Abstract

We present a differential interference contrast microscope using photonic crystals capable of real-time capture of both phase and amplitude components independently without moving parts. Unlike previous methods using rotating polarizers to discriminate each component, we propose using a special camera equipped with an arrayed polarizer whose instant polarization measurement allows real-time acquisition of the phase gradient information. A two-image algorithm is used to reconstruct the phase two- dimensional distribution of biological samples from the gradient information with a transmission-type microscope. We also talk about deducing a sample’s three-dimensional shape for a reflection-type microscope. The efficiency of the method is demonstrated experimentally.

© 2009 Optical Society of America

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References

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  1. F. Zernike, “How I discovered phase contrast,” Science 121, 345-349 (1955).
    [CrossRef] [PubMed]
  2. H. Ooki, Y. Iwasaki, and J. Iwasaki, “Differential interference contrast microscope with differential detection for optimizing image contrast,” Appl. Opt. 35, 2230-2234 (1996).
    [CrossRef] [PubMed]
  3. H. Ishiwata, M. Itoh, and T. Yatagai, “A new analysis for extending the measurement range of the retardation-modulated differential interference contrast (RM-DIC) microscope,” Opt. Commun. 281, 1412-1423 (2008).
    [CrossRef]
  4. M. Shriback and S. Inoue, “Orientation-independant differential interference contrast microscopy,” Appl. Opt. 45, 460-469(2006).
    [CrossRef]
  5. K. Takita, M. A. Muquit, T. Aoki, and T. Higuchi, “A sub-pixel correspondance search technique for computer vision application,” IEICE Trans. Fundam. E87-A, 1913-1918 (2004).
  6. S. Inoue and K. R. Spring, Video Microscopy, the Fundamentals, 2nd ed. (Plenum, 1997), Chap. 2.6.7.
    [CrossRef]
  7. S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three dimensional nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465 (1999).
    [CrossRef]
  8. T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
    [CrossRef]
  9. Y. Inoue, T. Kawashima, M. Sasaki, A. Galea, and S. Kawakami, “Highly durable deep ultraviolet polarizers based on auto-cloned photonic crystal,” in Japan Society of Applied Physics 55th Spring Meeting (2008).
  10. S. Kawakami, “Industrial applications of stacked photonic crystals,” Oyo Buturi 77, 508-514 (2008).
  11. S. Kawakami, T. Kawashima, Y. Inoue, Y. Homma, T. Sato, S. Ota, S. Nagashima, and T. Aoki, “Polarization imaging device utilizing photonic crystal polarizer,” J. IEICE J90-C, 17-24 (2007).
  12. T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46, 4963-4967 (2007).
    [CrossRef] [PubMed]
  13. A. K. Parulski, “Color filters and processing alternatives for one-chip cameras,” IEICE Trans. Electron. Devices ED32, 1381-1389 (1985).
    [CrossRef]
  14. E. J. Adams, “Interactions between color plane and other image processing functions in electronic photography,” Proc. SPIE 2416, 144-151 (1995).
    [CrossRef]
  15. E. J. Adams, “Design of practical color filter array interpolation algorithm for digital cameras,” Proc. SPIE 3028, 117-125(1997).
    [CrossRef]
  16. D. Xu, H. Zhang, Q. Wang, and H. Bao, “Poisson shape interpolation,” Graphical Models 68, 268-281 (2006).
    [CrossRef]
  17. M. Kahzdan, M. Bolitho, and H. Hoppe, “Poisson surface reconstruction,” in Eurographics Symposium on Geometry Processing (2006).
  18. K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. E86-A, 1925-1934(2003).
  19. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1988), Chap. 19.4.
  20. A. Agrawal, R. Chellappa, and R. Raskar, “An algebraic approach to surface reconstruction from gradient fields,” in Tenth International Conference on Computer Vision (IEEE, 2005).

2008 (2)

H. Ishiwata, M. Itoh, and T. Yatagai, “A new analysis for extending the measurement range of the retardation-modulated differential interference contrast (RM-DIC) microscope,” Opt. Commun. 281, 1412-1423 (2008).
[CrossRef]

S. Kawakami, “Industrial applications of stacked photonic crystals,” Oyo Buturi 77, 508-514 (2008).

2007 (2)

S. Kawakami, T. Kawashima, Y. Inoue, Y. Homma, T. Sato, S. Ota, S. Nagashima, and T. Aoki, “Polarization imaging device utilizing photonic crystal polarizer,” J. IEICE J90-C, 17-24 (2007).

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46, 4963-4967 (2007).
[CrossRef] [PubMed]

2006 (2)

M. Shriback and S. Inoue, “Orientation-independant differential interference contrast microscopy,” Appl. Opt. 45, 460-469(2006).
[CrossRef]

D. Xu, H. Zhang, Q. Wang, and H. Bao, “Poisson shape interpolation,” Graphical Models 68, 268-281 (2006).
[CrossRef]

2004 (1)

K. Takita, M. A. Muquit, T. Aoki, and T. Higuchi, “A sub-pixel correspondance search technique for computer vision application,” IEICE Trans. Fundam. E87-A, 1913-1918 (2004).

2003 (1)

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. E86-A, 1925-1934(2003).

2002 (1)

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

1999 (1)

S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three dimensional nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465 (1999).
[CrossRef]

1997 (1)

E. J. Adams, “Design of practical color filter array interpolation algorithm for digital cameras,” Proc. SPIE 3028, 117-125(1997).
[CrossRef]

1996 (1)

1995 (1)

E. J. Adams, “Interactions between color plane and other image processing functions in electronic photography,” Proc. SPIE 2416, 144-151 (1995).
[CrossRef]

1985 (1)

A. K. Parulski, “Color filters and processing alternatives for one-chip cameras,” IEICE Trans. Electron. Devices ED32, 1381-1389 (1985).
[CrossRef]

1955 (1)

F. Zernike, “How I discovered phase contrast,” Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Adams, E. J.

E. J. Adams, “Design of practical color filter array interpolation algorithm for digital cameras,” Proc. SPIE 3028, 117-125(1997).
[CrossRef]

E. J. Adams, “Interactions between color plane and other image processing functions in electronic photography,” Proc. SPIE 2416, 144-151 (1995).
[CrossRef]

Agrawal, A.

A. Agrawal, R. Chellappa, and R. Raskar, “An algebraic approach to surface reconstruction from gradient fields,” in Tenth International Conference on Computer Vision (IEEE, 2005).

Aoki, T.

S. Kawakami, T. Kawashima, Y. Inoue, Y. Homma, T. Sato, S. Ota, S. Nagashima, and T. Aoki, “Polarization imaging device utilizing photonic crystal polarizer,” J. IEICE J90-C, 17-24 (2007).

K. Takita, M. A. Muquit, T. Aoki, and T. Higuchi, “A sub-pixel correspondance search technique for computer vision application,” IEICE Trans. Fundam. E87-A, 1913-1918 (2004).

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. E86-A, 1925-1934(2003).

Araki, T.

Bao, H.

D. Xu, H. Zhang, Q. Wang, and H. Bao, “Poisson shape interpolation,” Graphical Models 68, 268-281 (2006).
[CrossRef]

Bolitho, M.

M. Kahzdan, M. Bolitho, and H. Hoppe, “Poisson surface reconstruction,” in Eurographics Symposium on Geometry Processing (2006).

Chellappa, R.

A. Agrawal, R. Chellappa, and R. Raskar, “An algebraic approach to surface reconstruction from gradient fields,” in Tenth International Conference on Computer Vision (IEEE, 2005).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1988), Chap. 19.4.

Galea, A.

Y. Inoue, T. Kawashima, M. Sasaki, A. Galea, and S. Kawakami, “Highly durable deep ultraviolet polarizers based on auto-cloned photonic crystal,” in Japan Society of Applied Physics 55th Spring Meeting (2008).

Higuchi, T.

K. Takita, M. A. Muquit, T. Aoki, and T. Higuchi, “A sub-pixel correspondance search technique for computer vision application,” IEICE Trans. Fundam. E87-A, 1913-1918 (2004).

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. E86-A, 1925-1934(2003).

Homma, Y.

S. Kawakami, T. Kawashima, Y. Inoue, Y. Homma, T. Sato, S. Ota, S. Nagashima, and T. Aoki, “Polarization imaging device utilizing photonic crystal polarizer,” J. IEICE J90-C, 17-24 (2007).

Hoppe, H.

M. Kahzdan, M. Bolitho, and H. Hoppe, “Poisson surface reconstruction,” in Eurographics Symposium on Geometry Processing (2006).

Inoue, S.

Inoue, Y.

S. Kawakami, T. Kawashima, Y. Inoue, Y. Homma, T. Sato, S. Ota, S. Nagashima, and T. Aoki, “Polarization imaging device utilizing photonic crystal polarizer,” J. IEICE J90-C, 17-24 (2007).

Y. Inoue, T. Kawashima, M. Sasaki, A. Galea, and S. Kawakami, “Highly durable deep ultraviolet polarizers based on auto-cloned photonic crystal,” in Japan Society of Applied Physics 55th Spring Meeting (2008).

Ishino, N.

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

Ishiwata, H.

H. Ishiwata, M. Itoh, and T. Yatagai, “A new analysis for extending the measurement range of the retardation-modulated differential interference contrast (RM-DIC) microscope,” Opt. Commun. 281, 1412-1423 (2008).
[CrossRef]

Itoh, M.

H. Ishiwata, M. Itoh, and T. Yatagai, “A new analysis for extending the measurement range of the retardation-modulated differential interference contrast (RM-DIC) microscope,” Opt. Commun. 281, 1412-1423 (2008).
[CrossRef]

Iwasaki, J.

Iwasaki, Y.

Kahzdan, M.

M. Kahzdan, M. Bolitho, and H. Hoppe, “Poisson surface reconstruction,” in Eurographics Symposium on Geometry Processing (2006).

Kawakami, S.

S. Kawakami, “Industrial applications of stacked photonic crystals,” Oyo Buturi 77, 508-514 (2008).

S. Kawakami, T. Kawashima, Y. Inoue, Y. Homma, T. Sato, S. Ota, S. Nagashima, and T. Aoki, “Polarization imaging device utilizing photonic crystal polarizer,” J. IEICE J90-C, 17-24 (2007).

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46, 4963-4967 (2007).
[CrossRef] [PubMed]

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three dimensional nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465 (1999).
[CrossRef]

Y. Inoue, T. Kawashima, M. Sasaki, A. Galea, and S. Kawakami, “Highly durable deep ultraviolet polarizers based on auto-cloned photonic crystal,” in Japan Society of Applied Physics 55th Spring Meeting (2008).

Kawashima, T.

S. Kawakami, T. Kawashima, Y. Inoue, Y. Homma, T. Sato, S. Ota, S. Nagashima, and T. Aoki, “Polarization imaging device utilizing photonic crystal polarizer,” J. IEICE J90-C, 17-24 (2007).

S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three dimensional nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465 (1999).
[CrossRef]

Y. Inoue, T. Kawashima, M. Sasaki, A. Galea, and S. Kawakami, “Highly durable deep ultraviolet polarizers based on auto-cloned photonic crystal,” in Japan Society of Applied Physics 55th Spring Meeting (2008).

Kobayashi, K.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. E86-A, 1925-1934(2003).

Miura, K.

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

Muquit, M. A.

K. Takita, M. A. Muquit, T. Aoki, and T. Higuchi, “A sub-pixel correspondance search technique for computer vision application,” IEICE Trans. Fundam. E87-A, 1913-1918 (2004).

Nagashima, S.

S. Kawakami, T. Kawashima, Y. Inoue, Y. Homma, T. Sato, S. Ota, S. Nagashima, and T. Aoki, “Polarization imaging device utilizing photonic crystal polarizer,” J. IEICE J90-C, 17-24 (2007).

Ohtera, Y.

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

Ooki, H.

Ota, S.

S. Kawakami, T. Kawashima, Y. Inoue, Y. Homma, T. Sato, S. Ota, S. Nagashima, and T. Aoki, “Polarization imaging device utilizing photonic crystal polarizer,” J. IEICE J90-C, 17-24 (2007).

Parulski, A. K.

A. K. Parulski, “Color filters and processing alternatives for one-chip cameras,” IEICE Trans. Electron. Devices ED32, 1381-1389 (1985).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1988), Chap. 19.4.

Raskar, R.

A. Agrawal, R. Chellappa, and R. Raskar, “An algebraic approach to surface reconstruction from gradient fields,” in Tenth International Conference on Computer Vision (IEEE, 2005).

Sasaki, M.

Y. Inoue, T. Kawashima, M. Sasaki, A. Galea, and S. Kawakami, “Highly durable deep ultraviolet polarizers based on auto-cloned photonic crystal,” in Japan Society of Applied Physics 55th Spring Meeting (2008).

Sasaki, Y.

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46, 4963-4967 (2007).
[CrossRef] [PubMed]

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. E86-A, 1925-1934(2003).

Sato, T.

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46, 4963-4967 (2007).
[CrossRef] [PubMed]

S. Kawakami, T. Kawashima, Y. Inoue, Y. Homma, T. Sato, S. Ota, S. Nagashima, and T. Aoki, “Polarization imaging device utilizing photonic crystal polarizer,” J. IEICE J90-C, 17-24 (2007).

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three dimensional nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465 (1999).
[CrossRef]

Shriback, M.

Spring, K. R.

S. Inoue and K. R. Spring, Video Microscopy, the Fundamentals, 2nd ed. (Plenum, 1997), Chap. 2.6.7.
[CrossRef]

Tadokoro, T.

Takita, K.

K. Takita, M. A. Muquit, T. Aoki, and T. Higuchi, “A sub-pixel correspondance search technique for computer vision application,” IEICE Trans. Fundam. E87-A, 1913-1918 (2004).

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. E86-A, 1925-1934(2003).

Tamamura, T.

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1988), Chap. 19.4.

Tsuru, T.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1988), Chap. 19.4.

Wang, Q.

D. Xu, H. Zhang, Q. Wang, and H. Bao, “Poisson shape interpolation,” Graphical Models 68, 268-281 (2006).
[CrossRef]

Xu, D.

D. Xu, H. Zhang, Q. Wang, and H. Bao, “Poisson shape interpolation,” Graphical Models 68, 268-281 (2006).
[CrossRef]

Yatagai, T.

H. Ishiwata, M. Itoh, and T. Yatagai, “A new analysis for extending the measurement range of the retardation-modulated differential interference contrast (RM-DIC) microscope,” Opt. Commun. 281, 1412-1423 (2008).
[CrossRef]

Zernike, F.

F. Zernike, “How I discovered phase contrast,” Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Zhang, H.

D. Xu, H. Zhang, Q. Wang, and H. Bao, “Poisson shape interpolation,” Graphical Models 68, 268-281 (2006).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three dimensional nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465 (1999).
[CrossRef]

Graphical Models (1)

D. Xu, H. Zhang, Q. Wang, and H. Bao, “Poisson shape interpolation,” Graphical Models 68, 268-281 (2006).
[CrossRef]

IEICE Trans. Electron. Devices (1)

A. K. Parulski, “Color filters and processing alternatives for one-chip cameras,” IEICE Trans. Electron. Devices ED32, 1381-1389 (1985).
[CrossRef]

IEICE Trans. Fundam. (2)

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. E86-A, 1925-1934(2003).

K. Takita, M. A. Muquit, T. Aoki, and T. Higuchi, “A sub-pixel correspondance search technique for computer vision application,” IEICE Trans. Fundam. E87-A, 1913-1918 (2004).

J. IEICE (1)

S. Kawakami, T. Kawashima, Y. Inoue, Y. Homma, T. Sato, S. Ota, S. Nagashima, and T. Aoki, “Polarization imaging device utilizing photonic crystal polarizer,” J. IEICE J90-C, 17-24 (2007).

Opt. Commun. (1)

H. Ishiwata, M. Itoh, and T. Yatagai, “A new analysis for extending the measurement range of the retardation-modulated differential interference contrast (RM-DIC) microscope,” Opt. Commun. 281, 1412-1423 (2008).
[CrossRef]

Opt. Quantum Electron. (1)

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

Oyo Buturi (1)

S. Kawakami, “Industrial applications of stacked photonic crystals,” Oyo Buturi 77, 508-514 (2008).

Proc. SPIE (2)

E. J. Adams, “Interactions between color plane and other image processing functions in electronic photography,” Proc. SPIE 2416, 144-151 (1995).
[CrossRef]

E. J. Adams, “Design of practical color filter array interpolation algorithm for digital cameras,” Proc. SPIE 3028, 117-125(1997).
[CrossRef]

Science (1)

F. Zernike, “How I discovered phase contrast,” Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Other (5)

Y. Inoue, T. Kawashima, M. Sasaki, A. Galea, and S. Kawakami, “Highly durable deep ultraviolet polarizers based on auto-cloned photonic crystal,” in Japan Society of Applied Physics 55th Spring Meeting (2008).

S. Inoue and K. R. Spring, Video Microscopy, the Fundamentals, 2nd ed. (Plenum, 1997), Chap. 2.6.7.
[CrossRef]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, 1988), Chap. 19.4.

A. Agrawal, R. Chellappa, and R. Raskar, “An algebraic approach to surface reconstruction from gradient fields,” in Tenth International Conference on Computer Vision (IEEE, 2005).

M. Kahzdan, M. Bolitho, and H. Hoppe, “Poisson surface reconstruction,” in Eurographics Symposium on Geometry Processing (2006).

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Figures (20)

Fig. 1
Fig. 1

Sample model.

Fig. 2
Fig. 2

(a) Differential interference contrast microscope structure and (b) Nomarski prism operation.

Fig. 3
Fig. 3

Each polarization beam amplitude and phase distribution is a spatially translated version of object’s distributions.

Fig. 4
Fig. 4

States of polarization modified by (a) amplitude variation and (b) phase variation.

Fig. 5
Fig. 5

DIC image computer simulation: (a) drawing of the sample with both amplitude and phase variations and (b) and (c) calculated images for two different shear directions.

Fig. 6
Fig. 6

Photonic crystal linear polarizer: (a) 3D structure, (b) SEM picture of the section, and (c) optical properties.

Fig. 7
Fig. 7

Image sensor equipped with a photonic crystal polarizer array: (a) SEM picture and (b) assembly outline.

Fig. 8
Fig. 8

DIC microscope equipped with the polarization imaging camera.

Fig. 9
Fig. 9

Polarizer array demosaicking.

Fig. 10
Fig. 10

Polarization ellipse measurement by the polarization imaging camera.

Fig. 11
Fig. 11

Comparison of surface slope measured by a mechanical profiler and the new DIC microscope; sample surface elevation is plotted in light gray.

Fig. 12
Fig. 12

(b) Height profile reconstructed from (a) a single unidirectional gradient image.

Fig. 13
Fig. 13

FFT-based Poisson solver.

Fig. 14
Fig. 14

Flooring of the distorted profile using parabolic segments: native reconstructed profile (solid curve with diamonds for floor points), fitted parabolic curve (dashed curve) and corrected profile (solid curve at the bottom).

Fig. 15
Fig. 15

Application of the method to HeLa cells: (a) gradient images, (b) Laplacian image, and (c) reconstructed phase distribution.

Fig. 16
Fig. 16

Phase profile line scan of HeLa cells (along the dashed line of Fig. 15c].

Fig. 17
Fig. 17

Example application of phase imaging with the proposed DIC observation method in transmission mode, material discrimination: (a) observed sample overview and (b) example of obtained phase distribution image.

Fig. 18
Fig. 18

Silicon pattern: (a) picture and (b) overview drawing.

Fig. 19
Fig. 19

Application of the method to patterned silicon substrate: (a) gradient images, (b) Laplacian image, and (c) reconstructed 3D shape.

Fig. 20
Fig. 20

Comparison of the reconstructed profile with a reference mechanical profiler line scan (along the dashed line of Fig. 19c].

Equations (21)

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

V 0 = [ 1 1 ] ,
V 1 = [ A e i φ A e i ( φ + ϕ ) ] .
V 2 = 1 2 [ 1 1 1 1 ] P 2   Jones matrix , V 1 = 1 2 [ A e i φ A e i ( φ + ϕ ) A e i φ + A e i ( φ + ϕ ) ] .
I = V 2 · V 2 * = ( A 2 + A 2 ) / 2 + A A sin Δ φ ,
pixel   1 :     I ( i , j ) = 1 2 [ I ( i , j 1 ) + I ( i , j + 1 ) ] ;
pixel 2 :     I ( i , j ) = 1 4 [ I ( i 1 , j 1 ) + I ( i 1 , j + 1 ) + I ( i + 1 , j 1 ) + I ( i + 1 , j + 1 ) ] ;
pixel 3 :     I ( i , j ) = 1 2 [ I ( i 1 , j ) + I ( i + 1 , j ) ] .
pixel 1 : if     | I ( i , j 1 ) I ( i , j + 1 ) | < 2 s σ     use Eq . ( 5 ) , otherwise I ( i , j ) = I ( i , j 1 ) if     | I ( i , j 1 ) I ( i , j ) | < | I ( i , j + 1 ) I ( i , j ) | or I ( i , j ) = I ( i , j + 1 )     otherwise ,
pixel 2 :     I ( i , j ) = mean ( pixels with highest standard deviation < s σ ) ;
pixel 3 : if     | I ( i 1 , j ) I ( i + 1 , j ) | < 2 s σ     use Eq . ( 7 ) , otherwise I ( i , j ) = I ( i 1 , j ) if     | I ( i 1 , j ) I ( i , j ) | < | I ( i + 1 , j ) I ( i , j ) | or I ( i , j ) = I ( i , j + 1 )     otherwise .
I 0 = A 2 , I 1 = I 0 + I 2 2 + A A sin Δ φ , I 2 = A 2 , I 3 = I 0 + I 2 2 A A sin Δ φ .
sin Δ φ = I 1 I 3 2 I 0 I 2 .
f x = PSF x * u u x , f y = PSF y * u f y ,
2 u x 2 + 2 u y 2 = g Δ * u = g .
Δ ˜ U ˜ = G ˜ ,
u = F 1 { G ˜ / Δ ˜ } .
Δ = [ 0 1 0 1 4 1 0 1 0 ] .
F { Δ } ( k , l ) = m = 0 H 1 n = 0 W 1 Δ ( m , n ) e 2 i π i m H e 2 i π j n W ,
= 2 ( cos 2 π k H + cos 2 π l W 2 ) .
u ( i , j ) = F 1 { G ˜ ( k , l ) 2 ( cos 2 π k I + cos 2 π l J 2 ) } .
w x ( i ) = | 1 / 2 [ 1 cos ( π i d ) ] if     x < d 1 if     d i H d 1 / 2 [ 1 + cos ( π i H d d ) ] if     i > H d .

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