RING LASER GYROSCOPE

Abstract

A ring laser gyroscope includes an optical block for generating laser beams that counter-propagate in a closed-loop type optical path, a dither mechanism for applying dither vibration for mitigating a lock-in phenomenon to the optical block, and a dither controller for controlling the dither vibration. The dither controller imparts randomness to the frequency of the angular velocity of the dither vibration.

Claims

1. A ring laser gyroscope comprising: an optical block including a closed-loop type optical path and configured to generate laser beams that counter-propagate in the closed-loop type optical path; a dither mechanism configured to apply dither vibration for mitigating a lock-in phenomenon to the optical block; and a dither controller configured to control the dither vibration, wherein the dither controller imparts randomness to a frequency of an angular velocity of the dither vibration.

2. The ring laser gyroscope according to claim 1, wherein the dither controller performs feedback control of the dither vibration on the basis of a displacement of the dither mechanism so that the dither mechanism vibrates at a natural frequency of the dither mechanism, and applies a random phase to a phase of a signal representing the dither vibration to impart randomness to the frequency of the angular velocity of the dither vibration.

3. The ring laser gyroscope according to claim 1, wherein a fluctuation range of the frequency to which randomness has been imparted does not exceed 2% of a natural frequency of the dither mechanism.

4. The ring laser gyroscope according to claim 2, wherein a fluctuation range of the frequency to which randomness has been imparted does not exceed 2% of a natural frequency of the dither mechanism.

5. The ring laser gyroscope according to claim 1, wherein the dither controller imparts randomness to the frequency of the angular velocity of the dither vibration at a random time interval.

6. The ring laser gyroscope according to claim 2, wherein the dither controller imparts randomness to the frequency of the angular velocity of the dither vibration at a random time interval.

7. The ring laser gyroscope according to claim 3, wherein the dither controller imparts randomness to the frequency of the angular velocity of the dither vibration at a random time interval.

8. The ring laser gyroscope according to claim 4, wherein the dither controller imparts randomness to the frequency of the angular velocity of the dither vibration at a random time interval.

9. The ring laser gyroscope according to claim 1, wherein the dither controller imparts randomness to an amplitude of the angular velocity of the dither vibration.

10. The ring laser gyroscope according to claim 2, wherein the dither controller imparts randomness to an amplitude of the angular velocity of the dither vibration.

11. The ring laser gyroscope according to claim 3, wherein the dither controller imparts randomness to an amplitude of the angular velocity of the dither vibration.

12. The ring laser gyroscope according to claim 4, wherein the dither controller imparts randomness to an amplitude of the angular velocity of the dither vibration.

13. The ring laser gyroscope according to claim 5, wherein the dither controller imparts randomness to an amplitude of the angular velocity of the dither vibration.

14. The ring laser gyroscope according to claim 6, wherein the dither controller imparts randomness to an amplitude of the angular velocity of the dither vibration.

15. The ring laser gyroscope according to claim 7, wherein the dither controller imparts randomness to an amplitude of the angular velocity of the dither vibration.

16. The ring laser gyroscope according to claim 8, wherein the dither controller imparts randomness to an amplitude of the angular velocity of the dither vibration.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The subject matter, which is regarded as the invention, is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The present invention itself, and manner in which it may be made or used, if any, may be better understood after a review of the following description in connection with the accompanying drawings in which:

[0022] FIG. 1 shows a configuration of a ring laser gyroscope of related art;

[0023] FIG. 2 shows a configuration of a dither mechanism;

[0024] FIG. 3 is a block diagram of a feedback system;

[0025] FIG. 4 shows an example of a primary phase shifter; and

[0026] FIG. 5 shows a configuration of a ring laser gyroscope of an embodiment.

LIST OF REFERENCE NUMERALS

[0027] With regard to reference numerals used, the following numbering is used throughout the drawings. [0028] 11: optical block [0029] 12: optical path [0030] 13: mirror [0031] 14: mirror [0032] 16: anode [0033] 18: cathode [0034] 19: opening portion [0035] 21: photosensor [0036] 22: prism [0037] 23: laser beam intensity measuring instrument [0038] 32: side wall portion [0039] 33: linking portion [0040] 34: shaft portion [0041] 34a: mounting portion [0042] 34b: hole [0043] 35: piezoelectric element [0044] 41: detection processor [0045] 42: bias signal eliminator [0046] 43: dither controller [0047] 100: ring laser gyroscope [0048] 200: dither mechanism [0049] 300: dither controller [0050] 302: A/D converter [0051] 304: amplitude control circuit [0052] 306: first random noise generator [0053] 308: phase shifter [0054] 310: second random noise generator [0055] 312: multiplier [0056] 314: D/A converter [0057] 316: amplification circuit [0058] 800: Feedback system [0059] 810: vibration system [0060] 820: sensor [0061] 830: primary phase shifter [0062] 900: ring laser gyroscope [0063] 910: optical mechanism [0064] 920: signal processor

DETAILED DESCRIPTION

[0065] Before describing an embodiment, a theoretical outline of the present invention will be described.

[0066] The lock-in phenomenon of a ring laser gyroscope originates from a synchronization phenomenon of counter-propagating laser beams. The time change rate of the phase difference ϕ(t) between the counter-propagating laser beams is represented by Equation (1) as Adler Equation. Here, t represents the time, Ω represents an input angular velocity, and Ω.sub.L represents an upper limit value (or the absolute value of a lower limit value) of the lock-in angular velocity range.

[00001]$\begin{array}{cc}\frac{d\varphi \left(t\right)}{\mathrm{dt}}=\Omega -{\Omega }_L\sin \left(\varphi \left(t\right)\right)& \left(1\right)\end{array}$

[0067] Adding, to Equation (1), for example, a sine wave representing the angular velocity of the dither vibration for mitigating the lock-in phenomenon yields Equation (2). Here, Ω.sub.d represents the amplitude of the angular velocity of dither vibration, and ω.sub.d represents the angular frequency of the angular velocity of dither vibration. The angular velocity of dither vibration is not limited to a sine wave, and it may be represented by a triangular wave, for example.

[00002]$\begin{array}{cc}\frac{d\varphi \left(t\right)}{\mathrm{dt}}=\Omega +{\Omega }_d\sin \left({\omega }_{d}t\right)-{\Omega }_L\sin \left(\varphi \left(t\right)\right)& \left(2\right)\end{array}$

[0068] When ω.sub.d is sufficiently large (typically several hundreds of radians per second), Equation (2) is approximately rewritten into Equation (3). Here, J.sub.0(x) represents the 0-th order Bessel function of the first kind, and ϕ.sub.0 represents an initial phase.

[00003]$\begin{array}{cc}\frac{d\varphi \left(t\right)}{\mathrm{dt}}=\Omega +{\Omega }_d\sin \left({\omega }_{d}t\right)-J_0\left({\Omega }_d/{\omega }_d\right){\Omega }_L\sin \left(\Omega t+{\varphi }_0\right)& \left(3\right)\end{array}$

[0069] According to the related art, random noise is added to the amplitude of the angular velocity of dither vibration in order to reduce the accumulation of degradation in accuracy of a detected angular velocity caused by the lock-in phenomenon that cannot be prevented even by the dither vibration. This implies Equation (4). Here, ξ(t) represents random noise. In this specification, the term “random” or “randomness” is used to mean having non-regularity or having non-periodicity, and it does not necessarily require having non-settlement or having non-reproducibility.

[00004]$\begin{array}{cc}\frac{d\varphi \left(t\right)}{\mathrm{dt}}=\Omega +\left({\Omega }_d+\xi \left(t\right)\right)\sin \left({\omega }_{d}t\right)-J_0\left({\Omega }_d/{\omega }_d\right){\Omega }_L\sin \left(\Omega t+{\varphi }_0\right)& \left(4\right)\end{array}$

[0070] According to the related art, even when random noise is added to the amplitude of the angular velocity of dither vibration, it cannot be sufficiently suppressed that the sampling for the digital processing of the signal processor is synchronized with occurrence of the lock-in phenomenon because ω.sub.d is constant. Therefore, in the present invention, random noise is added to the frequency of the angular velocity of dither vibration in order to reduce the accumulation of deterioration in accuracy of the detected angular velocity caused by the lock-in phenomenon that cannot be prevented even by the dither vibration. This implies Equation (5).

[00005]$\begin{array}{cc}\frac{d\varphi \left(t\right)}{\mathrm{dt}}=\Omega +{\Omega }_d\sin \left(\left({\omega }_d+\xi \left(t\right)\right)t\right)-J_0\left({\Omega }_d/{\omega }_d\right){\Omega }_L\sin \left(\Omega t+{\varphi }_0\right)& \left(5\right)\end{array}$

[0071] An example of a mechanism for applying random noise to ω.sub.d will be described below. Here, for the sake of simplicity, the description based on an analog circuit will be made, but the mechanism for applying random noise to ω.sub.d may be constructed by a digital circuit. A motion equation of rotational motion of an optical block caused by a dither mechanism for applying a sinusoidal torque u=M sin(ω.sub.dt) to the optical block is expressed by Equation (6). Here, θ.sub.d represents a displacement angle of the optical block caused by dither vibration, J represents the moment of inertia of the optical block, C represents a viscous damping coefficient, K represents a spring constant, and M represents the amplitude of the sinusoidal torque. θ.sub.d is a function of time t.

[00006]$\begin{array}{cc}J\frac{d^2{\theta }_d}{{\mathrm{dt}}^2}+C\frac{d{\theta }_d}{\mathrm{dt}}+K{\theta }_d=M\sin {\omega }_{d}t& \left(6\right)\end{array}$

[0072] Since the solution of a homogeneous equation when the right hand side of Equation (6) is equal to 0, that is, the solution of the damped free vibration decays with time, only a steady vibration which is a particular solution for a sinusoidal torque remains after a sufficient time has elapsed. Therefore, only the steady vibration will be investigated. Assuming that the particular solution is given by Equation (7), the relationship between the angular amplitude O and the phase angle ϕ will be determined.

θ.sub.d=θ sin(ω.sub.dt−ϕ)  (7)

[0073] Substituting Equation (7) into Equation (6) yields Equations (8) and (9). Here, η=ω.sub.d/ω.sub.n represents a frequency ratio, ζ=C/C.sub.C represents a damping ratio, ω.sub.n=√(K/J) represents an undamped natural angular frequency, C.sub.C=2√(JK)=2Jω.sub.n represents a critical damping coefficient, and Θ.sub.0=M/K.

[00007]$\begin{array}{cc}\ominus =\frac{{\ominus }_0}{\sqrt{{\left(1-{\eta }^2\right)}^2+4{\zeta }^2{\eta }^2}}& \left(8\right)\end{array}$$\begin{array}{cc}\tan \varphi =\frac{2\zeta \eta }{1-{\eta }^2}& \left(9\right)\end{array}$

[0074] When a vibration system including the optical block and the dither mechanism resonates, the frequency ratio η.sub.r that gives the maximum response magnification is called a resonance point, and given by Equation (10). The phase angle at the resonance point is given by Equation (11). Note that, since the viscous damping coefficient C of the actual optical block is sufficiently small, ϕ.sub.r is approximately 90 degrees.

[00008]$\begin{array}{cc}{\eta }_r=\sqrt{1-2{\zeta }^2}& \left(10\right)\end{array}$$\begin{array}{cc}{\varphi }_r={\tan }^{-1}\left(\frac{\sqrt{1-2{\zeta }^2}}{\zeta }\right)& \left(11\right)\end{array}$

[0075] As described above, by applying a sinusoidal torque u to the optical block at an angular frequency of ω.sub.d=η.sub.rω.sub.n, the vibration system resonates and the displacement angle θ.sub.d with a phase delay corresponding ϕ.sub.r in Equation (11) is detected. Therefore, when conceiving a feedback system 800 for performing feedback control of the sinusoidal torque u on the basis of the displacement angle θ.sub.d, the feedback system 800 can include the vibration system 810 described above, a sensor 820 for detecting the displacement angle θ.sub.d, and a primary phase shifter 830, and the optical block is given the sinusoidal torque u generated by driving the dither mechanism with a signal that the primary phase shifter 830 obtains by advancing, by only ϕ.sub.r, the phase of a signal representing the displacement angle θ.sub.d detected by the sensor 820, thereby indeed achieving a vibration system that can keep on vibrating at a resonance frequency. A block diagram of this feedback system 800 is shown in FIG. 3.

[0076] A transfer function of the vibration system 810, that is, a transfer function of Equation (6) is given by Equation (12). Since the numerator of Equation (12) is merely a gain, the following description will consider Equation (13) which is a transfer function of a general second-order delay system.

[00009]$\begin{array}{cc}G\left(s\right)=\frac{1/J}{s^2+2\zeta {\omega }_{n}s+{\omega }_n^2}& \left(12\right)\end{array}$$\begin{array}{cc}G\left(s\right)=\frac{{\omega }_n^2}{s^2+2\zeta {\omega }_{n}s+{\omega }_n^2}& \left(13\right)\end{array}$

[0077] A closed-loop transfer function W.sub.c of the feedback system 800 shown in FIG. 3 is expressed by Equation (14). L represents the gain of the sensor 820. Here, τ represents the time constant of the primary phase shifter 830, and particularly τ=CR when the primary phase shifter 830 has a configuration shown in FIG. 4 as an example.

[00010]$\begin{array}{cc}{W}_c=\frac{\frac{{\omega }_n^2}{s^2+2\zeta {\omega }_{n}s+{\omega }_n^2}}{1+\frac{{\omega }_n^2}{s^2+2\zeta {\omega }_{n}s+{\omega }_n^2}.Math.L.Math.\frac{\tau s-1}{\tau s+1}}& \left(14\right)\end{array}$

[0078] The second term of the denominator of W.sub.c is an open-loop transfer function W.sub.0, and it is known that the feedback system exhibits a resonance characteristic in a band where the gain |W.sub.0| (see Equation (15)) of the open-loop transfer function W.sub.0 is approximately equal to 1.

[00011]$\begin{array}{cc}.Math.W_0.Math.=.Math.\frac{{\omega }_n^2}{s^2+2\zeta {\omega }_{n}s+{\omega }_n^2}.Math.L.Math.\frac{\tau s-1}{\tau s+1}.Math.& \left(15\right)\end{array}$

[0079] W.sub.c is developed into Equation (16).

[00012]$\begin{array}{cc}{W}_c=\frac{{\omega }_n^{2}s+\frac{{\omega }_n^2}{\tau }}{s^3+\frac{1+2\zeta \tau {\omega }_n}{\tau }{s}^2+\frac{\tau {\omega }_n^2+L\tau {\omega }_n^2+2\zeta {\omega }_n}{\tau }s+\frac{{\omega }_n^2-L{\omega }_n^2}{\tau }}& \left(16\right)\end{array}$

[0080] It is assumed that W.sub.c can be represented with Equation (17) by decomposing Equation (16) into partial fractions.

[00013]$\begin{array}{cc}{W}_c=\frac{\mathrm{as}+b{\omega }_d}{s^2+{\omega }_d^2}-\frac{c}{s+\alpha }& \left(17\right)\end{array}$

[0081] The vibration system is designed such that the vibration is magnified or sustained, that is, the system is unstable or reaches a stability limit. Therefore, when sustained vibration is obtained at the stability limit, then c=a. Therefore, by comparing Equation (16) with Equation (17), Equations (18) to (23) are yielded. However, ω.sub.d>0, L<0, τ>0.

[00014]$\begin{array}{cc}a=\frac{2\zeta {\tau }^2{\omega }_n^3}{4{\zeta }^2{\tau }^2{\omega }_n^2+{\tau }^2{\omega }_d^2+4\zeta \tau {\omega }_n+1}& \left(18\right)\end{array}$$\begin{array}{cc}b=\frac{{\omega }_n^2\left({\tau }^2{\omega }_d^2+2\zeta \tau {\omega }_n+1\right)}{{\omega }_d\left(4{\zeta }^2{\tau }^2{\omega }_n^2+{\tau }^2{\omega }_d^2+4\mathrm{\zeta \tau }{\omega }_n+1\right)}& \left(19\right)\end{array}$$\begin{array}{cc}\alpha =\frac{2{\mathrm{\zeta \tau \omega }}_n+1}{\tau }& \left(20\right)\end{array}$$\begin{array}{cc}{\omega }_d=\sqrt{\frac{{\omega }_n\left(\tau {\omega }_n+\zeta \right)}{\tau \left(\zeta \tau {\omega }_n+1\right)}}& \left(21\right)\end{array}$$\begin{array}{cc}L=-\frac{-{\mathrm{\tau \omega }}_d^2+\tau {\omega }_n^2+2{\mathrm{\zeta \omega }}_n}{{\mathrm{\tau \omega }}_n^2}& \left(22\right)\end{array}$$\begin{array}{cc}\tau =\frac{{\omega }_n^2-{\omega }_d^2-L{\omega }_n^2}{2{\mathrm{\zeta \omega }}_d^2{\omega }_n}& \left(23\right)\end{array}$

[0082] Equations (22) and (23) yield Equation (24). As is well known, the gain of the primary phase shifter 830 is equal to 1 regardless of the frequency. Further, as is well known, the gain of the transfer function of the second-order delay system is given by Equation (25). Therefore, when the frequency of the second-order delay system is equal to ω.sub.d (ω=ω.sub.d), the gain |W.sub.0| of the open-loop transfer function W.sub.0 is equal to 1 and the feedback system 800 exhibits the resonance characteristic.

[00015]$\begin{array}{cc}L=-\sqrt{{\left(1-{\eta }^2\right)}^2+4{\zeta }^2{\eta }^2}& \left(24\right)\end{array}$$\begin{array}{cc}.Math.G\left(j\omega \right).Math.=\frac{1}{\sqrt{{\left(1-{\left(\frac{\omega }{{\omega }_n}\right)}^2\right)}^2+4{{\zeta }^2\left(\frac{\omega }{{\omega }_n}\right)}^2}}& \left(25\right)\end{array}$

[0083] Furthermore, Equations (24) and (8) yield Equation (26). Therefore, by performing control for keeping the angular amplitude of the optical block constant, L and ω.sub.d are settled to constant values. At this time, by randomly changing ti at a speed which is sufficiently lower than a response speed of the control, it is possible to randomly change ω.sub.d near the resonance point. In other words, random noise can be given to ω.sub.d by randomly changing the amount of phase shift by the phase shifter.

[00016]$\begin{array}{cc}L=-\frac{{\ominus }_0}{\ominus }& \left(26\right)\end{array}$

[0084] From the viewpoint of efficient driving of the dither mechanism, it is preferable that the upper limit of the phase shift amount does not exceed, for example, 1% of the natural frequency ω.sub.d of the dither mechanism. In other words, it is preferable that the fluctuation range of the frequency to which randomness has been imparted does not exceed 2% of the natural frequency of the dither mechanism. The lower limit of the phase shift amount can be determined according to, for example, the degree of change in the natural frequency of the dither mechanism caused by change in environmental temperature or aged deterioration, and is, for example, a shift amount that causes a change of 0.25 Hz in the natural frequency ω.sub.d of the dither mechanism.

[0085] A ring laser gyroscope 100 according to an embodiment will be described with reference to FIG. 5. The ring laser gyroscope 100 has the same configuration as the ring laser gyroscope 900 except that it includes a dither controller 300 instead of the dither controller 43 of the ring laser gyroscope 900. Therefore, duplicative description of the same components is omitted by stating here that the description of the ring laser gyroscope 900 except for the dither controller 43 is incorporated. In FIG. 5, illustration of components other than the dither controller 43 included in the signal processor 920 is omitted.

[0086] The dither controller 300 includes an analog-to-digital (A/D) converter 302, an amplitude control circuit 304, a first random noise generator 306, a phase shifter 308, and a second random noise generator 310, a multiplier 312, a digital-to-analog (D/A) converter 314, and an amplification circuit 316.

[0087] The A/D converter 302 converts a dither pickoff signal to a digital signal. The amplitude control circuit 304 compares a reference amplitude with an amplitude of the digital dither pick-off signal obtained, for example, by passing the digital dither pick-off signal through a low-pass filter and a square root operator, and performs proportional-integral-differential control (PID control) on the amplitude of the digital dither pickoff signal so that the amplitude thereof is constant. As a method of imparting randomness to the amplitude of the digital dither pickoff signal may be adopted, for example, a method of changing the reference amplitude on the basis of a pseudo-random value generated by the first random noise generator 306, or a method of adding an amplitude based on a pseudo-random value generated by the first random noise generator 306 to the amplitude of the digital pickoff signal obtained by the PID control.

[0088] The phase shifter 308 is, for example, a voltage-controlled digital phase shifter, and controls the phase of the digital dither pickoff signal such that stable self-vibration occurs as described above. As a method of imparting randomness to the phase of the digital dither pickoff signal may be adopted, for example, a method of changing the phase amount on the basis of a pseudo-random value generated by the second random noise generator 310.

[0089] The multiplier 312 multiplies the output of the amplitude control circuit 304 and the output of phase shifter 308. The D/A converter 314 converts the output of the multiplier 312 into an analog signal. The amplification circuit 316 performs power amplification on the output of the D/A converter 314. The power-amplified output of the D/A converter 314 is supplied to a piezoelectric element for generating dither vibration. Note that a pulse width modulation (PWM) converter may be used instead of the D/A converter 314.

[0090] The input of the A/D converter 302 is not limited to the dither pickoff signal, and may be, for example, a signal obtained by passing a signal representing the phase difference ϕ(t) between laser beams through a high-pass filter.

[0091] A configuration in which the dither controller 300 does not include the first random noise generator 306 is also allowed, without being limited to the above-described embodiment.

[0092] Random noise may be applied to the frequency of the angular velocity of dither vibration all the time, but only when the intensity of the output signal of the amplitude control circuit 304 falls below a predetermined threshold value, random noise may be applied to the frequency of the angular velocity of dither vibration. Random noise may be applied to the amplitude of the angular velocity of dither vibration all the time, but only when the intensity of the output signal of the amplitude control circuit 304 falls below a predetermined threshold value, random noise may be applied to the amplitude of the angular velocity of dither vibration.

[0093] The second random noise generator 310 may generate pseudo-random numeral values at regular time intervals, or may generate pseudo-random numeral values at random time intervals.

[0094] Whether randomness is imparted to the frequency of the angular velocity of dither vibration can be easily found, for example, by performing fast Fourier transform (FFT) analysis on the sound of dither vibration.

[0095] <Addendum>

[0096] While the invention has been described with reference to exemplary embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular system, device or component thereof to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiments disclosed for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.

[0097] Moreover, the use of the terms “first”, “second”, “i-th”, etc., if any, do not denote any order or importance, but rather the terms “first”, “second”, “i-th”, etc. are used to distinguish one element from another. The term “first” does not necessarily mean “coming before all others in order”. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention in any way. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprise”, “comprises”, and/or “comprising,” when used in this specification and/or the appended claims, specify the presence of stated features, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and/or groups thereof. The same goes for “include”, “includes”, and/or “including”. The term “and/or”, if any, includes any and all combinations of one or more of the associated listed items. In the claims and the specification, unless otherwise noted, “connect”, “join”, “couple”, “interlock”, or synonyms therefor and all the word forms thereof, if any, do not necessarily deny the presence of one or more intermediate elements between two elements, for instance, two elements “connected” or “joined” to each other or “interlocked” with each other. Connection between elements, if required, may be physical connection, electrical connection, or a combination thereof. In the claims and the specification, the term “any”, if any, is to be understood as a term synonymous with a universal quantification V unless otherwise specified. For example, the expression “for any X” has the same meaning as “for all X” or “for each X”.

[0098] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art to which the invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and the present disclosure and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0099] In describing the invention, it will be understood that a number of techniques and steps are disclosed. Each of these has individual benefit and each can also be used in conjunction with one or more, or in some cases all, of the other disclosed techniques. Accordingly, for the sake of clarity, this description will refrain from repeating every possible combination of the individual techniques or steps in an unnecessary fashion. Nevertheless, the specification and claims should be read with the understanding that such combinations are entirely within the scope of the invention and the claims.

[0100] The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below, if any, are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed.

[0101] The foregoing description of the embodiments of the invention has been presented for the purpose of illustration and description. It is not intended to be exhaustive and to limit the invention to the precise form disclosed. Modifications or variations are possible in light of the above teaching. The embodiments were chosen and described to provide the best illustration of the principles of the invention and its practical application, and to enable one of ordinary skill in the art to utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. All such modifications and variations are within the scope of the invention as determined by the appended claims when interpreted in accordance with the breadth to which they are fairly, legally, and equitably entitled.