Abstract

Mechanical vibrations of components of the optical system is one of the sources of blurring of interference pattern in coherent imaging systems. The problem is especially important in holography where the resolution of the reconstructed objects depends on the effective size of the hologram, which is on the extent of the interference pattern, and on the contrast of the interference fringes. We discuss the mathematical relation between the vibrations, the hologram contrast and the reconstructed object. We show how vibrations can be post-filtered out from the hologram or from the reconstructed object assuming a Gaussian distribution of the vibrations. We also provide a numerical example of compensation for directional motion blur. We demonstrate our approach for light optical and electron holograms, acquired with both, plane- as well as spherical-waves. As a result of such hologram deblurring, the resolution of the reconstructed objects is enhanced by almost a factor of 2. We believe that our approach opens up a new venue of post-experimental resolution enhancement in in-line holography by adapting the rich database/catalogue of motion deblurring algorithms developed for photography and image restoration applications.

© 2017 Optical Society of America

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References

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  25. J. Y. Mutus, L. Livadaru, J. T. Robinson, R. Urban, M. H. Salomons, M. Cloutier, and R. A. Wolkow, “Low-energy electron point projection microscopy of suspended graphene, the ultimate microscope slide,” New J. Phys. 13(6), 063011 (2011).
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  31. T. Latychevskaia, J.-N. Longchamp, C. Escher, and H.-W. Fink, “On artefact-free reconstruction of low-energy (30-250eV) electron holograms,” Ultramicroscopy 145, 22–27 (2014).
    [Crossref] [PubMed]
  32. J.-N. Longchamp, S. Rauschenbach, S. Abb, C. Escher, T. Latychevskaia, K. Kern, and H.-W. Fink, “Imaging proteins at the single-molecule level,” Proc. Natl. Acad. Sci. U.S.A. 114(7), 1474–1479 (2017).
    [Crossref] [PubMed]

2017 (1)

J.-N. Longchamp, S. Rauschenbach, S. Abb, C. Escher, T. Latychevskaia, K. Kern, and H.-W. Fink, “Imaging proteins at the single-molecule level,” Proc. Natl. Acad. Sci. U.S.A. 114(7), 1474–1479 (2017).
[Crossref] [PubMed]

2016 (2)

M. Muller, V. Kravtsov, A. Paarmann, M. B. Raschke, and R. Ernstorfer, “Nanofocused plasmon-driven sub-10 fs electron point source,” ACS Photonics 3(4), 611–619 (2016).
[Crossref]

T. Latychevskaia and H.-W. Fink, “Inverted Gabor holography principle for tailoring arbitrary shaped three-dimensional beams,” Sci. Rep. 6(1), 26312 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (2)

S. Wang, Z. Gao, G. Li, Z. Feng, and Q. Feng, “Continual mechanical vibration trajectory tracking based on electro-optical heterodyne interferometry,” Opt. Express 22(7), 7799–7810 (2014).
[Crossref] [PubMed]

T. Latychevskaia, J.-N. Longchamp, C. Escher, and H.-W. Fink, “On artefact-free reconstruction of low-energy (30-250eV) electron holograms,” Ultramicroscopy 145, 22–27 (2014).
[Crossref] [PubMed]

2013 (2)

M. Germann, T. Latychevskaia, C. Escher, and H.-W. Fink, “Pulsed electron holography,” Appl. Phys. Lett. 102(20), 203115 (2013).
[Crossref]

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

2012 (1)

2011 (1)

J. Y. Mutus, L. Livadaru, J. T. Robinson, R. Urban, M. H. Salomons, M. Cloutier, and R. A. Wolkow, “Low-energy electron point projection microscopy of suspended graphene, the ultimate microscope slide,” New J. Phys. 13(6), 063011 (2011).
[Crossref]

2009 (2)

2008 (2)

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33(2), 156–158 (2008).
[Crossref] [PubMed]

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graph. 27(3), 73 (2008).
[Crossref]

2007 (1)

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

2004 (2)

S. Farsiu, M. D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe super resolution,” IEEE Trans. Image Process. 13(10), 1327–1344 (2004).
[Crossref] [PubMed]

M. Ben-Ezra and S. K. Nayar, “Motion-based motion deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 689–698 (2004).
[Crossref] [PubMed]

1999 (1)

J. W. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

1996 (1)

D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. 13(3), 43–64 (1996).
[Crossref]

1995 (1)

T. Matsumoto, T. Tanji, and A. Tonomura, “Visualization of DNA in solution by Fraunhofer in-line electron holography. 2. Experiments,” Optik (Stuttg.) 100, 71–74 (1995).

1990 (2)

H.-W. Fink, W. Stocker, and H. Schmid, “Holography with low-energy electrons,” Phys. Rev. Lett. 65(10), 1204–1206 (1990).
[Crossref] [PubMed]

H.-W. Fink, W. Stocker, and H. Schmid, “Coherent point-source electron-beams,” J. Vac. Sci. Technol. 8(6), 1323–1324 (1990).
[Crossref]

1988 (1)

H.-W. Fink, “Point-source for ions and electrons,” Phys. Scr. 38(2), 260–263 (1988).
[Crossref]

1969 (1)

G. W. Stroke, F. Furrer, and D. R. Lamberty, “Deblurring of motion-blurred photographs using extended-range holographic Fourier-transform division,” Opt. Commun. 1(3), 141–145 (1969).
[Crossref]

1968 (2)

G. W. Stroke and R. G. Zech, “Photographic realization of an image-deconvolution filter for holographic Fourier-transform division,” Jpn. J. Appl. Phys. 7(7), 764–766 (1968).
[Crossref]

O. Bryngdahl and A. Lohmann, “Single-sideband holography,” J. Opt. Soc. Am. 58(5), 620–624 (1968).
[Crossref]

1949 (2)

C. E. Shannon, “Communication in the presence of noise,” Proc. Inst. Radio Eng. 37, 10–21 (1949).

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. Lond. A Math. Phys. Sci. 197(1051), 454–487 (1949).
[Crossref]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Abb, S.

J.-N. Longchamp, S. Rauschenbach, S. Abb, C. Escher, T. Latychevskaia, K. Kern, and H.-W. Fink, “Imaging proteins at the single-molecule level,” Proc. Natl. Acad. Sci. U.S.A. 114(7), 1474–1479 (2017).
[Crossref] [PubMed]

Agarwala, A.

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graph. 27(3), 73 (2008).
[Crossref]

Ben-Ezra, M.

M. Ben-Ezra and S. K. Nayar, “Motion-based motion deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 689–698 (2004).
[Crossref] [PubMed]

Bryngdahl, O.

Chang, C.-C.

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Chang, C.-S.

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Chang, Y.-C.

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Charalambous, P.

J. W. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

Cho, S.

S. Cho and S. Lee, “Fast motion deblurring,” ACM Trans. Graph. 28(5), 145 (2009).
[Crossref]

Cloutier, M.

J. Y. Mutus, L. Livadaru, J. T. Robinson, R. Urban, M. H. Salomons, M. Cloutier, and R. A. Wolkow, “Low-energy electron point projection microscopy of suspended graphene, the ultimate microscope slide,” New J. Phys. 13(6), 063011 (2011).
[Crossref]

Elad, M.

S. Farsiu, M. D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe super resolution,” IEEE Trans. Image Process. 13(10), 1327–1344 (2004).
[Crossref] [PubMed]

Ernstorfer, R.

M. Muller, V. Kravtsov, A. Paarmann, M. B. Raschke, and R. Ernstorfer, “Nanofocused plasmon-driven sub-10 fs electron point source,” ACS Photonics 3(4), 611–619 (2016).
[Crossref]

Escher, C.

J.-N. Longchamp, S. Rauschenbach, S. Abb, C. Escher, T. Latychevskaia, K. Kern, and H.-W. Fink, “Imaging proteins at the single-molecule level,” Proc. Natl. Acad. Sci. U.S.A. 114(7), 1474–1479 (2017).
[Crossref] [PubMed]

T. Latychevskaia, J.-N. Longchamp, C. Escher, and H.-W. Fink, “On artefact-free reconstruction of low-energy (30-250eV) electron holograms,” Ultramicroscopy 145, 22–27 (2014).
[Crossref] [PubMed]

M. Germann, T. Latychevskaia, C. Escher, and H.-W. Fink, “Pulsed electron holography,” Appl. Phys. Lett. 102(20), 203115 (2013).
[Crossref]

Farsiu, S.

S. Farsiu, M. D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe super resolution,” IEEE Trans. Image Process. 13(10), 1327–1344 (2004).
[Crossref] [PubMed]

Feng, Q.

Feng, Z.

Fienup, J. R.

Fink, H.-W.

J.-N. Longchamp, S. Rauschenbach, S. Abb, C. Escher, T. Latychevskaia, K. Kern, and H.-W. Fink, “Imaging proteins at the single-molecule level,” Proc. Natl. Acad. Sci. U.S.A. 114(7), 1474–1479 (2017).
[Crossref] [PubMed]

T. Latychevskaia and H.-W. Fink, “Inverted Gabor holography principle for tailoring arbitrary shaped three-dimensional beams,” Sci. Rep. 6(1), 26312 (2016).
[Crossref] [PubMed]

T. Latychevskaia and H.-W. Fink, “Practical algorithms for simulation and reconstruction of digital in-line holograms,” Appl. Opt. 54(9), 2424–2434 (2015).
[Crossref] [PubMed]

T. Latychevskaia, J.-N. Longchamp, C. Escher, and H.-W. Fink, “On artefact-free reconstruction of low-energy (30-250eV) electron holograms,” Ultramicroscopy 145, 22–27 (2014).
[Crossref] [PubMed]

M. Germann, T. Latychevskaia, C. Escher, and H.-W. Fink, “Pulsed electron holography,” Appl. Phys. Lett. 102(20), 203115 (2013).
[Crossref]

T. Latychevskaia, J.-N. Longchamp, and H.-W. Fink, “When holography meets coherent diffraction imaging,” Opt. Express 20(27), 28871–28892 (2012).
[Crossref] [PubMed]

T. Latychevskaia and H.-W. Fink, “Simultaneous reconstruction of phase and amplitude contrast from a single holographic record,” Opt. Express 17(13), 10697–10705 (2009).
[Crossref] [PubMed]

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

H.-W. Fink, W. Stocker, and H. Schmid, “Holography with low-energy electrons,” Phys. Rev. Lett. 65(10), 1204–1206 (1990).
[Crossref] [PubMed]

H.-W. Fink, W. Stocker, and H. Schmid, “Coherent point-source electron-beams,” J. Vac. Sci. Technol. 8(6), 1323–1324 (1990).
[Crossref]

H.-W. Fink, “Point-source for ions and electrons,” Phys. Scr. 38(2), 260–263 (1988).
[Crossref]

Furrer, F.

G. W. Stroke, F. Furrer, and D. R. Lamberty, “Deblurring of motion-blurred photographs using extended-range holographic Fourier-transform division,” Opt. Commun. 1(3), 141–145 (1969).
[Crossref]

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. Lond. A Math. Phys. Sci. 197(1051), 454–487 (1949).
[Crossref]

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Gao, Z.

Germann, M.

M. Germann, T. Latychevskaia, C. Escher, and H.-W. Fink, “Pulsed electron holography,” Appl. Phys. Lett. 102(20), 203115 (2013).
[Crossref]

Guizar-Sicairos, M.

Hati, A.

A. Hati, C. W. Nelson, and D. A. Howe, “Vibration sensitivity of optical components: A survey,” Proceedings of the 2011 Joint IEEE International Frequency Control Symposium and European Frequency and Time Forum, 532–535 (2011).
[Crossref]

Hatzinakos, D.

D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. 13(3), 43–64 (1996).
[Crossref]

Howe, D. A.

A. Hati, C. W. Nelson, and D. A. Howe, “Vibration sensitivity of optical components: A survey,” Proceedings of the 2011 Joint IEEE International Frequency Control Symposium and European Frequency and Time Forum, 532–535 (2011).
[Crossref]

Hwang, I.-S.

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Jeng, H.-T.

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Jia, J.

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graph. 27(3), 73 (2008).
[Crossref]

Kern, K.

J.-N. Longchamp, S. Rauschenbach, S. Abb, C. Escher, T. Latychevskaia, K. Kern, and H.-W. Fink, “Imaging proteins at the single-molecule level,” Proc. Natl. Acad. Sci. U.S.A. 114(7), 1474–1479 (2017).
[Crossref] [PubMed]

Kirz, J.

J. W. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

Kravtsov, V.

M. Muller, V. Kravtsov, A. Paarmann, M. B. Raschke, and R. Ernstorfer, “Nanofocused plasmon-driven sub-10 fs electron point source,” ACS Photonics 3(4), 611–619 (2016).
[Crossref]

Kundur, D.

D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. 13(3), 43–64 (1996).
[Crossref]

Kuo, H.-S.

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Lamberty, D. R.

G. W. Stroke, F. Furrer, and D. R. Lamberty, “Deblurring of motion-blurred photographs using extended-range holographic Fourier-transform division,” Opt. Commun. 1(3), 141–145 (1969).
[Crossref]

Latychevskaia, T.

J.-N. Longchamp, S. Rauschenbach, S. Abb, C. Escher, T. Latychevskaia, K. Kern, and H.-W. Fink, “Imaging proteins at the single-molecule level,” Proc. Natl. Acad. Sci. U.S.A. 114(7), 1474–1479 (2017).
[Crossref] [PubMed]

T. Latychevskaia and H.-W. Fink, “Inverted Gabor holography principle for tailoring arbitrary shaped three-dimensional beams,” Sci. Rep. 6(1), 26312 (2016).
[Crossref] [PubMed]

T. Latychevskaia and H.-W. Fink, “Practical algorithms for simulation and reconstruction of digital in-line holograms,” Appl. Opt. 54(9), 2424–2434 (2015).
[Crossref] [PubMed]

T. Latychevskaia, J.-N. Longchamp, C. Escher, and H.-W. Fink, “On artefact-free reconstruction of low-energy (30-250eV) electron holograms,” Ultramicroscopy 145, 22–27 (2014).
[Crossref] [PubMed]

M. Germann, T. Latychevskaia, C. Escher, and H.-W. Fink, “Pulsed electron holography,” Appl. Phys. Lett. 102(20), 203115 (2013).
[Crossref]

T. Latychevskaia, J.-N. Longchamp, and H.-W. Fink, “When holography meets coherent diffraction imaging,” Opt. Express 20(27), 28871–28892 (2012).
[Crossref] [PubMed]

T. Latychevskaia and H.-W. Fink, “Simultaneous reconstruction of phase and amplitude contrast from a single holographic record,” Opt. Express 17(13), 10697–10705 (2009).
[Crossref] [PubMed]

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

Lee, S.

S. Cho and S. Lee, “Fast motion deblurring,” ACM Trans. Graph. 28(5), 145 (2009).
[Crossref]

Lee, T.-K.

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Li, G.

Lin, C.-Y.

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Liu, S.-C.

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Livadaru, L.

J. Y. Mutus, L. Livadaru, J. T. Robinson, R. Urban, M. H. Salomons, M. Cloutier, and R. A. Wolkow, “Low-energy electron point projection microscopy of suspended graphene, the ultimate microscope slide,” New J. Phys. 13(6), 063011 (2011).
[Crossref]

Lohmann, A.

Longchamp, J.-N.

J.-N. Longchamp, S. Rauschenbach, S. Abb, C. Escher, T. Latychevskaia, K. Kern, and H.-W. Fink, “Imaging proteins at the single-molecule level,” Proc. Natl. Acad. Sci. U.S.A. 114(7), 1474–1479 (2017).
[Crossref] [PubMed]

T. Latychevskaia, J.-N. Longchamp, C. Escher, and H.-W. Fink, “On artefact-free reconstruction of low-energy (30-250eV) electron holograms,” Ultramicroscopy 145, 22–27 (2014).
[Crossref] [PubMed]

T. Latychevskaia, J.-N. Longchamp, and H.-W. Fink, “When holography meets coherent diffraction imaging,” Opt. Express 20(27), 28871–28892 (2012).
[Crossref] [PubMed]

Lu, C.-H.

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Matsumoto, T.

T. Matsumoto, T. Tanji, and A. Tonomura, “Visualization of DNA in solution by Fraunhofer in-line electron holography. 2. Experiments,” Optik (Stuttg.) 100, 71–74 (1995).

Miao, J. W.

J. W. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

Milanfar, P.

S. Farsiu, M. D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe super resolution,” IEEE Trans. Image Process. 13(10), 1327–1344 (2004).
[Crossref] [PubMed]

Muller, M.

M. Muller, V. Kravtsov, A. Paarmann, M. B. Raschke, and R. Ernstorfer, “Nanofocused plasmon-driven sub-10 fs electron point source,” ACS Photonics 3(4), 611–619 (2016).
[Crossref]

Mutus, J. Y.

J. Y. Mutus, L. Livadaru, J. T. Robinson, R. Urban, M. H. Salomons, M. Cloutier, and R. A. Wolkow, “Low-energy electron point projection microscopy of suspended graphene, the ultimate microscope slide,” New J. Phys. 13(6), 063011 (2011).
[Crossref]

Nayar, S. K.

M. Ben-Ezra and S. K. Nayar, “Motion-based motion deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 689–698 (2004).
[Crossref] [PubMed]

Nelson, C. W.

A. Hati, C. W. Nelson, and D. A. Howe, “Vibration sensitivity of optical components: A survey,” Proceedings of the 2011 Joint IEEE International Frequency Control Symposium and European Frequency and Time Forum, 532–535 (2011).
[Crossref]

Paarmann, A.

M. Muller, V. Kravtsov, A. Paarmann, M. B. Raschke, and R. Ernstorfer, “Nanofocused plasmon-driven sub-10 fs electron point source,” ACS Photonics 3(4), 611–619 (2016).
[Crossref]

Raschke, M. B.

M. Muller, V. Kravtsov, A. Paarmann, M. B. Raschke, and R. Ernstorfer, “Nanofocused plasmon-driven sub-10 fs electron point source,” ACS Photonics 3(4), 611–619 (2016).
[Crossref]

Rauschenbach, S.

J.-N. Longchamp, S. Rauschenbach, S. Abb, C. Escher, T. Latychevskaia, K. Kern, and H.-W. Fink, “Imaging proteins at the single-molecule level,” Proc. Natl. Acad. Sci. U.S.A. 114(7), 1474–1479 (2017).
[Crossref] [PubMed]

Robinson, J. T.

J. Y. Mutus, L. Livadaru, J. T. Robinson, R. Urban, M. H. Salomons, M. Cloutier, and R. A. Wolkow, “Low-energy electron point projection microscopy of suspended graphene, the ultimate microscope slide,” New J. Phys. 13(6), 063011 (2011).
[Crossref]

Robinson, M. D.

S. Farsiu, M. D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe super resolution,” IEEE Trans. Image Process. 13(10), 1327–1344 (2004).
[Crossref] [PubMed]

Salomons, M. H.

J. Y. Mutus, L. Livadaru, J. T. Robinson, R. Urban, M. H. Salomons, M. Cloutier, and R. A. Wolkow, “Low-energy electron point projection microscopy of suspended graphene, the ultimate microscope slide,” New J. Phys. 13(6), 063011 (2011).
[Crossref]

Sayre, D.

J. W. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

Schmid, H.

H.-W. Fink, W. Stocker, and H. Schmid, “Coherent point-source electron-beams,” J. Vac. Sci. Technol. 8(6), 1323–1324 (1990).
[Crossref]

H.-W. Fink, W. Stocker, and H. Schmid, “Holography with low-energy electrons,” Phys. Rev. Lett. 65(10), 1204–1206 (1990).
[Crossref] [PubMed]

Shan, Q.

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graph. 27(3), 73 (2008).
[Crossref]

Shannon, C. E.

C. E. Shannon, “Communication in the presence of noise,” Proc. Inst. Radio Eng. 37, 10–21 (1949).

Stocker, W.

H.-W. Fink, W. Stocker, and H. Schmid, “Coherent point-source electron-beams,” J. Vac. Sci. Technol. 8(6), 1323–1324 (1990).
[Crossref]

H.-W. Fink, W. Stocker, and H. Schmid, “Holography with low-energy electrons,” Phys. Rev. Lett. 65(10), 1204–1206 (1990).
[Crossref] [PubMed]

Stroke, G. W.

G. W. Stroke, F. Furrer, and D. R. Lamberty, “Deblurring of motion-blurred photographs using extended-range holographic Fourier-transform division,” Opt. Commun. 1(3), 141–145 (1969).
[Crossref]

G. W. Stroke and R. G. Zech, “Photographic realization of an image-deconvolution filter for holographic Fourier-transform division,” Jpn. J. Appl. Phys. 7(7), 764–766 (1968).
[Crossref]

Tanji, T.

T. Matsumoto, T. Tanji, and A. Tonomura, “Visualization of DNA in solution by Fraunhofer in-line electron holography. 2. Experiments,” Optik (Stuttg.) 100, 71–74 (1995).

Thurman, S. T.

Tonomura, A.

T. Matsumoto, T. Tanji, and A. Tonomura, “Visualization of DNA in solution by Fraunhofer in-line electron holography. 2. Experiments,” Optik (Stuttg.) 100, 71–74 (1995).

Tsong, T. T.

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Urban, R.

J. Y. Mutus, L. Livadaru, J. T. Robinson, R. Urban, M. H. Salomons, M. Cloutier, and R. A. Wolkow, “Low-energy electron point projection microscopy of suspended graphene, the ultimate microscope slide,” New J. Phys. 13(6), 063011 (2011).
[Crossref]

Wang, S.

Wolkow, R. A.

J. Y. Mutus, L. Livadaru, J. T. Robinson, R. Urban, M. H. Salomons, M. Cloutier, and R. A. Wolkow, “Low-energy electron point projection microscopy of suspended graphene, the ultimate microscope slide,” New J. Phys. 13(6), 063011 (2011).
[Crossref]

Zech, R. G.

G. W. Stroke and R. G. Zech, “Photographic realization of an image-deconvolution filter for holographic Fourier-transform division,” Jpn. J. Appl. Phys. 7(7), 764–766 (1968).
[Crossref]

ACM Trans. Graph. (2)

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graph. 27(3), 73 (2008).
[Crossref]

S. Cho and S. Lee, “Fast motion deblurring,” ACM Trans. Graph. 28(5), 145 (2009).
[Crossref]

ACS Photonics (1)

M. Muller, V. Kravtsov, A. Paarmann, M. B. Raschke, and R. Ernstorfer, “Nanofocused plasmon-driven sub-10 fs electron point source,” ACS Photonics 3(4), 611–619 (2016).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Germann, T. Latychevskaia, C. Escher, and H.-W. Fink, “Pulsed electron holography,” Appl. Phys. Lett. 102(20), 203115 (2013).
[Crossref]

IEEE Signal Process. Mag. (1)

D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. 13(3), 43–64 (1996).
[Crossref]

IEEE Trans. Image Process. (1)

S. Farsiu, M. D. Robinson, M. Elad, and P. Milanfar, “Fast and robust multiframe super resolution,” IEEE Trans. Image Process. 13(10), 1327–1344 (2004).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

M. Ben-Ezra and S. K. Nayar, “Motion-based motion deblurring,” IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 689–698 (2004).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

J. Vac. Sci. Technol. (1)

H.-W. Fink, W. Stocker, and H. Schmid, “Coherent point-source electron-beams,” J. Vac. Sci. Technol. 8(6), 1323–1324 (1990).
[Crossref]

Jpn. J. Appl. Phys. (1)

G. W. Stroke and R. G. Zech, “Photographic realization of an image-deconvolution filter for holographic Fourier-transform division,” Jpn. J. Appl. Phys. 7(7), 764–766 (1968).
[Crossref]

Nature (2)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

J. W. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

New J. Phys. (2)

J. Y. Mutus, L. Livadaru, J. T. Robinson, R. Urban, M. H. Salomons, M. Cloutier, and R. A. Wolkow, “Low-energy electron point projection microscopy of suspended graphene, the ultimate microscope slide,” New J. Phys. 13(6), 063011 (2011).
[Crossref]

I.-S. Hwang, C.-C. Chang, C.-H. Lu, S.-C. Liu, Y.-C. Chang, T.-K. Lee, H.-T. Jeng, H.-S. Kuo, C.-Y. Lin, C.-S. Chang, and T. T. Tsong, “Investigation of single-walled carbon nanotubes with a low-energy electron point projection microscope,” New J. Phys. 15(4), 043015 (2013).
[Crossref]

Opt. Commun. (1)

G. W. Stroke, F. Furrer, and D. R. Lamberty, “Deblurring of motion-blurred photographs using extended-range holographic Fourier-transform division,” Opt. Commun. 1(3), 141–145 (1969).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Optik (Stuttg.) (1)

T. Matsumoto, T. Tanji, and A. Tonomura, “Visualization of DNA in solution by Fraunhofer in-line electron holography. 2. Experiments,” Optik (Stuttg.) 100, 71–74 (1995).

Phys. Rev. Lett. (2)

H.-W. Fink, W. Stocker, and H. Schmid, “Holography with low-energy electrons,” Phys. Rev. Lett. 65(10), 1204–1206 (1990).
[Crossref] [PubMed]

T. Latychevskaia and H.-W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98(23), 233901 (2007).
[Crossref] [PubMed]

Phys. Scr. (1)

H.-W. Fink, “Point-source for ions and electrons,” Phys. Scr. 38(2), 260–263 (1988).
[Crossref]

Proc. Inst. Radio Eng. (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. Inst. Radio Eng. 37, 10–21 (1949).

Proc. Natl. Acad. Sci. U.S.A. (1)

J.-N. Longchamp, S. Rauschenbach, S. Abb, C. Escher, T. Latychevskaia, K. Kern, and H.-W. Fink, “Imaging proteins at the single-molecule level,” Proc. Natl. Acad. Sci. U.S.A. 114(7), 1474–1479 (2017).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

D. Gabor, “Microscopy by reconstructed wave-fronts,” Proc. R. Soc. Lond. A Math. Phys. Sci. 197(1051), 454–487 (1949).
[Crossref]

Sci. Rep. (1)

T. Latychevskaia and H.-W. Fink, “Inverted Gabor holography principle for tailoring arbitrary shaped three-dimensional beams,” Sci. Rep. 6(1), 26312 (2016).
[Crossref] [PubMed]

Ultramicroscopy (1)

T. Latychevskaia, J.-N. Longchamp, C. Escher, and H.-W. Fink, “On artefact-free reconstruction of low-energy (30-250eV) electron holograms,” Ultramicroscopy 145, 22–27 (2014).
[Crossref] [PubMed]

Other (3)

V. A. Kotelnikov, “On the transmission capacity of “ether” and wire in electrocommunications,” Proc. 1st All-Union Conf. Technological Reconstruction of the Commun. Sector and Low-Current Eng., 1–19 (1933).

A. Hati, C. W. Nelson, and D. A. Howe, “Vibration sensitivity of optical components: A survey,” Proceedings of the 2011 Joint IEEE International Frequency Control Symposium and European Frequency and Time Forum, 532–535 (2011).
[Crossref]

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

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Figures (7)

Fig. 1
Fig. 1 Simulated example of vibration compensation in an in-line hologram. (a) Sketch of the experimental arrangement. (b) Test object consisting of three sets of bars exhibiting widths and gaps between them of 10 μm, 20 μm and 40 μm. (c) In-line hologram simulated for a plane wave of wavelength λ=500nm, sample-to-detector distance 40 mm, sampled with 512 × 512 pixels, pixel size 10 × 10 μm2. (d) Amplitude of the object reconstructed from the hologram shown in (c). (e) Hologram obtained by superposition of 10000 shifted holograms, the shifts are Gaussian distributed with a standard deviation of σ=10μm (corresponding to 1 pixel). (f) Amplitude of the object reconstructed from the hologram shown in (d). (g) Deblurred hologram obtained by deconvolution of the hologram shown in (e) with the G( x,y ) function with σ=10μm. (h) Amplitude of the object reconstructed from the hologram shown in (g). (i) Hologram obtained by superposition of 10000 shifted holograms, the shifts are Gaussian distributed with a standard deviation of σ=20μm (2 pixel). (j) Amplitude of the object reconstructed from the hologram in (i). (k) Deblurred hologram obtained by deconvolution of the hologram (i) with the G( x,y ) function with σ=20μm. (l) Amplitude of the object reconstructed from the hologram in (k). (m) Radial averaged amplitude of the Fourier spectra (calculated as | FT(o) | f where ... f denotes averaging over frequenciesf) of the object reconstructed from the original, the blurred and deblurred holograms. The cut-off frequencies are calculated with Eq. (11) for a resolution of 20 μm, 40 μm and 60 μm. They amount to: 0.314 μm−1, 0.157 μm−1 and 0.105 μm−1 correspondingly and are marked in the spectra.
Fig. 2
Fig. 2 Deblurring with tuning the deblurring parameter σ. (a) In-line hologram simulated for a plane wave of wavelength λ=500nm, sample-to-detector distance 40 mm, sampled with 512 × 512 pixels, pixel size 10 × 10 μm2. The blurred hologram is obtained by a superposition of 10000 shifted holograms, the shifts are Gaussian distributed with a standard deviation of σ=10μm (corresponding to 1 pixel). (b) Amplitude of the object reconstructed from the hologram shown in (d). The next images are shown in pairs, left: deblurred hologram and right: amplitude of the reconstructed object. (c) – (d) σ=2.5 μm, (e) – (f) σ=5 μm, (g) – (h) σ=7.5 μm, (i) – (j) σ=10 μm, (k) – (l) σ=12.5 μm, (m) – (n) σ=15 μm, (o) – (p) σ=17.5 μm.
Fig. 3
Fig. 3 Simulated example of axial vibration compensation in an in-line hologram. (a) In-line hologram simulated for a plane wave of wavelength λ=500nm, sample-to-detector distance 40 mm, sampled with 512 × 512 pixels, pixel size 10 × 10 μm2. The hologram is obtained by superposition of 10000 holograms of a z-shifted object, the shifts are Gaussian distributed with a standard deviation of σ=2mm (2 pixel). (b) Amplitude of the object reconstructed from the hologram in (b). (c) Hologram obtained by deconvolution of the hologram in (a) with a G( x,y ) function with σ=14μm. (d) Amplitude of the object reconstructed from the hologram in (c).
Fig. 4
Fig. 4 Simulated example of a hologram blurred by a directional motion. (a) In-line hologram simulated for a plane wave of wavelength λ=500nm, sample-to-detector distance 40 mm, sampled with 512 × 512 pixels, pixel size 10 × 10 μm2. The blurred hologram is obtained by the superposition of 10 holograms that were shifted horizontally at a step of 10 μm, the motion path is shown in (b). (c) Amplitude of the object reconstructed from the blurred hologram shown in (a). (d) Hologram obtained by deblurring of the hologram shown in (a). (e) Amplitude of the object reconstructed from the deblurred hologram shown in (d).
Fig. 5
Fig. 5 Light optical hologram of a tungsten tip with a structure milled with a focused ion beam. (a) Sketch of the experimental arrangement. (b) Scanning electron micrograph of the micro-structured tip. (c) Light optical in-line hologram recorded with a divergent wave. The parameters for the hologram acquisition are: the source-to-detector distance is 5cm, the hologram size is 30 × 30 mm2 and sampled with 1000 × 1000 pixels, wavelength = 532 nm, the source-to-sample distance is obtained during reconstruction as the distance where the object appears in focus and it amounts to 257 μm. The hologram was normalized by division with the background image, that is obtained under the very same conditions but without the object being present [21-22]. (d) Hologram after deblurring with G( x,y ) with σ=1 μm as described by Eq. (8). (e) Object reconstructed from the original hologram and (f) from deblurred hologram. (g) Radial profile of the amplitude of the spectrum of the objects reconstructed from the two holograms. (h) Profiles along the colored arrows in the two reconstructions.
Fig. 6
Fig. 6 Low-energy electron hologram of a bundle of single-walled nano-tubes (SWNT). (a) Sketch of the experimental setup. (b) Hologram recorded with electrons of 220 eV kinetic energy (wavelength = 0.08 nm). The other parameters of the acquisition are: the source-to-detector distance is 180 mm, the hologram is 26 × 26 mm2 and it is sampled with 1000 × 1000 pixels, the source-to-sample distance is obtained during the reconstruction as the distance where the object appears in focus and amounts to 3.4 μm. The hologram was normalized by division of the original hologram with background image, which was obtained by surface fitting of the patches of the intensity distribution that are free from interference pattern. (c) Hologram (a) after deblurring with G( x,y ) with σ=1.5 nm as described by Eq. (8). (d) and (e) a magnified region in holograms (b) and (c), respectively. (f) Radial profiles of the amplitude of the spectrum of the objects reconstructed from the two holograms. (g) SWNT reconstructed (left) from the original hologram and (right) from deblurred hologram.
Fig. 7
Fig. 7 Enhancement of a low-energy electron hologram of a BSA protein which was previously published [32]. (a) Sketch of the experimental setup. (b) Hologram recorded with electrons of 62 eV kinetic energy (wavelength = 0.16 nm) at the source-to-detector distance of 70 mm, the source-to-sample distance is obtained during the reconstruction as the distance where the object appears in focus and amounts to 250 nm. (c) Hologram after deblurring with G( x,y ) with σ=1.8 nm as described by Eq. (8). (d) and (e) BSA reconstructed (left) from the original hologram and (right) from deblurred hologram.

Equations (14)

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H 0 (X+ΔX,Y+ΔY)= H 0 (X,Y)δ(X+ΔX,Y+ΔY),
H(X,Y)= H 0 (X,Y) i δ(X+Δ X i ,Y+Δ Y i ) .
V( X,Y )= i [ δ(Δ X i ,Δ Y i ) ] .
H(X,Y)= H 0 (X,Y)V( X,Y ).
H 0 (X,Y)= FT -1 { FT[ H(X,Y) ] FT[ V(X,Y) ] } FT -1 { ( FT[ H(X,Y) ] | FT[ V(X,Y) ] | 2 +β ) ( FT[ V(X,Y) ] ) * }
D( μ,ν )= 1 FT[ V(X,Y) ]
u( μ,ν )= U( X,Y )exp[ i( Xμ+Yν ) ] dXdY.
V( x,y )=G( x,y )=exp( x 2 + y 2 2 σ 2 ).
R NA = λ 2NA = λ 2sinϑ λ 2tanϑ = λz S ,
R S =2 Δ 0 .
R f = 2π f max .
( f max ) max = Δ f N 2 = 2π N Δ 0 N 2 = π Δ 0 ,
( R f ) max = 2π ( f max ) max =2 Δ 0 .
H(X,Y)= i H 0 ( M i X, M i Y ) .

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