IOP PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY Phys. Med. Biol. 52 (2007) 4171–4187 doi:10.1088/0031-9155/52/14/010 Analyser-based phase contrast image reconstruction using geometrical optics M J Kitchen 1 , K M Pavlov 1,2 , K K W Siu 1,3 , R H Menk 4 , G Tromba 4 and R A Lewis 1,2 1 School of Physics, Monash University, Victoria 3800, Australia 2 Monash Centre for Synchrotron Science, Monash University, Victoria 3800, Australia 3 Department of Medical Imaging and Radiation Sciences, Monash University, Victoria 3800, Australia 4 Sincrotrone Trieste, Strada Statale, 34012 Basovizza, Trieste, Italy E-mail: Marcus.Kitchen@sci.monash.edu.au Received 9 March 2007, in final form 8 May 2007 Published 15 June 2007 Online at stacks.iop.org/PMB/52/4171 Abstract Analyser-based phase contrast imaging can provide radiographs of exceptional contrast at high resolution (<100 µm), whilst quantitative phase and attenuation information can be extracted using just two images when the approximations of geometrical optics are satisfied. Analytical phase retrieval can be performed by fitting the analyser rocking curve with a symmetric Pearson type VII function. The Pearson VII function provided at least a 10% better fit to experimentally measured rocking curves than linear or Gaussian functions. A test phantom, a hollow nylon cylinder, was imaged at 20 keV using a Si(1 1 1) analyser at the ELETTRA synchrotron radiation facility. Our phase retrieval method yielded a more accurate object reconstruction than methods based on a linear fit to the rocking curve. Where reconstructions failed to map expected values, calculations of the Takagi number permitted distinction between the violation of the geometrical optics conditions and the failure of curve fitting procedures. The need for synchronized object/detector translation stages was removed by using a large, divergent beam and imaging the object in segments. Our image acquisition and reconstruction procedure enables quantitative phase retrieval for systems with a divergent source and accounts for imperfections in the analyser. 1. Introduction Analyser-based phase contrast imaging (ABI), or ‘diffraction enhanced imaging’ (DEI), is an extremely sensitive x-ray imaging technique that provides image contrast proportional to the phase gradients introduced by objects placed in the x-ray beam (F ¨ orster et al 1980, Somenkov 0031-9155/07/144171+17$30.00 © 2007 IOP Publishing Ltd Printed in the UK 4171