Patent Number: 
Section: claims

1. A method for providing an image of an object, comprising:obtaining a refraction image of the object;applying a regularized mathematical inversion algorithm to the refraction image to obtain a mass density image; anddisplaying the obtained mass density image. 2. The method of claim 1, wherein the regularized mathematical inversion algorithm comprises a constrained least-squares filter. 3. The method of claim 1, wherein the regularized mathematical inversion algorithm comprises an estimation of the projected mass-density image. 4. The method of claim 1, wherein the regularized mathematical inversion algorithm comprises estimation of the projected mass-density image {circumflex over (ρ)}T(m,n) by using:                                          ρ            ^                    T                ⁡                  (                      m            ,            n                    )                    =                                                  ρ              ^                                      T              ,              0                                ⁡                      (                          m              ,              n                        )                          +                                            ρ              ^                        T            *                    ⁡                      (            n            )                                ,                  ⁢    wherein                                ρ          ^                          T          ,          0                    ⁡              (                  m          ,          n                )              =                  DFT                  -          1                    ⁢              {                                            P              ^                        T                    ⁡                      (                          k              ,              l                        )                          }              wherein                                          P            ^                    T                ⁡                  (                      k            ,            l                    )                    =                                                  D              *                        ⁡                          (                              k                ,                l                            )                                                                                                            D                  ⁡                                      (                                          k                      ,                      l                                        )                                                                              2                        +                          γ              ⁢                                                                                      Q                    ⁡                                          (                                              k                        ,                        l                                            )                                                                                        2                                                    ⁢                  ΔΘ          ⁡                      (                          k              ,              l                        )                                ,  where DFT−1 denotes the two-dimensional inverse discrete Fourier transform in terms of discrete frequencies (k,l) with {circumflex over (P)}T(0,0) set to zero, and                              ρ          ^                T        *            ⁡              (        n        )              =                            ρ          ref                ⁢        t            -                        1          B                ⁢                              ∑                          m              =              1                        B                    ⁢                                                    ρ                ^                                            T                ,                0                                      ⁡                          (                              m                ,                n                            )                                            ,wherein ρreft is the known projected mass density of the material appearing in a reference region that is B pixels wide and lies outside the object. 5. A method for providing an image of an object, comprising:obtaining a refraction image of the object, wherein obtaining the refraction image comprises:transmitting an x-ray beam through the object and emitting from the object a transmitted beam;directing the transmitted beam at an angle of incidence upon a crystal analyzer;detecting a first image of the object from a first diffracted beam emitted from the crystal analyzer positioned at a first angular position;detecting a second image of the object from a second diffracted beam emitted from the crystal analyzer positioned at a second angular position; andcombining the first image and the second image to derive the refraction image;applying a regularized mathematical inversion algorithm to the refraction image to obtain a mass density image; anddisplaying the obtained mass density image. 6. The method of claim 5, further comprising:detecting a third image of the object from a third diffracted beam emitted from the crystal analyzer positioned at a third angular position; andcombining the first image, the second image, and the third image to derive a refraction image. 7. The method of claim 5, further comprising:detecting the first image of the object from the first diffracted beam emitted from the crystal analyzer at a low rocking curve angle setting of the crystal analyzer; anddetecting the second image of the object from the second diffracted beam emitted from the crystal analyzer at a high rocking curve angle setting of the crystal analyzer. 8. The method of claim 5, wherein the first image and the second image are exposed on a detector capable of producing a digitized image. 9. The method of claim 8, wherein the exposed first image and the exposed second image are digitized. 10. The method of claim 9, wherein the digitized images are mathematically combined to form a digitized refraction image. 11. The method of claim 10, wherein the refraction image and the mass density image are defined on a pixel-by-pixel basis. 12. The method of claim 5, wherein the x-ray beam has an energy level of at least about 16 keV. 13. The method of claim 5, wherein the x-ray beam has an energy level of at least about 40 keV. 14. The method of claim 5 wherein the x-ray beam has an energy level in a range of approximately 16 keV to approximately 100 keV. 15. The method of claim 5 wherein the x-ray beam is diffracted by a monochromator which is matched in orientation and lattice planes to the crystal analyzer. 16. The method of claim 5 further comprising increasing a relative intensity of the image of the object by adjusting an angular position of the crystal analyzer. 17. The method of claim 16 wherein the angular position of the crystal analyzer is adjusted in steps of approximately 1 microradian increments. 18. The method of claim 5, wherein the x-ray beam is monochromatic. 19. The method of claim 5, wherein the regularized mathematical inversion algorithm comprises a constrained least-squares filter. 20. The method of claim 5, wherein the regularized mathematical inversion algorithm comprises an estimation of the projected mass-density image.