Abstract

We present a method for full-field 3D measurement of substrate warpage and ball grid array coplanarity, which is suitable for inline back-end inspection and process monitoring. For evaluating the performance of the proposed system, the linearity between our system and a reference confocal microscope is studied by repeating measurements 35 times with a particular substrate sample (38mm×28.5mm). The point-to-point correlation coefficient with 1σ between two methods is 0.968±0.002, and the 2σ difference is 25.15±0.20μm for warpage measurement. 1σ repeatability of the substrate warpage is 4.2 μm. For BGA coplanarity inspection the bump level correlation coefficient is 0.957±0.001 and the 2σ difference is 28.79±0.14μm. 1σ repeatability of BGA coplanarity is 3.7 μm. Data acquisition takes about 0.2 s for full field measurements.

© 2014 Optical Society of America

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References

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  1. W. D. Brown, Electronic Packaging (IEEE, 2006).
  2. W. J. Greig, Integrated Circuit Packaging, Assembly and Interconnections (Springer, 2007).
  3. Texas Instruments, “Flip chip ball grid array package reference guide” (2005), http://www.ti.com/lit/ug/spru811a/spru811a.pdf.
  4. H. Tsukahara, Y. Nishiyama, F. Takahashi, and T. Fuse, “High-speed solder bump inspection system using a laser scanner and CCD Camera,” Systems and Computers in Japan 31, 94–102 (2000).
    [CrossRef]
  5. P. Kim and S. Rhee, “Three-dimensional inspection of ball grid array using laser vision system,” IEEE Trans. Electron. Packag. Manufact. 22, 151–155 (1999).
    [CrossRef]
  6. H. N. Yen and D. M. Tsai, “A fast full-field 3D measurement system for BGA coplanarity inspection,” Int. J. Adv. Manuf. Technol. 24, 132–139 (2004).
    [CrossRef]
  7. V. Bartulovic, M. Lucic, and G. Zacek, “Inspection of ball grid arrays (BGA) by using shadow images of the solder balls,” U.S. Patent6,177,682 B1 (23January2001).
  8. D. Marr and T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
    [CrossRef]
  9. U. R. Dhond and J. K. Aggarwal, “Structure from stereo—a review,” IEEE Trans. Syst. Man Cybern. 19, 1489–1510 (1989).
    [CrossRef]
  10. M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 993–1008 (2003).
    [CrossRef]
  11. R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3, 323–344 (1987).
    [CrossRef]
  12. Z. Zhang, “Flexible camera calibration by viewing a plane from unknown orientations,” in Proc. 7th Int. Conference on Computer Vision (IEEE, 1999), pp. 666–673.
  13. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
    [CrossRef]
  14. P. Luo, Y. Chao, and M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
    [CrossRef]
  15. J. J. Aguilar, F. Torres, and M. A. Lope, “Stereo vision for 3D measurement: accuracy analysis, calibration and industrial applications,” Measurements 18, 193–200 (1996).
    [CrossRef]
  16. C. J. Tay, X. Kang, C. Quan, X. Y. He, and H. M. Shang, “Height measurement of microchip connecting pins by use of stereovision,” Appl. Opt. 42, 3827–3831 (2003).
    [CrossRef]
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    [CrossRef]
  19. Z. Ren, J. Liao, and L. Cai, “Three-dimensional measurement of small mechanical parts under a complicated background based on stereo vision,” Appl. Opt. 49, 1789–1801 (2010).
    [CrossRef]
  20. Z.-Z. Tang, J. Liang, Z. Xial, C. Guo, and G. Hu, “Three-dimensional digital image correlation system for deformation measurement in experimental mechanics,” Opt. Eng. 49, 103601 (2010).
    [CrossRef]
  21. C. J. Tay, X. He, X. Kang, C. Quan, and H. M. Shang, “Coplanarity study on ball grid array packaging,” Opt. Eng. 40, 1608–1612 (2001).
    [CrossRef]
  22. M. Dong, R. Chung, E. Y. Lam, and K. S. M. Fung, “Height inspection of wafer bumps without explicit 3-D reconstruction,” IEEE Trans. Electron. Packag. Manufact. 33, 112–121 (2010).
    [CrossRef]
  23. C. Steger, Handbook of Machine Vision (Wiley-VCG, 2006).
  24. J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in Proc. Computer Vis. Patt. Recog.1106–1112 (1997).
  25. K. F. Riley, M. P. Hobson, and S. J. Bence, “Matrices and vector spaces,” in Mathematical Methods for Physics and Engineering (Cambridge University, 2002).
  26. R. Hartley, “In defense of the eight-point algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 580–593 (1997).
    [CrossRef]
  27. R. Hartley, “Triangulation,” Comput. Vis. Image Underst. 68, 146–157 (1997).
    [CrossRef]

2010

Z. Ren, J. Liao, and L. Cai, “Three-dimensional measurement of small mechanical parts under a complicated background based on stereo vision,” Appl. Opt. 49, 1789–1801 (2010).
[CrossRef]

Z.-Z. Tang, J. Liang, Z. Xial, C. Guo, and G. Hu, “Three-dimensional digital image correlation system for deformation measurement in experimental mechanics,” Opt. Eng. 49, 103601 (2010).
[CrossRef]

M. Dong, R. Chung, E. Y. Lam, and K. S. M. Fung, “Height inspection of wafer bumps without explicit 3-D reconstruction,” IEEE Trans. Electron. Packag. Manufact. 33, 112–121 (2010).
[CrossRef]

2009

2005

2004

H. N. Yen and D. M. Tsai, “A fast full-field 3D measurement system for BGA coplanarity inspection,” Int. J. Adv. Manuf. Technol. 24, 132–139 (2004).
[CrossRef]

2003

M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 993–1008 (2003).
[CrossRef]

C. J. Tay, X. Kang, C. Quan, X. Y. He, and H. M. Shang, “Height measurement of microchip connecting pins by use of stereovision,” Appl. Opt. 42, 3827–3831 (2003).
[CrossRef]

2001

C. J. Tay, X. He, X. Kang, C. Quan, and H. M. Shang, “Coplanarity study on ball grid array packaging,” Opt. Eng. 40, 1608–1612 (2001).
[CrossRef]

2000

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

H. Tsukahara, Y. Nishiyama, F. Takahashi, and T. Fuse, “High-speed solder bump inspection system using a laser scanner and CCD Camera,” Systems and Computers in Japan 31, 94–102 (2000).
[CrossRef]

1999

P. Kim and S. Rhee, “Three-dimensional inspection of ball grid array using laser vision system,” IEEE Trans. Electron. Packag. Manufact. 22, 151–155 (1999).
[CrossRef]

1997

R. Hartley, “In defense of the eight-point algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 580–593 (1997).
[CrossRef]

R. Hartley, “Triangulation,” Comput. Vis. Image Underst. 68, 146–157 (1997).
[CrossRef]

1996

J. J. Aguilar, F. Torres, and M. A. Lope, “Stereo vision for 3D measurement: accuracy analysis, calibration and industrial applications,” Measurements 18, 193–200 (1996).
[CrossRef]

1994

P. Luo, Y. Chao, and M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
[CrossRef]

1989

U. R. Dhond and J. K. Aggarwal, “Structure from stereo—a review,” IEEE Trans. Syst. Man Cybern. 19, 1489–1510 (1989).
[CrossRef]

1987

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3, 323–344 (1987).
[CrossRef]

1976

D. Marr and T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
[CrossRef]

Aggarwal, J. K.

U. R. Dhond and J. K. Aggarwal, “Structure from stereo—a review,” IEEE Trans. Syst. Man Cybern. 19, 1489–1510 (1989).
[CrossRef]

Aguilar, J. J.

J. J. Aguilar, F. Torres, and M. A. Lope, “Stereo vision for 3D measurement: accuracy analysis, calibration and industrial applications,” Measurements 18, 193–200 (1996).
[CrossRef]

Bartulovic, V.

V. Bartulovic, M. Lucic, and G. Zacek, “Inspection of ball grid arrays (BGA) by using shadow images of the solder balls,” U.S. Patent6,177,682 B1 (23January2001).

Bence, S. J.

K. F. Riley, M. P. Hobson, and S. J. Bence, “Matrices and vector spaces,” in Mathematical Methods for Physics and Engineering (Cambridge University, 2002).

Brown, M. Z.

M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 993–1008 (2003).
[CrossRef]

Brown, W. D.

W. D. Brown, Electronic Packaging (IEEE, 2006).

Burschka, D.

M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 993–1008 (2003).
[CrossRef]

Cai, L.

Chao, Y.

P. Luo, Y. Chao, and M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
[CrossRef]

Chung, R.

M. Dong, R. Chung, E. Y. Lam, and K. S. M. Fung, “Height inspection of wafer bumps without explicit 3-D reconstruction,” IEEE Trans. Electron. Packag. Manufact. 33, 112–121 (2010).
[CrossRef]

Dhond, U. R.

U. R. Dhond and J. K. Aggarwal, “Structure from stereo—a review,” IEEE Trans. Syst. Man Cybern. 19, 1489–1510 (1989).
[CrossRef]

Dong, M.

M. Dong, R. Chung, E. Y. Lam, and K. S. M. Fung, “Height inspection of wafer bumps without explicit 3-D reconstruction,” IEEE Trans. Electron. Packag. Manufact. 33, 112–121 (2010).
[CrossRef]

Fung, K. S. M.

M. Dong, R. Chung, E. Y. Lam, and K. S. M. Fung, “Height inspection of wafer bumps without explicit 3-D reconstruction,” IEEE Trans. Electron. Packag. Manufact. 33, 112–121 (2010).
[CrossRef]

Fuse, T.

H. Tsukahara, Y. Nishiyama, F. Takahashi, and T. Fuse, “High-speed solder bump inspection system using a laser scanner and CCD Camera,” Systems and Computers in Japan 31, 94–102 (2000).
[CrossRef]

Greig, W. J.

W. J. Greig, Integrated Circuit Packaging, Assembly and Interconnections (Springer, 2007).

Guo, C.

Z.-Z. Tang, J. Liang, Z. Xial, C. Guo, and G. Hu, “Three-dimensional digital image correlation system for deformation measurement in experimental mechanics,” Opt. Eng. 49, 103601 (2010).
[CrossRef]

Hager, G. D.

M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 993–1008 (2003).
[CrossRef]

Hartley, R.

R. Hartley, “In defense of the eight-point algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 580–593 (1997).
[CrossRef]

R. Hartley, “Triangulation,” Comput. Vis. Image Underst. 68, 146–157 (1997).
[CrossRef]

He, X.

C. J. Tay, X. He, X. Kang, C. Quan, and H. M. Shang, “Coplanarity study on ball grid array packaging,” Opt. Eng. 40, 1608–1612 (2001).
[CrossRef]

He, X. Y.

Heikkila, J.

J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in Proc. Computer Vis. Patt. Recog.1106–1112 (1997).

Hobson, M. P.

K. F. Riley, M. P. Hobson, and S. J. Bence, “Matrices and vector spaces,” in Mathematical Methods for Physics and Engineering (Cambridge University, 2002).

Hu, G.

Z.-Z. Tang, J. Liang, Z. Xial, C. Guo, and G. Hu, “Three-dimensional digital image correlation system for deformation measurement in experimental mechanics,” Opt. Eng. 49, 103601 (2010).
[CrossRef]

Kang, X.

C. J. Tay, X. Kang, C. Quan, X. Y. He, and H. M. Shang, “Height measurement of microchip connecting pins by use of stereovision,” Appl. Opt. 42, 3827–3831 (2003).
[CrossRef]

C. J. Tay, X. He, X. Kang, C. Quan, and H. M. Shang, “Coplanarity study on ball grid array packaging,” Opt. Eng. 40, 1608–1612 (2001).
[CrossRef]

Kim, P.

P. Kim and S. Rhee, “Three-dimensional inspection of ball grid array using laser vision system,” IEEE Trans. Electron. Packag. Manufact. 22, 151–155 (1999).
[CrossRef]

Lam, E. Y.

M. Dong, R. Chung, E. Y. Lam, and K. S. M. Fung, “Height inspection of wafer bumps without explicit 3-D reconstruction,” IEEE Trans. Electron. Packag. Manufact. 33, 112–121 (2010).
[CrossRef]

Li, Y. F.

Liang, J.

Z.-Z. Tang, J. Liang, Z. Xial, C. Guo, and G. Hu, “Three-dimensional digital image correlation system for deformation measurement in experimental mechanics,” Opt. Eng. 49, 103601 (2010).
[CrossRef]

Liao, J.

Lope, M. A.

J. J. Aguilar, F. Torres, and M. A. Lope, “Stereo vision for 3D measurement: accuracy analysis, calibration and industrial applications,” Measurements 18, 193–200 (1996).
[CrossRef]

Lucic, M.

V. Bartulovic, M. Lucic, and G. Zacek, “Inspection of ball grid arrays (BGA) by using shadow images of the solder balls,” U.S. Patent6,177,682 B1 (23January2001).

Luo, P.

P. Luo, Y. Chao, and M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
[CrossRef]

Marr, D.

D. Marr and T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
[CrossRef]

Nishiyama, Y.

H. Tsukahara, Y. Nishiyama, F. Takahashi, and T. Fuse, “High-speed solder bump inspection system using a laser scanner and CCD Camera,” Systems and Computers in Japan 31, 94–102 (2000).
[CrossRef]

Poggio, T.

D. Marr and T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
[CrossRef]

Quan, C.

C. J. Tay, X. Kang, C. Quan, X. Y. He, and H. M. Shang, “Height measurement of microchip connecting pins by use of stereovision,” Appl. Opt. 42, 3827–3831 (2003).
[CrossRef]

C. J. Tay, X. He, X. Kang, C. Quan, and H. M. Shang, “Coplanarity study on ball grid array packaging,” Opt. Eng. 40, 1608–1612 (2001).
[CrossRef]

Ren, Z.

Rhee, S.

P. Kim and S. Rhee, “Three-dimensional inspection of ball grid array using laser vision system,” IEEE Trans. Electron. Packag. Manufact. 22, 151–155 (1999).
[CrossRef]

Riley, K. F.

K. F. Riley, M. P. Hobson, and S. J. Bence, “Matrices and vector spaces,” in Mathematical Methods for Physics and Engineering (Cambridge University, 2002).

Shang, H. M.

C. J. Tay, X. Kang, C. Quan, X. Y. He, and H. M. Shang, “Height measurement of microchip connecting pins by use of stereovision,” Appl. Opt. 42, 3827–3831 (2003).
[CrossRef]

C. J. Tay, X. He, X. Kang, C. Quan, and H. M. Shang, “Coplanarity study on ball grid array packaging,” Opt. Eng. 40, 1608–1612 (2001).
[CrossRef]

Silven, O.

J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in Proc. Computer Vis. Patt. Recog.1106–1112 (1997).

Steger, C.

C. Steger, Handbook of Machine Vision (Wiley-VCG, 2006).

Sutton, M.

P. Luo, Y. Chao, and M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
[CrossRef]

Takahashi, F.

H. Tsukahara, Y. Nishiyama, F. Takahashi, and T. Fuse, “High-speed solder bump inspection system using a laser scanner and CCD Camera,” Systems and Computers in Japan 31, 94–102 (2000).
[CrossRef]

Tang, Z.-Z.

Z.-Z. Tang, J. Liang, Z. Xial, C. Guo, and G. Hu, “Three-dimensional digital image correlation system for deformation measurement in experimental mechanics,” Opt. Eng. 49, 103601 (2010).
[CrossRef]

Tay, C. J.

C. J. Tay, X. Kang, C. Quan, X. Y. He, and H. M. Shang, “Height measurement of microchip connecting pins by use of stereovision,” Appl. Opt. 42, 3827–3831 (2003).
[CrossRef]

C. J. Tay, X. He, X. Kang, C. Quan, and H. M. Shang, “Coplanarity study on ball grid array packaging,” Opt. Eng. 40, 1608–1612 (2001).
[CrossRef]

Torres, F.

J. J. Aguilar, F. Torres, and M. A. Lope, “Stereo vision for 3D measurement: accuracy analysis, calibration and industrial applications,” Measurements 18, 193–200 (1996).
[CrossRef]

Tsai, D. M.

H. N. Yen and D. M. Tsai, “A fast full-field 3D measurement system for BGA coplanarity inspection,” Int. J. Adv. Manuf. Technol. 24, 132–139 (2004).
[CrossRef]

Tsai, R. Y.

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3, 323–344 (1987).
[CrossRef]

Tsukahara, H.

H. Tsukahara, Y. Nishiyama, F. Takahashi, and T. Fuse, “High-speed solder bump inspection system using a laser scanner and CCD Camera,” Systems and Computers in Japan 31, 94–102 (2000).
[CrossRef]

Xial, Z.

Z.-Z. Tang, J. Liang, Z. Xial, C. Guo, and G. Hu, “Three-dimensional digital image correlation system for deformation measurement in experimental mechanics,” Opt. Eng. 49, 103601 (2010).
[CrossRef]

Xiao, Y. J.

Yen, H. N.

H. N. Yen and D. M. Tsai, “A fast full-field 3D measurement system for BGA coplanarity inspection,” Int. J. Adv. Manuf. Technol. 24, 132–139 (2004).
[CrossRef]

Zacek, G.

V. Bartulovic, M. Lucic, and G. Zacek, “Inspection of ball grid arrays (BGA) by using shadow images of the solder balls,” U.S. Patent6,177,682 B1 (23January2001).

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

Z. Zhang, “Flexible camera calibration by viewing a plane from unknown orientations,” in Proc. 7th Int. Conference on Computer Vision (IEEE, 1999), pp. 666–673.

Appl. Opt.

Comput. Vis. Image Underst.

R. Hartley, “Triangulation,” Comput. Vis. Image Underst. 68, 146–157 (1997).
[CrossRef]

IEEE J. Robot. Autom.

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3, 323–344 (1987).
[CrossRef]

IEEE Trans. Electron. Packag. Manufact.

P. Kim and S. Rhee, “Three-dimensional inspection of ball grid array using laser vision system,” IEEE Trans. Electron. Packag. Manufact. 22, 151–155 (1999).
[CrossRef]

M. Dong, R. Chung, E. Y. Lam, and K. S. M. Fung, “Height inspection of wafer bumps without explicit 3-D reconstruction,” IEEE Trans. Electron. Packag. Manufact. 33, 112–121 (2010).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

R. Hartley, “In defense of the eight-point algorithm,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 580–593 (1997).
[CrossRef]

M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 993–1008 (2003).
[CrossRef]

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

IEEE Trans. Syst. Man Cybern.

U. R. Dhond and J. K. Aggarwal, “Structure from stereo—a review,” IEEE Trans. Syst. Man Cybern. 19, 1489–1510 (1989).
[CrossRef]

Int. J. Adv. Manuf. Technol.

H. N. Yen and D. M. Tsai, “A fast full-field 3D measurement system for BGA coplanarity inspection,” Int. J. Adv. Manuf. Technol. 24, 132–139 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Measurements

J. J. Aguilar, F. Torres, and M. A. Lope, “Stereo vision for 3D measurement: accuracy analysis, calibration and industrial applications,” Measurements 18, 193–200 (1996).
[CrossRef]

Opt. Eng.

P. Luo, Y. Chao, and M. Sutton, “Application of stereo vision to three-dimensional deformation analyses in fracture experiments,” Opt. Eng. 33, 981–990 (1994).
[CrossRef]

Z.-Z. Tang, J. Liang, Z. Xial, C. Guo, and G. Hu, “Three-dimensional digital image correlation system for deformation measurement in experimental mechanics,” Opt. Eng. 49, 103601 (2010).
[CrossRef]

C. J. Tay, X. He, X. Kang, C. Quan, and H. M. Shang, “Coplanarity study on ball grid array packaging,” Opt. Eng. 40, 1608–1612 (2001).
[CrossRef]

Science

D. Marr and T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
[CrossRef]

Systems and Computers in Japan

H. Tsukahara, Y. Nishiyama, F. Takahashi, and T. Fuse, “High-speed solder bump inspection system using a laser scanner and CCD Camera,” Systems and Computers in Japan 31, 94–102 (2000).
[CrossRef]

Other

V. Bartulovic, M. Lucic, and G. Zacek, “Inspection of ball grid arrays (BGA) by using shadow images of the solder balls,” U.S. Patent6,177,682 B1 (23January2001).

W. D. Brown, Electronic Packaging (IEEE, 2006).

W. J. Greig, Integrated Circuit Packaging, Assembly and Interconnections (Springer, 2007).

Texas Instruments, “Flip chip ball grid array package reference guide” (2005), http://www.ti.com/lit/ug/spru811a/spru811a.pdf.

Z. Zhang, “Flexible camera calibration by viewing a plane from unknown orientations,” in Proc. 7th Int. Conference on Computer Vision (IEEE, 1999), pp. 666–673.

C. Steger, Handbook of Machine Vision (Wiley-VCG, 2006).

J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in Proc. Computer Vis. Patt. Recog.1106–1112 (1997).

K. F. Riley, M. P. Hobson, and S. J. Bence, “Matrices and vector spaces,” in Mathematical Methods for Physics and Engineering (Cambridge University, 2002).

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Figures (19)

Fig. 1.
Fig. 1.

Schematics of an IC package (concave warpage).

Fig. 2.
Fig. 2.

Epipolar geometry.

Fig. 3.
Fig. 3.

System setup.

Fig. 4.
Fig. 4.

(a) Image with radial distortion. Red dots show centroids of crosses; green circles are locations of ideal grids. (b) Image after radial distortion is corrected. Red dots show centroids of crosses; green circles are locations of ideal grids.

Fig. 5.
Fig. 5.

Camera center and the world coordinates.

Fig. 6.
Fig. 6.

Measurement procedures.

Fig. 7.
Fig. 7.

BGA side of IC package sample (top), images captured with Light 1 (bottom left), and on-axis light (bottom right).

Fig. 8.
Fig. 8.

Masked image. Image is captured with Light 1, while the mask is based on the on-axis light image.

Fig. 9.
Fig. 9.

Masked image with bump numbers. Camera 1 (top) and Camera 2 (bottom).

Fig. 10.
Fig. 10.

Bump image with the edge locations shown in the red dots.

Fig. 11.
Fig. 11.

Images of the Camera 1: the red dot is the point defined from the ball edge (top); Camera 2: the red line shows the epipolar line calculated from F matrix, and the green dot indicates the corresponding point (bottom).

Fig. 12.
Fig. 12.

3D warpage scatter plot with regression plane.

Fig. 13.
Fig. 13.

Correlation between our system and the reference confocal tool.

Fig. 14.
Fig. 14.

Simulated bump model.

Fig. 15.
Fig. 15.

Simulated image from the P matrices obtained from the experiment.

Fig. 16.
Fig. 16.

Relationship between the ball height and the ball diameter in pixels.

Fig. 17.
Fig. 17.

3D coplanarity scatter plot.

Fig. 18.
Fig. 18.

Correlation between our system and the reference confocal tool.

Fig. 19.
Fig. 19.

Bump image with different illumination conditions.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

a 1 = P 1 A ,
a 2 = P 2 A ,
[ X 1 Y 1 Z 1 1 0 0 0 0 x 1 X 1 x 1 Y 1 x 1 Z 1 x 1 0 0 0 0 X 1 Y 1 Z 1 1 y 1 X 1 y 1 Y 1 y 1 Z 1 y 1 X i Y i Z i 1 0 0 0 0 x i X i x i Y i x i Z i x i 0 0 0 0 X i Y i Z i 1 y i X i y i Y i y i Z i y i ] ( P 11 P 12 P 13 P 14 P 21 P 22 P 23 P 24 P 31 P 32 P 33 P 34 ) = 0
K = U S V T .
[ x 1 P 31 ( 1 ) P 11 ( 1 ) x 1 P 32 ( 1 ) P 12 ( 1 ) x 1 P 33 ( 1 ) P 13 ( 1 ) x 1 P 34 ( 1 ) P 14 ( 1 ) y 1 P 31 ( 1 ) P 21 ( 1 ) y 1 P 32 ( 1 ) P 22 ( 1 ) y 1 P 33 ( 1 ) P 23 ( 1 ) y 1 P 34 ( 1 ) P 24 ( 1 ) x 1 P 21 ( 1 ) y P 11 ( 1 ) x 1 P 22 ( 1 ) y 1 P 12 ( 1 ) x 1 P 23 ( 1 ) y 1 P 13 ( 1 ) x 1 P 24 ( 1 ) y 1 P 14 ( 1 ) x 2 P 31 ( 2 ) P 11 ( 2 ) x 2 P 32 ( 2 ) P 12 ( 2 ) x 2 P 33 ( 2 ) P 13 ( 2 ) x 2 P 34 ( 2 ) P 14 ( 2 ) y 2 P 31 ( 2 ) P 21 ( 2 ) y 2 P 32 ( 2 ) P 22 ( 2 ) y 2 P 33 ( 2 ) P 23 ( 2 ) y 2 P 34 ( 2 ) P 24 ( 2 ) x 2 P 21 ( 2 ) y P 11 ( 2 ) x 2 P 22 ( 2 ) y P 12 ( 2 ) x 2 P 23 ( 2 ) y 2 P 13 ( 2 ) x 2 P 24 ( 2 ) y 2 P 14 ( 2 ) ] ( X Y Z 1 ) = 0 ,
A = P 1 + a 1 .
l 2 = ( P 2 C 1 ) × ( P 2 P 1 + a 1 ) .
l 2 = ( e 2 ) × ( P 2 P 1 + a 1 ) = F a 1 .
a 2 T l 2 = 0 .
a 2 T F a 1 = 0 .
Warpage = 1 5 [ ( H 1 + H 2 + + H 5 ) ( L 1 + L 2 + + L 5 ) ] .
ρ = cov ( X , Y ) σ X σ Y ,

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