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Manuscript Title: Photofragment image analysis using the Onion-Peeling algorithm.
Authors: S. Manzhos, H.-P. Loock
Program title: Glass Onion
Catalogue identifier: ADRY_v1_0
Distribution format: zip
Journal reference: Comput. Phys. Commun. 154(2003)76
Programming language: Delphi 4.0.
Computer: IBM PC.
Operating system: Windows 98, Windows 2000, Windows NT.
RAM: 18M words
Word size: 32
Keywords: Photofragment image, Onion peeling, Anisotropy parameters, Photoionization, Photodissociation, Velocity-map imaging, Molecule, Experimental analysis.
Classification: 16.4.

Nature of problem:
Information about velocity and angular distributions of photofragments is the basis on which the analysis of the photolysis process resides. Reconstructing the three-dimensional distribution from the photofragment image is the first step, further processing involving angular and radial integration of the inverted image to obtain velocity and angular distributions. Provisions have to be made to correct for slight distortions of the image, and to verify the accuracy of the analysis process.

Solution method:
The "Onion Peeling" algorithm described by HelM [Rev. Sci. Instrum. 67 (6) (1966)] is used to perform the image reconstruction. Angular integration with a subsequent multi-Gaussian fit supplies information about the vElocity distribution of the photofragments, whereas radial integration with subsequent expansion of the angular distributions over Legendre Polynomials gives the spatial anisotropy parameters. Fitting algorithms have been developed to centre the image and to correct for image distortion.

Restrictions:
The maximum image size (1280 x 1280) and resolution (16 bit) are restricted by available memory and can be changed in the source code. Initial centre coordinates within 5 pixels may be required for the correction and the centering algorithm to converge. Peaks on the velocity profile separated by less than the peak width may not be deconvolved. In the charged particle image reconstruction, it is assumed that the kinetic energy released in the dissociation process is small compared to the energy acquired in the electric field. For the fitting parameters to be physically meaningful, cylindrical symmetry of the image has to be assumed but the actual inversion algorithm is stable to distortions of such symmetry in experimental images.

Unusual features:
Our centering and image correction algorithm is based on Fourier analysis of the radial distribution to insure the sharpest velocity profile and is insensitive to an uneven intensity distribution. There exists an angular averaging option to stabilize the inversion algorithm and not to lose the resolution at the same time.

Running time:
The analysis procedure can be divided into three parts: inversion, fitting, and geometry correction. The inversion time grows approximately as R^3, where R is the radius of the region of interest; for R = 200 pixels it is less than a minute, for R = 400 pixels less than 6 min on a 400 MHz IBM personal computer. The time for the velocity fitting procedure to converge depends strongly on the number of peaks in the velocity profile and the convergence criterion. It ranges between less than a second for simple curves and a few minutes for profiles with up to twenty peaks. The time taken for the image correction scales as R^2 and depends on the curve profile. It is of the order of a few minutes for images with R = 500 pixels.