Photofragment image analysis using the Onion-Peeling Algorithm

With the growing popularity of the velocity map imaging technique, a need for the analysis of photoion and photoelectron images arose. Here, a computer program is presented that allows for the analysis of cylindrically symmetric images. It permits the inversion of the projection of the 3D charged particle distribution using the Onion Peeling Algorithm. Further analysis includes the determination of radial and angular distributions, from which velocity distributions and spatial anisotropy parameters are obtained. Identification and quantification of the different photolysis channels is therefore straightforward. In addition, the program features geometry correction, centering, and multi-Gaussian fitting routines, as well as a user-friendly graphical interface and the possibility of generating synthetic images using either the fitted or user-defined parameters.

Program summary

Title of program: Glass OnionCatalogue identifier: ADRYProgram Summary URL:http://cpc.cs.qub.ac.uk/summaries/ADRYProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputer: IBM PCOperating system under which the program has been tested: Windows 98, Windows 2000, Windows NTProgramming language used: Delphi 4.0Memory required to execute with typical data: 18 MwordsNo. of bits in a word: 32No. of bytes in distributed program, including test data, etc.: 9 911 434Distribution format: zip fileKeywords: Photofragment image, onion peeling, anisotropy parametersNature of physical 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.Method of solution: The “Onion Peeling” algorithm described by Helm Rev. Sci. Instrum. 67 (6) (1996)] 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 on the complexity of the problem: The maximum image size (1280×1280) 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 then 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.Typical running time: The analysis procedure can be divided into three parts: inversion, fitting, and geometry correction. The inversion time grows approx. as R³, 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 then 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 then 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 R² and depends on the curve profile. It is on the order of a few minutes for images with R=500 pixels.Unusual features of the program: 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 loose the resolution at the same time.