Patent Number: 
Section: description

FIG. 1 is a diagrammatic an x-ray system utilizing the lenses of the present invention. The x-ray lens system is generally shown as 20 in this present embodiment and includes an x-ray filter 22, lens 24, a main lens 26, and an extension lens 28. The present invention may be used with only one of these lenses or any combination of these lenses or other lenses defined in this description. An x-ray generator 30 produces x-rays 32 which include direct or coaxial x-rays that are filtered by x-ray filter 22. The x-ray filter 22, which may be a bandpass, highpass or lowpass filter, is comprised of a ring 21 which blocks or absorbs off-axis x-rays that are not reflected by the interior of the lenses and/or do not converge to the focal point 34 of the lens system 20. A filtering medium 23 is placed within the ring 21 of the x-ray filter 22 to filter x-rays entering the lens system 20, bypassing the reflective surfaces of the lens system 20, and traveling directly to focal point 34. Alternatively, the filter 22 may be placed at the exit aperture of a lens system 20 or two filters 22 may be used simultaneously at both the entrance and exit apertures of a lens system 20. The x-rays 32 are collected by the x-ray lens system 20 and focused by the lens system 20 as x-rays 36 which converge to focal point 34. In radiotherapy, a system utilizing the x-ray focusing properties of the present invention can destroy a malignancy with reduced damage to collateral tissue and an energy use in the KeV range rather than the MeV range. This use of lower energy x-rays allows quicker fall-off behind the target tissue and reduced damage to tissue located behind the target tissue. A malignancy or target volume 38 is subjected to the greatest intensity of the focused x-rays 36 when the focal point 34 of the lens system is placed directly upon the malignancy 38. This focusing action also minimizes the radiation exposure of the healthy tissue surrounding the malignancy, decreasing collateral damage to the healthy tissue. The modular nature of the lens system 20 is evidenced by the ease at which the focal length and focal point area is adjusted. The focal length X and focal point 34 area of the x-ray lens system is easily changed by substituting different individual lens components with lenses of the desired aspect combinations. The focusing properties of the present invention also lead to the advantages of having improved flux and resolution in x-ray diffraction or other x-ray applications. The x-ray lenses of the present invention utilize the principles of Bragg reflection and Laue diffraction. FIG. 2 provides a graphical illustration of a simple Bragg reflector. X-ray radiation 40 of wavelength xcex is incident on a crystal or multilayer 42 having lattice or multilayer spacing d. Narrow band or generally monochromatic radiation 44 is than reflected according to Bragg""s Law. Mosaic graphite is the preferred crystal structure which may be utilized as a Bragg reflector to provide a narrow band or generally monochromatized x-ray beam. In other embodiments other crystals or Bragg structures such as multilayers can be substituted within the lens system to reflect radiation using Bragg""s law. Mosaic graphite and other Bragg structures only reflect radiation when Bragg""s equation is satisfied: nxcex=2dsin(xcex8) where n=the order of reflection xcex=wavelength of the incident radiation d=layer-set spacing of a Bragg structure or the lattice spacing of a crystal xcex8=angle of incidence Mosaic graphite was chosen as the preferred x-ray reflecting or diffracting material in the embodiments of the present invention because of its superior performance properties, such as a large reflection angle, large rocking curve width due to the mosaic structure, and high reflectivity. In both Bragg and Laue diffraction, Bragg""s law dictates the reflection and/or diffraction of the incident x-rays. The only difference is in Bragg diffraction the incident and diffracted beam share the same crystal surface, while in the Laue case the incident and diffracted beam use two different surfaces. The former is usually called a xe2x80x9creflection schemexe2x80x9d and the latter is referred to as a xe2x80x9ctransmission schemexe2x80x9d. The structure of the mosaic graphite consists of a regular three dimensional array of atoms which forms a natural diffraction grating for x-rays. The quantity d in Bragg""s equation is the perpendicular distance between the planes of atoms in the mosaic graphite forming the diffraction grating. Mosaic crystal consists of numerous tiny independent crystal regions which are nearly parallel but not quite parallel with one another. When x-rays from an x-ray source strike a reflective surface the incidence angle varies since the point of reflection of various x-rays are at differing distances from an x-ray source. As the incidence angle of x-rays falling upon the mosaic graphite is varied so will the crystal regions reflecting the x-rays. This is caused by the differing orientations of the individual crystal regions within the mosaic graphite. There is not only an incidence angle upon the general surface of the mosaic graphite but individual local incidence angles upon the independent crystal regions. An x-ray beam falling on the mosaic graphite will reflect at a wider incident angle than a perfect crystal because x-rays entering into the graphite at wider incident angles will reach mosaic elements oriented correctly for reflection at that angle. The mosaic graphite reflects over an angular range which depends on the scatter of the mosaic orientations but the range is greater than that of a perfect crystal or multi-layered thin film Bragg reflector. The arrangement of the lattice structure and crystal regions may be varied from slightly ordered to highly ordered depending on the application. For x-rays of differing energy, the Bragg angle is different and mosaicity provides the capability to accept more energy over a wider angular range. In the preferred embodiment, the main parameters of the graphite used in the Bragg reflective lenses of the present invention are: d-spacing d: 3.33 xc3x85 FWHM w: 0.5xc2x0 Reflectivity R.: 50% Density p: 2.25 g/cm3  Attenuation xcexc: 0.175 gxe2x88x921xc2x7cm2  FIG. 3 is a diagrammatic view of the crystal regions 46 in mosaic carbon reflecting x-rays. The reflecting surface 48 of the Bragg lens is curved in a circular manner. This curvature will improve the focusing properties of the lens by keeping the incident angle constant for x-rays that are incident throughout the extent of reflecting surface 48. This ideal reflective surface will allow x-rays 50 generated at point A and incident upon individual crystal regions 46 to be focused at point B. The individual crystal regions 46 are shown slightly out of parallel with respect to each other resulting in the focal point B. The Bragg condition is guaranteed by the following two conditions, the angle made by an incident x-ray and reflected x-ray is constant along the circle and the tiny crystal regions will make correct Bragg angle exits. For crystal with different d-spacings, and different source-focus point a different size circle will be chosen to meet the Bragg angle requirements. In a real application, x-rays might meet proper crystal regions not exactly on the circle due to using flat crystals. This will give a widened beam spot on focal point B. The parallelism and performance of a mosaic crystal reflector is characterized and described completely by its rocking curve width, its inherent reflectivity, and attenuation coefficient. In further embodiments of the present invention, the principle of Laue diffraction/transmission is utilized to direct and focus x-rays. As seen in FIG. 4, incident x-rays 52 penetrate a crystal 54 and a portion of the incident x-rays 52 is diffracted and travels through the crystal 54 along the diffracted direction and exits the crystal 54 as focused x-rays 56. In a Laue lens configured as a ring, x-rays are diffracted at different focusing circles within the crystal. The Bragg angles are different at different point in the crystal volume, which results in an overall wider spectrum than Bragg reflectors. The ideal inner mosaic graphite crystal surfaces and crystal planes of the lenses of the present invention follow the Johansson scheme. As seen in FIG. 5, a bent Johansson crystal 58 is used to reflect and focus x-rays. The bent Johansson crystal 58 will reflect x-rays according to Bragg""s law. The Johansson crystal 58 is made by bending a crystal into a cylindrical surface with a normal radius 2R, and then polishing the reflection surface 60 to a cylindrical surface with radius R. The angle made by each pair of incident rays 62 generated by x-ray source 64 and reflected rays 66 is the same. The lines 68 that connect reflection points 70 to the point 72 on the other side of the circle 74, which is the symmetric point to the source and the focal point, are always equal and bi-partition the angle. Therefore, the curve that is perpendicular to these lines will constitute a Bragg plane, which are the bent 2R crystal planes in this Figure. FIG. 6 is a perspective of the main x-ray lens 26 used in the present invention. The main x-ray lens 26 is cylindrical in form with a hollow interior lined with a graphite layer 76. Preformed or xe2x80x9cbentxe2x80x9d graphite blocks can be bonded together to form the graphite layer 76 on the interior of a lens housing 78. In one embodiment of the present invention four graphite blocks, each covering a quarter of the interior of the x-ray lens 26, are mounted on the interior of the x-ray long 26 to form a curved interior surface. In an alternate configuration graphite can be grown by deposition process inside the lens housing 78 to form a reflection layer. In the preferred embodiment of the present invention, as seen in FIG. 6, the mosaic graphite layer 76 will approximate the reflecting surface of the Johansson Crystal illustrated in FIG. 5. The surface of the interior of the main x-ray lens 26 will be curved in a circular manner relative to the housing and incident x-rays 75. The term circular is used when referring to a Gross section or two-dimensional picture of the lens system, but a person of ordinary skill in the art would recognize that in three dimensions the lenses would be curved relative to the housing. This curving results in a smaller focal point area, as the mosaic graphite crystal will be aligned in the ideal form of the Johansson crystal to improve the focusing properties of the main x-ray lens 26 FIG. 7 is a lengthwise cross sectional view of an alternate embodiment of the main Bragg reflective lens 26xe2x80x2 of the present invention focusing x-rays. The main Bragg reflective lens 26xe2x80x2, as shown by the drawing, has a graphite layer 76xe2x80x2 that is not inclined or angled, rather it is substantially concentrically flat relative to the cylindrical housing of the main lens 78xe2x80x2 relative to incident x-rays 75xe2x80x2. The barrel or interior surface of the main lens 26xe2x80x2 therefore has generally a constant inner diameter throughout its full length. The flat reflecting surface of the graphite layer 76xe2x80x2 is easier to fabricate than the curved graphite surface 76 shown in FIG. 6 and will roughly approximate the surface of a the Johansson crystal shown in FIG. 5. The focusing properties of flat reflecting surface of the graphite layer 76xe2x80x2 will have more aberration than the curved graphite surface 76, shown in FIG. 6 of the leading to a larger focal point 79xe2x80x2. FIG. 8 is a cross sectional view of a modular x-ray lens system of the present invention. The lens system 20 can be constructed from a plurality of lens components. In the present embodiment, the lens 24 is coupled to the main lens 26 which further couples to an extension lens 28 to focus x-rays. The lenses may be coaxially physically coupled by threaded members, flanges or other connection devices known in the art. The lenses are preferably in a cylindrical configuration. The inner mosaic graphite crystal surfaces 80, 76 and 82 of these lenses follow the Johansson scheme shown in FIG. 5 when adjacent to each other. The mosaic graphite surfaces have been configured to approximate the ideal Johansson crystal reflecting shape. As discussed previously, the term circular is used when referring to a cross section or two dimensional picture of the lens system, but a person of ordinary skill in the art would recognize that in three dimensions the lenses would be curved. The modularity of the system is also beneficial. The focal point and x-ray intensity of the present invention can be varied by simply arranging, removing, or adding lenses with various reflecting characteristics. Multiple combinations of individual lenses can be configured to meet almost any application. Referring to FIG. 9, the mosaic graphite layer 80xe2x80x2 of lens 24xe2x80x2 is sloped in linear fashion (conical in three dimensions), the mosaic graphite layer 76xe2x80x2 of main lens 26xe2x80x2 is flat (cylindrical in three dimensions), and the mosaic graphite layer 82xe2x80x2 of extension lens 28xe2x80x2 is also sloped in linear fashion (conical in three dimensions) opposite to that of mosaic graphite layer 80xe2x80x2. These lenses alone do not possess a curved shape but when placed together approximate the curved circular shape of the ideal reflective surface of the Johansson crystal with their angular and flat surfaces. This conical system is also modular and lenses may be added or removed to improve performance. The main performance of an x-ray lens is its collecting and transmitting capability for x-rays. It can be described by throughput which is defined as the solid angle from the source, which contains the same amount of photons the lens delivers to the focal point. If we define a solid angle which extends 1xc2x0 in both directions, as a unit for the throughput, this unit will be equal to:       unit    ⁢          xe2x80x83        ⁢    throughput    =                    ∫                  89.5          ⁢          xc2x0                          90.5          ⁢          xc2x0                    ⁢              sin        ⁢                  xe2x80x83                ⁢        θ        ⁢                  xe2x80x83                ⁢                  ⅆ          θ                ⁢                              ∫            0            0.01745                    ⁢                      xe2x80x83                    ⁢                      ⅆ            φ                                =          3.05      xc3x97              10                  -          4                    ⁢              xe2x80x83            ⁢      strad       All Bragg reflective lenses in this section will be estimated in this unit. The parameters of the main lens 26xe2x80x2 are: Inner diameter: 25 mm Length: 115 mm Source-lens center distance: 400 mm Lens center-focus distance: 400 mm Capture angle: 1.70xc3x9710xe2x88x923 strad Focal spot size: 2-4 mm Throughput 2.78 The wavelength of an x-ray at 60 KeV is calculated from the following formula:   λ  =            12.4              E        ⁡                  (          keV          )                      =                  12.4        60            =              0.207        ⁢                  xe2x80x83                ⁢        Angstroms             The Bragg angle is:   θ  =                    sin                  -          1                    ⁢              (                  λ                      2            ⁢            d                          )              =                            sin                      -            1                          ⁢                  (                      0.207                          2              xc3x97              3.33                                )                    =              1.779        ⁢        xc2x0             The capture angle will be determined by:       Δ    ⁢          xe2x80x83        ⁢    Ω    =                    ∫                  1.529          ⁢          xc2x0                          2.029          ⁢          xc2x0                    ⁢              sin        ⁢                  xe2x80x83                ⁢        θ        ⁢                  ⅆ          θ                ⁢                              ∫            0                          2              ⁢              π                                ⁢                      xe2x80x83                    ⁢                      ⅆ            φ                                =          1.70      xc3x97              10                  -          3                    ⁢              xe2x80x83            ⁢      strad       In the case of the main lens 26xe2x80x2, the throughput is equal to the capture angle multiplied by the average reflectivity. Therefore the throughput is 8.5xc3x9710xe2x88x924 strad. In the unit defined above, the throughput of our lens 26xe2x80x2 will be 2.78. The parameters of the lens 24xe2x80x2 are: Inner diameter of the exit: 25 mm Inner diameter of the entrance; 23.5 mm Length: 86.5mm Source-lens center distance: 299 mm Lens center-focus distance: 501 mm Capture angle: 2.18xc3x9710xe2x88x923 strad Focal spot size: 4-10 mm, depending on source size Throughput 3.57 The capture angle will be determined by:       Δ    ⁢          xe2x80x83        ⁢    Ω    =                    ∫                  2.029          ⁢          xc2x0                          2.529          ⁢          xc2x0                    ⁢              sin        ⁢                  xe2x80x83                ⁢        θ        ⁢                  ⅆ          θ                ⁢                              ∫            0                          2              ⁢              π                                ⁢                      xe2x80x83                    ⁢                      ⅆ            φ                                =          2.18      xc3x97              10                  -          3                    ⁢              xe2x80x83            ⁢      strad       As discussed above, the throughput is equal to the capture angle multiplied by the average reflectivity. Therefore the throughput is 1.09xc3x9710xe2x88x923 strad and in the unit defined above, the throughput of the lens 24xe2x80x2 will be 3.57. The lens 24xe2x80x2 will give a large throughput, but will generate a larger focal spot. The parameters of the extension lens 28xe2x80x2 are: Inner diameter of the exit: 23.5 mm Inner diameter of the entrance: 25 mm Length: 86.5 mm Source-lens center distance: 501 mm Lens center-focus distance: 299 mm Capture angle: 1.22xc3x9710xe2x88x923 strad Focal spot size: depends on source size Throughput 1.97 The capture angle will be determined by:       Δ    ⁢          xe2x80x83        ⁢    Ω    =                    ∫                  1.026          ⁢          xc2x0                          1.526          ⁢          xc2x0                    ⁢              sin        ⁢                  xe2x80x83                ⁢        θ        ⁢                  ⅆ          θ                ⁢                              ∫            0                          2              ⁢              π                                ⁢                      xe2x80x83                    ⁢                      ⅆ            φ                                =          1.22      xc3x97              10                  -          3                    ⁢              xe2x80x83            ⁢      strad       The throughput is 0.61xc3x9710xe2x88x924 strad and in the unit defined above, the throughput of lens 28xe2x80x2 will be 1.97. The extension lens 28xe2x80x2 has finer focus and larger convergent angle. The intensity distribution and throughput of a particular combination of lenses can be calculated based on source information, source projection size, intensity distribution, etc. In further embodiments of the present invention, Laue diffraction/transmission lenses are utilized to direct and focus x-rays. Referring to FIG. 10, a Laue lens 86 of the present invention is illustrated. Incident x-rays 84 penetrate the Laue lens or crystal 86 (in a ring configuration) and a portion of the x-rays 84 is diffracted and travels through the lens 86 along the diffracted direction and exits the lens 86 as focused x-rays 88. In Laue diffraction, x-rays are diffracted at different focusing circles within the crystal. The Bragg angles are different at different points in the crystal volume, which results in an overall wider spectrum than Bragg reflectors. The x-rays 84 are reflected from each lattice layer and directed towards a focal point 90. The distance between the source 92 and the lens 86 is f1 and the distance between the lens 86 and the focal point 90 is f2. The length of the lens is L. The inner diameter of the Laue lens 86 is R1 and the outer diameter is R2. In the case where f1 is not equal to f2, the direction of the atomic planes of the Laue lens 86 will need to change along the diameter direction. Otherwise, the x-rays will not be reflected to the desired focal point. With f1=f2, the lens will be a flat ring instead of a tilted ring with varying atomic planes. Following are two designs; one has symmetric design, and the other has asymmetric design. They have the same working distance and different focal spot size. The main reason for the asymmetric design is to conserve materials and reduce the overall dimension of the system. In the symmetric design, the performance parameters of the graphite for Laue reflection are the same as for Bragg reflection, except for the reflectivity. As measured recently by Applicants, it is about 18% around 60 KeV. d-spacing d: 3.33 ◯ FWHM w: 0.4 (24 arc minutes) Laue reflectivity R:  less than 18% Density xcfx81: 2.25 g/cm3  Attenuation xcexc: 0.175 gxe2x88x921xc2x7cm2  The following is a particular design of a Laue lens 86 for the performance estimation. The main parameters of the lens 86 are listed below: Inner diameter: 16.3 mm Outer diameter: 32.6 mm Length: variable Source-lens center distance: 350 mm Lens center-focus distance: 350 mm The inner edge of the Laue lens 86 is tuned to work at 80 KeV; and the outer edge is tuned to work at 40 KeV. The band pass at each point is given by       Δ    ⁢          xe2x80x83        ⁢    E    =            E      ⁢              xe2x80x83            ⁢      cos      ⁢              xe2x80x83            ⁢              θ        ·        Δ            ⁢              xe2x80x83            ⁢      θ              sin      ⁢              xe2x80x83            ⁢      θ       At the position where the incident angle xcex8, the energy of the x-rays which satisfy the Bragg law is   E  =      12.4          2      ⁢      d      ⁢              xe2x80x83            ⁢      sin      ⁢              xe2x80x83            ⁢      θ       Therefore the band pass as a function of q can be written as       Δ    ⁢          xe2x80x83        ⁢    E    =            12.4      ⁢      cos      ⁢              xe2x80x83            ⁢              θ        ·        Δ            ⁢              xe2x80x83            ⁢      θ              2      ⁢      d      ⁢              xe2x80x83            ⁢              sin        2            ⁢      θ       where xcex94xcex8 is the rocking curve width. The capture angle will be determined by,       Δ    ⁢          xe2x80x83        ⁢    Ω    =            ∫              θ        1                    θ        2              ⁢          sin      ⁢              xe2x80x83            ⁢              θ        ·                  xe2x80x83                ⁢                  ⅆ          θ                    ⁢                        ∫          0                      2            ⁢            π                          ⁢                  xe2x80x83                ⁢                  ⅆ          φ                     where xcex82 is the incident angle at the outer edge and xcex81 is the incident angle at inner edge.             θ      1        =                            sin                      -            1                          ⁡                  (                                    12.4              80                        ⁢                          1                              2                xc3x97                3.33                                              )                    =              1.33        ⁢        xc2x0                        θ      2        =                            sin                      -            1                          ⁡                  (                                    12.4              40                        ⁢                          1                              2                xc3x97                3.33                                              )                    =              2.67        ⁢        xc2x0                        Δ      ⁢              xe2x80x83            ⁢      Ω        =                            ∫                      θ            1                                θ            2                          ⁢                  sin          ⁢                      xe2x80x83                    ⁢                      θ            ·                          ⅆ              θ                                ⁢                                    ∫              0                              2                ⁢                π                                      ⁢                          xe2x80x83                        ⁢                          ⅆ              φ                                          =              5.13        xc3x97                  10                      -            3                          ⁢                  xe2x80x83                ⁢                  sterad          .                     The efficiency of the lens 86 can be written as   Efficiency  =                    ∫                  θ          1                          θ          2                    ⁢                        R          ·          Δ                ⁢                  xe2x80x83                ⁢                  E          ·          sin                ⁢                  xe2x80x83                ⁢                  θ          ·                      ⅆ            θ                          ⁢                              ∫            0                          2              ⁢              π                                ⁢                      xe2x80x83                    ⁢                      ⅆ            φ                                =                  ∫                  θ          1                          θ          2                    ⁢              R        ⁢                  xe2x80x83                ⁢                              12.4            ⁢            cos            ⁢                          xe2x80x83                        ⁢                          θ              ·              Δ                        ⁢                          xe2x80x83                        ⁢            θ                                2            ⁢            d            ⁢                          xe2x80x83                        ⁢            sin            ⁢                          xe2x80x83                        ⁢            θ                          ⁢                  ⅆ          θ                ⁢                              ∫            0                          2              ⁢              π                                ⁢                      xe2x80x83                    ⁢                      ⅆ            φ                               where R is 0.18 and xcex94xcex8=0.4xc2x0=0.00698 Rad.       Efficiency    =                  0.00234        ⁢                              ∫                          1.33              ⁢              xc2x0                                      2.67              ⁢              xc2x0                                ⁢                                                    cos                ⁢                                  xe2x80x83                                ⁢                θ                                            sin                ⁢                                  xe2x80x83                                ⁢                θ                                      ⁢                          xe2x80x83                        ⁢                          ⅆ              θ                        ⁢                                          ∫                0                                  2                  ⁢                  π                                            ⁢                              xe2x80x83                            ⁢                              ⅆ                φ                                                        =      0.021            Throughput    ≈          Efficiency              3.05        xc3x97                              10                          -              4                                ·          40                      ≈    0.82   In the unit xe2x80x9cEffective solid anglexe2x80x9d unit, the throughput should be xcex94xcexa9xe2x80x2≈8.2xc3x9710xe2x88x925 assuming the voltage setting is 120 kV. The performance summary is: Capture angle: 5.13xc3x9710xe2x88x923 strad Focal spot size: xcx9c3 mm (depends on fabrication accuracy) Throughput: 0.82 Effective solid angle: 8.2xc3x9710xe2x88x925  The asymmetric lens design shown in FIG. 12 can save material and shorten assembly time. However, as discussed above, theoretically the tilting angle of each layer 94 is different. In practice, it can be approximated by limited number of crystal layers. Each layer 94 is made of whole piece of crystal. Therefore the tilting angle of the crystal plane is the same within each layer 94. This particular lens 100 design includes three concentric layers 94 (rings) having a thickness of 2 mm in the preferred embodiment. The inner radius of the lens is 5.4 mm, while the outer radius of the lens is 11.4 mm. Each lens layer 94 has a conical configuration. The main parameters of this design are given in Table 1. Referring to FIG. 13, a further embodiment of the present invention is shown utilizing Laue reflection to focus x-rays. An x-ray source 92xe2x80x2 directs x-rays 84xe2x80x2 to the lens or crystal 86xe2x80x2 where some of the x-rays 88xe2x80x2 are diffracted and focused and transmitted x-rays 96 exit the crystal without being diffracted. Beam stopper 98 blocks these transmitted x-rays 96. Coaxial x-rays 102 will be filtered by x-ray filter 22xe2x80x2 similar to the previously described x-ray filter 22. A cross section of a combination Laue and Bragg lens system is illustrated by FIG. 14. The x-ray source 92xe2x80x3 directs a portion of the x-rays 84xe2x80x3 to a Bragg reflective surface 104, preferably comprised of mosaic graphite crystal, which reflects generally monochromatic x-rays to the focal point 90xe2x80x3. A portion of the x-rays 84xe2x80x3 also are directed to the graphite crystal 86xe2x80x3 where some of the x-rays 88xe2x80x3 are diffracted and focused to a focal point 90xe2x80x3. Transmitted x-rays 96xe2x80x2 which travel through the crystal 86xe2x80x3 are incident upon a second Bragg reflective surface or lens 106 configured to focus the transmitted x-rays 96xe2x80x2 to focal point 90xe2x80x3. This configuration of multiple Bragg and Laue lenses increases the flux concentrating power of the combination lens system. X-rays which were previously occluded or blocked ore now conditioned and directed towards focal point 90xe2x80x3. The graphite reflecting and diffraction layers of the x-ray lenses of the present invention may be formed by a variety methods including but not limited to direct growth on a lens housing and the bending of a generally flat graphite sheet. The bending process will allow the creation of a conical graphite lens at room temperature. Referring to FIGS. 15-17, in one embodiment of the present invention a generally conical lens is formed by the bending of four identical plates 110 of graphite, each bent plate 110 representing a quarter of the lens, i.e. ninety degrees. The bent plates 110 are assembled in a housing to create the complete conical lens. The quality of bending will directly affect the performance of a graphite lens since the positive stress (compressing force) along the layer direction during bending will damage the mosaicity of the graphite. For example, as shown in FIG. 15, there are three different layers 112 of stress if a graphite lens is bent without a supporting structure. The central layer 114 undergoes no stress during bending. Below and above this central layer the graphite layers 116 will experience negative and positive stresses. The magnitude of the stress is linearly proportional to the distance from the central layer 114 and the length of the graphite plate 110. Damage to the mosaicity of the graphite is directly related to positive stress. In order to minimize the damage to the graphite plate 110 during the bending procedure, three methods of bending may be used. In the first method, since a shorter graphite plate will experience lesser stress during the bending process, several bent graphite plates 110 can be used to form a complete circle as seen in the previous embodiments of the invention. The number of graphite plates 110 to be segmented depends on the radius of the graphite plate 110, thickness of the graphite plate 110 and the mechanical properties of the graphite plate 110. In the second bending method, as shown in FIG. 16, a reinforcement plate 118 is introduced to shift the zero-stress layer to the front surface of the graphite plate 110. In the preferred embodiment, the reinforcement plate 118 is comprised of a piece of transparent mylar sheet glued or affixed onto the front surface of the graphite sheet 110 before bending. The reinforcement plate 118 is removed after bending in order to expose the front surface of the graphite plate 110 to the environment. In the third method, as seen in FIG. 17, two guiding plates 120 and 122 are used to guide the graphite plate 110 for uniform bending. In the third method shown in FIG. 17, a conical rod 109 is placed on the inner guiding plate 120 and the graphite plate 110 is sandwiched by inner guiding plate 120 and outer guiding plate 122. The bending forces are applied to the graphite plate 110 through the guiding plates 120 and 122 so that the graphite plate 110 will form along the conical rod 109 and assume the shape of the conical rod 109. There are two methods for lens assembly to be used in the present invention. FIG. 18 shows a first method of lens mounting where individual bent graphite lens segments are assembled into a complete lens. The axis 128 of a lens holder 126 defines the axis of the lens system. The x-ray camera 130 is positioned at the focal point 132. The position and the angles of an individual bent graphite plate 134 are adjusted such that the reflected beam is focused on the focal point 132. The bent graphite plate 134 is fixed to the holder 126 after the alignment. All remaining graphite plate segments are mounted onto the holder 126 with this procedure. Referring to FIG. 19, another method of lens assembly using a conical ring 152 and a conical rod 150 formed with the desired conical angles is illustrated. All bent graphite plates 154 are assembled simultaneously in this single ring lens method. One or more spacers are needed to fill the gap caused by different conical angles between layers for a multi-layer lens system. The inner rod 150 and the spacers are made from a material with less x-ray absorption than the bent graphite plates 154 and enough mechanical strength and chemical stability to withstand the bending forces generated by the conical rod 150. It is to be understood that the invention is not limited to the exact construction illustrated and described above, but that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the following claims.