Abstract:
A modular x-ray lens system for use in directing x-rays comprising a radiation source which generates x-rays and a lens system which directs the x-rays, wherein the x-ray lens system may be configured to focus x-rays to a focal point and vary the intensity of said focal point.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    The present invention relates to an x-ray focusing system. More specifically the present invention relates to a modular system of lenses designed to focus high energy x-rays.  
           [0002]    There are various applications which may benefit from the use of focused x-rays. The following background and description illustrate applications of the present invention which are merely exemplary in nature and are in no way intended to limit the invention or its uses. Moreover, the following description, while depicting an x-ray lens system designed to be used in medical applications and crystal diffraction applications, is intended to adequately teach one skilled in the art to make and use the present invention in a variety of x-ray applications, including, but not limited to x-ray structural analysis and x-ray spectroscopy.  
           [0003]    Presently, medical applications such as radiotherapy use collimated x-rays for the destruction of malignant tissue. Radiotherapy is one of the major methods, sometimes the only method, in treating some types of cancers such as brain tumors. Linear accelerator systems generating x-rays have been widely used in radiotherapy in the destruction of such malignancies. Linear accelerator systems employed in radiotherapy generally use a multi-leaf collimator to create a shaped beam of x-rays. The shaped x-ray beam intensity has a flux density consistent throughout its extent. The energy range of x-rays generated by such a system usually reach into the MeV range to be effective. To destroy a tumor the linear accelerator system must be continually directed at and rotated about the targeted malignant tissue. The high energy (MeV) of linear accelerator systems and their collimated rays expose a large amount of healthy tissue surrounding a tumor to a potentially damaging concentrations of x-rays in the MeV range. The focused x-ray beam of the present invention provides a high brightness focal spot of lower energy x-rays which is used to treat a target in an accurate controlled fashion, as well as treat the target at an early stage. Lower energy x-rays have quicker fall-off behind the target and therefore reduce tissue damage to some sensitive organs which may be exposed to x-rays.  
           [0004]    A system utilizing the x-ray focusing properties of the present invention can achieve the same results with reduced damage to collateral tissue and an energy use in the 40 KeV-100 KeV range. The advantages of using this focusing system include: reduced exposure and damage of healthy body tissue to x-rays, the x-rays in the KeV range can be focused directly at a malignancy with decreasing radiation intensity surrounding the x-ray focal point/treatment area, eliminating damage to sensitive organs proximate the target; the energy of the x-rays can be set above the absorption edge of certain materials such as drugs that are delivered to the tumor; the treatment of very small tumors can be done in a more precise manner; and there is an overall lower cost of the present invention as compared with previous linear accelerator systems.  
           [0005]    The x-ray focusing properties of the present invention may also be used in the study of crystal structures. A common method used to study crystal structures is x-ray diffraction. The method is based on illuminating a sample crystal with a beam of x-rays. A portion of the x-ray beam is not able to travel directly through the sample crystal, rather some rays are deflected or diffracted and emerge from the sample at varying angles. The incident x-rays make their way along the spaces between the atoms of the crystal or are deflected by the atoms. A sensor is used which detects the x-ray diffraction pattern generated by the x-rays as they emerge from the sample crystal. This diffraction pattern corresponds to the atomic structural arrangement of the crystal. Such a system is known in the art as an x-ray diffractometer. The focusing properties of the present invention can improve the flux concentration on a sample crystal leading to improved diffraction patterns.  
           [0006]    Many devices can be used to focus, and/or reflect x-rays such as total reflection mirrors, bent single crystals, graded multi-layer devices, and mosaic crystals. The main purpose of these devices is to gather x-ray flux produced by an x-ray generator and direct it to a desired area. There are three main factors which determine the flux strength of a reflecting and focusing device: reflection angle, reflectivity, and rocking curve width. Reflection angle is the angle at which x-rays are reflected from the surface of the reflection surface, reflectivity is the amount of energy returned from a surface after x-rays are incident upon that surface, and rocking curve width is the ability to collect and reflect energy over a particular incident range.  
           [0007]    The total reflection mirror has the smallest reflection angle of all the previously mentioned devices, which results in the smallest capture angle and in turn, small throughput, although its reflectivity approaches 100%. The total reflection mirror will also reflect the desired and undesired x-ray wavelengths. In medical applications, these undesired x-ray wavelengths could potentially cause skin damage to a person undergoing treatment.  
           [0008]    Bent single crystals have a large reflection angle and high peak reflectivity but a very narrow bandpass limiting the gathered flux to a small amount.  
           [0009]    Multi-layered x-ray reflectors have a fairly wide rocking curve width and high peak reflectivity. The reflection angle is also larger than a total reflection mirror. The reflectivity and rocking curve width will drop when smaller d-layer spacing is used to achieve larger reflection angles. For high energy x-rays, such as in the multiple 10 KeV range, the x-ray focusing efficiency of the multi-layer reflector is not satisfactory.  
           [0010]    Mosaic crystals consist of numerous tiny independent crystal regions which are nearly parallel but not quite parallel to one another. Mosaic crystals such as a graphite crystal have high reflectivity, a large reflection angle, and therefore a large capture angle. Mosaic crystals also have a large rocking curve width due to their mosaic structure. All of these factors make the mosaic crystal an attractive choice for reflecting and directing high energy x-rays. The focusing lenses of the present invention are composed of mosaic crystals such as a graphite crystal.  
         SUMMARY OF THE INVENTION  
         [0011]    The present invention is a modular system of lenses used for focusing x-rays. The lenses are operated using the principles of Bragg reflection and Laue diffraction. The ideal crystal surfaces and crystal planes of these lenses follow the Johansson scheme. In practice, cylindrical, conical, even polygonal surfaces can be used for approaching the focusing scheme. The lenses using Bragg diffraction deliver a beam of narrow frequency band (substantially monochromatic) x-rays, while the lenses using Laue diffraction deliver a controlled wide frequency band of x-rays. Many lenses can be designed to have the same source-focal point distance. Each of the lenses has different source-lens and lens-focus distances, depending on the requirements of focal spot size, working distance (front end of the lens to focal point), and flux, different lenses or combinations of several lenses can be used. This modularity creates a simple yet flexible scheme for varying intensity, focal spot size, and working distance.  
           [0012]    The lenses utilizing Bragg reflection use mosaic graphite crystal on their inner surfaces arranged in a cylindrical configuration. The lenses are formed by the bending of graphite layers or alternatively the direct growth of graphite on a lens housing. Graphite was chosen as preferred mosaic crystal in the Bragg lenses because of its superior reflective properties. The Laue lenses utilizing a Laue transmission scheme are similarly comprised of mosaic graphite crystal, but the x-rays are transmitted and diffracted through the crystal volume rather than being reflected only from the incident surface of the mosaic graphite crystal.  
           [0013]    For many applications, different focal spot sizes and different intensities are needed for varying flux density requirements. These requirements can be met by the use of supplementary Bragg reflective x-ray lenses with internal spherical, cylindrical, conical, parabolic, ellipsoid or other conic type configuration, but are not limited to such configurations. These supplementary x-ray lenses can be used to collect x-rays and focus them at varying focal lengths and create varying focal point areas and intensities. This modularity creates a simple yet flexible scheme of varying the intensity, focal length, and focal point area of an x-ray beam.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0014]    [0014]FIG. 1 is a diagrammatic view of an x-ray system utilizing the lens system of the present invention;  
         [0015]    [0015]FIG. 2 is a diagram of a simple Bragg reflector;  
         [0016]    [0016]FIG. 3 is a diagrammatic view of the crystal regions in mosaic carbon reflecting x-rays;  
         [0017]    [0017]FIG. 4 is a diagrammatic view of Laue x-ray diffraction in an x-ray lens;  
         [0018]    [0018]FIG. 5 is a diagram of the bent Johansson crystal working principle;  
         [0019]    [0019]FIG. 6 is a lengthwise cross sectional view of the main lens of the present invention focusing x-rays and having a curved reflective surface with respect to incident x-rays;  
         [0020]    [0020]FIG. 7 is a lengthwise cross sectional view of the main lens of the present invention focusing x-rays and having a flat reflective surface with respect to incident x-rays;  
         [0021]    [0021]FIG. 8 is a lengthwise cross sectional view of a multiple x-ray lens system of the present invention having curved surfaces with respect to incident x-rays;  
         [0022]    [0022]FIG. 9 is a lengthwise cross sectional view of a multiple x-ray lens system of the present invention having flat and angled surfaces with respect to incident x-rays;  
         [0023]    [0023]FIG. 10 is a diagrammatic view of an x-ray lens of the present invention utilizing the principle of Laue x-ray diffraction;  
         [0024]    [0024]FIG. 11 is a perspective view of an x-ray lens of the present invention comprised of multiple concentric layers of mosaic graphite crystal;  
         [0025]    [0025]FIG. 12 is a cross sectional view taken along line  12 - 12  in FIG. 11;  
         [0026]    [0026]FIG. 13 is a cross sectional view of an x-ray lens of the present invention utilizing the principle of Laue x-ray diffraction and equipped with beam stoppers and filters;  
         [0027]    [0027]FIG. 14 is a cross section view of a combination x-ray lens utilizing the principles of Laue x-ray diffraction and Bragg x-ray reflection;  
         [0028]    FIGS.  15 - 17  illustrate the methods of bending graphite used to fabricate the x-ray lenses of the present invention;  
         [0029]    [0029]FIG. 18 illustrates the calibration of an x-ray lens and lens holder; and  
         [0030]    [0030]FIG. 19 illustrates the method of forming a conical surface for the lenses of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0031]    [0031]FIG. 1 is a diagrammatic view of 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 .  
         [0032]    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.  
         [0033]    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 X 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&#39;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&#39;s law. Mosaic graphite and other Bragg structures only reflect radiation when Bragg&#39;s equation is satisfied:  
           nλ =2 d  sin(θ)  
         [0034]    where  
         [0035]    n=the order of reflection  
         [0036]    λ=wavelength of the incident radiation  
         [0037]    d=layer-set spacing of a Bragg structure or the lattice spacing of a crystal  
         [0038]    θ=angle of incidence  
         [0039]    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&#39;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 “reflection scheme” and the latter is referred to as a “transmission scheme”.  
         [0040]    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&#39;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.  
         [0041]    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 Å           FWHM w:   0.5°           Reflectivity R:   50%           Density ρ:   2.25 g/cm 3             Attenuation μ:   0.175 g −1  · cm 2                        
 
         [0042]    [0042]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.  
         [0043]    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.  
         [0044]    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&#39;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.  
         [0045]    [0045]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 “bent” 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 lens  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.  
         [0046]    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 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 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  26 ′ of the present invention focusing x-rays. The main Bragg reflective lens  26 ′, as shown by the drawing, has a graphite layer  76 ′ that is not inclined or angled, rather it is substantially concentrically flat relative to the cylindrical housing of the main lens  78 ′ relative to incident x-rays  75 ′. The barrel or interior surface of the main lens  26 ′ therefore has generally a constant inner diameter throughout its full length. The flat reflecting surface of the graphite layer  76 ′ 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  76 ′ will have more aberration than the curved graphite surface  76 , shown in FIG. 6 of the leading to a larger focal point  79 ′.  
         [0047]    [0047]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.  
         [0048]    Referring to FIG. 9, the mosaic graphite layer  80 ′ of lens  24 ′ is sloped in linear fashion (conical in three dimensions), the mosaic graphite layer  76 ′ of main lens  26 ′ is flat (cylindrical in three dimensions), and the mosaic graphite layer  82 ′ of extension lens  28 ′ is also sloped in linear fashion (conical in three dimensions) opposite to that of mosaic graphite layer  80 ′. 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.  
         [0049]    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 1° in both directions, as a unit for the throughput, this unit will be equal to  
         unit                 throughput     =         ∫     89.5      °       90.5      °            sin                 θ           θ            ∫   0   0.01745             φ           =     3.05   ×     10     -   4          strad                             
 
         [0050]    All Bragg reflective lenses in this section will be estimated in this unit.  
         [0051]    The parameters of the main lens  26 ′ are:  
                                                       Inner diameter:   25 mm           Length:   115 mm           Source-lens center distance:   400 mm           Lens center-focus distance:   400 mm           Capture angle:   1.70 × 10 −3  strad           Focal spot size:   2-4 mm           Throughput   2.78                      
 
         [0052]    The wavelength of an x-ray at 60 KeV is calculated from the following formula:  
       λ   =       12.4     E        (     k                 e                 V     )         =       12.4   60     =     0.207                 Angstroms                               
 
         [0053]    The Bragg angle is:  
       θ   =         sin     -   1            (     λ     2                 d       )       =         sin     -   1            (     0.207     2   ×   3.33       )       =     1.779      °                               
 
         [0054]    The capture angle will be determined by:  
         Δ                 Ω     =         ∫     1.529      °       2.029      °            sin                 θ           θ            ∫   0     2      π               φ           =     1.70   ×     10     -   3          strad                             
 
         [0055]    In the case of the main lens  26 ′, the throughput is equal to the capture angle multiplied by the average reflectivity. Therefore the throughput is 8.5×10 −4  strad. In the unit defined above, the throughput of our lens  26 ′ will be 2.78.  
                                         The parameters of the lens 24′ are:                                Inner diameter of the exit:   25 mm       Inner diameter of the entrance:   23.5 mm       Length:   86.5 mm       Source-lens center distance:   299 mm       Lens center-focus distance:   501 mm       Capture angle:   2.18 × 10 −3  strad       Focal spot size:   4-10 mm, depending on source size       Throughput   3.57                  
 
         [0056]    The capture angle will be determined by:  
         Δ                 Ω     =         ∫     2.029      °       2.529      °            sin                 θ           θ            ∫   0     2      π               φ           =     2.18   ×     10     -   3          strad                             
 
         [0057]    As discussed above, the throughput is equal to the capture angle multiplied by the average reflectivity. Therefore the throughput is 1.09×10 −3  strad and in the unit defined above, the throughput of the lens  24 ′ will be 3.57. The lens  24 ′ will give a large throughput, but will generate a larger focal spot.  
         [0058]    The parameters of the extension lens  28 ′ 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:   1.22 × 10 −3  strad           Focal spot size:   depends on source size           Throughput   1.97                      
 
         [0059]    The capture angle will be determined by:  
         Δ                 Ω     =         ∫     1.026   °       1.526   °            sin                 θ                      θ            ∫   0     2      π                          φ           =     1.22   ×     10     -   3                     strad                             
 
         [0060]    The throughput is 0.61×10 −4  strad and in the unit defined above, the throughput of lens  28 ′ will be 1.97. The extension lens  28 ′ has finer focus and larger convergent angle.  
         [0061]    The intensity distribution and throughput of a particular combination of lenses can be calculated based on source information, source projection size, intensity distribution, etc.  
         [0062]    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 f 1  and the distance between the lens  86  and the focal point  90  is f 2 . The length of the lens is L. The inner diameter of the Laue lens  86  is R 1  and the outer diameter is R 2.    
         [0063]    In the case where f 1  is not equal to f 2 , 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 f 1 =f 2 , 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.  
         [0064]    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:   &lt;18%           Density ρ:   2.25 g/cm 3             Attenuation μ:   0.175 g −1  · cm 2                        
 
         [0065]    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                      
 
         [0066]    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                 E     =       E                 cos                   θ   ·   Δ                   θ       sin                 θ                             
 
         [0067]    At the position where the incident angle θ, the energy of the x-rays which satisfy the Bragg law is  
       E   =     12.4     2      d                 sin                 θ                             
 
         [0068]    Therefore the band pass as a function of q can be written as  
         Δ                 E     =       12.4                 cos                   θ   ·   Δ                   θ       2      d                   sin   2        θ                             
 
         [0069]    where Δθ is the rocking curve width.  
         [0070]    The capture angle will be determined by:  
       ΔΩ   =       ∫     θ   1       θ   2            sin                   θ   ·        θ              ∫   0     2      π               φ                                 
 
         [0071]    where θ 2  is the incident angle at the outer edge and θ 1  is the incident angle at inner edge.  
         θ   1     =         sin     -   1            (       12.4   80          1     2   ×   3.33         )       =     1.33      °                 θ   2     =         sin     -   1            (       12.4   40          1     2   ×   3.33         )       =     2.67      °               ΔΩ   =         ∫     θ   1       θ   2            sin                   θ   ·        θ              ∫   0     2      π               φ           =     5.13   ×     10     -   3            sterad   .                               
 
         [0072]    The efficiency of the lens  86  can be written as  
             Efficiency   =       ∫     θ   1       θ   2              R   ·   Δ                     E   ·   sin                     θ   ·        θ              ∫   0     2      π               φ                       =       ∫     θ   1       θ   2            R          12.4      cos                   θ   ·   Δθ         2      d                 sin                 θ               θ            ∫   0     2      π               φ                                       
 
         [0073]    where R is 0.18 and Δθ=0.4°=0.00698 Rad.  
       Efficiency   =       0.00234          ∫     1.33      °       2.67      °                cos                 θ       sin                 θ               θ            ∫   0     2      π               φ             =   0.021             Throughput   ≈     Efficiency     3.05   ×       10     -   4       ·   40         ≈   0.82                         
 
         [0074]    In the unit “Effective solid angle” unit, the throughput should be  
         ΔΩ′≈8.2×10 −5    
         [0075]    assuming the voltage setting is 120 kV.  
         [0076]    The performance summary is:  
                                       Capture angle:   5.13 × 10 −3  strad       Focal spot size:   ˜3 mm (depends on fabrication accuracy)       Throughput:   0.82       Effective solid angle:   8.2 × 10 −5                    
 
         [0077]    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 .  
         [0078]    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.  
                                                     TABLE 1                                       Major parameters of the asymmetric design   180           Object distance (Source-Lens, mm)           Image distance (Lens-focal plane, mm)   350                                    Energy   Conical           Rings   ID (mm)   OD (mm)   (KeV)   Angle (°)   Graphite (mm 3 )               Inner   10.8   14.8   60˜80   0.50   46.5 × 10 × 2*       Middle   14.8   18.8   47˜60   0.65   59 × 10 × 2*       Outer   18.8   22.8   40˜47   0.80   71.6 × 10 × 2*                  
 
         [0079]    Referring to FIG. 13, a further embodiment of the present invention is shown utilizing Laue reflection to focus x-rays. An x-ray source  92 ′ directs x-rays  84 ′ to the lens or crystal  86 ′ where some of the x-rays  88 ′ 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  22 ′ similar to the previously described x-ray filter  22 .  
         [0080]    A cross section of a combination Laue and Bragg lens system is illustrated by FIG. 14. The x-ray source  92 ″ directs a portion of the x-rays  84 ″ to a Bragg reflective surface  104 , preferably comprised of mosaic graphite crystal, which reflects generally monochromatic x-rays to the focal point  90 ″. A portion of the x-rays  84 ″ also are directed to the graphite crystal  86 ″ where some of the x-rays  88 ″ are diffracted and focused to a focal point  90 ″. Transmitted x-rays  96 ′ which travel through the crystal  86 ″ are incident upon a second Bragg reflective surface or lens  106  configured to focus the transmitted x-rays  96 ′ to focal point  90 ″. 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 are now conditioned and directed towards focal point 90″.  
         [0081]    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.  
         [0082]    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.  
         [0083]    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.  
         [0084]    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 .  
         [0085]    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.  
         [0086]    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 .  
         [0087]    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.