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)

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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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