Ke Engineering Materials Vols. 270-273 (2004) pp. 192-197 online at http://www.scientific.net (2004) Trans Tech Publications, Switzerland Online available since 2004/08/15 Citation & Copright (to be inserted b the publisher) 3D X-ra Laminograph with CMOS Image Sensor Using a Projection Method for Reconstruction of Arbitrar Cross-sectional Images Yong Ki Chi 1, Seong Ku Ahn 1, Kwang Hun Kim 1,2 and Guseong Cho 1 1 Korea Advanced Institute of Science and Technolog, Daejeon, Korea 2 Hun Dae Nuclear Engineering Co. Ltd., Seoul, Korea Kewords: 3D laminograph, Geometric projection, Tomosnthesis, Image Reconstruction Abstract. This stud describes 3D X-ra laminograph using a projection method for reconstruction of arbitrar cross-sectional images. The X-ra inspection images acquired from a single focal plane include information of the other focal planes as well. Hence projection images of the other focal planes can be obtained b the geometric projection method for arbitrar height and angle. This paper provides the reconstruction methods of arbitrar cross-sectional image for parallel and cone-beam X-ra and visualization of the object in three dimensions using 3D laminograph. 2D arbitrar projection images for the other focal planes were obtained b deriving the geometric projection formulae for arbitrar height and angle images. After arbitrar cross-sectional images had been reconstructed b 2D laminograph using projection image sets of all focal planes, 3D laminograph was realized so that the object of ball grid arra package was three-dimensionall visualized. For demonstrating 3D NDT (Non-destruction testing) method, we developed laminograph sstem with CMOS image sensor. Finall, it was shown b eperimental results that 3D laminograph of object could be reconstructed correctl b the geometric projection method. Introduction The non-destructive image reconstruction using X-ra imaging has been developed mostl for the medical application. Although recent computed tomograph (CT) algorithm was developed in advanced, the several digital tomosnthesis sstems (DTS) had been steadil studied for image reconstruction [1,2]. For the industrial application, these DTS are used for monitoring the qualit of ball grid arra (BGA) and printed circuit board (PCB) [3]. In case of flat components, the reconstruction method using projection data with an isocentric rotation is not eas because the objects have to be irradiated from all direction. However a laminograph can overcome these difficulties and also provides the depth information of the objects [4]. A classical laminograph can reconstruct a cross-sectional image on a focal plane b a single scan with a non-isocentric rotation. The X-ra inspection images, which are acquired from a single focal plane, also have information of the other focal planes as well. Therefore the projection images of the other focal planes can be obtained b the geometric projection method for arbitrar height and angle [5]. We propose a 3D X-ra laminograph using geometric projection and the laminograph sstem. The geometric projection formulae were derived for the reconstruction of all focal planes with an arbitrar thickness of thickness according to an arbitrar angle of view. B the geometric projection, 3D visualization of the object with internal information has been performed. Net, the design and construction of eperimental equipment were discussed, while BGA object was onl rotating. Finall, b image processing of the rotation and correction of X-ra inspection images, 3D laminograph with arbitrar thickness according to arbitrar angle are realized through the geometric projection of all focal planes. All rights reserved. No part of contents of this paper ma be reproduced or transmitted in an form or b an means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 143.248.62.210-06/10/07,13:11:29)
Materials and Methods Ke Engineering Materials Vols. 270-273 193 Title of Publication (to be inserted b the publisher) Geometric Projection Method. Parallel and cone-shaped X-ra beam was used for the geometric projection method and each inspection image is different as the beam tpe. Inspection images of parallel beam X-ra are not magnified but those of cone beam are magnified with SO, OD distances. The geometr of laminograph sstem and arbitrar plane are defined b several variables (Fig. 1). Fig. 1. Coordinates for defining an X-ra source (S), detector (D) and Object. The input variables are RS, RD, SO and OD as the X-ra inspection images are generated. The origin is the focal spot of a focal plane. φ, δ, h variables are input variables for arbitrar planes of object from original focal plane (X-Y plane). In the case of parallel beam tpe, the relation of the geometric projection is simple and similar form for arbitrar i-th, j-th piel projection of a detector. Fig.2 shows the shifting of original image caused b the projection of arbitrar height and angle for parallel X-ra beam. The variable θ means the degree between a normal vector of the detector and a beam path of Z-X or Z-Y plane. Since variable θ is not change b the movement of the piel position, the projection is dependent on the position of X-ra source (S) and detector (D). (a) (b) Fig. 2. The schematic diagram for the geometric projection of parallel X-ra. (a) focal plane of arbitrar height, (b) focal plane of arbitrar angle. F(i, j) is the piel value of i-th, j-th piel sensor and the formulae is given b below Eq. 1 and Eq. 2. Eq. 1 and Eq. 2 are the geometric projection formulae for arbitrar height and angle planes. Sine rule and trigonometric function were used for the formulae. F' ( i', j' ) = F( i + h tan( θ ), j + h tan( θ )) (1) : θ ( S z / SO) φ = φ cos( δ ), φ = φ sin( δ ) F' ( i', j' ) = F( i sin( π / 2 φ + θ ) / sin( π / 2 + θ ), j sin( π / 2 φ + θ ) / sin( π / 2 + θ )) z z z / OD), θ ( S / SO) / OD) (2)
194 Advances in Nondestructive Evaluation Title of Publication (to be inserted b the publisher) (a) (b) Fig. 3. The schematic diagram for the geometric projection of cone X-ra beam. (a) focal plane of arbitrar height (h), (b) focal plane of arbitrar angle (φ). In case of cone beam tpe, the projection of i-th, j-th piel depends on the magnification that occurred along the positions of X-ra source and detector. Therefore, piel position and detector size have to be considered for the geometric projection formulae due to the variation of θ value. Fig. 3 shows the schematic diagram for cone beam. As compared with parallel beam, the equation is comple and it takes long time for the calculation time of the projection. Eq. (3) and Eq. (4) are the geometric projection formulae for arbitrar height and angle planes. F'( i', j' ) = F( i + h' tan( θ ), j + h' tan( θ )) : θ z h' = h ( SO + OD) / SO b cone beam magnifation [ φ = φ cos( δ ), φ = φ sin( δ ) F'( i', j') = F( i sin( π / 2 φ + θ )/sin( π / 2 + θ ), j sin( π / 2 φ + θ )/sin( π / 2 + θ )) z Dsize / 2 + i) S ( SO + OD) z z ], θ [ D size / 2 + j) S ( SO + OD) ] (3) (4) Using the above equations, arbitrar projection image set for arbitrar focal plane can be obtained and slice thickness can be controlled b the projection of arbitrar height. Simulation and Reconstruction. For the simulation of our 3D laminograph method, we used the simulator of X-ra inspection image [6], which was coded in IDL (iterative data language). The BGA (ball grid arra) object was drawn with Auto-CAD. The attenuation coefficients of BGA for energ bin of input spectrum were integrated along X-ra beam line path. The inspection image is generated b the calculation of X-ra penetration with various sstem parameters of X-ra source, object and detector. Using simulated inspection image, a cross-section image was obtained b snthesizing the image set for a single focal plane of an object. The reconstruction of 2D laminograph was performed with RMM (root-mean-method) that solves the blurred edge problem in the average method [7]. Then, b the geometric projection, image sets of all focal planes were acquired and 3D laminograph was realized with slice thickness and desired view angle. Eperimental Sstem Overview. The 3D laminograph sstem has been arranged in our laborator and inspection image set of a single focal plane through onl rotating object is obtained. The specification of microfocus X-ra tube is a 9-160 kv high voltage, 0-1mA target current and 5-1000 µm adjustable focal spot. A micro-precision step motor for translating object is operated under the eperiment. The rotation and holder of object are controlled b hand (Fig. 4). An X-ra detector module is based on a CMOS image sensor of which the sensing area is 62 62 mm 2 [8]. The sample
Ke Engineering Materials Vols. 270-273 195 Title of Publication (to be inserted b the publisher) was composed of 9 lead ball arra on the circuit board and rotated b the holder. 18 projection data (20 degree/one projection) was used for the 3D laminograph. Object and holder Fig. 4. 3D laminograph sstem. (a) microfocus X-ra tube, (b) BGA objects and rotation holder and (c) CMOS X-ra detector. Reconstruction from eperimental projections. Fig. 5 shows the schematic diagram for our sstem that made inspection image set of a single focal plane. After eperiments, each image was corrected b flat field correction and converted to the value of attenuation coefficients. Due to onl the rotation of an object, finall inspection images have to be rearranged for laminograph image set of a focal plane b the image rotation. We obtained 20 dark and flood images in X-ra tube condition of 150keV and 0.9 ma for flat field correction. B flat field correction, entire noise on CMOS sensor was removed b subtraction of dark current and adjustment of signal gain and inflated beam in each piel. Fig. 5. The schematic diagram of eperimental equipment. The tilting angle (θ tilting = 45 ) of an object plas an important role in acquiring the image set of a focal plane instead of rotating the X-ra source and detector. Although the object has to be snchronousl rotated with detector, the rotation of detector will be performed using the image processing for the rotation of X-ra inspection images. Therefore this sstem has some differences compared with laminograph-based commercial sstems. The X-ra source-to-detector (SO) was set to 18 cm and the object-to-detector distance (OD) was set to 7 cm. Results The spherical BGA was simulated for X-ra inspection images of a single focal plane. BGA package was tilted to λ degree from the parallel plane of 9 balls for identifing 3D reconstruction of the arbitrar view angle. Figure 6 shows the X-ra inspection image set of BGA for parallel and cone X-ra beam. 0 90 180 270 (a) 16 parallel beam projection: tilted angle of BGA(λ)=26.57, SO=90, OD=120, RS=SO tan(30 ), RD=OD tan(30 ), ball radius=15
196 Advances in Nondestructive Evaluation Title of Publication (to be inserted b the publisher) 0 90 180 270 (b) 16 Cone beam projection: tilted angle of BGA(λ)=20.56, SO=300, OD=600, RS=SO tan(20 ), RD=OD tan(20 ), Ball radius=6 Fig. 6. X-ra inspection images. The are the image set for reconstructing single cross-sectional image. parallel cone parallel cone parallel cone parallel cone parallel cone (a) (b) (c) (d) (e) Fig. 7. 2D arbitrar cross-sectional image of several focal planes according to parallel beam and cone beam. The angles (φ) are 26.57 (parallel) and 20.56 (cone). The heights are 30 (parallel) and 15 (cone). Fig. 8. 3D X-ra NDT with internal information of spherical BGA. 16 cone beam projection data was used for 3D reconstruction. The slice thickness is equal to the piel pitch of the detector and the view angle is 20.56 (φ) Several cross-sectional images were correctl reconstructed and the cross-sectional images of all focal planes were reconstructed with arbitrar slice thickness and view angle (Fig. 7). The view angle was determined with the tilting angle (φ) due to the acquisition of optimal 3D reconstruction. Figure 8 shows 3D X-ra laminograph with the depth information of an object. (a) (b) (c) (d) Fig. 9. Original image and the results of image processing with flat field correction, rotation and conversion to the value of attenuation coefficients. (a) original (1024 1024), (b) correction (950 850), (c) rotation (400 400) and (d) conversion image (400 400). Figure 9 shows how the image was changed for laminograph image set of a single focal plane in eperiments. Original image was used with 80 rotated object. Finall it shows b the above geometric projection and image reconstruction that 3D BGA volume was reconstructed with the depth information (Fig. 10). The conditions of slice thickness and view angle was set to 100µm (h intervals), 5 (Φ), and 40 (δ) for the horizontal 9 ball volume. The results shows that 3D laminograph through X-ra inspection images for a single focal plane is helpful to monitor the
Ke Engineering Materials Vols. 270-273 197 Title of Publication (to be inserted b the publisher) soldering qualit such as the deformit and misalignment than the results from transmission images due to the depth and volume information. The eperiments were performed with the object rotation controlled b hand. Therefore the results for the reconstruction will be accurate if the rotation center of the image processing was precisel determined. (a) (b) Fig. 10. Image reconstruction. (a) the cross-sectional image (400 400) of original focal plane and (b) 3D laminograph (400 400 60) with 100µm (h intervals) and -5 (Φ), 40 (δ) view angle. Conclusion and Discussion This paper represented 3D laminograph and the laminograph sstem to monitor the soldering states of BGA. 3D laminograph was performed with arbitrar slice thickness and view angle b the geometric projection formulae. Also inspection image, cross-sectional image and 3D reconstruction could be predicted using the simulator of X-ra inspection image through Auto-CAD drawing before the eperiments of various objects. Finall the eperimental results showed that 3D laminograph through X-ra inspection images for a single focal plane correctl reconstructed the cross-sectional image and 3D volume of BGA. Our sstem onl need the object rotation, while the inspection image set of a single focal plane was acquired for the reconstruction. Therefore the operation of this sstem will be easil performed with not snchronous object/detector rotating motor but with single object rotation. And also 3D laminograph with CMOS image sensor will be helpful to monitor the soldering qualit of high densit packages such as a ball grid arra and is more reliable than the results from transmission images or 2D reconstruction image. We will remodel the sstem with the rotation holder of object controlled b micro-precision motor and appl this sstem to 3D laminograph of micro BGA. References [1] H. Matsuo, Three dimensional image reconstruction b digital tomosnthesis using inverse filtering, IEEE Trans on Med. Imaging, Vol.12 (1993), pp.307 313 [2] Z. Kolitsi, A multiple projection method for digital tomognthesis, Med. Phs., Vol. 19 (1992), pp.1045 1050 [3] S. Rook, Development of an inspection process for ball grid arra technolog using scanned-beam X-ra laminograph, IEEE Trans on Comp. Packag. Manuf. Tech. Part A, Vol. 18(1995), pp.851 856 [4] S. Gondrom, X-ra computed laminograph: an approach of computed tomograph for application with limited access, Nuclear Eng. And Design, Vol. 190 (1999), pp.141 147 [5] S. T. Kang, A projection method for reconstructing X-ra images of arbitrar cross-section, NDT&E International, Vol. 32(1999), pp.9 20 [6] S. K. Ahn, Y. K. Chi, A Computer Code for the Simulation of X-ra Imaging Sstems, IEEE NSS/MIC conference, October 19-25 (2003), Portland, Oregon, USA [7] S. T. Kang, A new digital tomosnthesis sstem to monitor the soldering state of a ball grid arra, SPIE, Vol. 3518(1998), pp.52 56 [8] TRADIX 100 Model, Star V-ra, http://www.starvra.com, Daejeon, Korea