We propose and investigate a new digital method for the reduction of twin-image noise from digital Fresnel

holograms. For the case of in-line Fresnel holography the unwanted twin is present as a highly corruptive noise

when the object image is numerically reconstructed. We propose to firstly reconstruct the unwanted twin-image

when it is in-focus and in this plane we calculate a segmentation mask that borders this in focus image. The

twin-image is then segmented and removed by simple spatial filtering. The resulting digital wavefield is the

inverse propagated to the desired object image plane. The image is free of the twin-image resulting in improved

quality reconstructions. We demonstrate the segmentation and removal of the unwanted twin-image from in-line

digital holograms containing real-world macroscopic objects. We offer suggestions for its rapid computational

implementation

Ahrenberg, Lukas

Hennelly, Bryan M.

McElhinney, Conor P.

Naughton, Thomas J.

English

MURAL - Maynooth University Research Archive Library

Removing the Twin Image in Digital Holography bySegmented Filtering of In-focus Twin ImageC. McElhinneya, B. M. Hennellya, L. Ahrenberga and T. J. Naughtona,baDepartment of Computer Science, National University of Ireland,Maynooth, Ireland;bUniversity of Oulu, RFMedia Laboratory, Oulu Southern Institute,Vierimaantie 5, 84100 Ylivieska, FinlandABSTRACTWe propose and investigate a new digital method for the reduction of twin-image noise from digital Fresnelholograms. For the case of in-line Fresnel holography the unwanted twin is present as a highly corruptive noisewhen the object image is numerically reconstructed. We propose to firstly reconstruct the unwanted twin-imagewhen it is in-focus and in this plane we calculate a segmentation mask that borders this in focus image. Thetwin-image is then segmented and removed by simple spatial filtering. The resulting digital wavefield is theinverse propagated to the desired object image plane. The image is free of the twin-image resulting in improvedquality reconstructions. We demonstrate the segmentation and removal of the unwanted twin-image from in-linedigital holograms containing real-world macroscopic objects. We offer suggestions for its rapid computationalimplementation.Keywords: Twin-image reduction, Digital Holography, Segmentation1. INTRODUCTIONSince the invention of holography by Gabor1 in 1948, the removal of the unwanted twin-image has remained apersistent area of research. The results of Gabor’s original in-line experiment were marred by the presence ofthis out of focus twin-image and the so called zero-order intensity terms. While some early attempts at removingthese unwanted noise terms were successful2 the additional experimental processing involved was laborious andtime consuming. Following the invention of the laser an innovative approach to separate the wanted image fromthe unwanted terms was invented.3 This entailed the use of an off-axis reference beam at some angle to theincident object wavefield. The new architecture proved to be a resounding success but notably increased theneed for recording materials with higher resolution capacities.Despite the obvious advantages of the off-axis method there remain a number of holographic applications forwhich it is either undesirable or is without implementation. The original in-line architecture remains the modeof choice in many cases such as electron holography, x-ray holography and gamma ray holography4 due to thelack of physical elements, e.g. an x-ray lens. In the case of optical digital holography4–9 the off-axis method hasbeen successfully proposed and investigated.6 However, the inherent high resolution requirements of the off-axistechnique impose a severe demand on the relatively low resolution of current digital cameras. The resultingrestrictions include the placement of macroscopic objects at large distances from the camera and the permissionof a very limited range of reconstruction angles (approximately 1-2 degrees for an acceptable image resolution).These parameters can be improved upon by an integer factor if an in-line set-up is used but this introduces theunwanted noise terms.Removal of the twin-image in digital holography, optical or otherwise, can be broken down into at least fivemain groups; (i) Off-axis techniques,3, 6 (ii) Phase shifting interferomtery (PSI),5 (iii) Linear filtering7 (iv)Phase retrieval methods4 and (v) filtering of the complex wavefront in reconstruction planes .8, 9 Phase-shiftingrequires multiple captures with different phase shifts of the reference beam and is therefore not ideal for singleFurther author information: (Send correspondence to C. McElhinney or T. Naughton)E-mail: conormc@cs.nuim.ie, tomn@cs.nuim.ieOptics and Photonics for Information Processing II, edited by Abdul Ahad Sami Awwal, Khan M. Iftekharuddin, Bahram Javidi, Proc. of SPIE Vol. 7072, 707208, (2008)0277-786X/08/$18 · doi: 10.1117/12.795894Proc. of SPIE Vol. 7072  707208-1Downloaded from SPIE Digital Library on 15 Jan 2010 to 130.231.240.13. Terms of Use:  http://spiedl.org/termscapture applications. Linear filtering can work with a single capture but it is generally limited to real objects andis often not as successful as (i) and (ii). Phase retrieval can also work with a single capture but generally requiresan intensive iterative computational process, the convergence of which is not always guaranteed. The methodoutlined in this paper falls into category (v). It requires only a single capture and no additional experimentalprocessing. It can be performed rapidly and shows results comparable with the best of the other methods.2. TWIN REDUCTION BY FILTERING THE RECONSTRUCTION PLANE OFDIGITAL HOLOGRAMSIn [ 9] the first instance of filtering the complex wavefront in the reconstruction planes of digital holograms ap-peared in the literature. This involved cutting out the wanted digitally reconstructed image from its surroundingpixels. However this area still contained considerable noise from the unwanted twin-image. In [ 6] spatial fil-tering was applied to an off-axis digital hologram. In [ 8] a novel method of filtering the complex wavefront inthe reconstruction domain was proposed and it is this method that we build upon in this paper. It was shownthat by cutting out the reconstructed focused unwanted twin and returning to the plane of the wanted imageby numerical propagation one could free oneself of the unwanted noise. The method was proposed only in thearea particle holography and the removal of the twin-images was a manual operation. In this paper we proposethe use of a similar technique for macroscopic objects and we make the significant addition of using automaticsegmentation algorithms to remove the unwanted macroscopic image. While this paper focuses on optical digitalholography, we note that it may be applied to any of the other holographic fields listed above.Several new approaches to the segmentation of holographic reconstructions into a compact representationof the useful information held in these reconstructions have been developed.10–14 These approaches have usedphase,12 intensity10, 14 and complex information13 as well as the estimated depth11 to segment a reconstructioninto object(s) and background. They can be further refined into approaches which segment using a singlereconstruction10, 12 or multiple independently focused reconstructions.11, 13, 14 Most of these methods have beendeveloped for segmenting reconstructions containing microscopic objects and plankton. The reconstructions ofthese near 2D biological organisms are relatively free of speckle noise compared to reconstructions of macroscopicobjects encoded in DHs. In this paper we will use a modified version of the object segmentation algorithm14developed for macroscopic objects, of which speckle is a fundamental characteristic.We use the Fresnel approximation, the propagation transfer function, to numerically propagate our digitalholograms.15 This is a lossless transform and ensures that the energy of the object signal is preserved afterpropagation. Due to its use of the discrete Fourier transform with finite support and the conservation of energythe object signal will be wrapped within the reconstruction window. We therefore have to pad at the hologramplane sufficiently that the reconstruction window is larger than the spatial extent of the object signal. This isevident from Fig. 1 where the original hologram data was 2048×2048 and is centered within the new 8196×8196hologram plane. This introduces a computational overhead onto that process which we have addressed throughthe implementation of the technique on a Graphics Processing Unit (GPU).3. THE ALGORITHMOur algorithm requires three inputs: a dc-term suppressed hologram HTI(x, y) in which the dc or zero orderterm has been removed by some means, the depth, dmm, of the focal plane of the twin-image, and a block sizen× n. Our algorithm can be described in three individual stages, and is displayed in Fig.13.1. Stage 1: Propagate to the twin-image planeThe first stage requires us to numerically propagate our hologram to the focal plane of the unwanted twin-imageusing our input hologram HTI(x, y) and the distance dmm. This reconstruction is stored in RTI(x, y) and it’sintensity is used to calculate the segmentation mask.Proc. of SPIE Vol. 7072  707208-2Downloaded from SPIE Digital Library on 15 Jan 2010 to 130.231.240.13. Terms of Use:  http://spiedl.org/termsFigure 1. Twin-image removal process stages: 1) propagate to the twin-image plane, 2) segment twin-image and 3)propagate to the hologram plane.3.2. Stage 2: Segment twin-imageTo segment the twin-image we need to calculate a segmentation mask SMask(x, y). We use a modified version ofthe segmentation approach developed for digital holograms containing macroscopic objects.14 In this modifiedapproach the segmentation mask is created through the thresholding of a single variance map. The variance mapis calculated by processing an in-focus reconstruction. We select a block size of n× n and process the intensityof our in-focus reconstruction |RTI(x, y)|2 by calculating variance on the overlapping blocks using:V (k, l) =1n2k+n−12 ∑x=k−n−12 l+n−12 ∑y=l−n−12 [|RTI(x, y)|2 − µ]2, (1)where µ is the arithmetic mean of the current block of n× n pixels and where any indexes (x, y) that go outsidethe extent of RTI(x, y) evaluate to 0. A location with high variance indicates the nearby presence of an object.A threshold τ is chosen and V (k, l) is transformed asSMask(k, l) = 0 if V (k, l) < τ ; 1 if V (k, l) ≥ τ, (2)where 1 denotes a background pixel and 0 denotes an object pixel. The binary image SMask is our segmentationmask and we obtain the segmented twin-image by simulating an inverse aperture usingRS(x, y) = RTI(x, y) · SMask(x, y) (3)where · indicates pointwise product.3.3. Stage 3: Propagate to the hologram planeOnce we have successfully segmented the twin-image we then propagate RS(x, y) to the hologram plane, adistance of dmm. We now have a hologram, H(x, y), free of the twin-image.The three stages has been implemented using stream programming16 and are executed on programmablegraphics hardware. This approach has been shown to render images from digital holograms far more efficientlyProc. of SPIE Vol. 7072  707208-3Downloaded from SPIE Digital Library on 15 Jan 2010 to 130.231.240.13. Terms of Use:  http://spiedl.org/termsthan traditional CPU based methods.17 We employ the convolution approach, as described in,17 directly for lightpropagation in Stage 1 and Stage 3. Stage 2, the segmentation stage, may present a problem if implementeddirectly from Eqn. 1, as the overlapping blocks will cause intensive calculations. However, by rewriting theequation asV (k, l) =⎡⎣ 1n2k+n−12 ∑x=k−n−12 l+n−12 ∑y=l−n−12 |RTI(x, y)|4⎤⎦− µ2, (4)we see that it consists of the difference between two sums over the same block area, the mean squared intensities,in brackets, and the squared mean intensities, µ2. We thus divide Stage 2 into two steps. First two summed areatables18 are computed, one for each sum in the equation. Second, the variance for a specific location is computedas the difference of the appropriate block areas in the two tables. Our PC has a 2Ghz core due processor with2GB of RAM and a Nvidia GeForce 8800GTX with 768MB of RAM. Using traditional numerical propagationand Eqn. 1 on a CPU the process takes over 2000 seconds for a hologram padded to 4096 × 4096. Due tomemory requirements this was the largest hologram we could reconstruct with the CPU. However, using thedescribed GPU implementation (and less RAM) we could pad the hologram to the needed 8196× 8196 samples(to guarantee that no wrapping of the object signal) and remove the twin-image in just 8.4 seconds as shown inTable 1.Table 1. Twin-image removal computation time (seconds)Process CPU time GPU timePixel Resolution 4096× 4096 8192× 8192Stage 1 25 3.4Stage 2 1992 1.59Stage 3 25 3.4Total 2042 8.44. RESULTSWe verify our twin-image removal technique using a DH of a real-world object. The knight object was positionedapproximately 377mm from the camera with a diameter of 17.5mm. Our CCD has 2048× 2048 pixels and wehave padded the hologram plane to 8192× 8192 pixels. A reconstruction of the hologram before suppression ofthe dc-term is shown in Fig. 2(a). We manually suppress the dc-term through applying a high pass filter to theFourier transformed hologram and inverse Fourier transforming the result.6, 19 We selected a circular aperturewith a radius of 200pixels for this hologram. The reconstruction after dc-term suppression is shown in Fig. 2(b).Our second input was selected by qualitatively determining the depth of the in-focus plane, we selected a depthof 377mm. Our final input is the block size, 81× 81. We display the calculated segmentation mask in Fig. 2(c)and the output reconstruction after twin-image removal in Fig. 2(d). In the future we intend to compare our twinreduced reconstructions with PSI holograms. PSI holograms are theoretically free of the dc-term and twin-imageand a comparison of the PSI reconstruction with the reconstruction from our new approach shows similar quality.Due to the large hologram size we decided to use the simplified segementation mask creation process outlinedin this paper instead of the more exhaustive approach from [14]. For objects with a large depth-of-focus it maybe necessary to use the depth-independent segmentation approach from [14]. The accuracy of our approach iscurrently limited by the manual selection of a threshold in to create the segmentation mask and the manualselection of the twin-image in-focus plane. We have demonstrated the rapid removal of the twin-image from ain-line digital hologram using only digital processing, removing the need for the use of experimental processing,multiple captures or an off-axis experimental setup.Proc. of SPIE Vol. 7072  707208-4Downloaded from SPIE Digital Library on 15 Jan 2010 to 130.231.240.13. Terms of Use:  http://spiedl.org/terms(a) (b) (c) (d) Figure 2. Numerical reconstructions of knight hologram, reconstruction of (a) unprocessed hologram, (b) hologram afterdc-term removal, (c) calculated segmentation mask,(d) hologram after dc-term and twin-image removal5. CONCLUSIONIn holography, the in-line architecture offers significant advantages over its off-axis counterpart. In particular wecan obtain a higher bandwidth signal and greatly reduce the so-called key-hole problem. However the presence ofthe twin for the in-line architecture often forces the use of the off-axis set-up. In this paper we have proposed andinvestigated a novel digital signal processing method for the reduction of twin-image noise from digital Fresnelholograms. We have demonstrated how to firstly reconstruct the unwanted twin-image when it is in-focus and inthis plane we calculate a segmentation mask that borders this in focus image. Care must be taken to ensure thatwe can digitally calculate the full support of the this plane. This is accomplished by considerable zero paddingin the reconstruction algorithm. The resultant increased computation is dealt with by employing dedicatedhardware devices. The twin-image is then segmented and removed by simple spatial filtering. The resultingdigital wavefield is the inverse propagated to the desired object image plane. The image is free of the twin-imageresulting in improved quality reconstructions. We have demonstrated the validity of the method and outlinedtimes taken for its implementation.ACKNOWLEDGMENTSThe research leading to these results has received funding from the European Community’s Seventh FrameworkProgramme FP7/2007-2013 under grant agreement no. 216105.REFERENCES1. D. Gabor, “A new microscopic principle,” Nature 161, p. 777, 1948.2. W. Bragg and G. Roger, “Elimination of the unwanted image in diffraction microscopy,” Nature 167, p. 190,1951.3. E. Leith and J. Upatnieks, “Wavefront reconstruction with continuous-tone objects,” J. Opt. Soc. Am. 53,pp. 1377–1381, 1963.4. T. Latychevskaia and H. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98,p. 23390, 2007.5. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, p. 1268, 1997.6. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination indigital off-axis holography,” Appl. Opt. 39, pp. 4070–4075, 2000.Proc. of SPIE Vol. 7072  707208-5Downloaded from SPIE Digital Library on 15 Jan 2010 to 130.231.240.13. Terms of Use:  http://spiedl.org/terms7. L. Onural and P. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, pp. 1124–1132, 1987.8. L. Denis, C. Fournier, T. Fournel, and C. Ducottet, “Twin-image noise reduction by phase retrieval in in-linedigital holography,” Proc. SPIE 5914, pp. 59140J–1, 2007.9. J. Pedrini, P. Frning, H. Fessler, and H. Tiziani, “In-line digital holographic interferometry,” Appl. Opt. 37,pp. 6262–6269, 1998.10. P. Hobson and J. Watson, “The principles and practice of holographic recording of plankton,” J. Opt. A:Pure Appl. Opt. 4, p. S32, 2002.11. E. Malkiel, J. Abras, and J. Katz, “Automated scanning and measurement of particle distributions withina holographic reconstructed volume,” Meas. Sci. and Tech. 15, pp. 601–612, 2004.12. M. Gustafsson and M. Sebesta, “Refractometry of microscopic objects with digital holography,” Appl. Opt.43, pp. 4796–4801, 2004.13. M. DaneshPanah and B. Javidi, “Segmentation of 3d holographic images using bivariate jointly distributedregion snake,” Opt. Exp. 14, pp. 5143–5153, 2006.14. C. McElhinney, J. McDonald, A. Castro, Y. Frauel, B. Javidi, and T. Naughton, “Depth-independentsegmentation of three-dimensional objects encoded in single perspectives of digital holograms,” Opt. Lett.32, pp. 1129–1231, 2007.15. T. Kreis, Handbook of Holographic Interferometry, Wiley-Vch, New York, 2005.16. U. Kapasi, S. Rixner, W. Dally, B. Khailany, J. Ahn, P. Mattson, and J. Owens, “Programmable streamprocessors,” IEEE Computer .17. L. Ahrenberg, A. Page, B. Hennelly, J. McDonald, and T. Naughton, “Using commodity graphics hardwarefor real-time digital hologram view reconstruction,” in preparation .18. F. Crow, “Summed-area tables for texture mapping,” SIGGRAPH Comput. Graph. 18, pp. 207–212, 1984.19. G. Chen, C. Lin, M. Kuo, and C. Chang, “Numerical suppression of zero-order image in digital holography,”SIGGRAPH Comput. Graph. 15, pp. 8851–8856, 2007.Proc. of SPIE Vol. 7072  707208-6Downloaded from SPIE Digital Library on 15 Jan 2010 to 130.231.240.13. Terms of Use:  http://spiedl.org/terms

Removing the twin image in digital holography by

segmented filtering of in-focus twin image

http://mural.maynoothuniversity.ie/2377/1/TN_Twin_Image.pdf

Removing the twin image in digital holography by segmented filtering of in-focus twin image

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