A LAPLACE TRANSFORM PAIR MODEL TO DETERMINE BREMSSTRAHLUNG SPECTRA FROM ATTENUATION DATA (RADIATION, X-RAY, SPECTRAL MODELING)

Every x-ray attenuation curve inherently contains all the information necessary to extract the complete energy spectrum of a beam. To date, attempts to obtain accurate spectral information from attenuation data have been inadequate.^ This investigation presents a mathematical pair model, grounded in physical reality by the Laplace Transformation, to describe the attenuation of a photon beam and the corresponding bremsstrahlung spectral distribution. In addition the Laplace model has been mathematically extended to include characteristic radiation in a physically meaningful way. A method to determine the fraction of characteristic radiation in any diagnostic x-ray beam was introduced for use with the extended model.^ This work has examined the reconstructive capability of the Laplace pair model for a photon beam range of from 50 kVp to 25 MV, using both theoretical and experimental methods.^ In the diagnostic region, excellent agreement between a wide variety of experimental spectra and those reconstructed with the Laplace model was obtained when the atomic composition of the attenuators was accurately known. The model successfully reproduced a 2 MV spectrum but demonstrated difficulty in accurately reconstructing orthovoltage and 6 MV spectra. The 25 MV spectrum was successfully reconstructed although poor agreement with the spectrum obtained by Levy was found.^ The analysis of errors, performed with diagnostic energy data, demonstrated the relative insensitivity of the model to typical experimental errors and confirmed that the model can be successfully used to theoretically derive accurate spectral information from experimental attenuation data. ^

AN INVESTIGATION OF THE EFFECT OF FORMALDEHYDE SPECIES ON ENVIRONMENTAL MEASUREMENT METHODS UNDER AMBIENT CONDITIONS

Species variations in formaldehyde solutions and gases were investigated by means of infrared spectral analysis. Double beam infrared spectrometry in conjunction with sodium chloride wafer technique and solvent compensation technique were employed. Formaldehyde species in various solutions were investigated. Formalin 37% was stable for many months. Refrigeration had no effects on its stability. Spectral changes were detected in 1000 ppm formaldehyde solutions. The absorbances of very diluted solutions up to 100 ppm were lower than the detection limit of the instruments. Solvent compensation improved resolution, but was associated with an observed lack of repeatability. Formaldehyde species in animal chambers containing animals and in mobile home air were analyzed with the infrared spectrophotometer equipped with a 10 cm gas cell. Spectra were not different from the spectrum of clean air. A portable single beam infrared spectrometer with a 20 meter pathlength was used for reinvestigation. Indoor formaldehyde could not be detected in the spectral; conversely, an absorption peak at 3.58 microns was found in the spectra of 3 and 15 ppm formaldehyde gas in animal chambers. This peak did not appear in the spectrum of the control chamber. Because of concerns over measurement bias among various analytical methods for formaldehyde, side-by-side comparisons were conducted in both laboratory and field measurements. The chromotropic acid method with water and 1% sodium bisulfite as collection media, the pararosaniline method, and a single beam infrared spectrometer were compared. Measurement bias was elucidated and the extent of the effects of temperature and humidity was also determined. The problems associated with related methods were discussed. ^