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[en] The limiting uncertainty in recent high accuracy measurements of the mass attenuation coefficient is the measurement of the integrated column density. An improvement in the design of the absorption foil holder is described which reduces the integrated column density uncertainty. The new design allows the edges of the foil to be more accurately mapped by the X-ray beam by reducing the largest source of uncertainty in the foil mapping: the uncertainty in the points along the foil edge. The method is shown to reduce the uncertainty in measurements of the mass attenuation coefficient of zinc foils. The reduced uncertainty in the full-foil mapping will allow the X-ray Extended Range Technique (XERT) to be applied to small non-metallic absorption foils more accurately.