Abstract:
A method and apparatus for characterizing an object with a wavefront from the object is disclosed. In one embodiment, the apparatus includes: a reticle positioned in a path of the wavefront, the reticle comprising two superimposed linear grating patterns; at least one light detector positioned relative to the reticle to receive a self-image diffraction pattern of the reticle produced by the wavefront; and at least one processor receiving signals from the light detector representative of the self-image diffraction pattern and deriving derivatives associated therewith, the processor using the derivatives to characterize said object.

Description:
RELATED APPLICATION INFORMATION  
       [0001]     This application is a continuation of U.S. patent application No. 10/314,906, filed Dec. 9, 2002, which is a continuation-in-part of U.S. patent application No. 10/014,037, filed Dec. 10, 2001, now U.S. Pat. No. 6,781,68 1, each of which are hereby incorporated by reference in their entireties. 
     
    
     FIELD OF THE INVENTION  
       [0002]     The present invention relates generally to systems and methods for measuring phase characteristics of electromagnetic wavefronts.  
       BACKGROUND  
       [0003]     Measuring how a wavefront deviates from being perfectly diffraction-limited has many applications. As non-limiting examples, measuring deviations, also referred to as “aberrations”, in a wavefront produced by an optical system, such as a telescope, can reveal manufacturing flaws in the system, since many optical systems, to function as best as is possible, preferably produce diffraction-limited wavefronts. By adding a component to the system that produces a wavefront that is the conjugate of the measured deviations, the system can be made to produce a more diffraction-limited wavefront and, thus, diffraction-limited performance (i.e., best possible performance).  
         [0004]     Another example of an application where knowing the aberrations in a wavefront is useful is in correcting human vision. For instance, as noted in U.S. Pat. No. 5,963,300, by measuring deviations from the perfectly spherical in reflections of laser light from the eye of a patient, aberrations of the eye can be measured and, hence, compensated for. In the &#39;300 patent, light that is reflected from a patient&#39;s eye is passed through two reticles, and the resulting moire shadow pattern is presented on a screen. An imaging system images the shadow on the screen onto a camera, with subsequent analysis being undertaken of the imaged shadow. The technique of the &#39;300 patent is based on geometrical or ray-tracing analysis, which as recognized herein requires theoretical assumptions to perform the geometrical analysis that limit the amplitude of the aberrations that can be measured as well as limit the accuracy with which the aberrations can be measured.  
         [0005]     Certain embodiments of the technology discussed below may provide solutions to one or more of these drawbacks.  
       SUMMARY OF THE INVENTION  
       [0006]     A system for determining aberrations in a coherent electromagnetic wavefront includes a reticle that is positioned in the path of the wavefront, and a detector also positioned in the path. In accordance with this aspect, the light detector is located at a diffraction pattern self-imaging plane or Talbot plane relative to the reticle.  
         [0007]     A processor may receive the output signal from the light detector and determine aberrations in the beam based thereon. The aberrations in the beam may represent aberrations in the wavefront due to the medium through which it passes, or an object from which it reflects, or the source of the wavefront itself.  
         [0008]     In a preferred, non-limiting embodiment, the processor executes logic that includes determining a phase gradient of the wavefront phase-front, and determining coefficients of polynomials based on the phase-front gradient which quantify the aberrations. The coefficients represent aberrations. Preferably, the gradient is obtained from a frequency domain transformation of the beam, wherein the gradient is the derivative of the phase of the wavefront in directions established by the reticle orientation. In a particularly preferred, non-limiting embodiment, the derivatives are determined in at least two directions, and the coefficients are determined by fitting derivatives of a set of known polynomials (such as e.g. Zernike polynomials) to the measured gradient.  
         [0009]     In another aspect, a method for determining aberrations in an object includes passing a light beam from the object through a reticle, and then determining derivatives that are associated with the light beam subsequent to the light beam passing through the reticle. Using the derivatives, a measure of aberrations in the object can be output.  
         [0010]     In yet another aspect, a computer program product includes a computer readable medium having a program of instructions stored thereon for causing a digital processing apparatus to execute method steps for determining aberrations in a wavefront. These method steps include representing a diffraction pattern produced by a wavefront, and determining directional derivatives of the representation. The derivatives are fit to known polynomials or derivatives thereof to obtain coefficients of polynomials. A wavefront characterization is provided based at least in part on the coefficients, with the wavefront characterization representing aberrations in the wavefront. A frequency domain representation of the image produced by the wavefront may also be generated. Furthermore, the directional derivatives may be determined in two directions.  
         [0011]     In still another aspect, an apparatus for detecting aberrations in an object as manifested in a wavefront includes a reticle positioned in a path of the wavefront and a light detector positioned relative to the reticle to receive the diffracted self-image that is associated with the wavefront. The self-imaging distances are at discrete distances from the reticle that are integral multiples of  
         d   =     (       n   ⁢           ⁢     p   2       λ     )       ,       
 
 where p is the period of the reticle and λ is the spectral wavelength of the wavefront. A processor receives signals from the light detector that represent the self-image. The processor derives the wavefront phase gradient associated with the wavefront and uses the coefficients of derivatives of polynomials that define the wavefront to determine the wavefront aberrations. 
 
         [0012]     Another aspect of the invention comprises a system for determining the shape of an electromagnetic wavefront. This system includes at least one reticle positioned in a path of the wavefront to be analyzed and at least one detector positioned to detect the wavefront passing through the reticle. The detector is substantially located at a diffraction pattern self-imaging plane relative to the reticle. The system further comprises at least one processor receiving an output signal from the light detector and calculating the shape of the wavefront based thereon.  
         [0013]     Still another aspect of the invention comprises a method for determining aberrations in an optical system comprising at least one optical element. In this method, a test beam is propagated along a path with the optical system in the path of the test beam so as to be illuminated by the test beam. A reticle is inserted in the path of the test beam at a location with respect to the optical system so as to receive light from the optical system. The light propagates through the reticle. Directional derivatives associated with the light are determined subsequent to passing through the reticle. Additionally, the derivatives are used to output a measure of the aberrations.  
         [0014]     Yet another aspect of the invention comprises a computer program product comprising a computer readable medium having a program of instructions stored thereon for causing a digital processing apparatus to execute method steps for determining aberrations in a wavefront. These method steps include representing at least a portion of an image produced by the wavefront and determining directional derivatives of the representation. In addition, directional derivatives are fit to known polynomials or derivatives thereof to obtain coefficients of polynomials. Furthermore, a wavefront characterization is provided based at least in part on the coefficients, the wavefront characterization representing aberrations in the wavefront.  
         [0015]     Still another aspect of the invention comprises an apparatus for characterizing an object with a wavefront from the object. The apparatus includes at least one reticle positioned in a path of the wavefront and at least one light detector positioned relative to the reticle to receive a self-image diffraction pattern of the reticle produced by the wavefront. The apparatus further includes at least one processor receiving signals from the light detector representative of the self-image diffraction pattern and deriving derivatives associated therewith. The processor uses the derivatives to characterize the object.  
         [0016]     Another aspect of the invention comprises a method for determining aberrations in a reflective or internally reflective object system. In this method, a light beam is passed from the object system through a reticle. This light beam produces a near field diffraction pattern at the Talbot plane. The method further comprises imaging the near field diffraction pattern at the Talbot plane and using the near field diffraction pattern to output a measure of aberrations in the light beam. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0017]     The details of the various preferred embodiments, both as to their structure and operation, can best be understood in reference to the accompanying drawings, in which like reference numerals refer to like parts, and in which:  
         [0018]      FIG. 1  is a block diagram of the one preferred embodiment of a system architecture for measuring and characterizing a wavefront;  
         [0019]      FIG. 1   a  is a block diagram of another implementation of the system shown in FIG. I;  
         [0020]      FIG. 2  is a flow chart of a preferred method of characterizing the wavefront by propagating the wavefront through a pattern and imaging the pattern at the self-image plane;  
         [0021]      FIGS. 3   a - 3   c  are schematic diagrams illustrating one method for converting the image produced at the self-image plane into gradient information corresponding to the wavefront at that self-image plane;  
         [0022]      FIG. 4  is a flow chart of preferred logic for data extraction in the spatial frequency domain; and  
         [0023]      FIG. 5  is a flow chart of further logic for extraction of the desired data from spatial frequency data. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0024]     Referring initially to  FIG. 1 , a wavefront sensor is shown, generally designated  10 . As illustrated in  FIG. 1 , a reference wavefront  11  can pass through (or, be reflected from) a system or element  12  (optical or otherwise). The system or element  12  can be an optics system, such as a telescope system, or it can be a human eye, or other object having properties, e.g., aberrations or curvature, sought to be measured.  
         [0025]     As shown in  FIG. 1 , a transferred wavefront  18 , i.e., the wavefront  11  after having passed through or having been reflected from the system or element  12 , passes through a reticle  20 . For example, this reticle  20  may comprise without limitation, a diffraction grating, Ronchi ruling, or grid pattern. The reticle  20  diffracts the wavefront  18 , and the diffracted wavefront self-images onto a sensor plane a self-imaging distance “d” away from the reticle  20  at which location is disposed a light sensor  22  such as but not limited to a CCD or other detector array. The self-imaging distance “d” is dependent on the spectral wavelength of the coherent wavefront and the spatial frequency of the reticle. Preferably, the CCD is within about .+−.10% or about .+−.20% of one of the self-imaging planes in the near field diffraction region.  
         [0026]     In a non-limiting, exemplary embodiment, the wavefront incident on the imaging detector can be represented by the following diffraction equation:  
         I   (       r   -&gt;     ,   z     )     =       I   0     ⁢     cos   ⁡     (       πλ   ⁢           ⁢   z       p   2       )       ⁢     cos   ⁡     [         2   ⁢   π     p     ⁢     (         r   -&gt;     ·     p   ^       -       r   ^     ·     (       z   -&gt;     ⁢           ⁢   X   ⁢       ∇   -&gt;     ⁢   w       )         )       ]             
 
         [0027]     where: λ is the wavelength of the coherent wavefront, z is the propagation distance with the associated vector {right arrow over (z)} in propagation direction, p is the period of the reticle (distance from the beginning of one grid line to the next grid line), r is the spatial dimension in the plane of the detector with its associated vector {right arrow over (r)}, {circumflex over (r)} is the corresponding unit vector, {circumflex over (p)} the unit vector representing the reticle orientation, and {right arrow over (∇)} is the directional—derivative (or, gradient) of the wavefront phase “w” that is being measured. The self-imaging distance is dependent on the spectral wavelength of the coherent wavefront and the spatial frequency of the reticle and is given by:  
       d   =     (       n   ⁢           ⁢     p   2       λ     )         
 
         [0028]     where n is the integer multiple at which distances the self-images occurs. For example, for a reticle having a grating spacing, p, of 50 micrometers (μm), this distance, d, may be between about 2.9 to 3.0 millimeters (mm) or in proximity thereto for light having a wavelength of 850 nanometers (nm). Integer multiples of this distance may be appropriate as well.  
         [0029]     As described below, this reticle  20  may comprise rulings in orthogonal x and y directions having substantially the same period p. In other embodiments, the spacing p x  and p y  of the orthogonal rulings may be different for the x and y directions. Corresponding self-image planes at distances d x  and d y  for the different directed rulings may result. Similarly, use of more than one or two reticle patterns superimposed on another having same or different periodicity are considered possible.  
         [0030]     The self-imaged reticle on the light sensor or detector  22  that is located at the self-image plane contains the desired information pertaining to the phase characteristics of the coherent wavefront. This information is extracted from the spatial signal collected at the sensor  22  and sent to a data processor (i.e., computer)  24  for processing in accordance with the disclosure below. To undertake the logic, the processor  24  accesses a preferably software-implemented module  26 , and outputs a signal representative of the wavefront (or a conjugate thereof) to an output device  28 , such as but not limited to a printer, monitor, computer, network, or other appropriate device.  
         [0031]     In various embodiments, the beam that emerges from the reticle  20  establishes a diffraction pattern. This pattern, however, substantially cannot be discerned except at the self-image planes that are spaced integer multiples of a distance “d” from the reticle  20 , as discussed above. Thus, the self image diffraction pattern can be detected by the light sensor or detector  22  that in one preferred embodiment is placed at the first (n=1) self-image plane as shown in  FIG. 1 , although it is to be understood that the sensor or detector  22  can be positioned at any of the self-image planes that are spaced from the reticle  20  by integer multiples of the distance “d”.  
         [0032]     Logic may be executed on the architecture shown in  FIG. 1  in accordance with processes and methods described and shown herein. These methods and processes include, but are not limited to, those depicted in at least some of the blocks in the flow chart of  FIG. 2  as well as the schematic representations in  FIGS. 3   a - 3   c  and flow charts in  FIGS. 4 and 5 . These and other representations of the methods and processes described herein illustrate the structure of the logic of various embodiments of the present invention which may be embodied in computer program software. Moreover, those skilled in the art will appreciate that the flow charts and description included herein illustrate the structures of logic elements, such as computer program code elements or electronic logic circuits. Manifestly, various embodiments include a machine component that renders the logic elements in a form that instructs a digital processing apparatus (that is, a computer, controller, processor, etc.) to perform a sequence of function steps corresponding to those shown.  
         [0033]     In other words, the logic may be embodied by a computer program that is executed by the processor  24  as a series of computer- or control element-executable instructions. These instructions may reside, for example, in RAM or on a hard drive or optical drive, or the instructions may be stored on magnetic tape, electronic read-only memory, or other appropriate data storage device that can be dynamically changed or updated.  
         [0034]      FIG. 1   a  shows a particular non-limiting implementation of the system  10  in which the electromagnetic energy is reflected from an object or is internally reflected from within an object. Examples of applications include microwave topography of large surfaces, wherein the electromagnetic energy is microwave and the object is the surface sought to be measured; optical topography of reflective surfaces, wherein the electromagnetic energy is laser light; retinal reflection within an eye in order to measure the aberrations of the eye, and gamma ray reflection within very small objects in order to characterize mechanical or optical properties.  
         [0035]     Accordingly, for illustration purposes  FIG. 1   a  shows that the reference wavefront  11  passes through (or, is reflected from) a transfer (optical or otherwise) system or element  15 , such as but not limited to a beamsplitter, along a propagation path  13 . The wavefront  11  is incident on an object  12  such as a human eye wherein it is either reflected externally or transmits into the object  12  where it is internally reflected. The return wavefront follows along a return path  17 , and can be reflected from or transmitted through the transfer system or element  15 . The wavefront may then pass through an optical relay system  19 . The transferred wavefront  18  passes through the reticle  20  and is processed as described above in reference to  FIG. 1 .  
         [0036]     The logic of the processor  24  can be appreciated in reference to  FIG. 2 . Commencing at block  30  in  FIG. 2 , the wavefront  18  of the beam passes through the reticle  20 . Diffraction effects cause a self-image of the reticle to appear at the self-image planes described above, including at the first plane located at a distance “d” from the reticle  20  where the detector  22  is positioned. The particular plane chosen for the position of the detector  22  preferably has sufficient resolution cells to resolve the diffraction pattern.  
         [0037]     The self-image diffraction pattern caused by the beam  18  passing through the reticle  20  is acquired at block  33  by the sensor or detector  22  and is represented by the signal output by the light detector  22 , as received by the processor  24 . Proceeding to block  34 , the signal in the spatial image domain is transformed to the spatial frequency domain. In one non-limiting embodiment, executing a Fast Fourier Transform (FFT) on the signal performs this, although it is to be understood that other mathematical transformations can be used. While  FIG. 2  indicates that the FFT is implemented in software, it is to be understood by those skilled in the art that alternatively, prior to being sent to the processor  24  an optical FFT of the return beam can be made using optics such as are known in the art.  
         [0038]     Proceeding to block  36 , regions of interest in the frequency domain may be selected based on the reticle period, illumination (i.e., wavelength), and other factors discussed further below. This selection can be a priori, and need not be undertaken during measurement. Essentially, at block  36  the regions of interest for which the gradient (directional derivative) of the wavefront is to be determined are located in the spatial frequency domain and isolated.  
         [0039]     In various preferred embodiments, the portions of the spatial frequency domain that contain the slope information and that consequently are isolated depend on the configuration of the reticle  20  and can be, e.g., represented by distributions mapped on different places on orthogonal axes in frequency space. Suitable spatial frequency domain manipulation is further illustrated in  FIG. 3 , discussed below.  
         [0040]     Proceeding to block  38 , an inverse transform is applied only to the isolated frequency space regions of the signal to render a spatial representation of the gradient of the wavefront preferably in the direction normal to the linear or segmented linear dimension of the reticle. Thus, if the reticle contains a singular set of linear grating lines, there will be two regions of the spatial frequency domain containing the desired information. If there are two sets of linear gratings superimposed in the reticle, the spatial frequency domain will contain four regions of interest. Each additional set of linear gratings provides more information pertaining to the wavefront gradient. In the limit, a circular grating reticle represents an infinite number of segmented linear gratings superimposed on each other. Preferably, the reticle contains two orthogonal superimposed linear grating patterns. In a non-limiting preferred embodiment, the wavefront gradient is determined in isolated regions in two directions. In a non-limiting example, when the object  12  is a human eye, the two directions are orthogonal to each other and lie in a plane defined by the front of and tangential to the patient&#39;s eye, with one of the directions extending from the center of the eye at a 45.degree. angle relative to the horizontal and tangent to the eye when the, patient is standing and facing directly forward.  
         [0041]     If desired, in a non-limiting embodiment filtering of random background noise can be further applied by using a “computationally-implemented” matte screen by which the spatial characteristics of the self-image are enhanced and the background reduced to very low (e.g., approximately zero) frequency components in the spatial frequency domain. This principle will be further discussed in relation to  FIG. 5 .  
         [0042]     Moving to block  40 , a set of known functions such as polynomials (and their derivatives) is defined or otherwise accessed for the two directions mentioned above. These polynomials can be used to model the wavefront. In one preferred, non-limiting embodiment, a set of 36 Zernike polynomials are used. Then, at block  42  the derivatives of the known polynomials are fit to the derivatives (i.e., gradient) determined at block  38  using, e.g., a least squares fit or other fitting algorithm.  
         [0043]     The outcome of the fitting step at block  42  is that each polynomial has an accompanying coefficient, also referred to as the “amplitude” of the polynomial. Each coefficient represents an aberration from the perfectly spherical in the return beam  18  and, hence, an aberration in the object  12 . Consequently, at block  44  a reconstructed wavefront equation can be output (to, e.g., the output device  28 ) that is the set of the known polynomials with the coefficients obtained in the fitting step at block  42 . At block  46 , the output, and in particular the coefficients in the reconstructed wavefront equation, can be used to indicate aberrations in the original wavefront and, hence, in the object  12 . Furthermore, the output can be used as a basis for implementing corrective optics for the system  12  that essentially represent the conjugate of the polynomials and/or coefficients to reduce or null out the aberrations of the object  12 .  
         [0044]     A schematic representation of an exemplary process for characterizing a wavefront gradient is depicted in  FIGS. 3   a - 3   c . A spatial image  100  of the reticle at the detector located in the self-image plane is converted by applying a Fourier transform, represented by block  102 , into spatial frequency data  104 . The result, is a spatial frequency pattern that includes four regions of interest  106   a ,  106   b ,  106   c , and  106   d  which may correspond to a set of first order components in frequency space. These four regions comprise point spread functions (PSF) displaced from the origin of the spatial frequency map in directions corresponding to ±f x  and ±f y . As shown in block  108 , one of these four regions is selected. In  FIG. 3   b , the point spread function at the (+f x0 0) location is selected and the inverse Fourier transform is performed on this spatial frequency distribution as represented by block  110 . In this manner, the gradient along the x direction of the wavefront at the self-image plane can be obtained as shown indicated by block  112 . Similarly,  FIG. 3   c  shows the point spread function at the (0, +f y0 ) position in block  114 . The inverse Fourier transform is performed on this point spread function as represented by block  116  to obtain the gradient of the wavefront in the y direction shown in block  118 .  
         [0045]      FIG. 4  shows further details of this process as discussed with respect to blocks  34 ,  36  and  38  in  FIG. 2 . At block  50  in  FIG. 4 , the self-image of the reticle is converted using software or optically from spatial data to spatial frequency data. As discussed above, this is preferably performed with a Fourier Transform algorithm and preferably a Fast Fourier Transform computer software algorithm (FFT). Moving to block  52 , from an a priori knowledge of the system  10  configuration, regions of interest in the spatial frequency domain are selected. The a priori information is provided at block  54  as follows. The reticle  20  has (a) periodic pattern(s) in known directions. The period of the reticle, the number of superimposed reticles, and the spatial orientations of the reticle relative to the wavefront path of propagation can be used to locate these regions. Gradient data in the individual regions of interest is accessed at block  56  and isolated at block  58 . This data has symmetry in the spatial frequency domain. Accordingly, in block  60  if desired only one of the symmetric data sets need be selected. Then in block  62  each set is converted back to the spatial domain. The offset of the location in frequency space of the “first order” region of interest may be used to calibrate the gradient information. This process of obtaining the wavefront phase gradient information is included in block  38  in  FIG. 2 .  
         [0046]     Without subscribing to any particular scientific theories, the above operations by which the wavefront is extracted from equation (1) can be expressed in analytical form as follows. First, the non-limiting Fourier transform on the wavefront executed at block  50  in  FIG. 4  can be expressed as:  
         F   ⁢     {     l   ⁡     (     r   ,   z     )       }     ⁢               f   2     ⁢   x     ,   y               f   4     ⁢   x     ,   y                   f   1     ⁢   x     ,   y               f   3     ⁢   x     ,   y             ⇒     F   ⁡     (     ∇   w     )           
 
         [0047]     wherein the notation f 1 x,y, f 2 x,y, f 3 x,y and f 4 x,y indicates that in certain embodiments described above such as illustrated in  FIGS. 3   a - 3   c , the relevant frequency information obtained by the Fourier transform is contained in four first order distributions or point spread functions  106   a ,  106   b ,  106   c ,  106   d  located in four sectors in frequency space. Similarly, the two spatial frequency regions f 1 x,y to f 2 x,y and f 3 x,y to f 4 x,y are the two dimensional areas in the frequency domain that contain the relevant data, and F(∇w) represents the received wavefront. The location of the point spread function may vary in different embodiments.  
         [0048]     Then, the gradient (∇w) of the wavefront is determined by performing the inverse Fourier transform (F −1 ) on equation (3) as follows: 
 
F −1 {F(∇w)}         ∇w
 
         [0049]     Next, the set of partial derivatives, or gradients, of the chosen polynomial set, e.g., Zernike polynomials (∇Z, or Z x  and Z y ) are made to best approximate the gradient of the phase front (∇w) via one or more fitting algorithms such as for example a least squares algorithm. That is.  
         ∇   w     =       ∑     i   =   1     n     ⁢       A   i     ⁢     Z   i             
 
 where, n is the number of polynomials chosen to best approximate the wavefront phase gradient, and A i  is the coefficient, or amplitude, of the polynomial Z i . The wavefront phase “w” can now be described as follows:  
       w   =       ∑     i   =   1     n     ⁢       A   i     ⁢     Z   i             
 
         [0050]     The aberrations in the wavefront can be described by the values of the coefficients A i .  
         [0051]     The flow chart of  FIG. 5  shows the process of the “computationally-implemented” matte screen discussed above in relation to  FIG. 2 . In a monochromatic system a high pass spectral filter may be used to eliminate signal noise. In one exemplary embodiment, this filter is a piece of hardware called a matte screen. In many applications a matte screen is not practical to integrate into the system. Accordingly, the matte screen can be computationally implemented on the self-images.  
         [0052]     The contrast of the image and the self-image fundamental spatial frequency are respectively received from blocks  70  and  71  and input to block  72 , where the two inputs are compared to discriminate the self-image signal. If the contrast from block  70  is lower than the fundamental spatial frequency from block  71 , the matte screen is implemented within block  34  of  FIG. 2 , with the location of the peak value in the region of interest in block  38  providing the fundamental (predominant) frequency within the self-image signal. From the peak, a finite impulse response (FIR) kernel is derived at block  74  that functions as a high-pass filter of spatial frequency data. Only frequencies higher then the designed limit will remain in the signal, and all others are eliminated at block  76  by mathematically convolving the kernel with the self-image signal.  
         [0053]     By employing methods such as described above, a mathematical representation of the wavefront and of the aberrations can be obtained. Additionally, conjugate structures, e.g., conjugate optics, can be created to substantially offset or cancel the aberrations in the wavefront. In the case, for example, where the wavefront in the eye is measured, these conjugate optics, e.g., may take the form of a corrective lens and the method of measuring the wavefront described above can be employed to determine the appropriate prescription for such a lens.  
         [0054]     Those skilled in the art will appreciate that the methods and designs described above have additional applications and that the relevant applications are not limited to those specifically recited above. Also, the present invention may be embodied in other specific forms without departing from the essential characteristics as described herein. The embodiments described above are to be considered in all respects as illustrative only and not restrictive in any manner.