A system and method of providing a micromirror pixel 400 that is highly resistant to bright failure states. The micromirror 400 uses an asymmetric yoke 402 to ensure the mirror is only attracted to the address electrode in one rotation direction. The landing mechanism on the other side of the torsion binge axis also is altered to allow the pixel to over rotate in the "off" direction. The over rotation ensures that light reflected by the mirror when in the off direction will miss the projection lens pupil, allowing the corresponding pixel to remain dark in both an operational and failed state.
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1. A micromirror device comprising:
a substrate; at least one address electrode supported by said substrate; a torsion hinge supported apart from said substrate; an asymmetric yoke supported by said torsion hinge; and a deflectable member supported by and apart from said yoke.
7. A micromirror device comprising:
a substrate; a torsion hinge supported apart from said substrate; a deflectable member supported by and apart from said torsion hinge; a means for rotating said deflectable member about said torsion hinge; and a means for limiting said deflection of said deflectable member in a first direction to a greater degree than in a second direction.
6. A micromirror device comprising:
a substrate; a torsion hinge supported apart from said substrate; a yoke supported by said torsion hinge; a deflectable member supported by and apart from said yoke; and an address electrode supported by said substrate on one side of an axis of said torsion hinge, said address electrode operable to attract said yoke only toward said one side of said torsion hinge axis.
5. A micromirror device comprising:
a substrate; at least one address electrode supported by said substrate; a torsion hinge supported apart from said substrate; a yoke supported by said torsion hinge; and a deflectable member supported by and apart from said yoke, said yoke limiting deflection of said deflectable member in a first direction of rotation about said torsion hinge and not so limiting said deflection in an opposite direction.
10. A display system comprising:
a light source for providing a beam of light along a light path; a micromirror on said light path for selectively modulating said beam of light, said micromirror comprising: a substrate; at least one address electrode supported by said substrate; a torsion hinge supported apart from said substrate; an asymmetric yoke supported by said torsion hinge; and a deflectable member supported by and apart from said yoke; and a projection lens for focusing said selectively modulated beam of light.
16. A display system comprising:
a light source for providing a beam of light along a light path; a micromirror on said light path for selectively modulating said beam of light, said micromirror comprising: a substrate; a torsion hinge supported apart from said substrate; a deflectable member supported by and apart from said torsion hinge; a means for rotating said deflectable member about said torsion hinge; and a means for limiting said deflection of said deflectable member in a first direction to a greater degree than in a second direction; and a projection lens for focusing said selectively modulated beam of light.
15. A display system comprising:
a light source for providing a beam of light along a light path; a micromirror on said light path for selectively modulating said beam of light, said micromirror comprising: a substrate; a torsion hinge supported apart from said substrate; a yoke supported by said torsion hinge; a deflectable member supported by and apart from said yoke; and an address electrode supported by said substrate on one side of an axis of said torsion hinge, said address electrode operable to attract said yoke only toward said one side of said torsion hinge axis; and a projection lens for focusing said selectively modulated beam of light.
13. A display system comprising:
a light source for providing a beam of light along a light path; a micromirror on said light path for selectively modulating said beam of light, said micromirror comprising: a substrate; at least one address electrode supported by said substrate; a torsion hinge supported apart from said substrate; a yoke supported by said torsion hinge; and a deflectable member supported by and apart from said yoke, said yoke limiting deflection of said deflectable member in a first direction of rotation about said torsion hinge and not so limiting said deflection in an opposite direction; and a projection lens for focusing said selectively modulated beam of light.
2. The micromirror device of
3. The micromirror of
an address electrode supported by said substrate on one side of an axis of said torsion hinge, said address electrode operable to attract said asymmetric yoke only toward said one side of said torsion hinge axis.
4. The micromirror of
an address electrode supported by said substrate on one side of an axis of said torsion hinge, said address electrode operable to attract said asymmetric yoke only toward said one side of said torsion hinge axis.
8. The micromirror device of
9. The micromirror device of
11. The display system of
12. The display system of
an address electrode supported by said substrate on one side of an axis of said torsion hinge, said address electrode operable to attract said asymmetric yoke only toward said one side of said torsion hinge axis.
14. The display system of
an address electrode supported by said substrate on one side of an axis of said torsion hinge, said address electrode operable to attract said asymmetric yoke only toward said one side of said torsion hinge axis.
17. The display system of
18. The display system of
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This application claims priority under 35 USC § 119(e)(1) of provisional application No. 60/343,636 filed Dec. 28, 2001.
The following patents and/or commonly assigned patent applications are hereby incorporated herein by reference:
Patent No. | Filing Date | Issue Date | Title |
5,061,049 | Sept. 13, 1990 | Oct. 29, 1991 | Spatial Light |
Modulator and | |||
Method | |||
5,583,688 | Dec. 21, 1993 | Dec. 10, 1996 | Multi-Level |
Digital Micro- | |||
mirror Device | |||
6,147,790 | May 13, 1999 | Nov. 14, 2000 | Spring-Ring |
Micromechanical | |||
Device | |||
This invention relates to the field of micromirror devices, more particularly to arrays of micromirror devices.
Micromechanical devices are small structures typically fabricated on a semiconductor wafer using techniques such as optical lithography, doping, metal sputtering, oxide deposition, and plasma etching which have been developed for the fabrication of integrated circuits.
Digital micromirror devices (DMDs), sometimes referred to as deformable micromirror devices, are a type of micromechanical device. Other types of micromechanical devices include accelerometers, pressure and flow sensors, gears and motors. While some micromechanical devices, such as pressure sensors, flow sensors, and DMDs have found commercial success, other types have not yet been commercially viable.
Digital micromirror devices are primarily used in optical display systems. In display systems, the DMD is a light modulator that uses digital image data to modulate a beam of light by selectively reflecting portions of the beam of light to a display screen. While analog modes of operation are possible, DMDs typically operate in a digital bistable mode of operation and as such are the core of the first true digital full-color image projection systems.
Micromirrors have evolved dramatically over the past fifteen to twenty years. Early devices used a deformable reflective membrane which, when electrostatically attracted to an underlying address electrode, dimpled toward the address electrode. Schlieren optics were used to illuminate the membrane and create an image from the light scattered by the dimpled portions of the membrane. Schlieren systems enabled the membrane devices to form images, but the images formed were very dim and had low contrast ratios, making them unsuitable for most image display applications.
Later micromirror devices used flaps or diving board-shaped cantilever beams of silicon or aluminum, coupled with dark-field optics to create images having improved contrast ratios. Flap and cantilever beam devices typically used a single metal layer to form a deformable top reflective layer of the device. This single metal layer tended to deform over a large region, however, which scattered light impinging on the deformed portion. Torsion beam devices use a thin metal layer to form a torsion beam, which is referred to as a hinge, and a thicker metal layer to form a rigid member, or beam, typically having a mirror-like surface: concentrating the deformation on a relatively small portion of the DMD surface. The rigid mirror remains flat while the hinges deform, minimizing the amount of light scattered by the device and improving the contrast ratio of the device.
Recent micromirror configurations, called hidden-hinge designs, further improve the image contrast ratio by fabricating the mirror on a pedestal above the torsion beams. The elevated mirror covers the torsion beams, torsion beam supports, and a rigid yoke connecting the torsion beams and mirror support, further improving the contrast ratio of images produced by the device.
Modern micromirror arrays often have on the order of 1.3 million individual mirrors. As with other complex devices, these large arrays are difficult to produce to the level of perfection required. Methods and devices to improve producibility and reliability are constantly needed.
Objects and advantages will be obvious, and will in part appear hereinafter and will be accomplished by the present invention that provides a method and device for an improved micromechanical device.
For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:
Objects and advantages will be obvious, and will in part appear hereinafter and will be accomplished by the present invention that provides a method and device for an improved micromirror device. According to one embodiment of the present invention, a micromirror device is provided. The micromirror device comprising: a substrate; at least one address electrode supported by the substrate; a torsion hinge supported apart from the substrate; an asymmetric yoke supported by the torsion hinge; and a deflectable member supported by and apart from the yoke.
According to another embodiment of the present invention, a micromirror device is provided. The micromirror device comprising: a substrate; at least one address electrode supported by the substrate; a torsion hinge supported apart from the substrate; a yoke supported by the torsion hinge; and a deflectable member supported by and apart from the yoke, the yoke limiting deflection of the deflectable member in a first direction of rotation about the torsion hinge and not so limiting the deflection in an opposite direction.
According to another embodiment of the present invention, a micromirror device is provided. The micromirror device comprising: a substrate; a torsion hinge supported apart from the substrate; a yoke supported by the torsion hinge; a deflectable member supported by and apart from the yoke; and an address electrode supported by the substrate on one side of an axis of the torsion hinge, the address electrode operable to attract the yoke only toward the one side of the torsion hinge axis.
According to another embodiment of the present invention, a micromirror device is provided. The micromirror device comprising: a substrate; a torsion hinge supported apart from the substrate; a deflectable member supported by and apart from the torsion hinge; a means for rotating the deflectable member about the torsion hinge; and a means for limiting the deflection of the deflectable member in a first direction to a greater degree than in a second direction.
According to another embodiment of the present invention, a display system is provided. The display system comprising: a light source for providing a beam of light along a light path; a micromirror on the light path for selectively modulating the beam of light, the micromirror comprising: a substrate; at least one address electrode supported by the substrate; a torsion hinge supported apart from the substrate; an asymmetric yoke supported by the torsion hinge; and a deflectable member supported by and apart from the yoke; and a projection lens for focusing the selectively modulated beam of light.
According to another embodiment of the present invention, a display system is provided. The display system comprising: a light source for providing a beam of light along a light path; a micromirror on the light path for selectively modulating the beam of light, the micromirror comprising: a substrate; at least one address electrode supported by the substrate; a torsion hinge supported apart from the substrate; a yoke supported by the torsion hinge; and a deflectable member supported by and apart from the yoke, the yoke limiting deflection of the deflectable member in a first direction of rotation about the torsion hinge and not so limiting the deflection in an opposite direction; and a projection lens for focusing the selectively modulated beam of light.
According to another embodiment of the present invention, a display system is provided. The display system comprising: a light source for providing a beam of light along a light path; a micromirror on the light path for selectively modulating the beam of light, the micromirror comprising: a substrate; a torsion hinge supported apart from the substrate; a yoke supported by the torsion hinge; a deflectable member supported by and apart from the yoke; and an address electrode supported by the substrate on one side of an axis of the torsion hinge, the address electrode operable to attract the yoke only toward the one side of the torsion hinge axis; and a projection lens for focusing the selectively modulated beam of light.
According to another embodiment of the present invention, a display system is provided. The display system comprising: a light source for providing a beam of light along a light path; a micromirror on the light path for selectively modulating the beam of light, the micromirror comprising: a substrate; a torsion hinge supported apart from the substrate; a deflectable member supported by and apart from the torsion hinge; a means for rotating the deflectable member about the torsion hinge; and a means for limiting the deflection of the deflectable member in a first direction to a greater degree than in a second direction; and a projection lens for focusing the selectively modulated beam of light.
A DMD is fabricated on a semiconductor, typically silicon, substrate 104. Electrical control circuitry is typically fabricated in or on the surface of the semiconductor substrate 104 using standard integrated circuit process flows. This circuitry typically includes, but is not limited to, a memory cell associated with, and typically underlying, each mirror 102 and digital logic circuits to control the transfer of the digital image data to the underlying memory cells. Voltage driver circuits to drive bias and reset signals to the mirror superstructure may also be fabricated on the DMD substrate, or may be external to the DMD. Image processing and formatting logic is also formed in the substrate 104 of some designs. For the purposes of this disclosure, addressing circuitry is considered to include any circuitry, including direct voltage connections and shared memory cells, used to control the direction of rotation of a DMD mirror.
Some DMD configurations use a split reset configuration which allows several DMD elements to share one memory cell--thus reducing the number of memory cells necessary to operate a very large array, and making more room available for voltage driver and image processing circuitry on the DMD integrated circuit. Split reset is enabled by the bistable operation of a DMD, which allows the contents of the underlying memory to change without affecting the position of the mirror 102 when the mirror has a bias voltage applied.
The silicon substrate 104 and any necessary metal interconnection layers are isolated from the DMD superstructure by an insulating layer 106 which is typically a deposited silicon dioxide layer on which the DMD superstructure is formed. Holes, or vias, are opened in the oxide layer to allow electrical connection of the DMD superstructure with the electronic circuitry formed in the substrate 104.
The first layer of the superstructure is a metalization layer, typically the third metalization layer and therefore often called M3. The first two metalization layers are typically required to interconnect the circuitry fabricated on the substrate. The third metalization layer is deposited on the insulating layer and patterned to form address electrodes 110 and a mirror bias connection 112. Some micromirror designs have landing electrodes which are separate and distinct structures but are electrically connects to the mirror bias connection 112. Landing electrodes limit the rotation of the mirror 102 and prevent the rotated mirror 102 or hinge yoke 114 from touching the address electrodes 110, which have a voltage potential relative to the mirror 102. If the mirror 102 contacts the address electrodes 110, the resulting short circuit could fuse the torsion hinges 116 or weld the mirror 102 to the address electrodes 110, in either case ruining the DMD.
Since the same voltage is always applied both to the landing electrodes and the mirrors 102, the mirror bias connection and the landing electrodes are preferably combined in a single structure when possible. The landing electrodes are combined with the mirror bias connection 112 by including regions on the mirror bias/reset connection 112, called landing sites, which mechanically limit the rotation of the mirror 102 by contacting either the mirror 102 or the torsion hinge yoke 114. These landing sites are often coated with a material chosen to reduce the tendency of the mirror 102 and torsion hinge yoke 114 to stick to the landing site.
Mirror bias/reset voltages travel to each mirror 102 through a combination of paths using both the mirror bias/reset metalization 112 and the mirrors and torsion beams of adjacent mirror elements. Split reset designs require the array of mirrors to be subdivided into multiple subarrays each having an independent mirror bias connection. The landing electrode/mirror bias 112 configuration shown in
A first layer of supports, typically called spacervias, is fabricated on the metal layer forming the address electrodes 110 and mirror bias connections 112. These spacervias, which include both hinge support spacervias 116 and upper address electrode spacervias 118, are typically formed by spinning a thin spacer layer over the address electrodes 110 and mirror bias connections 112. This thin spacer layer is typically a 1 μm thick layer of positive photoresist. After the photoresist layer is deposited, it is exposed, patterned, and deep UV hardened to form holes in which the spacervias will be formed. This spacer layer and a thicker spacer layer used later in the fabrication process are often called sacrificial layers since they are used only as forms during the fabrication process and are removed from the device prior to device operation.
A thin layer of metal is sputtered onto the spacer layer and into the holes. An oxide is then deposited over the thin metal layer and patterned to form an etch mask over the regions that later will form hinges 120. A thicker layer of metal, typically an aluminum alloy, is sputtered over the thin layer and oxide etch masks. Another layer of oxide is deposited and patterned to define the hinge yoke 114, hinge cap 122, and the upper address electrodes 124. After this second oxide layer is patterned, the two metals layers are etched simultaneously and the oxide etch stops removed to leave thick rigid hinge yokes 114, hinge caps 122, and upper address electrodes 124, and thin flexible torsion beams 120.
A thick spacer layer is then deposited over the thick metal layer and patterned to define holes in which mirror support spacervias 126 will be formed. The thick spacer layer is typically a 2 μm thick layer of positive photoresist. A layer of mirror metal, typically an aluminum alloy, is sputtered on the surface of the thick spacer layer and into the holes in the thick spacer layer. This metal layer is then patterned to form the mirrors 102 and both spacer layers are removed using a plasma etch.
Once the two spacer layers have been removed, the mirror is free to rotate about the axis formed by the torsion hinge. Electrostatic attraction between an address electrode 110 and a deflectable rigid member, which in effect form the two plates of an air gap capacitor, is used to rotate the mirror structure. Depending on the design of the micromirror device, the deflectable rigid member is the torsion beam yoke 114, the beam or mirror 102, a beam attached directly to the torsion hinges, or a combination thereof. The upper address electrodes 124 also electrostatically attract the deflectable rigid member.
The force created by the voltage potential is a function of the reciprocal of the distance between the two plates. As the rigid member rotates due to the electrostatic torque, the torsion beam hinges resist deformation with a restoring torque that is an approximately linear function of the angular deflection of the torsion beams. The structure rotates until the restoring torsion beam torque equals the electrostatic torque or until the rotation is mechanically blocked by contact between the rotating structure and a fixed component. As discussed below, most micromirror devices are operated in a digital mode wherein sufficiently large bias voltages are used to ensure full deflection of the micromirror superstructure.
Micromirror devices are generally operated in one of two modes of operation. The first mode of operation is an analog mode, sometimes called beam steering, wherein the address electrode is charged to a voltage corresponding to the desired deflection of the mirror. Light striking the micromirror device is reflected by the mirror at an angle determined by the deflection of the mirror. Depending on the voltage applied to the address electrode, the cone of light reflected by an individual mirror is directed to fall outside the aperture of a projection lens, partially within the aperture, or completely within the aperture of the lens. The reflected light is focused by the lens onto an image plane, with each individual mirror corresponding to a fixed location on the image plane. As the cone of reflected light is moved from completely within the aperture to completely outside the aperture, the image location corresponding to the mirror dims, creating continuous brightness levels.
The second mode of operation is a digital mode. When operated digitally, each micromirror is fully deflected in either of the two directions about the torsion beam axis. Digital operation uses a relatively large voltage to ensure the mirror is fully deflected. Since it is advantageous to drive the address electrode using standard logic voltage levels, a bias voltage, typically a negative voltage, is applied to the mirror metal layer to increase the voltage difference between the address electrodes and the mirrors. Use of a sufficiently large mirror bias voltage--a voltage above what is termed the collapse voltage of the device--ensures the mirror will deflect to the closest landing electrodes even in the absence of an address voltage. Therefore, by using a large mirror bias voltage, the address voltages need only be large enough to deflect the mirror slightly.
To create an image using the micromirror device, the light source is positioned at an angle equal to twice the angle of rotation so that mirrors rotated toward the light source reflect light in a direction normal to the surface of the micromirror device and into the aperture of a projection lens--creating a bright pixel on the image plane. Mirrors rotated away from the light source reflect light away from the projection lens--leaving the corresponding pixel dark. Intermediate brightness levels are created by pulse width modulation techniques in which the mirror is rapidly and repetitively rotated on and off. The duty cycle of the mirror determines the quantity of light reaching the image plane. The human eye integrates the light pulses and the brain perceives a flicker-free intermediate brightness level.
Full-color images are generated by using three micromirror devices to produce three single-color images, or by sequentially forming three single-color images using a single micromirror device illuminated by a beam of light passing through three color filters mounted on a rotating color wheel.
When used in an image projection display system, the micromirror provides an exceptional image. One very important characteristic of a high quality image is the contrast ratio, or the ratio between the brightness of the brightest pixel a display can form and the brightness of the darkest pixel a display can form. Micromirror displays have a very high contrast ratio. Using dark field illumination enables the micromirror system to produce extremely dark pixels. The pixels that are turned off, are so much darker than the structures used to define the border of the modulator array, that methods had to be devised to darken the border around the image.
To create a sharp dark border around the active portion of the array, a "sea of mirrors" is used. The sea of mirrors comprises an approximately 50 mirror wide border around the active mirrors. The mirrors in the sea of mirrors are always turned to the off position, creating a border at least as dark as the dark pixels in the image. In
The mirrors in the sea of mirrors borders of the prior art have been fabricated exactly like the active mirrors--that is the image forming mirrors in the center of the array--except that since the mirrors in the sea of mirrors need only turn in one direction, they are formed with smaller gaps between the mirrors. The smaller gaps are enabled by the fact that additional clearance is only needed to avoid interference between adjacent mirrors that are turning in opposite directions.
The sea of mirrors is a substantial portion of the total number of mirrors formed in the array. For example, in a 1024×768 array, the sea of mirrors uses 189,200 mirrors compared to the 786,432 mirrors in the active portion of the array. Some designs use a narrower border region, for example 20 mirrors, but forming a sea of mirrors 20 mirrors wide still requires 73,280 mirrors. The more mirrors used in the border region, the more likely it is that at least one of the mirrors will be defective. Because the sea of mirrors is always dark, any defect in the mirrors will result in an extremely noticeable image defect. It is therefore imperative that the sea of mirrors be formed in such a way that the chance of a defective part being formed is minimized, or better still in such a way that any defective pixels form a dark--less noticeable--defect.
Although all of the mechanisms are not well understood, prior art micromirror designs and manufacturing processes lead to a significant number of device failures due to bright defects in the sea of mirrors. What is needed is a pixel design and manufacturing process that prevents bright defect from occurring in the sea of mirrors. The present invention meets this need by providing a pixel design and manufacturing process that yields a bistable pixel with failure modes that create only dark defects.
Unlike prior art designs that use the same basic structure for elements in both the sea of mirrors and the active array, the present invention proposes a novel superstructure for the sea of mirrors. The novel superstructure uses an asymmetric beam to produce electrostatic attraction only towards the "off" state--thus preventing the deflectable member from being attracted to the "on" state where it could become a bright defect. The novel superstructure further alters the landing mechanism on the "on" state to ensure that any pixels that do rotate to the "on" position must rotate so far that the light reflected by the "on" failures misses the projection aperture--preventing the formation of a bright defect.
The metal layer used to form the address electrode typically is patterned to form two main features. One feature is the address electrode 404 and the other feature is an electrical shield 406. The shield layer 406 serves a variety of purposes. First, it provides electrical contact from the underlying circuitry to the micromirror superstructure. Second, it provides a landing site on which the yoke 402 or beam can come to rest. When serving the landing site function, it is important that the landing site and the yoke 402 or beam either be held at the same voltage level or else be insulated from each other. Third, the metal layer provides a planar surface on which to build the micromirror superstructure.
The design shown in
The metal layer used to form the address electrodes 404 and shield member 406 traditionally is the third metal layer used in the fabrication of the micromirror and therefore is referred to as the M3 layer. The first two metal layers are used to form interconnections between the circuitry controlling the micromirror array.
The intermediate layer of the micromirror superstructure is formed from two metal layers. Following the fabrication sequence described above, a photoresist layer is spun on the M3 metal layer, and holes are opened in the photoresist to allow interconnection between the hinge level and the underlying M3 layer.
After the holes are formed in the first photoresist layer, a thin hinge metal layer is deposited on a planar photoresist and into the holes. An oxide etch mask is then deposited on the thin metal layer and patterned to form the torsion hinge etch stops 604 shown in
After the beam layer is etched, the second photoresist layer is spun over the beam layer. Another hole or via is opened in the second photoresist layer using the mirror via pattern 606 shown in
The extent to which the micromirror 1106 deflects before it is stopped depends on the design of the micromirror element, but generally is between 10°C and 12°C. In projection displays, the light source 1104 commonly is placed at an angle equal to twice the deflection angle of the mirror so that the micromirror 1106 reflects the light along a path perpendicular to the micromirror substrate 1108. The reflected light 1110 enters a projection lens 1112 and is focused onto an image plane (not shown).
In
In
Many alternate pixel designs are possible using the various teachings of the present invention. For example, the same principle of unidirectional rotation coupled with over rotation in the opposite direction may be applied to other designs, including beamless designs.
Should the micromirror pixel element 1700 ever be rotated in the opposite direction, the lack of a spring tip will allow the mirror to over rotate. When used in the sea of mirrors, this over rotation prevents reflected light from entering the projection aperture and then reaching the displayed image. The same principles are also applicable to other designs, such as hidden hinge designs that land on the mirror rather than the yoke and spring ring designs.
The light passing through the color wheel 2110 is focused by lens group 2112. Aperture stop 2114 typically is located in lens group 2112. Lens group 2112 focuses the illumination light onto a spatial light modulator 2120 through a TIR prism assembly 2122. The off state light and the flat state light are directed to a light dump 2124 which absorbs the light.
On state light exits the TIR prism assembly 2122 and enters the projection lens 2118. Another aperture stop 2116 typically is used in the projection lens 2118 to block a portion of the light, preventing it from passing through the lens to the image plane 2122. Controller 2128 provides image data and control signals to the spatial light modulator 2120 to control the modulation of the illumination light in order to form an image on the image plane 2126. Similar projection methods are used with color splitting prisms and three modulators in high brightness color projectors.
Thus, although there has been disclosed to this point a particular embodiment for *** and method therefore etc., it is not intended that such specific references be considered as limitations upon the scope of this invention except insofar as set forth in the following claims. Furthermore, having described the invention in connection with certain specific embodiments thereof, it is to be understood that further modifications may now suggest themselves to those skilled in the art, it is intended to cover all such modifications as fall within the scope of the appended claims.
Meyer, Thomas J., Huffman, James D., Shih, Wei-Yan, Mangrum, Brett A., Mignardi, Michael A., Reed, Mark F.
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