DAVIS: A direct algorithm for velocity-map imaging system

Harrison, G. R.; Vaughan, J. C.; Hidle, B.; Laurent, G. M.

doi:10.1063/1.5025057

Title: DAVIS: A direct algorithm for velocity-map imaging system

Abstract

Here, we report a direct (non-iterative) algorithm to reconstruct the three-dimensional (3D) momentum-space picture of any charged particles collected with a velocity-map imaging system from the two-dimensional (2D) projected image captured by a position-sensitive detector. The technique consists of fitting the measured image with the 2D projection of a model 3D velocity distribution defined by the physics of the light-matter interaction. The meaningful angle-correlated information is first extracted from the raw data by expanding the image with a complete set of Legendre polynomials. Both the particle’s angular and energy distributions are then directly retrieved from the expansion coefficients. The algorithm is simple, easy to implement, fast, and explicitly takes into account the pixelization effect in the measurement.

Authors:

^[1]; Vaughan, J. C. ^[1]; Hidle, B. ^[1];

^[1]

Auburn Univ., AL (United States)

Publication Date:: Tue May 15 00:00:00 EDT 2018

Research Org.:: Auburn Univ., AL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1540181

Grant/Contract Number:: SC0017984

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 148; Journal Issue: 19; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats


                    Harrison, G. R., Vaughan, J. C., Hidle, B., and Laurent, G. M. DAVIS: A direct algorithm for velocity-map imaging system.  United States: N. p., 2018. 
Web.  doi:10.1063/1.5025057.

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                    Harrison, G. R., Vaughan, J. C., Hidle, B., & Laurent, G. M. DAVIS: A direct algorithm for velocity-map imaging system.  United States.  https://doi.org/10.1063/1.5025057

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                    Harrison, G. R., Vaughan, J. C., Hidle, B., and Laurent, G. M. Tue .  
"DAVIS: A direct algorithm for velocity-map imaging system".  United States.  https://doi.org/10.1063/1.5025057.  https://www.osti.gov/servlets/purl/1540181.

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@article{osti_1540181,

  title        = {DAVIS: A direct algorithm for velocity-map imaging system},

  author       = {Harrison, G. R. and Vaughan, J. C. and Hidle, B. and Laurent, G. M.},

  abstractNote = {Here, we report a direct (non-iterative) algorithm to reconstruct the three-dimensional (3D) momentum-space picture of any charged particles collected with a velocity-map imaging system from the two-dimensional (2D) projected image captured by a position-sensitive detector. The technique consists of fitting the measured image with the 2D projection of a model 3D velocity distribution defined by the physics of the light-matter interaction. The meaningful angle-correlated information is first extracted from the raw data by expanding the image with a complete set of Legendre polynomials. Both the particle’s angular and energy distributions are then directly retrieved from the expansion coefficients. The algorithm is simple, easy to implement, fast, and explicitly takes into account the pixelization effect in the measurement.},

  doi          = {10.1063/1.5025057},

  journal      = {Journal of Chemical Physics},

  number       = 19,

  volume       = 148,

  place        = {United States},

  year         = {Tue May 15 00:00:00 EDT 2018},

  month        = {Tue May 15 00:00:00 EDT 2018}

}

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Cited by: 11 works

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Works referenced in this record:

Ion Imaging of the Photodissociation of OCS Near 217 and 230 nm
journal, November 1995

Sato, Yoshihiro; Matsumi, Yutaka; Kawasaki, Masahiro
The Journal of Physical Chemistry, Vol. 99, Issue 44
DOI: 10.1021/j100044a017

Attosecond pulse characterization
journal, January 2013

Laurent, G.; Cao, W.; Ben-Itzhak, I.
Optics Express, Vol. 21, Issue 14
DOI: 10.1364/oe.21.016914

An iterative procedure for the inversion of two-dimensional ion/photoelectron imaging experiments
journal, November 2001

Vrakking, Marc J. J.
Review of Scientific Instruments, Vol. 72, Issue 11
DOI: 10.1063/1.1406923

Fourier moment analysis of velocity-map ion images
journal, November 2002

Bass, Mark J.; Brouard, Mark; Clark, Andrew P.
The Journal of Chemical Physics, Vol. 117, Issue 19
DOI: 10.1063/1.1514978

Direct current slice imaging
journal, April 2003

Townsend, Dave; Minitti, Michael P.; Suits, Arthur G.
Review of Scientific Instruments, Vol. 74, Issue 4
DOI: 10.1063/1.1544053

The angular distribution of the 3p electrons and the partial cross section of the 3s electrons of argon from threshold to 70 eV
journal, January 1976

Houlgate, R. G.; West, J. B.; Codling, K.
Journal of Electron Spectroscopy and Related Phenomena, Vol. 9, Issue 2
DOI: 10.1016/0368-2048(76)81030-4

Deconvolving two-dimensional images of three-dimensional momentum trajectories
journal, August 2002

Zhao, K.; Colvin, T.; Hill, W. T.
Review of Scientific Instruments, Vol. 73, Issue 8
DOI: 10.1063/1.1493231

Charged particle velocity map image reconstruction with one-dimensional projections of spherical functions
journal, March 2013

Gerber, Thomas; Liu, Yuzhu; Knopp, Gregor
Review of Scientific Instruments, Vol. 84, Issue 3
DOI: 10.1063/1.4793404

Inverting ion images without Abel inversion: maximum entropy reconstruction of velocity maps
journal, January 2014

Dick, Bernhard
Phys. Chem. Chem. Phys., Vol. 16, Issue 2
DOI: 10.1039/c3cp53673d

Photoelectron imaging spectrometry: Principle and inversion method
journal, June 1996

Bordas, C.; Paulig, F.; Helm, H.
Review of Scientific Instruments, Vol. 67, Issue 6
DOI: 10.1063/1.1147044

Slice imaging and velocity mapping using a single field
journal, August 2006

Papadakis, Vassilios; Kitsopoulos, Theofanis N.
Review of Scientific Instruments, Vol. 77, Issue 8
DOI: 10.1063/1.2222084

Reconstruction of Abel-transformable images: The Gaussian basis-set expansion Abel transform method
journal, July 2002

Dribinski, Vladimir; Ossadtchi, Alexei; Mandelshtam, Vladimir A.
Review of Scientific Instruments, Vol. 73, Issue 7
DOI: 10.1063/1.1482156

Application of time-sliced ion velocity imaging to crossed molecular beam experiments
journal, April 2003

Lin, Jim J.; Zhou, Jingang; Shiu, Weicheng
Review of Scientific Instruments, Vol. 74, Issue 4
DOI: 10.1063/1.1561604

Slicing photofragment spatial distribution by laser sheet ionization
journal, July 1994

Tonokura, Kenichi; Suzuki, Toshinori
Chemical Physics Letters, Vol. 224, Issue 1-2
DOI: 10.1016/0009-2614(94)00533-8

Two‐dimensional imaging of state‐selected photodissociation products detected by multiphoton ionization
journal, July 1987

Chandler, David W.; Houston, Paul L.
The Journal of Chemical Physics, Vol. 87, Issue 2
DOI: 10.1063/1.453276

An algorithm for the Fourier-Bessel transform
journal, August 1981

Candel, S. M.
Computer Physics Communications, Vol. 23, Issue 4
DOI: 10.1016/0010-4655(81)90175-2

Two-dimensional charged particle image inversion using a polar basis function expansion
journal, November 2004

Garcia, Gustavo A.; Nahon, Laurent; Powis, Ivan
Review of Scientific Instruments, Vol. 75, Issue 11
DOI: 10.1063/1.1807578

Velocity map imaging of ions and electrons using electrostatic lenses: Application in photoelectron and photofragment ion imaging of molecular oxygen
journal, September 1997

Eppink, André T. J. B.; Parker, David H.
Review of Scientific Instruments, Vol. 68, Issue 9
DOI: 10.1063/1.1148310

Abel inversion using transform techniques
journal, May 1988

Montgomery Smith, L.; Keefer, Dennis R.; Sudharsanan, S. I.
Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 39, Issue 5
DOI: 10.1016/0022-4073(88)90101-X

Finite slice analysis (FINA)—A general reconstruction method for velocity mapped and time-sliced ion imaging
journal, July 2017

Thompson, J. O. F.; Amarasinghe, C.; Foley, C. D.
The Journal of Chemical Physics, Vol. 147, Issue 1
DOI: 10.1063/1.4979305

Thick-lens velocity-map imaging spectrometer with high resolution for high-energy charged particles
journal, May 2014

Kling, N. G.; Paul, D.; Gura, A.
Journal of Instrumentation, Vol. 9, Issue 05
DOI: 10.1088/1748-0221/9/05/p05005

Measurement of bipolar moments for photofragment angular correlations in ion imaging experiments
journal, November 2001

Nestorov, Vilen K.; Hinchliffe, Robert D.; Uberna, Radoslaw
The Journal of Chemical Physics, Vol. 115, Issue 17
DOI: 10.1063/1.1408914

Incorporating real time velocity map image reconstruction into closed-loop coherent control
journal, November 2014

Rallis, C. E.; Burwitz, T. G.; Andrews, P. R.
Review of Scientific Instruments, Vol. 85, Issue 11
DOI: 10.1063/1.4899267

Inversion of velocity map ion images using iterative regularization and cross validation
journal, March 2006

Renth, F.; Riedel, J.; Temps, F.
Review of Scientific Instruments, Vol. 77, Issue 3
DOI: 10.1063/1.2176056

Nonstationary noise effects in the Abel inversion
journal, January 1988

Smith, L. M.
IEEE Transactions on Information Theory, Vol. 34, Issue 1
DOI: 10.1109/18.2619

Slice imaging: A new approach to ion imaging and velocity mapping
journal, October 2001

Gebhardt, Christoph R.; Rakitzis, T. Peter; Samartzis, Peter C.
Review of Scientific Instruments, Vol. 72, Issue 10
DOI: 10.1063/1.1403010

A “circularisation” method to repair deformations and determine the centre of velocity map images
journal, July 2017

Gascooke, Jason R.; Gibson, Stephen T.; Lawrance, Warren D.
The Journal of Chemical Physics, Vol. 147, Issue 1
DOI: 10.1063/1.4981024

Time-resolved photoelectron imaging of excited state relaxation dynamics in phenol, catechol, resorcinol, and hydroquinone
journal, November 2012

Livingstone, Ruth A.; Thompson, James O. F.; Iljina, Marija
The Journal of Chemical Physics, Vol. 137, Issue 18
DOI: 10.1063/1.4765104

Imaging of charged atomic reaction products: Inversion by a two-dimensional regularization method
journal, June 1999

Winterhalter, J.; Maier, D.; Honerkamp, J.
The Journal of Chemical Physics, Vol. 110, Issue 23
DOI: 10.1063/1.479060

Photofragment image analysis via pattern recognition
journal, July 2004

Manzhos, Sergei; Loock, Hans-Peter
Review of Scientific Instruments, Vol. 75, Issue 7
DOI: 10.1063/1.1764612

Angular distributions for the inelastic scattering of NO(X2Π) with O ₂ (X3Σg−)
journal, May 2017

Brouard, M.; Gordon, S. D. S.; Nichols, B.
The Journal of Chemical Physics, Vol. 146, Issue 20
DOI: 10.1063/1.4983706

Attosecond control of electron emission from atoms
journal, April 2014

Laurent, G.; Cao, W.; Ben-Itzhak, I.
Journal of Physics: Conference Series, Vol. 488, Issue 1
DOI: 10.1088/1742-6596/488/1/012008

P HOTOELECTRON A NGULAR D ISTRIBUTIONS
journal, October 2003

Reid, Katharine L.
Annual Review of Physical Chemistry, Vol. 54, Issue 1
DOI: 10.1146/annurev.physchem.54.011002.103814

Toward real-time charged-particle image reconstruction using polar onion-peeling
journal, May 2009

Roberts, G. M.; Nixon, J. L.; Lecointre, J.
Review of Scientific Instruments, Vol. 80, Issue 5
DOI: 10.1063/1.3126527

Abel inversion using transform techniques
conference, January 1987

Keefer, Dennis R.; Smith, L. Montgomery; Sudharsanan, S. I.
ICALEO® ‘86: Proceedings of the Flow & Particles Diagnostics Conference, International Congress on Applications of Lasers & Electro-Optics
DOI: 10.2351/1.5057809

Works referencing / citing this record:

MELEXIR: maximum entropy Legendre expanded image reconstruction. A fast and efficient method for the analysis of velocity map imaging or photoelectron imaging data
journal, January 2019

Dick, Bernhard
Physical Chemistry Chemical Physics, Vol. 21, Issue 35
DOI: 10.1039/c9cp03353j

Erratum: “DAVIS: A direct algorithm for velocity-map imaging system” [J. Chem. Phys. 148, 194101 (2018)]
journal, September 2018

Harrison, G. R.; Vaughan, J. C.; Hidle, B.
The Journal of Chemical Physics, Vol. 149, Issue 12
DOI: 10.1063/1.5055385

A direct comparison of high-speed methods for the numerical Abel transform
journal, June 2019

Hickstein, Daniel D.; Gibson, Stephen T.; Yurchak, Roman
Review of Scientific Instruments, Vol. 90, Issue 6
DOI: 10.1063/1.5092635

A direct comparison of high-speed methods for the numerical Abel transform
text, January 2019

Hickstein, Daniel D.; Gibson, Stephen T.; Yurchak, Roman
arXiv
DOI: 10.48550/arxiv.1902.09007

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Title: DAVIS: A direct algorithm for velocity-map imaging system

Abstract

Citation Formats

Ion Imaging of the Photodissociation of OCS Near 217 and 230 nm journal, November 1995

Attosecond pulse characterization journal, January 2013

An iterative procedure for the inversion of two-dimensional ion/photoelectron imaging experiments journal, November 2001

Fourier moment analysis of velocity-map ion images journal, November 2002

Direct current slice imaging journal, April 2003

The angular distribution of the 3p electrons and the partial cross section of the 3s electrons of argon from threshold to 70 eV journal, January 1976

Deconvolving two-dimensional images of three-dimensional momentum trajectories journal, August 2002

Charged particle velocity map image reconstruction with one-dimensional projections of spherical functions journal, March 2013

Inverting ion images without Abel inversion: maximum entropy reconstruction of velocity maps journal, January 2014

Photoelectron imaging spectrometry: Principle and inversion method journal, June 1996

Slice imaging and velocity mapping using a single field journal, August 2006

Reconstruction of Abel-transformable images: The Gaussian basis-set expansion Abel transform method journal, July 2002

Application of time-sliced ion velocity imaging to crossed molecular beam experiments journal, April 2003

Slicing photofragment spatial distribution by laser sheet ionization journal, July 1994

Two‐dimensional imaging of state‐selected photodissociation products detected by multiphoton ionization journal, July 1987

An algorithm for the Fourier-Bessel transform journal, August 1981

Two-dimensional charged particle image inversion using a polar basis function expansion journal, November 2004

Velocity map imaging of ions and electrons using electrostatic lenses: Application in photoelectron and photofragment ion imaging of molecular oxygen journal, September 1997

Abel inversion using transform techniques journal, May 1988

Finite slice analysis (FINA)—A general reconstruction method for velocity mapped and time-sliced ion imaging journal, July 2017

Thick-lens velocity-map imaging spectrometer with high resolution for high-energy charged particles journal, May 2014

Measurement of bipolar moments for photofragment angular correlations in ion imaging experiments journal, November 2001

Incorporating real time velocity map image reconstruction into closed-loop coherent control journal, November 2014

Inversion of velocity map ion images using iterative regularization and cross validation journal, March 2006

Nonstationary noise effects in the Abel inversion journal, January 1988

Slice imaging: A new approach to ion imaging and velocity mapping journal, October 2001

A “circularisation” method to repair deformations and determine the centre of velocity map images journal, July 2017

Time-resolved photoelectron imaging of excited state relaxation dynamics in phenol, catechol, resorcinol, and hydroquinone journal, November 2012

Imaging of charged atomic reaction products: Inversion by a two-dimensional regularization method journal, June 1999

Photofragment image analysis via pattern recognition journal, July 2004

Angular distributions for the inelastic scattering of NO(X2Π) with O 2 (X3Σg−) journal, May 2017

Attosecond control of electron emission from atoms journal, April 2014

P HOTOELECTRON A NGULAR D ISTRIBUTIONS journal, October 2003

Toward real-time charged-particle image reconstruction using polar onion-peeling journal, May 2009

Abel inversion using transform techniques conference, January 1987

MELEXIR: maximum entropy Legendre expanded image reconstruction. A fast and efficient method for the analysis of velocity map imaging or photoelectron imaging data journal, January 2019

Erratum: “DAVIS: A direct algorithm for velocity-map imaging system” [J. Chem. Phys. 148, 194101 (2018)] journal, September 2018

A direct comparison of high-speed methods for the numerical Abel transform journal, June 2019

A direct comparison of high-speed methods for the numerical Abel transform text, January 2019

Ion Imaging of the Photodissociation of OCS Near 217 and 230 nm
journal, November 1995

Attosecond pulse characterization
journal, January 2013

An iterative procedure for the inversion of two-dimensional ion/photoelectron imaging experiments
journal, November 2001

Fourier moment analysis of velocity-map ion images
journal, November 2002

Direct current slice imaging
journal, April 2003

The angular distribution of the 3p electrons and the partial cross section of the 3s electrons of argon from threshold to 70 eV
journal, January 1976

Deconvolving two-dimensional images of three-dimensional momentum trajectories
journal, August 2002

Charged particle velocity map image reconstruction with one-dimensional projections of spherical functions
journal, March 2013

Inverting ion images without Abel inversion: maximum entropy reconstruction of velocity maps
journal, January 2014

Photoelectron imaging spectrometry: Principle and inversion method
journal, June 1996

Slice imaging and velocity mapping using a single field
journal, August 2006

Reconstruction of Abel-transformable images: The Gaussian basis-set expansion Abel transform method
journal, July 2002

Application of time-sliced ion velocity imaging to crossed molecular beam experiments
journal, April 2003

Slicing photofragment spatial distribution by laser sheet ionization
journal, July 1994

Two‐dimensional imaging of state‐selected photodissociation products detected by multiphoton ionization
journal, July 1987

An algorithm for the Fourier-Bessel transform
journal, August 1981

Two-dimensional charged particle image inversion using a polar basis function expansion
journal, November 2004

Velocity map imaging of ions and electrons using electrostatic lenses: Application in photoelectron and photofragment ion imaging of molecular oxygen
journal, September 1997

Abel inversion using transform techniques
journal, May 1988

Finite slice analysis (FINA)—A general reconstruction method for velocity mapped and time-sliced ion imaging
journal, July 2017

Thick-lens velocity-map imaging spectrometer with high resolution for high-energy charged particles
journal, May 2014

Measurement of bipolar moments for photofragment angular correlations in ion imaging experiments
journal, November 2001

Incorporating real time velocity map image reconstruction into closed-loop coherent control
journal, November 2014

Inversion of velocity map ion images using iterative regularization and cross validation
journal, March 2006

Nonstationary noise effects in the Abel inversion
journal, January 1988

Slice imaging: A new approach to ion imaging and velocity mapping
journal, October 2001

A “circularisation” method to repair deformations and determine the centre of velocity map images
journal, July 2017

Time-resolved photoelectron imaging of excited state relaxation dynamics in phenol, catechol, resorcinol, and hydroquinone
journal, November 2012

Imaging of charged atomic reaction products: Inversion by a two-dimensional regularization method
journal, June 1999

Photofragment image analysis via pattern recognition
journal, July 2004

Angular distributions for the inelastic scattering of NO(X2Π) with O ₂ (X3Σg−)
journal, May 2017

Attosecond control of electron emission from atoms
journal, April 2014

P HOTOELECTRON A NGULAR D ISTRIBUTIONS
journal, October 2003

Toward real-time charged-particle image reconstruction using polar onion-peeling
journal, May 2009

Abel inversion using transform techniques
conference, January 1987

MELEXIR: maximum entropy Legendre expanded image reconstruction. A fast and efficient method for the analysis of velocity map imaging or photoelectron imaging data
journal, January 2019

Erratum: “DAVIS: A direct algorithm for velocity-map imaging system” [J. Chem. Phys. 148, 194101 (2018)]
journal, September 2018

A direct comparison of high-speed methods for the numerical Abel transform
journal, June 2019

A direct comparison of high-speed methods for the numerical Abel transform
text, January 2019