An Efficient Image Distortion Correction Method for an X-ray Digital Tomosynthesis System

Transcription

1 An Effiient Image Distortion Corretion Metho for an X-ray Digital Tomosynthesis System J.Y. Kim Dept. of Mehatronis Engineering, Tongmyong University of Information Tehnology, 55 Yongang-ong, Nam-gu, Busan , Korea Abstrat. Among X-ray ross-setional imaging methos, igital tomosynthesis (DT) is very useful to PCB inspetion beause it an obtain a ross-setional image of a loal inspetion area quily. The image intensifier, whih is usually use in DT systems, istorts X-ray images in shape an intensity. Therefore, image istortion orretion is one of the most important issues in realizing a DT system. This paper presents an image istortion orretion metho to aquire an arbitrary ross-setional image of an objet by using a istane ratio funtion in an X-ray DT system. The metho uses a simplifie istortion moel mae by a istane ratio funtion in intensity orretion, an by the D point mapping polynomials in shape orretion. 1 Introution X-ray tehnology has been wiely use in many inustrial appliations for inspeting inner efets whih an harly be foun by normal vision systems. PCB soler joint inspetion suh as ball gri array (BGA) or flip hip array (FCA) is one of the appliations that require suh an X-ray inspetion system[1,]. An X-ray rosssetional image an be obtaine from two or more images projete from ifferent iretions by the methos suh as tomography, laminography, or igital tomosynthesis. Tomography has been mainly use in meial area, but reently it is being applie in inustrial fiels suh as preision inspetion of asting prouts[]. aminography was originate by Boage[4]. Its priniple omes from the geometri fousing effet by a synhronize motion between an X-ray soure an a etetor, whih is shown in Fig. 1. Digital tomosynthesis is a igital version of laminography, where a set of images of ifferent views are store an synthesize through omputational operations in a omputer[5]. It is one of the most useful X-ray ross-setional imaging methos for PCB inspetion beause it an obtain a ross-setion of a loal inspetion area quily. Thus it has been often applie to PCB soler joint inspetion[5-8]. However, the shape an the intensity of the X-ray images obtaine by DT are istorte beause of the image intensifier use in DT systems. This istortion breas the orresponenes between those images an prevents us from aquiring aurate ross-setional images. Therefore, image istortion orretion is one of the most important issues in realizing a DT system. S.K. Pal et al. (Es.): PReMI 5, NCS 776, pp. 48 4, 5. Springer-Verlag Berlin Heielberg 5

2 An Effiient Image Distortion Corretion Metho for an X-ray DT System 49 D C A B X-ray soure A Objets Foal plane B (A+B+C+D)/4 A D Average image B C C D X-ray etetor Fig. 1. The priniple of aminography an Digital Tomosynthesis In this paper, an image istortion orretion metho for an X-ray DT system is presente. The metho uses a simplifie istortion moel that is built by uniformly spae gris an their istorte images. The intensity istortion moel is base on the istane ratio funtion between two gris, an the shape istortion moel is base on the two-imensional point mapping polynomials. Also this paper performs a series of experiments to aquire PCB soler joint images by the presente orretion metho. System Configuration an Image Distortion Fig. (a) shows a onfiguration of the evelope X-ray DT system, whih is ompose of a sanning X-ray tube, an image intensifier, a view seletor an a zoom amera. An image intensifier with a large input sreen is use as an X-ray etetor so as to get all images projete at various iretions. The area of interest of a PCB is projete on a irular trajetory on the image intensifier as the X-ray is steere on the trajetory, an eight or more images are sequentially aquire by the zoom amera through a view seletor. A galvanometer or a rotating prism an be use as a view seletor. The apture images are save in the igital memory of a omputer, an then synthesize to generate a ross-setional image. The urve image input surfae of the intensifier, however, istorts both of the shape an the intensity of the X-ray images. Fig. (b) shows eight istorte images of an uniformly spae gri pattern projete onto the image intensifier aoring to the steere X-ray soure loation. It is shown that the images are istorte more severely in the peripheral area than the entral area. It is not possible to get an aurate rosssetional image from these istorte images, sine the orresponenes between the images are not maintaine anymore.

3 4 J.Y. Kim ; UD\WXEH V\QFKURQ]H ;<=WDEOH &% 15r 9r 45r r PDJH QWHQVIHU FRPSXWHU 18r 5r 7r 15r ]RRP FDPHUD YVRQERDUG YHZVHOHFWRU (a) a shemati (b) istorte images from the system Fig.. The onfiguration of an X-ray Digital Tomosynthesis system Intensity Distortion Corretion by Using a Distane Ratio Funtion The entral area of the image intensifier is brighter than the peripheral area, sine the inient angle of the X-ray to the urve input surfae of the intensifier varies with the inient loations. In eah projete image, therefore, intensity is the highest in the viinity of the image intensifier enter an gets lower towar the peripheral area. To ompensate for the istorte intensity an mae it uniform over the image, the istorte intensity shoul be sale on the same level with an intensity value, for example, the maximum intensity level of the image. In orer to o it, intensities are sample over the image area an the istribution is moele numerially. The istorte intensity Φ at a point ( i, of an image an be orrete to the ompensate intensity Φ by iviing by the istane ratio funtion f ( ) for the point, as given in Eq. (1). Φ i, = Φ / f ( ). (1) ( f = +. ( ) () = ( i ih ) + ( j jh ) () where is efine as the istane from the highlight point H = ( i H, j H ) to the point ( i,. The istane ratio funtion f ( ) has a value ereasing with between an 1, thus plays a role of orreting an intensity Φ to Φ. To buil the ratio funtion f ( ), 1 intensity values are sample from the 1 small areas on the path from the point H to the point, as shown in the Fig.. The oeffiients of the polynomial f ) an be etermine by least square metho. (

4 An Effiient Image Distortion Corretion Metho for an X-ray DT System 41 Φ ar area Φ max 1. H bright area (i,.9.8 f ) ( (i, H bright area ar area Fig.. Distorte intensity profile for a istane ratio funtion 4 Shape Distortion Corretion by Using a Simplifie Polynomial Moel The shape istortion an be orrete by fining a mapping relationship between the uniformly spaing gri image an its istorte image. Thus, a point in the original unistorte image is mappe to a point ( x, y) in the istorte image by the mapping relation, as shown in Fig. 4. As the sample ata for istortion moeling, this paper use the ata sets whih onsist of the uniformly spae gri points of 11*11. There are two features in the shape istortion. One is that the istorte images are always symmetri with the projetion enter-line of the x-ray. Another one is that the peripheral area of the image intensifier is more elongate than the entral area. Base on the two features, the mapping relationship an be moele an represente by the following equations. y = α ( { x( i, x } P (. (4) + x = β ( i + i. (5) P ( = p α ( = a β ( = b + p1 j + p j + p j. + a j + a j + a j b j + b j + b j A istorte line, whih is a istortion of an original horizontal line, is moele by using a n orer polynomial as shown in Eq. (4). On the other han, the x oorinate values x of the istorte line are moele as shown in Eq. (5). The parameters P (, α (, β ( are funtions of j, an they are moele by using r orer polynomials as shown in Eq. (6). The oeffiients p ~ p, a ~ a, b ~ b are etermine by using least square fitting. (6)

5 4 J.Y. Kim j 5 i Projetion enterline i y 5 x Projetion enterline x y = α 1 (x-x ) +P 1 1 j i Axis 5 j i Axis 5 y = α (x-x ) +P 5 4 j N 5 4 y = α N (x-x ) +P N j axis (a) original gri points j axis (b) istorte gri points Fig. 4. Two-imensional point mapping for shape istortion orretion 5 Experiments for PCB Soler Joint Image Aquisition A series of experiments to get the DT images of BGA was performe by using the X- ray DT system shown in Fig. (a). In the aquire images shown in Fig. 5, the ar regions represent the ross-setions of the orresponing foal planes. The rosssetion at the mile of the lea ball has the maximum iameter. These DT images were aquire by integrating the 8 images taen from 8 ifferent off-axis images. In eah image of them, the intensity an shape istortion was orrete by using the orretion metho presente in above setions. These ross-setional images provie a goo ue or a unique solution to inspet the inner efets of the objets suh as BGA or J-lea type hips. Chip Paage Foal plane1 1 Ball Gri Array ea Ball soler joints (a) BGA (b) DT images for the foal plane 1- Fig. 5. X-ray DT images of BGA 6 Conlusions In orer to obtain an arbitrary ross-setional image with high quality in an X-ray DT system, this paper presente a metho to orret the istortion of image intensity an image shape. The metho uses a simplifie istortion moel mae by a istane ratio

6 An Effiient Image Distortion Corretion Metho for an X-ray DT System 4 funtion in intensity orretion, an by the D point mapping polynomials in shape orretion. An a series of experiments to get DT images of BGA was performe by using the presente orretion metho. The experimental results show that the presente orretion metho is effetive in aquiring an arbitrary ross-setional image of an objet. Referenes 1. Aams, J.: X-ray laminography analysis of ultra fine pith soler onnetions on ultra-thin boars. SPIE Integrate Ciruit Metrology, Inspetion, an Proess Control V, Vol (1991) Moore, T. D., Vanerstraeten, D., Forssell, P.M., Three-imensional x-ray laminography as a tool for etetion an haraterization of BGA paage efets. IEEE Tr. on Components an Paaging Tehnologies, Vol. 5. No.. () 4-9. Bossi, R. H. an Georgeson, G. E.: Casting evelopment savings with X-ray ompute tomography. Casting (199) Boage, E. M.: Frenh Patent (19) 5. Roos, M. an Sa, T.: X-ray inspetion of flip hip attah using igital tomosynthesis. Ciruit Worl, Vol. 1. No.. (1995) Bor, S., Clement, A., eomte, J. C., Marmeggi, J. C.: An X-ray tomography faility for IC inustry at STMiroeletronis Grenoble. Miroeletroni engineering, Vol. 6. () Sumimoto, T., Maruyamay, T., Azuma, Y., Goto, S., Mono, M., Furuawa, N., Oaa, S.: Detetion of efets at BGA soler joints by using X-ray imaging. IEEE Int. Conf. on Inustrial Tehnology, Vol. 1. () Roh, Y. J., Ko, K. W., Cho, H. S., Kim, J. Y., Byun, J. E.: The alibration of X-ray igital tomosynthesis system inluing the ompensation of the image istortion. SPIE Symp. on Intelligent Systems an Avane Manufaturing VII, Vol. 58. (1998) 48-59