Abstract

A moiré fringe approach is developed to identify simultaneously the global and local distortions in hot-embossed polymeric samples. A square grid pattern with a pitch of 63.5 μm is hot-embossed on the polymer substrate. When a reference grid, a polymeric film with the same pattern, is placed on top of the sample, a moiré fringe pattern is observed and recorded by a document scanner. The deviation of the intersections of the fringes from their ideal positions presents the residual distortion in the sample. With different sample-reference rotation angles eight images are acquired for the same sample to achieve the optimal result by a data fitting technique. The validity of this method is proved by the self-consistency of the results from the eight images. To the best of our knowledge, this is the first time distortion quantification has been achieved both in a large area up to that of a scanner and with a high resolution at the level of 1 μm. Furthermore, we do not use any expensive instrument, nor need to measure the sample–reference rotation angle or position the sample precisely, and the process is run automatically by a computer instead of manual operation.

© 2009 OSA

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References

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  1. P. P. Shiu, G. K. Knopf, M. Ostojic, and S. Nikumb, “Rapid fabrication of tooling for microfluidic devices via laser micromachining and hot embossing,” J. Micromech. Microeng. 18(2), 025012 (2008).
    [CrossRef]
  2. N. S. Cameron, H. Roberge, T. Veres, S. C. Jakeway, and H. John Crabtree, “High fidelity, high yield production of microfluidic devices by hot embossing lithography: rheology and stiction,” Lab Chip 6(7), 936–941 (2006).
    [CrossRef] [PubMed]
  3. O. Rotting and W. Ropke, “H, Becker, C. Gärtner, “Polymer microfabrication technologies,” Microsyst. Technol. 8, 32–36 (2002).
  4. H. K. Taylor, Z. G. Xu, S. G. Li, S. F. Yoon, and D. S. Boning, “Moiré fringe method for the measurement of distortions of hot-embossed polymeric substrates,” Proc. SPIE 7155(715528), 1–9 (2008).
  5. M. Dirckx, H. Taylor, and D. Hardt, “High-temperature demolding for cycle time reduction in hot embossing,” in Proc. Society of Plastics Engineers Annual Technical Conference, 2972–2976 (2007).
  6. Y. He, J. Z. Fu, and Z. C. Chen, “Research on optimization of the hot embossing process,” J. Micromech. Microeng. 17(12), 2420–2425 (2007).
    [CrossRef]
  7. W. M. Choi and O. O. Park, “The fabrication of submicron patterns on curved substrates using a polydimethylsiloxane film mould,” Nanatechnol. 15(12), 1767–1770 (2004).
    [CrossRef]
  8. W. W. Y. Chow, K. F. Lei, G. Shi, W. J. Li, and Q. Huang, “Microfluidic channel fabrication by PDMS-interface bonding,” Smart Mater. Struct. 15(1), S112–S116 (2006).
    [CrossRef]
  9. J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Quantifying distortions in soft lithography,” J. Vac. Sci. Technol. B 16(1), 88–97 (1998).
    [CrossRef]
  10. K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, 1993), Chap. 1.
  11. J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice Hall, 1990), Chap. 9.
  12. R. W. Cox and R. Tong, “Two- and three-dimensional image rotation using the FFT,” IEEE Trans. Image Process. 8(9), 1297–1299 (1999).
    [CrossRef]
  13. B. W. Yoon and W. J. Song, “Image contrast enhancement based on the generalized histogram,” J. Electron. Imaging 16(3), 033005 (2007).
    [CrossRef]
  14. J. Condeco, L. H. Christensen, and B. G. Rosen, “Software relocation of 3D surface topography measurements,” Int. J. Mach. Tools Manuf. 41(13–14), 2095–2101 (2001).
    [CrossRef]
  15. Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
    [CrossRef]

2009 (1)

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

2008 (2)

P. P. Shiu, G. K. Knopf, M. Ostojic, and S. Nikumb, “Rapid fabrication of tooling for microfluidic devices via laser micromachining and hot embossing,” J. Micromech. Microeng. 18(2), 025012 (2008).
[CrossRef]

H. K. Taylor, Z. G. Xu, S. G. Li, S. F. Yoon, and D. S. Boning, “Moiré fringe method for the measurement of distortions of hot-embossed polymeric substrates,” Proc. SPIE 7155(715528), 1–9 (2008).

2007 (2)

Y. He, J. Z. Fu, and Z. C. Chen, “Research on optimization of the hot embossing process,” J. Micromech. Microeng. 17(12), 2420–2425 (2007).
[CrossRef]

B. W. Yoon and W. J. Song, “Image contrast enhancement based on the generalized histogram,” J. Electron. Imaging 16(3), 033005 (2007).
[CrossRef]

2006 (2)

W. W. Y. Chow, K. F. Lei, G. Shi, W. J. Li, and Q. Huang, “Microfluidic channel fabrication by PDMS-interface bonding,” Smart Mater. Struct. 15(1), S112–S116 (2006).
[CrossRef]

N. S. Cameron, H. Roberge, T. Veres, S. C. Jakeway, and H. John Crabtree, “High fidelity, high yield production of microfluidic devices by hot embossing lithography: rheology and stiction,” Lab Chip 6(7), 936–941 (2006).
[CrossRef] [PubMed]

2004 (1)

W. M. Choi and O. O. Park, “The fabrication of submicron patterns on curved substrates using a polydimethylsiloxane film mould,” Nanatechnol. 15(12), 1767–1770 (2004).
[CrossRef]

2002 (1)

O. Rotting and W. Ropke, “H, Becker, C. Gärtner, “Polymer microfabrication technologies,” Microsyst. Technol. 8, 32–36 (2002).

2001 (1)

J. Condeco, L. H. Christensen, and B. G. Rosen, “Software relocation of 3D surface topography measurements,” Int. J. Mach. Tools Manuf. 41(13–14), 2095–2101 (2001).
[CrossRef]

1999 (1)

R. W. Cox and R. Tong, “Two- and three-dimensional image rotation using the FFT,” IEEE Trans. Image Process. 8(9), 1297–1299 (1999).
[CrossRef]

1998 (1)

J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Quantifying distortions in soft lithography,” J. Vac. Sci. Technol. B 16(1), 88–97 (1998).
[CrossRef]

Boning, D. S.

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

H. K. Taylor, Z. G. Xu, S. G. Li, S. F. Yoon, and D. S. Boning, “Moiré fringe method for the measurement of distortions of hot-embossed polymeric substrates,” Proc. SPIE 7155(715528), 1–9 (2008).

Burns, D. J.

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

Cameron, N. S.

N. S. Cameron, H. Roberge, T. Veres, S. C. Jakeway, and H. John Crabtree, “High fidelity, high yield production of microfluidic devices by hot embossing lithography: rheology and stiction,” Lab Chip 6(7), 936–941 (2006).
[CrossRef] [PubMed]

Chen, Z. C.

Y. He, J. Z. Fu, and Z. C. Chen, “Research on optimization of the hot embossing process,” J. Micromech. Microeng. 17(12), 2420–2425 (2007).
[CrossRef]

Choi, W. M.

W. M. Choi and O. O. Park, “The fabrication of submicron patterns on curved substrates using a polydimethylsiloxane film mould,” Nanatechnol. 15(12), 1767–1770 (2004).
[CrossRef]

Chow, W. W. Y.

W. W. Y. Chow, K. F. Lei, G. Shi, W. J. Li, and Q. Huang, “Microfluidic channel fabrication by PDMS-interface bonding,” Smart Mater. Struct. 15(1), S112–S116 (2006).
[CrossRef]

Christensen, L. H.

J. Condeco, L. H. Christensen, and B. G. Rosen, “Software relocation of 3D surface topography measurements,” Int. J. Mach. Tools Manuf. 41(13–14), 2095–2101 (2001).
[CrossRef]

Condeco, J.

J. Condeco, L. H. Christensen, and B. G. Rosen, “Software relocation of 3D surface topography measurements,” Int. J. Mach. Tools Manuf. 41(13–14), 2095–2101 (2001).
[CrossRef]

Cox, R. W.

R. W. Cox and R. Tong, “Two- and three-dimensional image rotation using the FFT,” IEEE Trans. Image Process. 8(9), 1297–1299 (1999).
[CrossRef]

Fang, Z. P.

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

Fu, J. Z.

Y. He, J. Z. Fu, and Z. C. Chen, “Research on optimization of the hot embossing process,” J. Micromech. Microeng. 17(12), 2420–2425 (2007).
[CrossRef]

He, Y.

Y. He, J. Z. Fu, and Z. C. Chen, “Research on optimization of the hot embossing process,” J. Micromech. Microeng. 17(12), 2420–2425 (2007).
[CrossRef]

Huang, Q.

W. W. Y. Chow, K. F. Lei, G. Shi, W. J. Li, and Q. Huang, “Microfluidic channel fabrication by PDMS-interface bonding,” Smart Mater. Struct. 15(1), S112–S116 (2006).
[CrossRef]

Jakeway, S. C.

N. S. Cameron, H. Roberge, T. Veres, S. C. Jakeway, and H. John Crabtree, “High fidelity, high yield production of microfluidic devices by hot embossing lithography: rheology and stiction,” Lab Chip 6(7), 936–941 (2006).
[CrossRef] [PubMed]

John Crabtree, H.

N. S. Cameron, H. Roberge, T. Veres, S. C. Jakeway, and H. John Crabtree, “High fidelity, high yield production of microfluidic devices by hot embossing lithography: rheology and stiction,” Lab Chip 6(7), 936–941 (2006).
[CrossRef] [PubMed]

Knopf, G. K.

P. P. Shiu, G. K. Knopf, M. Ostojic, and S. Nikumb, “Rapid fabrication of tooling for microfluidic devices via laser micromachining and hot embossing,” J. Micromech. Microeng. 18(2), 025012 (2008).
[CrossRef]

Lei, K. F.

W. W. Y. Chow, K. F. Lei, G. Shi, W. J. Li, and Q. Huang, “Microfluidic channel fabrication by PDMS-interface bonding,” Smart Mater. Struct. 15(1), S112–S116 (2006).
[CrossRef]

Li, S. G.

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

H. K. Taylor, Z. G. Xu, S. G. Li, S. F. Yoon, and D. S. Boning, “Moiré fringe method for the measurement of distortions of hot-embossed polymeric substrates,” Proc. SPIE 7155(715528), 1–9 (2008).

Li, W. J.

W. W. Y. Chow, K. F. Lei, G. Shi, W. J. Li, and Q. Huang, “Microfluidic channel fabrication by PDMS-interface bonding,” Smart Mater. Struct. 15(1), S112–S116 (2006).
[CrossRef]

Nikumb, S.

P. P. Shiu, G. K. Knopf, M. Ostojic, and S. Nikumb, “Rapid fabrication of tooling for microfluidic devices via laser micromachining and hot embossing,” J. Micromech. Microeng. 18(2), 025012 (2008).
[CrossRef]

Ostojic, M.

P. P. Shiu, G. K. Knopf, M. Ostojic, and S. Nikumb, “Rapid fabrication of tooling for microfluidic devices via laser micromachining and hot embossing,” J. Micromech. Microeng. 18(2), 025012 (2008).
[CrossRef]

Park, O. O.

W. M. Choi and O. O. Park, “The fabrication of submicron patterns on curved substrates using a polydimethylsiloxane film mould,” Nanatechnol. 15(12), 1767–1770 (2004).
[CrossRef]

Paul, K. E.

J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Quantifying distortions in soft lithography,” J. Vac. Sci. Technol. B 16(1), 88–97 (1998).
[CrossRef]

Reading, I.

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

Roberge, H.

N. S. Cameron, H. Roberge, T. Veres, S. C. Jakeway, and H. John Crabtree, “High fidelity, high yield production of microfluidic devices by hot embossing lithography: rheology and stiction,” Lab Chip 6(7), 936–941 (2006).
[CrossRef] [PubMed]

Rogers, J. A.

J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Quantifying distortions in soft lithography,” J. Vac. Sci. Technol. B 16(1), 88–97 (1998).
[CrossRef]

Ropke, W.

O. Rotting and W. Ropke, “H, Becker, C. Gärtner, “Polymer microfabrication technologies,” Microsyst. Technol. 8, 32–36 (2002).

Rosen, B. G.

J. Condeco, L. H. Christensen, and B. G. Rosen, “Software relocation of 3D surface topography measurements,” Int. J. Mach. Tools Manuf. 41(13–14), 2095–2101 (2001).
[CrossRef]

Rotting, O.

O. Rotting and W. Ropke, “H, Becker, C. Gärtner, “Polymer microfabrication technologies,” Microsyst. Technol. 8, 32–36 (2002).

Shi, G.

W. W. Y. Chow, K. F. Lei, G. Shi, W. J. Li, and Q. Huang, “Microfluidic channel fabrication by PDMS-interface bonding,” Smart Mater. Struct. 15(1), S112–S116 (2006).
[CrossRef]

Shilpiekandula, V.

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

Shiu, P. P.

P. P. Shiu, G. K. Knopf, M. Ostojic, and S. Nikumb, “Rapid fabrication of tooling for microfluidic devices via laser micromachining and hot embossing,” J. Micromech. Microeng. 18(2), 025012 (2008).
[CrossRef]

Song, W. J.

B. W. Yoon and W. J. Song, “Image contrast enhancement based on the generalized histogram,” J. Electron. Imaging 16(3), 033005 (2007).
[CrossRef]

Taylor, H. K.

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

H. K. Taylor, Z. G. Xu, S. G. Li, S. F. Yoon, and D. S. Boning, “Moiré fringe method for the measurement of distortions of hot-embossed polymeric substrates,” Proc. SPIE 7155(715528), 1–9 (2008).

Tong, R.

R. W. Cox and R. Tong, “Two- and three-dimensional image rotation using the FFT,” IEEE Trans. Image Process. 8(9), 1297–1299 (1999).
[CrossRef]

Veres, T.

N. S. Cameron, H. Roberge, T. Veres, S. C. Jakeway, and H. John Crabtree, “High fidelity, high yield production of microfluidic devices by hot embossing lithography: rheology and stiction,” Lab Chip 6(7), 936–941 (2006).
[CrossRef] [PubMed]

Whitesides, G. M.

J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Quantifying distortions in soft lithography,” J. Vac. Sci. Technol. B 16(1), 88–97 (1998).
[CrossRef]

Xu, Z. G.

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

H. K. Taylor, Z. G. Xu, S. G. Li, S. F. Yoon, and D. S. Boning, “Moiré fringe method for the measurement of distortions of hot-embossed polymeric substrates,” Proc. SPIE 7155(715528), 1–9 (2008).

Yoon, B. W.

B. W. Yoon and W. J. Song, “Image contrast enhancement based on the generalized histogram,” J. Electron. Imaging 16(3), 033005 (2007).
[CrossRef]

Yoon, S. F.

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

H. K. Taylor, Z. G. Xu, S. G. Li, S. F. Yoon, and D. S. Boning, “Moiré fringe method for the measurement of distortions of hot-embossed polymeric substrates,” Proc. SPIE 7155(715528), 1–9 (2008).

Youcef-Toumi, K.

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

Zhao, J. H.

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

IEEE Trans. Image Process. (1)

R. W. Cox and R. Tong, “Two- and three-dimensional image rotation using the FFT,” IEEE Trans. Image Process. 8(9), 1297–1299 (1999).
[CrossRef]

Int. J. Mach. Tools Manuf. (1)

J. Condeco, L. H. Christensen, and B. G. Rosen, “Software relocation of 3D surface topography measurements,” Int. J. Mach. Tools Manuf. 41(13–14), 2095–2101 (2001).
[CrossRef]

J. Electron. Imaging (1)

B. W. Yoon and W. J. Song, “Image contrast enhancement based on the generalized histogram,” J. Electron. Imaging 16(3), 033005 (2007).
[CrossRef]

J. Micromech. Microeng. (2)

P. P. Shiu, G. K. Knopf, M. Ostojic, and S. Nikumb, “Rapid fabrication of tooling for microfluidic devices via laser micromachining and hot embossing,” J. Micromech. Microeng. 18(2), 025012 (2008).
[CrossRef]

Y. He, J. Z. Fu, and Z. C. Chen, “Research on optimization of the hot embossing process,” J. Micromech. Microeng. 17(12), 2420–2425 (2007).
[CrossRef]

J. Vac. Sci. Technol. B (1)

J. A. Rogers, K. E. Paul, and G. M. Whitesides, “Quantifying distortions in soft lithography,” J. Vac. Sci. Technol. B 16(1), 88–97 (1998).
[CrossRef]

Lab Chip (1)

N. S. Cameron, H. Roberge, T. Veres, S. C. Jakeway, and H. John Crabtree, “High fidelity, high yield production of microfluidic devices by hot embossing lithography: rheology and stiction,” Lab Chip 6(7), 936–941 (2006).
[CrossRef] [PubMed]

Microsyst. Technol. (1)

O. Rotting and W. Ropke, “H, Becker, C. Gärtner, “Polymer microfabrication technologies,” Microsyst. Technol. 8, 32–36 (2002).

Nanatechnol. (1)

W. M. Choi and O. O. Park, “The fabrication of submicron patterns on curved substrates using a polydimethylsiloxane film mould,” Nanatechnol. 15(12), 1767–1770 (2004).
[CrossRef]

Opt. Commun. (1)

Z. G. Xu, S. G. Li, D. J. Burns, V. Shilpiekandula, H. K. Taylor, S. F. Yoon, K. Youcef-Toumi, I. Reading, Z. P. Fang, J. H. Zhao, and D. S. Boning, “Three-dimensional profile stitching based on the fiducial markers for microfluidic devices,” Opt. Commun. 282(4), 493–499 (2009).
[CrossRef]

Proc. SPIE (1)

H. K. Taylor, Z. G. Xu, S. G. Li, S. F. Yoon, and D. S. Boning, “Moiré fringe method for the measurement of distortions of hot-embossed polymeric substrates,” Proc. SPIE 7155(715528), 1–9 (2008).

Smart Mater. Struct. (1)

W. W. Y. Chow, K. F. Lei, G. Shi, W. J. Li, and Q. Huang, “Microfluidic channel fabrication by PDMS-interface bonding,” Smart Mater. Struct. 15(1), S112–S116 (2006).
[CrossRef]

Other (3)

K. Patorski, Handbook of the Moiré Fringe Technique (Elsevier, 1993), Chap. 1.

J. S. Lim, Two-Dimensional Signal and Image Processing (Prentice Hall, 1990), Chap. 9.

M. Dirckx, H. Taylor, and D. Hardt, “High-temperature demolding for cycle time reduction in hot embossing,” in Proc. Society of Plastics Engineers Annual Technical Conference, 2972–2976 (2007).

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Figures (12)

Fig. 1
Fig. 1

The acquired moiré fringe pattern with the precisely printed reference grid located on top of the embossed part at a small orientation angle.

Fig. 2
Fig. 2

Fraction of the image data before (a) and after (b) Wiener noise filtering. The unit in the x and y axes is pixel, and the image intensity is normalized in z axis.

Fig. 3
Fig. 3

Two-dimensional FFT of the image after noise filtering. (a): the central region in the image with fringe pattern extracted for the FFT; (b): the spectrum of (a), in which two significant frequency components corresponding to the fringe pitches in two directions can be easily identified.

Fig. 4
Fig. 4

Image data after rotating the image to make the fringe rows and columns planar and vertical, cutting off the useless regions (a), and enhancing the image contrast (b). Unit: pixel.

Fig. 5
Fig. 5

Histogram contributions of the image before and after contrast enhancement technique.

Fig. 6
Fig. 6

Correlation calculation between the typical fringe cross and each searched region with the same size of the cross. (a) The extracted fringe cross; (b) The calculation results throughout the image.

Fig. 7
Fig. 7

(a): Continuous pixels with the calculated correlation ratio larger than the threshold 0.6; (b) The centroids of all the continuous areas, which are taken as the positions of fringe intersections.

Fig. 8
Fig. 8

Local fringe deviations throughout the sample surface denoted by arrows, where the beginning point of each arrow represents the ideal position of the fringe intersection, and end point shows the practical position.

Fig. 9
Fig. 9

Local sample distortions throughout the sample surface, from which one can see the distortion at the edges is more significant than in the central region.

Fig. 10
Fig. 10

The acquired eight images of moiré fringe pattern with different sample-reference orientation angles. Form (1) to (8) the sample is rotated in the clockwise direction.

Fig. 11
Fig. 11

Results of fitting a moiré fringe model to fringe orientation and spacing data extracted from the eight acquired images. Solid lines represent the group of theoretical curves best fitting the practical data denoted by * marks.

Fig. 12
Fig. 12

Local distortions derived from image (5), (6) and (7), which show the self-consistency of our approach.

Tables (1)

Tables Icon

Table 1 Direct Information Derived from the Eight Images

Equations (5)

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

dM=rd(1+r22rcosθ)1/2
sinϕ=sinθ(1+r22rcosθ)1/2
A2(i,j)=ρ+σ2ν2σ2[A1(i,j)ρ]
ρ=1MNi,jεA1(i,j);σ2=1MNi,jεA12(i,j)ρ2
F(p,q)=i=1mj=1nA2(i,j)e2πi(ipM+jqN)

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