Patent Document ID: 8972191
Application ID: 13148198
Patent Status: 1

Claim One:
1. An imaging set-up for reverse projection to obtain quantitative X-ray images from a sample and to quantitatively extract both absorption and phase information from the sample, the imaging set-up comprising: an X-ray source generating an X-ray beam; gratings including a beam splitter grating and an analyzer grating having their respective lines parallel to each other, said beam splitter grating being a phase grating and said analyzer grating is a line absorption grating with high X-ray absorption; a mechanism for placing the sample to be investigated either between said X-ray source and the said beam splitter grating or between said beam splitter grating and said analyzer grating; a position-sensitive detector with spatially modulated detection sensitivity having a number of individual pixels; means for recording images of said position-sensitive detector, a series of M images is collected by continuously or stepwise rotating from zero (0) to pi (π) or 2pi (2π) either the sample or said gratings and said X-ray source relative to the sample, wherein each image taken at an angle 0≦φ≦π contains a corresponding reverse projection image taken at an angle π≦φ+π≦2π, yielding in total a number of M/2 pairs of specular images; means for calculating pixel-wise an absorption image M and an refraction angle θ r image out of the pairs of specular images without a need for phase stepping according to: M ⁡ ( x r , ϕ , z ) = ∫ - ∞ ∞ ⁢ μ ⁡ ( x , y , z ) ⁢ ⅆ y r = ln ( 2 ⁢ S ⁡ ( x g D ) ⁢ I 0 I ⁡ ( x r , ϕ , z ) + I ⁡ ( - x r , ϕ + π , z ) ) θ r ⁡ ( x r , ϕ , z ) = - ∫ - ∞ ∞ ⁢ ∂ δ ⁡ ( x , y , z ) ∂ x r ⁢ ⅆ y r = 1 C ⁢ I ⁡ ( x r , ϕ , z ) - I ⁡ ( - x r , ϕ + π , z ) I ⁡ ( x r , ϕ , z ) + I ⁡ ( - x r , ϕ + π , z ) where: (x, y, z) are first spatial coordinates associated with the sample; (x r , y r , z) are second spatial coordinates associated to the X-ray beam, the first and second coordinates being linked by a rotation matrix: ( x y ) = ( cos ⁢ ⁢ ϕ - sin ⁢ ⁢ ϕ sin ⁢ ⁢ ϕ cos ⁢ ⁢ ϕ ) ⁢ ( x r y r ) , where φ is a rotation angle between x r axis and x axis around a z axis; I o is an incident X-ray intensity; I(x r ,φ,z) is intensity recorded at said position-sensitive detector for a beam decided by x r , z and the rotation angle φ; x g denotes a relative displacement between said phase grating and said analyzer grating along a direction perpendicular to both an incoming beam and a line of said gratings; D is a distance between said phase grating and said analyzer grating; S ⁡ ( x g D ) is a shifting curve; C is a constant; and M(x r ,φ,z) and θ r (x r ,φ,z) are inline definitions representing an absorption signal and a refraction angle, respectively, for a given coordinate x r , z, and the rotation angle φ.