In digital holography (DH), the interference between light scattered from an object and a reference wave is recorded using a CCD camera. DH has various advantages over analog holography: no film processing is needed, reconstruction is performed using numerical methods, and no further experimental setup is necessary. However, one of the disadvantages of DH is that current CCDs have a resolution of approximately 1,000 lines/mm, which is less than that of photographic film

Banerjee, Partha P.

Kukhtarev, Nickolai

Nehmetallah, George

English

University of Dayton

University of DaytoneCommonsElectrical and Computer Engineering FacultyPublicationsDepartment of Electrical and ComputerEngineering3-2011Single-Beam Holographic Tomography createsImages in Three DimensionsGeorge NehmetallahThe Catholic University of AmericaPartha P. BanerjeeUniversity of Dayton, pbanerjee1@udayton.eduNickolai KukhtarevAlabama A & M UniversityFollow this and additional works at: http://ecommons.udayton.edu/ece_fac_pubPart of the Computer Engineering Commons, Electrical and Electronics Commons,Electromagnetics and Photonics Commons, Optics Commons, Other Electrical and ComputerEngineering Commons, and the Systems and Communications CommonsThis Article is brought to you for free and open access by the Department of Electrical and Computer Engineering at eCommons. It has been acceptedfor inclusion in Electrical and Computer Engineering Faculty Publications by an authorized administrator of eCommons. For more information, pleasecontact frice1@udayton.edu, mschlangen1@udayton.edu.eCommons CitationNehmetallah, George; Banerjee, Partha P.; and Kukhtarev, Nickolai, "Single-Beam Holographic Tomography creates Images in ThreeDimensions" (2011). Electrical and Computer Engineering Faculty Publications. Paper 237.http://ecommons.udayton.edu/ece_fac_pub/23710.1117/2.1201102.003474Single-beam holographictomography creates images inthree dimensionsPartha Banerjee, GeorgeNehmetallah, andNickolai KukhtarevA novel, nonintrusive technique can record and aid 3D reconstructionof the shapes of translucent objects.In digital holography (DH), the interference between lightscattered from an object and a reference wave is recorded using aCCD camera.1–3 DH has various advantages over analog holog-raphy: no film processing is needed, reconstruction is performedusing numerical methods, and no further experimental setupis necessary. However, one of the disadvantages of DH is thatcurrent CCDs have a resolution of approximately 1000lines/mm,which is less than that of photographic film.Considerable effort has been spent on determining the 2Dshape and distribution of water droplets as they fall or moveat high speed.4, 5 They are translucent, have large curvatures—like lenslets—and can scatter light at very large angles. In ourresearch, we have used DH and DH interferometry extensivelyto determine, for instance, model-aircraft attitudes in flight.6 Useof traditional DH to determine 3D shapes7 results in thousandsof fringes per millimeter, which easily exceeds the resolution ofCCD cameras. To solve this problem, we developed a novel tech-nique based on single-beam holographic tomography (SHOT)to record and reconstruct the 3D shapes and distribution ofwater droplets and lenslets.8 Since the beam width spans sev-eral water droplets, light transmitted between them acts like areference beam: it interferes with the object beam and recordsthe holograms. Thus, single-beam (‘in-line’) holography reducessystem complexity and can be used to determine droplet shape,although it does not provide details of the interior structure.To visualize the 3D shape, multiple projections from differentdirections—as in tomographic imaging systems—are required.Holographic reconstruction is used to generate a 2D visualiza-tion along a certain projection, and the 3D shape is reconstructedusing the SHOT multiplicative technique (SHOT-MT) or SHOTRadon-transform technique (SHOT-RTT).Figure 1. Experimental setup of our single-beam holographic-tomography (SHOT) recording scheme.Figure 2. Schematic showing the principle of how the beams are usedto generate a 3D image using the SHOT-multiplicative reconstructiontechnique.Continued on next page10.1117/2.1201102.003474 Page 2/3Figure 3. (a)–(c) Three holograms of two 1mm-diameter spherical ball lenses. (d)–(f) Reconstruction along the projection angles  = 0, 45, and 90◦.(g) Final 3D shape.Figure 4. (a)–(g) Series of holograms of a large water droplet hanging from one side of a dripper, along the orientations  = 0, 45, 90, 135, 180,225, and 270◦, respectively. (h) 3D reconstruction.In SHOT-MT, digital holograms hj .x; y/ are recorded that cor-respond to each orientation j D Œ0 W j=M W ; j D 1; 2; : : : ;Mwith respect to the y axis, i.e., the axis perpendicular to theplane of the diagram in Figure 1. Subsequently, hj .x; y/ are nu-merically reconstructed and the intensities Ij are computed onmultiple planes around the point at a distance d , correspondingto themiddle of the test volumewhere the droplet is located. Thenumerical reconstruction involves using the discretized formof the Fresnel diffraction formula.1–3, 7, 8 After some coordinatetransformations, the 3D shape and distribution of this dropletcan be reconstructed by multiplying the multiple reconstructedintensities I DMQ1Ij (see Figure 2).In SHOT-RTT, a 3D matrix of all numerically reconstructedholograms from different angles is formed and the inverse3D Radon transform is calculated by computing the inverse2D Radon transform of each slice using the Fourier sliceContinued on next page10.1117/2.1201102.003474 Page 3/3theorem.8 The Radon transform is an integral transform used intomography, where an image is created from the scattering dataassociated with cross-sectional scans of an object. Morphologicalimage-processing techniques are then applied to the inverted 3Dmatrix to get the final 3D shape.Both SHOT-MT and SHOT-RTT can be extended from visual-ization of a single to multiple droplets, such as in a cloud or rain.They enable visualization of the 3D shape of the droplet, as wellas estimation of the radii of curvature around each point on the3D shape. In addition, both methods allow accurate quantifica-tion of the number density of the droplets and their separation.We provide two illustrative examples of SHOT and a recon-struction using SHOT-MT. Figure 3(a)–(c) shows three holo-grams of two ball lenses glued onto the ends of syringe needles.Figure 3(d)–(f) shows their reconstruction along three projectionangles  D 0; 45, and 90◦ using the SHOT-MT technique.Figure 3(g) shows the 3D picture. Note that the needles attachedto hold the lenses result in some deformation, which will beabsent in regular experiments. Figure 4(a)–(g) shows a series ofholograms of a large droplet hanging from one side of a syringe,along the orientations j D 0; 45; 90; 135; 180; 225, and 270◦,respectively. Figure 4(h) shows the 3D picture. Again, deforma-tion where the syringe is attached to the droplet is apparent.In summary, we have described a nonintrusive techniquefor recording and 3D reconstruction of the shapes of lensletsand water droplets using SHOT-MT and SHOT-RTT. The mainadvantage of SHOT-MT is that it usually requires fewer projec-tions than SHOT-RTT and, hence, fewer CCD cameras. In ad-dition, the SHOT-MT algorithm is straightforward. However,its main disadvantage is that the reconstruction program needsmore memory for computation because of the 3D matrix rota-tions involved.Work toward techniques for multiplexing imageson the same CCD and development of more user-friendly andfaster software is currently in progress.Author InformationGeorge NehmetallahDepartment of Electrical and Computer EngineeringUniversity of DaytonDayton, OHGeorges Nehmetallah received his PhD from the Universityof Dayton in 2006. To date, he has published over 30 refer-eed journal papers and conference proceedings. He is a re-search associate, investigating digital holography, metamaterialapplications to sensors technology, and nanoparticle dispersedliquid-crystal cell fabrication and characterization.Partha BanerjeeDepartment of Electrical and Computer EngineeringandElectro-Optics Graduate ProgramUniversity of DaytonDayton, OHPartha Banerjee is a professor. He has published more than100 refereed journal papers and four books. His research areasare holography, metamaterials, acousto-optics, and photorefrac-tive crystals. He is a Fellow of SPIE and the Optical Society ofAmerica.Nickolai KukhtarevPhysics DepartmentAlabama A&M UniversityNormal, ALNickolai Kukhtarev is a research professor of physics. He haspublished more than 180 refereed journal papers and conferenceproceedings, and co-authored three books. His research areasare dynamic holography, photorefractive crystals and polymers,adaptive interferometry, holographic-electromagnetic force, andgeneration of electrons and x-rays. He is a Fellow of the OpticalSociety of America.References1. L. Yaroslavsky, Digital Holography and Digital Image Processing, Springer,2003.2. U. Schnars and W. Juptner,Digital Holography, Springer, 2005.3. T.-C. Poon,Digital Holography and 3D Display, Springer, 2006.4. A. Hanson, E. Domich, and H. Adams, Shock tube investigation of the breakup ofdrops by air blasts, Phys. Fluids 6, pp. 1070–1080, 1963. doi:10.1063/1.17068645. J. E. Matta and R. P. Tytus, Viscoelastic breakup in a high velocity airstream, J. Appl.Polym. Sci. 27, pp. 191–204, 1982. doi:10.1002/app.1982.0702702066. P. P. Banerjee, G. Nehmetallah, N. Kukhtarev, and S. C. Praharaj, Determinationof model airplane attitudes using dynamic holographic interferometry, Appl. Opt. 47,pp. 3877–3885, 2008. doi:10.1364/AO.47.0038777. G. Nehmetallah, P. P. Banerjee, N. Kukhtarev, and S. C. Praharaj, Digital holo-graphic interferometry of translucent objects, Proc. Opt. Soc. Am. Dig. Hologr. 3DImag. (DH), 2010. Paper DMC2.8. G. Nehmetallah and P. P. Banerjee, SHOT: single-beam holographic tomography,Proc. SPIE 7851, p. 785101, 2010.c 2011 SPIE

Single-Beam Holographic Tomography creates Images in Three Dimensions

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Single-Beam Holographic Tomography creates Images in Three Dimensions

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