Abstract

Image simulation remains under-exploited for the most widely used biological phase microscopy methods, because of difficulties in simulating partially coherent illumination. We describe an open-source toolbox, microlith (https://code.google.com/p/microlith), which accurately predicts three-dimensional images of a thin specimen observed with any partially coherent imaging system, as well as images of coherently illuminated and self-luminous incoherent specimens. Its accuracy is demonstrated by comparing simulated and experimental bright-field and dark-field images of well-characterized amplitude and phase targets, respectively. The comparison provides new insights about the sensitivity of the dark-field microscope to mass distributions in isolated or periodic specimens at the length-scale of 10nm. Based on predictions using microlith, we propose a novel approach for detecting nanoscale structural changes in a beating axoneme using a dark-field microscope.

© 2014 Optical Society of America

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2013

S. B. Mehta, M. Shribak, and R. Oldenbourg, “Polarized light imaging of birefringence and diattenuation at high resolution and high sensitivity,” J. Opt.15(9), 094007 (2013).
[CrossRef] [PubMed]

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc.249(1), 13–25 (2013).
[CrossRef] [PubMed]

H. Su, Z. Yin, S. Huh, and T. Kanade, “Cell segmentation in phase contrast microscopy images via semi-supervised classification over optics-related features,” Med. Image Anal.17(7), 746–765 (2013).
[CrossRef] [PubMed]

C. J. R. Sheppard, S. B. Mehta, and R. Heintzmann, “Superresolution by image scanning microscopy using pixel reassignment,” Opt. Lett.38(15), 2889–2892 (2013).
[CrossRef] [PubMed]

2012

2010

2009

2007

C. B. Lindemann and D. R. Mitchell, “Evidence for axonemal distortion during the flagellar beat of Chlamydomonas,” Cell Motil. Cytoskeleton64(8), 580–589 (2007).
[CrossRef] [PubMed]

2006

D. Nicastro, C. Schwartz, J. Pierson, R. Gaudette, M. E. Porter, and J. R. McIntosh, “The molecular architecture of axonemes revealed by cryoelectron tomography,” Science313(5789), 944–948 (2006).
[CrossRef] [PubMed]

H. Ishiwata, M. Itoh, and T. Yatagai, “A new method of three-dimensional measurement by differential interference contrast microscope,” Opt. Commun.260(1), 117–126 (2006).
[CrossRef]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
[CrossRef]

2004

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc.214(1), 7–12 (2004).
[CrossRef] [PubMed]

H. M. Sakakibara, Y. Kunioka, T. Yamada, and S. Kamimura, “Diameter oscillation of axonemes in sea-urchin sperm flagella,” Biophys. J.86(1), 346–352 (2004).
[CrossRef] [PubMed]

2001

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

1998

R. Oldenbourg, E. D. Salmon, and P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J.74(1), 645–654 (1998).
[CrossRef] [PubMed]

1995

T. E. Gureyev, A. Roberts, and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation: matrix solution with use of Zernike polynomials,” J. Opt. Soc. Am. A.12(9), 1932–1942 (1995).
[CrossRef]

1994

Y. C. Pati and T. Kailath, “Phase-shifting masks for microlithography: Automated design and mask requirements,” J. Opt. Soc. Am.11(9), 2438–2452 (1994).
[CrossRef]

K. Wakabayashi, Y. Sugimoto, H. Tanaka, Y. Ueno, Y. Takezawa, and Y. Amemiya, “X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction,” Biophys. J.67(6), 2422–2435 (1994).
[CrossRef] [PubMed]

1981

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38(1), 3–6 (1981).

1975

H. Sato, G. W. Ellis, and S. Inoué, “Microtubular origin of mitotic spindle form birefringence. Demonstration of the applicability of Wiener’s equation,” J. Cell Biol.67(3), 501–517 (1975).
[CrossRef] [PubMed]

1966

1964

1953

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. Lond.217(1130), 408–432 (1953).
[CrossRef]

1938

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica5(8), 785–795 (1938).
[CrossRef]

1893

A. Köhler, “Ein neues Beleuchtungsverfahren für mikrophotographische Zwecke,” Z. Für Wiss. Mikrosk. Für Mikrosk. Tech.10, 433–440 (1893).

Adam, K.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Aguet, F.

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc.249(1), 13–25 (2013).
[CrossRef] [PubMed]

Amemiya, Y.

K. Wakabayashi, Y. Sugimoto, H. Tanaka, Y. Ueno, Y. Takezawa, and Y. Amemiya, “X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction,” Biophys. J.67(6), 2422–2435 (1994).
[CrossRef] [PubMed]

Arnison, M. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc.214(1), 7–12 (2004).
[CrossRef] [PubMed]

Bunk, O.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
[CrossRef]

Cheng, M.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Cogswell, C. J.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc.214(1), 7–12 (2004).
[CrossRef] [PubMed]

Croffie, E. H.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

David, C.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
[CrossRef]

Davis, B. J.

Deng, Y.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Ellis, G. W.

H. Sato, G. W. Ellis, and S. Inoué, “Microtubular origin of mitotic spindle form birefringence. Demonstration of the applicability of Wiener’s equation,” J. Cell Biol.67(3), 501–517 (1975).
[CrossRef] [PubMed]

Gaudette, R.

D. Nicastro, C. Schwartz, J. Pierson, R. Gaudette, M. E. Porter, and J. R. McIntosh, “The molecular architecture of axonemes revealed by cryoelectron tomography,” Science313(5789), 944–948 (2006).
[CrossRef] [PubMed]

Gennari, F. E.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Gureyev, T. E.

T. E. Gureyev, A. Roberts, and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation: matrix solution with use of Zernike polynomials,” J. Opt. Soc. Am. A.12(9), 1932–1942 (1995).
[CrossRef]

Heintzmann, R.

Hopkins, H. H.

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. Lond.217(1130), 408–432 (1953).
[CrossRef]

Horie, T.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Huh, S.

H. Su, Z. Yin, S. Huh, and T. Kanade, “Cell segmentation in phase contrast microscopy images via semi-supervised classification over optics-related features,” Med. Image Anal.17(7), 746–765 (2013).
[CrossRef] [PubMed]

Inoué, S.

H. Sato, G. W. Ellis, and S. Inoué, “Microtubular origin of mitotic spindle form birefringence. Demonstration of the applicability of Wiener’s equation,” J. Cell Biol.67(3), 501–517 (1975).
[CrossRef] [PubMed]

Ishiwata, H.

H. Ishiwata, M. Itoh, and T. Yatagai, “A new method of three-dimensional measurement by differential interference contrast microscope,” Opt. Commun.260(1), 117–126 (2006).
[CrossRef]

Itoh, M.

H. Ishiwata, M. Itoh, and T. Yatagai, “A new method of three-dimensional measurement by differential interference contrast microscope,” Opt. Commun.260(1), 117–126 (2006).
[CrossRef]

Kailath, T.

Y. C. Pati and T. Kailath, “Phase-shifting masks for microlithography: Automated design and mask requirements,” J. Opt. Soc. Am.11(9), 2438–2452 (1994).
[CrossRef]

Kamimura, S.

H. M. Sakakibara, Y. Kunioka, T. Yamada, and S. Kamimura, “Diameter oscillation of axonemes in sea-urchin sperm flagella,” Biophys. J.86(1), 346–352 (2004).
[CrossRef] [PubMed]

Kanade, T.

H. Su, Z. Yin, S. Huh, and T. Kanade, “Cell segmentation in phase contrast microscopy images via semi-supervised classification over optics-related features,” Med. Image Anal.17(7), 746–765 (2013).
[CrossRef] [PubMed]

Kirshner, H.

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc.249(1), 13–25 (2013).
[CrossRef] [PubMed]

Köhler, A.

A. Köhler, “Ein neues Beleuchtungsverfahren für mikrophotographische Zwecke,” Z. Für Wiss. Mikrosk. Für Mikrosk. Tech.10, 433–440 (1893).

Kunioka, Y.

H. M. Sakakibara, Y. Kunioka, T. Yamada, and S. Kamimura, “Diameter oscillation of axonemes in sea-urchin sperm flagella,” Biophys. J.86(1), 346–352 (2004).
[CrossRef] [PubMed]

Larkin, K. G.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc.214(1), 7–12 (2004).
[CrossRef] [PubMed]

Lee, S. I.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Lindemann, C. B.

C. B. Lindemann and D. R. Mitchell, “Evidence for axonemal distortion during the flagellar beat of Chlamydomonas,” Cell Motil. Cytoskeleton64(8), 580–589 (2007).
[CrossRef] [PubMed]

McCutchen, C. W.

McIntosh, J. R.

D. Nicastro, C. Schwartz, J. Pierson, R. Gaudette, M. E. Porter, and J. R. McIntosh, “The molecular architecture of axonemes revealed by cryoelectron tomography,” Science313(5789), 944–948 (2006).
[CrossRef] [PubMed]

Mehta, S. B.

Mitchell, D. R.

C. B. Lindemann and D. R. Mitchell, “Evidence for axonemal distortion during the flagellar beat of Chlamydomonas,” Cell Motil. Cytoskeleton64(8), 580–589 (2007).
[CrossRef] [PubMed]

Neureuther, A. R.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Ng, K. C.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Nicastro, D.

D. Nicastro, C. Schwartz, J. Pierson, R. Gaudette, M. E. Porter, and J. R. McIntosh, “The molecular architecture of axonemes revealed by cryoelectron tomography,” Science313(5789), 944–948 (2006).
[CrossRef] [PubMed]

Nugent, K. A.

T. E. Gureyev, A. Roberts, and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation: matrix solution with use of Zernike polynomials,” J. Opt. Soc. Am. A.12(9), 1932–1942 (1995).
[CrossRef]

Oldenbourg, R.

S. B. Mehta, M. Shribak, and R. Oldenbourg, “Polarized light imaging of birefringence and diattenuation at high resolution and high sensitivity,” J. Opt.15(9), 094007 (2013).
[CrossRef] [PubMed]

R. Oldenbourg, E. D. Salmon, and P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J.74(1), 645–654 (1998).
[CrossRef] [PubMed]

Orimoto, T.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Pati, Y. C.

Y. C. Pati and T. Kailath, “Phase-shifting masks for microlithography: Automated design and mask requirements,” J. Opt. Soc. Am.11(9), 2438–2452 (1994).
[CrossRef]

Pfeiffer, F.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
[CrossRef]

Pierson, J.

D. Nicastro, C. Schwartz, J. Pierson, R. Gaudette, M. E. Porter, and J. R. McIntosh, “The molecular architecture of axonemes revealed by cryoelectron tomography,” Science313(5789), 944–948 (2006).
[CrossRef] [PubMed]

Pistor, T. V.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Pittenger, J.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Porter, M. E.

D. Nicastro, C. Schwartz, J. Pierson, R. Gaudette, M. E. Porter, and J. R. McIntosh, “The molecular architecture of axonemes revealed by cryoelectron tomography,” Science313(5789), 944–948 (2006).
[CrossRef] [PubMed]

Roberts, A.

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[CrossRef]

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S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

Sage, D.

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc.249(1), 13–25 (2013).
[CrossRef] [PubMed]

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H. M. Sakakibara, Y. Kunioka, T. Yamada, and S. Kamimura, “Diameter oscillation of axonemes in sea-urchin sperm flagella,” Biophys. J.86(1), 346–352 (2004).
[CrossRef] [PubMed]

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R. Oldenbourg, E. D. Salmon, and P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J.74(1), 645–654 (1998).
[CrossRef] [PubMed]

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H. Sato, G. W. Ellis, and S. Inoué, “Microtubular origin of mitotic spindle form birefringence. Demonstration of the applicability of Wiener’s equation,” J. Cell Biol.67(3), 501–517 (1975).
[CrossRef] [PubMed]

Schoonover, R. W.

Schwartz, C.

D. Nicastro, C. Schwartz, J. Pierson, R. Gaudette, M. E. Porter, and J. R. McIntosh, “The molecular architecture of axonemes revealed by cryoelectron tomography,” Science313(5789), 944–948 (2006).
[CrossRef] [PubMed]

Sheppard, C. J.

Sheppard, C. J. R.

Shribak, M.

S. B. Mehta, M. Shribak, and R. Oldenbourg, “Polarized light imaging of birefringence and diattenuation at high resolution and high sensitivity,” J. Opt.15(9), 094007 (2013).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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H. Su, Z. Yin, S. Huh, and T. Kanade, “Cell segmentation in phase contrast microscopy images via semi-supervised classification over optics-related features,” Med. Image Anal.17(7), 746–765 (2013).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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K. Wakabayashi, Y. Sugimoto, H. Tanaka, Y. Ueno, Y. Takezawa, and Y. Amemiya, “X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction,” Biophys. J.67(6), 2422–2435 (1994).
[CrossRef] [PubMed]

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K. Wakabayashi, Y. Sugimoto, H. Tanaka, Y. Ueno, Y. Takezawa, and Y. Amemiya, “X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction,” Biophys. J.67(6), 2422–2435 (1994).
[CrossRef] [PubMed]

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R. Oldenbourg, E. D. Salmon, and P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J.74(1), 645–654 (1998).
[CrossRef] [PubMed]

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K. Wakabayashi, Y. Sugimoto, H. Tanaka, Y. Ueno, Y. Takezawa, and Y. Amemiya, “X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction,” Biophys. J.67(6), 2422–2435 (1994).
[CrossRef] [PubMed]

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H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc.249(1), 13–25 (2013).
[CrossRef] [PubMed]

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K. Wakabayashi, Y. Sugimoto, H. Tanaka, Y. Ueno, Y. Takezawa, and Y. Amemiya, “X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction,” Biophys. J.67(6), 2422–2435 (1994).
[CrossRef] [PubMed]

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F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
[CrossRef]

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S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
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S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

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H. M. Sakakibara, Y. Kunioka, T. Yamada, and S. Kamimura, “Diameter oscillation of axonemes in sea-urchin sperm flagella,” Biophys. J.86(1), 346–352 (2004).
[CrossRef] [PubMed]

Yamazoe, K.

Yatagai, T.

H. Ishiwata, M. Itoh, and T. Yatagai, “A new method of three-dimensional measurement by differential interference contrast microscope,” Opt. Commun.260(1), 117–126 (2006).
[CrossRef]

Yin, Z.

H. Su, Z. Yin, S. Huh, and T. Kanade, “Cell segmentation in phase contrast microscopy images via semi-supervised classification over optics-related features,” Med. Image Anal.17(7), 746–765 (2013).
[CrossRef] [PubMed]

Yuan, L.

S. I. Lee, K. C. Ng, T. Orimoto, J. Pittenger, T. Horie, K. Adam, M. Cheng, E. H. Croffie, Y. Deng, F. E. Gennari, T. V. Pistor, G. Robins, M. V. Williamson, B. Wu, L. Yuan, and A. R. Neureuther, “LAVA web-based remote simulation: enhancements for education and technology innovation,” Proc. SPIE4346, 1500–1506 (2001).
[CrossRef]

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F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica5(8), 785–795 (1938).
[CrossRef]

Biophys. J.

R. Oldenbourg, E. D. Salmon, and P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J.74(1), 645–654 (1998).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

H. M. Sakakibara, Y. Kunioka, T. Yamada, and S. Kamimura, “Diameter oscillation of axonemes in sea-urchin sperm flagella,” Biophys. J.86(1), 346–352 (2004).
[CrossRef] [PubMed]

Cell Motil. Cytoskeleton

C. B. Lindemann and D. R. Mitchell, “Evidence for axonemal distortion during the flagellar beat of Chlamydomonas,” Cell Motil. Cytoskeleton64(8), 580–589 (2007).
[CrossRef] [PubMed]

J. Cell Biol.

H. Sato, G. W. Ellis, and S. Inoué, “Microtubular origin of mitotic spindle form birefringence. Demonstration of the applicability of Wiener’s equation,” J. Cell Biol.67(3), 501–517 (1975).
[CrossRef] [PubMed]

J. Microsc.

H. Kirshner, F. Aguet, D. Sage, and M. Unser, “3-D PSF fitting for fluorescence microscopy: implementation and localization application,” J. Microsc.249(1), 13–25 (2013).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

J. Opt.

S. B. Mehta, M. Shribak, and R. Oldenbourg, “Polarized light imaging of birefringence and diattenuation at high resolution and high sensitivity,” J. Opt.15(9), 094007 (2013).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

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[CrossRef]

Med. Image Anal.

H. Su, Z. Yin, S. Huh, and T. Kanade, “Cell segmentation in phase contrast microscopy images via semi-supervised classification over optics-related features,” Med. Image Anal.17(7), 746–765 (2013).
[CrossRef] [PubMed]

Nat. Phys.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
[CrossRef]

Opt. Commun

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38(1), 3–6 (1981).

Opt. Commun.

H. Ishiwata, M. Itoh, and T. Yatagai, “A new method of three-dimensional measurement by differential interference contrast microscope,” Opt. Commun.260(1), 117–126 (2006).
[CrossRef]

Opt. Express

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Supplementary Material (2)

» Media 1: MOV (311 KB)     
» Media 2: MOV (504 KB)     

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Figures (8)

Fig. 1
Fig. 1

(a) Experimental and (b) simulated image of the MBL/NNF amplitude target using a bright field microscope. The scale-bar in top-right corner is 5um long. (c) intensity profiles of the experimental and simulated images taken along a 20 µm long line shown in blue in images (a) and (b).The simulated image faithfully reproduces the varying resolution and contrast found in the experimental image.

Fig. 2
Fig. 2

Images of the Siemens star of the MBL/NNF phase target recorded with a dark-field microscope: (a) experimental image of the complete star pattern and (b) zoomed central region of (a). (c) zoomed center of a simulated pattern with equal sized wedges (black wedges represent etched silica layer, white wedges represent remaining silica layer). (d) simulated image of (c). (e,f) are images corresponding to (c,d), but assuming over etching by 4 nm. Scale bars: (a) 5μm, the central disk at the center in all images has a diameter of 1.2μm.

Fig. 3
Fig. 3

Mutual coherence due to dark-field source of NA 1.1-1.2 with center wavelength 0.546µm : (a) In the specimen plηane, (b) along the optical axis. 3D coherence is function of distance (Δx,Δy,Δz) from point (x,y) on the specimen. Red contour shows the distances from any point in the specimen within which the coherence is greater than 90%.

Fig. 4
Fig. 4

Dark-field image of a sea urchin sperm and arrangement of microtubules in its cross-section, which are key components of axoneme. Diameter of axoneme is ~200nm. The image was acquired with sCMOS camera using the same configuration as in Fig. 2.

Fig. 5
Fig. 5

A frame from movie Media 1 shows simulated dark-field intensity as a function of change in the axoneme cross-section: (a) pixel-map of singlet and doublet microtubules, black represents solvent, white tubulin mass. (b) optical path difference OPD(x) in radians and simulated dark-field intensity profile for a microscope configuration specified in Fig. 2. (c) Normalized mean intensity as a function of radius of the axoneme cross-section in the beat plane. Different frames of the movie show above plots as the axoneme’s radius in beat plane increases, but total area inscribed by doublet microtubules is preserved.

Fig. 6
Fig. 6

A frame from Media 2 showing (a) simulated dark-field image of a cylinder bent in the shape of logarithmic spiral with gradually increasing radius of curvature, (b) intensity distribution perpendicular to the cylinder as a function of radius of curvature, and (c) mean intensity as a function of radius of curvature. The simulation is repeated at different focal depths. The images are simulated assuming the same optical setup as in Fig. 2.

Fig. 7
Fig. 7

Analysis of intensity pattern observed in Fig. 2: (a) Illustration (drawn to scale) shows the angles of diffraction orders generated by the periodic phase grating at the radius of 4μm due to the steepest illuminating ray. (b) shows the range of angles occupied by the diffraction orders generated by the periodic grating at radii (r) ranging from 0.6 − 5μm. Note that sin θ N =sin θ 0 Nλ(36/2πr),where,N=1,2,3.

Fig. 8
Fig. 8

Single and double line features from MBL/NNF phase target imaged with dark-field microscope (a) experimental image, (b) simulated thickness profile (magenta) and simulated & experimental intensities. Markers show the total scattered intensity around line features. The number etched in (a) on top of each feature is twice the line width or line separation in microns.

Tables (1)

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Table 1 Speed-up achieved by parallelized implementation of sum over source algorithm

Equations (5)

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I(x,y)=S(ξ,η) | [T( f x ξ, f y η)P( f x , f y )] | 2 dξdη,
I(x,y,z)= i=1 Ns S i | [T( f x ξ i , f y η i )P( f x , f y ,z)] | 2
ϵ(x,y,z)= ϵ w +f(x,y,z)( ϵ p ϵ w ),
OPD(x,y)= Z c 2π λ [n(x,y,z) n w ] dz= Z c 2π λ [ ϵ(x,y,z) ϵ w ] dz
t(x,y)=exp[iOPD(x,y)].

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