Patent Publication Number: US-9898147-B2

Title: Mesh electrode matrix having finite repeat length

Description:
BACKGROUND 
     Capacitive touch sensors may comprise an array of electrically conducting electrodes, each electrode comprised of a metal electrode mesh. Applying such sensors to large format displays may require hundreds of electrodes and tens of millions of mesh elements forming unique electrode geometries. 
     SUMMARY 
     This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. Furthermore, the claimed subject matter is not limited to implementations that solve any or all disadvantages noted in any part of this disclosure. 
     An array of electrodes is comprised of a plurality of electrodes. Each electrode extends along a first direction X, and is periodically arrayed along a second direction Y perpendicular to X at a pitch p e . Each electrode further comprises a continuous periodic metal mesh having a square unit cell of edge length p m , the square unit cell having axes displaced by an oblique angle θ from X and Y. The array is configured such that θ=arctan (a/b) and p m =n*p e /(m*sqrt(a 2 +b 2 )), where a, b, m, and n are positive integers. In this way, the electrodes repeat with a finite repeat length, while rendering the common edges of the repeating units visually imperceptible by a user. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view of a large format multi-touch display device in accordance with one embodiment of the present disclosure. 
         FIG. 2  is a cross-sectional view of an optical stack for a capacitive touch sensitive display of the large format multi-touch display device of  FIG. 1 . 
         FIG. 3  shows an example metal-mesh electrode array for a capacitive touch sensor. 
         FIG. 4A  shows a portion of an electrode array including metal mesh electrodes flanked by an electrically discontinuous alley mesh, the array having an infinite repeat length. 
         FIG. 4B  shows a detailed view of edges of adjacent step-and-repeat units as shown in  FIG. 4A . 
         FIG. 5A  shows a portion of an electrode array including metal mesh electrodes flanked by an electrically discontinuous alley mesh, the array, having a finite repeat length. 
         FIG. 5B  shows a detailed view of edges of adjacent step-and-repeat units as shown in  FIG. 5A . 
         FIG. 6  is a schematic view of an image source for the display device of  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION 
     A capacitive touch sensor may consist of a matrix of electrically conducting transmit and receive electrodes, with electronics to measure the capacitance between transmit and receive electrodes. The proximity of a user&#39;s finger or other object may cause a change in the measured capacitance. The spacing of electrodes in a capacitive touch sensor is constrained by performance and cost considerations. For example, a smaller electrode pitch may increase the spatial precision of measurement, but may also increase the cost of transmit and receive electronics. Further, decreasing electrode pitch may degrade the sensitivity of the touch sensor. For a given electrode pitch, the number of electrodes, and thus electronics cost, is typically minimized by orienting the electrodes along the display&#39;s rows or columns of pixels. 
     When used with a display device, a capacitive touch sensor is typically attached to the user-facing surface of the display, to maximize the capacitance change. To avoid obstructing the user&#39;s view of the display panel, the sensor&#39;s electrodes may consist either of an optically transparent, electrically conductive material, or of an opaque electrically conductive material of low areal solidity, such as a mesh of narrow metal conductors. Because the available transparent conductive materials have relatively low electrical conductivity, metal mesh electrodes are presently favored for capacitive touch sensors requiring electrodes exceeding roughly 0.5 meters in length. 
     Metal mesh electrodes may be fabricated by a wide variety of manufacturing processes. For example, commonly used material-additive processes include intaglio printing of a conductive (e.g. silver-loaded) ink, and flexographic printing of a material that selectively promotes subsequent chemical deposition of metal. Commonly used material-subtractive processes include selective chemical etching and silver halide photography. In general, fabrication processes require a master tool such as an embossing roller (for intaglio printing), printing plate, or photomask that contains every detail of the electrodes and their constituent meshes (or their inverse, as in a negative-tone photoprocess). 
     It is well known that any superposition of two or more unlike periodic structures, or of identical periodic structures having a relative angular displacement, will produce moiré effects. Such effects undesirably arise when a touch sensor containing metal mesh electrodes is attached to a pixelated electronic display, such as an AMLCD or AMOLED device, in a touch display system. For a given display device, the visibility of such moiré effects is strongly dependent upon the spacing and directions of periodicity of the mesh openings. In most cases, the choice of these parameters is narrowly constrained by the need to minimize moiré visibility. The pattern of mesh openings must be oriented at specific oblique angles relative to the columns and rows of display pixels, with the openings spaced apart by specific non-integer multiples of the pixel pitch. 
     Each adjacent electrode may be separated by an inter-electrode alley. Because variations in display occlusion are readily visible to users as unwanted luminance contrasts, it is desirable that the metal mesh fill not only the electrodes (electrode mesh), but also the inter-electrode alleys (alley mesh) (See  FIGS. 4A and 5A  and related disclosure). Even where the mesh lines are too small for users to visually resolve, users may more easily perceive the electrode boundaries unless the lines comprising the alley meshes are aligned with those of the electrode meshes. This generally requires that all electrodes and inter-electrode alleys in one plane of the touch sensor be derived from a continuous mesh covering the entire display, interrupted by small gaps along the boundaries of the electrodes and within the alley mesh to provide electrical isolation. 
     Because this common mesh pattern is oriented obliquely to the electrodes, the boundaries of the electrodes cross the mesh differently from electrode to electrode. Indeed, in general, each electrode is geometrically unique. The design complexity is further greatly increased in the case of reentrant electrode shapes, such as a linked-diamond shape, which is commonly used to increase the sensitivity of capacitive touch sensors. In such cases, each individual diamond of each electrode is geometrically unique. 
     For a large touch sensor containing hundreds of electrodes, tens of thousands of diamonds, and tens of millions of mesh elements, this poses two major practical limitations in the design and fabrication of a master tool. First, the number of unique cases exceeds the computational limits of available CAD/CAM systems for the generation of mask works or tool paths. Second, step-and-repeat processes cannot be used during tool mastering. These limitations have been obstacles to the widespread manufacture of metal mesh touch sensors to date. 
     Other manufacturers have bypassed this problem by generating the mesh and gaps using two independent processes, so that the two designs can be decoupled. For example, one might fabricate a uniform metal mesh, and then use laser ablation to sever the mesh along the electrode boundaries. In this example, it may not be necessary to create a master tool containing many unique cases. However, this method is much more time consuming and costly than methods utilizing a single photolithographic process. Practitioners of the intaglio process can obtain an equivalent result by machining a grooved negative tool for a uniform mesh, replicating the grooved negative tool to create a ridged positive tool, grooving the positive tool to interrupt the ridges along the mesh boundaries, then using the positive tool to emboss the sensor substrate. However, this process is limited by high tooling costs, short positive tool lifetime, and high rates of electrical and cosmetic defects. 
       FIG. 1  shows a large format multi-touch display device  100  in accordance with an embodiment of the present disclosure. Display device  100  may have a diagonal dimension greater than 1 meter, for example. In other, particularly large-format embodiments, the diagonal dimension may be 55 inches or greater. Display device  100  may be configured to sense multiple sources of touch input, such as touch input applied by a digit  102  of a user or a stylus  104  manipulated by the user. Display device  100  may be connected to an image source S, such as an external computer or onboard processor. Image source S may receive multi-touch input from display device  100 , process the multi-touch input, and produce appropriate graphical output  106  in response. Image source S is described in greater detail below with reference to  FIG. 6 . 
     Display device  100  may include a capacitive touch-sensitive display  108  to enable multi-touch sensing functionality. A schematic view of a partial cross section of an optical stack for capacitive touch-sensitive display  108  is shown in  FIG. 2 . In this embodiment, display  108  includes an optically clear touch sheet  202  having a top surface  204  for receiving touch input, and an optically clear adhesive (OCA) layer  206  bonding a bottom surface of touch sheet  202  to a top surface of a touch sensor  208 . Touch sheet  202  may be comprised of a suitable material, such as glass or plastic. Those of ordinary skill in the art will appreciate that optically clear adhesives (OCAs) refer to a class of adhesives that transmit substantially all (e.g., about 99%) of visible light that is incident upon them. 
     As discussed in further detail below with reference to  FIGS. 3, 4A-4B, and 5A-5B , touch sensor  208  is equipped with a matrix of electrodes comprising capacitive elements positioned a distance below touch sheet  202 . As shown, the electrodes may be formed in two separate layers: a receive electrode layer  210  and a transmit electrode layer  212 , which may each be formed on a respective dielectric substrate comprising materials including but not limited to glass, polyethylene terephthalate (PET), polycarbonate (PC), or cyclic olefin polymer (COP) film. Receive and transmit electrode layers  210  and  212  may be bonded together by a second optically clear adhesive (OCA) layer  211 . Adhesive layer  211  may be an acrylic pressure-sensitive adhesive film, for example. In other embodiments, however, layers  210 ,  211 , and  212  may be integrally formed as a single layer with electrodes disposed on opposite surfaces of the integral layer. 
     Electrode layers  210  and  212  may be formed by a variety of suitable processes. Such processes may include deposition of metallic wires onto the surface of an adhesive, dielectric substrate; patterned deposition of a material that selectively promotes the subsequent deposition of a metal film (e.g., via plating); photoetching; patterned deposition of a conductive ink (e.g., via inkjet, offset, relief, or intaglio printing); filling grooves in a dielectric substrate with conductive ink; selective optical exposure (e.g., through a mask or via laser writing) of an electrically conductive photoresist followed by chemical development to remove unexposed photoresist; and selective optical exposure of a silver halide emulsion followed by chemical development of the latent image to metallic silver, in turn followed by chemical fixing. 
     In one example, metalized sensor films may be disposed on a user-facing side of a substrate, with the metal facing away from the user or alternatively facing toward the user with a protective sheet (e.g., comprised of PET) between the user and metal. Although a transparent conductive oxide (TCO) (e.g. tin-doped indium oxide (ITO)) is typically not used in the electrodes, partial use of TCO to form a portion of the electrodes with other portions being formed of metal is possible. 
     In one example, the electrodes may be thin metal of substantially constant cross section, and may be sized such that they may not be optically resolved and may thus be unobtrusive as seen from a perspective of a user. Materials from which electrodes may be formed include various suitable metals (e.g., aluminum, copper, nickel, silver, gold, etc.), metallic alloys, conductive allotropes of carbon (e.g., graphite, fullerenes, amorphous carbon, etc.), conductive polymers, and conductive inks (e.g., made conductive via the addition of metal or carbon particles). 
     Receive electrode layer  210  may be designated a column electrode layer in which electrodes are at least partially aligned to a longitudinal axis (illustrated as a vertical axis), while transmit electrode layer  212  may be designated a row electrode layer in which electrodes are at least partially aligned to a lateral axis (illustrated as a horizontal axis). Such designation, however, is arbitrary and may be reversed. It will be appreciated that the vertical and horizontal axes depicted herein and other vertical and horizontal orientations are relative, and need not be defined relative to a fixed reference point (e.g., a point on Earth). 
     To detect touch input, transmit electrodes may be successively driven with a time-varying voltage, while the receive electrodes are held at ground and the current flowing into each receive electrode is measured. The electrodes are configured to exhibit a change in capacitance of at least one of the capacitors in the matrix in response to a touch input on top surface  204 . Capacitors may be formed, for example, at each vertical intersection between a transmit electrode and a receive electrode. 
     Changes in capacitance may be detected by a detection circuit as time-varying voltages are applied. Based on the time of detection and the degree of attenuation and/or phase shift in a measured current, the capacitance under test can be estimated and a row and column identified as corresponding to a touch input. The structure of the transmit and receive electrodes is described in greater detail below with reference to  FIGS. 3, 4A-4B, and 5A-5B . 
     Various aspects of touch sensor  208  may be selected to maximize the SNR of capacitance measurements and thus increase the quality of touch sensing. In one approach, the distance between the receive electrodes and a light-emitting display stack  214  is increased. This may be accomplished by increasing the thickness of optically clear adhesive layer  211 , for example, which may reduce the noise reaching the receive electrodes. As non-limiting examples, the thickness of adhesive layer  211  may be less than 1 mm and in some embodiments less than 0.2 mm. The noise reaching the receive electrodes may alternatively or additionally be decreased by increasing the thickness of optically clear adhesive layer  211 . Moreover, the relative arrangement of column and row conductors maximizes the average distance between the column and row conductors in the plane of touch sensor  208 —e.g., in a direction substantially perpendicular to a direction in which light L is emitted from a light-emitting display stack  214 . 
     Continuing with  FIG. 2 , light-emitting display stack  214 , which may be a liquid crystal display (LCD) stack, organic light-emitting diode (OLED) stack, plasma display panel (PDP), or other flat panel display stack is positioned below the electrode layers  210  and  212 . An optically clear adhesive (OCA) layer  216  joins a bottom surface of transmit electrode layer  212  to a top surface of display stack  214 . Display stack  214  is configured to emit light L through a top surface of the display stack, such that emitted light travels in a light emitting direction through layers  216 ,  212 ,  211 ,  210 ,  206 , touch sheet  202 , and out through top surface  204 . In this way, emitted light may appear to a user as a displayed image on top surface  204  of touch sheet  202 . 
     Other embodiments are possible in which layers  211  and/or  216  are omitted. In this example, touch sensor  208  may be air-gapped and optically uncoupled to display stack  214 . Further, layers  210  and  212  may be laminated on top surface  204 . Still further, layer  210  may be disposed on top surface  204  while layer  212  may be disposed opposite and below top surface  204 . 
       FIG. 3  shows an example metal-mesh electrode matrix  300  that may be implemented in a capacitive touch sensor. As described above, electrode matrix  300  may be formed in electrode layers  210  or  212  via a variety of suitable processes, including deposition of metallic wires onto the surface of an adhesive, dielectric substrate; patterned deposition of a material that selectively catalyzes the subsequent deposition of a metal film (e.g., via plating); photoetching; patterned deposition of a conductive ink (e.g., via inkjet, offset, relief, or intaglio printing); filling grooves in a dielectric substrate with conductive ink; selective optical exposure (e.g., through a mask or via laser writing) of an electrically conductive photoresist followed by chemical development to remove unexposed photoresist; and selective optical exposure of a silver halide emulsion followed by chemical development of the latent image to metallic silver, in turn followed by chemical fixing. 
     In this example, four electrodes ( 301 ,  302 ,  303 , and  304 ) are shown. Along with a plurality of additional electrodes, electrodes  301 - 304  may form matrix  300 . In this example, the electrodes extend principally along a first direction Y, and are arrayed periodically along a second direction X, perpendicular to Y. As such, electrodes  301 - 304  constitute column electrodes. Electrodes  301 - 304  are arrayed with a pitch of p e , and thus a spatial frequency of 1/p e . Each electrode is defined by two electrode boundaries (e.g. electrode  301  is defined by boundaries  301   a  and  301   b , electrode  302  is defined by boundaries  302   a  and  302   b , etc.). Electrodes  301 - 304  are depicted as linked-diamond type electrodes, but other electrode shapes, including rectangular or concave polygonal shapes may be used. Electrodes  301 - 304  are flanked by inter-electrode alleys  305 - 309 . The electrode boundaries thus also act as boundaries for the inter-electrode alleys. For example, inter-electrode alley  306  is defined by boundaries  301   b  and  302   a , inter-electrode alley  307  is defined by boundaries  302   b  and  303   a , etc. 
     Each electrode is comprised of a metal mesh  310 . In this example, mesh  310  has a square unit cell with a mesh pitch of p m . However, in other examples, other mesh configurations may be used. The unit cells of the mesh are arrayed periodically along axes U and V, which are respectively separated from electrode axes X and Y by an angle θ. A repeat length may be defined as the distance between instances of identical geometric relationship between the mesh and electrode boundaries in a periodic array of electrodes, where each electrode mesh is derived from a continuously extending mesh. As shown in  FIG. 3A , each electrode  301 ,  302 ,  303 , and  304  has a unique geometric relationship with the mesh contained therein ( 310   a ,  310   b ,  301   c , and  310   d , respectively). Indeed, each diamond of each electrode has a unique geometric relationship with the metal mesh. 
     Arbitrary combinations of p m , p e , and θ typically result in either an infinite repeat length, or a finite repeat length that is longer than the dimensions of a given touch sensor. In either case, the electrode structure is effectively non-repeating. Any attempt to step-and-repeat such a mesh results in a discontinuity in the mesh that may be perceived by the display user, even if the individual mesh lines are too small for the user to visually resolve. There are, however, discrete combinations of these values that result in a repeat length that is a small integer multiple n of the electrode pitch. These combinations thus enable a metal mesh electrode structure in which the geometric relationship between the mesh and the electrode boundaries exactly repeats over a finite, relatively small number of electrodes. This allows both the design process and the tool mastering process to employ extensive step-and-repeat of a relatively simple design element. 
     Such combinations simultaneously satisfy the following equations:
 
θ=arctan ( a/b )  Equation (1)
 
 n*p   e   =m *sqrt( a   2   +b   2 )* p   m   Equation (2)
 
     In Equation (1) and Equation (2), a, b, m, and n are positive integers. These values can be chosen to sufficiently approximate the values of p m  and θ chosen to minimize moirés between the periodic display pixels and periodic mesh openings, for a given value of p e . Such a mesh exactly repeats itself with period (n*p e ) along the X and Y directions, so that only n unique electrodes are required regardless of the number of electrodes in the array. Furthermore, for electrodes of typical linked-diamond shape, the structure within each electrode repeats every n diamonds. These properties allow the tooling for an arbitrarily large electrode array to be designed and fabricated entirely of relatively small repeating units. 
       FIGS. 4A and 4B  show an example electrode matrix  400  for a capacitive touch display system that does not satisfy Equations (1) and (2) as described herein. Four electrodes ( 401 ,  402 ,  403 , and  404 ) are shown as representative electrodes of a plurality of electrodes that make up matrix  400 . Each electrode is defined by a pair of boundaries ( 401   a  and  401   b ,  402   a  and  402   b ,  403   a  and  403   b ,  404   a  and  404   b , respectively). Electrodes  401 - 404  extend principally along a first direction Y, and are arrayed periodically along a second direction X, perpendicular to Y with a pitch of p e , and thus a spatial frequency of 1/p e . Electrodes  401 - 404  are flanked by inter-electrode alleys  405 - 409 . 
     Metal mesh  410  forms electrodes  401 - 404 . Mesh  410  has a square unit cell with a mesh pitch of p m . The unit cells of the mesh  410  are arrayed periodically along axes U and V, which are respectively separated from electrode axes X and Y by an angle θ. Mesh  410  also covers inter-electrode alleys  405 - 409 . The electrode mesh and alley mesh are continuous, except that within the inter-electrode alleys, mesh  410  is interrupted by numerous small gaps to make it electrically discontinuous. 
     In this example, the following parameters are targeted to minimize moirés when used with an LCD panel comprising square RGB pixels on a 630 μm pitch: θ=29°, p e =6.5 mm, p m =360 μm. Because arctan (29°) is an irrational number, there exist no integers a and b that satisfy equation (1) above. There also exist no integers a, b, m, and n that satisfy equation (2). The repeat length of this matrix is infinite. Any attempt to step-and-repeat a matrix having these parameters, regardless of the size of the repeating unit, results in a discontinuity of the mesh at the edges of adjacent repeated units. 
       FIG. 4B  shows a magnified view  420  of the mesh misalignment at the common edges of four repeating units  421 ,  422 ,  423 , and  424  which intersect at unit edges  425  and  426 . In particular, discontinuities in the electrode mesh may be seen at  430 , while discontinuities in the alley mesh may be seen at  431 . These mesh discontinuities result in an excess of pixel occlusion that is perceptible to the display user as a grid of darkened lines along the edges of the repeated units. 
       FIGS. 5A and 5B  show an example electrode matrix  500  for a capacitive touch display system that does satisfy both Equations (1) and (2) as put forth herein. Four electrodes ( 501 ,  502 ,  503 , and  504 ) are shown as representative electrodes of a plurality of electrodes that make up matrix  500 . Each electrode is defined by a pair of boundaries ( 501   a  and  501   b ,  502   a  and  502   b ,  503   a  and  503   b ,  504   a  and  504   b , respectively). Electrodes  501 - 504  extend principally along a first direction Y, and are arrayed periodically along a second direction X, perpendicular to Y with a pitch of p e , and thus a spatial frequency of 1/p e . Electrodes  501 - 504  are flanked by inter-electrode alleys  505 - 509 . 
     Metal mesh  510  forms electrodes  501 - 504 . Mesh  510  has a square unit cell with a mesh pitch of p m . The unit cells of the mesh  510  are arrayed periodically along axes U and V, which are respectively separated from electrode axes X and Y by an angle θ. Mesh  510  also covers inter-electrode alleys  505 - 509 . The electrode mesh and alley mesh are continuous, except that within the inter-electrode alleys, mesh  510  is interrupted by numerous small gaps to make it electrically discontinuous. 
     The example in  FIG. 5A  shows a unit of an electrode matrix with a finite repeat length, in which a=5, b=9, m=7, and n=4. Holding p e constant at 6.5 mm, p m ≈360.8 μm and θ≈29.06°, sufficiently close to the target parameters to minimize the visibility of moirés. Because tan (θ) is a rational number, and this combination of a, b, m, n, p e , and p m  satisfies Equation (2), this matrix is exactly periodic along X and Y with a repeat length of 26 mm (4*p e ), and any 26 mm×26 mm unit can be stepped-and-repeated with exact alignment of the mesh at the edges of adjacent units. 
       FIG. 5B  shows a magnified view  520  of the mesh alignment at the common edges of four repeating units  521 ,  522 ,  523 , and  524  which intersect at unit edges  525  and  526 . In particular, the continuity in the electrode mesh may be seen at  530 , while continuity in the alley mesh may be seen at  531 . 
     When used in a touch display system having a diagonal display dimension of 84″, this particular step-and-repeat results in an approximately 3000-fold reduction in the complexity of CAD data required to represent the electrode matrix and its tooling. 
     By appropriate choice of a, b, m, and n, an electrode matrix can approximate any desired  0  and pm closely enough to not adversely affect moiré performance, typically without n being greater than 16. For example values for a, b, m, and n may be selected such that 1≦a≦20; 1≦b≦20; 1≦m≦16; and 1≦n≦16. More specifically, values for a, b, m, and n may be selected such that 3≦a≦13; 4≦b≦16; 1≦m≦8; and 1≦n≦8. 
     Although the example shown in  FIGS. 5A-5B  includes a mesh having square openings, the proposed solution is equally applicable to a mesh having openings of any shape, provided the unit cell of the mesh is square. 
       FIG. 6  illustrates an exemplary image source S according to one embodiment of the present invention. As discussed above, image source S may be an external computing device, such as a server, laptop computing device, set top box, game console, desktop computer, tablet computing device, mobile telephone, or other suitable computing device. Alternatively, image source S may be integrated within display device  100 . 
     Image source S includes a processor, volatile memory, and non-volatile memory, such as mass storage, which is configured to store software programs in a non-volatile manner. The stored programs are executed by the processor using portions of volatile memory. Input for the programs may be received via a variety of user input devices, including touch sensor  208  integrated with display  108  of display device  100 . The input may be processed by the programs, and suitable graphical output may be sent to display device  100  via a display interface for display to a user. 
     The processor, volatile memory, and non-volatile memory may be formed of separate components, or may be integrated into a system on a chip, for example. Further the processor may be a central processing unit, a multi-core processor, an ASIC, system-on-chip, or other type of processor. In some embodiments, aspects of the processor, volatile memory and non-volatile memory may be integrated into devices such as field-programmable gate arrays (FPGAs), program- and application-specific integrated circuits (PASIC/ASICs), program- and application-specific standard products (PSSP/ASSPs), system-on-a-chip (SOC) systems, and complex programmable logic devices (CPLDs), for example. 
     A communications interface may also be provided to communicate with other computing devices, such as servers, across local and wide area network connections, such as the Internet. 
     The non-volatile memory may include removable media and/or built-in devices. For example, non-volatile memory may include optical memory devices (e.g., CD, DVD, HD-DVD, Blu-Ray Disc, etc.), semiconductor memory devices (e.g., FLASH, EPROM, EEPROM, etc.) and/or magnetic memory devices (e.g., hard disk drive, floppy disk drive, tape drive, MRAM, etc.), among others. 
     Removable computer readable storage media (CRSM) may be provided, which may be used to store data and/or instructions executable to implement the methods and processes described herein. Removable computer-readable storage media may take the form of CDs, DVDs, HD-DVDs, Blu-Ray Discs, EEPROMs, and/or floppy disks, among others. 
     Although the non-volatile memory and CRSM are physical devices configured to hold instructions for a duration of time, typically even upon power down of the image source, in some embodiments, aspects of the instructions described herein may be propagated by a computer readable communication medium, such as the illustrated communications bus, in a transitory fashion by a pure signal (e.g., an electromagnetic signal, an optical signal, etc.) that is not held by a physical device for at least a finite duration. 
     The term “program” may be used to describe software firmware, etc. of the system that is implemented to perform one or more particular functions. In some cases, such a program may be instantiated via the processor executing instructions held by non-volatile memory, using portions of volatile memory. It is to be understood that different programs may be instantiated from the same application, service, code block, object, library, routine, API, function, etc. Likewise, the same program may be instantiated by different applications, services, code blocks, objects, routines, APIs, functions, etc. The term “program” is meant to encompass individual or groups of executable files, data files, libraries, drivers, scripts, database records, etc. 
     It will be understood that the configurations and/or approaches described herein are exemplary in nature, and that these specific embodiments or examples are not to be considered in a limiting sense, because numerous variations are possible. The specific routines or methods described herein may represent one or more of any number of processing strategies. As such, various acts illustrated and/or described may be performed in the sequence illustrated and/or described, in other sequences, in parallel, or omitted. Likewise, the order of the above-described processes may be changed. 
     The subject matter of the present disclosure includes all novel and nonobvious combinations and subcombinations of the various processes, systems and configurations, and other features, functions, acts, and/or properties disclosed herein, as well as any and all equivalents thereof. 
     In one example, an array of electrodes is provided, comprising a plurality of electrodes, each electrode extending along a first direction X and periodically arrayed along a second direction Y perpendicular to X at a pitch p e , wherein each electrode comprises a continuous periodic metal mesh having a square unit cell of edge length p m , the square unit cell having axes displaced by an oblique angle θ from X and Y, wherein θ=arctan (a/b) and p m =n*p e /(m*sqrt(a 2 +b 2 )), and a, b, m, and n are positive integers. In such an example, inter-electrode alleys between the electrodes may additionally or alternatively be filled with an electrically discontinuous opaque mesh having a unit cell of edge length p m  aligned with meshes of the electrodes. In such an example, the electrodes may additionally or alternatively be concave polygonal in shape. In such an example, the electrodes may additionally or alternatively be linked-diamond type electrodes. In such an example, the array of electrodes may additionally or alternatively comprise a plurality of repeating electrode units comprising one or more electrode segments extending along the direction X and repeating along the direction X and the direction Y at a period of  n *p e . In such an example, the array of electrodes may be additionally or alternatively configured such that 1≦a≦20, 1≦b≦20, 1≦m≦16, and 1≦n≦16. Any or all of the above-described examples may be combined in any suitable manner in various implementations. 
     In another example, a capacitive touch sensor is provided, comprising one or more arrays of electrodes, each array of electrodes comprising a plurality of electrodes, each electrode extending along a first direction X, and periodically arrayed along a second direction Y perpendicular to the first direction X at a pitch p e , wherein each electrode comprises a continuous periodic metal mesh having a square unit cell of edge length p m , the square unit cell having axes displaced by an oblique angle θ from the X and Y, wherein θ=arctan (a/b) and p m =n*p e /(m*sqrt(a 2 +b 2 )), and a, b, m, and n are positive integers. In such an example inter-electrode alleys between the electrodes may additionally or alternatively be filled with an electrically discontinuous opaque mesh having a unit cell of edge length p m  aligned with meshes of the electrodes. In such an example the electrodes may additionally or alternatively be concave polygonal in shape. In such an example the electrodes may additionally or alternatively be linked-diamond type electrodes. In such an example, the capacitive touch sensor may additionally or alternatively comprise a plurality of repeating electrode units comprising one or more electrode segments extending along the direction X, and repeating along the direction X and the direction Y at a period of  n *p e . In such an example, the capacitive touch sensor may additionally or alternatively be configured such that 1≦a≦20, 1≦b≦20, 1≦m≦16, and 1≦n≦16. Any or all of the above-described examples may be combined in any suitable manner in various implementations. 
     In yet another example, a touch sensing display device is provided, comprising: a display device including periodically arrayed pixels, and a capacitive touch sensor, comprising one or more arrays of electrodes, each array of electrodes comprising a plurality of electrodes, each electrode extending along a first direction X, and periodically arrayed along a second direction Y perpendicular to the first direction X at a pitch p e , wherein each electrode comprises a continuous periodic metal mesh having a square unit cell of edge length p m , the square unit cell having axes displaced by an oblique angle θ from X and Y, wherein θ=arctan (a/b) and p m =n*p e /(m*sqrt(a 2 +b 2 )), and a, b, m, and n are positive integers. In such an example, inter-electrode alleys between the electrodes may additionally or alternatively be filled with an electrically discontinuous opaque mesh having a unit cell of edge length p m  aligned with meshes of the electrodes. In such an example, the electrodes may additionally or alternatively be concave polygonal in shape. In such an example, the electrodes may additionally or alternatively be linked-diamond type electrodes. In such an example, the touch sensing display device may additionally or alternatively comprise a plurality of repeating electrode units comprising one or more electrode segments extending along the direction X and repeating along the direction X and the direction Y directions at a period of  n *p e . In such an example, the touch sensing display device may additionally or alternatively be configured such that 1≦a≦20, 1≦b≦20, 1≦m≦16, and 1≦n≦16. In such an example, the display device may additionally or alternatively have a diagonal display dimension of at least 0.5 meters. In such an example, the one or more arrays of electrodes may additionally or alternatively comprise a receive electrode array and a transmit electrode array. Any or all of the above-described examples may be combined in any suitable manner in various implementations.