We demonstrate a Digital Holographic method where two diﬀerent substances in a blend can be discerned. The method requires only one set of exposures and one reconstruction in the plane of focus. The large scale phase variation of the phase image is unwrapped by Flynn’s discontinuity algorithm to reveal which regions in the sample the phase has decreased or increased upon transmission of the illuminating wave. Objects with higher or lower index of refraction than the mounting liquid can be detected as regions where the phase has been shifted. We also present a method to calculate the volume distribution of substrates in a sample. Experimental results of both methods are demonstrated with crystals of NaCl and KCl

Gustafsson, Mats

Sebesta, Mikael

Lund University Publications

LUND UNIVERSITYPO Box 117221 00 Lund+46 46-222 00 00Object characterization with refractometric digital holographySebesta, Mikael; Gustafsson, Mats2004Link to publicationCitation for published version (APA):Sebesta, M., & Gustafsson, M. (2004). Object characterization with refractometric digital holography. (TechnicalReport LUTEDX/(TEAT-7126)/1-6/(2004); Vol. TEAT-7126). [Publisher information missing].Total number of authors:2General rightsUnless other specific re-use rights are stated the following general rights apply:Copyright and moral rights for the publications made accessible in the public portal are retained by the authorsand/or other copyright owners and it is a condition of accessing publications that users recognise and abide by thelegal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private studyor research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portalRead more about Creative commons licenses: https://creativecommons.org/licenses/Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will removeaccess to the work immediately and investigate your claim.CODEN:LUTEDX/(TEAT-7126)/1-6/(2004)Object characterization withrefractometric digital holographyMikael Sebesta and Mats GustafssonDepartment of ElectroscienceElectromagnetic TheoryLund Institute of TechnologySwedenMikael SebestaPhase Holographic Imaging PHI ABSE-224 75 LundSwedenMats GustafssonDepartment of ElectroscienceElectromagnetic TheoryLund Institute of TechnologyP.O. Box 118SE-221 00 LundSwedenEditor: Gerhard Kristenssonc© Mikael Sebesta and Mats Gustafsson, Lund, August 25, 20041AbstractWe demonstrate a Digital Holographic method where two different substancesin a blend can be discerned. The method requires only one set of exposuresand one reconstruction in the plane of focus. The large scale phase variationof the phase image is unwrapped by Flynn’s discontinuity algorithm to re-veal which regions in the sample the phase has decreased or increased upontransmission of the illuminating wave. Objects with higher or lower indexof refraction than the mounting liquid can be detected as regions where thephase has been shifted. We also present a method to calculate the volumedistribution of substrates in a sample. Experimental results of both methodsare demonstrated with crystals of NaCl and KCl.1 IntroductionThe increasing interest in Digital Holography (DH) in recent years is mainly due tothe dramatic development of digital sensors and computers. These two are crucialcomponents for the recording of interference patterns and the reconstruction ofimages. DH has a number of features that makes it an interesting alternative toconventional optical microscopy. Holography incorporates the registration of theinterference pattern between the object field and the reference source. By doingthis, all information of an experimental volume is recorded without any mechanicalmotion of the set up. In one exposure the complete 3D image of an object iscompressed into the hologram [5, 8–10].Several methods have been proposed to use the advantages of DH over con-ventional microscopy. 3D imaging has been suggested in a number of various solu-tions [2, 11]. The phase information obtained in holographic measurements have alsobeen used in pattern recognition and depth resolution by the use of low-coherentillumination [1, 6].We propose a method to discern different types of objects in a sample usingdigital holographic refractometry [5]. The objects considered here are transparentisotropic crystals of Sodium Chloride (NaCl) and Potassium Chloride (KCl). Theseobjects have one index of refraction irrespective of the direction of the illumination.The method uses digital holography to record the interference pattern between thescattered wave from the objects and the reference point source. The plane of recon-struction is set such that the objects are in focus. A phase contrast image is thencalculated which gives a map of the variation of the phase over the objects.2 Digital holographic refractometryConsider two isotropic objects, Object1 and Object2, mounted in a refractive indexliquid as depicted in Figure 1. The objects have different index of refraction and theindex of refraction of the mounting liquid is chosen so that, n1 < nm < n2, where n1,n2, and nm are the index of refraction of Object1, Object2, and the mounting liquidrespectively. A coherent plane wave illuminates the sample from below. The plane2Object2 (n2)Object1 (n1)Coherent illuminationFigure 1: Illustration of the phase shift when a wave impinges on objects with lowerand higher index of refraction than the mounting medium. Object1 and Object2have lower and higher index of refraction than the mounting liquid, respectively.The phase shift is proportional to the variation of the relative index of refractiontimes the thickness of the object.10 mW He-Ne Laser1. 2. 3. 4. 5. 6.8.9.10. 11.1. Mirror2. Polarizing    beamsplitter cube3. Half-wave plate4. Polarizer5. Polarizer6. Shutter7. Half-wave plate8. Half-wave plate9. CCD sensor10. Beamsplitter cube11. Mirror12. GRIN-lens13. Object14. Virtual point source12.13.14.7.Figure 2: The digital Fourier holographic setup. A beam splitter reflects thereference point source which creates a virtual point source close to the object.wave enters the sample and the phase shifts upon propagation through the sample.If the phase of the illuminating wave is chosen such that it increases in the direc-tion of propagation, the phase contrast image increases (decreases) in regions withhigher (lower) refractive index. This behavior is due to the corresponding increase(decrease) of the optical distance for the illuminating wave in such regions [4].A Fourier holography set-up is used to record the holograms, see Figure 2. AJDS Uniphase 10 mW, 633 nm laser is divided in one reference beam and one objectbeam by a polarizing beam splitter. A half wave plate is used before the beamsplitter to control the intensity ratio of the object beam and the reference beam. Tocreate a reference point source a 0.25 pitch GRIN lens is used to focus the referencebeam at the surface of the second beam splitter. The second beam splitter thenreflects the point source on to the CCD sensor. The object beam is directed on tothe object that is placed at the surface of the second beam splitter. The parallelbeam illuminates the object and the scattered light is transmitted through the beamsplitter to the CCD sensor. By using the beam splitter to reflect the reference pointsource, a virtual point source is created and can be placed arbitrary close to theobject by alignment [5]. The used sensor is a Kodak KAF-3200E monochromaticCCD with 2184 × 1472 pixels and a pixel size of 6.8 × 6.8 µm.3500µmFigure 3: Phase contrast image of KCl crystals mounted in a refractive index liquid.The large scale variation of the phase over the image is due to the change in opticaldistance the illuminating wave has traveled through the crystals.500µmFigure 4: Phase image of KaCl crystals. The KCl crystals appear darker than thesurrounding due to their relatively lower index of refraction.Totally, three images are taken, i.e., the hologram, the reference image, andthe object image, respectively. These are then evaluated by the reconstructionalgorithm. For the presented setup, a scheme based on 2-dimensional FFTs hasbeen chosen due to its large numerical aperture and the size of the objects. TheFFT structure is favorable for a hardware implementation, but still computationallyintensive due to the size of the recorded images. Therefore, to improve the recon-struction time, a dedicated hardware solution is being developed [7]. The aim is todevelop a dedicated solution that is more powerful than using a standard computeror a modern signal processor.3 Experimental ResultsFigure 3 shows a phase contrast image of KCl crystals mounted in a refractiveindex liquid. As seen in the image the phase is dramatically changed when goingthrough the crystals. The phase delay can be observed as a color change fromwhite, over gray, to black and back to white. The background also suffers fromphase variation due to the slightly divergent beam of the illuminating wave. The4Figure 5: Phase image of NaCl crystals. The NaCl crystals appear brighter thanthe surrounding due to their relatively higher index of refraction.phase image is then unwrapped by Flynn’s discontinuity algorithm [3] and the largescale background phase variation is removed. The phase variation of the illuminatingwave is removed by fitting the unwrapped phase image to a second order polynomial.In the unwrapped phase images the amplitude is proportional to the contrast inrefractive index times the propagation length through each crystal, i.e., the opticaldistance.In Figure 4, KCl with n = 1.490 has been mounted in a refractive index liquidwith n = 1.520 and the unwrapped phase image has been re-wrapped to the range−2π to 2π to increase the contrast. The size of the larger crystals are about 40µmand considering the relative small difference in index of refraction between the crys-tals and the surrounding liquid the method gives a substantial contrast in the phase.It is noticed that all crystals in the image appear darker than the surrounding andhence confirms the crystals relatively lower index of refraction.In Figure 5, crystals of NaCl mounted in the same liquid as was used in theimages of KCl are depicted. NaCl has an index of refraction of 1.540 which meansthat the phase should decrease on propagation through the crystals. The unwrappedphase image shows that all crystals appear brighter than the background. Here,the difference in refractive index between the crystals and the mounting liquid isapproximately the same, but positive, and again the phase contrast is large.In Figure 6, KCl and NaCl have been mixed and mounted in a mounting liquidwith n = 1.520. In this image the dark crystals of KCl are easily distinguishedfrom the brighter crystals of NaCl. This image shows that digital holography canbe used to separate two different isotropic substrates in a blend. The unwrappedphase image clearly separates the two substrates and an analysis of the distributionof each crystal can easily be made.As the phase contrast image gives a map of the change in optical distance throughthe crystals the index of refraction can be determined if the thickness of the crys-tals are known. However, this is difficult to accomplish as the crystals are highlyasymmetric and there is no reliable method to determine the thickness. However,in this case the index of refraction is known of both the crystals and the mountingliquid. The unwrapped phase image can then be used to calculate the thickness5Figure 6: In a mixture, the KCl and NaCl crystals are identified as dark and brightobjects, respectively.2520151050-5-10-15-20-25Volume1 = 54.6%Volume2 = 45.4%Figure 7: Volume image of a mixture of NaCl and KCl.of each individual crystal. In Figure 7, the volume distribution of NaCl and KClin the sample has been calculated. This is done by using the relative index of re-fraction as ∆OP = d ∆n, where ∆OP is the change in optical path length. ForKCl ∆nk = −0.03 and for NaCl ∆nn = 0.02. The background is set as zero leveland a noise level is used to reduce the errors in the volume calculation. The imageamplitude is now proportional to the distance the illuminating wave have traveledthrough each crystal. Adding the values of each pixel of positive and negative signrespectively in the image gives the volume distribution of each substance in thesample. Dispersion effects have not been considered in these calculations. At thewavelength 633 nm the index of refractions of the liquid and the crystals are lowerthan the tabulated values at 589.3 nm used here, and, hence, the results presentedhere should be considered approximative.References[1] F. Dubois, C. Minetti, O. Monnom, C. Yourassowsky, J. C. Legros, andP. Kischel. Pattern recognition with a digital holographic microscope work-6ing in partially coherent illumination. Appl. Opt., 41(20), 4108–4119, July2002.[2] F. Dubois, L. Joannes, and L.-C. Legros. Improved three-dimensional imagingwith a digital holography microscope with a source of partial spatial coherence.Appl. Opt., 38(34), 7085–7094, December 1999.[3] D. C. Ghiglia and M. d. Pritt. Two-Dimensional Phase Unwrapping: theory,algorithms, and software. John Wiley & Sons, New York, 1998.[4] M. Gustafsson and M. Sebesta. Refractometry of microscopic objects using dig-ital holography. Technical Report LUTEDX/(TEAT-7120)/1–10/(2003), LundInstitute of Technology, Department of Electroscience, P.O. Box 118, S-211 00Lund, Sweden, 2003. http://www.es.lth.se, accepted by Applied Optics.[5] M. Gustafsson, M. Sebesta, B. Bengtsson, S.-G. Pettersson, P. Egelberg, andT. Lenart. High resolution digital transmission microscopy—a fourier hologra-phy approach. Optics and Lasers in Engineering, 41(3), 553–563, 2004.[6] G. Indebetouw and P. Klysubun. Imaging through scattering media with depthresolution by use of low-coherence gating in spatiotemporal digital holography.Opt. Lett., 25(4), 212–214, February 2000.[7] T. Lenart, V. Öwall, M. Gustafsson, M. Sebesta, and P. Egelberg. Acceleratingsignal processing algorithms in digital holography using an FPGA platform.International Conference on Field Programmable Technology (FPT), Tokyo,Japan, December 2003.[8] U. Schnars and W. P. O. Jüptner. Digital recording and numerical reconstruc-tion of holograms. Meas. Sci. Technol, 13, R85–R101, 2002.[9] S. Seebacher, W. Osten, T. Baumbach, and W. Jüptner. The determination ofmaterial parameters of microcomponents using digital holography. Optics andLasers in Engineering, 36, 103–126, 2001.[10] W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer. Digital in-line holography for biological applications. Cell Biology, 98(20), 11301–11305,September 2001.[11] T. Zhang and I. Yamaguchi. Three-dimensional microscopy with phase-shiftingdigital holography. Opt. Lett., 23(15), 1221–1223, August 1998.

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