### Abstract

We explore how phase and amplitude gradients, which are almost inevitable in a coherent illumination probe, affect the atomic reconstruction of an isolated molecule based on diffraction intensities. By modeling the probe as a defocused Gaussian source, we show that structural distortion can be introduced in the reconstructed object if plane-wave illumination is assumed in the diffraction phase-retrieval algorithm. For the plane-wave approximation, we conclude that the standard deviation σ_{d} describing the source width should be such that σ_{d} ∼ 10 R_{c}, where R_{c} is the nominal radius of the molecule. In a pulsed source, where diffraction data are obtained when the moving molecule is at an instantaneous location within the illumination window, the effects of wave front curvature can be reduced by defocusing the illumination. This improvement comes at the expense of a weaker diffraction signal. For the three-dimensional reconstruction of a molecule, diffraction patterns from many different orientations of identical molecules are required. Since phase-retrieval methods are inherently solving for the probe plus the molecule, irreproducibility of wave front curvature or molecule location within the probe will introduce additional degrees of freedom to the structure solution problem.

Original language | English (US) |
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Article number | 245401 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 78 |

Issue number | 24 |

DOIs | |

State | Published - Dec 1 2008 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*78*(24), [245401]. https://doi.org/10.1103/PhysRevB.78.245401

**Beam transit effects in single molecule coherent diffraction.** / Gibson, J. M.; Treacy, Michael.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 78, no. 24, 245401. https://doi.org/10.1103/PhysRevB.78.245401

}

TY - JOUR

T1 - Beam transit effects in single molecule coherent diffraction

AU - Gibson, J. M.

AU - Treacy, Michael

PY - 2008/12/1

Y1 - 2008/12/1

N2 - We explore how phase and amplitude gradients, which are almost inevitable in a coherent illumination probe, affect the atomic reconstruction of an isolated molecule based on diffraction intensities. By modeling the probe as a defocused Gaussian source, we show that structural distortion can be introduced in the reconstructed object if plane-wave illumination is assumed in the diffraction phase-retrieval algorithm. For the plane-wave approximation, we conclude that the standard deviation σd describing the source width should be such that σd ∼ 10 Rc, where Rc is the nominal radius of the molecule. In a pulsed source, where diffraction data are obtained when the moving molecule is at an instantaneous location within the illumination window, the effects of wave front curvature can be reduced by defocusing the illumination. This improvement comes at the expense of a weaker diffraction signal. For the three-dimensional reconstruction of a molecule, diffraction patterns from many different orientations of identical molecules are required. Since phase-retrieval methods are inherently solving for the probe plus the molecule, irreproducibility of wave front curvature or molecule location within the probe will introduce additional degrees of freedom to the structure solution problem.

AB - We explore how phase and amplitude gradients, which are almost inevitable in a coherent illumination probe, affect the atomic reconstruction of an isolated molecule based on diffraction intensities. By modeling the probe as a defocused Gaussian source, we show that structural distortion can be introduced in the reconstructed object if plane-wave illumination is assumed in the diffraction phase-retrieval algorithm. For the plane-wave approximation, we conclude that the standard deviation σd describing the source width should be such that σd ∼ 10 Rc, where Rc is the nominal radius of the molecule. In a pulsed source, where diffraction data are obtained when the moving molecule is at an instantaneous location within the illumination window, the effects of wave front curvature can be reduced by defocusing the illumination. This improvement comes at the expense of a weaker diffraction signal. For the three-dimensional reconstruction of a molecule, diffraction patterns from many different orientations of identical molecules are required. Since phase-retrieval methods are inherently solving for the probe plus the molecule, irreproducibility of wave front curvature or molecule location within the probe will introduce additional degrees of freedom to the structure solution problem.

UR - http://www.scopus.com/inward/record.url?scp=57749093314&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57749093314&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.78.245401

DO - 10.1103/PhysRevB.78.245401

M3 - Article

AN - SCOPUS:57749093314

VL - 78

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 24

M1 - 245401

ER -