Abstract

In this study, the differential interference contrast (DIC) approach originally used for image enhancement to increase the contrast between a transparent object and the background is adopted for the dimension measurement of transparent structures. With the phase difference image retrieved using the DIC technique, the phase map of the examined object can be approximated by integrating the phase difference. The need of integration accuracy is much higher for measurement than for image enhancement. In this study, a modified Fourier phase integration is proposed to reduce the effects of noise on surface profile reconstruction. The simulation results show that the proposed approach can effectively reduce the effects of noise. Experimental results are also conducted to study the feasibility of using the transmitted DIC with the proposed integration method for transparent object measurement. The results show that the height of a transparent structure measured using the DIC method is quite close to those measured using an atomic force microscope, while those measured using the white-light interference method result in a much larger measurement than all others.

© 2010 Optical Society of America

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References

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  1. D. B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging (Wiley, 2003), pp. 153–168.
  2. R. Danz and P. Gretscher, “C-DIC: a new microscopy method for rational study of phase structures in incident light arrangement,” Thin Solid Films 462–463, 257–262 (2004).
    [CrossRef]
  3. M. Shribak and S. Inoué, “Orientation-independent differential interference contrast microscopy,” Appl. Opt. 45, 460–469(2006).
    [CrossRef] [PubMed]
  4. M. Shribak, “Orientation independent differential interference contrast microscopy technique and device,” U.S. patent 7,233,434 (19 June 2007).
  5. M. Shribak, “Orientation independent differential interference contrast microscopy technique and device,” U.S. patent 7,564,618 (21 July 2009).
  6. C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
    [CrossRef]
  7. S. V. King, A. R. Libertun, C. Preza, and C. J. Cogswell, “Calibration of a phase-shifting DIC microscope for quantitative phase imaging,” Proc. SPIE 6443, 64430M (2007).
    [CrossRef]
  8. C. Preza, “Rotational-diversity phase estimation from differential-interference-contrast microscopy images,” J. Opt. Soc. Am. A 17, 415–424 (2000).
    [CrossRef]
  9. W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525–529 (1991).
    [CrossRef]
  10. Z. Kam, “Microscopic differential interference contrast image processing by line integration (LID) and deconvolution,” Bio-imaging 6, 166–176 (1998).
    [CrossRef]
  11. B. Heise, A. Sonnleitner, and R. P. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312–320 (2005).
    [CrossRef] [PubMed]
  12. Z. Liu, X. Dong, Q. Chen, C. Yin, Y. Xu, and Y. Zheng, “Nondestructive measurement of an optical fiber refractive-index profile by a transmitted-light differential interference contact microscope,” Appl. Opt. 43, 1485–1492 (2004).
    [CrossRef] [PubMed]
  13. A. Talmi and E. N. Ribak, “Wavefront reconstruction from its gradients,” J. Opt. Soc. Am. A 23, 288–297 (2006).
    [CrossRef]
  14. M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12(2004).
    [CrossRef] [PubMed]
  15. K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1862–1870 (2001).
    [CrossRef]
  16. K. G. Larkin, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1871–1881 (2001).
    [CrossRef]
  17. E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
    [CrossRef]
  18. M. Shribak, J. LaFountain, D. Biggs, and S. Inoué, “Orientation-independent differential interference contrast (DIC) microscopy and its combination with orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
    [CrossRef] [PubMed]
  19. F. Kagalwala and T. Kanade. “Reconstructing specimens using DIC microscope images,” IEEE Trans. Syst. Man Cybern. B 33, 728–737 (2003).
    [CrossRef]
  20. N. Axelrod, A. Radko, A. Lewis, and N. Ben-Yosef, “Topographical profiling and refractive index analysis by use of differential interference contrast with bright-filed intensity and atomic force imaging,” Appl. Opt. 43, 2272–2284 (2004).
    [CrossRef] [PubMed]

2008 (1)

M. Shribak, J. LaFountain, D. Biggs, and S. Inoué, “Orientation-independent differential interference contrast (DIC) microscopy and its combination with orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
[CrossRef] [PubMed]

2007 (1)

S. V. King, A. R. Libertun, C. Preza, and C. J. Cogswell, “Calibration of a phase-shifting DIC microscope for quantitative phase imaging,” Proc. SPIE 6443, 64430M (2007).
[CrossRef]

2006 (2)

2005 (1)

B. Heise, A. Sonnleitner, and R. P. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312–320 (2005).
[CrossRef] [PubMed]

2004 (4)

R. Danz and P. Gretscher, “C-DIC: a new microscopy method for rational study of phase structures in incident light arrangement,” Thin Solid Films 462–463, 257–262 (2004).
[CrossRef]

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12(2004).
[CrossRef] [PubMed]

Z. Liu, X. Dong, Q. Chen, C. Yin, Y. Xu, and Y. Zheng, “Nondestructive measurement of an optical fiber refractive-index profile by a transmitted-light differential interference contact microscope,” Appl. Opt. 43, 1485–1492 (2004).
[CrossRef] [PubMed]

N. Axelrod, A. Radko, A. Lewis, and N. Ben-Yosef, “Topographical profiling and refractive index analysis by use of differential interference contrast with bright-filed intensity and atomic force imaging,” Appl. Opt. 43, 2272–2284 (2004).
[CrossRef] [PubMed]

2003 (2)

F. Kagalwala and T. Kanade. “Reconstructing specimens using DIC microscope images,” IEEE Trans. Syst. Man Cybern. B 33, 728–737 (2003).
[CrossRef]

D. B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging (Wiley, 2003), pp. 153–168.

2001 (2)

2000 (1)

1998 (1)

Z. Kam, “Microscopic differential interference contrast image processing by line integration (LID) and deconvolution,” Bio-imaging 6, 166–176 (1998).
[CrossRef]

1997 (2)

E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
[CrossRef]

1991 (1)

W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525–529 (1991).
[CrossRef]

Arnison, M. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12(2004).
[CrossRef] [PubMed]

Aten, J. A.

E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

Axelrod, N.

Ben-Yosef, N.

Biggs, D.

M. Shribak, J. LaFountain, D. Biggs, and S. Inoué, “Orientation-independent differential interference contrast (DIC) microscopy and its combination with orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
[CrossRef] [PubMed]

Bone, D. J.

Chen, Q.

Cogswell, C.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12(2004).
[CrossRef] [PubMed]

Cogswell, C. J.

S. V. King, A. R. Libertun, C. Preza, and C. J. Cogswell, “Calibration of a phase-shifting DIC microscope for quantitative phase imaging,” Proc. SPIE 6443, 64430M (2007).
[CrossRef]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
[CrossRef]

Danz, R.

R. Danz and P. Gretscher, “C-DIC: a new microscopy method for rational study of phase structures in incident light arrangement,” Thin Solid Films 462–463, 257–262 (2004).
[CrossRef]

Dong, X.

Gretscher, P.

R. Danz and P. Gretscher, “C-DIC: a new microscopy method for rational study of phase structures in incident light arrangement,” Thin Solid Films 462–463, 257–262 (2004).
[CrossRef]

Hariharan, P.

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
[CrossRef]

Heise, B.

B. Heise, A. Sonnleitner, and R. P. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312–320 (2005).
[CrossRef] [PubMed]

Inoué, S.

M. Shribak, J. LaFountain, D. Biggs, and S. Inoué, “Orientation-independent differential interference contrast (DIC) microscopy and its combination with orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
[CrossRef] [PubMed]

M. Shribak and S. Inoué, “Orientation-independent differential interference contrast microscopy,” Appl. Opt. 45, 460–469(2006).
[CrossRef] [PubMed]

Kagalwala, F.

F. Kagalwala and T. Kanade. “Reconstructing specimens using DIC microscope images,” IEEE Trans. Syst. Man Cybern. B 33, 728–737 (2003).
[CrossRef]

Kam, Z.

Z. Kam, “Microscopic differential interference contrast image processing by line integration (LID) and deconvolution,” Bio-imaging 6, 166–176 (1998).
[CrossRef]

Kanade, T.

F. Kagalwala and T. Kanade. “Reconstructing specimens using DIC microscope images,” IEEE Trans. Syst. Man Cybern. B 33, 728–737 (2003).
[CrossRef]

King, S. V.

S. V. King, A. R. Libertun, C. Preza, and C. J. Cogswell, “Calibration of a phase-shifting DIC microscope for quantitative phase imaging,” Proc. SPIE 6443, 64430M (2007).
[CrossRef]

Klement, R. P.

B. Heise, A. Sonnleitner, and R. P. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312–320 (2005).
[CrossRef] [PubMed]

LaFountain, J.

M. Shribak, J. LaFountain, D. Biggs, and S. Inoué, “Orientation-independent differential interference contrast (DIC) microscopy and its combination with orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
[CrossRef] [PubMed]

Larkin, K. G.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12(2004).
[CrossRef] [PubMed]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1862–1870 (2001).
[CrossRef]

K. G. Larkin, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1871–1881 (2001).
[CrossRef]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
[CrossRef]

Lewis, A.

Libertun, A. R.

S. V. King, A. R. Libertun, C. Preza, and C. J. Cogswell, “Calibration of a phase-shifting DIC microscope for quantitative phase imaging,” Proc. SPIE 6443, 64430M (2007).
[CrossRef]

Liu, Z.

Murphy, D. B.

D. B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging (Wiley, 2003), pp. 153–168.

Oldfield, M. A.

Preza, C.

S. V. King, A. R. Libertun, C. Preza, and C. J. Cogswell, “Calibration of a phase-shifting DIC microscope for quantitative phase imaging,” Proc. SPIE 6443, 64430M (2007).
[CrossRef]

C. Preza, “Rotational-diversity phase estimation from differential-interference-contrast microscopy images,” J. Opt. Soc. Am. A 17, 415–424 (2000).
[CrossRef]

Radko, A.

Ribak, E. N.

Sato, T.

W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525–529 (1991).
[CrossRef]

Sheppard, C. J. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12(2004).
[CrossRef] [PubMed]

Shimada, W.

W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525–529 (1991).
[CrossRef]

Shribak, M.

M. Shribak, “Orientation independent differential interference contrast microscopy technique and device,” U.S. patent 7,564,618 (21 July 2009).

M. Shribak, J. LaFountain, D. Biggs, and S. Inoué, “Orientation-independent differential interference contrast (DIC) microscopy and its combination with orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
[CrossRef] [PubMed]

M. Shribak and S. Inoué, “Orientation-independent differential interference contrast microscopy,” Appl. Opt. 45, 460–469(2006).
[CrossRef] [PubMed]

M. Shribak, “Orientation independent differential interference contrast microscopy technique and device,” U.S. patent 7,233,434 (19 June 2007).

Smith, N. I.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12(2004).
[CrossRef] [PubMed]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
[CrossRef]

Sonnleitner, A.

B. Heise, A. Sonnleitner, and R. P. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312–320 (2005).
[CrossRef] [PubMed]

Talmi, A.

Van Munster, E. B.

E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

Van Vliet, L. J.

E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

Xu, Y.

Yatagai, T.

W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525–529 (1991).
[CrossRef]

Yin, C.

Zheng, Y.

Appl. Opt. (3)

Bio-imaging (1)

Z. Kam, “Microscopic differential interference contrast image processing by line integration (LID) and deconvolution,” Bio-imaging 6, 166–176 (1998).
[CrossRef]

IEEE Trans. Syst. Man Cybern. B (1)

F. Kagalwala and T. Kanade. “Reconstructing specimens using DIC microscope images,” IEEE Trans. Syst. Man Cybern. B 33, 728–737 (2003).
[CrossRef]

J. Biomed. Opt. (1)

M. Shribak, J. LaFountain, D. Biggs, and S. Inoué, “Orientation-independent differential interference contrast (DIC) microscopy and its combination with orientation-independent polarization system,” J. Biomed. Opt. 13, 014011 (2008).
[CrossRef] [PubMed]

J. Microsc. (2)

E. B. Van Munster, L. J. Van Vliet, and J. A. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12(2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (4)

Microsc. Res. Tech. (1)

B. Heise, A. Sonnleitner, and R. P. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. 66, 312–320 (2005).
[CrossRef] [PubMed]

Proc. SPIE (3)

W. Shimada, T. Sato, and T. Yatagai, “Optical surface microtopography using phase-shifting Nomarski microscope,” Proc. SPIE 1332, 525–529 (1991).
[CrossRef]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter,” Proc. SPIE 2984, 72–81 (1997).
[CrossRef]

S. V. King, A. R. Libertun, C. Preza, and C. J. Cogswell, “Calibration of a phase-shifting DIC microscope for quantitative phase imaging,” Proc. SPIE 6443, 64430M (2007).
[CrossRef]

Thin Solid Films (1)

R. Danz and P. Gretscher, “C-DIC: a new microscopy method for rational study of phase structures in incident light arrangement,” Thin Solid Films 462–463, 257–262 (2004).
[CrossRef]

Other (3)

D. B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging (Wiley, 2003), pp. 153–168.

M. Shribak, “Orientation independent differential interference contrast microscopy technique and device,” U.S. patent 7,233,434 (19 June 2007).

M. Shribak, “Orientation independent differential interference contrast microscopy technique and device,” U.S. patent 7,564,618 (21 July 2009).

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Figures (13)

Fig. 1
Fig. 1

Progression of rays and formation of a DIC image.

Fig. 2
Fig. 2

Phantoms used in the simulation test.

Fig. 3
Fig. 3

Phase maps reconstructed by different integration methods (1% noise).

Fig. 4
Fig. 4

Comparison of phase errors (1% noise).

Fig. 5
Fig. 5

Comparison of phase errors for all simulation tests.

Fig. 6
Fig. 6

Reflective DIC.

Fig. 7
Fig. 7

Line analysis of step height standard sample measured by reflective DIC.

Fig. 8
Fig. 8

Comparison of the step height standard sample measurement by reflective DIC and WLI.

Fig. 9
Fig. 9

Transmitted DIC.

Fig. 10
Fig. 10

Test specimens and their measurements by AFM.

Fig. 11
Fig. 11

Measurement of sample 1 (2D array): upper, AFM measurement; lower, transmitted DIC measurement.

Fig. 12
Fig. 12

Measurement of sample 2 (1D grating): upper, AFM measurement; lower, transmitted DIC measurement.

Fig. 13
Fig. 13

Measurement of sample 3 (spacer): upper, AFM measurement; lower, transmitted DIC measurement.

Tables (4)

Tables Icon

Table 1 System Parameters for Simulation Test

Tables Icon

Table 2 Comparison of Average Phase Error (Unit, Radians)

Tables Icon

Table 3 Parameters for Reflective Differential Interference Contrast Test

Tables Icon

Table 4 Summary of Test Results for the Transparent Specimen

Equations (6)

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

θ ( x ) = θ ( x ) d x + c .
θ ( x , y ) x = θ ( x , y ) x d x + c ( y ) x ,
θ ( x , y ) y θ ( x , y ) y d y + c ( x ) y .
F { θ ( x ) } = F { θ ( x ) } / i w ,
θ ( i , j ) x = D F 1 { D F { θ ( i , j ) } 1 h i sin ( 2 π h u M ) } + c ( j ) x ,
θ ( i , j ) y = D F 1 { D F { θ ( i , j ) } 1 k j sin ( 2 π k v N ) } + c ( i ) y ,

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