Analysis of x-ray images and spectra.

Four research projects are reported. They are all concerned with X-ray data analysis techniques and although each project is different there is a common theme which links all four. Part I considers the use of grazing incidence optics to produce two dimensional X-ray pictures with the emphasis on the data analysis and presentation. The mathematical development within this project forms a foundation for the subsequent reports. The research concentrates on viable methods of cleaning up blurred and noisy X-ray images using Fourier filtering and the Maximum Entropy Method including a practical implementation of the theory using digital computers. The major product of this project was a software package for the processing of large matrices and this is documented in Appendix I. This package was used to process astronomical X-ray data from a sounding rocket flight to yield a soft X-ray image of the Cygnus Loop supernova remnant and these results are presented to allow comparison of the analysis techniques developed. The second project presented in Part II applies the deconvolution theory developed in Part I to the problem of decoding data from coded mask telescopes. The design of such devices is described and computer simulations of X-ray burst monitors are reported with analysis and comment to give a realistic estimate of the expected performance of proposed instruments and to compare the different methods of analysis available. Part III reports a small project in which the possibility of analysing anode pulse height data from proportional counters using the Maximum Entropy Method was investigated. A computer program was written to both simulate and analyse real data. The algorithm was used to analyse pulse height spectra from the Cygnus Loop observations. The final project, concerned with the calibration of crystal spectrometers, was somewhat different from the other three and is presented in Part IV. The mathematical description of crystal spectrometers is shown to be very similar to that used for imaging devices but instead of studying data analysis methods which require an accurate description of the instrument response, the more fundamental problem of characterising and calibrating the response is addressed. Both theoretical and practical methods for finding crystal reflection parameters are discussed and then applied to three crystals; Langmuir- Blodgett lead stearate multilayers, gypsum 020 and beryl 1010. Sophisticated theoretical calculations using an atomic model developed by other workers were used to predict the crystal response. Direct measurements of the response at a set of wavelengths through each crystal's range were made using a two crystal X-ray spectrometer. The combination of theory and measurement provide a nearly complete description of current pseudo lead stearate crystal production while the excellent agreement between theory and measurement for both gypsum and beryl demonstrates the power of both the theoretical and practical techniques employed. The results from all three crystal types provide excellent calibration data for use in subsequent spectral analysis using these crystals as Bragg Analysers. Measurement of the response across the sulphur k and aluminium k edges in gypsum and beryl respectively also provided direct experimental evidence of k electron resonance in these two atomic types.