Sample transparency aberration in Bragg–Brentano geometry affected by interference with opaque and translucent sample holders has been formulated. The formulation for an opaque sample holder should be classified to 5 cases, depending on the apparent diffraction angle, beam width, specimen width, and specimen thickness. The cumulants of the aberration function for a translucent sample holder with an arbitrary linear attenuation coefficient can numerically be evaluated by a Gauss–Legendre quadrature. The use of a function defined by the convolution of truncated exponential and rectangular functions has been tested as the model for the aberration function. A double deconvolutional treatment (DCT) designed to cancel the effects of the first and third order cumulants of the aberration function has been applied to the XRD data of Si standard powder, NIST SRM640d. The diffraction peak profile in the data treated by the DCT method certainly shows improved symmetry. The main features of the symmetrized peak profile in the DCT data have been simulated by instrumental and specimen parameters. It is suggested that the current analytical method could be utilized for texture analysis, if the manufacturer of an XRD instrument should supply a more accurate information about the instrument.

A deconvolutional method for preprocessing powder diffraction data has been improved. The cumulants of instrumental aberration functions of Bragg-Brentano (Parrish) diffractometer calculated up to the fourth order are presented. The treatments of axial-divergence aberration and the effective spectroscopic profile of the source X-ray have been simplified from those used in previous methods. The current method has been applied to powder diffraction data collected with a Cu-target X-ray tube, used over 20 years, and a Ni-foil Kβ filter.