Abstract

The longitudinal coherence properties of self-amplifiedspontaneous-emission x-ray free electron lasers limit the resolution of single-particle diffraction imaging. We found that for the Linac Coherent Light Source (LCLS) at a wavelength of 1.5 Å the particles have to be smaller than 500 nm in diameter to achieve atomic-resolution imaging with a resolution length of less than 2 Å, suggesting that the longitudinal coherence is sufficient for imaging most biomolecular samples of interest.

©2008 Optical Society of America

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References

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  1. R. Neutze et al., “Potential for biomolecular imaging with femtosecond X-ray pulses,” Nature 406, 752–757 (2000).
    [Crossref] [PubMed]
  2. A. Kondratenko and E. Saldin, “Generation of coherent radiation by a relativistic electron beam in an ondulator,” Part. Accel. 10, 207–216 (1980).
  3. Y. Derbenev, A. Kondratenko, and E. Saldin, “On the possibility of using a free electron laser for polarization of electrons in storage rings,” Nucl. Instrum. Methods Phys. Res. 193, 415–421 (1982).
    [Crossref]
  4. R. Bonifacio, C. Pellegrini, and L. Narducci, “Collective instabilities and high-gain regime in a free electron laser,” Opt. Commun. 50, 373–378 (1984).
    [Crossref]
  5. Linac Coherent Light Source (LCLS) Design Study Report, SLAC-R-521, 1998, available from the National Technical Information Services, 5285 Port Royal Road, Springfield, Virginia, 22161.
  6. E. Saldin, E. Schneidmiller, and M. Yurkov, “Statistical properties of radiation from VUV and x-ray free electron laser,” Opt. Commun. 148, 383–403 (1998).
    [Crossref]
  7. Z. Huang and K.-J. Kim, “Review of x-ray free-electron laser theory,” Phys. Rev. ST Accel. Beams 10, 034801 (2007).
    [Crossref]
  8. Z. Huang, private communication.
  9. J. Miao et al., “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
    [Crossref]
  10. V. Ayvazyan et al., “First operation of a free-electron laser generating GWpower radiation at 32 nm wavelength,” Eur. Phys. J. D 37, 297–303 (2006).
    [Crossref]
  11. H. N. Chapman et al., “Femtosecond diffractive imaging with a soft-X-ray free-electron laser,” Nature Phys. 2, 839–843 (2006).
    [Crossref]
  12. S. P. Hau-Riege et al., “Pulse requirements for x-ray diffraction imaging of single biological molecules,” Phys. Rev. E 71, 0619191 (2005).
    [Crossref]
  13. A. Szoke, “Diffraction of partially coherent x-rays and the crystallographic phase problem,” Acta Cryst. A 57, 586–603 (2001).
    [Crossref]
  14. Y. Li, et al., “Characterization of a chaotic optical field using a high-gain, self-amplified free electron laser,” Phys. Rev. Lett. 91, 243602 (2003).
    [Crossref] [PubMed]
  15. H. M. Berman et al., “The Protein Data Bank,” Nucl. Acids Res. 28, 235–242 (2000).
    [Crossref]
  16. J. C. H. Spence, et al., “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Cryst. A A61, 237–245 (2005).
    [Crossref]

2007 (1)

Z. Huang and K.-J. Kim, “Review of x-ray free-electron laser theory,” Phys. Rev. ST Accel. Beams 10, 034801 (2007).
[Crossref]

2006 (2)

V. Ayvazyan et al., “First operation of a free-electron laser generating GWpower radiation at 32 nm wavelength,” Eur. Phys. J. D 37, 297–303 (2006).
[Crossref]

H. N. Chapman et al., “Femtosecond diffractive imaging with a soft-X-ray free-electron laser,” Nature Phys. 2, 839–843 (2006).
[Crossref]

2005 (2)

S. P. Hau-Riege et al., “Pulse requirements for x-ray diffraction imaging of single biological molecules,” Phys. Rev. E 71, 0619191 (2005).
[Crossref]

J. C. H. Spence, et al., “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Cryst. A A61, 237–245 (2005).
[Crossref]

2003 (1)

Y. Li, et al., “Characterization of a chaotic optical field using a high-gain, self-amplified free electron laser,” Phys. Rev. Lett. 91, 243602 (2003).
[Crossref] [PubMed]

2001 (1)

A. Szoke, “Diffraction of partially coherent x-rays and the crystallographic phase problem,” Acta Cryst. A 57, 586–603 (2001).
[Crossref]

2000 (2)

R. Neutze et al., “Potential for biomolecular imaging with femtosecond X-ray pulses,” Nature 406, 752–757 (2000).
[Crossref] [PubMed]

H. M. Berman et al., “The Protein Data Bank,” Nucl. Acids Res. 28, 235–242 (2000).
[Crossref]

1999 (1)

J. Miao et al., “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

1998 (1)

E. Saldin, E. Schneidmiller, and M. Yurkov, “Statistical properties of radiation from VUV and x-ray free electron laser,” Opt. Commun. 148, 383–403 (1998).
[Crossref]

1984 (1)

R. Bonifacio, C. Pellegrini, and L. Narducci, “Collective instabilities and high-gain regime in a free electron laser,” Opt. Commun. 50, 373–378 (1984).
[Crossref]

1982 (1)

Y. Derbenev, A. Kondratenko, and E. Saldin, “On the possibility of using a free electron laser for polarization of electrons in storage rings,” Nucl. Instrum. Methods Phys. Res. 193, 415–421 (1982).
[Crossref]

1980 (1)

A. Kondratenko and E. Saldin, “Generation of coherent radiation by a relativistic electron beam in an ondulator,” Part. Accel. 10, 207–216 (1980).

Ayvazyan, V.

V. Ayvazyan et al., “First operation of a free-electron laser generating GWpower radiation at 32 nm wavelength,” Eur. Phys. J. D 37, 297–303 (2006).
[Crossref]

Berman, H. M.

H. M. Berman et al., “The Protein Data Bank,” Nucl. Acids Res. 28, 235–242 (2000).
[Crossref]

Bonifacio, R.

R. Bonifacio, C. Pellegrini, and L. Narducci, “Collective instabilities and high-gain regime in a free electron laser,” Opt. Commun. 50, 373–378 (1984).
[Crossref]

Chapman, H. N.

H. N. Chapman et al., “Femtosecond diffractive imaging with a soft-X-ray free-electron laser,” Nature Phys. 2, 839–843 (2006).
[Crossref]

Derbenev, Y.

Y. Derbenev, A. Kondratenko, and E. Saldin, “On the possibility of using a free electron laser for polarization of electrons in storage rings,” Nucl. Instrum. Methods Phys. Res. 193, 415–421 (1982).
[Crossref]

Hau-Riege, S. P.

S. P. Hau-Riege et al., “Pulse requirements for x-ray diffraction imaging of single biological molecules,” Phys. Rev. E 71, 0619191 (2005).
[Crossref]

Huang, Z.

Z. Huang and K.-J. Kim, “Review of x-ray free-electron laser theory,” Phys. Rev. ST Accel. Beams 10, 034801 (2007).
[Crossref]

Z. Huang, private communication.

Kim, K.-J.

Z. Huang and K.-J. Kim, “Review of x-ray free-electron laser theory,” Phys. Rev. ST Accel. Beams 10, 034801 (2007).
[Crossref]

Kondratenko, A.

Y. Derbenev, A. Kondratenko, and E. Saldin, “On the possibility of using a free electron laser for polarization of electrons in storage rings,” Nucl. Instrum. Methods Phys. Res. 193, 415–421 (1982).
[Crossref]

A. Kondratenko and E. Saldin, “Generation of coherent radiation by a relativistic electron beam in an ondulator,” Part. Accel. 10, 207–216 (1980).

Li, Y.

Y. Li, et al., “Characterization of a chaotic optical field using a high-gain, self-amplified free electron laser,” Phys. Rev. Lett. 91, 243602 (2003).
[Crossref] [PubMed]

Miao, J.

J. Miao et al., “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Narducci, L.

R. Bonifacio, C. Pellegrini, and L. Narducci, “Collective instabilities and high-gain regime in a free electron laser,” Opt. Commun. 50, 373–378 (1984).
[Crossref]

Neutze, R.

R. Neutze et al., “Potential for biomolecular imaging with femtosecond X-ray pulses,” Nature 406, 752–757 (2000).
[Crossref] [PubMed]

Pellegrini, C.

R. Bonifacio, C. Pellegrini, and L. Narducci, “Collective instabilities and high-gain regime in a free electron laser,” Opt. Commun. 50, 373–378 (1984).
[Crossref]

Saldin, E.

E. Saldin, E. Schneidmiller, and M. Yurkov, “Statistical properties of radiation from VUV and x-ray free electron laser,” Opt. Commun. 148, 383–403 (1998).
[Crossref]

Y. Derbenev, A. Kondratenko, and E. Saldin, “On the possibility of using a free electron laser for polarization of electrons in storage rings,” Nucl. Instrum. Methods Phys. Res. 193, 415–421 (1982).
[Crossref]

A. Kondratenko and E. Saldin, “Generation of coherent radiation by a relativistic electron beam in an ondulator,” Part. Accel. 10, 207–216 (1980).

Schneidmiller, E.

E. Saldin, E. Schneidmiller, and M. Yurkov, “Statistical properties of radiation from VUV and x-ray free electron laser,” Opt. Commun. 148, 383–403 (1998).
[Crossref]

Spence, J. C. H.

J. C. H. Spence, et al., “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Cryst. A A61, 237–245 (2005).
[Crossref]

Szoke, A.

A. Szoke, “Diffraction of partially coherent x-rays and the crystallographic phase problem,” Acta Cryst. A 57, 586–603 (2001).
[Crossref]

Yurkov, M.

E. Saldin, E. Schneidmiller, and M. Yurkov, “Statistical properties of radiation from VUV and x-ray free electron laser,” Opt. Commun. 148, 383–403 (1998).
[Crossref]

Acta Cryst. A (2)

A. Szoke, “Diffraction of partially coherent x-rays and the crystallographic phase problem,” Acta Cryst. A 57, 586–603 (2001).
[Crossref]

J. C. H. Spence, et al., “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Cryst. A A61, 237–245 (2005).
[Crossref]

Eur. Phys. J. D (1)

V. Ayvazyan et al., “First operation of a free-electron laser generating GWpower radiation at 32 nm wavelength,” Eur. Phys. J. D 37, 297–303 (2006).
[Crossref]

Nature (2)

R. Neutze et al., “Potential for biomolecular imaging with femtosecond X-ray pulses,” Nature 406, 752–757 (2000).
[Crossref] [PubMed]

J. Miao et al., “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Nature Phys. (1)

H. N. Chapman et al., “Femtosecond diffractive imaging with a soft-X-ray free-electron laser,” Nature Phys. 2, 839–843 (2006).
[Crossref]

Nucl. Acids Res. (1)

H. M. Berman et al., “The Protein Data Bank,” Nucl. Acids Res. 28, 235–242 (2000).
[Crossref]

Nucl. Instrum. Methods Phys. Res. (1)

Y. Derbenev, A. Kondratenko, and E. Saldin, “On the possibility of using a free electron laser for polarization of electrons in storage rings,” Nucl. Instrum. Methods Phys. Res. 193, 415–421 (1982).
[Crossref]

Opt. Commun. (2)

R. Bonifacio, C. Pellegrini, and L. Narducci, “Collective instabilities and high-gain regime in a free electron laser,” Opt. Commun. 50, 373–378 (1984).
[Crossref]

E. Saldin, E. Schneidmiller, and M. Yurkov, “Statistical properties of radiation from VUV and x-ray free electron laser,” Opt. Commun. 148, 383–403 (1998).
[Crossref]

Part. Accel. (1)

A. Kondratenko and E. Saldin, “Generation of coherent radiation by a relativistic electron beam in an ondulator,” Part. Accel. 10, 207–216 (1980).

Phys. Rev. E (1)

S. P. Hau-Riege et al., “Pulse requirements for x-ray diffraction imaging of single biological molecules,” Phys. Rev. E 71, 0619191 (2005).
[Crossref]

Phys. Rev. Lett. (1)

Y. Li, et al., “Characterization of a chaotic optical field using a high-gain, self-amplified free electron laser,” Phys. Rev. Lett. 91, 243602 (2003).
[Crossref] [PubMed]

Phys. Rev. ST Accel. Beams (1)

Z. Huang and K.-J. Kim, “Review of x-ray free-electron laser theory,” Phys. Rev. ST Accel. Beams 10, 034801 (2007).
[Crossref]

Other (2)

Z. Huang, private communication.

Linac Coherent Light Source (LCLS) Design Study Report, SLAC-R-521, 1998, available from the National Technical Information Services, 5285 Port Royal Road, Springfield, Virginia, 22161.

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Figures (2)

Fig. 1.
Fig. 1.

Sketch of the scattering geometry.

Fig. 2.
Fig. 2.

R factor as a function of the image resolution for different particle diameters. The different curves are labeled with the diameter in nm.

Equations (11)

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

δ d max λ ( t c c ) ,
d p ( ξ ) d ξ = a η ( a ξ ) 5 0 d ν ( 3 2 ( a ξ ) 2 + ( 1 ( a ξ ) 2 + ν 2 ) 2 ) 5 2 ,
E in ( t , r ) = E 0 σ 2 π e ( t r · k ω ) 2 4 σ 2 e i ( ω t r · k ) ,
dE rad ( t ) = r 0 ρ dV e ik R r R r cos ( ψ r ) E in ( t ret , a ) .
E rad ( t ) = V d E rad ( t )
r 0 e ik R 0 R 0 cos ( ψ 0 ) E 0 σ 2 π e i ω t 0 F ( q , t 0 )
F ( q , t 0 ) V ρ ( r ) e i r · q e ( t 0 r · q ω ) 2 4 σ 2 d V ,
R ( u m ) u < u m F 0 ( u ) u < u m F 0 ( u ) F 1 ( u ) u < u m F 1 ( u ) ,
ρ ( r ) = i = 1 N q i δ ( r r i ) ,
F ( q , t 0 ) = i = 1 N q i e i r i · q e ( t 0 r i · q ω ) 2 4 σ 2 .
R ( u m ) u < u m F 0 ( u ) u u < u m F 0 ( u ) u F 1 ( u ) u u < u m F 1 ( u ) u .

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