Photonic monopulse comparator

Monopulse radar, also known as simultaneous lobe comparison, provides the direction of arriving radiation (e.g., radio frequency (RF) or other electromagnetic signals) by comparing the signals produced by monopulse elements in slightly different directions (“squinted” subarrays or signals). Monopulse radar may be useful for determining angle of arrival in one or more dimensions, but electronic or fiber optic components may provide challenges with respect to their performance, loss, or relative size.

In one aspect, embodiments of the inventive concepts disclosed herein are directed to a photonic monopulse comparator for determining an angle of arrival (e.g., azimuthal angle, elevational angle) of an inbound signal. The photonic monopulse comparator includes an array of squinted monopulse elements (e.g., a one-dimensional array of two elements, a two-dimensional array of four elements). Each monopulse element includes an antenna element for receiving the inbound signal; the squinted elements will each receive the inbound signal at a squinted, or slightly different, angle or direction. Each monopulse element includes receiver circuitry capable of producing an RF signal in response to the receiving of the inbound signal, each generated signal having a squinted RF voltage. The photonic monopulse comparator includes a continuous-wave or pulsed laser or like photonic source capable of generating an optical signal. The optical signal may be routed through integrated waveguides or optical fibers and through one or more cascading optical phase modulators, each optical phase modulator connected to a monopulse element and capable of modulating the optical signal according to the RF signal received therefrom. The photonic monopulse comparator includes an array of optical hybrid couplers capable of receiving the modulated optical signals and generating balanced outputs, e.g., 2×2 hybrid couplers capable of receiving an in-phase modulated optical signal and a quadrature modulated optical signal. The modulated optical output of the hybrid couplers is fed to an array of balanced photodiode pairs, each pair of photodiodes capable of detecting a hybrid output signal and generating an RF output signal corresponding to the output signal and having an output voltage. Each RF output may be digitized by analog-digital converters (ADC), the resulting digital output signal having a voltage proportional to either a sum or a difference (e.g., azimuthal or elevational) from which the angle of arrival can be calculated.

In a further aspect, embodiments of the inventive concepts disclosed herein are directed to an integrated photonics monopulse comparator. The integrated photonics monopulse comparator includes an array of squinted monopulse elements (e.g., a one-dimensional array of two elements, a two-dimensional array of four elements). Each monopulse element includes an antenna element for receiving the inbound signal; the antenna elements will each receive the inbound signal at a squinted, or slightly different, angle or direction. Each monopulse element includes receiver circuitry capable of producing an RF signal in response to the receiving of the inbound signal, each generated signal having a squinted RF voltage. The photonic monopulse comparator includes a continuous-wave or pulsed laser or like photonic source capable of generating an optical signal, e.g., a wavelength division multiplexed (WDM) optical signal comprising component optical signals, each component optical signal having a discrete wavelength. The WDM optical signal is fed through a linear array of wavelength demultiplexers (capable of splitting the WDM optical signal into its component signals) and multiplexers (capable of combining the component signals into the WDM optical signal). The linear array of multiplexers and demultiplexers is interspersed with cascaded optical phase modulators, each optical phase modulator connected to a monopulse element and capable of modulating one or more component optical signals according to the RF voltage of the input signal produced by the corresponding monopulse element. The optical phase modulators may be cascaded in that, for example, a component optical signal passing through a first and then a second phase modulator will be modulated according to both signals, or to the sum or difference of their corresponding voltages. The integrated photonics monopulse comparator includes an array of paired photodiodes at the end of the linear array opposite the laser signal source. Each pair of photodiodes receives two component optical signals of shared wavelength, the RF output signal generated therefrom having an output voltage based on the sum or difference of the modulated voltages of the component optical signals and proportional to a sum or difference of the squinted signals produced by the monopulse elements (e.g., a sum, azimuthal difference, or elevational difference), from which an angle of arrival (e.g., azimuthal angle, elevational angle) may be calculated.

Implementations of the inventive concepts disclosed herein may be better understood when consideration is given to the following detailed description thereof. Such description makes reference to the included drawings, which are not necessarily to scale, and in which some features may be exaggerated and some features may be omitted or may be represented schematically in the interest of clarity. Like reference numerals in the drawings may represent and refer to the same or similar element, feature, or function. In the drawings:

FIG. 1 is a combination view of an embodiment of a one-dimensional squinted monopulse array; and

FIG. 2 is a graphic illustration of an off-axis angle and its components of the squinted monopulse arrays of FIG. 1 ;

FIG. 3 is an isometric view of an embodiment of a two-dimensional squinted monopulse array;

FIG. 4 is a diagrammatic illustration of a photonic monopulse comparator incorporating the squinted monopulse array of FIG. 3 ;

FIGS. 5A and 5B illustrate cascading photonics operations according to the inventive concepts disclosed herein;

and FIG. 6 is a diagrammatic illustration of an integrated photonics monopulse comparator according to the inventive concepts disclosed herein.

Before explaining at least one embodiment of the inventive concepts disclosed herein in detail, it is to be understood that the inventive concepts are not limited in their application to the details of construction and the arrangement of the components or steps or methodologies set forth in the following description or illustrated in the drawings. In the following detailed description of embodiments of the instant inventive concepts, numerous specific details are set forth in order to provide a more thorough understanding of the inventive concepts. However, it will be apparent to one of ordinary skill in the art having the benefit of the instant disclosure that the inventive concepts disclosed herein may be practiced without these specific details. In other instances, well-known features may not be described in detail to avoid unnecessarily complicating the instant disclosure. The inventive concepts disclosed herein are capable of other embodiments or of being practiced or carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein is for the purpose of description and should not be regarded as limiting.

As used herein a letter following a reference numeral is intended to reference an embodiment of the feature or element that may be similar, but not necessarily identical, to a previously described element or feature bearing the same reference numeral (e.g., 1 , 1 a , 1 b ). Such shorthand notations are used for purposes of convenience only, and should not be construed to limit the inventive concepts disclosed herein in any way unless expressly stated to the contrary.

Further, unless expressly stated to the contrary, “or” refers to an inclusive or and not to an exclusive or. For example, a condition A or B is satisfied by anyone of the following: A is true (or present) and B is false (or not present), A is false (or not present) and B is true (or present), and both A and B are true (or present).

In addition, use of the “a” or “an” are employed to describe elements and components of embodiments of the instant inventive concepts. This is done merely for convenience and to give a general sense of the inventive concepts, and “a” and “an” are intended to include one or at least one and the singular also includes the plural unless it is obvious that it is meant otherwise.

Finally, as used herein any reference to “one embodiment,” or “some embodiments” means that a particular element, feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the inventive concepts disclosed herein. The appearances of the phrase “in some embodiments” in various places in the specification are not necessarily all referring to the same embodiment, and embodiments of the inventive concepts disclosed may include one or more of the features expressly described or inherently present herein, or any combination of sub-combination of two or more such features, along with any other features which may not necessarily be expressly described or inherently present in the instant disclosure.

Broadly, embodiments of the inventive concepts disclosed herein are directed to a photonic monopulse comparator for determining the angle and direction of an arriving inbound RF signal in the optical domain. Optical signals are modulated by the RF input signals generated by the squinted monopulse subarrays (e.g., elements) to determine angle of arrival in one or more angular dimensions, at high speed and across an ultrawide bandwidth.

Referring to FIG. 1 , a one-dimensional (1D) monopulse array 100 (e.g., aperture) may include subarrays 102 and 104 , each subarray including antenna elements 106 and 108 and receiver elements 110 and 112 . For example, the two subarrays 102 and 104 may receive an inbound signal 114 via their respective antenna element(s) 106 and 108 from squinted, or slightly different, directions. The respective receiver elements 110 , 112 each produce a radio frequency (RF) signal (e.g., associated with the squinted beam) V 1 ( 116 ) and V 2 ( 118 ). In some embodiments, the monopulse array 100 may include a phased array, steerable array, or steerable subarrays. A subarray may consist of a single element or many elements configured to produce a single output.

Referring now to FIG. 2 , the squinted beams V 1 , V 2 ( 116 , 118 ; FIG. 1 ) may be associated with RF voltage patterns 202 and 204 (per the vertical axis 206 ) relative to the off-axis angle (e.g., the angle of arrival of the inbound signal 114 of FIG. 1 ) (per the horizontal axis 208 ). From the squinted beams V 1 and V 2 ( 116 , 118 ), related signals may be calculated, e.g., a “sum” S ( 210 ) and “difference” D ( 212 ) such that

S = V ⁢ ⁢ 1 + V ⁢ ⁢ 2 2 ; D = V ⁢ ⁢ 1 - V ⁢ ⁢ 2 2

where the angle of arrival of the inbound signal 114 is approximately proportional to D/S ( 214 ).

Referring to FIG. 3 , the 2D monopulse array 100 a may be implemented and may function similarly to the 1D monopulse array 100 of FIG. 1 except that the 2D monopulse array 200 may incorporate four subarrays 302 , 304 , 306 , 308 which receive four squinted beams A, B, C, D ( 310 , 312 , 314 , 316 ). For example, the 2D monopulse array 100 a may be an amplitude-comparison monopulse array configured to determine the direction from which the inbound signal 114 originates by determining an azimuthal angle 318 (e.g., relative to broadside 320 ) and an elevational angle 322 (e.g., relative to the broadside). With respect to the 2D monopulse array 100 a , the azimuthal angle 318 and elevational angle 322 are proportional to the ratios D EL /S and D AZ /S, respectively, where the sum S is:

S = ( A + B ) + ( C + D ) 2

the elevational difference D EL is:

D EL = ( A + C ) - ( B + D ) 2

and the azimuthal difference D AZ is:

D AZ = ( C + D ) - ( A + B ) 2

relative to the squinted beams A, B, C, D ( 310 , 312 , 314 , 316 ).

Referring to FIG. 4 , a photonic monopulse comparator 400 may incorporate a photonic signal source (PSS) 402 ; optical phase modulators 404 , 406 , 408 , 410 ; hybrid couplers 412 , 414 , 416 , 418 ; an array 420 of balanced photodiode pairs 422 a - b , 424 a - b , 426 a - b (e.g., photodiode array); and an array 428 of analog-digital converters 430 , 432 , 434 (ADC).

The PSS 402 may be either a continuous-wave (CW) or pulsed laser; the former implementation may reduce complexity while the latter may provide low-jitter optical sampling and a higher signal/noise ratio (SNR) during the sampling pulse while remaining under the maximum average photocurrent. The PSS 402 may generate an optical signal 436 (e.g., CW or pulsed laser beam) which may be split ( 402 a ) and fed to the optical phase modulators 404 , 406 , 408 , 410 . Optical signal routing may use optical fibers, integrated optical waveguides, or combinations thereof.

The subarrays 302 , 304 , 306 , 308 of the 2D monopulse array ( 100 a , FIG. 3 ) may respectively feed RF signals corresponding to their respective squinted beams A, B, C, and D ( 310 , 312 , 314 , 316 ) to optical phase modulators 404 , 406 , 408 , and 410 and may modulate the optical signal 436 by the respective RF signals. The modulated optical signals 436 a - d may be fed to the hybrid couplers 412 , 414 , 416 , 418 ; the modulated optical signals 436 b - c may first pass through optical phase shifters 438 , 440 respectively shifting the phases of the optical signals 90° and −90°.

The hybrid couplers 412 , 414 , 416 , 418 may preferably include 90-degree integrated optical hybrid couplers, e.g., 2×2 devices capable of providing outputs for in-phase and quadrature signals (e.g., the in-phase modulated optical signals 436 a , 436 d and the quadrature modulated optical signals 436 b , 436 c , respectively). However, the hybrid couplers 412 , 414 , 416 , 418 may include fiber-optic hybrids depending upon size, weight, loss, and wideband performance considerations (e.g., amplitude or phase balance across a broad bandwidth). The array of hybrid couplers 412 , 414 , 416 , 418 may be a 2×2 array of 2×2 couplers, each coupler having input ports 1 , 2 and output ports 3 , 4 such that, according to transfer functions:

where the phase-modulated optical signals from squinted beams A, B, C, D ( 310 , 312 , 314 , 316 ) are treated as complex quantities. The outputs of the hybrid couplers 412 , 414 may be fed to the input ports of the hybrid couplers 416 , 418 , e.g., such that the latter pair of hybrid couplers also provide outputs for in-phase and quadrature modulated optical signals.

The optical signal 436 may further be split (by optical splitter 442 ) into local oscillator (LO) signals 436 d - f . For example, the hybrid couplers 416 , 418 may output the hybrid output signals 444 (Output 3 of the hybrid coupler 416 ) and 446 , 448 (Output 3 and Output 4 respectively of the hybrid coupler 418 ); the hybrid Output 4 450 of the hybrid coupler 416 , corresponding to a diagonal difference, may remain unused and terminate in a dummy load 452 . The hybrid output signals 444 , 446 , 448 may respectively be fed into optical 90-degree couplers 454 , 456 , 458 (e.g., terminal hybrid couplers positioned at the terminal end of the array of hybrid couplers 412 - 418 ) along with the LO signals 436 d - f (e.g., so that the phase of the hybrid output signals may be measured). The resulting outputs may each be fed into balanced photodiodes 422 a - b , 424 a - b , 426 a - b for coherent photodetection and then digitized by the ADCs 430 , 432 , 434 . The resulting digital output signals 460 , 462 , 464 may respectively correspond to the elevational difference D EL , the sum S, and the azimuthal difference D AZ ; from these digital output signals the azimuthal angle ( 318 , FIG. 3 ) and elevational angle ( 322 , FIG. 3 ) of the inbound signal ( 114 , FIG. 3 ) may be calculated.

As noted above, the architecture of the photonic monopulse comparator 400 may provide improved amplitude and phase balance across an ultrawide bandwidth (e.g., 40˜100 GHz), high linearity (e.g., 70 dB spurious free dynamic range (SFDR) or better) via the optical phase modulators, as well as passive hybrid processing—all in a very small size. As most calculations are performed in the optical domain, electronic calculations, latency, and power consumption are minimized compared to digital signal processors.

The optical-domain components of the photonic monopulse comparator 400 , e.g., the optical splitter, optical phase modulators 404 , 406 , 408 , 410 , and optical hybrid couplers 412 , 414 , 416 , 418 , may be situated in a photonic integrated circuit (PIC) 466 incorporating lithium niobite (LiNbO 3 ) or any appropriate materials from which the PIC may be fashioned. For example, the PIC 466 may be a bulk LiNbO 3 chip or thin-film LiNbO 3 incorporating monolithically integrated couplers, low-loss waveguides, or thermal-optic phase shifters. Alternatively, the PIC 466 may incorporate LiNbO 3 modulators feeding optical signals to a glass-on-silicon chip.

Some of the advantages of photonics-based as opposed to RF-based monopulse comparator systems have been noted above: broad bandwidth, high linearity, immunity to RF interference. RF splitting and combining may be eliminated, and with it the associated dependency on bandwidth and frequency. Wavelength-division multiplexing (WDM) technology may provide additional dimensions of freedom for RF/photonics-based monopulse systems by enabling linear additional and subtraction of RF signals in the optical domain.

Referring to FIG. 5A , the photonic circuit 500 may incorporate a PSS 402 , optical splitters/combiners 502 , 504 , cascading optical phase modulators 506 , 508 , and balanced photodiode pair 510 . Similarly to a Mach-Zehnder interferometer (MZI), the photonic circuit splits ( 502 ) the optical signal 436 into a first, or “upper” arm 512 (e.g., optical path), and a second, or “lower” arm 514 . The upper arm 512 (e.g., the component optical signal thereof) may undergo phase biasing (via low-speed phase shifter 516 ) and optical phase modulation: first by the optical phase modulator 506 being driven by the RF input signal 518 (having RF voltage V 1 (t)) and subsequently by the optical phase modulator 508 driven by the RF input signal 520 (having RF voltage V 2 (t)). The component optical signals of the upper and lower arms 512 , 514 may then undergo coherent photodetection by the balanced photodiode pair 510 . The RF output voltage 522 (V out1 ) of the balanced photodiode pair 510 (e.g., the balanced output of the upper and lower photodiodes 510 a - b ) may be proportional to the sum [V 1 (t)+V 2 (t)] of the input RF voltages V 1 (t), V 2 (t) of the RF input signals 518 , 520 ; the component optical signal of the lower arm 514 is unmodulated, while the upper arm 512 is modulated by the cascaded optical phase modulators 506 , 508 .

Referring now to FIG. 5B , the photonic circuit 500 a may be implemented and may function similarly to the photonic circuit 500 of FIG. 5A , except that the photonic circuit 500 a may incorporate the optical phase modulator 508 in the lower arm 514 . For example, the component optical signal of the upper arm 512 may be modulated only by the optical phase modulator 506 (and its corresponding RF input signal 518 having RF voltage V 1 (t)), while the component optical signal of the lower arm 514 may be modulated by the optical phase modulator 508 (and its corresponding RF input signal 520 having RF voltage V 2 (t). Accordingly, the RF output voltage 524 (V out2 ) of the balanced photodiode pair 510 may be proportional to the difference [V 1 (t)−V 2 (t)] of the input RF voltages V 1 (t), V 2 (t) of the RF input signals 518 , 520 .

Referring to FIG. 6 , the integrated photonics monopulse comparator 600 may incorporate a monopulse array 100 a (including subarrays 302 , 304 , 306 , 308 ), splitter/combiner 502 , wavelength demultiplexers 602 a - d (demuxes), wavelength multiplexers 604 a - c (muxes), optical phase shifters 606 , cascading optical phase modulators 608 , 610 , 612 , 614 , and balanced photodiode pairs 616 , 618 , 620 (which may be implemented and may function similarly to the balanced photodiode pair 510 of FIGS. 5A /B).

The PSS 622 may generate a wavelength division multiplexed (WDM) signal 616 incorporating any number of component optical signals having discrete wavelengths, e.g., λ 1 , λ 2 , λ 3 . The WDM optical signal 616 can incorporate two, three, or any other number of component optical signals as needed.

The integrated photonics monopulse comparator 600 may incorporate the cascaded additive and subtractive properties of the optical component cascade (based on the arrangement of the individual optical phase modulators 608 , 610 , 612 , 614 ) to determine RF output voltages 624 a - c (via the balanced photodiode pairs 616 , 618 , 620 ; e.g., the RF output voltage 624 a (V out1 (t)) may correspond to the balanced output of the upper and lower photodiodes 616 a , 616 b ) respectively proportional to the sum S, azimuthal difference D AZ , and elevational difference D EL . From the RF output voltages 624 a - c , then, it is possible to calculate the azimuthal and elevational angles of the inbound signal 114 received by the monopulse subarrays 302 , 304 , 306 , 308 of the monopulse array 100 a.

For example, the WDM optical signal 616 may be split ( 502 ) into an upper arm 626 and a lower arm 628 . The lower arm 628 is demuxed ( 602 e ) into component optical signals 628 a , 628 b , 628 c . The upper arm 626 is first modulated by the optical phase modulator 608 (according to the RF voltage V A (t) of the RF input signal A ( 310 ) produced by the monopulse subarray 302 in response to the inbound signal 114 ) before demuxing ( 602 a ) into its component optical signals 626 a , 626 b , 626 c . All three component signals 626 a , 626 b , 626 c of the upper arm 626 are modulated by the RF voltage V A (t) associated with the optical phase modulator 608 .

The component optical signal 628 c may be fed into the upper arm 626 of the integrated photonics monopulse comparator 600 , replacing the component optical signal 626 c which is fed into the lower arm 628 (along with component optical signals 628 a , 628 b ). The upper-arm component optical signals 626 a , 626 b , 628 c are then muxed ( 604 a ) into an upper-arm WDM optical signal ( 630 ) which is modulated by the optical phase modulator 610 (according to the RF voltage V B (t) of the RF input signal B ( 312 ) produced by the monopulse subarray 304 ) and demuxed ( 602 b ) into the component optical signals 626 a , 626 b , 628 c . At this point the component optical signals 626 a , 626 b have been modulated by both cascaded optical phase modulators 608 , 610 (V A (t)+V B (t)) while the component optical signal 628 c has been modulated solely by the optical phase modulator 610 (V B (t)). The component optical signal 626 c has been modulated solely by the optical phase modulator 608 (V A (t)), and not by the optical phase modulator 610 (V B (t)).

The component optical signal 626 b may then be fed into the lower arm 628 (along with component optical signals 626 c , 628 a ) and replaced in the upper arm 626 by the as yet unmodulated component optical signal 628 b . The resulting upper-arm component optical signals 626 a , 628 b , 628 c may be muxed ( 604 b ) into an upper-arm WDM optical signal 632 . The upper-arm WDM optical signal 632 is then modulated by the optical phase modulator 612 (according to the RF voltage V D (t) of the RF input signal D ( 316 ) produced by the monopulse subarray 308 ) and demuxed ( 602 c ) into component optical signals 626 a (V A (t)+V B (t)+V D (t)), 628 b (V D (t)), and 628 c +(V B (t)+V D (t)). The component optical signal 628 c may then be fed back into the lower arm 628 (along with component optical signals 626 b , 628 a ) and replaced in the upper arm with the component optical signal 626 c (V A (t)).

The component optical signals 626 a , 628 b , 626 c may be muxed ( 604 c ) into an upper-arm WDM optical signal 634 and modulated by the optical phase modulator 614 (according to the RF voltage V C (t) of the RF input signal C ( 314 ) produced by the monopulse subarray 306 ) before demuxing ( 602 d ) into the component optical signals 626 a (V A (t)+V B (t)+V C (t)+V D (t)), 628 b (V C (t)+V D (t)), and 626 c +(V A (t)+V C (t)). Each balanced photodiode pair 616 , 618 , 620 receives a pair of upper-arm and lower-arm component optical signals of shared wavelength: component optical signals 626 a , 628 a of wavelength λ 1 are fed into the upper and lower photodiodes 616 a - b of the balanced photodiode pair 616 , component optical signals 628 b , 626 b of wavelength λ 2 are fed into the upper and lower photodiodes 618 a - b of the balanced photodiode pair 618 , and component optical signals 626 c , 628 c of wavelength λ 3 are fed into the upper and lower photodiodes 620 a - b of the balanced photodiode pair 620 .

The three output channels V out1 (t), V out2 (t), and V out3 (t) correspond to the three RF output voltages 624 a - c of the balanced photodiode pairs 616 , 618 , 620 , each RF output voltage 624 a , 624 b , 624 c respectively proportional to the difference of the upper and lower photodiodes 616 a - b , 618 a - b , 620 a - b . For example, with respect to the output channel V out1 (t), the upper-arm phase (component optical signal 626 a ) is proportional to V A +V B +V C +V D as the component optical signal 626 a is modulated by the four cascading optical phase modulators 608 , 610 , 612 , 614 . Similarly, the lower-arm phase (component optical signal 628 a is unmodulated, so the RF output voltage 624 a of the output channel V out1 (t) through balanced photodiode pair 616 is proportional to V A +V B +V C +V D (e.g., the sum S).

With respect to the output channel V out2 (t), the upper-arm phase (component optical signal 628 b ) is proportional to V C +V D while the lower-arm phase (component optical signal 626 b ) is proportional to +V A +V B . Accordingly, the RF output voltage 624 b of the output channel V out2 (t) through balanced photodiode pair 618 is proportional to [V C +V D ]−[V A +V B ] or [V A +V B ]−[V C +V D ] (e.g., the azimuthal difference D AZ ).

With respect to the output channel V out3 (t), the upper-arm phase (component optical signal 626 c ) is proportional to V A +V C while the lower-arm phase (component optical signal 628 c ) is proportional to +V B +V D . Accordingly, the RF output voltage 624 c of the output channel V out3 (t) through balanced photodiode pair 620 is proportional to [V A +V C ]−[V B +V D ] (e.g., the elevational difference D EL ). From these three RF output voltages 624 a (V out1 (t) ∝[V A +V B ]+[V C +V D ]∝S), 624 b (V out2 (t)∝[V A +V B ]−[V C +V D ]∝D AZ ), and 624 c (V out3 (t)∝[V A +V C ]−[V B +V D ]∝D EL ), the azimuthal angle ( 318 , FIG. 3 ) and elevational angle ( 322 , FIG. 3 ) of the inbound signal 114 can be calculated.

As will be appreciated from the above, systems and methods according to embodiments of the inventive concepts disclosed herein may provide for high speed, high resolution, high linearity and resolution, and improved amplitude/phase balance across an ultrawide bandwidth at a small chip size. As RF signal operations are implemented in the optical domain, conversion to RF and RF interference are not complicating factors.

It is to be understood that embodiments of the methods according to the inventive concepts disclosed herein may include one or more of the steps described herein. Further, such steps may be carried out in any desired order and two or more of the steps may be carried out simultaneously with one another. Two or more of the steps disclosed herein may be combined in a single step, and in some embodiments, one or more of the steps may be carried out as two or more sub-steps. Further, other steps or sub-steps may be carried in addition to, or as substitutes to one or more of the steps disclosed herein.

From the above description, it is clear that the inventive concepts disclosed herein are well adapted to carry out the objects and to attain the advantages mentioned herein as well as those inherent in the inventive concepts disclosed herein. While presently preferred embodiments of the inventive concepts disclosed herein have been described for purposes of this disclosure, it will be understood that numerous changes may be made which will readily suggest themselves to those skilled in the art and which are accomplished within the broad scope and coverage of the inventive concepts disclosed and claimed herein.