyperspectral multiplex 3D lens3D objectobjectivelenscollectorlensdigitalcameraXYZXYZvisiblerainbow slices3D lens(multiplex)MIT 2.71/2.710 Optics12/07/05 wk14-b-13Rainbow volume holographic imagingslice #1slice #1slice #2slice #22½D shape2½D shapeWenyang Sun, George BarbastathisMIT 3D Optical Systems groupOptics Letters 30:976, 2005MIT 2.71/2.710 Optics12/07/05 wk14-b-14Multiplex imaging of 3D fluorescent object3D object:fluorescent beadsin waterXYZthree three ““slicesslices””throughthroughfluorescent (3D) object, stacked fluorescent (3D) object, stacked along along longitudinallongitudinaldirection direction ……XYZ……are viewed are viewed simultaneouslysimultaneouslyand and sideside--byby--sidesideon the digital cameraon the digital cameraWenhai Liu,* Demetri Psaltis,* George Barbastathis***Caltech Optical Info. Proc. group **MIT 3D Optical Systems groupOptics Letters 27:854, 2002MIT 2.71/2.710 Optics12/07/05 wk14-b-15Camera pixel layout for 4D (3D spatial + spectral) imaging#1λ1λ2λwslice index#2 #NM pixelsW pixels3D object#1#2 #Nslice indexWNMWzyx×××=×××λ#1#2#Wslitindexcamera dieMIT 2.71/2.710 Optics12/07/05 wk14-b-163D opticalimagetraditionalcamera0 100 200 300 400 500 600 700406080100120140160180200220240irradiance acrossimage cross-sectionSun Light (completely passive) illumination~10cm~5mobjective0 100 200 300 400 500 600 706080100120140160180MIT 2.71/2.710 Optics12/07/05 wk14-b-17Temporal Heterodyninginput signallocal oscillatorlow pass filtertransducerMIT 2.71/2.710 Optics12/07/05 wk14-b-18Temporal Heterodyninginput signallocal oscillatorlow pass filtertransducer()φω+tAiicos()tALLcosω()()φωω−−tAA cosiLiLMIT 2.71/2.710 Optics12/07/05 wk14-b-191D Spatial Heterodyninginput signallocal oscillator(){}φ+xkiAii cos(){}xkiALL cos?MIT 2.71/2.710 Optics12/07/05 wk14-b-201D Spatial Heterodyninginput signallocal oscillator(){}φ+xkiAii exp()()2SSSRRexpexpφ++ xikAxikAthintransparencyMIT 2.71/2.710 Optics12/07/05 wk14-b-211D Spatial HeterodyningSRikkk ++SRikkk −+SRikkk +−SRikkk −−input signallocal oscillator(){}φ+xkiAii exp()()2SSSRRexpexpφ++ xikAxikAMIT 2.71/2.710 Optics12/07/05 wk14-b-221D Spatial Heterodyninginput signallocal oscillator(){}φ+xkiAii exp()()2SSSRRexpexpφ++ xikAxikAMIT 2.71/2.710 Optics12/07/05 wk14-b-231D Spatial Heterodyninginput signallocal oscillator(){}φ+xkiAii exp()()2SSSRRexpexpφ++ xikAxikAMIT 2.71/2.710 Optics12/07/05 wk14-b-241D Spatial HeterodyningSRikkk+−input signallocal oscillator(){}φ+xkiAii exp()()2SSSRRexpexpφ++ xikAxikAMIT 2.71/2.710 Optics12/07/05 wk14-b-251D Spatial HeterodyningSRikkk+−low pass filterinput signallocal oscillator(){}φ+xkiAii exp()()2SSSRRexpexpφ++ xikAxikA()()⎭⎬⎫⎩⎨⎧⎥⎦⎤⎢⎣⎡++′+−SSRiSRi expφφxkkkiAAAMIT 2.71/2.710 Optics12/07/05 wk14-b-261D Spatial Heterodyning in the Fourier domaininput signallocal oscillator(){}φ+′′xkii exp()()2SSSRRexpexpφ+′′+′′xikAxikAℑ⎟⎠⎞⎜⎝⎛−πλδ2ifkxMIT 2.71/2.710 Optics12/07/05 wk14-b-271D Spatial Heterodyning in the Fourier domaininput signallocal oscillator()()2SSSRRexpexpφ+′′+′′xikAxikAℑℑspatial filter()⎥⎦⎤⎢⎣⎡+−−′πλδ2SRikkkfx⎟⎠⎞⎜⎝⎛−πλδ2ifkx(){}φ+′′xkii expMIT 2.71/2.710 Optics12/07/05 wk14-b-2833D Spatial Heterodyning in the Fourier domaininput signallocal oscillator(){}φ+′′⋅rki exp i()()2SSSRRexpexpφ+′′⋅+′′⋅ rkrk iAiA⎟⎠⎞⎜⎝⎛−πλδ2ifkxℑ?MIT 2.71/2.710 Optics12/07/05 wk14-b-2933D Spatial Heterodyning in the Fourier domaininput signallocal oscillator()()2SSSRRexpexpφ+′′⋅+′′⋅ rkrk iAiA⎟⎠⎞⎜⎝⎛−πλδ2ifkxℑ?()⎥⎦⎤⎢⎣⎡+−−′πλδ2SRikkkfx(){}φ+′′⋅rki exp iMIT 2.71/2.710 Optics12/07/05 wk14-b-3033D Spatial Heterodyning in the Fourier domaininput signallocal oscillator()()2SSSRRexpexpφ+′′⋅+′′⋅ rkrk iAiA⎟⎠⎞⎜⎝⎛−πλδ2ifkxℑ?()⎥⎦⎤⎢⎣⎡+−−′πλδ2SRikkkfx(){}φ+′′⋅rki exp iMIT 2.71/2.710 Optics12/07/05 wk14-b-3133D Spatial Heterodyning in the Fourier domaininput signallocal oscillator()()2SSSRRexpexpφ+′′⋅+′′⋅ rkrk iAiA⎟⎠⎞⎜⎝⎛−πλδ2ifkxℑ?()⎥⎦⎤⎢⎣⎡+−−′πλδ2SRikkkfx(){}φ+′′⋅rki exp iMIT 2.71/2.710 Optics12/07/05 wk14-b-32Phase matching as a filter for 3D spatial heterodyningRecording Bragg-matched readoutDiffracted beams from elemental thin