MIT 2 717 - Real-time spectral imaging in three spatial dimensions

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854 OPTICS LETTERS / Vol. 27, No. 10 / May 15, 2002Real-time spectral imaging in three spatial dimensionsWenhai Liu* and Demetri PsaltisDepartment of Electrical Engineering, California Institute of Technology, Mail Stop 136-93, Pasadena, California 91125George BarbastathisDepartment of Mechanical Engineering, Massachusetts Institute of Technology, Room 3-461c, 77 Massachusetts Avenue,Cambridge, Massachusetts 02139Received December 17, 2001We report what is to our knowledge the first volume-holographic optical imaging instrument with the capa-bility to return three-dimensional spatial as well as spectral information about semitranslucent microscopicobjects in a single measurement. The four-dimensional volume-holographic microscope is characterized theo-retically and experimentally by use of f luorescent microspheres as objects. © 2002 Optical Society of AmericaOCIS codes: 090.2890, 110.0110, 090.1970, 090.7330, 100.6890.Classical imaging systems process the optical f ield byuse of elements such as lenses, apertures and stops,and thin diffraction gratings. By placing several suchelements in tandem, one can capture projections of verygeneral objects, e.g., containing three-dimensional (3D)spatial as well as spectral information. We refer tosuch objects as four dimensional (4D). The projectionsthat these systems are capable of forming are two-dimensional (2D) or lower; scanning is needed to spanthe entire 3D or 4D object space.For example, a classical confocal microscope1–3usesa combination of objective–collector lenses and apinhole to capture information about a single point inthe object and acquires a zero-dimensional projectionat every measurement. Scanning along three dimen-sions is needed to acquire the 3D spatial structureof the object. By providing spectral scanning means(e.g., a monochromator or a scanning Fabry–Perotinterferometer), one can also acquire spectral infor-mation, albeit in a very time-consuming procedure.Optical coherence tomography4requires only 3Dscanning for capturing spatial information, whereasspectral information is recovered digitally fromthe phase of the correlation function of the opticalbeam.5Coherence imaging6–9returns 2D projec-tions in the Fourier共k兲 space at the expense ofdynamic range. Here we report what is, to ourknowledge, the first instrument with the capabilityto acquire spatial and spectral information simul-taneously (in a single measurement). Therefore,real-time 4D imaging becomes possible at ratesspecified by the photon count and not the scanningspeed.The 4D imaging capability is based on the Braggdiffraction selectivity and degeneracy properties ofvolume holograms.10 – 12The principle of volume-holo-graphic imaging is illustrated in Fig. 1. The opticalfield emitted or scattered by a 4D object is transformedby the appropriate combination of lenses and subse-quently diffracted by a volume-holographic opticalelement, which has been prerecorded to multiplesuperimposed holograms. Each hologram is tunedto its corresponding 2D slice of the 4D object. If theprojected slices span the entire 4D object space, thenthe need for scanning is eliminated.In this Letter we discuss and experimentallycharacterize a specif ic holographic imaging of trans-mission geometry. With the detailed structure shownin Fig. 2, the hologram is recorded by interferingthe signal beam, collimated from a monochromaticcoherent point source at 共xr, yr, zr, lr兲 and its co-herent plane reference beam in the 2ˆx direction.An imaging lens focuses the diffracted beam fromthe volume-holographic optical element onto a 2Ddetector array surface. For simplicity we considerthe simplest possible object: a probe point source ofarbitrary wavelength lp, located in the vicinity of therecording point source.When the probe is displaced by Dxp共jDxpj ,, fc兲in the ˆx direction, the collimated signal beam ro-tates in the xz plane. According to the well-knownangle selectivity, the diffraction efficiency, h共Dxp兲 苷sinc2共Dxp兾fcDu兲, drops to zero (the first null) at DuS:DuS苷jDxpjfc苷lD1cos uS共tan uSn1 tan uRn兲,(1)where D is the thickness of the hologram and uSn, uRn,and uSare the incident angles inside or outside theholographic material in Fig. 2. If instead the probepoint source is displaced relative to the recording pointsource by Dzpin depth, the light after the collimatorlens is a spherical wave. The diffraction efficiencycan be approximated to first order by incoherent ad-dition of all spatial frequency components of the defo-cused beam in the xz plane10asFig. 1. Volume-holographic 4D imaging principle.0146-9592/02/100854-03$15.00/0 © 2002 Optical Society of AmericaMay 15, 2002 / Vol. 27, No. 10 / OPTICS LETTERS 855Fig. 2. Experimental recording and imaging geometry.h共Dzp兲 苷1aZa0sinc2µtDuS∂dt 艐DuS2paSiµ2paDuS∂,(2)where Si共s兲⬅Rs0共sin t兾t兲dt, a 苷 LDzp兾2fc2, andL is the collimating lens aperture. Finally, for asmall probe wavelength deviation jDlpj ⬅ jlp2lrj ,, lr, the diffraction efficiency drops, to firstorder, as h共Dlp兲 苷 sinc2共Dlp兾lrDb兲, whereDb 苷lrnDcos uRn1 2 cos共uSn1uRn兲.(3)The experimental and theoretical spatial selectivitiesare compared in Fig. 3 and have good agreement.These diffraction eff iciencies give the imaging resolu-tion on Dxp, Dzp, and Dlp, which are determined bythe hologram thickness, D, and the objective lens, fc.Two basic Bragg degeneracies (i.e., Bragg matchingwith a probing source that is different from therecording source13) exist in the transmission geometry.Consider a single grating K recorded by the refer-ence-signal wave-vector pair 共kRr, kSr兲, kr苷 2p兾lr,all probe-diffracted wave-vector pairs 共kRp, kSp兲 areBragg matched when K 苷 kRp2 kSp. The first de-generacy is 共kRp, kSp兲 at wavelength lp苷 lr, obtainedby rotation of 共kRp, kSr兲 about K.13In Fig. 2, thisdegeneracy means the probe source moving along Dypand the imaging point along Dyi苷 Dyp共 fi兾fp兲.Thesecond degeneracy is for pairs 共kRp, kSp兲 at wave-lengths lpfilr.10,14This corresponds to the probesource along a spatial–spectral coupled direction inFig. 2, satisfyingDxpfc苷 2Dlplr(4)and yielding an image at the output plane with Dz0苷共 fi兾fc兲Dxprelative to the location of the reference im-age point.All object (or probe) point sources along the twoBragg degenerate dimensions are reconstructed ontothe image y0z0plane. Therefore, a 2D slice at a fixeddepth in a yp2 共xp兾lp兲


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