Abstract

An exact solution for the intensity distribution of shadow moiré fringes produced by a broad spectrum light is presented. A mathematical study quantifies errors in fractional fringe orders determined by the phase-shifting technique, and its validity is corroborated experimentally. The errors vary cyclically as the distance between the reference grating and the specimen increases. The amplitude of the maximum error is approximately 0.017 fringe, which defines the theoretical limit of resolution enhancement offered by the phase-shifting technique.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Creath, "Phase-measurement interferometry techniques," in Progress in Optics, E. Wolf, ed. (North-Holland, 1988), Vol. 26, pp. 349-393.
    [CrossRef]
  2. J. E. A. Liao and A. S. Voloshin, "Enhancement of the shadow-moiré method through digital image processing," Exper. Mech. 33, 59-63 (1993).
    [CrossRef]
  3. Y. Wang and P. Hassell, "Measurement of thermally induced warpage of BGA packages/substrates using phase-stepping shadow moiré," in Proceedings of the 1997 1st Electronic Packaging Technology Conference (IEEE, 1997), pp. 283-289.
  4. G. J. Petriccione and I. C. Ume, "Warpage studies of HDI test vehicles during various thermal profiling," IEEE Trans. Advanced Packag. 22, 624-637 (1999).
    [CrossRef]
  5. J. C. L. Wu, H. Shine, S. Wu, M. Hung, and J. J. Lee, "Study of rapid cure BGA mold compound on warpage with shadow moiré," in 1999 Proceedings of 49th Electronic Components and Technology Conference (IEEE, 1999), pp. 708-713.
  6. Y. Polsky, W. Sutherlin, and I. C. Ume, "A comparison of PWB warpage due to simulated infrared and wave soldering processes," IEEE Trans. Electron. Packag. Manuf. 23, 191-199 (2000).
    [CrossRef]
  7. A. X. H. Dang, I. C. Ume, and S. K. Bhattacharya, "Process induced warpage in multitiled alumina substrates for large area MCM-D processing," IEEE Trans. Advanced Packag. 23, 436-445 (2000).
    [CrossRef]
  8. R. C. Dunne and S. K. Sitaraman, "An integrated process modeling methodology and module for sequential multilayered substrate fabrication using a coupled cure-thermal-stress analysis approach," IEEE Trans. Electron. Packag. Manuf. 25, 326-334 (2002).
    [CrossRef]
  9. I. D. Vrinceanu and S. Danyluk, "Measurement of residual stress in single crystal silicon wafers," in Proceedings of 8th International Symposium on Advanced Packaging Materials (IEEE, 2002), pp. 297-301.
  10. J. Zhang, H. Ding, D. F. Baldwin, and I. C. Ume, "Characterization of in-process substrate warpage of underfilled flip chip assembly," in 2003 IEEE/CPMT/SEMI International Electronics Manufacturing Technology Symposium (IEEE, 2003), pp. 291-297.
    [CrossRef]
  11. K. Chen, T. Y. F. Chen, C. C. Chuang, and I. K. Lin, "Full-field wafer level thin film stress measurement by phase-stepping shadow moiré," IEEE Tran. Components Packag. Technol. 27, 594-601 (2004).
    [CrossRef]
  12. D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.
  13. Y. Arai and S. Yokozeki, "Improvement of measurement accuracy in shadow moiré by considering the influence of harmonics in the moiré profile," Appl. Opt. 38, 3503-3507 (1999).
    [CrossRef]
  14. A. Asundi and C. S. Chan, "Phase shifting applied to nonsinusoidal intensity distribution: an error simulation," Opt. Lasers Eng. 21, 3-30 (1994).
    [CrossRef]
  15. K. Patorski, "The self-imaging phenomenon and its applications," in Progress in Optics, E. Wolf, ed. (North-Holland, 1989), Vol. 27, pp. 1-108.
    [CrossRef]
  16. E. Keren and O. Kafri, "Diffraction effects in moiré deflectometry," J. Opt. Soc. Am. A 2, 111-120 (1985).
    [CrossRef]
  17. M. Testorf, J. Jahns, N. Khilo, and A. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
    [CrossRef]
  18. R. F. Edgar, "The Fresnel diffraction images of periodic structures," Opt. Acta 16, 281-287 (1969).
    [CrossRef]
  19. C. Han and B. Han, "Contrast of shadow moiré at high-order Talbot distances," Opt. Eng. 44, 28002 (2005).
    [CrossRef]
  20. C. Han, "Shadow moiré using non-zero Talbot distance and application of diffraction theory to moiré interferometry," Ph.D. dissertation (University of Maryland, College Park, 2005).
  21. D. Post, B. Han, and P. Ifju, "Geometric moiré," in High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials (Springer-Verlag, 1994), Chap. 3.
    [CrossRef]
  22. J. B. Allen and D. M. Meadows, "Removal of unwanted patterns from moiré contour maps by grid translation techniques," Appl. Opt. 10, 210-212 (1971).
    [CrossRef] [PubMed]
  23. M. Halioua, R. S. Krishnamurthy, H. Liu, and F. P. Chiang, "Projection moiré with moving gratings for automated 3-D topography," Appl. Opt. 22, 850-855 (1983).
    [CrossRef] [PubMed]
  24. J. Janssens, W. F. Decraemer, and V. J. Vanhuyse, "Visibility depth of shadow-moiré fringes in function of extend of light source and aperture of recording system," Optik 71, 45-51 (1985).
  25. H. M. Ladak, W. F. Decraemer, J. J. J. Dirckx, and W. R. J. Funnell, "Systematic errors in small deformations measured by use of shadow-moiré topography," Appl. Opt. 39, 3266-3275 (2000).
    [CrossRef]
  26. O. Kafri and E. Keren, "Fringe observation and depth of field in moiré analysis," Appl. Opt. 20, 2885-2886 (1981).
    [CrossRef] [PubMed]

2005 (1)

C. Han and B. Han, "Contrast of shadow moiré at high-order Talbot distances," Opt. Eng. 44, 28002 (2005).
[CrossRef]

2004 (1)

K. Chen, T. Y. F. Chen, C. C. Chuang, and I. K. Lin, "Full-field wafer level thin film stress measurement by phase-stepping shadow moiré," IEEE Tran. Components Packag. Technol. 27, 594-601 (2004).
[CrossRef]

2002 (1)

R. C. Dunne and S. K. Sitaraman, "An integrated process modeling methodology and module for sequential multilayered substrate fabrication using a coupled cure-thermal-stress analysis approach," IEEE Trans. Electron. Packag. Manuf. 25, 326-334 (2002).
[CrossRef]

2000 (3)

H. M. Ladak, W. F. Decraemer, J. J. J. Dirckx, and W. R. J. Funnell, "Systematic errors in small deformations measured by use of shadow-moiré topography," Appl. Opt. 39, 3266-3275 (2000).
[CrossRef]

Y. Polsky, W. Sutherlin, and I. C. Ume, "A comparison of PWB warpage due to simulated infrared and wave soldering processes," IEEE Trans. Electron. Packag. Manuf. 23, 191-199 (2000).
[CrossRef]

A. X. H. Dang, I. C. Ume, and S. K. Bhattacharya, "Process induced warpage in multitiled alumina substrates for large area MCM-D processing," IEEE Trans. Advanced Packag. 23, 436-445 (2000).
[CrossRef]

1999 (2)

G. J. Petriccione and I. C. Ume, "Warpage studies of HDI test vehicles during various thermal profiling," IEEE Trans. Advanced Packag. 22, 624-637 (1999).
[CrossRef]

Y. Arai and S. Yokozeki, "Improvement of measurement accuracy in shadow moiré by considering the influence of harmonics in the moiré profile," Appl. Opt. 38, 3503-3507 (1999).
[CrossRef]

1996 (1)

M. Testorf, J. Jahns, N. Khilo, and A. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
[CrossRef]

1994 (1)

A. Asundi and C. S. Chan, "Phase shifting applied to nonsinusoidal intensity distribution: an error simulation," Opt. Lasers Eng. 21, 3-30 (1994).
[CrossRef]

1993 (1)

J. E. A. Liao and A. S. Voloshin, "Enhancement of the shadow-moiré method through digital image processing," Exper. Mech. 33, 59-63 (1993).
[CrossRef]

1985 (2)

J. Janssens, W. F. Decraemer, and V. J. Vanhuyse, "Visibility depth of shadow-moiré fringes in function of extend of light source and aperture of recording system," Optik 71, 45-51 (1985).

E. Keren and O. Kafri, "Diffraction effects in moiré deflectometry," J. Opt. Soc. Am. A 2, 111-120 (1985).
[CrossRef]

1983 (1)

1981 (1)

1971 (1)

1969 (1)

R. F. Edgar, "The Fresnel diffraction images of periodic structures," Opt. Acta 16, 281-287 (1969).
[CrossRef]

Allen, J. B.

Arai, Y.

Asundi, A.

A. Asundi and C. S. Chan, "Phase shifting applied to nonsinusoidal intensity distribution: an error simulation," Opt. Lasers Eng. 21, 3-30 (1994).
[CrossRef]

Bajaj, M.

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

Baldwin, D. F.

J. Zhang, H. Ding, D. F. Baldwin, and I. C. Ume, "Characterization of in-process substrate warpage of underfilled flip chip assembly," in 2003 IEEE/CPMT/SEMI International Electronics Manufacturing Technology Symposium (IEEE, 2003), pp. 291-297.
[CrossRef]

Bhattacharya, S. K.

A. X. H. Dang, I. C. Ume, and S. K. Bhattacharya, "Process induced warpage in multitiled alumina substrates for large area MCM-D processing," IEEE Trans. Advanced Packag. 23, 436-445 (2000).
[CrossRef]

Brady, K.

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

Chan, C. S.

A. Asundi and C. S. Chan, "Phase shifting applied to nonsinusoidal intensity distribution: an error simulation," Opt. Lasers Eng. 21, 3-30 (1994).
[CrossRef]

Chen, K.

K. Chen, T. Y. F. Chen, C. C. Chuang, and I. K. Lin, "Full-field wafer level thin film stress measurement by phase-stepping shadow moiré," IEEE Tran. Components Packag. Technol. 27, 594-601 (2004).
[CrossRef]

Chen, T. Y. F.

K. Chen, T. Y. F. Chen, C. C. Chuang, and I. K. Lin, "Full-field wafer level thin film stress measurement by phase-stepping shadow moiré," IEEE Tran. Components Packag. Technol. 27, 594-601 (2004).
[CrossRef]

Chiang, F. P.

Chuang, C. C.

K. Chen, T. Y. F. Chen, C. C. Chuang, and I. K. Lin, "Full-field wafer level thin film stress measurement by phase-stepping shadow moiré," IEEE Tran. Components Packag. Technol. 27, 594-601 (2004).
[CrossRef]

Creath, K.

K. Creath, "Phase-measurement interferometry techniques," in Progress in Optics, E. Wolf, ed. (North-Holland, 1988), Vol. 26, pp. 349-393.
[CrossRef]

Dang, A. X. H.

A. X. H. Dang, I. C. Ume, and S. K. Bhattacharya, "Process induced warpage in multitiled alumina substrates for large area MCM-D processing," IEEE Trans. Advanced Packag. 23, 436-445 (2000).
[CrossRef]

Danyluk, S.

I. D. Vrinceanu and S. Danyluk, "Measurement of residual stress in single crystal silicon wafers," in Proceedings of 8th International Symposium on Advanced Packaging Materials (IEEE, 2002), pp. 297-301.

Decraemer, W. F.

H. M. Ladak, W. F. Decraemer, J. J. J. Dirckx, and W. R. J. Funnell, "Systematic errors in small deformations measured by use of shadow-moiré topography," Appl. Opt. 39, 3266-3275 (2000).
[CrossRef]

J. Janssens, W. F. Decraemer, and V. J. Vanhuyse, "Visibility depth of shadow-moiré fringes in function of extend of light source and aperture of recording system," Optik 71, 45-51 (1985).

Dickerson, M.

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

Ding, H.

J. Zhang, H. Ding, D. F. Baldwin, and I. C. Ume, "Characterization of in-process substrate warpage of underfilled flip chip assembly," in 2003 IEEE/CPMT/SEMI International Electronics Manufacturing Technology Symposium (IEEE, 2003), pp. 291-297.
[CrossRef]

Dirckx, J. J. J.

Dunne, R. C.

R. C. Dunne and S. K. Sitaraman, "An integrated process modeling methodology and module for sequential multilayered substrate fabrication using a coupled cure-thermal-stress analysis approach," IEEE Trans. Electron. Packag. Manuf. 25, 326-334 (2002).
[CrossRef]

Edgar, R. F.

R. F. Edgar, "The Fresnel diffraction images of periodic structures," Opt. Acta 16, 281-287 (1969).
[CrossRef]

Funnell, W. R. J.

Goncharenko, A.

M. Testorf, J. Jahns, N. Khilo, and A. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Halioua, M.

Han, B.

C. Han and B. Han, "Contrast of shadow moiré at high-order Talbot distances," Opt. Eng. 44, 28002 (2005).
[CrossRef]

D. Post, B. Han, and P. Ifju, "Geometric moiré," in High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials (Springer-Verlag, 1994), Chap. 3.
[CrossRef]

Han, C.

C. Han and B. Han, "Contrast of shadow moiré at high-order Talbot distances," Opt. Eng. 44, 28002 (2005).
[CrossRef]

C. Han, "Shadow moiré using non-zero Talbot distance and application of diffraction theory to moiré interferometry," Ph.D. dissertation (University of Maryland, College Park, 2005).

Hassell, P.

Y. Wang and P. Hassell, "Measurement of thermally induced warpage of BGA packages/substrates using phase-stepping shadow moiré," in Proceedings of the 1997 1st Electronic Packaging Technology Conference (IEEE, 1997), pp. 283-289.

Hung, M.

J. C. L. Wu, H. Shine, S. Wu, M. Hung, and J. J. Lee, "Study of rapid cure BGA mold compound on warpage with shadow moiré," in 1999 Proceedings of 49th Electronic Components and Technology Conference (IEEE, 1999), pp. 708-713.

Ifju, P.

D. Post, B. Han, and P. Ifju, "Geometric moiré," in High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials (Springer-Verlag, 1994), Chap. 3.
[CrossRef]

Jahns, J.

M. Testorf, J. Jahns, N. Khilo, and A. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Janssens, J.

J. Janssens, W. F. Decraemer, and V. J. Vanhuyse, "Visibility depth of shadow-moiré fringes in function of extend of light source and aperture of recording system," Optik 71, 45-51 (1985).

Kafri, O.

Keren, E.

Khilo, N.

M. Testorf, J. Jahns, N. Khilo, and A. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Klein, L.

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

Krishnamurthy, R. S.

Ladak, H. M.

Lee, J. J.

J. C. L. Wu, H. Shine, S. Wu, M. Hung, and J. J. Lee, "Study of rapid cure BGA mold compound on warpage with shadow moiré," in 1999 Proceedings of 49th Electronic Components and Technology Conference (IEEE, 1999), pp. 708-713.

Liao, J. E. A.

J. E. A. Liao and A. S. Voloshin, "Enhancement of the shadow-moiré method through digital image processing," Exper. Mech. 33, 59-63 (1993).
[CrossRef]

Lin, I. K.

K. Chen, T. Y. F. Chen, C. C. Chuang, and I. K. Lin, "Full-field wafer level thin film stress measurement by phase-stepping shadow moiré," IEEE Tran. Components Packag. Technol. 27, 594-601 (2004).
[CrossRef]

Liu, H.

Liutkus, G.

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

McCarron, S.

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

Meadows, D. M.

Messina, J.

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

Patorski, K.

K. Patorski, "The self-imaging phenomenon and its applications," in Progress in Optics, E. Wolf, ed. (North-Holland, 1989), Vol. 27, pp. 1-108.
[CrossRef]

Peak, R.

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

Petriccione, G. J.

G. J. Petriccione and I. C. Ume, "Warpage studies of HDI test vehicles during various thermal profiling," IEEE Trans. Advanced Packag. 22, 624-637 (1999).
[CrossRef]

Polsky, Y.

Y. Polsky, W. Sutherlin, and I. C. Ume, "A comparison of PWB warpage due to simulated infrared and wave soldering processes," IEEE Trans. Electron. Packag. Manuf. 23, 191-199 (2000).
[CrossRef]

Post, D.

D. Post, B. Han, and P. Ifju, "Geometric moiré," in High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials (Springer-Verlag, 1994), Chap. 3.
[CrossRef]

Shine, H.

J. C. L. Wu, H. Shine, S. Wu, M. Hung, and J. J. Lee, "Study of rapid cure BGA mold compound on warpage with shadow moiré," in 1999 Proceedings of 49th Electronic Components and Technology Conference (IEEE, 1999), pp. 708-713.

Sitaraman, S. K.

R. C. Dunne and S. K. Sitaraman, "An integrated process modeling methodology and module for sequential multilayered substrate fabrication using a coupled cure-thermal-stress analysis approach," IEEE Trans. Electron. Packag. Manuf. 25, 326-334 (2002).
[CrossRef]

Spradling, A.

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

Sutherlin, W.

Y. Polsky, W. Sutherlin, and I. C. Ume, "A comparison of PWB warpage due to simulated infrared and wave soldering processes," IEEE Trans. Electron. Packag. Manuf. 23, 191-199 (2000).
[CrossRef]

Testorf, M.

M. Testorf, J. Jahns, N. Khilo, and A. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Thurman, T.

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

Ume, I. C.

Y. Polsky, W. Sutherlin, and I. C. Ume, "A comparison of PWB warpage due to simulated infrared and wave soldering processes," IEEE Trans. Electron. Packag. Manuf. 23, 191-199 (2000).
[CrossRef]

A. X. H. Dang, I. C. Ume, and S. K. Bhattacharya, "Process induced warpage in multitiled alumina substrates for large area MCM-D processing," IEEE Trans. Advanced Packag. 23, 436-445 (2000).
[CrossRef]

G. J. Petriccione and I. C. Ume, "Warpage studies of HDI test vehicles during various thermal profiling," IEEE Trans. Advanced Packag. 22, 624-637 (1999).
[CrossRef]

J. Zhang, H. Ding, D. F. Baldwin, and I. C. Ume, "Characterization of in-process substrate warpage of underfilled flip chip assembly," in 2003 IEEE/CPMT/SEMI International Electronics Manufacturing Technology Symposium (IEEE, 2003), pp. 291-297.
[CrossRef]

Vanhuyse, V. J.

J. Janssens, W. F. Decraemer, and V. J. Vanhuyse, "Visibility depth of shadow-moiré fringes in function of extend of light source and aperture of recording system," Optik 71, 45-51 (1985).

Voloshin, A. S.

J. E. A. Liao and A. S. Voloshin, "Enhancement of the shadow-moiré method through digital image processing," Exper. Mech. 33, 59-63 (1993).
[CrossRef]

Vrinceanu, I. D.

I. D. Vrinceanu and S. Danyluk, "Measurement of residual stress in single crystal silicon wafers," in Proceedings of 8th International Symposium on Advanced Packaging Materials (IEEE, 2002), pp. 297-301.

Wang, Y.

Y. Wang and P. Hassell, "Measurement of thermally induced warpage of BGA packages/substrates using phase-stepping shadow moiré," in Proceedings of the 1997 1st Electronic Packaging Technology Conference (IEEE, 1997), pp. 283-289.

Wu, J. C. L.

J. C. L. Wu, H. Shine, S. Wu, M. Hung, and J. J. Lee, "Study of rapid cure BGA mold compound on warpage with shadow moiré," in 1999 Proceedings of 49th Electronic Components and Technology Conference (IEEE, 1999), pp. 708-713.

Wu, S.

J. C. L. Wu, H. Shine, S. Wu, M. Hung, and J. J. Lee, "Study of rapid cure BGA mold compound on warpage with shadow moiré," in 1999 Proceedings of 49th Electronic Components and Technology Conference (IEEE, 1999), pp. 708-713.

Yokozeki, S.

Zhang, J.

J. Zhang, H. Ding, D. F. Baldwin, and I. C. Ume, "Characterization of in-process substrate warpage of underfilled flip chip assembly," in 2003 IEEE/CPMT/SEMI International Electronics Manufacturing Technology Symposium (IEEE, 2003), pp. 291-297.
[CrossRef]

Zwemer, D.

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

Appl. Opt. (5)

Exper. Mech. (1)

J. E. A. Liao and A. S. Voloshin, "Enhancement of the shadow-moiré method through digital image processing," Exper. Mech. 33, 59-63 (1993).
[CrossRef]

IEEE Tran. Components Packag. Technol. (1)

K. Chen, T. Y. F. Chen, C. C. Chuang, and I. K. Lin, "Full-field wafer level thin film stress measurement by phase-stepping shadow moiré," IEEE Tran. Components Packag. Technol. 27, 594-601 (2004).
[CrossRef]

IEEE Trans. Advanced Packag. (2)

G. J. Petriccione and I. C. Ume, "Warpage studies of HDI test vehicles during various thermal profiling," IEEE Trans. Advanced Packag. 22, 624-637 (1999).
[CrossRef]

A. X. H. Dang, I. C. Ume, and S. K. Bhattacharya, "Process induced warpage in multitiled alumina substrates for large area MCM-D processing," IEEE Trans. Advanced Packag. 23, 436-445 (2000).
[CrossRef]

IEEE Trans. Electron. Packag. Manuf. (2)

R. C. Dunne and S. K. Sitaraman, "An integrated process modeling methodology and module for sequential multilayered substrate fabrication using a coupled cure-thermal-stress analysis approach," IEEE Trans. Electron. Packag. Manuf. 25, 326-334 (2002).
[CrossRef]

Y. Polsky, W. Sutherlin, and I. C. Ume, "A comparison of PWB warpage due to simulated infrared and wave soldering processes," IEEE Trans. Electron. Packag. Manuf. 23, 191-199 (2000).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

R. F. Edgar, "The Fresnel diffraction images of periodic structures," Opt. Acta 16, 281-287 (1969).
[CrossRef]

Opt. Commun. (1)

M. Testorf, J. Jahns, N. Khilo, and A. Goncharenko, "Talbot effect for oblique angle of light propagation," Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Opt. Eng. (1)

C. Han and B. Han, "Contrast of shadow moiré at high-order Talbot distances," Opt. Eng. 44, 28002 (2005).
[CrossRef]

Opt. Lasers Eng. (1)

A. Asundi and C. S. Chan, "Phase shifting applied to nonsinusoidal intensity distribution: an error simulation," Opt. Lasers Eng. 21, 3-30 (1994).
[CrossRef]

Optik (1)

J. Janssens, W. F. Decraemer, and V. J. Vanhuyse, "Visibility depth of shadow-moiré fringes in function of extend of light source and aperture of recording system," Optik 71, 45-51 (1985).

Other (9)

K. Patorski, "The self-imaging phenomenon and its applications," in Progress in Optics, E. Wolf, ed. (North-Holland, 1989), Vol. 27, pp. 1-108.
[CrossRef]

C. Han, "Shadow moiré using non-zero Talbot distance and application of diffraction theory to moiré interferometry," Ph.D. dissertation (University of Maryland, College Park, 2005).

D. Post, B. Han, and P. Ifju, "Geometric moiré," in High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials (Springer-Verlag, 1994), Chap. 3.
[CrossRef]

K. Creath, "Phase-measurement interferometry techniques," in Progress in Optics, E. Wolf, ed. (North-Holland, 1988), Vol. 26, pp. 349-393.
[CrossRef]

D. Zwemer, M. Bajaj, R. Peak, T. Thurman, K. Brady, S. McCarron, A. Spradling, M. Dickerson, L. Klein, G. Liutkus, and J. Messina, "PWB warpage analysis and verification using an AP210 standards-based engineering framework and shadow moiré," Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2004), pp. 121-131.

I. D. Vrinceanu and S. Danyluk, "Measurement of residual stress in single crystal silicon wafers," in Proceedings of 8th International Symposium on Advanced Packaging Materials (IEEE, 2002), pp. 297-301.

J. Zhang, H. Ding, D. F. Baldwin, and I. C. Ume, "Characterization of in-process substrate warpage of underfilled flip chip assembly," in 2003 IEEE/CPMT/SEMI International Electronics Manufacturing Technology Symposium (IEEE, 2003), pp. 291-297.
[CrossRef]

J. C. L. Wu, H. Shine, S. Wu, M. Hung, and J. J. Lee, "Study of rapid cure BGA mold compound on warpage with shadow moiré," in 1999 Proceedings of 49th Electronic Components and Technology Conference (IEEE, 1999), pp. 708-713.

Y. Wang and P. Hassell, "Measurement of thermally induced warpage of BGA packages/substrates using phase-stepping shadow moiré," in Proceedings of the 1997 1st Electronic Packaging Technology Conference (IEEE, 1997), pp. 283-289.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Convex surface measured by shadow moiré with a contour interval of 100 µm / fringe ; fringe patterns with a phase shift of (a) 0, (b) π / 4 , (c) π / 2 and (d) 3 π / 4 . (e) The results are compared with the exact geometry.

Fig. 2
Fig. 2

Convex surface measured by shadow moiré with a contour interval of 500 µm / fringe ; fringe patterns with a phase shift of (a) 0, (b) π / 4 , (c) π / 2 , and (d) 3 π / 4 . (e) The results are compared with the exact geometry.

Fig. 3
Fig. 3

Illustration of shadow grating for an oblique illumination.

Fig. 4
Fig. 4

Phase-shifting error of shadow moiré fringe with a contour interval of 1 mm ( g = 1 mm , α = 45 ° , and λ = 400 700 nm ), over (a) the normalized distance z / D T α = 0 to 0.2 and (b) a smaller segment corresponding to the fringe order N = 4 to 8.

Fig. 5
Fig. 5

Phase-shifting error of shadow moiré fringe with a contour interval of 100 µm ( g = 0.1 mm , α = 45 ° , and λ = 400 700 nm ), over (a) the normalized distance z / D T α = 0 to 0.2 and (b) a smaller segment corresponding to the fringe order N = 4 to 8.

Fig. 6
Fig. 6

(a) Experimental setup of shadow moiré and (b) fringe pattern of an optical flat with rigid-body displacement.

Fig. 7
Fig. 7

Experimental results with a contour interval of 1 mm : (a) 0, (b) π / 4 , (c) π / 2 , and (d) 3 π / 4 phase-shifted images; (e) unwrapped phase map, (f) displacement along BB , (g) phase errors, and (h) phase errors along BB are compared with the theoretical values.

Fig. 8
Fig. 8

Phase-shifting error with g = 0.1 , α = 45 ° , and λ = 400 700 nm for (a) d e = 0.01 and (b) d e = 0.03 .

Equations (28)

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

E ( x , z ) = n = a n exp [ i 2 π λ ( x sin θ n + z cos θ n ) ] ,
cos θ n cos α { 1 1 2 [ ( n λ g cos α ) 2 + 2 n λ g sin α cos 2 α ] } ,
E ( x , z ) exp [ i 2 π λ ( x sin α + z cos α ) ] n = a n exp [ i 2 π ( n g x n g z tan α n 2 D T α z ) ] ,
I ( x , z ) = E ( x , z ) E ( x , z ) ¯ = n = m = a n a m exp [ i 2 π ( n m ) x z tan α g ] exp [ i 2 π ( m 2 n 2 D T α z ) ] .
I Δλ ( x , z ) = 1 Δλ λ 1 λ 2 I ( x , z ) = 1 Δλ λ 1 λ 2 { n = m = a n a m exp [ i 2 π ( n m ) x z tan α g ] exp [ i π ( m 2 n 2 g 2 cos 3 α z ) λ ] } = 1 Δλ n = m = a n a m exp [ i 2 π ( n m ) x z tan α g ] λ 1 λ 2 exp [ i π ( m 2 n 2 g 2 cos 3 α z ) λ ] ,
I s ( z ) = 1 g - g / 2 g / 2 { I ( x , 0 ) I Δλ ( x , z ) } d x = 1 g - g / 2 g / 2 [ I ( x , 0 ) ] { 1 Δλ n = - m = - a n a m exp [ i 2 π ( n - m ) ( x - z tan α g ) ] λ 1 λ 2 exp [ ( m 2 - n 2 g 2 cos 2 α z ) λ ] } d x = 1 Δλ n = - m = - a n a m exp [ i 2 π ( n - m ) ( - z tan α g ) ] 1 g - g / 2 g / 2 I ( x , 0 ) exp [ i 2 π ( n - m ) ( x g ) ] d x λ 1 λ 2 exp [ ( m 2 - n 2 g 2 cos 3 α z ) λ ] .
I s ( z ) = 1 4 + n = 1 2 π 2 ( 2 n 1 ) 2 cos [ 2 π z ( 2 n 1 ) 2 D T α ] cos [ 2 π z ( 2 n 1 ) g / tan α ] sinc [ 2 z ( 2 n 1 ) 2 D T , secondary α ] ,
D T α = 2 g 2 cos 3 α ( λ 1 + λ 2 ) / 2 = 2 g 2 cos 3 α λ c ( Talbot distance for broad spectrum light ) , D T , secondary α = 2 g 2 cos 3 α ( λ 1 λ 2 ) / 2 = 2 g 2 cos 3 α Δλ / 2 ( secondary Talbot distance ) , sinc ( x ) = sin ( π x ) ( π x ) ,
I ( x , y ) = I m ( x , y ) + I a ( x , y ) cos [ ϕ ( x , y ) ] ,
I i ( x , y ) = I m ( x , y ) + I a ( x , y ) cos [ ϕ ( x , y ) + π ( i 1 ) 2 ] ,
i = 1 , 2 , 3 , 4.
ϕ ( x , y ) = arctan [ I 4 ( x , y ) I 2 ( x , y ) I 1 ( x , y ) I 3 ( x , y ) ] .
I i S ( z ) = I s [ z + ( g 4 tan α ) ( i 1 ) ] , i = 1 , 2 , 3 , 4.
I i R ( z ) = 1 + cos { 2 π g / tan α [ z + ( g 4 tan α ) ( i 1 ) ] } ,
i = 1 , 2 , 3 , 4.
ϕ S ( x , y ) = arctan [ I 4 S ( x , y ) I 2 S ( x , y ) I 1 S ( x , y ) I 3 S ( x , y ) ] ,
ϕ R ( x , y ) = arctan [ I 4 R ( x , y ) I 2 R ( x , y ) I 1 R ( x , y ) I 3 R ( x , y ) ] .
e N = 1 2 π [ ϕ S ( x , y ) ϕ R ( x , y ) ] .
I s ( z ) = 1 4 + n = 1 2 π 2 ( 2 n 1 ) 2 ( 1 8 d e z 3 π g )   cos [ 2 πz ( 2 n 1 ) 2 D T α ] × cos [ 2 π z ( 2 n 1 ) g / tan α ] sinc [ 2 z ( 2 n 1 ) 2 D T , secondary α ] ,
d e = d L = f / ( f / # ) f ( M + 1 ) / M = M ( M + 1 ) ( f / # ) ,
a n = { ( 1 ) ( n 1 ) / 2 / π n if   n = odd 1 / 2 if   n = 0 0 if n = even ,
1 g g / 2 g / 2 I ( x , 0 ) exp [ i 2 π ( n m ) ( x g ) ] d x = 1 g g / 4 g / 4 exp [ i 2 π ( n m ) ( x g ) ] d x = { 0 if   n m = even ( 0 ) ( 1 ) ( n m 1 ) / 2 π ( n m ) if   n m = odd 1 / 2 if   n m = 0 ,
λ 1 λ 2 exp [ i π ( m 2 n 2 g 2 cos 3 α z ) λ ] = { g 2 cos 3 α i π ( m 2 n 2 ) z exp [ i π ( m 2 n 2 ) z g 2 cos 3 α λ ] | λ 1 λ 2 if   m 2 n 2   and   z 0 λ 2 λ 1 if   m 2 = n 2   or   z = 0 .
I s ( z ) = { 1 8 ( n = m = 0 ) n = 1 π 2 n 2 1 2 = 1 8 ( n = m , not   0 ) 1 Δλ m = 1 2 π 2 ( 2 m 1 ) 2 g 2 cos 3 α ( 2 m 1 ) 2 exp [ i 2 π ( 2 m 1 ) ( z tan α g ) ] × 1 z { exp [ i π ( 2 m 1 ) 2 z g 2 cos 3 α λ 2 ] exp [ i π ( 2 m 1 ) 2 z g 2 cos 3 α λ 1 ] } ( n = 0 , m = 2 m 1 ) 1 Δλ n = 1 2 π 2 ( 2 n 1 ) 2 g 2 cos 3 α i π ( ( 2 n 1 ) 2 ) exp [ i 2 π ( 2 n 1 ) ( z tan α g ) ] × 1 z { exp [ i π ( 2 n 1 ) 2 z g 2 cos 3 α λ 2 ] exp [ i π ( 2 n 1 ) 2 z g 2 cos 3 α λ 1 ] } ( m = 0 , n = 2 n 1 ) ,
I s ( z ) = 1 4 + 1 Δλ n = g 2 cos 3 α π 3 ( 2 n 1 ) 4 1 z { sin [ π ( 2 n 1 ) 2 z g 2 cos 3 α λ 2 + 2 π ( 2 n 1 ) z g / tan α ] sin [ π ( 2 n 1 ) 2 z g 2 cos 3 α λ 1 + 2 π ( 2 n 1 ) z g / tan α ] } ,
sin [ π ( 2 n 1 ) 2 z g 2 cos 3 α λ 2 + 2 π ( 2 n 1 ) z g / tan α ] sin [ π ( 2 n 1 ) 2 z g 2 cos 3 α λ 1 + 2 π ( 2 n 1 ) z g / tan α ] = 2 cos [ 2 π ( 2 n 1 ) 2 z D T α + 2 π ( 2 n 1 ) z g / tan α ] sin [ 2 π ( 2 n 1 ) 2 z D T , secondary α ] .
I s ( z ) = 1 4 + n = 1 π 2 ( 2 n 1 ) 2 cos [ 2 π z ( ( 2 n 1 ) 2 D T α + ( 2 n 1 ) g / tan α ) ] sinc [ 2 z ( 2 n 1 ) 2 D T , secondary α ] .
I s ( z ) = 1 4 + n = 1 2 π 2 ( 2 n 1 ) 2 cos [ 2 π z ( 2 n 1 ) 2 D T α ] cos [ 2 π z ( 2 n 1 ) g / tan α ] sinc [ 2 z ( 2 n 1 ) 2 D T , secondary α ] .

Metrics