Abstract

Soft X-ray tomography (SXT) is becoming a powerful imaging technique to analyze eukaryotic whole cells close to their native state. Central to the analysis of the quality of SXT 3D reconstruction is the estimation of the spatial resolution and Depth of Field of the X-ray microscope. In turn, the characterization of the Modulation Transfer Function (MTF) of the optical system is key to calculate both parameters. Consequently, in this work we introduce a fully automated technique to accurately estimate the transfer function of such an optical system. Our proposal is based on the preprocessing of the experimental images to obtain an estimate of the input pattern, followed by the analysis in Fourier space of multiple orders of a Siemens Star test sample, extending in this way its measured frequency range.

© 2015 Optical Society of America

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  1. R. Burge, X.-C. Yuan, G. Morrison, P. Charalambous, M. Browne, and Z. An, “Incoherent imaging with the soft X-ray microscope,” Ultramicroscopy 83, 75–92 (2000).
    [Crossref] [PubMed]
  2. R. R. Meyer and A. I. Kirkland, “Characterisation of the signal and noise transfer of CCD cameras for electron detection,” Microsc. Res. Techniq. 49, 269–280 (2000).
    [Crossref]
  3. H. Takano, S. Konishi, T. Koyama, Y. Tsusaka, S. Ichimaru, T. Ohchi, H. Takenaka, and Y. Kagoshima, “Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture,” J. Synchrotron Radiat. 21, 446–448 (2014).
    [Crossref] [PubMed]
  4. S. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
    [Crossref]
  5. C. D. Claxton and R. C. Staunton, “Measurement of the point-spread function of a noisy imaging system,” J. Opt. Soc. Am. A 25, 159–170 (2008).
    [Crossref]
  6. L. Chen, J. McGinty, H. B. Taylor, L. Bugeon, J. R. Lamb, M. J. Dallman, and P. M. W. French, “Incorporation of an experimentally determined MTF for spatial frequency filtering and deconvolution during optical projection tomography reconstruction,” Opt. Express 20, 7323–7337 (2012).
    [Crossref] [PubMed]
  7. W. V. D. Broek, S. V. Aert, and D. V. Dyck, “Fully automated measurement of the modulation transfer function of charge-coupled devices above the Nyquist frequency,” Microsc. Microanal. 18, 336–342 (2012).
    [Crossref] [PubMed]
  8. R. S. Ruskin, Z. Yu, and N. Grigorieff, “Quantitative characterization of electron detectors for transmission electron microscopy,” J. Struct. Biol. 184, 385–393 (2013).
    [Crossref] [PubMed]
  9. P. a. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226, 175–181 (2007).
    [Crossref] [PubMed]
  10. M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
    [Crossref]
  11. S. Rehbein, P. Guttmann, S. Werner, and G. Schneider, “Characterization of the resolving power and contrast transfer function of a transmission X-ray microscope with partially coherent illumination,” Opt. Express 20, 1–3 (2012).
    [Crossref]
  12. D. B. Carlson, J. Gelb, V. Palshin, and J. E. Evans, “Laboratory-based cryogenic soft X-ray tomography with correlative cryo-light and electron microscopy,” Microsc. Microanal. 19, 22–29 (2013).
    [Crossref] [PubMed]
  13. R. Reulke, S. Becker, N. Haala, and U. Tempelmann, “Determination and improvement of spatial resolution of the CCD-line-scanner system ADS40,” ISPRS J. Photogramm. Remote Sens. 60, 81–90 (2006).
    [Crossref]
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  15. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999), 7.
    [Crossref]
  16. C. Chang and T. Nakamura, “Partially coherent image formation theory for X-ray microscopy,” in “Microscopy: Science, Technology, Applications and Education,”, A. Mendez-Vilas and J. Diaz, eds. (Formatex Research Center, 2010), 3, pp. 1897–1904, 4.
  17. J. W. Goodman, Statistical Optics (Wiley, 2000).
  18. E. Pereiro, J. Nicolás, S. Ferrer, and M. R. Howells, “A soft X-ray beamline for transmission X-ray microscopy at ALBA,” J. Synchrotron Radiat. 16, 505–512 (2009).
    [Crossref] [PubMed]

2014 (1)

H. Takano, S. Konishi, T. Koyama, Y. Tsusaka, S. Ichimaru, T. Ohchi, H. Takenaka, and Y. Kagoshima, “Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture,” J. Synchrotron Radiat. 21, 446–448 (2014).
[Crossref] [PubMed]

2013 (2)

R. S. Ruskin, Z. Yu, and N. Grigorieff, “Quantitative characterization of electron detectors for transmission electron microscopy,” J. Struct. Biol. 184, 385–393 (2013).
[Crossref] [PubMed]

D. B. Carlson, J. Gelb, V. Palshin, and J. E. Evans, “Laboratory-based cryogenic soft X-ray tomography with correlative cryo-light and electron microscopy,” Microsc. Microanal. 19, 22–29 (2013).
[Crossref] [PubMed]

2012 (3)

2009 (1)

E. Pereiro, J. Nicolás, S. Ferrer, and M. R. Howells, “A soft X-ray beamline for transmission X-ray microscopy at ALBA,” J. Synchrotron Radiat. 16, 505–512 (2009).
[Crossref] [PubMed]

2008 (2)

C. D. Claxton and R. C. Staunton, “Measurement of the point-spread function of a noisy imaging system,” J. Opt. Soc. Am. A 25, 159–170 (2008).
[Crossref]

M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
[Crossref]

2007 (1)

P. a. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226, 175–181 (2007).
[Crossref] [PubMed]

2006 (1)

R. Reulke, S. Becker, N. Haala, and U. Tempelmann, “Determination and improvement of spatial resolution of the CCD-line-scanner system ADS40,” ISPRS J. Photogramm. Remote Sens. 60, 81–90 (2006).
[Crossref]

2000 (2)

R. Burge, X.-C. Yuan, G. Morrison, P. Charalambous, M. Browne, and Z. An, “Incoherent imaging with the soft X-ray microscope,” Ultramicroscopy 83, 75–92 (2000).
[Crossref] [PubMed]

R. R. Meyer and A. I. Kirkland, “Characterisation of the signal and noise transfer of CCD cameras for electron detection,” Microsc. Res. Techniq. 49, 269–280 (2000).
[Crossref]

1991 (1)

S. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[Crossref]

Aert, S. V.

W. V. D. Broek, S. V. Aert, and D. V. Dyck, “Fully automated measurement of the modulation transfer function of charge-coupled devices above the Nyquist frequency,” Microsc. Microanal. 18, 336–342 (2012).
[Crossref] [PubMed]

An, Z.

R. Burge, X.-C. Yuan, G. Morrison, P. Charalambous, M. Browne, and Z. An, “Incoherent imaging with the soft X-ray microscope,” Ultramicroscopy 83, 75–92 (2000).
[Crossref] [PubMed]

Becker, S.

R. Reulke, S. Becker, N. Haala, and U. Tempelmann, “Determination and improvement of spatial resolution of the CCD-line-scanner system ADS40,” ISPRS J. Photogramm. Remote Sens. 60, 81–90 (2006).
[Crossref]

Bertilson, M. C.

M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999), 7.
[Crossref]

Broek, W. V. D.

W. V. D. Broek, S. V. Aert, and D. V. Dyck, “Fully automated measurement of the modulation transfer function of charge-coupled devices above the Nyquist frequency,” Microsc. Microanal. 18, 336–342 (2012).
[Crossref] [PubMed]

Browne, M.

R. Burge, X.-C. Yuan, G. Morrison, P. Charalambous, M. Browne, and Z. An, “Incoherent imaging with the soft X-ray microscope,” Ultramicroscopy 83, 75–92 (2000).
[Crossref] [PubMed]

Bugeon, L.

Burge, R.

R. Burge, X.-C. Yuan, G. Morrison, P. Charalambous, M. Browne, and Z. An, “Incoherent imaging with the soft X-ray microscope,” Ultramicroscopy 83, 75–92 (2000).
[Crossref] [PubMed]

Carlson, D. B.

D. B. Carlson, J. Gelb, V. Palshin, and J. E. Evans, “Laboratory-based cryogenic soft X-ray tomography with correlative cryo-light and electron microscopy,” Microsc. Microanal. 19, 22–29 (2013).
[Crossref] [PubMed]

Chang, C.

C. Chang and T. Nakamura, “Partially coherent image formation theory for X-ray microscopy,” in “Microscopy: Science, Technology, Applications and Education,”, A. Mendez-Vilas and J. Diaz, eds. (Formatex Research Center, 2010), 3, pp. 1897–1904, 4.

Charalambous, P.

R. Burge, X.-C. Yuan, G. Morrison, P. Charalambous, M. Browne, and Z. An, “Incoherent imaging with the soft X-ray microscope,” Ultramicroscopy 83, 75–92 (2000).
[Crossref] [PubMed]

Chen, L.

Claxton, C. D.

Dallman, M. J.

Dyck, D. V.

W. V. D. Broek, S. V. Aert, and D. V. Dyck, “Fully automated measurement of the modulation transfer function of charge-coupled devices above the Nyquist frequency,” Microsc. Microanal. 18, 336–342 (2012).
[Crossref] [PubMed]

Evans, J. E.

D. B. Carlson, J. Gelb, V. Palshin, and J. E. Evans, “Laboratory-based cryogenic soft X-ray tomography with correlative cryo-light and electron microscopy,” Microsc. Microanal. 19, 22–29 (2013).
[Crossref] [PubMed]

Ferrer, S.

E. Pereiro, J. Nicolás, S. Ferrer, and M. R. Howells, “A soft X-ray beamline for transmission X-ray microscopy at ALBA,” J. Synchrotron Radiat. 16, 505–512 (2009).
[Crossref] [PubMed]

French, P. M. W.

Gelb, J.

D. B. Carlson, J. Gelb, V. Palshin, and J. E. Evans, “Laboratory-based cryogenic soft X-ray tomography with correlative cryo-light and electron microscopy,” Microsc. Microanal. 19, 22–29 (2013).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2000).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Grigorieff, N.

R. S. Ruskin, Z. Yu, and N. Grigorieff, “Quantitative characterization of electron detectors for transmission electron microscopy,” J. Struct. Biol. 184, 385–393 (2013).
[Crossref] [PubMed]

Guttmann, P.

Haala, N.

R. Reulke, S. Becker, N. Haala, and U. Tempelmann, “Determination and improvement of spatial resolution of the CCD-line-scanner system ADS40,” ISPRS J. Photogramm. Remote Sens. 60, 81–90 (2006).
[Crossref]

Hertz, H. M.

M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
[Crossref]

P. a. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226, 175–181 (2007).
[Crossref] [PubMed]

Holmberg, A.

P. a. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226, 175–181 (2007).
[Crossref] [PubMed]

Howells, M. R.

E. Pereiro, J. Nicolás, S. Ferrer, and M. R. Howells, “A soft X-ray beamline for transmission X-ray microscopy at ALBA,” J. Synchrotron Radiat. 16, 505–512 (2009).
[Crossref] [PubMed]

Ichimaru, S.

H. Takano, S. Konishi, T. Koyama, Y. Tsusaka, S. Ichimaru, T. Ohchi, H. Takenaka, and Y. Kagoshima, “Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture,” J. Synchrotron Radiat. 21, 446–448 (2014).
[Crossref] [PubMed]

Johansson, G. A.

P. a. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226, 175–181 (2007).
[Crossref] [PubMed]

Kagoshima, Y.

H. Takano, S. Konishi, T. Koyama, Y. Tsusaka, S. Ichimaru, T. Ohchi, H. Takenaka, and Y. Kagoshima, “Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture,” J. Synchrotron Radiat. 21, 446–448 (2014).
[Crossref] [PubMed]

Kirkland, A. I.

R. R. Meyer and A. I. Kirkland, “Characterisation of the signal and noise transfer of CCD cameras for electron detection,” Microsc. Res. Techniq. 49, 269–280 (2000).
[Crossref]

Konishi, S.

H. Takano, S. Konishi, T. Koyama, Y. Tsusaka, S. Ichimaru, T. Ohchi, H. Takenaka, and Y. Kagoshima, “Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture,” J. Synchrotron Radiat. 21, 446–448 (2014).
[Crossref] [PubMed]

Koyama, T.

H. Takano, S. Konishi, T. Koyama, Y. Tsusaka, S. Ichimaru, T. Ohchi, H. Takenaka, and Y. Kagoshima, “Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture,” J. Synchrotron Radiat. 21, 446–448 (2014).
[Crossref] [PubMed]

Lamb, J. R.

Lindblom, M.

M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
[Crossref]

P. a. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226, 175–181 (2007).
[Crossref] [PubMed]

McGinty, J.

Meyer, R. R.

R. R. Meyer and A. I. Kirkland, “Characterisation of the signal and noise transfer of CCD cameras for electron detection,” Microsc. Res. Techniq. 49, 269–280 (2000).
[Crossref]

Morrison, G.

R. Burge, X.-C. Yuan, G. Morrison, P. Charalambous, M. Browne, and Z. An, “Incoherent imaging with the soft X-ray microscope,” Ultramicroscopy 83, 75–92 (2000).
[Crossref] [PubMed]

Nakamura, T.

C. Chang and T. Nakamura, “Partially coherent image formation theory for X-ray microscopy,” in “Microscopy: Science, Technology, Applications and Education,”, A. Mendez-Vilas and J. Diaz, eds. (Formatex Research Center, 2010), 3, pp. 1897–1904, 4.

Narayanswamy, R.

S. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[Crossref]

Nicolás, J.

E. Pereiro, J. Nicolás, S. Ferrer, and M. R. Howells, “A soft X-ray beamline for transmission X-ray microscopy at ALBA,” J. Synchrotron Radiat. 16, 505–512 (2009).
[Crossref] [PubMed]

Ohchi, T.

H. Takano, S. Konishi, T. Koyama, Y. Tsusaka, S. Ichimaru, T. Ohchi, H. Takenaka, and Y. Kagoshima, “Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture,” J. Synchrotron Radiat. 21, 446–448 (2014).
[Crossref] [PubMed]

Palshin, V.

D. B. Carlson, J. Gelb, V. Palshin, and J. E. Evans, “Laboratory-based cryogenic soft X-ray tomography with correlative cryo-light and electron microscopy,” Microsc. Microanal. 19, 22–29 (2013).
[Crossref] [PubMed]

Park, S. K.

S. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[Crossref]

Pereiro, E.

E. Pereiro, J. Nicolás, S. Ferrer, and M. R. Howells, “A soft X-ray beamline for transmission X-ray microscopy at ALBA,” J. Synchrotron Radiat. 16, 505–512 (2009).
[Crossref] [PubMed]

Rehbein, S.

Reichenbach, S.

S. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[Crossref]

Reulke, R.

R. Reulke, S. Becker, N. Haala, and U. Tempelmann, “Determination and improvement of spatial resolution of the CCD-line-scanner system ADS40,” ISPRS J. Photogramm. Remote Sens. 60, 81–90 (2006).
[Crossref]

Ruskin, R. S.

R. S. Ruskin, Z. Yu, and N. Grigorieff, “Quantitative characterization of electron detectors for transmission electron microscopy,” J. Struct. Biol. 184, 385–393 (2013).
[Crossref] [PubMed]

Schneider, G.

Staunton, R. C.

Stollberg, H.

P. a. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226, 175–181 (2007).
[Crossref] [PubMed]

Takano, H.

H. Takano, S. Konishi, T. Koyama, Y. Tsusaka, S. Ichimaru, T. Ohchi, H. Takenaka, and Y. Kagoshima, “Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture,” J. Synchrotron Radiat. 21, 446–448 (2014).
[Crossref] [PubMed]

Takenaka, H.

H. Takano, S. Konishi, T. Koyama, Y. Tsusaka, S. Ichimaru, T. Ohchi, H. Takenaka, and Y. Kagoshima, “Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture,” J. Synchrotron Radiat. 21, 446–448 (2014).
[Crossref] [PubMed]

Takman, P. a. C.

P. a. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226, 175–181 (2007).
[Crossref] [PubMed]

Taylor, H. B.

Tempelmann, U.

R. Reulke, S. Becker, N. Haala, and U. Tempelmann, “Determination and improvement of spatial resolution of the CCD-line-scanner system ADS40,” ISPRS J. Photogramm. Remote Sens. 60, 81–90 (2006).
[Crossref]

Tsusaka, Y.

H. Takano, S. Konishi, T. Koyama, Y. Tsusaka, S. Ichimaru, T. Ohchi, H. Takenaka, and Y. Kagoshima, “Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture,” J. Synchrotron Radiat. 21, 446–448 (2014).
[Crossref] [PubMed]

Vogt, U.

M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
[Crossref]

von Hofsten, O.

M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
[Crossref]

Werner, S.

Wilhein, T.

M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999), 7.
[Crossref]

Yu, Z.

R. S. Ruskin, Z. Yu, and N. Grigorieff, “Quantitative characterization of electron detectors for transmission electron microscopy,” J. Struct. Biol. 184, 385–393 (2013).
[Crossref] [PubMed]

Yuan, X.-C.

R. Burge, X.-C. Yuan, G. Morrison, P. Charalambous, M. Browne, and Z. An, “Incoherent imaging with the soft X-ray microscope,” Ultramicroscopy 83, 75–92 (2000).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

M. C. Bertilson, O. von Hofsten, M. Lindblom, T. Wilhein, H. M. Hertz, and U. Vogt, “Compact high-resolution differential interference contrast soft X-ray microscopy,” Appl. Phys. Lett. 92, 064104 (2008).
[Crossref]

ISPRS J. Photogramm. Remote Sens. (1)

R. Reulke, S. Becker, N. Haala, and U. Tempelmann, “Determination and improvement of spatial resolution of the CCD-line-scanner system ADS40,” ISPRS J. Photogramm. Remote Sens. 60, 81–90 (2006).
[Crossref]

J. Microsc. (1)

P. a. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226, 175–181 (2007).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

J. Struct. Biol. (1)

R. S. Ruskin, Z. Yu, and N. Grigorieff, “Quantitative characterization of electron detectors for transmission electron microscopy,” J. Struct. Biol. 184, 385–393 (2013).
[Crossref] [PubMed]

J. Synchrotron Radiat. (2)

H. Takano, S. Konishi, T. Koyama, Y. Tsusaka, S. Ichimaru, T. Ohchi, H. Takenaka, and Y. Kagoshima, “Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture,” J. Synchrotron Radiat. 21, 446–448 (2014).
[Crossref] [PubMed]

E. Pereiro, J. Nicolás, S. Ferrer, and M. R. Howells, “A soft X-ray beamline for transmission X-ray microscopy at ALBA,” J. Synchrotron Radiat. 16, 505–512 (2009).
[Crossref] [PubMed]

Microsc. Microanal. (2)

W. V. D. Broek, S. V. Aert, and D. V. Dyck, “Fully automated measurement of the modulation transfer function of charge-coupled devices above the Nyquist frequency,” Microsc. Microanal. 18, 336–342 (2012).
[Crossref] [PubMed]

D. B. Carlson, J. Gelb, V. Palshin, and J. E. Evans, “Laboratory-based cryogenic soft X-ray tomography with correlative cryo-light and electron microscopy,” Microsc. Microanal. 19, 22–29 (2013).
[Crossref] [PubMed]

Microsc. Res. Techniq. (1)

R. R. Meyer and A. I. Kirkland, “Characterisation of the signal and noise transfer of CCD cameras for electron detection,” Microsc. Res. Techniq. 49, 269–280 (2000).
[Crossref]

Opt. Eng. (1)

S. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[Crossref]

Opt. Express (2)

Ultramicroscopy (1)

R. Burge, X.-C. Yuan, G. Morrison, P. Charalambous, M. Browne, and Z. An, “Incoherent imaging with the soft X-ray microscope,” Ultramicroscopy 83, 75–92 (2000).
[Crossref] [PubMed]

Other (4)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999), 7.
[Crossref]

C. Chang and T. Nakamura, “Partially coherent image formation theory for X-ray microscopy,” in “Microscopy: Science, Technology, Applications and Education,”, A. Mendez-Vilas and J. Diaz, eds. (Formatex Research Center, 2010), 3, pp. 1897–1904, 4.

J. W. Goodman, Statistical Optics (Wiley, 2000).

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Figures (2)

Fig. 1
Fig. 1 (a) Siemens star test pattern; (b) Polar decomposition of (a); (c) I S S r , r e f profile calculated from the binarization of I S S r by thresholding, remarked by red lines in (d) and (b), respectively; (d) I S S r , r e f image in polar coordinates; (e) 1D Fourier transform of profile at largest radius from (d).

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Fig. 2
Fig. 2 (a) Plot of the Fourier coefficient values for 1st and 3rd diffraction orders for I S S r and I S S r , r e f against the corresponding spatial frequency; (b) | ℋ A | curves obtained from plots in (a); (c) Final experimental | ℋ A | curve obtained by combining curves in (b); (d) Comparison of simulated and measured MTF profiles for ZP with drN = 25 nm at different defocus distances.

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Equations (6)

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ℋ A ( f x , f y ) = I ˜ o u t ( f x , f y ) I ˜ i n ( f x , f y ) ,
f ( θ ) = ∑ m = − ∞ ∞ C m cos ( 2 π m θ Λ ) ,
I S S r ( θ ) = ∑ m = − ∞ ∞ C m cos ( 2 π m θ Λ ) = ∑ m = − ∞ ∞ C m cos ( 2 π m l P ( r ) ) = I S S ( l , r ) ,
I ˜ S S r ( ω ) = ∑ m = − ∞ ∞ C m 2 [ δ ( ω − m Λ ) + δ ( ω + m Λ ) ] ,
I ˜ S S ( u , r ) = 1 | r | ∑ m = − ∞ ∞ C m 2 [ δ ( u − m Λ r ) + δ ( u + m Λ r ) ] ,
ℋ A ( u = m Λ r ) = I ˜ S S r ( ω = m Λ ) I ˜ S S , r e f r ( ω = m Λ ) .

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