Digital Tomosynthesis in Cone-beam Geometry for Industrial Applications: Feasibility and Preliminary Study

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1 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 9, pp SEPTEMBER 01 / 1533 DOI: /s Digital Tomosynthesis in Cone-beam Geometry for Industrial Applications: Feasibility and Preliminary Study Min Kook Cho 1, Hanbean Youn 1, Sun Young Jang 1, Suk Lee 1,, Myung-Chul Han 1,, and Ho Kyung Kim 1,,# 1 School of Mechanical Engineering, Pusan National University, Jangjeon-dong, Keumjeong-gu, Busan, South Korea, Center for Advanced Medical Engineering Research, Pusan National University, Jangjeon-dong, Keumjeong-gu, Busan, South Korea, # Corresponding Author / hokyung@pusan.ac.kr, TEL: , FAX: KEYWORDS: Computed tomography, Filtered backprojection, Image reconstruction, Limited angle tomography, Nondestructive evaluation, Tomosynthesis We introduce a cone-beam computed tomography with insufficient projections obtained from a limited-angle scan, the socalled digital tomosynthesis, and demonstrate its feasibility for the industrial applications by implementing to the reconstruction of internal slice images of a multilayer printed circuit board. The image reconstruction algorithm is based on the filtered-backprojection approach for the cone-beam geometry with isocentric linear motion in the scanning trajectory of the X-ray source and imaging detector pair. Although the slice image reconstructed at the plane of interest was affected by the structures outside, we could reconstruct the plane of interest with the total scan angle less than 0 degrees and 11 projections. The digital tomosynthesis is expected to be practical for industrial tomography restricted to the limited-angle scan. Manuscript received: January 11, 01 / Accepted: April 13, Introduction The X-ray computed tomography (CT) technology is popularly being used for medical diagnoses 1-3 as well as industrial quality control and nondestructive evaluation. 4-6 Recent developments in large-area flat-panel detectors have created the concept of conebeam volumetric CT (CBCT), which can enable a threedimensional (3D) scanning covering a field of view larger than 300 mm in a single circular scan. 7-9 The CT with insufficient projection images suffers from the sparse-view artifact which normally appears as streaking patterns. 10,11 To avoid the sparse-view artifact, CT typically requires as many projection images as possible over more than half a single circular motion around an object. However, many situations are restrictive in obtaining the adequate number of projection images; sometimes, the size as well as the geometrical complexity of an object to be imaged might limit the complete traverse motion of the CT gantry system. This situation is frequently met in industrial nondestructive testing and evaluation. For the fast scan and the scanning in a certain limited angular range, the limited-angle tomography has been greatly studied. 1,13 Digital tomosynthesis is a technique that produces sectional, or slice, images from a series of projection images acquired as the X-ray source moves over a prescribed path. 13 Therefore, it can provide 3D information at a lower X-ray irradiation and potentially lower cost than conventional CT in certain imaging situations. It was also reported that the spatial resolution in tomosynthesis images is better than that in CT by a factor of three. 14 Although the basic theoretical framework for tomosynthesis was already provided in the 1930s, its renewed interest has been in the spotlight since large-area flat-panel detectors, which are stable, self-scanned imaging devices showing high signal-to-noise performances in images, had been introduced in the late 1990s. 15 In this paper, we describe a modified filtered-backprojection (FBP) method for digital tomosynthesis in cone-beam geometry with isocentric linear motion in the scanning trajectory of the X-ray source and imaging detector which face each other with an object located at the axis of rotation (AOR). While a large amount of efforts has been invested in the development of digital tomosynthesis techniques for medicine, 13,15 there has not been sufficient attention paid to industry. In this work, we demonstrate the applicability of digital tomosynthesis to industrial purposes by extracting slice images from a multilayer printed circuit board (PCB) as a preliminary study. Further detailed quantitative analysis for its image characteristics can be found in ref. 16. KSPE and Springer 01

2 1534 / SEPTEMBER 01 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 9. Theoretical Background The basic reconstruction algorithm for tomosynthesis is the shift-and-add (SAA) method that shifts each of the projection images by a given amount and then adds them together to make objects in a given plane to be sharpened while objects from other planes to be blurred. 17 This SAA method is basically equivalent to the simple backprojection (BP) method. 18 It is, however, insufficient to use SAA alone for high-quality tomosynthesis because of blur from outside of the plane of interest (POI). Therefore, the SAA or BP method requires a deblurring procedure to compensate for the out-of-plane blur. 19 For the cone-beam digital tomosynthesis, we adopt the modified FBP method with insufficient projection data obtained from a limited-angle scan. The strategy is based on the conventional FBP method with an additional filter to control the incomplete frequency responses due to sampling in limited angular range in cone-beam geometry. 0,1 Cone-beam geometry with planar detectors is very attractive because of the simple geometry and quick scan for large volumetric objects, and thus it is popular in many technical applications. However, since a single circular X-ray source trajectory in conebeam geometry does not provide complete Radon data, the exact 3D image reconstruction is not available following the Tuy-Smith sufficiency condition. Instead, an approximate version of the exact reconstruction developed by Feldkamp, Davis, and Kress, the socalled FDK method, 3 is typically used. The FDK method is a simple extended version of the conventional FBP method in longitudinal direction by considering the cone angle. It is, therefore, an approximate approach and may cause distortion when the cone angle is wide. However, since the FDK algorithm is very fast and easily applicable, it is mostly widely used in commercial CBCT systems. 4 Figure 1 illustrates a reconstruction scheme of a voxel value of an object f at r = (x, y, z) with projection p (ξ, η) obtained at angle. The cone-beam geometry employs the isocentric linear motion for scanning. Following the notations described in Fig. 1, the FDK reconstruction formula for the range of projection angle from min to max can be given by where f() r = max d SD p (, ) h() d ξη ξ, (1) min ( d r ( n ) SO ξ nη ) p ( ξη, ) = cos ϕ p ( ξη, ) () for correcting the different ray length in cone beam. h( ) is the highpass filter, expressed in the space domain, to compensate the distance-weighted blur arising in the backprojection operation and only depends upon the ξ direction in projection images. The symbol implies the one-dimensional (1D) convolution operation between the cosine-weighted projection and the high-pass filter. Distance parameters d SD and d SO denote the source-to-detector and source-to-aor distances, respectively. n ξ and n η denote the unit vectors describing the direction of two perpendicular axes in Fig. 1 Sketch describing image reconstruction in cone-beam geometry employing the isocentric linear motion for scanning. For the reconstruction of a voxel value located at r = (x, y, z), the contribution of projection value at (ξ, η) in the planar detector obtained at the projection angle is illustrated projection images. Since d r ( n ) SO ξ n η or d z designates the distance from the source to the reconstruction plane or the POI in the object, denoted by f(x, y; z), d d implies the magnification SD z of the POI for the projection plane. Therefore, the weighting term ( d d ) is to correct the contribution of projection signal toward SD z the voxel to be reconstructed by considering distance or magnification. Unlike the conventional CBCT, which reconstructs crosssectional images perpendicular to the AOR, the digital tomosynthesis can reconstruct images parallel to the AOR. In this regard, Eq. (1) can be expressed in a more practical form: f( x, y; z) = max d d d (3) SD SD SD p (, ) h t d d, ξη ξ ξ min d d z d + ξ + η z SD where t denotes the rotated x system with respect to the projection angle. Therefore, Eq. (3) describes that the 1D filtered preweighted projection signals are added in each virtual voxel, which eventually constitutes the object, considering magnification between the voxel and the corresponding projected pixel over the scanned angular range. 3. Materials and Methods 3.1 Experimental We employed an object-rotation system instead of gantry rotation, as illustrated in Fig. 1, to acquire projection images for digital tomosynthesis. The detailed description of the experimental

3 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 9 SEPTEMBER 01 / 1535 setup is as follows. 16 X-ray image intensifier (XRII) system (TH 9464, Thales Electron Device, France) was used as the imaging detector, and it had a pixel format in an output image. The diameter of XRII was about 7 mm so that the imaging pixel pitch was about 0.07 mm in square geometry. The X-ray tube had a thin transmission tungsten target designed to have a focal spot size of the order of micro-millimeters (SEC Co., Ltd., Korea). The maximum operation conditions were 160 kvp and 0. ma. The X- ray tube and XRII were fixed with a distance of 500 mm in an upright position. A rotational object jig was attached at a linear guide bar, which had linear translational motion against the X-ray tube that was located at the bottom side of the imaging configuration. As a sample object, we used a multilayer PCB having two chips mounted onto the top and bottom. 16 The chips had a package format in a ball-grid array (BGA). The sample was mounted on the object jig and it was positioned at d SO in order to provide magnification of 10 at the imaging detector plane. For the prepared sample, the projection images were acquired at every 0.9 for a 360 circular scan. Therefore, the total number of projection images was 400 views for a single circular motion. During the acquisition of the projection images, the X-ray tube was maintained at the operation condition of 60 kvp and 0.1 ma. Typical correction procedures for the geometric distortion, and gain and offset in the XRII system were applied to all images before image reconstruction and analysis Image Reconstruction and Evaluation Geometric calibration was performed to determine geometric parameters, such as d SD, d SO, misalignment of the detector plane with respect to the central beam of X-rays, and tilted angle of the detector plane axis. To measure geometric parameters, multiple projection images of small metal balls with a diameter of 0.5 mm to mimic point-like objects were acquired with the configured system, and the images were analyzed to determine the parameters based on the algorithm, which analytically calculates the phantom trajectories, reported in ref. 5. Although about 15% misalignments in distance parameters were measured, the magnification factor was almost unchanged. The misalignment of the center position at the detector plane for the central beam from the X-ray tube was -10 pixels and 7 pixels in ξ and η directions, respectively. The rotation of the η-axis of the detector plane was measured to about 0.3. The determined misalignment parameters were used for the correction during image reconstruction. Although the accuracy in misalignment measurement itself could not be quantitatively estimated, we did not observe any artifacts resulted from the misalignments after correction. As the filter function in the image reconstruction, we employed the Shepp-Logan filter. 6 Since incomplete sampling over the limited angular range results in an out-of-plane artifact in the reconstructed images, 7 we incorporated an additional filter to limit the frequency response in the depth or z direction by using the Hann window function: 8 1 π w Kw ( ) = 1 cos + B, (4) Fig. Projection images of the PCB sample for two different tilted angles of the object jig: (a) -45 and (b) 0 where w designates the Fourier conjugate corresponding to z in the space Cartesian coordinates. B determines the bandwidth and is multiples of u tan( ) in which u N scan N is the Nyquist frequency in the u direction in the Frequency domain (corresponding to x in the space domain) 9 and scan denotes the total scan angle, max min. The filter K limits the bandwidth of the projection images hence reducing high-frequency noise, spectral leakage and aliasing. This filtering operation results in anisotropic voxel size to avoid aliasing artifact, consequently a scan-angle-dependent slice thickness which is inversely proportional to tan( scan ). 30 The size of the voxel in x and y directions was the same as the pixel pitch of the detector divided by the system magnification factor. The quality of tomosynthesis was investigated with respect to the angular range and the number of projection images used for image reconstruction. For the comparison with the conventional reconstruction methods, the SAA method was also applied. Contrast-to-noise ratios (CNRs) for both reconstruction methods were measured and compared each another. The CNR was calculated by 4 µ µ CNR = σ lead PCB + σ lead PCB where µ and σ are the mean and standard deviation of the voxel values over the prescribed region of interests, respectively. The subscripts lead and PCB denote the lead soldering ball and neighboring background PCB regions in the sample, respectively. 4. Results Figure shows projection images obtained for two different rotation angles of the object jig: (a) -45 and (b) 0. The projection image obtained at the tilted angle well demonstrates the structure of the sample, such as via holes and BGA both at the opposite sides of the PCB. Comparison of slice images reconstructed by two different methods with 1 projection images for scan = 7 is shown in Fig. 3: (a) the SAA method and (b) the tomosynthesis method. As expected, the image reconstructed by the SAA method is blurry compared to the other method which incorporates the deblurring (or filtering) procedures. The calculated CNRs are 3. and 8.1, respectively. An approach of simply adding projection images gives, (5)

4 1536 / SEPTEMBER 01 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 9 Fig. 3 Comparison of slice images reconstructed by (a) the shiftand-add and (b) modified FBP tomosynthesis techniques Fig. 6 Volume-rendered images obtained from the modified FBP tomosynthesis technique for a wide range of scan angles with a given step angle of 0.9. For comparisons, the reference image obtained with the CBCT approach for the complete circular scan of 360 Fig. 4 Enlarged image of Fig. 3(b) to demonstrate small voids in lead soldering balls. The open arrows indicate very tiny voids in lead soldering balls. The solid arrows indicate blur artifacts from out of planes Figure 5 summarizes slice images reconstructed by tomosynthesis with respect to various scanning angular ranges scan and the number of projection images N. As the angular range narrows, the image sharpens but the depth resolution worsens because the effective slice thickness increases. As the number of projection images used for tomosynthesis increases, the signal-to-noise ratio or CNR improves significantly because the CNR is typically proportional to the square root of an x-ray dose or the number of projections. 4 Figure 6 compares the 3D volume-rendered images reconstructed by tomosynthesis with respect to various scan angles for a fixed step angle of 9. For comparisons, the reference 3D volumerendered image obtained with the CBCT approach for the scan angle of 360 is also displayed in Fig. 6. As addressed in the section 3., the effective slice thickness in tomosynthesis increases with narrowing scan, hence reducing the depth resolution Discussion and Conclusion Fig. 5 Slice images obtained from the modified FBP tomosynthesis technique for a wide range of scan angle (18 90 ) and the number of projection images (11 and 1) a higher CNR value while the filtering method gives relatively lower value; however, the SAA method cannot be employed as a practical use due to significant reconstruction artifact, i.e. the outof-plane blur. 31,3 For a detailed evaluation, an enlarged image of Fig. 3(b) is shown in Fig. 4. Voids in lead soldering balls are clearly visible, which could not be achieved in projection images as demonstrated in Fig.. Very tiny voids are visible as indicated by the open arrows. However, some blurs from out-of-planes, which would not be completely removed by the deblurring procedure, still appeared as indicated by the solid arrows. We have introduced the digital tomosynthesis algorithm as it is applied into industrial nondestructive X-ray imaging in the conebeam geometry having isocentric linear motion. Digital tomosynthesis is a limited-angle tomography and basically shares the same mathematical framework with the conventional CT technique in this study. The limited angular scan gives rise to incomplete data sampling in the Fourier domain, and consequently the out-of-plane artifacts are appeared in the reconstructed images. To remedy these artifacts, we employed a windowing function to restrict the sampled data in the depth direction; hence reducing spectral leakage and aliasing. However, this approach results in the anisotropic voxel size, and which may limit the utilization of digital tomosynthesis for a full 3D volume reconstruction. Instead the digital tomosynthesis technique can be used for providing slice images parallel to the axis of rotation, and which is a great advantage when investigating objects having thin slab geometries, printed circuit boards for example. 16 It has been also reported that

5 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 9 SEPTEMBER 01 / 1537 synthesis of two volume-reconstructed datasets, taken separately, for two different limited-angle scans performed at orthogonal angels could enhance the depth resolution in digital tomosynthesis. 34 A great effort in the development of the tomosynthesis technique for medical diagnoses, such as, breast, chest, abdominal, and musculoskeletal applications, has been devoted because of a relatively lower dose and higher spatial resolution compared to the conventional CT. However, tomosynthesis with large-area flat-panel detectors has not been given much paid attention in industry. As we demonstrated in this work, tomosynthesis has potential in industrial applications. The use of fewer projection images for image reconstruction would make a faster evaluation of internal structures. The flexible selection of scanning angular range may make the tomosynthesis technique promising in terms of the accessibility for complex systems to be evaluated. A real-time in-line system with the tomosynthesis technique can be expected if we utilize a hardware-based image reconstruction, for example, graphics processing unit, or the parallel computing method for the image reconstruction. ACKNOWLEDGEMENTS The research on the image reconstruction based on the dataparallelization approach was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( ). REFERENCES 1. Kalender, W. A., X-ray Computed Tomography, Phys. Med. Biol., Vol. 51, No. 13, pp. R9-R43, Pan, X., Siewerdsen, J., La Riviere, P. J., and Kalender, W. A., Anniversary Paper: Development of X-ray Computed Tomography: The Role of Medical Physics and AAPM from the 1970s to Present, Med. Phys., Vol. 35, No. 8, pp , Yin, Z. and Kim, H. K., Computed Tomography Systems in Medicine: Past, Present and Future, J. KSPE, Vol. 5, No. 1, pp. 35-4, Kim, H. K., Yun, S., Han, J. C., Youn, H. B., Cho, M. K., Lim, C. H., Heo, S. K., Shon, C.-S., Kim, S.-S., Cho, B. H., and Achterkirchen, T. G., Performance Characterization of Microtomography with Complementary Metal-oxidesemiconductor Detectors for Computer-aided Defect Inspection, J. Appl. Phys., Vol. 105, No. 9, pp , Flanner, B. P., Deckman, H. W., Roberge, W. G., and D'Amico, K. L., Three-dimensional X-ray Microtomography, Science, Vol. 37, No. 481, pp , Rao, D. V., Cesareo, R., Brunetti, A., and Gigante, G. E., Computed Tomography with Image Intensifier: Potential Use for Nondestructive Testing and Imaging of Small Objects, NDT&E Int., Vol. 33, No. 8, pp , Kim, H. K., Cunningham, I. A., Yin, Z., and Cho, G., On the Development of Digital Radiography Detectors: A Review, Int. J. Precis. Eng. Manuf., Vol. 9, No. 4, pp , Jaffray, D. A. and Siewerdsen, J. H., Cone-beam computed tomography with a flat-panel imager: Initial performance characterization, Med. Phys., Vol. 7, No. 6, pp , Kim, H. K., Lee, S. C., Cho, M. H., Lee, S. Y., and Cho, G., Use of a flat-panel detector for microtomography: A feasibility study for small-animal imaging, IEEE Trans. Nucl. Sci., Vol. 5, No. 1, pp , Bian, J., Siewerdsen, J. H., Han, X., Sidky, E. Y., Prince, J. L., Pelizzari, C. A., and Pan, X., Evaluation of sparse-view reconstruction from flat-panel-detector cone-beam CT, Phys. Med. Biol., Vol. 55, No., pp , Park, J. C., Song, B., Kim, J. S., Park, S. H., Kim, H. K., Liu, Z., Suh, T. S., and Song, W. Y., Fast compressed sensing-based CBCT reconstruction using Barzilai-Borwein formulation for application to on-line IGRT, Med. Phys., Vol. 39, No. 3, pp , Verhoeven, D., Limited-data computed tomography algorithms for the physical sciences, Appl. Optics, Vol. 3, No. 0, pp , Dobbins III, J. T. and Godfrey, D. J., Digital Tomosynthesis: Current State of the Art and Clinical Potential, Phys. Med. Biol., Vol. 48, No. 19, pp. R65-R106, Flynn, M. J., McGee, R., and Blechinger, J., Spatial Resolution of X-ray Tomosynthesis in Relation to Computed Tomography for Coronal/Sagittal Images of the Knee, Proc. Soc. Photo-Opt. Instrum. Eng., Vol. 6510, Paper No D, Dobbins III, J. T., Tomosynthesis Imaging: At a Translational Crossroads, Med. Phys., Vol. 36, No. 6, pp , Cho, M. K., Youn, H. B., Jang, S. Y., and Kim, H. K., Conebeam digital tomosynthesis for thin slab objects, NDT&E Int., Vol. 47, pp , Shon, C.-S., Cho, M. K., Lim, C. H., Cheong, M. H., Kim, H. K., and Kim, S. S., Enhancement of image sharpness in X-ray Digital Tomosynthesis, J. Kor. Soc. Nondestructive Testing, Vol. 7, No. 1, pp. 8-14, Wu, T., Moore, R. H., Rafferty, E. A., and Kopans, D. B., A Comparison of Reconstruction Algorithms for Breast Tomosynthesis, Med. Phys., Vol. 31, No. 9, pp , Youn, H., Kim, J. Y., Jang, S. Y., Cho, M. K., Cho, S., and Kim, H. K., Deblurring in Digital Tomosynthesis by Iterative Self-layer Subtraction, Proc. Soc. Photo-Opt. Instrum. Eng., Vol. 76, Paper No. 765J, 010.

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