### Abstract

Two limiting-case algorithms have previously been proposed for holographically imaging atoms near surfaces using photoelectron diffraction data and other diffraction data associated with electron emission: (i) a phased sum of Fourier transforms of scanned-angle data taken at several energies from Barton, (ii) and a phased sum of Fourier transforms of scanned-energy data taken along several directions due to Tong et al. We first point out that both methods are equivalent three-dimensional transforms in the wave vector k of the emitted electron, differing only in the way they sample k-space. A continuum of different sampling densities in the direction and magnitude of k exists in such holography, spanning the two limits previously discussed. An additional variant on these methods involves using only a small cone of data in k-space for each transform. Using model diffraction calculations for localized electron emission (e.g., core photoelectron emission) from Cu(001) clusters, we have explored the full range of k-space sampling possible, and find that optimum image quality is expected for choices intermediate between the extreme limits of scanned-angle or scanned-energy. General rules for optimizing image quality for a given data-set range are also discussed, and used to evaluate the sampling choices made in some prior experimental studies.

Original language | English |
---|---|

Pages (from-to) | 535-546 |

Number of pages | 12 |

Journal | Surface Science |

Volume | 365 |

Issue number | 2 |

DOIs | |

Publication status | Published - 20 Sep 1996 |

Externally published | Yes |

### Fingerprint

### Keywords

- Angle resolved photoemission
- Copper
- Electron-solid interactions, scattering, diffraction
- Photoelectron diffraction
- Photoelectron holography
- Semi-empirical models and model calculations
- Single crystal surfaces

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Condensed Matter Physics
- Surfaces and Interfaces

### Cite this

*Surface Science*,

*365*(2), 535-546. https://doi.org/10.1016/0039-6028(96)00719-4

**Optimization of k-space sampling in atomic imaging by electron emission holography.** / Len, P. M.; Thevuthasan, S.; Kaduwela, A. P.; Van Hove, M. A.; Fadley, C. S.

Research output: Contribution to journal › Article

*Surface Science*, vol. 365, no. 2, pp. 535-546. https://doi.org/10.1016/0039-6028(96)00719-4

}

TY - JOUR

T1 - Optimization of k-space sampling in atomic imaging by electron emission holography

AU - Len, P. M.

AU - Thevuthasan, S.

AU - Kaduwela, A. P.

AU - Van Hove, M. A.

AU - Fadley, C. S.

PY - 1996/9/20

Y1 - 1996/9/20

N2 - Two limiting-case algorithms have previously been proposed for holographically imaging atoms near surfaces using photoelectron diffraction data and other diffraction data associated with electron emission: (i) a phased sum of Fourier transforms of scanned-angle data taken at several energies from Barton, (ii) and a phased sum of Fourier transforms of scanned-energy data taken along several directions due to Tong et al. We first point out that both methods are equivalent three-dimensional transforms in the wave vector k of the emitted electron, differing only in the way they sample k-space. A continuum of different sampling densities in the direction and magnitude of k exists in such holography, spanning the two limits previously discussed. An additional variant on these methods involves using only a small cone of data in k-space for each transform. Using model diffraction calculations for localized electron emission (e.g., core photoelectron emission) from Cu(001) clusters, we have explored the full range of k-space sampling possible, and find that optimum image quality is expected for choices intermediate between the extreme limits of scanned-angle or scanned-energy. General rules for optimizing image quality for a given data-set range are also discussed, and used to evaluate the sampling choices made in some prior experimental studies.

AB - Two limiting-case algorithms have previously been proposed for holographically imaging atoms near surfaces using photoelectron diffraction data and other diffraction data associated with electron emission: (i) a phased sum of Fourier transforms of scanned-angle data taken at several energies from Barton, (ii) and a phased sum of Fourier transforms of scanned-energy data taken along several directions due to Tong et al. We first point out that both methods are equivalent three-dimensional transforms in the wave vector k of the emitted electron, differing only in the way they sample k-space. A continuum of different sampling densities in the direction and magnitude of k exists in such holography, spanning the two limits previously discussed. An additional variant on these methods involves using only a small cone of data in k-space for each transform. Using model diffraction calculations for localized electron emission (e.g., core photoelectron emission) from Cu(001) clusters, we have explored the full range of k-space sampling possible, and find that optimum image quality is expected for choices intermediate between the extreme limits of scanned-angle or scanned-energy. General rules for optimizing image quality for a given data-set range are also discussed, and used to evaluate the sampling choices made in some prior experimental studies.

KW - Angle resolved photoemission

KW - Copper

KW - Electron-solid interactions, scattering, diffraction

KW - Photoelectron diffraction

KW - Photoelectron holography

KW - Semi-empirical models and model calculations

KW - Single crystal surfaces

UR - http://www.scopus.com/inward/record.url?scp=0030244247&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030244247&partnerID=8YFLogxK

U2 - 10.1016/0039-6028(96)00719-4

DO - 10.1016/0039-6028(96)00719-4

M3 - Article

VL - 365

SP - 535

EP - 546

JO - Surface Science

JF - Surface Science

SN - 0039-6028

IS - 2

ER -