Abstract:
Methods and systems for the analysis of solid materials are disclosed. The present invention comprises x-ray and Raman analytical techniques and systems which facilitate the rapid characterization of a plurality of solid samples.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application claims the benefit of priority of U.S. Provisional Application Ser. No. 60/562,358, filed Apr. 15, 2004, which is hereby incorporated by reference herein in its entirety, including any figures, tables or drawings. 
     
    
     TECHNICAL FIELD OF THE INVENTION 
       [0002]    This invention relates to methods and apparatuses for transferring and manipulating solids for the purpose of automating PXRD (powder X-ray diffraction), Raman spectroscopy, or other compatible methods of analysis. Specific embodiments of the invention are particularly suited for the automated transfer and analysis of small quantities of solid particles. 
       BACKGROUND OF THE INVENTION 
       [0003]    Structure plays an important role in determining the properties of substances. The properties of many compounds can be modified by structural changes, for example, different polymorphs of the same pharmaceutical compound can have different therapeutic activities. Understanding structure-property relationships is crucial in efforts to maximize the desirable properties of substances, such as, but not limited to, the therapeutic effectiveness of a pharmaceutical. 
         [0004]    This invention relates generally to systems and methods for rapidly determining the characteristics of an array of diverse materials, and to systems and methods for rapidly determining the characteristics of a library of diverse materials using electromagnetic radiation. 
       SUMMARY OF THE INVENTION 
       [0005]    In a first embodiment, the present invention provides a method for the analysis of a solid material, comprising:
   (a) coring the solid material with a coring tool such that a plug is formed;   (b) extruding the plug of solid material;   (c) exposing the plug of solid material to radiation; and detecting scattered radiation.   
 
         [0009]    In another embodiment, the present invention provides a method for the analysis of a plurality of solid samples, comprising:
   (a) coring each solid sample with a coring tool such that each solid sample forms a plug;   (b) extruding each plug of solid material;   (c) exposing each plug of solid material to radiation; and   (d) detecting scattered radiation.   
 
         [0014]    In another embodiment, the present invention provides a system for analyzing a solid material, comprising:
   (a) a coring tool comprising a means for extruding a plug of solid material;   (b) a means for exposing the plug of solid material to radiation; and   (c) a means for detecting scattered radiation.   
 
         [0018]    In another embodiment, the present invention provides a system for analyzing a plurality of solid samples, comprising:
   (a) a plurality of coring tools, each comprising a means for extruding a plug of solid;   (b) a means for exposing the plugs of solid to radiation; and   (c) a means for detecting scattered radiation.   
 
     
    
     
       BRIEF DESCRIPTION OF THE FIGURES  
         [0022]    FIG.  1 —Illustrates a coring tool with a narrow region; 
           [0023]    FIG.  2 —Illustrates a coring tool with a bent rod; 
           [0024]    FIG.  3 —Illustrates an apparatus used to set cavity depth of coring tools; 
           [0025]    FIG.  4 —Illustrates loading a coring tool with solid material; 
           [0026]    FIG.  5 —Illustrates a coring tool after solid material is captured; 
           [0027]    FIGS.  6 A- 6 D—Illustrates various tapers for coring tips; 
           [0028]    FIG.  7 —Illustrates compression of a sample plug; 
           [0029]    FIG.  8 —Illustrates extrusion of a sample plug; 
           [0030]    FIG.  9 —Illustrates a coring tool rack; 
           [0031]    FIG.  10 —Illustrates a coring tool rack with lifting plate in raised position; 
           [0032]    FIG.  11 —Illustrates a coring tool rack with lifting plate in lowered position; 
           [0033]    FIG.  12 —Illustrates a pin bed for removal of coring rods; 
           [0034]    FIG.  13 —Illustrates important dimensions for sample analysis; 
           [0035]    FIG.  14 —Illustrates an unoptimized plate for sample analysis; 
           [0036]    FIG.  15 —Illustrates a plate with 2 holes per diagonal; 
           [0037]    FIG.  16 —Illustrates a plate with 3 holes per diagonal; 
           [0038]    FIG.  17 —Illustrates a plate with 4 holes per diagonal; 
           [0039]    FIG.  18 —Illustrates a plate with 8 holes per diagonal; 
           [0040]    FIG.  19 —Illustrates a plate for applications where the incident beam length is less than 10.00 mm; 
           [0041]    FIG.  20 —Illustrates a plate for applications with a maximum beam intensity. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0042]    The present invention encompasses methods and apparatuses for picking up, compressing, and precisely positioning small samples of material (e.g. amounts of less than about 5.00 mg), for the purpose of automating PXRD (Powder X-ray Diffraction), Raman Spectroscopy, or other compatible methods of analysis. Sample quantities can be, for example, less than about 5.00 mg, 2.5.00 mg, 1.00 mg, 750.00 micrograms, 500.00 micrograms, 250.00 micrograms, 100.00 micrograms, 50.00 micrograms, 25.00 micrograms, 10.00 micrograms, 5.00 micrograms, or 1.00 microgram of solid particles. Particular embodiments of the present invention involve coring a sample plug of powder from the bottom or sides of a vial using a coring tool that comprises a hollow needle with a slideable close fitting rod contained inside the hollow needle. See, Published Application No. US20040146434, filed Nov. 3, 2003, and International Publication No. WO04/042327, filed Nov. 3, 2003, the contents of which are incorporated by reference in their entireties. To provide optimal signal quality, a sample plug contained inside the needle tip can be compressed by the rod and extruded above the needle tip a small distance (e.g., about 0.10 mm to 1.00 mm) to allow optimal exposure to a beam of electromagnetic radiation. Each coring tool is, optionally, placed in a coring tool rack, which is defined as a substrate that precisely positions the sample plugs in x, y, and z coordinates relative to the rack base. The samples(s) is/are then placed on a cradle in a machine, such as a surface PXRD, that emits an electromagnetic beam of radiation which is directed through each sample plug to obtain information about the crystalline structure of each sample plug. 
         [0043]    This method has several advantages over other methods known in the prior art. For example, a system described in the art involves forming crystals on a substrate that is used for PXRD and Raman spectroscopic analysis (See U.S. Pat. Nos. 6,371,640 and 6,605,473). The present invention has the following advantages over such a system for both PXRD and Raman Spectroscopy: 1) The coring tool of the present method serves to both mill and compress powder crystals prior to analysis, thus improving signal quality; 2) The coring tool of the present method also requires a smaller amount of sample for quantitative analysis; 3) The present method allows the heights of sample plugs to be adjusted so they are coplanar. This allows the angle of incidence of the X-ray beam to be closer to horizontal, thus improving signal quality without picking up signals from neighboring sample plugs; 4) The present invention leaves material behind that is not exposed to x-ray radiation and, hence, decreases the existence of radiation-damaged material; and 5) The present invention can be used to extract sample material prepared in sealable individual vials, which provide superior flexibility and protection of crystalline samples from the environment. 
         [0044]    As used herein, the term “processing parameters” means the physical or chemical conditions under which a sample is subjected and the time during which the sample is subjected to such conditions. Processing parameters include, but are not limited to, adjusting the temperature; adjusting the time; adjusting the pH; adjusting the amount or the concentration of the sample; adjusting the amount or the concentration of a component; component identity (adding one or more additional components); adjusting the solvent removal rate; introducing a nucleation event; introducing a precipitation event; controlling evaporation of the solvent (e.g., adjusting a value of pressure or adjusting the evaporative surface area); and adjusting the solvent composition. Solid samples can be subjected to a diverse range of processing conditions before analysis is completed. The present invention provides the capacity to alter processing conditions from one sample to the next, or from one array of samples to the next, or from one sub-array of samples to the next. The isolation of each sample facilitates a more accurate analysis of solid material and is significantly less prone to contamination than other methods (e.g., plate-based methods). 
         [0045]    Sub-arrays or even individual samples within an array can be subjected to processing parameters that are different from the processing parameters to which other sub-arrays or samples, within the same array, are subjected. Processing parameters can differ between sub-arrays or samples when they are intentionally varied to induce a measurable change in the sample&#39;s properties. Thus, according to the invention, minor variations, such as those introduced by slight adjustment errors, are not considered intentionally varied. 
         [0046]    Embodiments of the invention are particularly suited for the automated or high-throughput analysis of solids such as, but not limited to, pharmaceuticals, excipients, dietary substances, alternative medicines, nutraceuticals, agrochemicals, sensory compounds, the active components of industrial formulations, and the active components of consumer formulations. Solids analyzed using the methods and devices of the invention can be amorphous, crystalline, or mixtures thereof. 
         [0047]    In a first embodiment, the present invention provides a method for the analysis of a solid material, comprising:
   (a) coring the solid material with a coring tool such that a plug is formed;   (b) extruding the plug of solid material;   (c) exposing the plug of solid material to radiation; and   (d) detecting scattered radiation.   
 
         [0052]    In a specific embodiment of the present invention, the analysis comprises x-ray scattering. In another embodiment, the analysis comprises Raman scattering. 
         [0053]    In another embodiment, the method further comprises compressing the solid material after the plug is formed. 
         [0054]    In another embodiment, the method further comprises loading the coring tool onto a rack after the solid material is extruded. 
         [0055]    A specific method of this embodiment comprises the steps of: (a) coring the solid material with a coring tool which comprises a narrow region in the needle of said coring tool or a bent rod inserted in the needle of said coring tool, such that a plug is formed; (b) compressing the plug of solid material with a mallet and a pin; (c) extruding the plug of compressed solid material with a pin; (d) loading the coring tool onto a rack; (e) exposing the compressed solid material to radiation; and (f) detecting scattered radiation. 
         [0056]    In another embodiment, the position of a pin in step (b) is adjusted by a micrometer. 
         [0057]    In another embodiment, the rack in step (d) comprises a top plate with one or more holes, and optionally, side walls and a bottom plate. Each hole in the top plate has a diameter which is about 10.00 micrometers, 20.00 micrometers, 30.00 micrometers, 40.00 micrometers, 50.00 micrometers, 60.00 micrometers, 70.00 micrometers, 80.00 micrometers, 90.00 micrometers, 100.00 micrometers, 150.00 micrometers, 200.00 micrometers, or 250.00 micrometers or more, greater than the diameter of the coring tool. In another embodiment, the rack comprises a top plate which is optionally made of polyvinyl chloride (PVC), chlorinated polyvinyl chloride (CPVC), or another material that absorbs X-ray radiation (or infrared or other radiation). In another embodiment, the rack comprises a plurality of holes. 
         [0058]    In another embodiment, the rack in step (d) optionally comprises a lifting plate. The lifting plate optionally comprises one or more holes corresponding to the holes in the top plate. Optionally, the lifting plate can be locked into place via thumbscrews or another device. Stops may be used to define a maximum height, a minimum height, or an intermediate height of the lifting plate. The bottom plate of the rack optionally comprises one or more set screws for leveling, raising, or lowering the lifting plate. 
         [0059]    In another embodiment, the rack in step (d) optionally further comprises a pin bed for removing one or more rods from the needle(s) of the coring tool(s). Optionally, the needles are held in place by a retainer plate. The retainer plate rests on walls (legs) which facilitate removal of coring tool rods. Alignment and stabilization of the retainer plate can optionally be performed by screws, pins, or other means. 
         [0060]    In another embodiment, an x-ray probe emits radiation in a beam with a beam length less than or equal to about 50.00 mm, 40.00 mm, 30.00 mm, 20.00 mm, 10.00 mm, or 5.00 mm. The beam length is defined as the distance between the x-ray probe emission aperture and the solid material loaded onto the coring tool (See item 98 of  FIG. 13 ). Optionally, the beam is collimated. The angle of incidence between the emitted beam and the top plate of the rack is, for example, but not limited to, less than or equal to about 2.50 degrees, 2.25 degrees, 2.00 degrees, 1.75 degrees, 1.50 degrees, 1.25 degrees, or 1.00 degrees. For example, about 2.50, 2.40, 2.30, 2.20, 2.10, 2.00, 1.90, 1.80, 1.70, 1.60, 1.50, 1.40, 1.30, 1.20, 1.10, 1.00, 0.90, 0.80, 0.70, 0.60, or 0.50 degrees. 
         [0061]    In another embodiment, the present invention provides a method for the analysis of a plurality of solid samples, comprising:
   (a) coring each solid sample with a coring tool such that each solid sample forms a plug;   (b) extruding each plug of solid material;   (c) exposing each plug of solid material to radiation; and   (d) detecting scattered radiation.   
 
         [0066]    In another embodiment, the present invention provides a system for analyzing a solid material, comprising:
   (a) a coring tool comprising a means for extruding a plug of solid material;   (b) a means for exposing the plug of solid material to radiation; and   (c) a means for detecting scattered radiation.   
 
         [0070]    In another embodiment, the present invention provides a system for analyzing a plurality of solid samples, comprising:
   (a) a plurality of coring tools, each comprising a means for extruding a plug of solid;   (b) a means for exposing the plugs of solid to radiation; and   (c) a means for detecting scattered radiation.   
 
         [0074]    Certain embodiments of the invention, as well as certain novel and unexpected advantages of the invention, are illustrated by the following non-limiting examples. 
       Exemplification 
       [0075]      FIG. 1  shows coring tool  9  comprising rod  1  partially inserted into hollow needle  2  with square end  28 . Narrow region  29  on needle  2  provides a light friction fit with rod  1 , thus allowing the position of rod  1  to remain stationary relative to needle  2  until adjusted with the application of a small force (e.g., from about 0.10 Newtons to about 4.00 Newtons). 
         [0076]      FIG. 2  shows coring tool  27  comprising bent rod  25  partially inserted into hollow needle  26  with square end  38 . Rod  25  is slightly bent to provide a light friction fit with needle  26 , thus allowing the position of rod  25  to remain stationary relative to needle  26  until adjusted with the application of a small force (e.g., from about 0.10 Newtons to about 4.00 Newtons). A suitable material for needles and rods is, for example, but not limited to, steel (e.g., stainless steel, 300 series stainless steel). For the present invention a useful inner needle diameter range is from about 50.00 micrometers to about 2000.00 micrometers, for example, about 50.00, 60.00, 70.00, 80.00, 90.00, 100.00, 125.00, 150.00, 175.00, 200.00, 250.00, 300.00, 400.00, 500.00, 600.00, 700.00, 800.00, 900.00, 1000.00, 1100.00, 1200.00, 1300.00, 1400.00, 1500.00, 1600.00, 1700.00, 1800.00, 1900.00, or 2000.00 micrometers or any intermediate value, and a useful needle wall thickness range is from about 10.00 micrometers to about 300.00 micrometers, for example, about 10.00, 15.00, 20.00, 25.00, 30.00, 40.00, 50.00, 60.00, 70.00, 80.00, 90.00, 100.00, 125.00, 150.00, 175.00, 200.00, 225.00, 250.00, 275.00, or 300.00 micrometers. A useful needle length is from about 1.00 mm to about 100.00 mm, for example, about 1.00, 1.50, 2.00, 2.50, 3.00, 4.00, 5.00, 6.00, 7.00, 8.00, 9.00, 10.00, 15.00, 20.00, 25.00, 30.00, 40.00, 50.00, 60.00, 70.00, 80.00, 90.00, or 100.00 mm. All ranges of distance and force mentioned herein (e.g., 50.00, 60.00, 70.00, 80.00, 90.00, 100.00, 125.00, 150.00, 175.00, 200.00, 250.00, 300.00, 400.00, 500.00, 600.00, 700.00, 800.00, 900.00, 1000.00, 1100.00, 1200.00, 1300.00, 1400.00, 1500.00, 1600.00, 1700.00, 1800.00, 1900.00, or 2000.00 micrometers) are to be taken as including, and providing written description and support for, any fractional value, in intervals of, for example, 0.01 micrometers, 0.01 mm, or 0.01 Newtons. 
         [0077]    The first step of the present coring method involves setting the height of a coring cavity in needle  2 .  FIG. 3  shows the depth of needle tip cavity  17  of coring tool  9  being set by pin  16 . The height of pin  16  above surface  15  can be adjusted by micrometer  14 . Next, as shown in  FIG. 4 , coring tool  9  can be inserted into vial  3  which is supported by vial block  4 , or another means. As shown in  FIG. 5 , cavity  17  can be filled by moving coring tool  9  up and down inside vial  3 , or another means, so that powder S is scraped off the walls or removed from the bottom of vial  3 . To facilitate the scraping and milling process, needles with tip geometries shown in  FIGS. 6   a  through  6   d  can be used instead of needle  2  with square end  28  ( FIG. 1 ).  FIG. 6   a  shows sharp end  10  with an exterior taper,  FIG. 6   b  shows sharp end  11  with an interior taper,  FIG. 6   c  shows sharp end  12  with both interior and exterior tapers, and  FIG. 6   d  shows flared sharp end  13  with an interior taper. 
         [0078]    Next, sample plug  23  can be compressed and extruded, as illustrated in  FIG. 7  and  FIG. 8 , respectively. In  FIG. 7 , mallet  22  strikes thimble  20  which includes pin  21 , thus pushing rod  1  and thus compressing sample plug  23  into block  24 . In  FIG. 8 , needle  2  is inverted and placed on base  31 , causing pin  32  to push rod  1  a distance sufficient to extrude plug top  36  a distance  34  ranging from, for example, about 0.10 mm to about 1.00 mm above needle tip  35 . Distance  34  can be adjusted by micrometer  30 , or another means. 
         [0079]    Next, coring tools can be loaded into coring tool rack  39  shown in  FIG. 9 . Coring tool rack  39  comprises top plate  41  with a plethora of holes  45 , side walls  42  and  43 , and a bottom plate  44 . Next, each sample plug can be sequentially exposed to electromagnetic radiation. Holes  45  have diameters that are about10.00 micrometers to about 100.00 micrometers larger than coring tools  9  to allow coring tools  9  to be accurately constrained laterally but to slide freely vertically.  FIG. 9  illustrates X-ray beam  40  passing through sample plug  23  and being diffracted, allowing sample plug  23  to be analyzed. For X-ray applications, top plate  41  material is optionally PVC or CPVC to fully absorb X-rays (or infrared or other radiation) that strike top plate  41  and thus eliminate the occurrence of reflected x-rays. 
         [0080]      FIGS. 10 and 11  show a coring tool rack which allows needle tips to be held above the top plate during the needle loading step, thus allowing for easier manual insertion of the needles. Coring tool rack  47  comprises top plate  51 , side walls  52   a  and  52   b , base  54 , and lifting plate  55 . Coring tools  50  can be inserted through top plate  51  and into holes  57  in lifting plate  55  while lifting plate  55  is locked via thumbscrew  58  in a raised position. Stops  53   a  and  53   b  define the maximum height of lifting plate  55 . After rack  47  is fully loaded, thumb screw  58  is loosened and lifting plate  55  is lowered so that plug top surfaces  61  are nominally above top plate  51  a distance between 0.00 mm and 2.00 mm, as shown in  FIG. 11 . Lifting plate  55  can be leveled, raised or lowered via set screws in base  54  such as screw  59 . 
         [0081]      FIG. 12  shows pin bed  70  which allows coring tool pins  49  in rack  47  to be removed from needles  48  in one motion, thus reducing labor required to remove pins  49 . Pin bed  70 , comprising base  71  and pins  72 , is inserted through chamfered holes  69  in lifting plate  55 , pushing pins  49  out of needles  48 . Needles  48  are held in place by retainer plate  80  secured by screws  82  and aligned by pins  81 . Retainer plate  80  rests on walls  83   a  and  83   b  that are sufficiently high to allow pins  49  to be completely removed. 
         [0082]      FIG. 13  illustrates important dimensions associated with X-ray diffraction analysis using a coring tool rack of the present invention. X-ray probe  95  emits beam  96  which intersects with sample plug  91  and is diffracted. In order to obtain a high signal to noise ratio it is important to minimize the incident beam length  98  of X-ray beam  96 . As an example, for a model D8 Discover Powder X-Ray Diffraction machine manufactured by Bruker AXS Limited, (Congleton, Cheshire, UK), using a snout style collimator equipped with 0.50 mm pin holes, a suitable incident beam length  98  is 50.00 mm or less to achieve acceptable beam intensity. To ensure that undiffracted x-rays (or infrared or other radiation) are absorbed, top plate  100  should extend a distance  104  of 15.00 mm or greater beyond the farthest plugs  91 . Also, it is important for angle of incidence  97  to be 2.50 degrees or less to allow complete information to be obtained from the sample plugs being analyzed. To ensure probe  9  does not collide with leading edge  101  or sample plugs, given incident beam length  98  is equal to 50.00 mm, total array width  103  must be less than 50.00 mm. Within this maximum array width constraint, it is desirable to design a coring tool rack that maximizes sample plug spacing  102  between adjacent sample plugs in the direction of beam  96  to allow beam  96  to pass over adjacent plugs such as  90  when there is a height difference between neighboring plugs (shown for example as height difference  92 ) due to an inaccurate adjustment of plug heights. Given beam  96  has a nominal diameter of 0.50 mm, and angle of incidence  97  is two degrees, it is desirable for sample plug spacing  102  to be greater than 18.00 mm in order to tolerate a plug height difference of 0.50 mm. To accommodate an even larger height difference, a sample plug spacing of larger than 18.00 mm is desirable. The following coring tool rack embodiments address these conflicting design requirements while also maximizing the number of sample plugs present per rack, providing ease of needle loading, and providing intuitive placement and labeling of rows and columns. 
         [0083]      FIG. 14  shows a top view of an unoptimized top plate  110  with holes  111  arrayed in a traditional grid format, with hole rows  112  and hole columns  113 . X-ray beam  107  and hole columns  113  are nominally parallel and are in the x-direction relative to top plate  110 . At an incident beam length  108  of 50.00 mm, beam width  109  is commonly 0.50 mm to 1.00 mm, but can range from about 0.10 mm to about 5.00 mm, depending on the beam diameter that is needed for a particular application. To prevent beam  107  from intersecting neighboring sample plugs in the y-direction in the event of positioning errors, y-hole spacing  117  should be equal to beam width  109  plus a tolerance of 0.40 mm or greater. 
         [0084]      FIG. 15 ,  FIG. 16 ,  FIG. 17  and  FIG. 18  show top plates  130 ,  150 ,  170 , and  190  respectively, with hole patterns that maximize hole spacing in the x-direction, given a minimum allowed hole spacing in the y-direction, and a minimum allowed distance between holes. To aid discussion and allow formulas to be presented, Table 1 assigns variable names to the dimension labels shown in  FIGS. 14 through 18 . 
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Variable names assigned to dimension labels in FIGS. 14 through 18 
               
             
          
           
               
                   
                 Dimension Labels 
               
             
          
           
               
                 Variable Name 
                 Symbol 
                 FIG. 14 
                 FIG. 15 
                 FIG. 16 
                 FIG. 17 
                 FIG. 18 
               
               
                   
               
               
                 Holes per Diagonal 
                 n d   
                 item 120 
                 item 140 
                 item 160 
                 item 180 
                 item 200 
               
               
                 Array Length 
                 L a   
                 dim. 114 
                 dim. 134 
                 dim. 154 
                 dim. 174 
                 Dim. 194 
               
               
                 Array Width 
                 W a   
                 dim. 116 
                 dim. 136 
                 dim. 156 
                 dim. 176 
                 Dim. 196 
               
               
                 X Hole Spacing 1 
                 s 1x   
                 dim. 115 
                 dim. 138 
                 dim. 158 
                 dim. 178 
                 Dim. 198 
               
               
                 X Hole Spacing 2 
                 s 2x   
                 dim. 115 
                 dim. 135 
                 dim. 155 
                 dim. 175 
                 NA 
               
               
                 Y Hole Spacing 
                 s y   
                 dim. 117 
                 dim. 137 
                 dim. 157 
                 dim. 177 
                 Dim. 197 
               
               
                 Min. Hole Distance 
                 s 
                 dim. 115 
                 dim. 139 
                 dim. 159 
                 dim. 179 
                 Dim. 199 
               
               
                   
               
             
          
         
       
     
         [0085]    Given the number of holes per diagonal in a column, represented by n d , the number of holes per row n y , the array width W a , and X hole spacing 1 s 1x , the Y hole spacing s y  and minimum hole distance s can be computed via equation (1) and equation (2), respectively. 
         [0000]    
       
         
           
             
               
                 
                   
                     s 
                     y 
                   
                   = 
                   
                     
                       W 
                       a 
                     
                     
                       
                         
                           n 
                           d 
                         
                          
                         
                           n 
                           y 
                         
                       
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   s 
                   = 
                   
                     
                       
                         s 
                         
                           1 
                            
                           
                               
                           
                            
                           x 
                         
                         2 
                       
                       + 
                       
                         s 
                         y 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0086]    Given 8 holes per column (n x =8), the resulting X hole spacing 2 S 2x  can be computed given the number of holes per diagonal nd, the array length La, and X hole spacing 1 s 1x , according to Table 2. 
         [0000]    
       
         
               
             
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 s 2x  versus n d  given n x  = 8 
               
             
          
           
               
                 n d  = 
                 S 2x  = 
               
               
                   
               
               
                 1 
                 L a /7 
               
               
                 2 
                 (L a  − s 1x )/3 
               
               
                 3 
                 (L a  − s 1x )/2 
               
               
                 4 
                 L a  − 3s 1x   
               
               
                 5 
                 L a  − 2s 1x   
               
               
                 6 
                 L a  − s 1x   
               
               
                 7 
                 L a   
               
               
                 8 
                 infinity 
               
               
                   
               
             
          
         
       
     
         [0087]    Table 3 shows computed values for s, s y  and S 2x , given some example values for the input variables in Equation (1), Equation (2), and the equations in Table 2. 
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Computed values for s, s y  and s 2x   
               
             
          
           
               
                   
                 Variable Values 
               
             
          
           
               
                 Variable Name 
                 Symbol 
                 FIG. 14 
                 FIG. 15 
                 FIG. 16 
                 FIG. 17 
                 FIG. 18 
               
               
                   
               
               
                 Holes per Diagonal 
                 n d   
                 1 
                 2 
                 3 
                 4 
                 8 
               
               
                 Holes per Column 
                 n x   
                 8 
                 8 
                 8 
                 8 
                 8 
               
               
                 Holes per Row 
                 n y   
                 12  
                 12  
                 12  
                 12  
                 12  
               
             
          
           
               
                 Array Length 
                 L a   
                 46.90 
                 mm 
                 46.90 
                 mm 
                 46.90 
                 mm 
                 46.90 
                 mm 
                 14.00 
                 mm 
               
               
                 Array Width 
                 W a   
                 99.00 
                 mm 
                 99.00 
                 mm 
                 99.00 
                 mm 
                 99.00 
                 mm 
                 99.00 
                 mm 
               
               
                 X Hole Spacing 1 
                 s 1x   
                 9.00 
                 mm 
                 6.70 
                 mm 
                 6.70 
                 mm 
                 5.00 
                 mm 
                 2.00 
                 mm 
               
               
                 Min. Hole Distance 
                 s 
                 9.00 
                 mm 
                 8.00 
                 mm 
                 7.30 
                 mm 
                 5.40 
                 mm 
                 2.30 
                 mm 
               
               
                 Y Hole Spacing 
                 s y   
                 9.00 
                 mm 
                 4.30 
                 mm 
                 2.80 
                 mm 
                 2.10 
                 mm 
                 1.00 
                 mm 
               
             
          
           
               
                 X Hole Spacing 2 
                 s 2x   
                 6.70 
                 mm 
                 13.40 
                 mm 
                 20.10 
                 mm 
                 31.90 
                 mm 
                 NA 
               
               
                   
               
             
          
         
       
     
         [0088]    As an example which includes realistic constraints, given a beam width of 1.00 mm and a width tolerance of 0.40 mm, s y  should be 1.40 mm or larger. As stated earlier, given a beam incident angle of 2 degrees, s 2x  should be greater than 18.00 mm to tolerate a 0.50 mm plug height difference. Lastly, it is desirable for array length L a  to be 50.00 mm or less to minimize beam travel. As can be seen in Table 3, the n d =4 embodiment in  FIG. 17  more than satisfies these constraints. Given L a =46.90 mm, the n d =4 design can provide s y =2.10 mm while providing S 2x =31.90 mm. At the same time, the conventional grid embodiment in  FIG. 14  indicated by n d =1 yields only s 2x =6.70 mm, which is far from satisfying the constraints in this example. 
         [0089]    If the beam width used was 0.60 mm instead of 1.00 mm, then an s y  value of 1.00 mm could be tolerated, and the n d =8 embodiment in  FIG. 18  could be used. The n d =8 embodiment has two advantages: 1) it eliminates neighbors altogether in the x-direction; and 2) the array length La is reduced to 14 mm in the Table 3 example, thus allowing a significantly shorter incident beam length and hence a potentially higher beam intensity. A disadvantage of the n d =8 embodiment is that needles are more difficult to insert into holes without disrupting neighbors because the minimum hole distance 199 is significantly reduced. 
         [0090]    For applications where the incident beam length used is less than 10.00 mm, the hole pattern shown on top plate  210  in  FIG. 19  is suitable. An advantage over the previous embodiments is that array length  214  is significantly reduced, and thus the incident beam length used and hence signal strength could be increased. In such an embodiment, the y hole spacing  217  and minimum hole distance  219  are more constrained given a maximum array width  216 . 
         [0091]      FIG. 20  shows top plate  220  which enables maximum beam intensity. As a consequence, the  FIG. 20  embodiment results in the smallest minimum hole distance  229  given an array width  226 , compared to the previous embodiments. 
         [0092]    Having now fully described this invention, it will be understood by those of ordinary skill in the art that the same can be performed within a wide and equivalent range of conditions and other parameters without affecting the scope of the invention or any embodiment thereof For example, functional aspects of the present invention such as, but not limited to, thumbscrews, pins, and screws may also be satisfied using alternative means and, therefore, are included in the present invention. All patents and publications cited herein are fully incorporated by reference in their entireties.