the following description is provided , alongside all chapters of the present invention , so as to enable any person skilled in the art to make use of the aforesaid invention , and sets forth the best modes contemplated by the inventor of carrying out this invention . various modifications , however , are adapted to remain apparent to those skilled in the art , since the generic principles of the present invention have been defined specifically to provide an x - ray reflective lens arrangement for forming an intensity pattern in a focal region and methods of using the same . the term “ elemental ” hereinafter refers to infinitely small portion of a physical entity . the term “ focal track ” hereinafter refers to an ordered ensemble of elemental focal points created by a reflecting surface of an x - ray lens . the term “ intensity weighted centroid of the x - ray source ” hereinafter refers to a point defined by a vector r sc , the term “ intensity weighted centroid of the focal pattern ” hereinafter refers to a point defined by a vector { dot over ( r )} fc i focus ( x , y , z ) is a spatial distribution of radiation intensity in the focal region , and i source ( x , y , z ,) is the spatial distribution of source intensity at the source space . it should be appreciated that the radiation pattern has a three - dimensional shape . referring to the medical use of the x - ray system for tumor treatment , the known therapeutic devices comprising focusing elements are characterized by concentration of x - ray radiation into a sharp focal spot . it should be emphasized that uniform x - ray exposure of a target volume is a desirable condition of successful therapy or surgery because the optimal effect is achieved when all target tissue is exposed to a uniform dose . thus , there is a long - felt and unmet need to provide a therapeutic device for x - ray treatment of tumors adapted for forming substantially uniform x - ray intensity within the target volume . reference is now made to fig1 , illustrating a simple bragg reflector utilizing the principles of bragg reflection . x - ray radiation 4 of wavelength λ is incident on a crystal having lattice planes 2 of plane spacing d . narrow band or generally monochromatic radiation 6 is then reflected according to bragg &# 39 ; s law . bragg structures only reflect radiation when bragg &# 39 ; s equation is satisfied : where n is the reflection order , λ is the incident radiation wavelength , d is the lattice plane spacing , and θ b is the bragg angle . reference is now made to fig2 , presenting a two - dimensional longitudinal cut of the johansson scheme . a johansson bent and machined crystal 10 is used to reflect and focus x - rays . the johansson bent and machined crystal 10 reflects x - rays according to bragg &# 39 ; s law . the johansson crystal 10 is made by bending and grinding a crystal into a barrel shaped surface with a longitudinal bending radius 2r , and then the reflection surface 14 is machined to a cylindrical surface with longitudinal radius r . in a special symmetrical case , the angles of incidence of rays 15 generated by the x - ray source s and angles of reflection of rays 17 converging into the point f , are equal . the transversal curvature radius of the machined surface at a midpoint between the source and the focal point r s is given by l is half of the distance from the source to the focal point . reference is now made to fig3 , elucidating a subject matter of the current invention . an elemental point 11 is a part of the image of an elemental x - ray source point 9 in source space x s y s formed by an elemental portion 60 of reflective lens which lies in a rowland arc 70 subtended by a chord 25 . lines 40 and 50 refer to rays emitted by the x - ray source elemental point 9 and reflected from the lens portion 60 , respectively . an axis 18 is a main axis of the entire lens . the chord 25 is the optical axis of the narrow reflective lens portion 60 . the aforesaid point 11 is at location r im on the x i y i plane of the image space . the elemental point source 9 makes an angle φ s relative to the x s axis in source space . the elemental point 11 makes an angle φ i relative to the x i axis in image space , wherein φ s and φ i are generally not the same , thus in general the image point 11 can be rotated relative to the source point 9 . reference is now made to fig4 , presenting a lens arrangement 100 continuously defined by an ensemble of elemental arcs 60 being rotated around the main axis 18 . the lens arrangement 100 focuses radiation emitted by the x - ray source 12 into a curved radiation pattern 31 . it should be emphasized that the curved pattern of radiation pattern 31 is an ensemble of elemental points 11 ( not shown ) created by the plurality of elemental arcs 60 integrally forming the reflective surface 100 . the main axis 18 is defined by two points which are : ( 1 ) the intensity weighted centroid c 1 of the x - ray source , and ( 2 ) a centroid c 2 of the linear radiation pattern 30 . the centroids are intensity weighted average points of the source and the radiation patter 31 . reference is now made to fig5 and 6 , presenting exemplary embodiments of the current invention . specifically , a lens arrangement 100 a is configured to provide an elliptic radiation pattern 30 a while a lens arrangement 100 b focuses radiation from the x - ray source into an orthogon 30 b with rounded angles . the designation p refers to a point source . reference is now made to fig7 to 9 , presenting exemplary radiation patterns focused by optional embodiments of the current invention . simple closed curves radiation patterns are shown in fig7 . the radiation patterns comprising two curved radiation tracks ( one inside another ) are depicted in fig8 ( concentric radiation patterns ) and fig9 ( non - concentric radiation patterns ). reference is now made to fig1 , presenting an alternative embodiment of the current invention . a lens arrangement 100 c is portioned into two parts , which are configured to provide the x - ray radiation into same curved radiation pattern 30 c . reference is now made to fig1 , presenting a cross - sectional schematic view of a lens arrangement of the current invention which comprises a plurality of reflective surfaces ( for example , three surfaces 61 , 62 and 63 ). the aforesaid tracks are formed by revolution of rowland arcs 71 , 72 and 73 around the main axis 18 , and its elemental image are defined as intersection chords 26 , 27 and 28 with the corresponding arcs 71 , 72 and 73 , respectively . the reflective surface 61 , 62 and 63 reflect the radiation emitted by the point source p to ring - like radiation patterns 32 , 33 and 34 , respectively . the chords 26 , 27 and 28 extend from the point source p , and are tilted in this example to the main axis 18 of the lens arrangement . thus , at output of the lens arrangement , a resulting radiation pattern comprising a plurality of the ring - like radiation patterns 32 , 33 and 34 is provided . the aforesaid patterns are distributed over the main axis 18 . reference is now made to fig1 , presenting a cross - sectional schematic view of a double reflection lens arrangement . the lens arrangement comprises a pair of oppositely directed reflective surfaces 60 d and 60 e residing on the rowland arcs 70 d and 70 e which are subtended by chords 25 d and 25 e , respectively . specifically , the reflective surface 60 d provides a ring - like radiation pattern 31 a . then , the reflective surface 60 e further reflects the radiation of the pattern 31 a into a point pattern 30 d . a significant advantage of the depicted double reflection lens arrangement is in providing a wide - angle convergent beam essentially to a surface region of a patient &# 39 ; s body without extensive damage to surrounding tissues and the use of low order high reflective crystallographic planes for more than one reflective ring . the wide angle of the beam convergence results in very quick drop in radiation in a space behind the focus point 30 d . thus , the proposed lens arrangement can be effectively used for x - ray therapy of surface tumors . it also enables having a relatively large lens for higher solid angle of radiation collection . reference is now made to fig1 , presenting a cross - sectional schematic view of a lens arrangement comprising two pluralities of reflective surfaces ( for example , two surfaces in each plurality ). radiation from the point source p is focused by reflecting surfaces 60 g and 60 f into ring - like radiation patterns 31 f and 31 g , respectively . then , the aforesaid radiation from patterns 31 f and 31 g are further reflected by surfaces 60 h and 60 i into a point radiation pattern 30 f . the rowland arcs 70 f , 70 g , 70 h and 70 i are subtended by chords 25 f , 25 g , 25 h and 25 i , respectively . reference is now made to fig1 , presenting a cross - sectional schematic view of an alternative embodiment of the current invention . the lens arrangement provides an output radiation pattern comprising a point focal spot 30 n and at least one ring - like pattern 30 m . radiation from the point source p is focused by reflecting surfaces 60 k and 60 l into ring - like radiation patterns 31 k and 31 l , respectively . then , the aforesaid radiation from patterns 31 k and 31 l are further reflected by surfaces 60 m and 60 n into a ring - like pattern 30 m and a point radiation pattern 30 n , respectively . the rowland arcs 70 k , 70 l , 70 m and 70 n are subtended by chords 25 k , 25 l , 25 m and 25 n , respectively . reference is now made to fig1 , presenting an exemplary combined lens arrangement comprising at least one single - reflection lens and at least one double reflection lens assembly . specifically , the combined arrangement comprises of a single lens 60 r and a double reflection lens arrangement 60 o - 60 p . each component ( single and double lens arrangements ) can be replaced with a plurality of similar elements . in addition , each element can be configured for focusing point or non - point source into any focal point or focal track . one core purpose of the proposed invention is to describe a lens array design for providing higher efficiency in transmitting the radiation from the x - ray tube to the focul track . for example , the known technical solutions comprise a multiplicity of rings containing bragg reflector single crystals . however , the present invention , concentrates the radiation within the targeted volume and different rings required crystals cut in different crystallographic planes . however , different crystallographic planes do not have the same reflectivities . therefore some rings &# 39 ; crystals have higher efficiency than others . the present invention overcoms this limitation and allows the higher efficiency crystal orientations to be used in multiple rings . the proposed technical solution significantly improves the overall efficiency of a lens array and provides more efficient lens array designs which can reduce exposure times or reduce lens complexity for equivalent exposure times . reference is now made to fig1 , presenting an exemplary lens comprising an inverted image assembly . the lens arrangement is designed so that each of the elemental image points 11 l and 11 u belongs to opposite elemental lenses . the aforesaid points called inverted points are located in the same plane defined by their rowland arcs . for example , the inverted points 11 l and 11 u are opposite to each other on the ring focal track 30 s relative to the elemental surface 60 su and 60 sl which produced them . in the drawing , the lower and upper drawn cuts of the elements in the drawings are labeled separately . lens upper surface is labeled 60 su and the lower part in the drawing is labeled 60 sl . the same applies to the rowland arcs , 70 su for upper drawing and 70 sl for the lower drawing and also for the cords suspending the rowland arcs 25 su and 25 sl and the elemental image points 11 u and 11 l connected to the x - rays shown as being a part of the ring 30 w . it should be emphasized that the two points 11 u and 11 l lay oppositely with respect to the symmetry line 18 that passes between them in their mutual plane containing the two inverted points . reference is now made to fig1 presenting double lens wide convergence angle comprising an inverted image assembly . an approach similar to fig1 is a double lens wide convergence angle setup , comprising an inverted image assembly applied also to double reflection assembly . the second reflector 60 wu and 60 pl flips the inverted points 11 u and 11 l on their mutual plane . this type of assembly hereinafter refers will be referred to as “ inverted image assembly ” the advantages of the present design solution are the following . an inverted image assembly causes the intersection of rays from the inverted sides of each plane containing the inverted points . the area of intersection can be seen as 80 s in a single reflection assembly of fig1 and 80 u in the double reflection assembly of fig1 . summing up the x - ray radiation from the entire surface of the lens forms a secondary concentration around the symmetry line that results in a somewhat higher dose along the symmetry line . concerning the ordinary non - inverted design solutions , the overlapping areas where secondary concentration of x - ray radiation occurs , are located behind the target volume of treatment . this is relatively distant from the location where the radiation has passed the volume of treatment . thus the radiation damage effect is much weaker due to attenuation of the beam and divergence angle of the x - ray beam . the strength of the effect depends on the convergence angle and the width of the reflecting surface . these parameters are controllable by means of changing design parameters . this approach is especially effective in the double reflection assembly where the overlapping area is close to the treated volume . this can serve as part of the treatment plan improving the capability and control of the treated volume . the embodiments depicted in fig1 and 17 are more effective for treatment of a shallow tumor , since the intersection area will occur before the x - rays hit the body , while the non inverted embodiments are more effective for deeper tumor treatments since the intersection area is a minor phenomenon or located outside of the patient &# 39 ; s body . an additional benefit of the current invention is in the use of single crystals exhibiting some degree of mosaicity . the focal tracks thus created by the present invention are characterized by three - dimensional broadening which serves the purpose of allowing for homogeneity of the created radiation pattern within the target volume . the present invention is specifically advantageous in assembling multiple reflecting surfaces of elements having the same crystallographic plane index for different surfaces . in the case of double reflection arrangement , the dependency of the setup on bragg angle is further avoided , and thus the limitations caused by higher order low reflectivity miller index are overcome . thus , the present invention provides multiple low order and high reflectivity surfaces . special benefits can be made in cases where the body has to be irradiated from the front , e . g . after breast mastectomy . the existing technology provides irradiation of the entire depth of the body over relatively large area . the current invention provides a high convergence angle . thus , utilizing the high convergence angle yields a large attenuation after the target volume , spearing healthy tissues .
an x - ray lens arrangement for forming a radiation pattern as a focal track is disclosed . the pattern comprises at least one 3 - dimensional focal track of radiation . the aforesaid lens arrangement has a main axis passing through intensity weighted centroids of the x - ray source and the pattern . the lens arrangement includes at least one reflecting surface of continuously varying rowland arcs . each point belonging to the focal track is linked to each elemental point composing an emitting surface of said source by a corresponding rowland arc .