Global Least Squares Algorithm for 3D Elemental Surface Topography Reconstruction Using Quad-Segment Detector in X-ray Spectrometry

2D elemental imaging techniques such as micro-X-ray fluorescence (micro-XRF) and micro-particle-induced X-ray emission (micro-PIXE) play a critical role in elemental mapping across diverse fields such as biology, geology, materials science, and engineering. However, surface irregularities often introduce shadow effects, hindering accurate spectrometric analysis. Knowing the topography information is essential for addressing this issue. Here, we propose integrating a global least squares algorithm for reconstructing the 3D surface topography in micro-PIXE analysis which is applicable in other similar techniques based on X-ray microscopy. This algorithm utilizes two independent gradient components, distorted by noise, to calculate the gradient vector from X-ray data acquired by an annular quad-segment spectrometer. We demonstrate the capability of this approach on a real homogeneous sample, yielding 3D elemental surface topography. This noniterative code provides surface reconstructions which in turn could find application to enhance the correction of spatial elemental distributions across heterogeneous sample types.