Abstract

Small structures, as inside living cells, move on millisecond timescales, which is usually far beyond the imaging rate of superresolution fluorescence microscopes. In contrast, label-free imaging techniques providing high photon densities can operate at >100  Hz. For simple structures, an oblique, coherent illumination with a static laser beam increases image contrast and resolution considerably, whereas illumination of complex structures results in an image full of speckles. Remarkably, an artifact-free image is generated by subsequent oblique illumination of the structure from all azimuthal directions. This is the working principle of ROCS microscopy, which currently achieves 150 nm spatial and 10 ms temporal resolution without fluorophore bleaching, and is therefore highly beneficial for live-cell imaging. However, the complicated formation of ROCS images and image spectra during one sweep, i.e., the superposition of different speckle patterns is still unclear. Here, we investigate with experiments and computer simulations the influence of speckle-like interference patterns on the final image contrast and resolution, in darkfield mode and, by adding a reference wave, in brightfield mode. In close comparison to experimental results, we present a theoretical framework, which describes the ROCS image formation in real space and in k space by identifying different spectral components. In addition, we vary the degree of coherence by a rotating diffuser and thereby demonstrate that maximal spatial coherence and maximal speckle interference from multiple scattering provide the best image contrast and resolution. We find that the cross correlations of elementary waves emitted in a distance of several micrometers to each other positively contribute to image formation and do not, as commonly believed, distort image formation. By understanding the composition of image speckles in time and space, future coherent microscopes should provide new insights into the high-speed world of living cells.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. D. M. Chudakov, M. V. Matz, S. Lukyanov, and K. A. Lukyanov, “Fluorescent proteins and their applications in imaging living cells and tissues,” Physiol. Rev. 90, 1103–1163 (2010).
    [Crossref]
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    [Crossref]
  3. T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photon. Rev. 10, 13–39 (2016).
    [Crossref]
  4. S. Culley, D. Albrecht, C. Jacobs, P. M. Pereira, C. Leterrier, J. Mercer, and R. Henriques, “Quantitative mapping and minimization of super-resolution optical imaging artifacts,” Nat. Methods 15, 263–266 (2018).
    [Crossref]
  5. G. Vicidomini, P. Bianchini, and A. Diaspro, “STED super-resolved microscopy,” Nat. Methods 15, 173–182 (2018).
    [Crossref]
  6. R. Heintzmann and T. Huser, “Super-resolution structured illumination microscopy,” Chem. Rev. 117, 13890–13908 (2017).
    [Crossref]
  7. M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
    [Crossref]
  8. E. Abbe, “Contributions to the theory of the microscope and of microscopic perception,” Archiv f. mikrosk. Anatomie 9, 413–418 (1873).
    [Crossref]
  9. K. Wicker and R. Heintzmann, “Resolving a misconception about structured illumination,” Nat. Photonics 8, 342–344 (2014).
    [Crossref]
  10. D. J. Cronin and A. E. Smith, “Dynamic coherent optical system,” Opt. Eng. 12, 120250 (1973).
    [Crossref]
  11. P. V. Olshausen and A. Rohrbach, “Coherent total internal reflection dark field microscopy—an approach to label-free imaging beyond the diffraction limit,” Opt. Lett. 38, 4066–4069 (2013).
    [Crossref]
  12. Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
    [Crossref]
  13. G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
    [Crossref]
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    [Crossref]
  15. F. Jünger, P. V. Olshausen, and A. Rohrbach, “Fast, label-free super-resolution live-cell imaging using rotating coherent scattering (ROCS) microscopy,” Sci. Rep. 6, 30393–30311 (2016).
    [Crossref]
  16. F. Jünger and A. Rohrbach, “Strong cytoskeleton activity on millisecond time scales during particle binding and uptake revealed by ROCS microscopy,” Cytoskeleton, 1–15 (2018).
    [Crossref]
  17. M. D. Koch and A. Rohrbach, “Label-free imaging and bending analysis of microtubules by ROCS microscopy and optical trapping,” Biophys. J. 114, 168–177 (2018).
    [Crossref]
  18. Macrophages, were generated from bone marrow cell suspensions of Lifeact-GFP transgenic mice and cultured at 37°C and 5% CO2 over 6 days in RPMI-1640 + GlutaMAX medium.
  19. A. Rohrbach and E. H. Stelzer, “Optical trapping of dielectric particles in arbitrary fields,” J. Opt. Soc. Am. A 18, 839–853 (2001).
    [Crossref]
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    [Crossref]

2018 (4)

S. Culley, D. Albrecht, C. Jacobs, P. M. Pereira, C. Leterrier, J. Mercer, and R. Henriques, “Quantitative mapping and minimization of super-resolution optical imaging artifacts,” Nat. Methods 15, 263–266 (2018).
[Crossref]

G. Vicidomini, P. Bianchini, and A. Diaspro, “STED super-resolved microscopy,” Nat. Methods 15, 173–182 (2018).
[Crossref]

M. D. Koch and A. Rohrbach, “Label-free imaging and bending analysis of microtubules by ROCS microscopy and optical trapping,” Biophys. J. 114, 168–177 (2018).
[Crossref]

G. Maire, H. Giovannini, A. Talneau, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Phase imaging and synthetic aperture super-resolution via total internal reflection microscopy,” Opt. Lett. 43, 2173–2176 (2018).
[Crossref]

2017 (1)

R. Heintzmann and T. Huser, “Super-resolution structured illumination microscopy,” Chem. Rev. 117, 13890–13908 (2017).
[Crossref]

2016 (2)

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photon. Rev. 10, 13–39 (2016).
[Crossref]

F. Jünger, P. V. Olshausen, and A. Rohrbach, “Fast, label-free super-resolution live-cell imaging using rotating coherent scattering (ROCS) microscopy,” Sci. Rep. 6, 30393–30311 (2016).
[Crossref]

2014 (1)

K. Wicker and R. Heintzmann, “Resolving a misconception about structured illumination,” Nat. Photonics 8, 342–344 (2014).
[Crossref]

2013 (3)

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

P. V. Olshausen and A. Rohrbach, “Coherent total internal reflection dark field microscopy—an approach to label-free imaging beyond the diffraction limit,” Opt. Lett. 38, 4066–4069 (2013).
[Crossref]

2010 (1)

D. M. Chudakov, M. V. Matz, S. Lukyanov, and K. A. Lukyanov, “Fluorescent proteins and their applications in imaging living cells and tissues,” Physiol. Rev. 90, 1103–1163 (2010).
[Crossref]

2009 (1)

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6, 24–32 (2009).
[Crossref]

2001 (1)

2000 (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[Crossref]

1973 (1)

D. J. Cronin and A. E. Smith, “Dynamic coherent optical system,” Opt. Eng. 12, 120250 (1973).
[Crossref]

1953 (1)

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
[Crossref]

1873 (1)

E. Abbe, “Contributions to the theory of the microscope and of microscopic perception,” Archiv f. mikrosk. Anatomie 9, 413–418 (1873).
[Crossref]

Abbe, E.

E. Abbe, “Contributions to the theory of the microscope and of microscopic perception,” Archiv f. mikrosk. Anatomie 9, 413–418 (1873).
[Crossref]

Albrecht, D.

S. Culley, D. Albrecht, C. Jacobs, P. M. Pereira, C. Leterrier, J. Mercer, and R. Henriques, “Quantitative mapping and minimization of super-resolution optical imaging artifacts,” Nat. Methods 15, 263–266 (2018).
[Crossref]

Belkebir, K.

Bianchini, P.

G. Vicidomini, P. Bianchini, and A. Diaspro, “STED super-resolved microscopy,” Nat. Methods 15, 173–182 (2018).
[Crossref]

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Chaumet, P. C.

Chudakov, D. M.

D. M. Chudakov, M. V. Matz, S. Lukyanov, and K. A. Lukyanov, “Fluorescent proteins and their applications in imaging living cells and tissues,” Physiol. Rev. 90, 1103–1163 (2010).
[Crossref]

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Cronin, D. J.

D. J. Cronin and A. E. Smith, “Dynamic coherent optical system,” Opt. Eng. 12, 120250 (1973).
[Crossref]

Culley, S.

S. Culley, D. Albrecht, C. Jacobs, P. M. Pereira, C. Leterrier, J. Mercer, and R. Henriques, “Quantitative mapping and minimization of super-resolution optical imaging artifacts,” Nat. Methods 15, 263–266 (2018).
[Crossref]

Depeursinge, C.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Diaspro, A.

G. Vicidomini, P. Bianchini, and A. Diaspro, “STED super-resolved microscopy,” Nat. Methods 15, 173–182 (2018).
[Crossref]

Giovannini, H.

Goddard, L. L.

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photon. Rev. 10, 13–39 (2016).
[Crossref]

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[Crossref]

Heintzmann, R.

R. Heintzmann and T. Huser, “Super-resolution structured illumination microscopy,” Chem. Rev. 117, 13890–13908 (2017).
[Crossref]

K. Wicker and R. Heintzmann, “Resolving a misconception about structured illumination,” Nat. Photonics 8, 342–344 (2014).
[Crossref]

Hell, S. W.

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6, 24–32 (2009).
[Crossref]

Henriques, R.

S. Culley, D. Albrecht, C. Jacobs, P. M. Pereira, C. Leterrier, J. Mercer, and R. Henriques, “Quantitative mapping and minimization of super-resolution optical imaging artifacts,” Nat. Methods 15, 263–266 (2018).
[Crossref]

Hopkins, H. H.

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
[Crossref]

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Huser, T.

R. Heintzmann and T. Huser, “Super-resolution structured illumination microscopy,” Chem. Rev. 117, 13890–13908 (2017).
[Crossref]

Jacobs, C.

S. Culley, D. Albrecht, C. Jacobs, P. M. Pereira, C. Leterrier, J. Mercer, and R. Henriques, “Quantitative mapping and minimization of super-resolution optical imaging artifacts,” Nat. Methods 15, 263–266 (2018).
[Crossref]

Jourdain, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Jünger, F.

F. Jünger, P. V. Olshausen, and A. Rohrbach, “Fast, label-free super-resolution live-cell imaging using rotating coherent scattering (ROCS) microscopy,” Sci. Rep. 6, 30393–30311 (2016).
[Crossref]

F. Jünger and A. Rohrbach, “Strong cytoskeleton activity on millisecond time scales during particle binding and uptake revealed by ROCS microscopy,” Cytoskeleton, 1–15 (2018).
[Crossref]

Kim, T.

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photon. Rev. 10, 13–39 (2016).
[Crossref]

Koch, M. D.

M. D. Koch and A. Rohrbach, “Label-free imaging and bending analysis of microtubules by ROCS microscopy and optical trapping,” Biophys. J. 114, 168–177 (2018).
[Crossref]

Leterrier, C.

S. Culley, D. Albrecht, C. Jacobs, P. M. Pereira, C. Leterrier, J. Mercer, and R. Henriques, “Quantitative mapping and minimization of super-resolution optical imaging artifacts,” Nat. Methods 15, 263–266 (2018).
[Crossref]

Lukyanov, K. A.

D. M. Chudakov, M. V. Matz, S. Lukyanov, and K. A. Lukyanov, “Fluorescent proteins and their applications in imaging living cells and tissues,” Physiol. Rev. 90, 1103–1163 (2010).
[Crossref]

Lukyanov, S.

D. M. Chudakov, M. V. Matz, S. Lukyanov, and K. A. Lukyanov, “Fluorescent proteins and their applications in imaging living cells and tissues,” Physiol. Rev. 90, 1103–1163 (2010).
[Crossref]

Magistretti, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Maire, G.

Marquet, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Matz, M. V.

D. M. Chudakov, M. V. Matz, S. Lukyanov, and K. A. Lukyanov, “Fluorescent proteins and their applications in imaging living cells and tissues,” Physiol. Rev. 90, 1103–1163 (2010).
[Crossref]

Mercer, J.

S. Culley, D. Albrecht, C. Jacobs, P. M. Pereira, C. Leterrier, J. Mercer, and R. Henriques, “Quantitative mapping and minimization of super-resolution optical imaging artifacts,” Nat. Methods 15, 263–266 (2018).
[Crossref]

Olshausen, P. V.

F. Jünger, P. V. Olshausen, and A. Rohrbach, “Fast, label-free super-resolution live-cell imaging using rotating coherent scattering (ROCS) microscopy,” Sci. Rep. 6, 30393–30311 (2016).
[Crossref]

P. V. Olshausen and A. Rohrbach, “Coherent total internal reflection dark field microscopy—an approach to label-free imaging beyond the diffraction limit,” Opt. Lett. 38, 4066–4069 (2013).
[Crossref]

Pavillon, N.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Pereira, P. M.

S. Culley, D. Albrecht, C. Jacobs, P. M. Pereira, C. Leterrier, J. Mercer, and R. Henriques, “Quantitative mapping and minimization of super-resolution optical imaging artifacts,” Nat. Methods 15, 263–266 (2018).
[Crossref]

Popescu, G.

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photon. Rev. 10, 13–39 (2016).
[Crossref]

Rohrbach, A.

M. D. Koch and A. Rohrbach, “Label-free imaging and bending analysis of microtubules by ROCS microscopy and optical trapping,” Biophys. J. 114, 168–177 (2018).
[Crossref]

F. Jünger, P. V. Olshausen, and A. Rohrbach, “Fast, label-free super-resolution live-cell imaging using rotating coherent scattering (ROCS) microscopy,” Sci. Rep. 6, 30393–30311 (2016).
[Crossref]

P. V. Olshausen and A. Rohrbach, “Coherent total internal reflection dark field microscopy—an approach to label-free imaging beyond the diffraction limit,” Opt. Lett. 38, 4066–4069 (2013).
[Crossref]

A. Rohrbach and E. H. Stelzer, “Optical trapping of dielectric particles in arbitrary fields,” J. Opt. Soc. Am. A 18, 839–853 (2001).
[Crossref]

F. Jünger and A. Rohrbach, “Strong cytoskeleton activity on millisecond time scales during particle binding and uptake revealed by ROCS microscopy,” Cytoskeleton, 1–15 (2018).
[Crossref]

Sentenac, A.

Smith, A. E.

D. J. Cronin and A. E. Smith, “Dynamic coherent optical system,” Opt. Eng. 12, 120250 (1973).
[Crossref]

Stelzer, E. H.

Talneau, A.

Toy, F.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Vicidomini, G.

G. Vicidomini, P. Bianchini, and A. Diaspro, “STED super-resolved microscopy,” Nat. Methods 15, 173–182 (2018).
[Crossref]

Wicker, K.

K. Wicker and R. Heintzmann, “Resolving a misconception about structured illumination,” Nat. Photonics 8, 342–344 (2014).
[Crossref]

Yang, C.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Zheng, G.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Zhou, R.

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photon. Rev. 10, 13–39 (2016).
[Crossref]

Archiv f. mikrosk. Anatomie (1)

E. Abbe, “Contributions to the theory of the microscope and of microscopic perception,” Archiv f. mikrosk. Anatomie 9, 413–418 (1873).
[Crossref]

Biophys. J. (1)

M. D. Koch and A. Rohrbach, “Label-free imaging and bending analysis of microtubules by ROCS microscopy and optical trapping,” Biophys. J. 114, 168–177 (2018).
[Crossref]

Chem. Rev. (1)

R. Heintzmann and T. Huser, “Super-resolution structured illumination microscopy,” Chem. Rev. 117, 13890–13908 (2017).
[Crossref]

J. Microsc. (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
[Crossref]

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

Laser Photon. Rev. (1)

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photon. Rev. 10, 13–39 (2016).
[Crossref]

Nat. Methods (3)

S. Culley, D. Albrecht, C. Jacobs, P. M. Pereira, C. Leterrier, J. Mercer, and R. Henriques, “Quantitative mapping and minimization of super-resolution optical imaging artifacts,” Nat. Methods 15, 263–266 (2018).
[Crossref]

G. Vicidomini, P. Bianchini, and A. Diaspro, “STED super-resolved microscopy,” Nat. Methods 15, 173–182 (2018).
[Crossref]

S. W. Hell, “Microscopy and its focal switch,” Nat. Methods 6, 24–32 (2009).
[Crossref]

Nat. Photonics (3)

K. Wicker and R. Heintzmann, “Resolving a misconception about structured illumination,” Nat. Photonics 8, 342–344 (2014).
[Crossref]

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Opt. Eng. (1)

D. J. Cronin and A. E. Smith, “Dynamic coherent optical system,” Opt. Eng. 12, 120250 (1973).
[Crossref]

Opt. Lett. (2)

Physiol. Rev. (1)

D. M. Chudakov, M. V. Matz, S. Lukyanov, and K. A. Lukyanov, “Fluorescent proteins and their applications in imaging living cells and tissues,” Physiol. Rev. 90, 1103–1163 (2010).
[Crossref]

Proc. R. Soc. London Ser. A (1)

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
[Crossref]

Sci. Rep. (1)

F. Jünger, P. V. Olshausen, and A. Rohrbach, “Fast, label-free super-resolution live-cell imaging using rotating coherent scattering (ROCS) microscopy,” Sci. Rep. 6, 30393–30311 (2016).
[Crossref]

Other (2)

F. Jünger and A. Rohrbach, “Strong cytoskeleton activity on millisecond time scales during particle binding and uptake revealed by ROCS microscopy,” Cytoskeleton, 1–15 (2018).
[Crossref]

Macrophages, were generated from bone marrow cell suspensions of Lifeact-GFP transgenic mice and cultured at 37°C and 5% CO2 over 6 days in RPMI-1640 + GlutaMAX medium.

Supplementary Material (5)

NameDescription
» Supplement 1       Derivations of formula and additional figures
» Visualization 1       Darkfield images from single direction show different interference structures
» Visualization 2       Brightfield images from single direction show different interference structures
» Visualization 3       Darkfield ROCS Image quality increases during angular integration (2 pi sweep)
» Visualization 4       Brightfield ROCS Image quality increases during angular integration (2 pi sweep)

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Figures (8)

Fig. 1.
Fig. 1. (a) ROCS image (DF mode) of a living mouse-macrophage recorded with a 405 nm laser within 9 ms. (b) The corresponding LifeAct GFP-actin labeled fluorescence image was recorded within 200 ms. Both images were recorded in TIR mode. Inset: The correlation between two spherical waves is quantified by the degree of coherence γ.
Fig. 2.
Fig. 2. Sketch of setup. Simplified side view of the ROCS microscope with illumination light (light blue) incident with polar angle θ and laser light scattered at the particles (mid blue). Inset 1: Variation of the polar angle θ±ϵ controls the spatial coherence γ and the coupling strength of two scatterers in a distance d. Inset 2: Top view of plane wave incident at azimuthal angle ϕ and spherical waves emitted from three particles.
Fig. 3.
Fig. 3. Enhanced resolution and contrast by adding an interference pattern. The simulation shows: (a) a darkfield ROCS image, which can be split into the sum of (b) an incoherent (fluorescence) image, and (c) a multiple interference pattern (with positive values in red and negative values in blue). The small circles indicate the positions of the point-like scatterers. (d) Two exemplary intensity line scans L1 (solid) and L2 (dashed). Parameters: NAdet=1.27, NAill=1.42, λ=405  nm.
Fig. 4.
Fig. 4. Coherent scattering in real space and Fourier space with simple plane wave illumination. (a) Measured and simulated brightfield intensity ISD(x,y) from scattering of an oblique incident plane wave (orange k vector) at a 200 nm bead. (b) Sketch in Fourier space indicating the intensities I˜mSD(k,ϕ=90°) (m=1.4) adding up to single direction brightfield and darkfield image spectra. (c) Determination of the scattered field in k space within the red OTF area Hc(k). The red dashed circle represents the OTF for the DF case, such that the reflected light is not detected. (d) Fourier spectrum of the measured intensity in (a) with incident lateral k vector ki and exemplary scattered lateral k vector ks>ki. (e) Composition of measured single direction brightfield image spectra for three different polar illumination angles θ. Scalebar: 10/μm=2π·1.59/μm.
Fig. 5.
Fig. 5. Simulated image generation of an object consisting of three lines. (a) The electric fields on the camera from single direction illumination as indicated by the white arrows. (b) The corresponding phase distribution φcam(x,y)[0,2π] and (c) the corresponding single direction image intensity. (d) The single direction image spectra are obtained by autocorrelation AC[E˜cam] of the electric fields Fourier transforms at the camera E˜cam(kx,ky). (e) The object and the modulus of its Fourier transform and the resulting ROCS image from 64 illumination directions with the modulus of its Fourier transform.
Fig. 6.
Fig. 6. Interference intensity of scattered and unscattered light in real space and Fourier space. Identical distribution of 200 nm beads is imaged in brightfield mode (a, b) and darkfield mode (c). In (a) a rotating diffuser wheel reduces the spatial coherence. Illumination from a single direction (SD) produces speckles and interference fringes. Subsequent illumination from all ϕ directions results in all cases (3rd column of a, b, c) in an artifact-free image. Three beads in a row are highlighted with a rectangle, and the contrast is analyzed through a line scan. The two regions of interest marked with dashed rectangles are analyzed in the following figures. Scalebar: 10/μm=2π·1.59/μm.
Fig. 7.
Fig. 7. Interference intensity of scattered and unscattered light in real space and Fourier space. Two adjacent 200 nm beads (see ROI in Fig. 6) are imaged in DF and BF modes. (a) and (c) show experimental results, (b) and (d) show simulation results. The white arrows indicate the illumination directions.
Fig. 8.
Fig. 8. Interference intensity of scattered and unscattered light in real space and Fourier space. Three beads (see ROI in Fig. 6) are imaged in DF and BF modes. (a) shows experimental results, (b) shows simulation results.

Equations (18)

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f(r)=jfj(rrj)=jαj·sj(rrj),
F(k)=jFj(k)·exp(ikrj).
F2P(k)=F0(k)·(exp(i12kxd)+exp(i12kxd))=2F0(k)·cos(12kxd)=F2P*(k).
F3P(k)=F0(k)·(eikr12cos(12kd12)+eikr13cos(12kd13)+eikr23cos(12kd23)).
Ei(r,ϕ,θ,ϵ)=E0·eiφ(ϵ)·eikir=E0·ei(δk+ki)r.
γ(ϵ)=12θ0θ0θ0eiki(θ)·r·eiki(θ+ϵ)·rdθ=|eikir|2·ACϵ[exp(iφ(ϵ))],
Es(r,ϕ,ϵ)=(Ei(r,ϕ,ϵ)·k2·f(r))*g(r)=(Ei(r,ϕ,ϵ)·k2jαj·sj(rrj))*g(r),
Ecam(r,ϕ,q,ϵ)=[q·Ei(r,ϕ,ϵ)+Es(r,ϕ,ϵ)]*hc(r)=[Ei(r,ϕ,ϵ)(q+f(r)*g(r))]*hc(r).
ISD(r,ϕ,q,ϵ)=ACϵ[Ecam(r,ϕ,q,ϵ)]=I1SD(r,ϕ,ϵ)+ISDDF(r,ϕ,ϵ)+ISDinf(r,ϕ,ϵ).
ISDinf(r,ϕ,ϵ)=2C·γ(ϵ)·j(fj(rrj)*hc(r))·sin(ki(rjr)),
ISDDF(r,ϕ,ϵ)=|j|Ecam,j(r,ϕ)|·exp(iφj(r,ϕ))|2=j|Ecam,j(r,ϕ)|2+γ(ϵ)·jk|Ecam,j||Ecam,k|cos(Δφjk(r,ϕ)).
I(r,q,ϵ)=02πACϵ[Ecam(r,ϕ,q,ϵ)]dϕ=ϵ=002π|((q+i·f(r))·Ei(r,ϕ,0))*hc(r)|2dϕ.
E˜cam(k,ϕ)=E˜0·(δ(kki(ϕ))*(q˜·δ(k)+iF(k)))·Hc(k)=E˜0·(q˜δ(kki(ϕ))+iF(kki(ϕ)))·Hc(k),
I˜SD(k,ϕ,q˜)=AC[E˜cam(k,ϕ)]=E˜02·AC[(q˜δ(kki)·Hc(k)+iF(kki)·Hc(k))].
I˜SD(k)=I˜1SD(k)+I˜2SD(k)+I˜3SD(k)+I˜4SD(k).
I˜SDinf(k,ϕ,q˜,τ)=iγ(ϵ)·B·q˜·(F(k)·Hc(k+ki)F(k)·Hc(kki)),
I˜(k,q˜,ϵ)=02πI˜SD(k,ϕ,q˜,ϵ)dϕ=Aδ(k)+02πI˜SDDF(k,ϕ)dϕ+02πI˜SDinf(k,ϕ)dϕ,
I˜DF(k,ϵ)=E˜022θ0·02πθ0θ0AC[F(k)·Hc(k+ki(ϕ,θ+ϵ))]dθdϕ=E˜02·F(k+k)·F*(k)·HeffDF(k,k,ϵ)dk.

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