Patent Publication Number: US-7898735-B2

Title: Methods and systems for writing an optical code within or on a fiber substrate

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of and claims benefit to U.S. patent application Ser. No. 11/454,307, filed on Jun. 16, 2006, which is a continuation of U.S. patent application Ser. No. 10/661,116, filed on Sep. 12, 2003, which is a continuation in part of Ser. No. 10/645,689, filed on Aug. 20, 2003 and claims benefit to U.S. Provisional Patent Application No. 60/410,541, filed on Sep. 12, 2002, all of which are incorporated by reference in their entirety. 
     U.S. patent application Ser. No. 10/661,234 and application Ser. No. 10/661,082, were filed contemporaneously with the parent application, contains subject matter related to that disclosed herein, which is incorporated by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     This invention relates to identification elements, and more particularly to method of manufacturing diffraction grating based optical identification elements. 
     BACKGROUND ART 
     Many industries have a need for uniquely identifiable objects or for the ability to uniquely identify objects, for sorting, tracking, and/or identification/tagging. Existing technologies, such as bar codes, electronic microchips/transponders, radio-frequency identification (RFID), and fluorescence and other optical techniques, are often inadequate. For example, existing technologies may be too large for certain applications, may not provide enough different codes, or cannot withstand harsh temperature, chemical, nuclear and/or electromagnetic environments. 
     Therefore, it would be desirable to obtain a coding element or platform that provides the capability of providing many codes (e.g., greater than 1 million codes), that can be made vera small, and/or that can withstand harsh environments. 
     SUMMARY OF THE INVENTION 
     Objects of the present invention include a method of manufacturing a plurality of diffraction grating based optical identification elements (microbeads) having unique codes. 
     According to the present invention, a method of manufacturing optical identification elements comprises forming a diffraction grating in a fiber substrate along a longitudinal axis of said substrate, said grating having a resultant refractive index variation, and cutting the substrate transversely to form a plurality of optical identification elements, said elements having said grating therein along substantially the entire length of said elements and each of said elements have substantially the same resultant refractive index variation. 
     The foregoing and other objects, features and advantages of the present invention will become more apparent in light of the following detailed description of exemplary embodiments thereof. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a side view of an optical identification element, in accordance with the present invention. 
         FIG. 2  is a top level optical schematic for reading a code in an optical identification element, in accordance with the present invention. 
         FIG. 3  is a block diagram of the steps of manufacturing a diffraction grating-based optical identification element or microbead, in accordance with the present invention. 
         FIG. 4  is an elevational view of a fiber stripping station, in accordance with the present invention. 
         FIG. 5  is a perspective view of a cage having a pair of fiber ribbons wound thereabout, in accordance with the present invention. 
         FIG. 6  is a side view of a cage having a fiber ribbon wound thereabout, in accordance with the present invention. 
         FIG. 7  is a perspective view of a disk having a fiber ribbon wound thereabout, in accordance with the present invention. 
         FIG. 8  is a top view of a grating writing station, in accordance with the present invention. 
         FIG. 9  is a top view of another embodiment of a grating writing station, in accordance with the present invention. 
         FIG. 10  is a front view of a section of a fiber ribbon and a projection of a UV beam from a laser for writing a grating that is narrower than the width of the fiber ribbon, in accordance with the present invention. 
         FIG. 11  is a front view of a section of a fiber ribbon and a projection of a UV beam from a laser for writing a grating that is wider than the width of the fiber ribbon, in accordance with the present invention. 
         FIG. 12  is a front view of a section of a fiber ribbon and a projection of a UV beam from a laser and a phase mask tilted at a blaze angle, in accordance with the present invention. 
         FIG. 13  is a perspective view of a plurality of fiber ribbons adhered to a test fixture, in accordance with the present invention. 
         FIG. 14  is a side view of a plurality of fiber ribbons adhered to a test fixture, in accordance with the present invention. 
         FIG. 15  is an expanded top view of a portion of the diced fiber ribbon, in accordance with the present invention. 
         FIG. 16  is a side view of separation station having a section of fiber ribbon disposed in a vessel, in accordance with the present invention. 
         FIG. 17  is a side view of the vessel of  FIG. 16  having a vial disposed on one end of the vessel, in accordance with the present invention. 
         FIG. 18  is a side view of the vessel and vial of  FIG. 16  in a turned over orientation, in accordance with the present invention. 
         FIG. 19  is a side view of microbeads disposed within a vial, in accordance with the present invention. 
         FIG. 20  is a top view of another embodiment of a grating writing station, in accordance with the present invention. 
         FIG. 21  is a perspective of another embodiment of a grating writing station, in accordance with the present invention. 
         FIG. 22  is a side view of a pair of lasers scoring opposing sides of a fiber to form microbeads, in accordance with the present invention. 
         FIG. 23  is a side view of a laser scoring one side of a fiber to form microbeads, in accordance with the present invention. 
         FIG. 24  is a side view of an anvil and support used to separate the microbeads from the scored fiber, in accordance with the present invention. 
         FIG. 25  is a schematic illustration of another method of manufacturing microbeads, in accordance with the present invention. 
         FIG. 26  is a side view of another embodiment for cutting a fiber to form microbeads, in accordance with the present invention. 
         FIG. 27  is an optical schematic for reading a code in an optical identification element, in accordance with the present invention. 
         FIG. 28  is an image of a code on a CCD camera from an optical identification element, in accordance with the present invention. 
         FIG. 29  is a graph showing an digital representation of bits in a code in an optical identification element, in accordance with the present invention. 
         FIG. 30  illustrations (a)-(c) shown images of digital codes on a CCD camera, in accordance with the present invention. 
         FIG. 31  illustrations (a)-(d) show graphs of different refractive index pitches and a summation graph, in accordance with the present invention. 
         FIG. 32  is an alternative optical schematic for reading a code in an optical identification element, in accordance with the present invention. 
         FIG. 33  illustrations (a)-(b) are graphs of reflection and transmission wavelength spectrum for an optical identification element, in accordance with the present invention. 
         FIGS. 34-35  are side views of a thin grating for an optical identification element, in accordance with the present invention. 
         FIG. 36  is a perspective view showing azimuthal multiplexing of a thin grating for an optical identification element, in accordance with the present invention. 
         FIG. 37  is side view of a blazed grating for an optical identification element, in accordance with the present invention. 
         FIG. 38  is a graph of a plurality of states for each bit in a code for an optical identification element, in accordance with the present invention. 
         FIG. 39  is a side view of an optical identification element where light is incident on an end face, in accordance with the present invention. 
         FIGS. 40-41  are side views of an optical identification element where light is incident on an end face, in accordance with the present invention. 
         FIG. 42 , illustrations (a)-(c) are side views of an optical identification element having a blazed grating, in accordance with the present invention. 
         FIG. 43  is a side view of an optical identification element having a coating, in accordance with the present invention. 
         FIG. 44  is a side view of whole and partitioned optical identification element, in accordance with the present invention. 
         FIG. 45  is a side view of an optical identification element having a grating across an entire dimension, in accordance with the present invention. 
         FIG. 46 , illustrations (a)-(c), are perspective views of alternative embodiments for an optical identification element, in accordance with the present invention. 
         FIG. 47 , illustrations (a)-(b), are perspective views of an optical identification element having multiple grating locations, in accordance with the present invention. 
         FIG. 48 , is a perspective view of an alternative embodiment for an optical identification element, in accordance with the present invention. 
         FIG. 49  is a view an optical identification element having a plurality of gratings located rotationally around the optical identification element, in accordance with the present invention. 
         FIG. 50  illustrations (a)-(e) show various geometries of an optical identification element that may have holes therein, in accordance with the present invention. 
         FIG. 51  illustrations (a)-(c) show various geometries of an optical identification element that may have teeth thereon, in accordance with the present invention. 
         FIG. 52  illustrations (a)-(c) show various geometries of an optical identification element, in accordance with the present invention. 
         FIG. 53  is a side view an optical identification element having a reflective coating thereon, in accordance with the present invention. 
         FIG. 54  illustrations (a)-(b) are side views of an optical identification element polarized along an electric or magnetic field, in accordance with the present invention. 
     
    
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
     Referring to  FIG. 1 , a diffraction grating-based optical identification element  8  (or encoded element or coded element) comprises a known optical substrate  10 , having an optical diffraction grating  12  disposed (or written, impressed, embedded, imprinted, etched, grown, deposited or otherwise formed) in the volume of or on a surface of a substrate  10 . The grating  12  is a periodic or aperiodic variation in the effective refractive index and/or effective optical absorption of at least a portion of the substrate  10 . 
     The optical identification element  8  described herein is the same as that described in Copending patent application Ser. No. 10/661,234, filed contemporaneously with the parent application, which is incorporated herein by reference in its entirety. 
     In particular, the substrate  10  has an inner region  20  where the grating  12  is located. The inner region  20  may be photosensitive to allow the writing or impressing of the grating  12 . The substrate  10  has an outer region  18 , which does not have the grating  12  therein. 
     The grating  12  is a combination of one or more individual spatial periodic sinusoidal variations (or components) in the refractive index that are collocated at substantially the same location on the substrate  10  along the length of the grating region  20 , each having a spatial period (or pitch) Λ. The resultant combination of these individual pitches is the grating  12 , comprising spatial periods (Λ 1 -Λn) each representing a bit in the code. Thus, the grating  12  represents a unique optically readable code, made up of bits, where a bit corresponds to a unique pitch Λ within the grating  12 . Accordingly, for a digital binary (0-1) code, the code is determined by which spatial periods (Λ 1 -Λn) exist (or do not exist) in a given composite grating  12 . The code or bits may also be determined by additional parameters (or additional degrees of multiplexing), and other numerical bases for the code may be used, as discussed herein and/or in the aforementioned patent application. 
     The grating  12  may also be referred to herein as a composite or collocated grating. Also, the grating  12  may be referred to as a “hologram”, as the grating  12  transforms, translates, or filters an input optical signal to a predetermined desired optical output pattern or signal. 
     The substrate  10  has an outer diameter D 1  and comprises silica glass (SiO 2 ) having the appropriate chemical composition to allows the grating  12  to be disposed therein or thereon. Other materials for the optical substrate  10  may be used if desired. For example, the substrate  10  may be made of any glass, e.g., silica, phosphate glass, borosilicate glass, or other glasses, or made of glass and plastic, or solely plastic. For high temperature or harsh chemical applications, the optical substrate  10  made of a glass material is desirable. If a flexible substrate is needed, plastic, rubber or polymer-based substrate may be used. The optical substrate  10  may be any material capable of having the grating  12  disposed in the grating region  20  and that allows light to pass through it to allows the code to be optically read. 
     The optical substrate  10  with the grating  12  has a length L and an outer diameter D 1 , and the inner region  20  diameter D. The length L can range from very small “microbeads” (or microelements, micro-particles, or encoded particles), about 1-1000 microns or smaller, to larger “macrobeads” or “macroelements” for larger applications (about 1.0-1000 mm or greater). In addition, the outer dimension D 1  can range from small (less than 1000 microns) to large (1.0-1000 mm and greater). Other dimensions and lengths for the substrate  10  and the grating  12  may be used. 
     The grating  12  may have a length Lg of about the length L of the substrate  10 . Alternatively the length Lg of the grating  12  may be shorter than the total length L of the substrate  10 . 
     The outer region  18  is made of pure silica (SiO 2 ) and has a refractive index n 2  of about 1.458 (at a wavelength of about 1553 nm), and the inner grating region  20  of the substrate  10  has dopants, such as germanium and/or boron, to provide a refractive index n 1  of about 1.453, which is less than that of outer region  18  by about 0.005. Other indices of refraction n 1 ,n 2  for the grating region  20  and the outer region  18 , respectively, may be used, if desired, provided the grating  12  can be impressed in the desired grating region  20 . For example, the grating region  20  may have an index of refraction that is larger than that of the outer region  18  or grating region  20  may have the same index of refraction as the outer region  18  if desired. 
     Referring to  FIG. 2 , an incident light  24  of a wavelength λ, e.g., 532 nm from a known frequency doubled Nd:YAG laser or 632 nm from a known Helium-Neon laser, is incident on the grating  12  in the substrate  10 . Any other input wavelength λ can be used if desired provided λ is within the optical transmission range of the substrate (discussed more herein and/or in the aforementioned patent application). A portion of the input light  24  passes straight through the grating  12 , as indicated by a line  25 . The remainder of the input light  24  is reflected by the grating  12 , as indicated by a line  27  and provided to a detector  29 . The output light  27  may be a plurality of beams, each having the same wavelength λ as the input wavelength λ and each having a different output angle indicative of the pitches (Λ 1 -Λn) existing in the grating  12 . Alternatively, the input light  24  may be a plurality of wavelengths and the output light  27  may have a plurality of wavelengths indicative of the pitches (Λ 1 -Λn) existing in the grating  12 . Alternatively, the output light may be a combination of wavelengths and output angles. The above techniques are discussed in more detail herein and/or in the aforementioned patent application. 
     The detector  29  has the necessary optics, electronics, software and/or firmware to perform the functions described herein. In particular, the detector reads the optical signal  27  diffracted or reflected from the grating  12  and determines the code based on the pitches present or the optical pattern, as discussed more herein or in the aforementioned patent application. An output signal indicative of the code is provided on a line  31 . 
       FIG. 3  shows a method  800  of manufacturing a microbead  8  similar to that described hereinbefore in accordance with the present invention. The first step  802  includes providing a photosensitive substrate or fiber  830 . To simplify the description of the method of manufacturing, the substrate will be referred to as a fiber with the understanding that the microbeads  8  may be formed of any photosensitive substrate. 
     The fiber  830  may be made of any material that has sufficient photosensitivity to allows a diffraction grating  12  to be disposed therein, that represents a code that can be interrogated as described herein and/or in the aforementioned patent application. The fiber  830  may be doped or loaded with any dopant now known or later discovered that allows the fiber to exhibit the necessary level of photosensitivity for the incident radiation (e.g., UV or other actinic radiation) used for writing the grating  12 , such as, hydrogen, deuterium, boron, germanium, lead, or other dopants that provide photosensitivity, some of which are described in Patent Nos.: U.S. Pat. No. 6,436,857 to Brueck et al, U.S. Pat. No. 5,287,427 to Atkins et al, U.S. Pat. No. 5,235,659 to Atkins et al, U.S. Pat. No. 6,327,406 to Cullen et al, WO 00/44683 to Samsung Electronics Co. LTD, U.S. Pat. No. 6,221,566 to Kohnke et al, U.S. Pat. No. 6,097,512 to Ainslie et al; and U.S. Pat. No. 6,075,625 to Ainslie et al. 
     In step  804 , the photosensitive fiber  830  is then stripped of the coating or buffer disposed on its outer surface and then cleaned. In step  806 , the stripped fiber is then wound around a cage or basket  832  having a generally polygon shape so that the wound fiber has sections  831  of flat areas. 
       FIG. 4  illustrates a fixture/set-up  834  for accomplishing steps  802 - 804 . The photosensitive fiber  830  is threaded through a blade  836  for stripping the buffer from the fiber. A heater  838  is disposed prior to the stripper  836  to heat and soften the buffer to ease the removal of the buffer from the fiber. The stripped fiber then passes through or between a pair of pads  840  soaked with a solvent, such as acetone, to clean the fiber. The fiber  830  is then wound about the cage  832 . While not shown, the set-up  834  may include one or more pulleys or rollers to provide tension on the fiber when winding the fiber onto the cage. 
     As best shown in  FIGS. 5 and 6 , the cage  832  has a lower plate  842  and an upper ring support  844  with a plurality of rods  846  connected therebetween. The rods are equi-spaced about the circumference of the cage. In the embodiment shown, the cage  832  includes 16 openings  848 , however, the invention contemplates having any number of openings. When wound around the rods  846  of the cage  832 , each wrap of fiber is adjacent to and touches each adjacent wrap to form a single layer of fiber ribbon  850  around the cage. The fiber is wrapped around the cage between 100-120 times to effectively form a single layer ribbon of fibers. The invention contemplates any number of wraps of fiber around the cage. The fiber ribbon  850  forms a polygonal shape when wrapped around the cage  832  to provide a plurality of flat sections (16 sections)  831 . These flat sections  831  of the fiber ribbon  850  provides the area of the fiber that a grating  12  is written in, which will be described in greater detail hereafter. As best shown in  FIG. 6 , one section  831  of the fiber ribbon  850  is tape together at  852 , including the ends of the fiber, to maintain the tension of the fiber around the cage and to maintain the single layer of the fiber ribbon. 
     While  FIG. 6  shows a single fiber ribbon  850  disposed on the cage  832 , the present invention contemplates that a plurality of fiber ribbons  850  may be axially spaced on the cage, as shown in  FIG. 5 . 
       FIG. 7  illustrates that the stripped fiber  830  may by wound around a disk  854  having a plurality of circumferentially spaced dovetailed slots  856 , wherein the fiber ribbon  850  is taped at  858  to the outer circumference of the disk. 
     The next step  808  of  FIG. 3  is to write or shoot the diffraction grating(s)  12  into each section  831  (see  FIGS. 8 and 9 ) of the fiber ribbon  850 . The grating  12  may be impressed in the fiber  830  by any technique for writing, impressed, embedded, imprinted, or otherwise forming a diffraction grating in the volume of or on a surface of a substrate  10 . Examples of some known techniques are described in U.S. Pat. Nos. 4,725,110 and 4,807,950, entitled “Method for Impressing Gratings Within Fiber Optics”, to Glenn et al; and U.S. Pat. No. 5,388,173, entitled “Method and Apparatus for Forming Aperiodic Gratings in Optical Fibers”, to Glenn, respectively, and U.S. Pat. No. 5,367,588, entitled “Method of Fabricating Bragg Gratings Using a Silica Glass Phase Grating Mask and Mask Used by Same”, to Hill, and U.S. Pat. No. 3,916,182, entitled “Periodic Dielectric Waveguide Filter”, Dabby et al, and U.S. Pat. No. 3,891,302, entitled “Method of Filtering Modes in Optical Waveguides”, to Dabby et al, which are all incorporated herein by reference to the extent necessary to understand the present invention. 
     Alternatively, instead of the grating  12  being impressed within the fiber material, the grating  12  may be partially or totally created by etching or otherwise altering the outer surface geometry of the substrate to create a corrugated or carving surface geometry of the substrate, such as is described in U.S. Pat. No. 3,891,302, entitled “Method of Filtering Modes in Optical Waveguides”, to Dabby et al, which is incorporated herein by reference to the extent necessary to understand the present inventions provided the resultant optical refractive profile for the desired code is created. 
     Further, alternatively, the grating  12  may be made by depositing dielectric layers onto the substrate, similar to the way a known thin film filter is created, so as to create the desired resultant optical refractive profile for the desired code. 
       FIG. 8  shows the method of writing a grating  12  into the fibers  830  of the ribbon  850  using at least one phase mask  860 . A laser  862 , such as an excimer laser or CO 2  laser, provides an ultra-violet (UV) beam  864 , which passes through the phase mask to write a grating  12  having a predetermined profile corresponding to the phase mask. In one embodiment, one phase mask  860  may be used to write the grating into the fiber  830  to provide one unique code for the microbead  8 . Each unique phase mask therefore represents one unique code, thereby requiring a phase mask for each code used. Using only one phase mask to generate each code becomes very expensive and difficult to manufacture when the number of unique codes needed increases. 
     In another embodiment each unique code may be generated by writing a plurality of co-located grating  12  into each section  831  of the fiber ribbon  850 . For example, the resulting grating in a particular section  831  (or microbead  8 ) may comprise any combination of eight (8) gratings using eight (8) different phase masks  860 . Consequently the number of unique gratings or codes using eight phase masks equal 2 8 . The phase mask may be mounted to a carriage  866 , similar to that shown in  FIGS. 20 and 21 , that translates parallel to the fiber ribbon  850  to select the mask  860  for writing the desired grating  12 . The invention further contemplates that the phase masks are mounted on a wheel (not shown) that can be rotated to select the desired phase mask. 
     Each of the 16 sections  831  of the fiber ribbon  850  may be written with the same grating  12 . Alternatively, each section may have a different grating written therein, each section therefore having a different code associated therewith. To provide different gratings  12  for each section  831  using the co-located grating method, each section would use a different combination of phase masks to write each grating. For example, the first, third and fifth phase masks of the 8 phase masks may be used to write the grating that comprises the three co-located gratings written into the first section  831  of the fiber ribbon  850 . For the second section  831  of the fiber ribbon, the first, fifth, sixth and eight phase masks may be used to write the grating that comprises the four co-located gratings written into the second section. The other sections of the fiber ribbon may be similarly written using different combinations of phase masks. While the embodiment shows two grating writing stations  868 , it is contemplated the only one station may be used or any number of stations. 
       FIG. 9  shows another method of writing the gratings  12  into each section  831  of the fiber ribbons  850  by using interfering beams  870  provided by a laser  862 . As shown the UV beam  864  is split by a mirror  872  and reflected to a pair of complementary mirrors  874 . The complementary mirrors  874  reflect the UV beams  870  back to interfere with each other at the fiber ribbon  850  to form the grating  12 . Similar to that described hereinbefore, a single grating may be written in the sections  831  of the fiber ribbon or a plurality of co-located gratings may be written. To change the grating profile or interference pattern to create a different grating  12 , the complementary mirrors  874  may be tilted to a different angle. 
       FIG. 10  illustrates a scanning method for exposing each section  831  of the fiber ribbon  850  using a phase mask  860 . In this method, the width of the UV beam  864  used to write the grating  12  is smaller than the width of the fiber ribbon  850 . The UV beam  864  translates along the width of the fiber ribbon to scan each of the wraps of fiber  830  in the section of fiber ribbon. In this instance, the beam scan direction  876  is from bottom to top, however, the direction of scan may be from top to bottom of the section. The UV beam  864  may be scanned upward by translating the laser  862 , or alternatively, the cage  832  may translated upward and downward in the axial direction. 
     Alternatively,  FIG. 11  illustrates a stationary or blanket method for exposing each section  831  of the fiber ribbon  850  using a phase mask  860 . In this method, the width of the UV beam  864  used to write the grating  12  is as wide as or wider than the width of the fiber ribbon  850 . This method enables the entire section  831  to be exposed and a grating written in a single exposure. 
     It is important that the phase mask  860  is square, and not angle, to the section  831  of the fiber ribbon  850  to minimize the blaze angle  878  of the grating  12  as illustrated in  FIG. 12 . If the blaze angle  878  is too large (e.g., &gt;0.1 degree), the microbeads  8  may not exhibit a code to the reader, as the Bragg condition no longer falls with the Bragg envelope. 
     In step  810  of  FIG. 3 , after the gratings  12  are written into each section  831  of the fiber ribbon  850  (except the taped section), a strip of tape  880  (e.g., Kapton tape) is adhered to the outer surface of the fiber ribbon  850  as best shown in  FIG. 14 . In step  812  of  FIG. 3 , once taped, the fiber ribbon is cut off the cage  832  by cutting through the taped section  852  of the fiber ribbon  850  at  882  as shown in  FIG. 6 . 
     In step  814 , the fiber ribbon  850  is flattened and mounted to a thermally conductive fixture  884 , as shown in  FIGS. 13 and 14 . As best shown in  FIG. 14 , each ribbon  850  is bonded to a plastic sheet material  886  (e.g., polyimide sheet material) that is bonded to the fixture. The adhesive  888  used to bond the polyimide sheet  886  to the fixture  884  and the fiber ribbon  850  to the polyimide sheet is a water-soluble thermoset adhesive, such as that known as Aquabond®. In  FIG. 13 , the fiber ribbons are secured to the fixture by a pair of clamps  890 . The length of the fiber ribbons is approximately 632 mm. Once the fiber ribbons are clamped to the fixture  884 , the fixture is heated to liquefy the adhesive  888 , which then encases the fibers  830  in the adhesive. The adhesive  888  is allowed to cool and harden to thereby encase the fibers and bond to the polyimide sheet  886  and bond the polyimide sheet to the fixture. 
     In step  816  of  FIG. 3 , the kapton tape  880  is then removed from the fiber ribbons  850 . In step  818 , each section  831  having a grating  12  is cut or diced to form the microbeads  8 , as shown in  FIG. 15 . The intermediate sections  892  having no gratings (see  FIG. 13 ) are not dice and left long. The blades cut sufficiently deep to cut the fibers  830  and score the polyimide sheet  886  without cutting fully through the sheet.  FIG. 15  shows a portion of the fiber ribbon  850  and the kerfs  894  created by the cutting blade. Before removing the fiber ribbons from the fixture  884 , the intermediate sections  892  are removed from the polyimide sheet  886 . One method is to cut that portion away with a blade having a wide kerf. Alternatively, the fixture can be heated to soften the adhesive  888  to permit the intermediate sections  892  of the ribbon  850  to be scraped away. Once the intermediate sections  892  are removed from the fiber ribbons  850 , the fiber ribbons are removed from the fixture  884  by heating the fixture to soften the adhesive between the polyimide sheet and the fixture. 
     In step  820  of  FIG. 3 , the microbeads  8  are removed from each of section  831  of the fiber ribbon  850 . The polyimide sheet  886  is cut across each of the intermediate sections to separate each of the sections  831  having a group of microbeads  8 . As shown in  FIG. 16 , one or more sections  831  having the same code are place within a vessel  896  having a tapered open end  898  and another end having a removable filter  900  (40 um filter material). The section  850  having microbeads  8  is placed into the vessel  896  by removing the filter  900  and replacing it. The vessel is placed filter end down within a vat  902  having water and solvent (e.g., Aquaclean®) solution  904  heated to approximately 86 degrees Celsius. The vat  902  is then placed within an ultrasonic bath  906  of pure water  908 , which vibrates the water at approximately 80 KHz. The solution  902  passes through the filter  900  of the vessel  896  and dissolves the water soluble adhesive  888  holding the microbeads  8  to the polyimide sheet  886 . The ultrasonic vibration assists with separating the microbeads from the polyimide sheet. 
     In step  822  of  FIG. 3 , the microbeads  8  are cleaned and stored. As shown in  FIGS. 17 and 18 , the vessel  896  is then removed from the vat  902  and a polyethylene vial  910  is placed over the tapered opening  898  of the vessel  896 , as shown in  FIGS. 17-18 . The vessel and vile are then turned upside down and flushed with de-ionized water to clean the microbeads  8 . Consequently, the microbeads  8  flows from the vessel  896  to the vial  910 . The de-ionized water passes through a dense filter  912  disposed on the bottom of the vial. The polyimide sheet  886  is retained within the vessel  896  because the tapered opening  898  of the vessel is smaller than the sheet. Referring to  FIG. 19 , another filter  914  is place in the vial  910  to secure the microbeads therein for storage. 
       FIGS. 20 and 21  illustrate a method of writing at least one grating  12  in a section  831  of a fiber ribbon  850 . In this embodiment the fiber ribbon, similar to that described hereinbefore, is wound around a spool  916 . The fiber ribbon is drawn through a grating writing station  868  to a take up spool  918 . The grating writing station  868  includes a carriage  866  having a plurality of phase masks  860  that linearly translates parallel to the flat section  831  of the fiber ribbon  850 . The carriage translates to position the desired phase mask in position to write the proper grating  12 . As the fiber ribbon is fed to the grating writing station  868 , a set of rollers  920  separate the tape  880  from the fibers  830  and directs the tape away from the ultraviolet (UV) beam  864  to thereby protect the tape from the UV beam. The rollers direct the tape and fibers back together and a pair pinch rollers  922  adhere the fibers  830  back onto the tape  880  to form the fiber ribbon  850 . In the operation of the writing station  868 , each section  831  of ribbon  850  is sequentially positioned in the writing station. When a section of ribbon is positioned in the writing station, the carriage  866  translates to position a desired phase mask  860  between the laser  862  and the fibers  830 . The laser then provides the UV beam to write the grating  12  in the fibers  830 . The carriage  866  then translates to position another phase mask to write a second grating onto the section  831  of fibers  830 . This operation continues until all the desired gratings are written. The second spool  918  then draws the next section of fibers  830  into the writing station to write the desired grating(s) into the fibers. The grating(s) written into each section of fibers may be the same or different. 
     Referring to  FIGS. 22 and 23 , the present invention contemplates cutting/dicing the fibers  830  using a laser  924  (e.g., CO 2  laser or excimer laser). In one embodiment the laser  924  may be used to completely cut through the fibers  830 . Alternatively, the laser can be used to score the fibers as shown in  FIGS. 22 and 23 . In  FIG. 22 , two lasers  924  are used to score both sides of the fibers  830  at the same location, while in  FIG. 23 , one laser  924  is used to score only one side of the fibers. Once scored, the fibers  830  may be separated to form the microbeads  8  by placing the scored fibers  830  in an ultrasonic bath (at 49 KHz) to vibrate the microbeads  8  apart. Alternatively, as shown in  FIG. 24  the microbeads  8  may be separated using a mechanical anvil  928  that snaps or breaks each microbead  8  from the scored fiber  830 . 
       FIG. 25  is a schematic illustration of an alternative method of manufacturing the microbeads  8 . As shown, the photosensitive fiber  830  is first stripped and cleaned  930 . The gratings  12  are then written into the fiber  932  and then wound  934  onto a second a spool  936 . The fiber  830  is then cut off  938  the spool  936  in a plurality of strips  940  of fiber that are flattened out. The strips of fibers are then cut or diced with a blade  942 . 
     If the microbeads  8  should be used to perform a chemical experiment or assay similar to that described in U.S. patent application Ser. No. 10/661,031 and U.S. patent application Ser. No. 10/661,115, both filed contemporaneously, which are incorporated herein by reference, the probe compound or chemical may be coated or applied to the fiber or microbeads at any step in the process of manufacture of the microbeads described hereinbefore. 
       FIG. 26  illustrates another method of cutting dicing the fibers  830  to form the microbeads  8 . As shown, after the grating(s)  12  have been written into the fiber (and in this particle instance, coated/tagged with a probe compound (e.g., Oligo), the fiber  830  is fed into a tubular fiber holder  944 . As the fiber is pushed through the holder  944 , a cutting device  946  having a blade  948  cuts or scores the fiber  830  to the appropriate length, which is then separates the microbead from the fiber by a torque element  950 . 
     Referring to  FIG. 27 , the reflected light  27 , comprises a plurality of beams  26 - 36  that pass through a lens  37 , which provides focused light beams  46 - 56 , respectively, which are imaged onto a CCD camera  60 . The lens  37  and the camera  60 , and any other necessary electronics or optics for performing the functions described herein, make up the reader  29 . Instead of or in addition to the lens  37 , other imaging optics may be used to provide the desired characteristics of the optical image/signal onto the camera  60  (e.g., spots, lines, circles, ovals, etc.), depending on the shape of the substrate  10  and input optical signals. Also, instead of a CCD camera other devices may be used to read/capture the output light. 
     Referring to  FIG. 28 , the image on the CCD camera  60  is a series of illuminated stripes indicating ones and zeros of a digital pattern or code of the grating  12  in the element  8 . Referring to  FIG. 29 , lines  68  on a graph  70  are indicative of a digitized version of the image of  FIG. 28  as indicated in spatial periods (Λ 1 -Λn). 
     Each of the individual spatial periods (Λ 1 -Λn) in the grating  12  is slightly different, thus producing an array of N unique diffraction conditions (or diffraction angles) discussed more hereinafter. When the element  8  is illuminated from the side, in the region of the grating  12 , at an appropriate input angle, e.g., about 30 degrees, with a single input wavelength λ (monochromatic) source, the diffracted (or reflected) beams  26 - 36  are generated. Other input angles θi may be used if desired, depending on various design parameters as discussed herein and/or in the aforementioned patent application, and provided that a known diffraction equation (Eq. 1 below) is satisfied:
 
sin(θ i )+sin(θ o )= mλ/nΛ   Eq. 1
 
where Eq. 1 is diffraction (or reflection or scatter) relationship between input wavelength λ, input incident angle θi, output incident angle θo, and the spatial period Λ of the grating  12 . Further, m is the “order” of the reflection being observed, and n is the refractive index of the substrate  10 . The value of m=1 or first order reflection is acceptable for illustrative purposes. Eq. 1 applies to light incident on outer surfaces of the substrate  10  which are parallel to the longitudinal axis of the grating (or the k B  vector). Because the angles θi,θo are defined outside the substrate  10  and because the effective refractive index of the substrate  10  is substantially a common value, the value of n in Eq. 1 cancels out of this equation.
 
     Thus, for a given input wavelength λ, grating spacing Λ, and incident angle of the input light θi, the angle θo of the reflected output light may be determined. Solving Eq. 1 for θo and plugging in m=1, gives:
 
θ o =sin −1 (λ/Λ−sin(θ i ))  Eq. 2
 
For example, for an input wavelength λ=532 nm, a grating spacing Λ=0.532 microns (or 532 nm), and an input angle of incidence θi=30 degrees, the output angle of reflection will be θo=30 degrees. Alternatively, for an input wavelength λ=632 nm, a grating spacing Λ=0.532 microns (or 532 nm), and an input angle θi of 30 degrees, the output angle of reflection θo will be at 43.47 degrees, or for an input angle θi=37 degrees, the output angle of reflection will be θo=37 degrees. Any input angle that satisfies the design requirements discussed herein and/or in the aforementioned patent application may be used.
 
     In addition, to have sufficient optical output power and signal to noise ratio, the output light  27  should fall within an acceptable portion of the Bragg envelope (or normalized reflection efficiency envelope) curve  200 , as indicated by points  204 , 206 , also defined as a Bragg envelope angle θB, as also discussed herein and/or in the aforementioned patent application. The curve  200  may be defined as: 
                     I   ⁡     (     ki   ,   ko     )       ≈         [   KD   ]     2     ⁢   sin   ⁢           ⁢       c   2     ⁡     [         (     ki   -   ko     )     ⁢   D     2     ]                 Eq   .           ⁢   3               
where K=2πδn/λ, where, δn is the local refractive index modulation amplitude of the grating and λ is the input wavelength, sin c(x)=sin(x)/x, and the vectors k i =2π cos(θ i )/λ and k o =2π cos(θ o )/λ are the projections of the incident light and the output (or reflected) light, respectively, onto the line  203  normal to the axial direction of the grating  12  (or the grating vector k B ), D is the thickness or depth of the grating  12  as measured along the line  203  (normal to the axial direction of the grating  12 ). Other substrate shapes than a cylinder may be used and will exhibit a similar peaked characteristic of the Bragg envelope. We have found that a value for δn of about 10 −4  in the grating region of the substrate is acceptable; however, other values may be used if desired.
 
     Rewriting Eq. 3 gives the reflection efficiency profile of the Bragg envelope as: 
                     I   ⁡     (     ki   ,   ko     )       ≈           [       2   ⁢     π   ·   δ     ⁢           ⁢     n   ·   D       λ     ]     2     ⁡     [       Sin   ⁡     (   x   )       x     ]       2             Eq   .           ⁢   4               
where:
 
 x =( ki−ko ) D/ 2=(π D /λ)*(cos θ i −cos θ o  
 
     Thus, when the input angle θi is equal to the output (or reflected) angle θ o  (i.e., θi=θ o ), the reflection efficiency I (Eqs. 3 &amp; 4) is maximized which is at the center or peak of the Bragg envelope. When θi=θo, the input light angle is referred to as the Bragg angle as is known. The efficiency decreases for other input and output angles (i.e., θi≠θ o ), as defined by Eqs. 3 &amp; 4. Thus, for maximum reflection efficiency and thus output light power, for a given grating pitch Λ and input wavelength, the angle θi of the input light  24  should be set so that the angle θo of the reflected output light equals the input angle θi. 
     Also, as the thickness or diameter D of the grating decreases, the width of the sin(x)/x function (and thus the width of the Bragg envelope) increases and, the coefficient to or amplitude of the sin c 2  (or (sin(x)/x) 2  function (and thus the efficiency level across the Bragg envelope) also increases, and vice versa. Further, as the wavelength λ increases, the half-width of the Bragg envelope as well as the efficiency level across the Bragg envelope both decrease. Thus, there is a trade-off between the brightness of an individual bit and the number of bits available under the Bragg envelope. Ideally, δn should be made as large as possible to maximize the brightness, which allows D to be made smaller. 
     From Eq. 3 and 4, the half-angle of the Bragg envelope θ B  is defined as: 
     
       
         
           
             
               
                 
                   
                     θ 
                     B 
                   
                   = 
                   
                     
                       η 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       λ 
                     
                     
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       D 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           
                             θ 
                             i 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   5 
                 
               
             
           
         
       
     
     where η is a reflection efficiency factor which is the value for x in the sin c 2 (x) function where the value of sin c 2 (x) has decreased to a predetermined value from the maximum amplitude as indicated by points  204 , 206  on the curve  200 . 
     We have found that the reflection efficiency is acceptable when η≦1.39. This value for η corresponds to when the amplitude of the reflected beam (i.e., from the sin c 2 (x) function of Eqs. 3 &amp; 4) has decayed to about 50% of its peak value. In particular, when x=1.39=η, sin c 2 (x)=0.5. However, other values for efficiency thresholds or factor in the Bragg envelope may be used if desired. 
     The beams  26 - 36  are imaged onto the CCD camera  60  to produce the pattern of light and dark regions  120 - 132  representing a digital (or binary) code, where light=1 and dark=0 (or vice versa). The digital code may be generated by selectively creating individual index variations (or individual gratings) with the desired spatial periods Λ 1 -Λn. Other illumination, readout techniques, types of gratings, geometries, materials, etc. may be used as discussed in the aforementioned patent application. 
     Referring to  FIG. 30 , illustrations (a)-(c), for the grating  12  in a cylindrical substrate  10  having a sample spectral 17 bit code (i.e., 17 different pitches Λ 1 -Λ 17 ), the corresponding image on the CCD (Charge Coupled Device) camera  60  is shown for a digital pattern 17 bit locations  89 , including  FIG. 30  illustrations (b), (c) and (d), respectively, of 7 bits turned on (10110010001001001); 9 bits turned on of (11000101010100111); and all 17 bits turned on of (11111111111111111). 
     For the images in  FIG. 30 , the length of the substrate  10  was 450 microns, the outer diameter D 1  was 65 microns, the inner diameter D was 14 microns, δn for the grating  12  was about 10 −4 , n 1  in portion  20  was about 1.458 (at a wavelength of about 1550 nm), n 2  in portion  18  was about 1.453, the average pitch spacing Λ for the grating  12  was about 0.542 microns, and the spacing between pitches ΔΛ was about 0.36% of the adjacent pitches Λ. 
     Referring to  FIG. 31  illustration (a), the pitch Λ of an individual grating is the axial spatial period of the sinusoidal variation in the refractive index n 1  in the region of the substrate  10  along the axial length of the grating  12  as indicated by a curve  90  on a graph  91 . Referring to  FIG. 31 , illustration (b), a sample composite grating  12  comprises three individual gratings that are co-located on the substrate  10 , each individual grating having slightly different pitches, Λ 1 , Λ 2 , Λ 3 , respectively, and the difference (or spacing) ΔΛ between each pitch Λ being about 3.0% of the period of an adjacent pitch Λ as indicated by a series of curves  92  on a graph  94 . Referring to  FIG. 31  illustration (c), three individual gratings, each having slightly different pitches, Λ 1 , Λ 2 , Λ 3 , respectively, are shown, the difference ΔΛ between each pitch Λ being about 0.3% of the pitch Λ of the adjacent pitch as shown by a series of curves  95  on a graph  97 . The individual gratings in  FIG. 31 , illustrations (b) and (c) are shown to all start at 0 for illustration purposes however, it should be understood that, the separate gratings need not all start in phase with each other. Referring to  FIG. 31 , illustration (d), the overlapping of the individual sinusoidal refractive index variation pitches Λ 1 -Λn in the grating region  20  of the substrate  10 , produces a combined resultant refractive index variation in the composite grating  12  shown as a curve  96  on a graph  98  representing the combination of the three pitches shown in  FIG. 31 , illustration (b). Accordingly, the resultant refractive index variation in the grating region  20  of the substrate  10  may not be sinusoidal and is a combination of the individual pitches Λ (or index variation). 
     The maximum number of resolvable bits N, which is equal to the number of different grating pitches Λ (and hence the number of codes), that can be accurately read (or resolved) using side-illumination and side-reading of the grating  12  in the substrate  10 , is determined by numerous factors, including: the beam width w incident on the substrate (and the corresponding substrate length L and grating length Lg), the thickness or diameter D of the grating  12 , the wavelength λ of incident light, the beam divergence angle θ R , and the width of the Bragg envelope θ B  (discussed more in the aforementioned patent application), and may be determined by the equation: 
     
       
         
           
             
               
                 
                   N 
                   ≅ 
                   
                     
                       η 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       β 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       L 
                     
                     
                       2 
                       ⁢ 
                       D 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           
                             θ 
                             i 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
             
           
         
       
     
     Referring to  FIG. 32 , instead of having the input light  24  at a single wavelength λ (monochromatic) and reading the bits by the angle θo of the output light, the bits (or grating pitches Λ) may be read/detected by providing a plurality of wavelengths and reading the wavelength spectrum of the reflected output light signal. In this case, there would be one bit per wavelength, and thus, the code is contained in the wavelength information of the reflected output signal. 
     In this case, each bit (or Λ) is defined by whether its corresponding wavelength falls within the Bragg envelope, not by its angular position within the Bragg envelope  200 . As a result, it is not limited by the number of angles that can fit in the Bragg envelope  200  for a given composite grating  12 , as in the embodiment discussed hereinbefore. Thus, using multiple wavelengths, the only limitation in the number of bits N is the maximum number of grating pitches A that can be superimposed and optically distinguished in wavelength space for the output beam. 
     Referring to  FIGS. 32 and 33 , illustration (a), the reflection wavelength spectrum (λ 1 -λn) of the reflected output beam  310  will exhibit a series of reflection peaks  695 , each appearing at the same output Bragg angle θo. Each wavelength peak  695  (λ 1 -λn) corresponds to an associated spatial period (Λ 1 -Λn), which make up the grating  12 . 
     One way to measure the bits in wavelength space is to have the input light angle θi equal to the output light angle θo, which is kept at a constant value, and to provide an input wavelength λ that satisfies the diffraction condition (Eq. 1) for each grating pitch Λ. This will maximize the optical power of the output signal for each pitch Λ detected in the grating  12 . 
     Referring to  33 , illustration (b), the transmission wavelength spectrum of the transmitted output beam  330  (which is transmitted straight through the grating  12 ) will exhibit a series of notches (or dark spots)  696 . Alternatively, instead of detecting the reflected output light  310 , the transmitted light  330  may be detected at the detector/reader  308 . It should be understood that the optical signal levels for the reflection peaks  695  and transmission notches  696  will depend on the “strength” of the grating  12 , i.e., the magnitude of the index variation n in the grating  12 . 
     In  FIG. 32 , the bits may be detected by continuously scanning the input wavelength. A known optical source  300  provides the input light signal  24  of a coherent scanned wavelength input light shown as a graph  304 . The source  300  provides a sync signal on a line  306  to a known reader  308 . The sync signal may be a timed pulse or a voltage ramped signal, which is indicative of the wavelength being provided as the input light  24  to the substrate  10  at any given time. The reader  308  may be a photodiode, CCD camera, or other optical detection device that detects when an optical signal is present and provides an output signal on a line  309  indicative of the code in the substrate  10  or of the wavelengths present in the output light, which is directly related to the code, as discussed herein. The grating  12  reflects the input light  24  and provides an output light signal  310  to the reader  308 . The wavelength of the input signal is set such that the reflected output light  310  through an optical lens  321  will be substantially in the center  314  of the Bragg envelope  200  for the individual grating pitch (or bit) being read. 
     Alternatively, the source  300  may provide a continuous broadband wavelength input signal such as that shown as a graph  316 . In that case, the reflected output beam  310  signal is provided to a narrow band scanning filter  318  which scans across the desired range of wavelengths and provides a filtered output optical signal  320  to the reader  308 . The filter  318  provides a sync signal on a line  322  to the reader, which is indicative of which wavelengths are being provided on the output signal  320  to the reader and may be similar to the sync signal discussed hereinbefore on the line  306  from the source  300 . In this case, the source  300  does not need to provide a sync signal because the input optical signal  24  is continuous. Alternatively, instead of having the scanning filter being located in the path of the output beam  310 , the scanning filter may be located in the path of the input beam  24  as indicated by the dashed box  324 , which provides the sync signal on a line  323 . 
     Alternatively, instead of the scanning filters  318 , 324 , the reader  308  may be a known optical spectrometer (such as a known spectrum analyzer), capable of measuring the wavelength of the output light. 
     The desired values for the input wavelengths λ (or wavelength range) for the input signal  24  from the source  300  may be determined from the Bragg condition of Eq. 1, for a given grating spacing Λ and equal angles for the input light θi and the angle light θo. Solving Eq. 1 for λ and plugging in m=1, gives:
 
λ=Λ[sin(θ o )+sin(θ i )]  Eq. 7
 
     It is also possible to combine the angular-based code detection with the wavelength-based code detection, both discussed hereinbefore. In this case, each readout wavelength is associated with a predetermined number of bits within the Bragg envelope. Bits (or grating pitches Λ) written for different wavelengths do not show up unless the correct wavelength is used. 
     Accordingly, the bits (or grating pitches Λ) can be read using one wavelength and many angles, many wavelengths and one angle, or many wavelengths and many angles. 
     Referring to  FIG. 34 , the grating  12  may have a thickness or depth D which is comparable or smaller than the incident beam wavelength λ. This is known as a “thin” diffraction grating (or the full angle Bragg envelope is 180 degrees). In that case, the half-angle Bragg envelope θB is substantially 90 degrees however, δn must be made large enough to provide sufficient reflection efficiency per Eqs. 3 and 4. In particular, for a “thin” grating, D*δn≈λ/2, which corresponds to a π phase shift between adjacent minimum and maximum refractive index values of the grating  12 . 
     It should be understood that there is still a trade-off discussed hereinbefore with beam divergence angle θ R  and the incident beam width (or length L of the substrate), but the accessible angular space is theoretically now 90 degrees. Also, for maximum efficiency the phase shift between adjacent minimum and maximum refractive index values of the grating  12  should approach a π phase shift however, other phase shifts may be used. 
     In this case, rather than having the input light  24  coming in at the conventional Bragg input angle θi, as discussed hereinbefore and indicated by a dashed line  701 , the grating  12  is illuminated with the input light  24  oriented on a line  705  orthogonal to the longitudinal grating vector  703 . The input beam  24  will split into two (or more) beams of equal amplitude, where the exit angle θ o  can be determined from Eq. 1 with the input angle θ i =0 (normal to the longitudinal axis of the grating  12 ). 
     In particular, from Eq. 1, for a given grating pitch Λ 1 , the +/−1 st  order beams (m=+1 and m=−1) corresponds to output beams  700 , 702 , respectively, the +/−2 nd  order beams (m=+2 and m=−2) corresponds to output beams  704 , 706 , respectively; and the 0 th  order (undiffracted) beam (m=0) corresponds to beam  708  and passes straight through the substrate. The output beams  700 - 708  project spectral spots or peaks  710 - 718 , respectively, along a common plane, shown from the side by a line  709 , which is parallel to the upper surface of the substrate  10 . 
     For example, for a grating pitch Λ=1.0 um, and an input wavelength λ=400 nm, the exit angles θ o  are ˜+/−23.6 degrees (for m=+/−1), and +/−53.1 degrees (from m=+/−2), from Eq. 1. It should be understood that for certain wavelengths, certain orders (e.g., m=+/−2) may be reflected back toward the input side or otherwise not detectable at the output side of the grating  12 . 
     Alternatively, one can use only the +/−1 st  order (m=+/−1) output beams for the code, in which case there would be only 2 peaks to detect,  712 ,  714 . Alternatively, one can also use any one or more pairs from any order output beam that is capable of being detected. Alternatively, instead of using a pair of output peaks for a given order, an individual peak may be used. 
     Referring to  FIG. 35 , if two pitches Λ 1 ,Λ 2  exist in the grating  12 , two sets of peaks will exist. In particular, for a second grating pitch Λ 2 , the +/−1 st  order beams (m=+1 and m=−1) corresponds to output beams  720 , 722 , respectively, the +/−2 nd  order beams (m=+2 and m=−2) corresponds to output beams  724 , 726 , respectively, and the 0 th  order (un-diffracted) beam (m=0) corresponds to beam  718  and passes straight through the substrate. The output beams  720 - 726  corresponding to the second pitch Λ 2  project spectral spots or peaks  730 - 736 , respectively, which are at a different location than the point  710 - 716 , but along the same common plane, shown from the side by the line  709 . 
     Thus, for a given pitch Λ (or bit) in a grating, a set of spectral peaks will appear at a specific location in space. Thus, each different pitch corresponds to a different elevation or output angle which corresponds to a predetermined set of spectral peaks. Accordingly the presence or absence of a particular peak or set of spectral peaks defines the code. 
     In general, if the angle of the grating  12  is not properly aligned with respect to the mechanical longitudinal axis of the substrate  10 , the readout angles may no longer be symmetric, leading to possible difficulties in readout. With a thin grating, the angular sensitivity to the alignment of the longitudinal axis of the substrate  10  to the input angle θi of incident radiation is reduced or eliminated. In particular, the input light can be oriented along substantially any angle θi with respect to the grating  12  without causing output signal degradation, due the large Bragg angle envelope. Also, if the incident beam  24  is normal to the substrate  10 , the grating  12  can be oriented at any rotational (or azimuthal) angle without causing output signal degradation. However, in each of these cases, changing the incident angle θi will affect the output angle θo of the reflected light in a predetermined predictable way, thereby allowing for accurate output code signal detection or compensation. 
     Referring to  FIG. 36 , for a thin grating, in addition to multiplexing in the elevation or output angle based on grating pitch Λ, the bits can also be multiplexed in an azimuthal (or rotational) angle θa of the substrate. In particular, a plurality of gratings  750 , 752 , 754 , 756  each having the same pitch Λ are disposed in a surface  701  of the substrate  10  and located in the plane of the substrate surface  701 . The input light  24  is incident on all the gratings  750 , 752 , 754 , 756  simultaneously. Each of the gratings provides output beams oriented based on the grating orientation. For example, the grating  750  provides the output beams  764 , 762 , the grating  752  provides the output beams  766 , 768 , the grating  754  provides the output beams  770 , 772 , and the grating  756  provides the output beams  774 , 776 . Each of the output beams provides spectral peaks or spots (similar to that discussed hereinbefore), which are located in a plane  760  that is parallel to the substrate surface plane  701 . In this case, a single grating pitch Λ can produce many bits depending on the number of gratings that can be placed at different azimuthal (rotational) angles on the surface of the substrate  10  and the number of output beam spectral peaks that can be spatially and optically resolved/detected. Each bit may be viewed as the presence or absence of a pair of peaks located at a predetermined location in space in the plane  760 . Note that this example uses only the m=+/−1 st  order for each reflected output beam. Alternatively, the detection may also use the m=+/−2 nd  order. In that case, there would be two additional output beams and peaks (not shown) for each grating (as discussed hereinbefore) that may lie in the same plane as the plane  760  and may be on a concentric circle outside the circle  760 . 
     In addition, the azimuthal multiplexing can be combined with the elevation or output angle multiplexing discussed hereinbefore to provide two levels of multiplexing. Accordingly for a thin grating, the number of bits can be multiplexed based on the number of grating pitches Λ and/or geometrically by the orientation of the grating pitches. 
     Furthermore, if the input light angle θi is normal to the substrate  10 , the edges of the substrate  10  no longer scatter light from the incident angle into the “code angular space”, as discussed herein and/or in the aforementioned patent application. 
     Also, in the thin grating geometry, a continuous broadband wavelength source may be used as the optical source if desired. 
     Referring to  FIG. 37 , instead of or in addition to the pitches A in the grating  12  being oriented normal to the longitudinal axis, the pitches may be created at a angle θg. In that case, when the input light  24  is incident normal to the surface  792 , will produce a reflected output beam  790  having an angle θo determined by Eq. 1 as adjusted for the blaze angle θg. This can provide another level of multiplexing bits in the code. 
     Referring to  FIG. 38 , instead of using an optical binary (0-1) code, an additional level of multiplexing may be provided by having the optical code use other numerical bases, if intensity levels of each bit are used to indicate code information. This could be achieved by having a corresponding magnitude (or strength) of the refractive index change (δn) for each grating pitch Λ. Four intensity ranges are shown for each bit number or pitch Λ, providing for a Base-4 code (where each bit corresponds to 0,1,2, or 3). The lowest intensity level, corresponding to a 0, would exist when this pitch Λ is not present in the grating  12 . The next intensity level  450  would occur when a first low level δn 1  exists in the grating that provides an output signal within the intensity range corresponding to a 1. The next intensity level  452  would occur when a second higher level δn 2  exists in the grating  12  that provides an output signal within the intensity range corresponding to a 2. The next intensity level  454  would occur when a third higher level δn 3  exists in the grating  12  that provides an output signal within the intensity range corresponding to a 3. 
     Referring to  FIG. 39 , the input light  24  may be incident on the substrate  10  on an end face  600  of the substrate  10 . In that case, the input light  24  will be incident on the grating  12  having a more significant component of the light (as compared to side illumination discussed hereinbefore) along the longitudinal grating axis  207  of the grating (along the grating vector k B ), as shown by a line  602 . The light  602  reflects off the grating  12  as indicated by a line  604  and exits the substrate as output light  608 . Accordingly it should be understood by one skilled in the art that the diffraction equations discussed hereinbefore regarding output diffraction angle θo also apply in this case except that the reference axis would now be the grating axis  207 . Thus, in this case, the input and output light angles θi,θo, would be measured from the grating axis  207  and length Lg of the grating  12  would become the thickness or depth D of the grating  12 . As a result, a grating  12  that is 400 microns long, would result in the Bragg envelope  200  being narrow. It should be understood that because the values of n 1  and n 2  are close to the same value, the slight angle changes of the light between the regions  18 , 20  are not shown herein. 
     In the case where incident light  610  is incident along the same direction as the grating vector (Kb)  207 , i.e., θi=0 degrees, the incident light sees the whole length Lg of the grating  12  and the grating provides a reflected output light angle θo=0 degrees, and the Bragg envelope  612  becomes extremely narrow, as the narrowing effect discussed above reaches a limit. In that case, the relationship between a given pitch Λ in the grating  12  and the wavelength of reflection λ is governed by a known “Bragg grating” relation:
 
λ=2n eff Λ  Eq. 8
 
where n eff  is the effective index of refraction of the substrate, λ is the input (and output wavelength) and Λ is the pitch. This relation, as is known, may be derived from Eq. 1 where θi=θo=90 degrees.
 
     In that case, the code information is readable only in the spectral wavelength of the reflected beam, similar to that discussed hereinbefore for wavelength based code reading. Accordingly the input signal in this case may be a scanned wavelength source or a broadband wavelength source. In addition, as discussed hereinbefore for wavelength based code reading, the code information may be obtained in reflection from the reflected beam  614  or in transmission by the transmitted beam  616  that passes through the grating  12 . 
     It should be understood that for shapes of the substrate  10  or element  8  other than a cylinder, the effect of various different shapes on the propagation of input light through the element  8 , substrate  10 , and/or grating  12 , and the associated reflection angles, can be determined using known optical physics including Snell&#39;s Law, shown below:
 
n in  sin θin=n out  sin θout  9
 
     where n in  is the refractive index of the first (input) medium, and n out  is the refractive index of the second (output) medium, and θin and θout are measured from a line  620  normal to an incident surface  622 . 
     Referring to  FIG. 40 , if the value of nil in the grating region  20  is greater than the value of n 2  in the non-grating region  18 , the grating region  20  of the substrate  10  will act as a known optical waveguide for certain wavelengths. In that case, the grating region  20  acts as a “core” along which light is guided and the outer region  18  acts as a “cladding” which helps confine or guide the light. Also, such a waveguide will have a known “numerical aperture” (θna) that will allow light  630  that is within the aperture θna to be directed or guided along the grating axis  207  and reflected axially off the grating  12  and returned and guided along the waveguide. In that case, the grating  12  will reflect light having the appropriate wavelengths equal to the pitches Λ present in the grating  12  back along the region  20  (or core) of the waveguide, and pass the remaining wavelengths of light as the light  632 . Thus, having the grating region  20  act as an optical waveguide for wavelengths reflected by the grating  12  allows incident light that is not aligned exactly with the grating axis  207  to be guided along and aligned with the grating  12  axis  207  for optimal grating reflection. 
     If an optical waveguide is used any standard waveguide may be used, e.g., a standard telecommunication single mode optical fiber (125 micron diameter or 80 micron diameter fiber with about a 8-10 micron diameter), or a larger diameter waveguide (greater than 0.5 mm diameter), such as is describe in U.S. patent application Ser. No. 09/455,868, filed Dec. 6, 1999, entitled “Large Diameter Waveguide, Grating”. Further, any type of optical waveguide may be used for the optical substrate  10 , such as, a multi-mode, birefringent, polarization maintaining, polarizing, multi-core, multi-cladding, or microstructured optical waveguide, or a flat or planar waveguide (where the waveguide is rectangular shaped), or other waveguides. 
     Referring to  FIG. 41  if the grating  12  extends across the entire dimension D of the substrate, the substrate  10  does not behave as a waveguide for the incident or reflected light and the incident light  24  will be diffracted (or reflected) as indicated by lines  642 , and the codes detected as discussed hereinbefore for the end-incidence condition discussed hereinbefore with  FIG. 45 , and the remaining light  640  passes straight through. 
     Referring to  FIG. 42 , illustrations (a)-(c), in illustration (a), for the end illumination condition, if a blazed or angled grating is used, as discussed hereinbefore, the input light  24  is coupled out of the substrate  10  at a known angle as shown by a line  650 . Referring to  FIG. 42 , illustration (b), alternatively, the input light  24  may be incident from the side and, if the grating  12  has the appropriate blaze angle, the reflected light will exit from the end face  652  as indicated by a line  654 . Referring to  FIG. 42 , illustration (c), the grating  12  may have a plurality of different pitch angles  660 , 662 , which reflect the input light  24  to different output angles as indicated by lines  664 ,  666 . This provides another level of multiplexing (spatially) additional codes, if desired. 
     The grating  12  may be impressed in the substrate  10  by any technique for writing, impressed, embedded, imprinted, or otherwise forming a diffraction grating in the volume of or on a surface of a substrate  10 . Examples of some known techniques are described in U.S. Pat. Nos. 4,725,110 and 4,807,950, entitled “Method for Impressing Gratings Within Fiber Optics”, to Glenn et al, and U.S. Pat. No. 5,388,173, entitled “Method and Apparatus for Forming Aperiodic Gratings in Optical Fibers”, to Glenn, respectively, and U.S. Pat. No. 5,367,588, entitled “Method of Fabricating Bragg Gratings Using a Silica Glass Phase Grating Mask and Mask Used by Same”, to Hill, and U.S. Pat. No. 3,916,182, entitled “Periodic Dielectric Waveguide Filter”, Dabby et al, and U.S. Pat. No. 3,891,302, entitled “Method of Filtering Modes in Optical Waveguides”, to Dabby et al, which are all incorporated herein by reference to the extent necessary to understand the present invention. 
     Alternatively, instead of the grating  12  being impressed within the substrate material, the grating  12  may be partially or totally created by etching or otherwise altering the outer surface geometry of the substrate to create a corrugated or carving surface geometry of the substrate, such as is described in U.S. Pat. No. 3,891,302, entitled “Method of Filtering Modes in Optical Waveguides”, to Dabby et al, which is incorporated herein by reference to the extent necessary to understand the present invention, provided the resultant optical refractive profile for the desired code is created. 
     Further, alternatively, the grating  12  may be made by depositing dielectric layers onto the substrate, similar to the way a known thin film filter is created, so as to create the desired resultant optical refractive profile for the desired code. 
     The substrate  10  (and/or the element  8 ) may have end-view cross-sectional shapes other than circular, such as square, rectangular, elliptical, clam-shell, D-shaped, or other shapes, and may have side-view sectional shapes other than rectangular, such as circular, square, elliptical, clam-shell, D-shaped, or other shapes. Also, 3D geometries other than a cylinder may be used, such as a sphere, a cube, a pyramid or any other 3D shape. Alternatively, the substrate  10  may have a geometry that is a combination of one or more of the foregoing shapes. 
     The shape of the element  8  and the size of the incident beam may be made to minimize any end scatter off the end face(s) of the element  8 , as is discussed herein and/or in the aforementioned patent application. Accordingly to minimize such scatter, the incident beam  24  may be oval shaped where the narrow portion of the oval is smaller than the diameter D 1 , and the long portion of the oval is smaller than the length L of the element  8 . Alternatively, the shape of the end faces may be rounded or other shapes or may be coated with an antireflective coating. 
     It should be understood that the size of any given dimension for the region  20  of the grating  12  may be less than any corresponding dimension of the substrate  10 . For example, if the grating  12  has dimensions of length Lg, depth Dg, and width Wg, and the substrate  12  has different dimensions of length L, depth D, and width W, the dimensions of the grating  12  may be less than that of the substrate  12 . Thus, the grating  12 , may be embedded within or part of a much larger substrate  12 . Also, the element  8  may be embedded or formed in or on a larger object for identification of the object. 
     The dimensions, geometries, materials, and material properties of the substrate  10  are selected such that the desired optical and material properties are met for a given application. The resolution and range for the optical codes are scalable by controlling these parameters as discussed herein and/or in the aforementioned patent application. 
     Referring to  FIG. 43 , the substrate  10  may have an outer coating  799 , such as a polymer or other material that may be dissimilar to the material of the substrate  10 , provided that the coating  799  on at least a portion of the substrate, allows sufficient light to pass through the substrate for adequate optical detection of the code. The coating  799  may be on any one or more sides of the substrate  10 . Also, the coating  799  may be a material that causes the element  8  to float or sink in certain fluids (liquid and/or gas) solutions. 
     Also, the substrate  10  may be made of a material that is less dense than certain fluid (liquids and/or gas) solutions, thereby allowing the elements  8  to float or be buoyant or partially buoyant. Also, the substrate may be made of a porous material, such as controlled pore glass (CPG) or other porous material, which may also reduce the density of the element  8  and may make the element  8  buoyant or partially-buoyant in certain fluids. 
     Referring to  FIG. 44 , the grating  12  is axially spatially invariant. As a result, the substrate  10  with the grating  12  (shown as a long substrate  21 ) may be axially subdivided or cut into many separate smaller substrates  30 - 36  and each substrate  30 - 36  will contain the same code as the longer substrate  21  had before it was cut. The limit on the size of the smaller substrates  30 - 36  is based on design and performance factors discussed herein and/or in the aforementioned patent application. 
     Referring to  FIG. 45 , one purpose of the outer region  18  (or region without the grating  12 ) of the substrate  10  is to provide mechanical or structural support for the inner grating region  20 . Accordingly the entire substrate  10  may comprise the grating  12 , if desired. Alternatively, the support portion may be completely or partially beneath, above, or along one or more sides of the grating region  20 , such as in a planar geometry, or a D-shaped geometry, or other geometries, as described herein and/or in the aforementioned patent application. The non-grating portion  18  of the substrate  10  may be used for other purposes as well, such as optical lensing effects or other effects (discussed herein or in the aforementioned patent application). Also, the end faces of the substrate  10  need not be perpendicular to the sides or parallel to each other. However, for applications where the elements  8  are stacked end-to-end, the packing density may be optimized if the end faces are perpendicular to the sides. 
     Referring to  FIG. 46 , illustrations (a)-(c), two or more substrates  10 , 250 , each having at least one grating therein, may be attached together to form the element  8 , e.g., by an adhesive, fusing or other attachment techniques. In that case, the gratings  12 , 252  may have the same or different codes. 
     Referring to  FIG. 47 , illustrations (a) and (b), the substrate  10  may have multiple regions  80 , 90  and one or more of these regions may have gratings in them. For example, there may be gratings  12 , 252  side-by-side (illustration (a)), or there may be gratings  82 - 88 , spaced end-to-end (illustration (b)) in the substrate  10 . 
     Referring to  FIG. 48 , the length L of the element  8  may be shorter than its diameter D, thus, having a geometry such as a plug, puck, wafer, disc or plate. 
     Referring to  FIG. 49 , to facilitate proper alignment of the grating axis with the angle θi of the input beam  24 , the substrate  10  may have a plurality of the gratings  12  having the same codes written therein at numerous different angular or rotational (or azimuthal) positions of the substrate  10 . In particular, two gratings  550 ,  552 , having axial grating axes  551 ,  553 , respectively may have a common central (or pivot or rotational) point where the two axes  551 , 553  intersect. The angle θi of the incident light  24  is aligned properly with the grating  550  and is not aligned with the grating  552 , such that output light  555  is reflected off the grating  550  and light  557  passes through the grating  550  as discussed herein. If the element  8  is rotated as shown by the arrows  559 , the angle θi of incident light  24  will become aligned properly with the grating  552  and not aligned with the grating  550  such that output light  555  is reflected off the grating  552  and light  557  passes through the grating  552 . When multiple gratings are located in this rotational orientation, the bead may be rotated as indicated by a line  559  and there may be many angular positions that will provide correct (or optimal) incident input angles θi to the grating. While this example shows a circular cross-section, this technique may be used with any shape cross-section. 
     Referring to  FIG. 50 , illustrations (a), (b), (c), (d), and (e) the substrate  10  may have one or more holes located within the substrate  10 . In illustration (a), holes  560  may be located at various points along all or a portion of the length of the substrate  10 . The holes need not pass all the way through the substrate  10 . Any number, size and spacing for the holes  560  may be used if desired. In illustration (b), holes  572  may be located very close together to form a honeycomb-like area of all or a portion of the cross-section. In illustration (c), one (or more) inner hole  566  may be located in the center of the substrate  10  or anywhere inside of where the grating region(s)  20  are located. The inner hole  566  may be coated with a reflective coating  573  to reflect light to facilitate reading of one or more of the gratings  12  and/or to reflect light diffracted off one or more of the gratings  12 . The incident light  24  may reflect off the grating  12  in the region  20  and then reflect off the surface  573  to provide output light  577 . Alternatively, the incident light  24  may reflect off the surface  573 , then reflect off the grating  12  and provide the output light  575 . In that case the grating region  20  may run axially or circumferentially  571  around the substrate  10 . In illustration (d), the holes  579  may be located circumferentially around the grating region  20  or transversely across the substrate  10 . In illustration (e), the grating  12  may be located circumferentially around the outside of the substrate  10 , and there may be holes  574  inside the substrate  10 . In that case, the incident light  24  reflects off the grating  12  to provide the optical light  576 . 
     Referring to  FIG. 51 , illustrations (a), (b), and (c), the substrate  10  may have one or more protruding portions or teeth  570 ,  578 , 580  extending radially and/or circumferentially from the substrate  10 . Alternatively, the teeth  570 ,  578 , 580  may have any other desired shape. 
     Referring to  FIG. 52 , illustrations (a), (b), (c) a D-shaped substrate, a flat-sided substrate and an eve-shaped (or clam-shell or teardrop shaped) substrate  10 , respectively, are shown. Also, the grating region  20  may have end cross-sectional shapes other than circular and may have side cross-sectional shapes other than rectangular, such as any of the geometries described herein for the substrate  10 . For example, the grating region  20  may have an oval cross-sectional shape as shown by dashed lines  581 , which may be oriented in a desired direction, consistent with the teachings herein. Any other geometries for the substrate  10  or the grating region  20  may be used if desired, as described herein. 
     Referring to  FIG. 53 , at least a portion of a side of the substrate  10  may be coated with a reflective coating  514  to allows incident light  510  to be reflected back to the same side from which the incident light came, as indicated by reflected light  512 . 
     Referring to  FIG. 54 , illustrations (a) and (b), alternatively, the substrate  10  can be electrically and/or magnetically polarized, by a dopant or coating, which may be used to ease handling and/or alignment or orientation of the substrate  10  and/or the grating  12 , or used for other purposes. Alternatively, the bead may be coated with conductive material, e.g., metal coating on the inside of a holey substrate, or metallic dopant inside the substrate. In these cases, such materials can cause the substrate  10  to align in an electric or magnetic field. Alternatively, the substrate can be doped with an element or compound that fluoresces or glows under appropriate illumination, e.g., a rare earth dopant, such as Erbium, or other rare earth dopant or fluorescent or luminescent molecule. In that case, such fluorescence or luminescence may aid in locating and/or aligning substrates. 
     The dimensions and/or geometries for any of the embodiments described herein are merely for illustrative purposes and, as such, any other dimensions and/or geometries may be used if desired, depending on the application, size, performance, manufacturing requirements, or other factors, in view of the teachings herein. 
     It should be understood that, unless stated otherwise herein, any of the features, characteristics, alternatives or modifications described regarding a particular embodiment herein may also be applied, used, or incorporated with any other embodiment described herein. Also, the drawings herein are not drawn to scale. 
     Although the invention has been described and illustrated with respect to exemplary embodiments thereof, the foregoing and various other additions and omissions may be made therein and thereto without departing from the spirit and scope of the present invention.