Abstract

X-ray phase contrast imaging offers a complementary modality next to conventional absorption. To reveal internal structures of soft materials in high resolution, an X-ray phase imaging microscope has been developed by installing a Lau interferometer into a commercially available ZEISS Xradia 800 Ultra-nano computed tomography X-ray microscope. On this system, a twin phase image is once generated through measurements of interference fringes. In order to produce a quantitative X-ray phase map, the twin phase image should be treated by deconvolution. However, conventional deconvolution results showed a reduction in image quality due to noise and artifacts. Therefore, we propose and evaluate the performance of an iterative deconvolution method. The results show that the proposed deconvolution method does not affect spatial resolution, increases the signal to noise ratio compared to that of the twin phase image, and is capable of imaging complex structures.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

H. Takano, Y. Wu, J. Irwin, S. Maderych, M. Leibowitz, A. Tkachuk, A. Kumar, B. Hornberger, and A. Momose, Appl. Phys. Lett. 113, 063105 (2018).
[Crossref]

2017 (3)

H. Takano, Y. Wu, and A. Momose, Proc. SPIE 10391, 1039110(2017).
[Crossref]

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
[Crossref]

A. Momose, J. Microsc. 66, 155 (2017).
[Crossref]

2016 (1)

S. Bouchemousse, J. D. D. Bishop, and F. Viard, Sci. Rep. 6, 24875 (2016).
[Crossref]

2013 (1)

M. Holt, R. Harder, R. Winarski, and V. Rose, Annu. Rev. Mater. Res. 43, 183 (2013).
[Crossref]

2011 (2)

B. Kaulich, P. Thibault, A. Gianoncelli, and M. Kiskinova, J. Phys. Condens. Matter 23, 083002 (2011).
[Crossref]

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, Appl. Phys. Express 4, 062502 (2011).
[Crossref]

2010 (1)

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. A 82, 043822 (2010).
[Crossref]

2009 (1)

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. Lett. 103, 180801 (2009).
[Crossref]

2008 (2)

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, Appl. Phys. Express 1, 117002 (2008).
[Crossref]

Y. Suzuki and A. Takeuchi, Jpn. J. Appl. Phys. 47, 8595 (2008).
[Crossref]

2007 (1)

K. Hotta, K. Mitsuhara, H. Takahashi, K. Inaba, K. Oka, T. Gojobori, and K. Ikeo, Dev. Dyn. 236, 1790 (2007).
[Crossref]

2006 (1)

T. Koyama, T. Tsuji, K. Yoshida, H. Takano, Y. Tsusaka, and Y. Kagoshima, Jpn. J. Appl. Phys. 45, L1159 (2006).
[Crossref]

2003 (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, Jpn. J. Appl. Phys. 42, L866 (2003).
[Crossref]

1996 (1)

A. Momose, T. Takeda, Y. Itai, and K. Hirano, Nat. Med. 2, 473(1996).
[Crossref]

1995 (1)

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[Crossref]

1994 (1)

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, Optik 97, 181 (1994).

1974 (1)

1972 (1)

R. W. Gerchberg and G. O. Saxton, Optik 35, 237 (1972).

Bishop, J. D. D.

S. Bouchemousse, J. D. D. Bishop, and F. Viard, Sci. Rep. 6, 24875 (2016).
[Crossref]

Bouchemousse, S.

S. Bouchemousse, J. D. D. Bishop, and F. Viard, Sci. Rep. 6, 24875 (2016).
[Crossref]

Brangaccio, D. J.

Bruning, J. H.

Davis, T. J.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[Crossref]

Gallagher, J. E.

Gao, D.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[Crossref]

Gerchberg, R. W.

R. W. Gerchberg and G. O. Saxton, Optik 35, 237 (1972).

Gianoncelli, A.

B. Kaulich, P. Thibault, A. Gianoncelli, and M. Kiskinova, J. Phys. Condens. Matter 23, 083002 (2011).
[Crossref]

Gojobori, T.

K. Hotta, K. Mitsuhara, H. Takahashi, K. Inaba, K. Oka, T. Gojobori, and K. Ikeo, Dev. Dyn. 236, 1790 (2007).
[Crossref]

Gureyev, T. E.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[Crossref]

Guttmann, P.

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, Optik 97, 181 (1994).

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, Jpn. J. Appl. Phys. 42, L866 (2003).
[Crossref]

Harasse, S.

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, Appl. Phys. Express 4, 062502 (2011).
[Crossref]

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. A 82, 043822 (2010).
[Crossref]

Harder, R.

M. Holt, R. Harder, R. Winarski, and V. Rose, Annu. Rev. Mater. Res. 43, 183 (2013).
[Crossref]

Hattori, T.

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, Appl. Phys. Express 1, 117002 (2008).
[Crossref]

Herriott, D. R.

Hirano, K.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, Nat. Med. 2, 473(1996).
[Crossref]

Holt, M.

M. Holt, R. Harder, R. Winarski, and V. Rose, Annu. Rev. Mater. Res. 43, 183 (2013).
[Crossref]

Hornberger, B.

H. Takano, Y. Wu, J. Irwin, S. Maderych, M. Leibowitz, A. Tkachuk, A. Kumar, B. Hornberger, and A. Momose, Appl. Phys. Lett. 113, 063105 (2018).
[Crossref]

Hotta, K.

K. Hotta, K. Mitsuhara, H. Takahashi, K. Inaba, K. Oka, T. Gojobori, and K. Ikeo, Dev. Dyn. 236, 1790 (2007).
[Crossref]

Ikeo, K.

K. Hotta, K. Mitsuhara, H. Takahashi, K. Inaba, K. Oka, T. Gojobori, and K. Ikeo, Dev. Dyn. 236, 1790 (2007).
[Crossref]

Inaba, K.

K. Hotta, K. Mitsuhara, H. Takahashi, K. Inaba, K. Oka, T. Gojobori, and K. Ikeo, Dev. Dyn. 236, 1790 (2007).
[Crossref]

Irwin, J.

H. Takano, Y. Wu, J. Irwin, S. Maderych, M. Leibowitz, A. Tkachuk, A. Kumar, B. Hornberger, and A. Momose, Appl. Phys. Lett. 113, 063105 (2018).
[Crossref]

Ishikawa, T.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
[Crossref]

Itai, Y.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, Nat. Med. 2, 473(1996).
[Crossref]

Kagoshima, Y.

T. Koyama, T. Tsuji, K. Yoshida, H. Takano, Y. Tsusaka, and Y. Kagoshima, Jpn. J. Appl. Phys. 45, L1159 (2006).
[Crossref]

Kaulich, B.

B. Kaulich, P. Thibault, A. Gianoncelli, and M. Kiskinova, J. Phys. Condens. Matter 23, 083002 (2011).
[Crossref]

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, Jpn. J. Appl. Phys. 42, L866 (2003).
[Crossref]

Kiskinova, M.

B. Kaulich, P. Thibault, A. Gianoncelli, and M. Kiskinova, J. Phys. Condens. Matter 23, 083002 (2011).
[Crossref]

Kohmura, Y.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
[Crossref]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, Jpn. J. Appl. Phys. 42, L866 (2003).
[Crossref]

Koyama, T.

T. Koyama, T. Tsuji, K. Yoshida, H. Takano, Y. Tsusaka, and Y. Kagoshima, Jpn. J. Appl. Phys. 45, L1159 (2006).
[Crossref]

Kumar, A.

H. Takano, Y. Wu, J. Irwin, S. Maderych, M. Leibowitz, A. Tkachuk, A. Kumar, B. Hornberger, and A. Momose, Appl. Phys. Lett. 113, 063105 (2018).
[Crossref]

Kuwabara, H.

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, Appl. Phys. Express 4, 062502 (2011).
[Crossref]

Leibowitz, M.

H. Takano, Y. Wu, J. Irwin, S. Maderych, M. Leibowitz, A. Tkachuk, A. Kumar, B. Hornberger, and A. Momose, Appl. Phys. Lett. 113, 063105 (2018).
[Crossref]

Maderych, S.

H. Takano, Y. Wu, J. Irwin, S. Maderych, M. Leibowitz, A. Tkachuk, A. Kumar, B. Hornberger, and A. Momose, Appl. Phys. Lett. 113, 063105 (2018).
[Crossref]

Matsuyama, S.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
[Crossref]

Mitsuhara, K.

K. Hotta, K. Mitsuhara, H. Takahashi, K. Inaba, K. Oka, T. Gojobori, and K. Ikeo, Dev. Dyn. 236, 1790 (2007).
[Crossref]

Mizutani, H.

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, Appl. Phys. Express 4, 062502 (2011).
[Crossref]

Momose, A.

H. Takano, Y. Wu, J. Irwin, S. Maderych, M. Leibowitz, A. Tkachuk, A. Kumar, B. Hornberger, and A. Momose, Appl. Phys. Lett. 113, 063105 (2018).
[Crossref]

H. Takano, Y. Wu, and A. Momose, Proc. SPIE 10391, 1039110(2017).
[Crossref]

A. Momose, J. Microsc. 66, 155 (2017).
[Crossref]

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, Appl. Phys. Express 4, 062502 (2011).
[Crossref]

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. A 82, 043822 (2010).
[Crossref]

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. Lett. 103, 180801 (2009).
[Crossref]

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, Appl. Phys. Express 1, 117002 (2008).
[Crossref]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, Jpn. J. Appl. Phys. 42, L866 (2003).
[Crossref]

A. Momose, T. Takeda, Y. Itai, and K. Hirano, Nat. Med. 2, 473(1996).
[Crossref]

Niemann, B.

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, Optik 97, 181 (1994).

Oka, K.

K. Hotta, K. Mitsuhara, H. Takahashi, K. Inaba, K. Oka, T. Gojobori, and K. Ikeo, Dev. Dyn. 236, 1790 (2007).
[Crossref]

Okada, H.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
[Crossref]

Rose, V.

M. Holt, R. Harder, R. Winarski, and V. Rose, Annu. Rev. Mater. Res. 43, 183 (2013).
[Crossref]

Rosenfield, D. P.

Rudolph, D.

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, Optik 97, 181 (1994).

Saxton, G. O.

R. W. Gerchberg and G. O. Saxton, Optik 35, 237 (1972).

Schmahl, G.

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, Optik 97, 181 (1994).

Schneider, G.

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, and B. Niemann, Optik 97, 181 (1994).

Stevenson, A. W.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[Crossref]

Suzuki, Y.

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. A 82, 043822 (2010).
[Crossref]

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. Lett. 103, 180801 (2009).
[Crossref]

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, Appl. Phys. Express 1, 117002 (2008).
[Crossref]

Y. Suzuki and A. Takeuchi, Jpn. J. Appl. Phys. 47, 8595 (2008).
[Crossref]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, Jpn. J. Appl. Phys. 42, L866 (2003).
[Crossref]

Takahashi, H.

K. Hotta, K. Mitsuhara, H. Takahashi, K. Inaba, K. Oka, T. Gojobori, and K. Ikeo, Dev. Dyn. 236, 1790 (2007).
[Crossref]

Takai, K.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, Jpn. J. Appl. Phys. 42, L866 (2003).
[Crossref]

Takano, H.

H. Takano, Y. Wu, J. Irwin, S. Maderych, M. Leibowitz, A. Tkachuk, A. Kumar, B. Hornberger, and A. Momose, Appl. Phys. Lett. 113, 063105 (2018).
[Crossref]

H. Takano, Y. Wu, and A. Momose, Proc. SPIE 10391, 1039110(2017).
[Crossref]

T. Koyama, T. Tsuji, K. Yoshida, H. Takano, Y. Tsusaka, and Y. Kagoshima, Jpn. J. Appl. Phys. 45, L1159 (2006).
[Crossref]

Takeda, T.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, Nat. Med. 2, 473(1996).
[Crossref]

Takeda, Y.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. Lett. 103, 180801 (2009).
[Crossref]

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, Appl. Phys. Express 1, 117002 (2008).
[Crossref]

Takeuchi, A.

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. A 82, 043822 (2010).
[Crossref]

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. Lett. 103, 180801 (2009).
[Crossref]

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, Appl. Phys. Express 1, 117002 (2008).
[Crossref]

Y. Suzuki and A. Takeuchi, Jpn. J. Appl. Phys. 47, 8595 (2008).
[Crossref]

Thibault, P.

B. Kaulich, P. Thibault, A. Gianoncelli, and M. Kiskinova, J. Phys. Condens. Matter 23, 083002 (2011).
[Crossref]

Tkachuk, A.

H. Takano, Y. Wu, J. Irwin, S. Maderych, M. Leibowitz, A. Tkachuk, A. Kumar, B. Hornberger, and A. Momose, Appl. Phys. Lett. 113, 063105 (2018).
[Crossref]

Tsuji, T.

T. Koyama, T. Tsuji, K. Yoshida, H. Takano, Y. Tsusaka, and Y. Kagoshima, Jpn. J. Appl. Phys. 45, L1159 (2006).
[Crossref]

Tsusaka, Y.

T. Koyama, T. Tsuji, K. Yoshida, H. Takano, Y. Tsusaka, and Y. Kagoshima, Jpn. J. Appl. Phys. 45, L1159 (2006).
[Crossref]

Viard, F.

S. Bouchemousse, J. D. D. Bishop, and F. Viard, Sci. Rep. 6, 24875 (2016).
[Crossref]

White, A. D.

Wilkins, S. W.

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, Nature 373, 595 (1995).
[Crossref]

Winarski, R.

M. Holt, R. Harder, R. Winarski, and V. Rose, Annu. Rev. Mater. Res. 43, 183 (2013).
[Crossref]

Wu, Y.

H. Takano, Y. Wu, J. Irwin, S. Maderych, M. Leibowitz, A. Tkachuk, A. Kumar, B. Hornberger, and A. Momose, Appl. Phys. Lett. 113, 063105 (2018).
[Crossref]

H. Takano, Y. Wu, and A. Momose, Proc. SPIE 10391, 1039110(2017).
[Crossref]

Yabashi, M.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
[Crossref]

Yamada, J.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
[Crossref]

Yamauchi, K.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
[Crossref]

Yashiro, W.

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, Appl. Phys. Express 4, 062502 (2011).
[Crossref]

W. Yashiro, S. Harasse, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. A 82, 043822 (2010).
[Crossref]

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, Phys. Rev. Lett. 103, 180801 (2009).
[Crossref]

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, Appl. Phys. Express 1, 117002 (2008).
[Crossref]

Yasuda, S.

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
[Crossref]

Yoshida, K.

T. Koyama, T. Tsuji, K. Yoshida, H. Takano, Y. Tsusaka, and Y. Kagoshima, Jpn. J. Appl. Phys. 45, L1159 (2006).
[Crossref]

Annu. Rev. Mater. Res. (1)

M. Holt, R. Harder, R. Winarski, and V. Rose, Annu. Rev. Mater. Res. 43, 183 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Express (2)

Y. Takeda, W. Yashiro, T. Hattori, A. Takeuchi, Y. Suzuki, and A. Momose, Appl. Phys. Express 1, 117002 (2008).
[Crossref]

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, Appl. Phys. Express 4, 062502 (2011).
[Crossref]

Appl. Phys. Lett. (1)

H. Takano, Y. Wu, J. Irwin, S. Maderych, M. Leibowitz, A. Tkachuk, A. Kumar, B. Hornberger, and A. Momose, Appl. Phys. Lett. 113, 063105 (2018).
[Crossref]

Dev. Dyn. (1)

K. Hotta, K. Mitsuhara, H. Takahashi, K. Inaba, K. Oka, T. Gojobori, and K. Ikeo, Dev. Dyn. 236, 1790 (2007).
[Crossref]

J. Microsc. (1)

A. Momose, J. Microsc. 66, 155 (2017).
[Crossref]

J. Phys. Condens. Matter (1)

B. Kaulich, P. Thibault, A. Gianoncelli, and M. Kiskinova, J. Phys. Condens. Matter 23, 083002 (2011).
[Crossref]

Jpn. J. Appl. Phys. (3)

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[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Schematic of optical arrangement of the X-ray phase microscope.
Fig. 2.
Fig. 2. X-ray microscope images of a resolution test pattern where the smallest features are 50 nm in size; (a) absorption contrast image, (b) twin phase image, (c) phase map calculated by simple deconvolution. Scale bar: 10 μm.
Fig. 3.
Fig. 3. Flow of deconvolution method with iterative calculation.
Fig. 4.
Fig. 4. Images of a polystyrene sphere of 3 μm in diameter. (a) Twin phase image by a 29-step fringe scanning measurement (each exposure time: 2 min), (b) phase map obtained by the simple deconvolution, (c) and (d) phase map obtained by the iterative deconvolution with iteration number of 1 and 20. Overlaid plots represent an averaged phase profile along each yellow line of 32 pixel width in a blank area. Scale bar: 2 μm. The gray scale for the images is 0.6+0.6 in radian.
Fig. 5.
Fig. 5. Plot of SNRs against the iteration number. The signals are extracted from the center of the sphere. The noise is the standard deviation in an empty area near the sphere. The extraction area is a circular area of 32 pixels (0.5 μm) in diameter.
Fig. 6.
Fig. 6. Comparison of power spectra between the twin phase image (in Fig. 3) (red lines) and the calculated phase map of the resolution test chart (g20 in Fig. 3) (black lines). The spectra were obtained by the circumference average of two-dimensional (2D) FFT of images. (a) Raw power spectra. (b) Power spectra subtracting the power at the Nyquist frequency.
Fig. 7.
Fig. 7. (a) Twin phase image, (b) the phase map by simple deconvolution, and (c) the phase map by the proposed iterative algorithm with n=20 of a larval Ciona robusta obtained by a 30-step fringe scanning measurement (each exposure time: 2 min). The gray scale of (a) and (b) are 2.6+2.6 and 0.2+2.6 in radian, respectively. Scale bar: 10 μm.

Tables (1)

Tables Icon

Table 1. Phase Shift Values and Those Standard Deviations (Phase Shift/Standard Deviation, in Radian) Extracted from the Center of the Sphere and Near the Center of the FOVa

Equations (3)

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

ψ(x,y)=m=0±amδ(xmp2,y),
m=0±|am|=1.
FFT{g0(x,y)}=FFT{t0(x,y)}FFT{ψ(x,y)},