Imaging using volume holograms

Imaging using volume holograms

Arnab SinhaGeorge BarbastathisMassachusetts Institute of TechnologyDepartment of Mechanical EngineeringRoom 3-46677 Massachusetts AvenueCambridge, Massachusetts 02139E-mail: [email protected]

Wenhai LiuOndax Incorporated850 East Duarte RoadMonrovia, California 91016

Demetri Psaltis, FELLOW SPIECalifornia Institute of TechnologyDepartment of Electrical Engineering1200 East California BoulevardMS 136-93Pasadena, California 91125

Abstract. We present an overview of imaging systems that incorporatea volume hologram as one of the optical field processing elements in thesystem. We refer to these systems as volume holographic imaging (VHI)systems. The volume hologram is recorded just once, and the recordingparameters depend on the functional requirements of the imaging sys-tem. The recording step offers great flexibility in designing application-specific imaging systems. We discuss how a VHI system can be config-ured for diverse imaging applications ranging from surface profilometryto real-time hyperspectral microscopy, and summarize recent develop-ments in this field. © 2004 Society of Photo-Optical Instrumentation Engineers.[DOI: 10.1117/1.1775230]

Subject terms: imaging systems; volume holography.

Paper VHOE-B02 received Dec. 10, 2003; revised manuscript received Jan. 29,2004; accepted for publication Feb. 27, 2004.

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1 Introduction

Traditional optical imaging systems, such as photograpcameras, microscopes, telescopes, and projection lensecomposed of an optical train, i.e., several lenses in sucsion. The role of the lenses is to transform the optical fisuch that the resulting field distribution at the image plameets the functional requirements of the system. Forample, in traditional photographic imaging the goal iscreate a projection of a 3-D field onto a 2-D receptor pla~photosensitive film or digital sampling plane!. Within theconstraints of projective geometry, the 2-D image istended to be geometrically similar to the original 3-D oject. The dependence of the selection of the optical trainthe goal of the instrument can be seen by comparinmicroscope and a telescope. In the microscope, one afor lateral magnification from an object plane at a findistance, whereas in the telescope the object is at infiand the goal is angular magnification.1 So the two systemsare very different in the way they transform ray bundles~orequivalently, spatial frequencies!.

Nevertheless, traditional optical systems are very simwith respect to certain other features. Most prominamong these features is defocus, which is directly relatedepth information~that is, the third spatial dimension!. Inclassical optics, a defocused object creates a blurred imindependent of the type of optics used~even though theblur transfer function is of course highly dependent onspecific choice of optics!. Information about the third di-mension is lost in the process, but it can be partially recered with digital postprocessing even from a single camimage, for example depth from defocus,2 depth fromshading,3,4 etc., or from multiple cameras.5 The confocalmicroscope6 is exceptional because the confocal pinhoalmost eliminates out-of-focus light at the expense of fiof view. Other optical instruments, such as coherence

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agers in the space domain7–10 and time domain,11 laserradar,12 and Radon transform tomographers13 acquire depthinformation via different mechanisms and tradeoffs.

We describe a new type of optical element, a volumholographic lens.14 The volume holographic lens is a prerecorded volume hologram15 that is incorporated into theoptical train in addition to the other traditional lenses thare already present in the train. The traditional refractlenses perform simple 2-D processing operations onoptical field16 as it passes through the optical train andincident on the volume holographic lens. The volume hlographic lens processes the optical field in 3-D on accoof its thickness,17 i.e., it has Bragg selectivity.18 The fielddiffracted by the volume holographic lens is measuredobtain the specific information that is required about toptical field.

The volume holographic lens is manufactured by recoing a 3-D interference pattern of two~or more! mutuallycoherent beams, as shown in Fig. 1~a!. The recording isindependent of the object to be imaged, although the setion of the type of hologram to be recorded~e.g., the typeof reference beam! can be based on prior information abothe type of objects to be imaged~e.g., the average workingdistance, reflective versus fluorescent, etc.!. Simple record-ing schemes include interfering a spherical reference~SR!or planar reference~PR! beam with a planar signal beam trecord holograms~see Fig. 2! in the transmission, reflection, or 90-deg geometry.14 After recording is complete, thehologram is fixed;19,20 no further processing is done on thhologram~just like the fixed lenses in an imaging instrument after they are ground and polished!. Despite the ap-parent simplicity of recording, these holograms offunique imaging capabilities that are not available in trational lenses.

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Sinha et al.: Imaging using volume holograms

During imaging, the recorded holograms are probedthe incident illumination, as shown in Fig. 1~b!. If an SRhologram is used, the imaging system is referred to asVHI. Similarly, a PR-VHI system refers to a system thcontains a planar reference volume hologram. The hogram diffracts the Bragg-matched17,18 components of theincident illumination. The diffracted field is monitored bydetector or a detector array. The diffracted field intenscaptured by the detector is the ‘‘image’’ formed by the VHsystem, and can be used to determine the required obinformation like the 3-D spatial and/or spectral charactetics of the object of interest.

This work is arranged as follows. In Sec. 2, we descrvarious classes of imaging systems with particular empsis on their VHI implementations. In Sec. 3, we presevarious VHI systems that we have demonstrated andcuss each in detail. Finally, we conclude in Sec. 4 wsome directions for future work in VHI.

2 Classification of VHI Systems

2.1 Type of Object/Illumination

The material properties of the object and the type of ilmination determine the nature of the image as follows.

1. Reflective surfaces are opaque. A system imaginreflective surface typically returns an image of t

Fig. 1 General schematic of volume holographic imaging. (a) Thevolume grating is the recorded 3-D interference pattern of two mu-tually coherent beams. (b) The imaging step consists of reading outthe volume hologram by an unknown object illumination. The vol-ume hologram diffracts only the Bragg-matched components of theobject illumination. This effect is used in conjunction with scanningto recover the object illumination.

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form $z(x,y),r (x,y)%. The function r specifies thereflectivity of the surface as a function of the latercoordinates (x,y). The functionz(x,y) is referred toas the surface ‘‘profile’’ of the object, and the imaging instrument is called a surface profilometer.

2. 3-D point scatterers consist of a several small posources distributed over a volume. A system imagthis object returns an imageI (x,y,z), where thefunction I specifies the scattering strength at objelocation (x,y,z). Fluorescent particles suspendewithin a fluid are a good example of this kind oobject.

3. A 3-D translucent/absorptive object has some refrtive index and absorption variation within the objevolume. A system imaging this object would retuan imagen(x,y,z)1 ia(x,y,z), wheren refers to therefractive index anda the absorption coefficient aobject location (x,y,z). Tomographic imaging systems like computed tomography~CT! are used to im-age 3-D absorptive objects.

Further, the nature of the illumination used for imaging cbe classified as follows. 1. Active illumination relies oexternal sources to pump light to the object. The imagsystem collects the reflected/backscattered light for im

Fig. 2 Simple volume holographic recording schematics: (a) spheri-cal reference (SR) hologram and (b) planar reference (PR) holo-gram. Note that both schematics are transmission holograms. Otherrecording geometries can also be used.

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ing. 2. Passive illumination schemes rely on either sluminescence or ambient light to provide the necessarylumination for imaging.

VHI can be implemented for all of these classes of ojects and illumination, as we discuss later in Sec. 3.

2.2 Single Hologram/Many Multiplexed Holograms

The Bragg selectivity property of volume diffraction allowseveral gratings to be multiplexed inside the same voluof the photosensitive material.18 This means that a VHIsystem can comprise: 1. one single volume holograpgrating that acts as a lens for imaging, or 2. several gings, i.e., several lenses multiplexed21 within the same vol-ume element. Each of these gratings can independentlycess the optical information; this reduces both the back-digital computation and the scanning time required. Hoever, there is a tradeoff involved, since the diffraction eciency decreases22 as the number of multiplexed gratingincrease.

We discuss both schemes later in Sec. 3.

2.3 Single/Multiple VHI Sensors in the ImagingSystem

The resolution of VHI, like most other imaging systemdegrades23 with increasing object distance. Often, tradtional lens-based imaging systems use triangulation mods to accurately determine depth information aboutjects, even though each sensor by itself can image onl2-D. In triangulation,5 several sensors image the same oject from different directions. The different images acombined geometrically to yield a high-resolution profilethe object. A similar approach can be used for VHI to offsthe degradation of depth resolution by using multiple Vsensors to acquire different perspectives of the objecinterest and improve image resolution by reconciling thperspectives into one consolidated image. Thus, a VHI stem could comprise: 1. a single VHI sensor to acquireobject information on its own, or 2. multiple VHI sensorsacquire multiple perspectives of the same object. Thespectives can be reconciled using various numerical teniques such as point multiplication of the individual poispread functions~PSFs!, least-squares error optimizatioor an expectation maximization algorithm. We refer to thsetup asN-ocular VHI.

We discuss both single andN-ocular VHI schemes inSec. 3.

2.4 Type of Objective Optical System

A volume hologram is very sensitive to the incident illumnation and diffracts only the Bragg-matched componentthe illumination. Often, it is possible to manipulate thelumination to Bragg match the hologram at different objedistances by using specific objective optical systems,instance, microscope objective optics placed in front ofvolume hologram can configure the VHI system to imaobjects at short working distances with very high resotions, and telescope and telephoto objective optics placefront of the hologram can configure the VHI systemimage objects at long working distances also with hresolution.

We discuss both microscope and telescope schemeSec. 3.

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3 VHI Implementations

Volume holograms possess Bragg selectivity, which helpVHI system to optically segment14 the object space andselectively identify special attributes~for instance spatiallocations, spectral signatures, etc.! of interest. We havepreviously24 derived the impulse response as a functionaxial defocus for both SR- and PR-VHI systems. Figu3~a! is a schematic of a SR-VHI system. The diffractefield intensity as a function of the detector coordinatescalculated under the first Born approximation to be

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In Eq. ~1!, (x8,y8) are the detector coordinates,l is thewavelength of light used,d is the longitudinal defocus fromthe Bragg-matched longitudinal locationd, us!1 rad is theinclination of the planar signal beam,L is the thickness ofthe hologram,a is the radius of the hologram aperture, aI b(usE,0;d) is the diffraction intensity at the Braggmatched detector coordinates.L~•,•! is a function that rep-resents the intensity distribution near the focus of a leFigure 3~b! shows an experimentally obtained diffractefield for a SR-VHI system to verify the theory.

Figure 4~a! is a schematic of a PR-VHI system. Thdiffracted field intensity in this case is derived as in Ref.and,

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The depth resolution can be calculated from the impuresponse by integrating over the diffracted field for diffeent values of the defocusd. This results in the longitudinaPSF; we define the full width at half maximum~FWHM! ofthe PSF as the depth resolution of the system. From R24,

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1961Optical Engineering, Vol. 43 No. 9, September 2004


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Fig. 3 (a) Schematic for transmission geometry SR-VHI. (b) Experimentally observed diffracted field,the bright strip inside the disk represents the Bragg-matched portion of the object visible to the SRhologram. Note that the strip is curved on account of the curved fringes that constitute the SR holo-gram. All dimensions are in millimeters unless otherwise noted.

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In Eq. ~4!, d5 f 1 is the working distance of the PR-VHimaging system, all other parameters have already beenfined. From Eqs.~3! and ~4!, we see that the depth resolution degrades quadratically with increasing object distansimilar to most imaging systems. This degradation canoffset to some extent by either making the hologram thic~thus improving its Bragg selectivity! or increasingus ~thisalso makes the hologram more Bragg selective by reduthe grating period!. We notice thatDzFWHM~SR-VHI) de-pends on 1/a2, whereasDzFWHM~PR-VHI) depends only on1/a. This means that the constant 18.2 in Eq.~3! is unitless,but the constant 5.34 in Eq.~4! has dimensions of lengthThe difference between Eqs.~3! and~4! is because the SRVHI system images objects in the Fresnel diffractiongime, whereas the PR-VHI system images objects inFraunhofer~on account of the collimating lens! diffractionregime.24 This leads to interesting problems while desiging the appropriate objective optics for the VHI system, awe have shown that the inverse linear dependence on ature size of PR-VHI can be exploited to achieve optimdepth resolution at a particular working distance.24

VHI systems in several of the subcategories mentioin Sec. 2 have been designed based on the simple SRPR-VHI models. We present a brief overview and workiprinciple for each implementation.

3.1 Reflective Object1Active Illumination, SingleHologram, Single Sensor, No ObjectiveOptics

Figure 5 is the setup for stand-alone VHI without any o

neering, Vol. 43 No. 9, September 2004

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jective optics. The single-volume hologram is recordeding a spherical reference and planar reference beam thinclined at an angleus with respect to the optical axis. Thorigin of the spherical reference is the Bragg-matchedcation for the SR-VHI system. The impulse response ofSR-VHI system is known,24 and the resolution has beeverified experimentally.24,27

The surface profile is recovered as follows. A laser beis focused on the object surface and the SR-VHI systcaptures the reflected light. If the focused spot lies exaon the object surface, the SR hologram is Bragg matcand a strong diffracted signal is measured. On the othand, if the focused spot does not coincide with the objsurface, the volume hologram is Bragg mismatched anddiffracted signal is much weaker. The entire object surfais recovered by scanning completely in 3-D by moving tfocused spot. Figure 6 shows the experimentally obtaisurface reconstruction24 of an artifact consisting of the letters MIT that was located at a distance ofd55 cm from thevolume hologram. The depth resolution of the system wDzFWHM'1 mm.

3.2 Reflective Object1Active Illumination, SingleHologram, Single Sensor, MicroscopeObjective Optics

Figure 7 shows the schematic for VHI with microscoobjective optics. A single PR-volume hologram is used. Timaging is done by focusing laser light on the surfacereflective object. The light reflected by the object surfacecollected by a microscope objective lens placed in front


Fig. 4 (a) Schematic for transmission geometry PR-VHI. (b) Experimentally observed PR-VHI dif-fracted field. The straight bright slit represents the Bragg-matched slit of the object.

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the hologram. If the focused spot on the surface lies atfront focal point of the microscope lens, the light is colmated and a Bragg-matched plane wave is incident onhologram.

The detector monitors the diffracted beam from the hlogram as the object is scanned in 3-D to recover the ensurface profile. Figure 8 shows experimental results for PVHI with microscope objective optics. The object is aanalog tunable MEMS grating. The grating was locatedworking distance ofd52 cm from the microscope objec

tive and the depth resolution for the system wasDzFWHM

'2 mm.

3.3 Reflective Object1Active Illumination, SingleHologram, Single Sensor, Telescope/Telephoto Objective Optics

Figure 9 shows the schematic for VHI with objective optifor long-range surface profilometry applications. Thscheme can be implemented for both SR and PR h

Fig. 5 VHI for reflective object1active illumination, single hologram, single sensor, no objective optics.An intensity detector monitors the beam by the SR hologram diffracted while the object is scanned in3-D.



1964 Optical Engi

Fig. 6 Experimental VH image (from Ref. 24) of a fabricated artifact obtained using 2-mm-thick crystalof 0.03% (molar) Fe-doped LiNbO3 with diffraction efficiency h'5% recorded at l5532 nm. Theworking distance d55 cm; a53.5 mm; us530 deg; and DzFWHM'1 mm. (a) is the actual CAD ren-dering of the object and (b) is a volume holographic image of the object obtained by a complete lateralscan with surface of the letter M being placed at the Bragg-matched location, which consequentlyappears to be bright.

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grams. The depth resolution for most optical systemsgrade quadratically with increasing object distance.23 Oneway to offset this is by using optical elements with larapertures. This is expensive and impractical for volumelograms. A properly designed demagnifying telescopehave a large entrance pupil while ensuring that the fiincident on the hologram placed behind the telescope ithe correct lateral extent. This permits us to increase


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effective aperture of the imaging system and offset somethe degradation of depth resolution.27

A PR-VHI system requires collimating objective opticto Bragg match the PR hologram. In this case, a telephsystem can yield the optimal depth resolution24 for a par-ticular working distance. This is achieved by designing tobjective optical system such that the first principal planeas close to the object as possible. This reduces the effec

Fig. 7 VHI for reflective object1active illumination, single hologram, single sensor, microscope optics.The microscope objective collimates the light reflected from the surface and an intensity detectormonitors the diffracted beam as the active probe is scanned with respect to the object.


Fig. 8 VH image of a MEMS grating using microscope objective optics using the same LiNbO3 crystalbut recorded with a normally incident planar reference beam instead of the spherical reference. Theobjective optics microscope had a working distance of d52 cm with a50.5 cm. (a) is a picture of aMEMS grating being imaged; the height difference in between the top and bottom of the reflectivegrating is 24 mm. (b) VH image with laser point focused on the bottom of the grating, and (c) VH imageafter the focus is raised 24 mm to focus on the top of the grating surface. Note that there is a completecontrast reversal to indicate that the surfaces are indeed at different heights.

Fig. 9 VHI for reflective object1active illumination, single hologram, single sensor, telescope optics.The telescope creates a real image of the distant object in front of the SR hologram, which thendiffracts according to the Bragg condition. An intensity detector monitors the diffracted beam. Theentire object surface is recovered by scanning.


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focal length of the system and enhances the depth restion to the optimal diffraction-limited value.

Figure 10 shows the surface profile of a MEMfabricated turbine located at a working distanced516 cmaway from the aperture of the objective telescope. The

Fig. 10 VH image from Ref. 27 of a microturbine. The hologramwas the same LiNbO3 crystal described in Fig. 6. The telescope hadangular magnification Ma51.5 with d516 cm and a51.2 cm. (a)Image of the microturbine captured with a standard digital camera;the microturbine was manufactured to have surface height featuresof 225 mm. (b) Experimental depth response for a point source ob-ject at the same distance DzFWHM'100 mm; (c) through (f) VH tele-scope scans at progressive increments of 100 mm through the ob-ject. At any given depth, the Bragg-matched portions of the objectare brightest.


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magnifying telescope allowed us to resolve surface featuat a resolutionDzFWHM'100mm.

3.4 Reflective Object1Active Illumination, SingleHologram, Single Sensor, Inclined TelephotoObjective Optics

Figure 11 is a schematic for active VHI for reflective ojects incorporatinga priori object information to enhancedepth resolution. It was noted in Sec. 3.3 that telephobjective optics can achieve the optimal diffraction-limitedepth resolution for a particular working distance whnothing is known in advance about the object. Howeveris possible to incorporatea priori object information andenhance depth resolution even more.

For instance, consider the case when it is known thatreflective object consists of segments of flat surfaces.28 Inthis case, a single PR-VHI sensor inclined with respecthe object surface can achieve substantially better deresolution. This is possible because thea priori knowledgeof the object surface allows us to translate the supelateral resolution of the telephoto PR-VHI system intoapparent depth resolution by scanning the object in a dition that is inclined with respect to the object surface. Fure 12 shows the surface profile of a MEMS device, tnanogate29 located at a working distance ofd546 cm mea-sured using an inclined PR-VHI sensor inclined at anf530 deg with respect to the object surface. This sencan resolve depth features at a resolutionDzFWHM

'50mm.

3.5 Reflective Object1Active Illumination, SingleHologram, Multiple Sensors, TelescopeObjective Optics

The 3-D resolution of a stand-alone hologram imagingreflective target is comparable to triangulation-based bocular imaging systems with considerable angular seption between the two cameras.27 The resolution of VHI sys-tems can be even further improved using multiple Vsensors to look at the same object, as shown in Fig. 13.two images are reconciled by point multiplying the PSF

Fig. 11 VHI for reflective object1active illumination, single hologram, single sensor, inclined telephotooptics. If it is known that the object consists only of flat surfaces, depth resolution can be improved byinclining the object surface with respect to the scanning direction at an angle f, as indicated. Thisapproach exploits the superior depth resolution to improve the apparent depth resolution.


Fig. 12 From Ref. 28, a surface scan of a nanogate, which has surface features '150 mm using aninclined telephoto PR-VHI sensor with d546 cm. (a) Image of a nanogate captured using a standardcharge-coupled device (CCD). (b) PR-VHI image of device with the top surface in focus. (c) and (d)PR-VHI images focused 50 and 100 mm below the top surface. (e) PR-VHI image focused on the baseof the turbine 150 mm below the top surface. Note that again there is a complete contrast reversalbetween images (b) and (e).

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each image. The resulting image has better resolution30 be-cause the measurement is now overconstrained by thetiple measurements.

There are several ways to combine the multiple msurements by using digital processing, like least-squaoptimization, expectation maximization, etc. The pomultiplication method was implemented in the experimeof Fig. 14. Note that the point-multiplied image has betresolution than both the normal VHI and the inclined VH

l-sensor. However, the improvement over the inclined senis only marginal because the inclined sensor itself hascellent resolution. This is discussed in Sec. 3.4.

3.6 3-D Fluorescent Object1Active Illumination,Single Hologram, Multiple Sensors,Telephoto Objective Optics

Figure 15 is the schematic for VHI of a 3-D point-scatteretype object. The individual sources in this case are sm

Fig. 13 VHI for reflective object1active illumination, single hologram, multiple (N52) sensors, tele-scope optics. Multiple (we depict N52) VH sensors, similar to the one described in Fig. 10, are usedto simultaneously image the object. This leads to overconstraining the solution to the imaging inverseproblem and results in better resolution.



1968 Optical Engi

Fig. 14 Surface profiles obtained using two VHI sensors imaging the turbine described in Fig. 10. Onesensor was normal to the turbine surface, the other was inclined at an angle f530 deg with respect tothe turbine surface. The resultant binocular VH image is obtained by point multiplying the individualimages. Note that there is a significant improvement between the binocular and normal VHI images.However, the improvement is not as discernible between the inclined sensor and the binocular image,on account of the phenomenon described in Sec. 3.4.

Fig. 15 VHI for 3-D fluorescent object1active illumination, single hologram, multiple (N53) sensors,telephoto optics. Multiple (we depict N53) VH sensors similar to that described in Fig. 12 acquiredifferent perspectives of the fluorescent 3-D object. The multiple measurements allow for an overcon-strained solution to overcome the degradation of depth resolution32 on account of the broadbandnature of the fluorescence.



Fig. 16 3-D image of a set of fluorescent particles arranged in a helical pattern. The object waslocated at a working distance of d510 cm from three broadband N-ocular PR-VHI sensors. The imageinversion was done using pseudo-inverse techniques.33

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beads that fluoresce on being pumped by laser illuminatEach of the three VHI sensors contains a single PR hgram with telephoto objective optics for collecting the flurescent light. The bandwidth of the fluorescent light resuin an increased field of view~FOV! with accompanyingdegradation of depth resolution.31,32

In this case, it is beneficial to reconcile the three Vimages using a least-squares optimization to obtain thetual 3-D intensity distribution of the object. The experimetal results are shown in Fig. 16.33 The 3-D object was ahelical arrangement of fluorescent beads that was recovby three VHI sensors by overconstraining the measuments using a matrix pseudo-inverse method.

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3.7 Reflective Object1Broadband PassiveIllumination, Single Hologram, SingleSensor, Telephoto Objective Optics

Figure 17 shows the schematic when a reflective objecused with a single hologram VHI sensor under conditioof broadband illumination at a long working distance. Tvolume hologram still has some depth resolution oncount of Bragg selectivity. However, the broader the illmination bandwidth, the worse the depth resolution.32 As aresult, it is not advisable to image reflective objects usbroadband VHI on account of the reduced contrast adepth resolution. This is shown in Fig. 18, which compathe contrast between surfaces for the same object as

Fig. 17 VHI for reflective object1broadband (passive) illumination, single hologram, single sensor,telephoto optics. Increased illumination bandwidth improves the field of view of the VHI system, thusreducing the amount of scanning required. However, this is accompanied by degradation of the depthresolution.



Fig. 18 From Ref. 32, surface profiles obtained using broadband illumination and PR-VHI. The objectis the bottom chassis of a toy car shown in (a). The particular region of interest is a raised screw on thechassis. (b) is the VH image obtained under narrowband (Dl'10 nm) illumination, whereas in (c) thefield of view improves under broadband (Dl'120 nm) illumination. However, (d) indicates that thedepth resolution degrades as the illumination bandwidth increases, i.e., there is a price to pay for theenhanced field of view with respect to poorer depth discriminating ability.

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illumination bandwidth is increased. The object is the btom chassis of a toy car. Notice that the contrast betwobject surface features at different heights degrades asillumination bandwidth is increased.

However, this phenomenon can be exploited to buVHI-based spectrum analyzers to measure the spectralfile of the illumination.32

3.8 3-D Fluorescent Object1Active Illumination,Multiple Holograms, Single Sensor,Microscope Objective Optics

Figure 19 is the schematic of a real-time hyperspecmicroscope.31 The object is a 3-D distribution of fluorescent beads. Three PR holograms are multiplexed insideholographic material. Each hologram is Bragg matcheddifferent depth, and diffracts in a direction specified by tcorresponding recording signal beam. As a result, this V


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system can simultaneously image multiple depth layersthe 3-D object. Moreover, since the fluorescent illuminatiis broadband, it is possible to image wide slices of ealayer. The width of the slice depends on the fluorescebandwidth. The experimental results of imaging three sliare shown in Fig. 20. To our knowledge, this is the fiexperimental demonstration of a real-time hyperspecmicroscope in three spatial dimensions.

4 Discussion and Conclusions

We discuss several VHI implementations for a wide varieof imaging applications and demonstrate the great degredesign flexibility afforded by incorporating volume holograms in imaging systems. However, the limited diffractiof volume holograms means that some part of the obinformation is discarded, since we only monitor the dfracted beam in the system. An information theore


Fig. 19 VHI for 3-D fluorescent object1active illumination, multiple holograms, single sensor, micro-scope optics. Multiple gratings can be recorded inside the same hologram volume. This results inreduced scanning, as the VHI system can simultaneously image multiple locations within the object.This is illustrated in the figure. There are three multiplexed gratings, each observing a different depthslice of the object and then diffracting to a different location on the detector. Thus, the VHI system cansimultaneously monitor three locations without any scanning.

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comparison34 between a confocal microscope with a pihole and a confocal microscope implemented using aume holographic filter suggests that there is a minimdiffraction efficiency required for the VHI system to ouperform the nonVHI implementation. Resonant volumholography24 is a technique that can be used to enhancediffraction efficiency of volume holograms. It can also bused to improve the resolution in active imaging applictions.

In conclusion, VHI offers great promise in designinefficient application-specific computational imaging sytems where the hologram acts as a front-end processothe optical field, and the postprocessing algorithms, sucpoint multiplication and the pseudo-inverse, increaseinformation extracted from the raw image data. We dscribe several systems incorporating various features fthe categories described in Sec. 2. Experiments arerently underway to demonstrate VHI implementations3-D translucent objects using Radon transform approacOur future research goals include building resonant ho

Fig. 20 From Ref. 31, experimental demonstration of real-time hy-perspectral microscope. Three holograms were multiplexed withinthe same volume to look at three different depth layers of a 3-Dobject that consisted of fluorescent microspheres of diameter 15mm. The Bragg selectivity of the hologram allows us to simulta-neously image three depth slices (one slice is much fainter than theother on account of some recording irregularities); the width of eachslice corresponds to the fluorescence bandwidth.

rs

-

.

graphic imaging systems for surface profilometry aimplementing efficient inversion algorithms to obtain reatime data fromN-ocular VHI systems.

Acknowledgments

We are grateful to Tina Shih, Kehan Tian, Robert Murphand Brian H. Miles for helpful discussions. This projewas funded by the Air Force Research Laboratories~EglinAir Force Base! and the Charles Stark Draper LaboratoGeorge Barbastathis also acknowledges the support ofNational Science Foundation through the CAREER~for-merly Young Investigator! Award.

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Imaging using volume holograms

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