Modelling of vignetting effects in full-field X-ray fluorescence imaging system based on pinhole optics

Abstract

The full field X-ray fluorescence (FF-XRF) imaging is a technique capable of analysing the spatial distribution of elements in a sample. An alternative technique is the scanning macro-XRF method. Both techniques are powerful tools for non-destructive analysis of artworks mainly historical paintings. Technically, FF-XRF imaging is usually realised by coupling of a pinhole camera and a position sensitive and energy dispersive X-ray detector. The main advantages of the pinhole camera are its simplicity and infinite depth of field, however it introduces vignetting. For a visible light pinhole camera one distinguishes natural vignetting following the cos4 law and mechanical vignetting due to finite thickness of the camera. For an X-ray pinhole camera one has to take into account an additional component of vignetting due to absorption of X-rays in the air or other gas unless the setup is kept in vacuum. The goal of this study is to work out an analytical model of vignetting effects for a FF-XRF apparatus using an X-ray pinhole camera. Complete quantitative characterisation of the vignetting effects is a key step towards proper correction of the vignetting artefacts in recorded images. The elaborated analytical model has been applied to the images acquired with the FF-XRF apparatus being developed and an example of vignetting correction is presented.