Abel inversion using transform techniques

Smith, Laurie G.; Keefer, Dennis; Sudharsanan, Subramania I.

doi:10.1016/0022-4073(88)90101-x

Cited by 163 publications

(23 citation statements)

References 6 publications

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“…The three-dimensional recoil distribution of fragments is cylindrically symmetric around the direction of the polarization of the dissociation laser and is projected onto the two-dimensional plane of the MCP detector. This projection is perpendicular to the symmetry axis of the original three-dimensional distribution which makes it possible to reconstruct the three-dimensional distribution of recoiling fragments via a mathematical process called Abel inversion . The resulting Abel-inverted images are shown in panels d−f of Figure corresponding to the two-dimensional data of panels a−c, respectively.…”

Section: Resultsmentioning

confidence: 99%

Imaging of Oriented Molecules^†

Janssen¹,

Mastenbroek²,

Stolte³

1997

J. Phys. Chem. A

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Hexapole state selection and orientation of parent molecules is combined with two-dimensional ion imaging of photofragments to study the direct photolysis of deuterated methyl iodide molecules (CD 3 I) at 266 nm. The combination of these two techniques allows us to create an essentially single quantum state-selected beam of oriented molecules, which are subsequently photodissociated, and to measure the final state-, velocity-, and angle-resolved recoil distribution of the photofragments. Extensive measurements have been done on the variation of the recoil distribution with the orientation field strength applied. These measurements allow a quantitative comparison of the orientation distribution of state-selected methyl iodide molecules with theoretical Stark effect calculations. For the prompt dissociation of CD 3 I at 266 nm the angular recoil distribution of the I( 2 P 1/2 ) photofragment reflects predominantly the initial spatial orientation of the stateselected parent. A comparison is presented between the fragment recoil distributions when different initial oriented parent states are selected.

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Section: Resultsmentioning

confidence: 99%

Imaging of Oriented Molecules^†

Janssen¹,

Mastenbroek²,

Stolte³

1997

J. Phys. Chem. A

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“…As a final step and in order to estimate the 3D refractive index distribution in the volume of the phase object we assume cylindrical symmetry and apply a Fourier-Hankel transform implementation of the inverse Abel technique. 6 The projection plane where the Abel inversion is preformed is chosen by digitally propagating the wavefront along z until the amplitude variation is minimized. This practically corresponds to the edge of the phase object and is very close to plane 3 of Fig.…”

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confidence: 99%

In-line holography for the characterization of ultrafast laser filamentation in transparent media

Papazoglou

Tzortzakis

2008

Applied Physics Letters

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A powerful experimental method, based on holographic microscopy, is used to retrieve the spatiotemporal distribution of small (<10−3) refractive index perturbations induced by ultrafast laser pulses in transparent media. A numerical iterative wavefront propagation approach is used to accurately reconstruct both the phase and the amplitude of the perturbed probe beam wavefront, while Abel inversion recovers the exact three dimensional distribution of the perturbation. For demonstration, a laser filament induced plasma string in air is fully characterized.

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“…In general, the inverse Abel transform is ill-conditioned, being susceptible to experimental noise [26]. Several inversion algorithms [18][19][20][21][22] have been developed to mitigate this issue and to robustly reconstruct the underlying 3D momentum distribution. In our method we adopt the basis functions employed in the well-known pBasex [18] algorithm to represent χ(r, ω) and combine the inversion procedure with spectral domain ghost imaging [9,10].…”

Section: Methodsmentioning

confidence: 99%

“…A VMI spectrometer typically measures the two-dimensional (2D) projection of the three-dimensional (3D) momentum distribution of charged particles. In most cases, however, the quantity of interest is the underlying 3D distribution or another related quantity such as the kinetic energy (KE) spectrum, access to which requires post-processing of the 2D projection which inverts the Abel transform [18][19][20][21][22]. In trying to apply SDGI to Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Photon energy-resolved velocity map imaging from spectral domain ghost imaging

Wang

Driver²,

Allum³

et al. 2023

New J. Phys.

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We present an approach that combines photon spectrum correlation analysis with the reconstruction of three-dimensional momentum distribution from velocity map images in an efficient, single-step procedure.We demonstrate its efficacy with the results from the photoionization of the 2p-shell of argon using the FLASH free-electron laser (FEL). Distinct spectral features due to the spin-orbit splitting of Ar+(2p-1) are resolved, despite the large average bandwidth of the ionizing pulses from the FEL.This demonstrates a clear advantage over the conventional analysis method, and it will be broadly beneficial for velocity map imaging experiments with FEL sources.The retrieved linewidth of the binding energy spectrum approaches the resolution limitation prescribed by the spectrometers used to collect the data.Our approach presents a path to extend spectral-domain ghost imaging to the case where the photoproduct observable is high-dimensional.

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Abel inversion using transform techniques

Cited by 163 publications

References 6 publications

Imaging of Oriented Molecules^†

Imaging of Oriented Molecules^†

In-line holography for the characterization of ultrafast laser filamentation in transparent media

Photon energy-resolved velocity map imaging from spectral domain ghost imaging

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Abel inversion using transform techniques

Cited by 163 publications

References 6 publications

Imaging of Oriented Molecules†

Imaging of Oriented Molecules†

In-line holography for the characterization of ultrafast laser filamentation in transparent media

Photon energy-resolved velocity map imaging from spectral domain ghost imaging

Contact Info

Product

Resources

About

Imaging of Oriented Molecules^†

Imaging of Oriented Molecules^†