Three terminal liquid crystal lens cell

A three-terminal liquid crystal (LC) lens cell includes a center-biased symmetrical quadratic electrode network that has a center electrode electrically coupled to a bias voltage source, and a first and a second network electrode circuit. The respective bias voltage terminus of each network electrode circuit is coupled to the bias voltage source, and the respective control voltage terminus of each network electrode circuit is electrically coupled to a selectively variable lens focus control power supply. Each network electrode circuit further includes respective pluralities of network electrodes electrically coupled together in series and quadratic gradient network biasing resistors respectively electrically coupled therebetween to provide a symmetric quadratic voltage pattern. Each LC cell further is typically thin-film resistor biased, having an optically transparent electrically resistive planar layer disposed in electrical contact with each electrode in the center-biased symmetrical quadratic electrode network.

RELATED APPLICATIONS AND PATENTS 
This application is related to the application entitled "Programmable 
Liquid Crystal Optical Wavefront Device", Ser. No. 08/348,403, filed 
contemporaneously herewith and incorporated herein by reference. 
BACKGROUND OF THE INVENTION 
Electro-optic devices such as liquid crystal cells are used in optical 
signal processing to control the passage of light beams through the 
processor. Optical signal processing is used in laser communication 
systems, optical recording and reading systems, and optical computing and 
associated interconnection architectures. One element commonly used in 
optical processing systems is a lens for focusing light beams on a 
particular point or in a desired pattern. 
Liquid crystal (LC) cells used in optical processors typically control the 
passage of a light beam used in the signal processing. Although 
electro-optic devices such as LC cells typically have many desirable 
characteristics, such as rapid response, to date electro-optic liquid 
crystal lenses have proved to be rather cumbersome, requiring a large 
number of LC pixels (e.g., 100 or more independently controlled pixels in 
a device having a pixel pitch of about 100 .mu.m) with an associated grid 
of control electronics. Each independently controlled pixel requires an 
associated driver to generate signals to control the pixel in coordination 
with other pixels to provide the desired lens focusing effect. In addition 
to the complexity of the control electronics, such devices often exhibit 
substantial attenuation of the light passing through the lens as a result 
of the non-ideal focusing resulting from the non-quadratic index variation 
caused by the electric fields in the EO device resulting from the 
respective discrete voltages applied to respective electrodes. 
It is an object of this invention to provide a high quality electro-optic 
lens (e.g., with a diffraction limited spot) that is compact, robust, 
readily fabricated, does not require extensive control electronics, and 
that efficiently focuses the light passing therethrough. 
SUMMARY OF THE INVENTION 
In accordance with this invention a three-terminal liquid crystal (LC) lens 
cell includes a center-biased symmetrical quadratic electrode network 
having a center electrode electrically coupled to a bias voltage terminal, 
and a first and a second network electrode circuit, each of the network 
electrode circuits having a bias voltage terminus and a control voltage 
terminus. The respective bias voltage terminus of each network electrode 
circuit is coupled to the bias voltage terminal (so as to be at the same 
potential as the center electrode), and the respective control voltage 
terminus of each network electrode circuit is electrically coupled to a 
lens focus control terminal. Each network electrode circuit further 
includes respective pluralities of network biasing electrodes electrically 
coupled together in series and respective stages of quadratic gradient 
network biasing resistors, respective stages of the biasing resistors 
being electrically coupled in series between sequentially-coupled pairs of 
biasing electrodes to provide a symmetric quadratic voltage pattern across 
the LC cell. The symmetric quadratic voltage pattern refers to an electric 
field that varies in accordance with a quadratic relationship from either 
side of the center electrode. 
Each LC cell further is typically thin-film resistor biased, having an 
optically transparent electrically resistive planar layer disposed in 
electrical contact with the center-biased symmetrical quadratic electrode 
network. The resistive planar layer has a substantially uniform 
resistivity so that a substantially linear voltage gradient exists across 
gaps between respective electrodes in the center-biased symmetrical 
quadratic electrode network. The resistive planar layer typically 
comprises a high resistance thin film material, such as a layer of n+ type 
(or alternatively, n- type) amorphous silicon. 
Spherical and elliptical LC lenses typically include two LC cells optically 
coupled together in a cascade, with the respective focal lines of the LC 
cells disposed orthogonal to one another. In an alternative embodiment, 
such lenses may comprise a single cell having two center-biased quadratic 
electrode networks, one network disposed on each plate forming the cell 
(the respective focal lines of these networks being disposed orthogonal to 
the other). 
An LC cell having a single focal line (that is, a cylindrical lens) has 
three terminals--the bias voltage terminal (coupled to the center 
electrode), the control voltage terminal coupled to each of the first and 
second network electrode circuits, and the ground terminal coupled to a 
ground electrode that is disposed on the opposite cover (or plate) of the 
LC cell, with the liquid crystal material disposed therebetween. In a cell 
having two respective center-biased symmetric quadratic biasing electrode 
networks disposed on opposite plates of the cell, the three terminals 
include the bias voltage terminal (coupled respectively to the center 
electrode on both cell plates) and respective lens focus control terminals 
for each network. The control voltage applied to the LC cell controls the 
symmetrical quadratic voltage gradient across the LC cell and thus the 
distance of the focal line from the cell.

DETAILED DESCRIPTION OF THE INVENTION 
A three terminal liquid crystal cell 100 comprises a first cover 110, and a 
second cover 112 that is coupled to first cover 110 via sidewalls 114 so 
as to form a chamber 115 (or envelope) in which liquid crystal (LC) 
material 117 is disposed (FIG. 1). In accordance with this invention, LC 
cell 100 further comprises a center-biased quadratic electrode network 130 
disposed on first cover 110 and a ground electrode 120 disposed on second 
cover 112 so as to generate (when a potential is applied to electrode 
network 130) an electric field across chamber 115 so as to control the 
orientation of molecules of liquid crystal material 117 (representative 
molecules being illustrated with the oblong shapes in chamber 115). LC 
cell 100 typically further comprises a resistive planar layer 180 on first 
cover 110 in electrical contact with center-biased quadratic electrode 
network 130. 
First and second covers 110, 112 comprise glass such as Corning 7059 or the 
like. Liquid crystal material 117 typically comprises a nematic liquid 
crystal having a positive optical anisotropy, that is, having a 
birefringence (.DELTA.n) that has a value of about 0.2 or more. As used 
herein, .DELTA.n or the positive optical anisotropy refers to the 
difference between the extraordinary index of refraction (n.sub.e) of the 
LC material and the ordinary index of refraction (n.sub.o) of the LC 
material (that is, .DELTA.n=n.sub.e -n.sub.o &gt;0). The larger the 
(.DELTA.n)T of an LC cell, the greater will be its capacity to bend light 
rays. Use of NLC material with a relatively large (e.g., &gt;0.2) .DELTA.n is 
desirable because the thickness "T" of LC cell 100 is relatively small (or 
thin), that is less than about 20 .mu.m, and typically in the range 
between about 2 .mu.m and 20 .mu.m. It is necessary in design to 
compromise between cell thickness and cell response time (the rapidity 
with which a liquid crystals in the cell respond to an applied electric 
signal) as the response time of the cell is proportional to the square of 
the cell thickness. By way of example and not limitation, nematic liquid 
crystal (NLC) material such as E63 NLC material available from Merck 
Company has a .DELTA.n of 0.227 at 589 nm). Alternatively, cell 100 may 
comprise other liquid crystal materials that show gray scale control 
behavior, such as twisted NLC and smectic `A` liquid crystal. 
Ground electrode 120 is disposed on the surface of second cover 112 facing 
chamber 115. Ground electrode 120 comprises a transparent conductive 
material such as indium tin oxide or the like, and is typically deposited 
on second cover 112 in evaporative process (a sputter process can also be 
used) to a thickness of several hundred angstroms. The portion of LC cell 
100 containing liquid crystal material 117 comprises an active lens area 
125 (illustrated in FIG. 2) of the cell (that is, light passing through 
this area of the cell is influenced by the position of the LC molecules in 
chamber 115). Ground electrode 120 is disposed across second plate 112 
such that it has an area at least the same as that of active area 125. 
Ground electrode 120 is electrically coupled to a ground terminal 127 
(FIG. 2) that provides a contact point for an external electrical 
connector to LC cell 100. 
Center-biased symmetrical quadratic electrode network 130 comprises a 
center electrode 140, a first network electrode circuit 150, and a second 
network electrode circuit 160. As used herein, "center-biased" refers to 
an electrode network in which center electrode 140 is biased at a 
potential near the LC threshold value (that is, the minimum potential that 
results in deflection of the LC molecules from their non-biased 
orientation); for example, a typical center bias voltage potential is 
about 1 Volt (e.g., the peak voltage for a 1 KHz square wave) for the NLC 
material discussed above. Further, as used herein "symmetrical quadratic" 
or the like refers to an electric field that varies in accordance with a 
quadratic relationship from either side of center-biased electrode 140 
(e.g., laterally along the plane of first cover 110); as the field is 
symmetrical, the magnitude of the electric field at the same distance on 
either side of center electrode 140 is the same (as illustrated in FIG. 2, 
the electric field is the same under first network electrode circuit 150 
and second network electrode circuit 160). 
Center electrode 140 comprises an electrically conductive material having a 
low resistance (e.g., less than 10 ohms per square, and desirably less 
than 1 ohm per square); for example, molybdenum, titanium, or chrome can 
be used to form center electrode 140. Alternatively, a transparent 
conducting material, such as indium tin oxide (ITO), can be used. Such 
transparent conducting material is typically not as conductive (having a 
resistance in the range of hundreds of ohms per square) as metals such as 
those mentioned above, but provides an advantage in that the electrode 
body does not block light passing through LC cell 100 (as do the more 
highly conductive metals mentioned above). The position of center 
electrode (in the symmetrical quadratic bias electrode network) on LC cell 
100 determines the optical axis of LC cell 100, that is, the line along 
which the focal points of the cell (the focal line) will fall. Thus the 
focal line of the cell is corresponds to the axis of the center electrode. 
Center electrode 140 is electrically coupled to a bias voltage source 142 
via a LC cell bias voltage terminal 144. 
First and second network electrode circuits 150, 160 are in essence mirror 
images of the other. For purposes of illustration and not limitation, 
first network electrode circuit 150 is described below; second network 
electrode circuit 160 comprises corresponding components arranged in a 
similar fashion. First network electrode circuit comprises a plurality of 
LC biasing electrodes 152.sub.1 -152.sub.n. For ease of illustration, five 
representative electrodes (152.sub.1 through 152.sub.5) are illustrated in 
FIG. 2; the actual number of electrodes in a network electrode circuit is 
a function of how accurately a designer wants to approximate a continuous 
quadratic function. For example, 98 electrodes disposed on a 1 mm by 1 mm 
active area has been shown to provides a very good approximation of a 
cylindrical lens. Additionally, the arrangement of the electrode network 
is selected to provided the desired lens aperture and focal depth. 
First network electrode circuit 150 further comprises a plurality of thin 
film quadratic gradient network biasing resistors 154.sub.1 -154.sub.n 
(representative resistor stages 154.sub.1 -154.sub.5 being illustrated in 
FIG. 2). Each biasing resistor stage may comprise one or more resistors 
electrically coupled together to provide the desired resistance for that 
stage in the respective network electrode circuit to provide the desired 
quadratic voltage gradient across respective biasing electrodes in network 
electrode circuit 150. By way of example and not limitation, in FIG. 2 
single resistors are illustrated for each stage. 
First network LC biasing electrodes 152 are coupled together in series, 
with one stage of network biasing resistor 154 electrically coupled 
between each set of sequentially coupled electrodes 152. For example, 
first stage biasing resistor 154.sub.1 is electrically coupled in series 
between center electrode 140 and first biasing electrode 152.sub.1, second 
stage biasing resistor 154.sub.2 is electrically coupled in series between 
first biasing electrode 152.sub.1 and second biasing electrode 152.sub.2, 
and so forth. First network electrode circuit 150 further comprises a bias 
voltage terminus 151 that is electrically coupled to bias voltage supply 
142 (via LC cell bias voltage terminal 144) so that this terminus of first 
network electrode circuit 150 is maintained at the same voltage potential 
as center electrode 140. First network electrode circuit 150 further 
comprises a second terminus 159, which is at the electrically opposite end 
of the series circuit, and which is electrically coupled to a lens focus 
control voltage source 170 via a lens focus control terminal 172. 
The respective resistance values of each stage of biasing resistors 154 are 
selected to provide the desired voltage drop across each stage (bias 
electrode and associated biasing resistor) to provide a quadratic voltage 
profile extending from center electrode 140 towards the last biasing 
electrode 154.sub.n in the network electrode circuit. Such a nominal 
quadratic relationship corresponds to: 
EQU r.sub.m =(2m-1)r.sub.1, 
wherein r.sub.m is the total resistance across stage m and r is the total 
resistance across the first stage. If desired, different design parameters 
can be used to account for optical system aberrations (such as lens 
materials that cause distortion or the like) such that the above formula 
may differ to account for such optical aberrations. Similarly, different 
nominal mathematical relations can be used if desired for a particular 
optical application (e.g., use of a cubed or squared relationship). 
The example below for a nominal quadratic arrangement for a lens assumes a 
highly conductive biasing electrode without significant resistance itself 
and that the resistance of planar resistive layer 180 is large enough that 
it can be neglected (that is, assuming ideal conditions). As a design 
matter, however, the total resistance across each stage (including the 
biasing electrode, planar resistive layer, and any other components) is 
used to size the respective biasing resistor 154 for a given stage. 
In the series coupling illustrated in FIG. 2, for example, first stage 
biasing resistor has a nominal resistance value of r ohms; second stage 
biasing resistor 154.sub.2 has a nominal resistance value of 3r ohms; 
third and subsequent stage biasing resistors have nominal values of 5r, 
7r, 9r and so forth continuing on in the same series. These nominal 
resistance values, added to the resistance of the preceding biasing 
resistors (that is, resistors between the subject biasing resistor and 
center electrode 140) generate the desired quadratic voltage profile 
across biasing electrodes 152. Because the biasing electrodes in each 
network are electrically coupled together in series, the current i through 
each stage of the network is the same. Thus the voltage drop across the 
first stage is ir, across the second stage i(r+3r)=4ir; across the third 
stage i(4r+5r)=9ir, and so forth. In the typical arrangement, the distance 
between each respective biasing electrode is uniform so that the voltage 
on respective sequentially-coupled electrodes varies as the square of the 
distance from center electrode 140 (that is, the optical axis of LC cell 
100). 
Mathematically, the quadratic relation is established by summing all of the 
ir drops across each stage. The total voltage at the nth electrode is 
expressed by the relation: 
EQU v.sub.n =ir.sub.1 +ir.sub.2 +ir.sub.3 +. . . ir.sub.m +. . . ir.sub.n 
=.SIGMA..sub.m=1.sup.n r.sub.m. 
Substituting the formula for r.sub.m provides the following relation: 
EQU v.sub.n =i.SIGMA..sub.m=1.sup.n (2m-1)r. 
Note that for n=1, 2, 3, 4 . . . , the value of v.sub.n is ir, 4ir, 9ir, 
16ir . . . respectively. Thus v.sub.n varies quadratically as v.sub.n 
=n.sup.2 ir 
Second network electrode circuit 160 comprises biasing electrodes 162.sub.1 
-162.sub.n and corresponding biasing resistors 164.sub.1 -164.sub.n. 
Second network electrode circuit first terminus 161 is electrically 
coupled to bias voltage source 142 (as illustrated in FIG. 2, such 
connection can be through center electrode 140; alternatively, a separate 
connection to bias voltage source 140 can be made. Second terminus 169 of 
second network electrode circuit 160 is similarly coupled to lens focus 
control voltage source 170 via terminal 172. Biasing resistors 164 have 
corresponding resistance values to biasing resistors 154 (e.g., biasing 
resistors 154.sub.1 and 164.sub.1 have the same resistance value, and so 
forth), thus the quadratic voltage gradient generated by second network 
electrode circuit 160 is the same as that of first network electrode 
circuit 150 and provides the symmetrical quadratic voltage gradient around 
center electrode 140. 
LC cell 100 in accordance with the present invention typically further 
comprises a thin film resistive planar layer 180 disposed in electrical 
contact with center-biased symmetrical quadratic electrode network 130. 
Resistive planar layer 180 is typically disposed on first cover 110 with 
quadratic electrode network disposed thereover. The thin film resistive 
planar layer and quadratic electrode network are thus disposed on the same 
substrate. Resistive planar layer 180 comprises a high resistivity 
material (e.g., having a resistance that is at least one or more orders of 
magnitude greater than that of the respective stage biasing resistors 
154). For example, planar resistive layer comprises amorphous silicon, 
such as n+ type silicon, having a resistance of about 16 M.OMEGA. per 
square; alternatively n- type amorphous silicon can be used. Because the 
resistance of the portion of planar layer 180 that is between two 
sequentially-coupled biasing electrodes 152 is greater than the resistance 
of the respective biasing resistor 154 through which the biasing 
electrodes are coupled in the respective network electrode circuit, 
substantially all current flow is through the biasing electrodes and 
associated stages of biasing resistors. The presence of resistive planar 
layer 180 between respective electrodes in symmetrical quadratic electrode 
network 130 results in a substantially linear voltage gradient across the 
respective gap between adjacent electrodes in active area 125 of LC cell 
100. This arrangement provides a smoother approximation of the desired 
continuous quadratic index perturbation required for lens effect, thus 
improving lens efficiency by reducing the diffracted light that is lost 
when the biasing voltages are applied across LC cell 100 only in discrete 
steps (e.g., the biasing voltages are applied to approximate the quadratic 
voltage gradient only at the points along the respective biasing 
electrodes and the center electrode). In the embodiment in which ITO 
electrodes are used in lieu of highly conductive materials such as 
titanium, the physical size of the ITO electrodes is typically so large 
that the distance between two sequentially coupled ITO bias electrodes is 
small enough to obviate the need for planar layer 180. 
By way of example and not limitation, an LC cell 100 that is adapted for 
use in an electro-optic lens is fabricated as follows: a thin film of 
substantially transparent (typically the material has optical transmission 
of 25% or greater, although device design can accomodate materials with 
lesser degrees of optical transmission) resistive material is formed at 
least over a portion of first cover 110 (FIG. 1) corresponding to LC cell 
active area 125 (FIG. 2) to form resistive planar layer 180. The n+ type 
amorphous silicon is deposited in a sputter, or alternatively, an 
evaporative, process to a thickness that is typically less than the 
thickness "T" (FIG. 1) (typically about 0.2 .mu.m to 20 .mu.m) of chamber 
115 in which the liquid crystal material is disposed; in one example, a 
cell having a liquid crystal material thickness of about 9 .mu.m, the 
amorphous silicon of resistive planar layer is about 0.13 .mu.m. 
Center-biased quadratic electrode network 130 is next formed on the surface 
of resistive planar layer 180, such as by depositing the conductive 
material (e.g., molybdenum) and etching the desired pattern so as to form 
center electrode 140 and the plurality of biasing electrodes in each 
network electrode circuit 150 and 160. From the design standpoint, it is 
desirable for optical characteristics that the biasing electrodes have a 
width (in the plane of resistive planar layer 180) that is as small as 
possible (typically limited by photolithographic fabrication techniques) 
consistent with having an electrode with acceptable electrical 
characteristics (such as resistance). In one example of an LC cell 100 
fabricated in accordance with this invention, the width of the biasing 
electrodes is about 2.5 .mu.m and the biasing electrodes are disposed on 
resistive planar layer 180 on about 12 .mu.m centers, such that there is a 
gap of about 9.5 .mu.m between respective sequential biasing electrodes. 
These biasing electrodes are readily used in an LC cell having an active 
area with a width of 1 mm or more, that is, the respective biasing 
electrodes have a length of about 1 mm. Biasing electrodes fabricated from 
Mo have a resistance in the range of about 0.25 .OMEGA./sq to 0.4 
.OMEGA./sq, which is significantly less than the resistance of resistive 
planar layer 180. The same conductive material that is used to form 
biasing electrodes is typically further used to provide connecting lines 
to the respective stage biasing resistors. 
Next, the respective stages of biasing resistors that couple respective 
biasing electrodes together in series to form the network electrode 
circuits are typically fabricated with ITO having a resistance of 450 
.OMEGA./sq. One arrangement of biasing resistors, with the biasing 
resistors disposed outside of active area 125, is illustrated in FIG. 2. 
As noted above, each stage of biasing resistor may comprise one resistor 
or multiple resistors electrically coupled together (either in series or 
parallel) (splitting resistors for a given stage can provide space-saving 
advantages on the substrate or cover plate on which the network is 
formed). Additionally, the resistors can be disposed all on one side of 
the quadratic electrode network or on alternating sides, as illustrated in 
FIG. 2. Alternative arrangements (not illustrated) include disposing the 
respective stages of biasing resistors on active area 125 (e.g., using a 
non-opaque material such as indium tin oxide), with the respective stages 
of resistors coupling adjacent biasing electrodes, thus making available 
more space on the substrate or cover plate for the active area of the 
device. 
Following fabrication of the quadratic electrode network and resistive 
planar layer on first cover 110, and the deposition of ground electrode 
120 on second cover 112, LC cell 100 is assembled to form chamber 115 with 
liquid crystal material 117 disposed between first cover 110 and second 
cover 112. Due to the thin film nature of the resistive planar layer and 
the quadratic electrode network the assembled cell is thin, typically 
having a thickness that is not greater than the center to center spacing 
of sequentially coupled bias electrodes (so that adequate optical 
resolution is provided by the lens). Commonly LC cell has a thickness in 
the range between about 0.2 .mu.m and 20 .mu.m, with a typical value of 
about 9 .mu.m. Further, the thin film nature of the bias electrodes and 
resistor networks for generating the desired bias voltage gradient (e.g., 
these components are thin film in that they are disposed on a common 
substrate, such as one plate of the LC cell) provides a device that is 
rugged, compact, and readily fabricated. 
A single LC cell 100 as described can be controlled to focus light passing 
through the cell onto a focal line, that is, the focal points generated 
across the lens form a line along the axis of the optical axis of the LC 
cell in the same plane as the optical axis of the cell. The position of 
the focal line from the cell (that is, the respective focal points) is 
dependent on the magnitude of the lens focus control voltage applied to LC 
cell 100. For a spherical electro-optic lens (that is, the lens will focus 
light to a single point), two such LC cells are typically optically 
coupled together in a cascade (that is, light passing from one LC cell is 
directed into the second LC cell) as illustrated in FIG. 3B, with a first 
LC cell 100.sub.1 and a second LC cell 100.sub.2, with the respective 
optical axis (which axis corresponds with the orientation of the center 
electrode 140 in each respective quadratic electrode network 130) of the 
respective LC cells disposed orthogonal to one another. Similarly, an 
elliptical electro-optic lens can be provided by applying different 
control voltages to the respective lens focus control terminals of the 
respective cells, such that the focal lines of the two lenses in the 
cascade are not disposed the same distance from the lens. 
In operation, LC cell 100 in accordance with this invention need have only 
three terminals for coupling to components external to the cell: the 
ground connection for ground electrode 120 on second cover 112; the bias 
voltage connection for center electrode 140; and the lens focus control 
voltage connection for applying the drive voltage to the respective second 
terminus of each the first and second network electrode circuits. 
Maintenance of the biasing voltage on center electrode ensures that the 
range of the voltage gradient generated by the symmetrical quadratic 
electrode network is of a polarity and magnitude to be able to cause 
deflection of the molecules of liquid crystal material. Lens focus control 
voltage is typically a constant amplitude AC signal (e.g., a 1 KHz square 
wave); the magnitude of the voltage potential applied determines the 
quadratic voltage gradient generated across LC cell 100 and hence the 
distance of the focal point from the cell. 
In a further alternative embodiment in accordance with this invention, a 
lens can be formed in a single LC cell 100. Such a cell (as illustrated in 
FIG. 3A) comprises one center-biased symmetric electrode network disposed 
on one cover of the cell and a second, independent, center-biased 
symmetric electrode network disposed on the opposing cover of the cell, 
with the respective optical axis of each symmetric electrode network (the 
optical axis corresponding to the orientation of center electrode 140 in 
each respective quadratic electrode network 130) being disposed orthogonal 
to the other (just as the respective optical axis of each cell in a 
cascade of cells is disposed orthogonal to the optical axis of the other 
cell in the cascade). In this embodiment, each respective center biased 
symmetric electrode network is the same as described above; in this 
embodiment, however, there is no ground electrode, but rather the 
threshold-potential biased center electrode on the opposing face of the 
cell serves as the reference potential for the liquid crystals. This cell 
similarly comprises three terminals: a bias voltage terminal coupled to 
the respective center electrodes of the electrode networks on the opposing 
faces of the cell, and a respective lens focus control voltage terminal 
for each of the center-biased electrode networks, one for each face of the 
cell. 
While only certain features of the invention have been illustrated and 
described herein, many modifications and changes will occur to those 
skilled in the art. It is, therefore, to be understood that the appended 
claims are intended to cover all such modifications and changes as fall 
within the true spirit of the invention.