Abstract:
A system for spectral analysis of a multi-wavelength signal is disclosed. The illustrative embodiment of the present invention, like the prior art, uses a grating or prism to disperse the spectral components of a multi-wavelength signal, and then uses a reciprocating or rotating mirror to direct the spectral components, one at a time, into a photodetector. The illustrative embodiment uses a telescope between the grating and the mirror to improve the spectral resolution of the system.

Description:
FIELD OF THE INVENTION 
   The present invention relates to optics in general, and, more particularly, to spectrum analyzers. 
   BACKGROUND OF THE INVENTION 
   The spectral analysis of multi-wavelength signals is vital in many fields. For example, in the field of telecommunications voice, data, and video signals are often transmitted on optical carriers of different wavelengths in optical fibers. In these systems, it is essential for the operators of an optical telecommunications system to be able to perform a high-resolution spectral analysis of its signals to ensure that they are within their intended operating parameters. 
   In the field of medicine, for example, optical coherence tomography (hereinafter “OCT”) is a well known and widely-used technique for tissue sample analysis. One version of OCT, called Fourier-Domain Optical Coherence Tomography, involves the spectral analysis of the light scattered by a tissue sample. The widespread adoption of Fourier-Domain OCT has been limited, however, because the available systems are not capable of performing the spectral analysis at a level sufficient for many applications. Therefore, the need exists for a Fourier-Domain OCT system that has a higher spectral resolution than systems in the prior art. 
   SUMMARY OF THE INVENTION 
   The present invention enables the spectral analysis of a multi-wavelength signal without some of the costs and disadvantages for doing so in the prior art. For example, embodiments of the present invention are particularly well-suited for use in optical telecommunications systems and in Fourier-Domain Optical Coherence Tomography. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, what the other applications are for embodiments of the present invention. 
   The illustrative embodiment of the present invention, like the prior art, uses a grating or prism to disperse the spectral components of a multi-wavelength signal, and then uses a reciprocating or rotating mirror to direct the spectral components, one at a time, into a photodetector. The photodetector is fast enough, in comparison to the movement of the mirror to enable many samples to be taken of the entire signal, which enables the intensity of the spectral components to be determined. 
   The incorporation of a telescope in the illustrative embodiment has several ramifications. First, the telescope relays the dispersive element onto the scanning mirror such that the mirror can sequentially direct each wavelength along the optical axis and into the center of the focusing lens. The fact that all wavelengths are on-axis and centered on the focusing lens enables the use of a focusing lens with a lower f/#, which causes the blur spot on the photodetector to be smaller than in the prior art. This improves the spectral resolution of the illustrative embodiment. 
   Second, the telescope magnifies the angular divergence of the beams that strike the mirror, which itself magnifies the spectral angular divergence of the light off of the mirror, which increases the effective spectral resolution of the illustrative embodiment. 
   Third, the telescope both (1) shrinks the width of the beams of light that strike the mirror, and (2) causes all of the beams of light to be coincident on the mirror, and both of these effects enable the embodiment to have a smaller mirror than in the prior art. The smaller mirror is advantageous because—all other things being equal—it can sweep the signal across the photodetector more quickly than a larger mirror and this enables the illustrative embodiment to have a greater temporal resolution than systems in the prior art. 
   The illustrative embodiment of the present invention comprises: a first device for radiating a first beam characterized by a first wavelength in a first direction and a second beam characterized by a second wavelength in a second direction, wherein the first wavelength is different than the second wavelength, and wherein the first direction is oblique to the second direction; and a second device for receiving the first beam and the second beam and for directing the first beam onto a locality from a third direction and the second beam onto the locality from a fourth direction, wherein the first beam arrives as collimated at the locality, wherein the second beam arrives as collimated at the locality, and wherein the third direction is oblique to the fourth direction. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  depicts a schematic drawing of the salient aspects of a Fourier Domain Optical Coherence Tomography system in accordance with the illustrative embodiment of the present invention. 
       FIG. 2  depicts a block diagram of the salient components of optical spectrum analyzer  105  in accordance with the illustrative embodiment of the present invention. 
       FIG. 3  depicts a schematic diagram of the salient components of optical system  201 A in accordance with the prior art. 
       FIGS. 4A and 4B  depict schematic diagrams of the salient components of optical system  201 B in accordance with the prior art. 
       FIG. 5  depicts a drawing of the face of scanning mirror  402  and depicts the projection of the spectral components onto that face. 
       FIGS. 6A and 6B  depict schematic diagrams of the salient components of optical system  201 C in accordance with the illustrative embodiment of the present invention. 
       FIG. 7  depicts a schematic diagram of the salient components of telescope  606  and specifically depicts how telescope  606  manipulates the center rays of beams λ 1  and λ N . 
       FIG. 8  depicts a schematic diagram of the salient components of telescope  606  and specifically depicts how telescope  606  manipulates beam λ N . 
       FIG. 9  depicts a drawing of the face of scanning mirror  602  and depicts the projection of the spectral components onto that face. 
       FIG. 10  depicts a flowchart of the salient processes performed by the illustrative embodiment of the present invention. 
   

   DETAILED DESCRIPTION 
     FIG. 1  depicts a schematic drawing of the salient aspects of a Fourier Domain Optical Coherence Tomography system in accordance with the illustrative embodiment of the present invention. Fourier Domain Optical Coherence Tomography system  100  comprises: sample  101 , mirror  102 , light source  103 , beam splitter  104 , and optical spectrum analyzer  105 , interconnected as shown. The configuration is well known as a Michelson interferometer. 
   Sample  101  is a mass of biological tissue, which is to be analyzed in accordance with the illustrative embodiment of the present invention. 
   Mirror  102  is 1 cm by 1 cm and is reflective at 870 nm and is located at a fixed position as shown. It will be clear to those skilled in the art how to make and use mirror  102 . 
   Light source  103  is a partially-coherent light source that emits a light beam characterized by a center wavelength of 870 nm and a spectral width of 40 nm. It will be clear to those skilled in the art how to make and use light source  103 . 
   Beam splitter  104  is a 1 cm-wide by 1 cm-high by 0.5 cm-thick piece of glass which comprises surface coatings that are partially reflective for 870 nm-wavelength incident light. It will be clear to those skilled in the art how to make and use beam splitter  104 . 
   Optical spectrum analyzer  104  is a system for separating and analyzing the spectral components contained in a multi-wavelength signal. Optical spectrum analyzer  104  is described in detail below and with respect to  FIG. 2 . 
   Light source  103  and beam splitter form source arm  113  of the Michelson interferometer. Beam splitter  104  and mirror  102  form reference arm  112  of the Michelson interferometer. Beam splitter  104  and sample  101  form sample arm  111  of the Michelson interferometer. Beam splitter  104  and optical spectrum analyzer  105  form detector arm  114  of the Michelson interferometer. 
   In operation, beam splitter  104  splits the light beam received from light source  103  into a reference and sample signal in reference arm  112  and sample arm  111 , respectively. In reference arm  112 , light is reflected back by mirror  102 . In sample arm  111 , light is reflected back by sample  101 . Beam splitter  104  mixes the light from reference arm  112  and sample arm  111  and directs the combined light into detector arm  114  which conveys it to optical spectrum analyzer  105 . Optical spectrum analyzer  105  discriminates and measures the intensities of the spectral components of the light in detector arm  114 . The measurement of the intensities of the spectral components enables depth-localized measurement of sample  101 , the measurement resolution of which is a function of the spectral resolution of optical spectrum analyzer  105 . 
     FIG. 2  depicts a block diagram of the salient components of optical spectrum analyzer  105  in accordance with the illustrative embodiment of the present invention. Optical spectrum analyzer  105  comprises: optical system  201 , processor  202 , and memory  203 , interconnected as shown. 
   Optical system  201  is a free-space optical system that is capable of resolving the spectral components of the light in detector arm  114  and reporting on the intensity of the components. 
   Processor  202  is a general-purpose processor that is capable of reading data and instructions from memory  203 , of executing instructions, of writing data to memory  203 , of receiving data from optical system  201 , and of controlling optical system  201 . It will be clear to those skilled in the art, after reading this specification, how to make and use processor  202 . 
   Memory  203  is a non-volatile memory that is capable of storing data and instructions for processor  202  in well-known fashion. 
     FIG. 3  depicts a schematic diagram of the salient components of optical system  201 A in accordance with the prior art. Optical system  201 A comprises dispersive element  301  and photodetector array  302 , interrelated as shown. 
   Dispersive element  301  is a device that is capable of dispersing the spectral components of an optical signal so that each component emerges from dispersive element  301  at a different angle, depending on its wavelength, and collimated. To prevent  FIG. 3  from being too cluttered, only those spectral components with the shortest and longest wavelengths (i.e., λ 1  and λ N ) are shown. As is well known in the prior art, dispersive element  301  is a free-space diffraction grating that receives a pre-collimated free-space optical signal. 
   Photodetector array  302  is a one-dimensional array of individual photodetectors, each of which is capable of generating an electrical signal based on the intensity of the light incident on that photodetector. Photodetector array  302  is positioned so that each spectral component emitted from dispersive element  301  is incident on and substantially fills a different photodetector. Each individual photodetector measures the intensity of the light that is incident on it and transmits a signal indicative of that intensity to processor  202 . 
   An advantage of optical system  201 A is that it is simple, inexpensive, and it can be made substantially immune to shock and vibration. 
   A disadvantage of optical system  201 A is that the fixed spacing between the individual photodetectors prevents the full spectral content from being determined, which makes optical system  201 A inappropriate for many applications. A further disadvantage is that photodetector arrays are expensive and the reliability of photodetector array  302  is lower than that of a single detector. A further disadvantage is that photodetector arrays are difficult to cool in order to reduce the thermal and shot noise that are inherent to photodetector. 
     FIGS. 4A and 4B  depict schematic diagrams of the salient components of optical system  201 B in accordance with the prior art. Optical system  201 B comprises: dispersive element  301 , scanning mirror  402 , controller  403 , focusing lens  404 , and photodetector  405 , interrelated as shown. 
   Scanning mirror  402  is capable of rotation about rotation axis  407  and the face of scanning mirror  402  is 2 cm by 2 cm and reflective at 870 nm. Scanning mirror  402  receives beams  1  through λ N  from dispersive element  301  and redirects them so that one of the N beams (e.g., λ 1  in  FIG. 4 ) is directed toward lens  404  at any one time. The reflecting surface of scanning mirror  402  is sized so that all of the beams are reflected with minimal clipping. The angular position of scanning mirror  402  about rotation axis  407  determines which spectral component is received by lens  404 . As shown in  FIG. 4A , the angular position of scanning mirror  402  directs beam  1  into lens  404 , and, as shown in  FIG. 4B , the slightly rotated position of scanning mirror  402  directs beam λ N  into lens  404 . The rotation of scanning mirror  402  about rotation axis  407  is controlled via a control signal received from controller  403 . It will be clear to those skilled in the art how to make and use scanning mirror  402 . 
   Controller  403  is a general-purpose processor that receives a control signal from processor  202  and transmits a control signal to control the rotation of scanning mirror  402 . The control signal from processor  202  instructs controller  403  to operate in either sweep mode or static mode. When controller  403  is in sweep mode, controller  403  instructs scanning mirror  402  to smoothly reciprocate around axis  407  so that all N beams are reflected and swept across focusing lens  404  during each half-cycle. When controller  403  is in static mode, controller instructs scanning mirror  402  to assume one angle and remain there, which reflects the desired beam into focusing lens  404 . It will be clear to those skilled in the art how to make and use controller  403 . 
   Focusing lens  404  is a thin convex lens with a clear aperture slightly larger than beam diameter D 1  (as described below and with respect to  FIG. 5 ) and a focal length of f L1 . The purpose of focusing lens  404  is to capture and focus the light reflected off of scanning mirror  402  into photodetector  405 . Focusing lens  404  is positioned a distance of f L1  from photodetector  405 . Focusing lens  404  is positioned a sufficient distance from scanning mirror  402  so as to not impede the rotation of scanning mirror  402  and so that scanning mirror  402  is able to direct all of the spectral components through lens  404  and onto photodetector  405 . The purpose of focusing lens  404  is to capture and focus the light reflected off of scanning mirror  402  into photodetector  405 . 
   Photodetector  405  is a high-speed, low-noise, single-element photodetector that can be readily cooled to reduce thermal and shot noise. Photodetector  405  has a photodetection region which is slightly larger than the blur spot associated with the light received from lens  404 . Photodetector  405  measures the intensity of the light that is incident on it and transmits a signal indicative of that intensity to processor  202 . 
   An advantage of optical system  201 B in comparison to optical system  201 A is that the small size of photodetector  405  facilitates cooling to enable high-speed photodetection and low noise operation. In addition, acquisition of many data points from the single-element photodetector enables the measurement of more spectral components than can be measured using optical system  201 A. 
   A disadvantage of optical system  201 B is that scanning mirror  402  must be large in order to accommodate the spatially diverse spectral components that emanate from dispersive element  301  (as described below and with respect to  FIG. 5 ). Large mirrors are unable to scan rapidly, which limits the temporal resolution of optical spectrum analyzer  201 . 
     FIG. 5  depicts a drawing of the face of scanning mirror  402  and depicts the projection of the spectral components onto that face. To prevent  FIG. 5  from being too cluttered, only those spectral components with the shorted and longest wavelengths (i.e., λ 1  and λ N ) are shown. 
   The separation of the projections of λ 1  and λ N  on the face of scanning mirror  402  is a function of their angular divergence upon emission from dispersive element  301  and the distance that separates dispersive element  301  and scanning mirror  402 . Additionally, in order to avoid clipping of the spectral components, the face must be larger in the direction of rotation axis  407  than the diameter D 1  of the collimated beams. For the purposes of this disclosure, the diameter of a beam is defined as the full width at half-maximum intensity. Further, in the direction of scan axis  508 , the projection of each beam is enlarged due to the mirror angle. Therefore, the mirror face must be sufficiently large to avoid clipping in that direction as well. 
     FIGS. 6A and 6B  depict schematic diagrams of the salient components of optical system  201 C in accordance with the illustrative embodiment of the present invention. Optical system  201 C comprises: dispersive element  601 , scanning mirror  602 , controller  403 , focusing lens  604 , photodetector  605 , and telescope  606 , interrelated as shown. 
   Source  601  is a fiber Bragg grating, which launches the spectral components of an optical signal into free-space as collimated light. In some alternative embodiments, source  601  is a free-space diffraction grating which receives a pre-collimated free-space optical signal. In yet some other alternative embodiments, source  601  is a prism that receives a pre-collimated free-space optical signal. In yet some other alternative embodiments, source  601  is a holographic element that receives a free-space optical signal. In yet some other alternative embodiments, source  601  is a plurality of dispersive elements that includes:
         i. prisms; or   ii. fiber Bragg gratings; or   iii. free-space diffraction gratings; or   iv. holographic elements; or   v. any combination of i, ii, iii, and iv.       

   It will be clear to those skilled in the art how to make and use source  601 . 
   Scanning mirror  602  is an actuated mirror that is capable of turning about rotation axis  607  under the control of controller  403 . The reflective face of scanning mirror  602  is 0.5 cm-high by 0.6 cm-wide and is reflective at 870 nm. The reflecting surface of scanning mirror  602  is sized so that all beams are reflected with minimal clipping. Although the illustrative embodiment comprises a scanning mirror to select which beam is directed into photodetector  605 , it will be clear to those skilled in the art, after reading this specification, how to make and use alternative embodiments of the present invention in which a scanning prism or acousto-optic scanner is used instead of the scanning mirror. 
   Focusing lens  604  is a thin convex lens with a clear aperture slightly larger than beam diameter D 2  (as described below and with respect to  FIG. 8 ) and a focal length of f L2 . Focusing lens  604  is positioned a distance of f L2  from photodetector  605 . Focusing lens  604  is positioned a sufficient distance from scanning mirror  602  so as to not impede the rotation of scanning mirror  602  and scanning mirror  602  is able to direct all desired spectral components toward focusing lens  604 . The purpose of focusing lens  604  is to capture and focus the light reflected off of scanning mirror  602  into photodetector  605 . 
   Photodetector  605  is a small-area, high-speed, low-noise, single-element photodetector, which can be readily cooled to reduce thermal and shot noise. Photodetector  605  has a photodetection region which is slightly larger than the blur spot associated with the light received from lens  604 . Photodetector  605  measures the intensity of the light that is incident on it and transmits a signal indicative of that intensity to processor  202 . Because beam diameter D 2  is smaller than beam diameter D 1 , lens  604  and photodetector  605  can be smaller than lens  404  and photodetector  405 . 
   Telescope  606  is an a focal optical element whose axis is orthogonal to the rotational axis of scanning mirror  602 . The function of telescope  606  is three-fold. First, telescope  606  shrinks the width of the beams of light that strike the mirror, which enables the illustrative embodiment to have a smaller mirror than in the prior art. Second, telescope  606  causes all of the beams of light to be coincident on the mirror, which also enables the illustrative embodiment to have a smaller mirror than in the prior art. And third, telescope  606  magnifies the angular divergence of the beams that strike the mirror, which itself magnifies the spectral angular divergence of the light off of the mirror, which increases the spectral resolution of the illustrative embodiment. Telescope  606  is described below and with respect to  FIGS. 7 and 8 . 
   Dispersive element  601 , telescope  606 , scanning mirror  602 , focusing lens  604 , and photodetector  605  define an optical path, the axis of which includes crossing point  703 . The distance of telescope  606  from dispersive element  601  on the optical path is such that telescope  606  captures all N beams emitted from dispersive element  601  without the occurrence of clipping. The distance of telescope  606  from scanning mirror  602  is such that crossing point  703  (as described below and with respect to  FIG. 7 ) of telescope  606  is on the reflective surface of scanning mirror  602 . 
   It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention wherein crossing point  703  is not on the reflective surface of scanning mirror  602 . 
   An advantage of optical system  201 C in comparison to optical system  201 A is that on-axis propagation of each wavelength into lens  604  allows for a smaller blur disk at photodetector  605 . The smaller blur disk allows photodetector  605  to be small, facilitating its cooling and enabling high-speed photodetection with lower noise operation. 
   An advantage of optical system  201 C in comparison to optical system  201 B is that the beam diameters of the beams received by scanning mirror  602  are smaller than those received by scanning mirror  402  and all of the centers of beams λ 1  through λ N  cross at crossing point  703 , thus allowing the use of a smaller and faster scanning mirror which increases the temporal resolution of the system. 
   A further advantage of optical system  201 C in comparison to optical system  201 B is that telescope  606  magnifies the angular divergence of beams λ 1  through λ N  as received by scanning mirror  602  (as described below and with respect to  FIG. 7 ), which thereby improves the spectral resolution of optical spectrum analyzer  105 . 
   A further advantage of optical system  201 C in comparison to optical system  201 B is that the small diameter of the beams received by focusing lens  604  enables the use of focusing lens  604  and photodetector  605  that are smaller-area than lens  404  and photodetector  405 . Smaller components lead to lower cost, simpler packaging. In addition, its smaller size makes photodetector  602  easier to cool than photodetector  405  thereby improving its optical signal to noise ratio. 
   A further advantage of optical system  201 C in comparison to optical systems  201 A and  201 B is that its ability to enable fast spectra generation and the use of a single-element photodetector enables the generation of a large number of data points per spectrum, which in turn enables deconvolution of the optical transfer function of optical system  201 C from the output spectrum, which thereby results in a more accurate representation of the spectrum of the input signal. 
   A further advantage of optical system derives from the abundance of data points per spectrum. The angular dispersion of the output of any diffraction grating contains a sinusoidal dependency. The acceleration and deceleration of scanning mirror  602  during rocking motion naturally leads to a substantially sinusoidal variation in the number and distribution of the data points taken during each half-cycle of motion. The abundance of data points enables compensation for the sinusoidal variation of the output of fiber Bragg grating  601 . In addition, the motion of scanning mirror  602  can be further controlled to improve compensation further. 
     FIG. 7  depicts a schematic diagram of the salient components of telescope  606  and specifically depicts how telescope  606  manipulates the center rays of beams λ 1  and λ N . To prevent  FIG. 7  from being too cluttered, only those spectral components with the shorted and longest wavelengths (i.e., λ 1  and λ N ) are shown. Telescope  606  comprises lens  701  and lens  702 , which are coaxial. 
   Lens  701  is a thin convex lens with a focal length equal to f 1 , and lens  702  is a thin convex lens with a focal length equal to f 2 . Lens  701  and lens  702  are coaxial with optical axis  704  and are held apart at a distance of f 1 +f 2 . 
   As  FIG. 7  depicts, the center rays of beams λ 1  and λ N  enter telescope  701  diverging at the angles of θ 1-in  and θ N-in , respectively, with respect to optical axis  704 , and emerge from telescope  701  converging at an angle of θ 1-out  and θ N-out , respectively, wherein θ i-out &gt;θ i-in , for i=1 through N. The ratio of θ i-out  to θ i-in  is a function of f 1  and f 2 , and θ i-out  is equal to: 
                   θ     i   -   out       =       tan     -   1       ⁡     (         f   1     ⁢   tan   ⁢           ⁢     θ     i   -   in           f   2       )               (     Eq   .           ⁢   1     )               
and, therefore, θ i-out /θ i-in  is approximately equal to f 1 /f 2 , for small values of θ i-in  and θ i-out .
 
     FIG. 8  depicts a schematic diagram of the salient components of telescope  606  and specifically depicts how telescope  606  manipulates beam λ N . To prevent  FIG. 8  from being too cluttered, only the center and outer rays of beam λ N  are shown. 
   As  FIG. 8  depicts, beam λ N  enters telescope  606  with a beam diameter of D 1  and emerges from telescope  606  with a beam diameter of D 2 . The ratio of D 2  to D 1  is a function of f 1  and f 2 , the focal lengths of lens  701  and lens  702  respectively, and D 2  is equal to: 
   
     
       
         
           
             
               
                 
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     FIG. 9  depicts a drawing of the face of scanning mirror  602  and depicts the projection of the spectral components onto that face. To prevent  FIG. 9  from being too cluttered, only those spectral components with the shortest and longest wavelengths (i.e., λ 1  and λ N ) are shown. 
   The center ray of the projections of λ 1  and λ N  on the face of scanning mirror  602  are coincident with crossing point  703 . Their width of their projection in the direction of rotation axis  607  is equal to beam diameter D 2 . Their projection along scan axis  908  is elongated by the angle of the mirror with respect to their propagation direction. For example, the projection of beam λ N  on the face is more elliptical than the projection of λ 1  since it hits the face at a larger angle. In order to avoid clipping of the spectral components, the face of scanning mirror  602  is made slightly larger in the direction of scan axis  908  than in the direction of rotation axis  607 . 
     FIG. 10  depicts a flowchart of the salient processes performed by the illustrative embodiment of the present invention. 
   At task  1001 , source  601  radiates N wavelength-disparate optical spectral components, which are each collimated and angularly diverse. The spectral components are received by lens  701  of telescope  606 . 
   At task  1002 , telescope  606  reduces the beam diameter of each beam it has received. When telescope receives a beam, it has a diameter of D 1 , and when the beam emerges from telescope  606 , it has a diameter of D 2 , which is smaller than D 1 , as described above and with respect to  FIG. 8 . 
   At task  1003 , scanning mirror  602  rotates to direct one spectral component toward focusing lens  604 . 
   At task  1004 , focusing lens  604  receives a spectral component from scanning mirror  602  and focuses its light energy onto the photodetection region of photodetector  605 . 
   At task  1005 , photodetector  605  measures the intensity of the light that is incident on it and transmits a signal indicative of that intensity to processor  202 . 
   It is to be understood that the above-described embodiments are merely illustrative of the present invention and that many variations of the above-described embodiments can be devised by those skilled in the art without departing from the scope of the invention. For example, in this Disclosure, numerous specific details are provided in order to provide a thorough description and understanding of the illustrative embodiments of the present invention. Those skilled in the art will recognize, however, that the invention can be practiced without one or more of those details, or with other methods, materials, components, etc. 
   Furthermore, in some instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the illustrative embodiments. It is understood that the various embodiments shown in the Figures are illustrative, and are not necessarily drawn to scale. Reference throughout the disclosure to “one embodiment” or “an embodiment” or “some embodiments” means that a particular feature, structure, material, or characteristic described in connection with the embodiment(s) is included in at least one embodiment of the present invention, but not necessarily all embodiments. Consequently, the appearances of the phrase “in one embodiment,” “in an embodiment,” or “in some embodiments” in various places throughout the Disclosure are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments. It is therefore intended that such variations be included within the scope of the following claims and their equivalents.