Electro-optic displays

Abstract

A method for driving an electro-optic display having a plurality of display pixels is described. The method includes determining a stress level of a display pixel based on at least one previous update of the optical state of a display pixel of the electro-optic display; and receiving one of a request to update the optical state of the display pixel. The method also includes applying a driving waveform from a first or second update scheme to the display pixel based on an update scheme for the previous update of the display pixel and a comparison of the stress level with two stress level thresholds.

Description

Technical Field

[0001] [Reference Materials for Comparison of Related Applications] This application claims priority to U.S. Provisional Application No. 63 / 492,217, filed March 24, 2023, the entire contents of which are incorporated herein by reference.

[0002] This application is related to U.S. Patent Nos. 5,930,026; 6,445,489; 6,504,524; 6,512,354; 6,531,997; 6,753,999; 6,825,970; 6,900,851; 6,995,550; 7,012,600; 7,023,420; 7,034,783; 7,116,466; 7,119,772; 7,193,625; 7,202,847; 7,259,744; 7,304,787; and 7,312. ,794;7,327,511;7,453,445;7,492,339;7,528,822;7,545,358;7,583,251;7,602,374;7,612,760;7,679,599;7,688,297;7,729,039;7,733,311;7,733,335;7,787,169;7,952,557;7,956,841;7,999,787;8,077,141;10,672,350; 11,145,261; and 11,462,183, and U.S. Patent Application Publications 2003 / 0102858; 2005 / 0122284; 2005 / 0179642; 2005 / 0253777; 2006 / 0139308; 2007 / 0013683; 2007 / 0091418; 2007 / 0103427; 2007 / 0200874; 2008 / 0024429; 2008 / 0024482; 2008 / 0048969; 2008 This is related to / 0129667;2008 / 0136774;2008 / 0150888;2008 / 0291129;2009 / 0174651;2009 / 0179923;2009 / 0195568;2009 / 0256799;2009 / 0322721;2010 / 0045592;2010 / 0220121;2010 / 0220122;2010 / 0265561;2011 / 0285754; and 2022 / 0415268.

[0003] For convenience, the aforementioned patents and applications are collectively referred to below as the "MEDEOD" (Method for Driving an Electro-Optical Display) applications. The entire contents of these patents and pending applications, as well as all other U.S. patents and published pending applications, or other published works mentioned below, are incorporated herein by reference.

[0004] This invention relates to a method for driving electro-optic displays (particularly bistable electro-optic displays) and the apparatus used in this method. More specifically, the invention relates to a driving method that can allow for reduction of ghosting and edge effects, as well as flicker reduction, in such displays. The invention is particularly, but not exclusively, intended for use in particle-based electrophoretic displays, wherein one or more types of charged particles exist in a fluid and move through the fluid under the influence of an electric field to alter the display's appearance. Prior Technology

[0005] The term "electro-optic," used herein in its conventional sense for imaging techniques, refers to a material having first and second display states that differ in at least one optical property, which can be changed from the first display state to the second display state by applying an electric field to the material. While the optical property is typically color perceptible to the human eye, it can be another optical property, such as light transmission, reflection, emission, or, in the case of a display intended for machine reading, a false color in the sense of a change in reflectivity at electromagnetic wavelengths outside the visible light range.

[0006] The term "gray state" is used herein in its conventional sense within imaging technology to refer to the state between two extreme optical states of a pixel, and does not necessarily imply a black-white transition between these two extreme states. For example, several E Ink patents and published applications mentioned below describe electrophoretic displays where the extreme states are white and dark blue, such that the intermediate "gray state" is actually light blue. More precisely, as stated, the change in optical state may not be a color change at all. The terms "black" and "white" can be used below to refer to the two extreme optical states of a display, and should be understood to generally include extreme optical states that are not black and white at all, such as the aforementioned white and dark blue states. The term "monochrome" can be used below to refer to a driving scheme that drives pixels only to their two extreme optical states that do not have an intermediate gray state.

[0007] The terms "bistable" and "bistability" are used herein in their conventional sense to refer to a display comprising display elements having first and second display states that are different in at least one optical property, and to present either the first or second display state after any given element is driven by an addressing pulse of finite duration, and to that state persisting at least several times, for example, at least four times, after the addressing pulse terminates; the addressing pulse requires a minimum duration to change the state of the display element. U.S. Patent No. 7,170,670 shows that some particle-based electrophoretic displays with grayscale capabilities are stable not only in their extreme black and white states but also in their intermediate gray states, and so are some other types of electro-optical displays. This type of display may be appropriately called multi-stable rather than bistable, but for convenience, the term "bistable" may be used herein to encompass both bistable and multi-stable displays.

[0008] The term "pulse" is used herein in its conventional sense as the integral of voltage with respect to time. However, some bistable electro-optic dielectrics act as charge transducers, and for such dielectrics, an alternative definition of a pulse can be used: the integral of current with respect to time (which equals the total amount of charge applied). The appropriate definition of a pulse should be used depending on whether the dielectric acts as a voltage-time pulse transducer or a charge pulse transducer.

[0009] Much of the following discussion will focus on methods for driving one or more pixels of an electro-optic display by transitions from an initial grayscale to a final grayscale (which may or may not differ from the initial grayscale). The term "waveform" will be used to refer to the entire voltage-to-time curve used to achieve a transition from a particular initial grayscale to a particular final grayscale. Typically, such a waveform will consist of a plurality of waveform elements; wherein these elements are essentially rectangular (i.e., wherein a given element includes the application of a fixed voltage for a period of time); these elements may be referred to as "pulses" or "driving pulses." The term "driving scheme" indicates that a set of waveforms is sufficient to achieve all possible transitions between grayscales of a particular display. A display may use more than one driving scheme; for example, U.S. Patent No. 7,012,600 teaches that the driving scheme may need to be modified based on parameters such as the temperature of the display or the time the display has been used in its lifetime, and therefore, a display may have a plurality of different driving schemes for different temperatures, etc. A set of driving schemes used in this manner may be referred to as a "set of related driving schemes." As described in several of the aforementioned MEDEOD applications, more than one driving scheme can be used simultaneously in different areas of the same display, and a group of driving schemes used in this manner can be called a "group of synchronous driving schemes".

[0010] Several types of electro-optic displays are known. One type of electro-optic display is, for example, the rotating bichromal member type described in U.S. Patents 5,808,783; 5,777,782; 5,760,761; 6,054,071; 6,055,091; 6,097,531; 6,128,124; 6,137,467; and 6,147,791 (although this type of display is often referred to as a "rotating bichromal ball" display, the term "rotating bichromal member" is preferred because in some of the aforementioned patents, the rotating member is not spherical). Such a display uses a large number of small objects (typically spherical or cylindrical) having two or more parts with different optical properties and an internal dipole. These objects are suspended in liquid-filled bubbles within a matrix, wherein the liquid-filled bubbles allow the objects to rotate freely. By applying an electric field, these objects are rotated to various positions and the portion of these objects visible through a viewing surface is altered, thereby changing the display. This type of electro-optic medium is typically bistable.

[0011] Another type of electro-optic display uses an electrochromic medium, such as an electrochromic film in the form of a nanochromic film, comprising an electrode at least partially composed of a semiconductor metal oxide and a plurality of dye molecules with reversible color-changing capabilities attached to the electrode; see, for example, ORegan, B., et al., Nature 1991, 353, 737; and Wood, D., Information Display, 18(3), 24 (March 2002). See also Bach, U., et at., Adv. Mater., 2002, 14(11), 845. This type of nanochromic film is also described, for example, in U.S. Patents 6,301,038; 6,870,657; and 6,950,220. This type of medium is also typically bistable.

[0012] Another type of electro-optic display is the electro-wetting display developed by Philips and described in Hayes, RA, et al., “Video-Speed ​​Electronic Paper Based on Electrowetting”, Nature, 425, 383-385 (2003). U.S. Patent No. 7,420,549 shows that such an electro-wetting display can be fabricated to be bistable.

[0013] One type of electro-optic display has been the subject of intensive research for several years: particle-based electrophoretic displays, in which multiple charged particles move through a fluid under the influence of an electric field. Compared to liquid crystal displays (LCDs), electrophoretic displays offer superior brightness and contrast, wide viewing angles, dual stability, and low power consumption. However, long-term image quality issues hinder their widespread adoption. For example, the particles constituting an electrophoretic display tend to settle, leading to a shorter lifespan for these displays.

[0014] As mentioned above, the electrophoretic medium requires the presence of a fluid. In most prior art electrophoretic media, this fluid system is liquid, but a gaseous fluid can be used to produce the electrophoretic medium; see, for example, Kitamura, T., et al., Electrical toner movement for electronic paper-like display, IDW Japan, 2001, Paper HCS1-1 and Yamaguchi, Y., et al., Toner display using insulative particles charged triboelectrically, IDW Japan, 2001, Paper AMD4-4. See also U.S. Patents 7,321,459 and 7,236,291. When such media are used in an orientation that allows particle settling (e.g., in the presentation of media arranged in a vertical plane), such gas-based electrophoretic media appear to be susceptible to the same type of problems caused by particle settling as liquid-based electrophoretic media. More precisely, particle sedimentation appears to be a more serious problem in gas-based electrophoretic media than in liquid-based electrophoretic media, because the lower viscosity of gas suspensions allows for faster sedimentation of these electrophoretic particles compared to liquid suspensions.

[0015] Numerous patents and applications, assigned to or in the name of the Massachusetts Institute of Technology (MIT) and E Ink Corporation, describe various techniques used in capsule electrophoresis and other electro-optic media. Such capsule media comprise a plurality of small capsules, each capsule comprising an internal phase of electrophoretically moving particles contained in a fluid medium and a capsule wall surrounding the internal phase. Typically, these capsules are held in a polymeric binder to form a coherent layer between two electrodes. The techniques described in these patents and applications include: (a) Electrophoretic particles, fluids, and fluid additives; see, for example, U.S. Patent Nos. 7,002,728 and 7,679,814; (b) Capsules, binders, and encapsulation processes; see, for example, U.S. Patent Nos. 6,922,276 and 7,411,719; (c) Thin films and subassemblies containing electro-optic materials; see, for example, U.S. Patent Nos. 6,982,178 and 7,839,564; (d) Backplates, adhesive layers and other auxiliary layers used in displays, and methods thereof; see, for example, U.S. Patent Nos. 7,116,318 and 7,535,624; (e) Color formation and color adjustment; see, for example, U.S. Patent No. 7,075,502 and U.S. Patent Application Publication No. 2007 / 0109219; (f) A method for driving a display; see the aforementioned MEDEOD application; (g) Applications in displays; see, for example, U.S. Patent No. 7,312,784 and U.S. Patent Application Publication No. 2006 / 0279527; (h) Non-electrophoretic displays, as described in U.S. Patent Nos. 6,241,921, 6,950,220 and 7,420,549 and U.S. Patent Application Publication No. 2009 / 0046082.

[0016] Many of the aforementioned patents and applications recognize that the walls surrounding discrete microcapsules in a capsule-type electrophoretic medium can be replaced by a continuous phase, thereby producing a so-called polymer dispersion electrophoretic display, wherein the electrophoretic medium comprises electrophoretic fluids of a plurality of discrete droplets and a continuous phase of polymeric material, and even without discrete capsule membranes associated with each individual droplet, the electrophoretic fluids of the discrete droplets within such a polymer dispersion electrophoretic display can be considered as capsules or microcapsules; see, for example, U.S. Patent No. 6,866,760. Thus, for the purposes of this application, such polymer dispersion electrophoretic media are considered a subtype of capsule-type electrophoretic media.

[0017] One related type of electrophoretic display is the so-called "microcellular electrophoresis display." In a microcellular electrophoresis display, instead of encapsulating charged particles and fluids in microcapsules, they are held within a plurality of cavities formed in a carrier medium (e.g., a polymeric membrane). See, for example, U.S. Patents 6,672,921 and 6,788,449, which were assigned to Sipix Imaging Inc.

[0018] Although electrophoretic media are typically opaque (because, for example, in many electrophoretic media, particles substantially block the transmission of visible light through the display) and operate in reflective mode, some electrophoretic displays can operate in a so-called "shutter mode," in which one display state is substantially opaque and another display state is transparent. See, for example, U.S. Patents 5,872,552; 6,130,774; 6,144,361; 6,172,798; 6,271,823; 6,225,971; and 6,184,856. Dielectrophoretic displays (similar to electrophoretic displays but dependent on changes in electric field strength) can operate in a similar mode; see U.S. Patent 4,418,346. Other types of electro-optic displays can also operate in shutter mode. Electro-optic media operating in raster mode can be used in the multilayer structure of a full-color display; in such a structure, at least one layer adjacent to the viewing surface of the display operates in raster mode to expose or hide a second layer further away from the viewing surface.

[0019] An encapsulated electrophoretic display typically does not suffer from the clustering and settling failure modes of conventional electrophoresis apparatus and offers additional advantages, such as the ability to print or coat the display on a variety of flexible and rigid substrates. (The use of the word "printing" is intended to encompass all forms of printing and coating, including but not limited to: pre-metered coatings (e.g., patch die coating, slot or extrusion coating, slide or cascade coating, and curtain coating); roll coating (e.g., knife over roll coating and forward and reverse roll coating); gravel coating; dip coating; spray coating; meniscus coating; spin coating; brush coating; air-knife coating; silk screen printing processes; electrostatic printing processes; thermal printing processes; inkjet printing processes.) Jet printing processes; electrophoretic deposition (see U.S. Patent No. 7,339,715); and other similar techniques). Therefore, the resulting display can be flexible. Furthermore, because the display medium can be printed (using various methods), the display itself can be manufactured inexpensively.

[0020] Other types of electro-optic media can also be used in the display of this invention.

[0021] The bistable and multistable behavior of particle-based electrophoretic displays and other electro-optic displays exhibiting similar behavior (for convenience, such displays can be referred to below as "pulse-driven displays") contrasts sharply with the behavior of conventional liquid crystal ("LC") displays. Twisted nematic liquid crystals are not bistable or multistable, but they can act as voltage converters, such that applying a given electric field to a pixel of such a display will produce a specific grayscale on that pixel, regardless of the grayscale that was previously present on that pixel. Furthermore, LC displays are driven in only one direction (from nontransmissive or "dark" to transmissive or "bright"); the reverse transition from a brighter state to a darker state can be achieved by reducing or removing the electric field. Finally, the grayscale of a pixel in an LC display is not affected by the polarity of the electric field, but only by its size, and more precisely, for technical reasons, commercial LC displays often reverse the polarity of the driving electric field at frequency intervals. In contrast, bistable electro-optic displays can largely act as pulse converters, so that the final state of a pixel depends not only on the applied electric field and the time of application, but also on the state of the pixel before the electric field is applied.

[0022] Regardless of whether the electro-optic medium used is steady-state, for a high-resolution display to be achieved, individual pixels of the display must be addressable without interference from neighboring pixels. One method to achieve this is to provide an array of nonlinear elements (e.g., transistors or diodes) with at least one nonlinear element associated with each pixel to produce an "active matrix" display. An addressable pixel electrode is used to address a pixel and is connected to a suitable voltage source via the associated nonlinear element. Typically, when the nonlinear element is a transistor, the pixel electrode is connected to the drain of the transistor, and this configuration will be used in the following description, but it is essentially arbitrary, and the pixel electrode can be connected to the source of the transistor. Traditionally, in high-resolution arrays, pixels are configured in a two-dimensional array of columns and rows, such that any particular pixel is uniquely defined by the intersection of a particular column and a particular row. The sources of all transistors in each row are connected to a single row electrode, and the gates of all transistors in each column are connected to a single column electrode; furthermore, the source-to-column and gate-to-row assignments are conventional, but essentially arbitrary, and can be reversed if necessary. These column electrodes are connected to a column driver that essentially ensures that only one column is selected at any given time; that is, a voltage is applied to the selected column electrode to ensure that all transistors in that selected column are turned on, while a voltage is applied to all other columns to ensure that all transistors in those unselected columns remain off. These row electrodes are connected to a plurality of row drivers that apply voltages to different row electrodes selected to drive the pixels in the selected column to their desired optical state. (These aforementioned voltages are relative to a common front voltage, which is conventionally located on the opposite side of the electro-optic medium away from the nonlinear array and extends across the entire display.) After a preselected interval called "line address time," the selected column is deselected, the next column is selected, and the voltage on the row drivers is changed to write the next line of the display. This procedure is repeated to write the entire display column by column.

[0023] Initially, it seemed that the ideal method for addressing such pulse-driven electro-optic displays was the so-called "general grayscale image stream," in which a controller schedules each write of the image so that each pixel transitions directly from its initial grayscale to its final grayscale. However, inevitably, there are some errors in the written image on a pulse-driven display. Some of these errors encountered in practice include: (a) Prior state dependence: For at least some electro-optic media, the pulse required to switch a pixel to a new optical state depends not only on the currently desired optical state, but also on the pixel's previous optical state. (b) Dwell time dependence: For at least some electro-optic media, the number of pulses required to switch a pixel to a new optical state depends on the time that pixel spends in its various optical states. The exact nature of this dependence is not well understood, but generally, the longer the pixel remains in its current optical state, the more pulses are required. (c) Temperature dependence: The pulse required to switch a pixel to a new optical state is highly temperature dependent. (d) Humidity dependence: For at least some types of electro-optic media, the pulse required to switch a pixel to a new optical state is dependent on the ambient humidity. (e) Mechanical uniformity: The pulse required to switch a pixel to a new optical state may be affected by mechanical variations in the display (e.g., variations in the thickness of the electro-optic medium or associated adhesive). Other types of mechanical uniformity may be caused by unavoidable variations in the medium between different production batches, manufacturing tolerances, and material variations. (f) Voltage errors: Due to the unavoidable slight error in the voltage transmitted by the driver, the actual pulse applied to a pixel will inevitably be slightly different from the theoretically applied pulse.

[0024] Grayscale image streams typically experience an "accumulation of errors" phenomenon. For example, imagine that temperature dependence causes 0.2L* in the positive direction during each transfer (where L* has the general CIE definition: L*=116(R / R0)1 / 3-16, The R-coefficient and R0-coefficient (standard reflectance values) represent errors. After 50 transfers, this error will accumulate to 10L*. Perhaps more realistically, the average error in each transfer (expressed as the difference between the display's theoretical and actual reflectance values) is ±0.2L*. After 100 consecutive transfers, these pixels will display an average deviation of 2L* from their desired state; such a deviation is noticeable to the average viewer in certain types of images.

[0025] Error accumulation applies not only to temperature-related errors but also to all types of errors listed above. As described in U.S. Patent No. 7,012,600, compensation for such errors is possible, but only with limited accuracy. For example, temperature errors can be compensated using a temperature sensor and a look-up table, but the temperature sensor has limited resolution and can only read temperatures slightly different from those of the electro-optic medium. Similarly, dependencies between previous states can be compensated by storing previous states and using a multidimensional transition matrix, but the controller memory limits the number of states that can be recorded and the size of the transition matrix that can be stored, thus limiting the accuracy of this type of compensation.

[0026] Therefore, a typical grayscale image stream requires very precise control of external pulses to provide good results, and it has been found through experience that, given the current state of electro-optical display technology, a typical grayscale image stream is not feasible in commercial displays.

[0027] In some cases, it may be desirable for a single display to use multiple driving schemes. For example, a display capable of more than two grayscale levels can use a grayscale driving scheme ("GSDS") that enables transitions between all possible grayscale levels and a monochrome driving scheme ("MDS") that enables transitions between only two grayscale levels, wherein the MDS provides faster rewriting of the display compared to the GSDS. The MDS is used when all pixels that change during a display rewriting implement the transitions between only two grayscale levels used by the MDS. For example, the aforementioned U.S. Patent No. 7,119,772 describes a display in the form of an e-book or a similar device capable of displaying grayscale images and also capable of displaying a monochrome dialog box that allows a user to access text about the displayed image. When a user accesses the text, a fast MDS is used for rapid updates of the dialog box, thus providing the user with rapid confirmation of the text accessed. On the other hand, a slower GSDS is used when changing the entire grayscale image displayed on the display.

[0028] Alternatively, the display can use both GSDS and a "Direct Update" driving scheme ("DUDS"). DUDS can have two or more gray levels, typically fewer than GSDS, but the most important characteristic of DUDS is that it handles the transition from the initial gray level to the final gray level with a simple unidirectional drive, as opposed to the "indirect" transition often used in GSDS, where in at least some transitions, a pixel is driven from the initial gray level to an extreme optical state and then driven in the opposite direction to the final gray level; in some cases, the transition can be achieved by driving from the initial gray level to an extreme optical state, from there to the opposite extreme optical state, and then only to the final extreme optical state. See, for example, the driving scheme described in Figures 11A and 11B of the aforementioned U.S. Patent No. 7,012,600. Therefore, current electrophoretic displays can have an update time in grayscale mode that is about two or three times the length of the saturation pulse (where the "length of the saturation pulse" is defined as the time period at a specific voltage sufficient to drive the pixels of the display from one extreme optical state to another), or about 700-900 milliseconds, while DUDS has a maximum update time equal to the length of the saturation pulse, or about 200-300 milliseconds.

[0029] However, variations in driving schemes are not limited to differences in the number of gray levels used. For example, driving schemes can be categorized into global drive schemes, where a driving voltage is applied to every pixel in the region where the global update driving scheme (more accurately called a "global complete" or "GC" driving scheme) is applied (this region can be the entire display or some defined portion thereof); and partial update driving schemes, where a driving voltage is applied only to pixels undergoing non-zero transitions (i.e., transitions where the initial gray level and the final gray level are different from each other), but no driving voltage is applied during zero transitions (where the initial gray level and the final gray level are the same). An intermediate form of driving scheme (called a "global limited" or "GL" driving scheme) is similar to the GC driving scheme, except that no driving voltage is applied to pixels undergoing zero, white-to-white transitions. In displays used as e-book readers, for example (which display black text against a white background), there are many white pixels, particularly in the margins and between lines of text that remain unchanged from one page to the next; therefore, not rewriting these white pixels can substantially reduce the noticeable "flickering" of display rewriting. However, some problems persist in this type of GL-driven scheme.

[0030] First, as detailed in some of the aforementioned MEDEOD applications, bistable electro-optic media are generally not perfectly bistable, and pixels in an extreme optical state gradually drift toward an intermediate grayscale over a period of minutes to hours. Specifically, pixels driven to white slowly drift toward a light gray. Therefore, if in a GL-driven scheme a white pixel is allowed to remain undriven during some page turns (while other white pixels, such as those constituting the text characters, are driven during this time), the most recently updated white pixel will be slightly brighter than the undriven white pixel, and finally, even to an untrained user, the difference will become noticeable.

[0031] These drifts can also be caused by "residual voltage," a term used to describe the persistent or decaying voltage (also known as open-circuit potential, typically measured in volts or millivolts) that may remain in an electro-optic display after the addressing pulse (a voltage pulse used to change the optical state of an electro-optic medium) has terminated. Residual voltage can cause optical state drift because the optical state of a pixel may depend on the pixel's residual voltage, and the residual voltage of a pixel may decay over time.

[0032] Secondly, such residual voltage can adversely affect the images displayed on electro-optical displays, including but not limited to the so-called "ghosting" phenomenon, where traces of the previous image remain visible after the display has been rewritten. Residual voltage may cause edge effects, such as "edge ghosting," a type of ghosting where the outline (edge) of a portion of the previous image remains visible.

[0033] Furthermore, in monochrome and color systems, the electric field generated by the pixel electrode tends to affect a wider electro-optical medium region than the pixel electrode itself, such that, in effect, the optical state of one pixel extends into a portion of the region of an adjacent pixel. For example, when an undriven pixel is adjacent to a newer pixel, a phenomenon called "blooming" occurs, in which the driving of the driven pixel causes a change in the optical state over an area slightly larger than the driven pixel, and this area encroaches into the region of the adjacent pixel. Such blooming manifests itself as an edge effect along the edge of the undriven pixel adjacent to the driven pixel. In some cases, driving adjacent pixels in the region between pixels results in a final optical state that differs from the optical state achieved by any one of the adjacent pixels on its own. This final optical state in the region between adjacent pixels is caused by the electric field experienced in the inter-pixel region, which is the average of the electric fields applied to the adjacent pixels.

[0034] When using area updates (where only a specific area of ​​the display is updated, for example, to display an image), similar edge effects occur in addition to the edge effects that occur at the boundaries of the updated area due to area updates. Such edge effects cause visual distraction over time and must be eliminated.

[0035] To date, such edge effects (and color drift effects in undriven white pixels) are typically removed by using a single GC update at intervals. Unfortunately, the use of such occasional GC updates introduces the problem of "flashy" updates, and more precisely, the flickering of updates may be more pronounced because they only occur at long intervals. This invention relates to reducing or eliminating the above-mentioned problems while still avoiding flickering updates as much as possible.

[0036] It has also been found that edge ghosting can be mitigated by driving electro-optic displays with a DC unbalanced waveform. However, as discussed in many of the aforementioned MEDEOD applications, if the driving scheme used is not substantially DC balanced (i.e., if the algebraic sum of the pulses applied to a pixel during the start and end of any series of transitions at the same grayscale is not close to zero), it may adversely affect the electro-optical characteristics and operational lifespan of the display. See in particular U.S. Patent No. 7,453,445, which discusses the problem of DC balance in so-called "heterogeneous loops" involving transitions implemented using more than one driving scheme. A DC balanced driving scheme ensures that the total net pulse bias is constrained at any given time (for a finite number of gray states). In a DC balanced driving scheme, each optical state of the display is assigned a pulse potential (IP) and defines an individual transition between optical states such that the net pulse of the transition is equal to the difference in pulse potential between the initial and final states of the transition. In a DC balanced driving scheme, any round-trip net pulse needs to be substantially zero.

[0037] DC unbalanced waveforms can also produce residual voltages. For example, U.S. Patent No. 7,012,600 describes how DC unbalanced waveforms can produce residual voltages, which can be determined by measuring the open-circuit electrochemical potential of the display pixel. Furthermore, the use of DC unbalanced waveforms can lead to polarization kick-back, a change in the optical state of the electro-optic medium that occurs shortly after the medium is no longer driven. "Kick-back" or "self-erasure" is a phenomenon observed in some electro-optic displays. See, for example, Ota, I., et al., "Developments in Electrophoretic Displays", Proceedings of the SID, 18, 243 (1977), where self-erasure is reported in unencapsulated electrophoretic displays, whereby the electro-optic medium may at least partially reverse its optical state shortly after the voltage across the electro-optic medium is no longer applied. For example, a pixel driven as black may revert to dark gray shortly after the pixel is deselected. In some cases, reverse voltages, potentially greater than the operating voltage, can be observed on the electrodes, often leading to electrode damage.

[0038] Traditionally, Driven After Discharge ("PDD") technology has been used to reduce or eliminate residual voltage by discharging charge from display pixels after a display update is complete. For example, U.S. Patent No. 10,475,396 describes a PDD technique for discharging residual voltage, which involves, for example, activating the transistors of the display pixels and setting the voltages of the front and rear electrodes of the display pixels to approximately the same voltage for a specified period of time and / or until the residual voltage decreases to below a critical value. The use of PDD technology in conjunction with a deliberately unbalanced DC waveform drive scheme (which builds up residual voltage more quickly) is particularly important.

[0039] However, a drawback of traditional PDD technology is that it requires time to discharge residual voltage after an update, and the display device essentially becomes "frozen" and unresponsive to user input during the execution of the PDD routine. Typical use cases for display devices may involve largely fixed interactions and inputs from the user, requiring several consecutive updates to the display, often using an unbalanced DC waveform, which can perform faster updates than the waveform used in standard update modes. Therefore, locking the display device to allow time for residual voltage discharge routines results in an unsatisfactory user experience.

[0040] To reduce or eliminate time spent unresponsive to user interaction, conventional driving methods can be configured to interrupt the execution of the PDD routine to allow subsequent requested updates to be performed. However, conventional driving methods operate on the assumption that use cases requiring interruption of PDD routine execution or with short dwell times between display updates are rare, and that the interrupted PDD routine is shortly followed by a fully executed PDD routine to discharge the display. Considering the typical display device use cases described above, the PDD routine may be interrupted several times before the fully executed PDD routine can adequately discharge the display. This can accumulate residual charge sufficient to cause display degradation or display artifacts (e.g., ghosting) that negatively impact the user experience. The present invention also relates to reducing or eliminating the aforementioned accumulation of residual charge while still minimizing prolonged device unresponsiveness that could lead to an unsatisfactory user experience. Summary of the Invention

[0041] Therefore, in one embodiment, the present invention provides a (first) method for driving an electro-optic display having a plurality of pixels using a first driving scheme and a second driving scheme; in the first driving scheme, all pixels are driven at each transition, while in the second driving scheme, pixels undergoing certain transitions are not driven. In the first method of the present invention, the first driving scheme is applied to a small proportion of non-zero pixels during a first update of the display, while the second driving scheme is applied to the remaining pixels during the first update. During a second update following the first update, the first driving scheme is applied to a different small proportion of non-zero pixels, while the second driving scheme is applied to the remaining pixels during the second update.

[0042] For convenience, the first driving method of the present invention may be referred to in the following as the "Selective General Update" or "SGU" method of the present invention.

[0043] This invention provides a (second) method for driving an electro-optic display having a plurality of pixels, each pixel being driven using a first driving scheme or a second driving scheme. When a complete overall update is required, the pixels are divided into two (or more) groups, and a different driving scheme is used for each group, such that for at least one transition, pixels in different groups having the same optical state do not experience the same waveform. For convenience, the second driving method of this invention may be referred to hereinafter as the "Global Complete Multiple Driving Scheme" or "GCMDS" method of this invention.

[0044] The SGU and GCMDS methods discussed above reduce perceived flicker during image updates. However, the present invention also provides various methods for reducing or eliminating edge artifacts when driving bistable electro-optic displays. One such edge artifact reduction method (hereinafter referred to as the third method of the present invention) requires applying one or more balanced pulse pairs (balanced pulse pairs or "BPPs" are a pair of driving pulses of opposite polarities such that the net pulse of the balanced pulse pair is substantially zero) during white-to-white transitions in pixels that can be identified as likely to cause edge artifacts and are in a spatiotemporal configuration, such that the balanced pulse pairs effectively eliminate or reduce edge artifacts. Desiredly, pixels to which BPPs are applied are selected such that the BPPs are masked by other update activities. Note that applying one or more BPPs does not affect the desired DC balance of the driving scheme because each BPP is essentially zero net pulse and therefore does not change the DC balance of the driving scheme. For convenience, the third driving method of the present invention may be referred to hereinafter as the "balanced pulse pair white / white transition driving scheme" or the "BPPWWTDS" method of the present invention.

[0045] In the fourth method of the present invention for reducing or eliminating edge artifacts, a "top-off" pulse is applied during the white-to-white transition of pixels that are identified as likely to cause edge artifacts and are in a spatiotemporal configuration, such that the top-off pulse effectively eliminates or reduces edge artifacts. For convenience, the fourth driving method of the present invention may be referred to hereinafter as the "white / white top-off pulse driving scheme" or the "WWTOPDS method" of the present invention.

[0046] The fifth method of the present invention also attempts to reduce or eliminate edge artifacts. This fifth method seeks to eliminate such artifacts that appear along a straight edge between driven and undriven pixels without special adjustment. In this fifth method, a two-stage driving scheme is used, such that in the first stage, some "extra" pixels on the "undriven" side of the straight edge are actually driven to the same color as the pixels on the "driven" side of the edge. In the second stage, these pixels on the driven side of the edge and these extra pixels on the undriven side of the edge are both driven to their final optical state. Therefore, the present invention provides a method for driving an electro-optic display having a plurality of pixels, wherein a two-stage driving scheme is used when a plurality of pixels located in a first region of the display are driven to change their optical state, and a plurality of pixels located in a second region of the display do not need to change their optical state (the first region and the second region are in contact along a straight line). In the first stage, some pixels located in the second region and adjacent to the straight line are actually driven to the same color as those pixels in the first region adjacent to the straight line, and in the second stage, those pixels in the first region and some pixels in the second region are driven to their final optical state. It has been found that driving a limited number of additional pixels in this way greatly reduces the visibility of edge artifacts, because any edge artifacts appearing along the curved edge defined by the additional pixels are less noticeable than the corresponding edge artifacts along the original straight edge. For convenience, the fifth driving method of the present invention may be referred to hereinafter as the "Straight Edge Additional Pixel Driving Scheme" or the "SEEPDS" method of the present invention.

[0047] The sixth method of the present invention allows pixels to temporarily deviate from DC balance. In many cases, temporarily allowing pixels to deviate from DC balance is beneficial. For example, a pixel may need a specific pulse toward white because it is expected to contain dark artifacts, or a rapid display switch may be required so that the full pulse required for balancing cannot be applied. The transition may be interrupted by unpredictable events. In such cases, a method is necessary or at least desirable to allow and correct pulse deviations, especially on short time scales.

[0048] In the sixth method of the present invention, the display maintains a "pulse group register," which contains a value for each pixel of the display. When a pixel needs to deviate from the normal DC-balanced drive scheme, the pulse group register of the relevant pixel is adjusted to indicate the deviation. When the register value of any pixel is non-zero (i.e., when the pixel has deviated from the normal DC-balanced drive scheme), at least one subsequent transfer of the pixel is performed using a waveform that differs from the corresponding waveform of the normal DC-balanced drive scheme and reduces the absolute value of the register value. The absolute value of the register value of any pixel is not allowed to exceed a predetermined amount. For convenience, the sixth driving method of the present invention may be referred to hereinafter as the "pulse group drive scheme" or "IBDS" method of the present invention.

[0049] In the seventh method of the present invention, a state machine algorithm monitors display updates that are more likely to result in residual voltage accumulation and dwell time between updates. The algorithm calculates a number of stress levels experienced by the display based on the number of DC imbalance updates, after which there is insufficient dwell time for residual voltage to dissipate naturally or for the PDD routine to be fully executed. When the calculated number increases to a first threshold indicating the limit of the stress levels the display device can withstand, the algorithm cancels the next requested DC imbalance update and replaces it with an update mode that is less stressful on the display. For example, the algorithm can cancel the requested DC imbalance update with a DC balancing update scheme and / or a scheme that allows for a longer display update duration and reduces accumulated residual charge. For convenience, the seventh driving method of the present invention may hereinafter be referred to as the "Mode Update Request Cancellation Driving Scheme" or the "MURODS" method of the present invention.

[0050] The seventh method of the present invention is a method for driving an electro-optic display having a plurality of display pixels. The method includes determining a stress level of a display pixel based on at least one previous update of the optical state of a display pixel of the electro-optic display. The method also includes receiving a request for updating the optical state of the display pixel. The method further includes applying a driving waveform from a first update scheme to the display pixel when: (i) the driving waveform from the first update scheme was used for a previous update of the display pixel and the stress level is not greater than a first stress level threshold, or (ii) the driving waveform from a second update scheme was used for a previous update of the display pixel and the stress level is less than a second stress level threshold. The method also includes applying a driving waveform from the second update scheme to the display pixel when: (i) the driving waveform from the first update scheme was used for a previous update of the display pixel and the stress level is greater than the first stress level threshold, or (ii) the driving waveform from the second update scheme was used for a previous update of the display pixel and the stress level is not greater than the second stress level threshold.

[0051] In some embodiments, the request to update the optical state of the display pixel of the electro-optical display is triggered by interaction with a user of the electro-optical display. In some embodiments, the user interaction includes swiping the screen surface of the electro-optical display. In some embodiments, the user interaction includes displaying an animation on the electro-optical display.

[0052] In some embodiments, the first update scheme includes a DC-unbalanced drive waveform. In some embodiments, the second update scheme includes a DC-balanced drive waveform.

[0053] In some embodiments, the second update scheme includes a drive waveform that is longer in duration than the drive waveform of the first update scheme. In some embodiments, the drive waveform of the second update scheme is approximately 350 ms to 500 ms longer in duration than the drive waveform of the first update scheme. In some embodiments, the drive waveform of the second update scheme is approximately 30% to 55% longer in duration than the drive waveform of the first update scheme. In some embodiments, the drive waveform of the second update scheme is approximately 50% to 70% longer in duration than the drive waveform of the first update scheme.

[0054] In some embodiments, the stress level is an approximation of the actual amount of residual voltage accumulated on the display pixel. In some embodiments, the stress level is a scalar quantity that indicates an index of the increase or decrease in the amount of residual voltage accumulated on the display pixel.

[0055] In some embodiments, determining the stress level of the display pixel includes calculating the following equation:

[0056] Where x(n) represents the stress level of updating n, UT(n) represents the duration (in milliseconds) of the driving waveform used for the previous update of the display pixel, DT(n) represents how many milliseconds a post-drive discharge routine is performed after the previous update of the display pixel, TAU represents the time constant of the decay of the stress level x(n), x(n-1) is the stress level calculated based on the previous update of the display pixel, and B has a value that changes according to the driving mode used to update n.

[0057] In some embodiments, after applying the driving waveform from the first update scheme to the display pixel, B is set to a non-zero positive value. In some embodiments, after applying the driving waveform from the second update scheme to the display pixel, the value of B is set to zero.

[0058] In some embodiments, the method further includes interrupting a post-drive discharge routine after applying the drive waveform from the first update scheme. In some embodiments, the method further includes substantially not performing a dwell time after applying the drive waveform from the first update scheme.

[0059] In some embodiments, the method further includes interrupting a post-drive discharge routine after applying the drive waveform from the second update scheme. In some embodiments, the method further includes substantially not performing a dwell time after applying the drive waveform from the second update scheme.

[0060] In some embodiments, the first stress level threshold represents the limit of the stress level that the electro-optic display can withstand.

[0061] The present invention also provides a novel display controller configured to perform the methods of the present invention. In such a novel display controller, a standard image, or one of alternative standard images, flashes on the display during an intermediate stage of a transition from a first arbitrary image to a second arbitrary image. To display such a standard image, the waveform used for the transition from the first image to the second image needs to be changed for any given pixel according to the state of that pixel in the displayed standard image. For example, if the standard image is monochrome, each transition between a specific grayscale in the first and second images will require two possible waveforms, depending on whether a specific pixel in the standard image is black or white. On the other hand, if the standard image has 16 grayscale levels, each transition will require 16 possible waveforms. For convenience, this type of controller may be referred to hereinafter as the "intermediate standard image" or "ISI" controller of the present invention.

[0062] Furthermore, in some methods of the present invention (e.g., the SEEDPS method), it is necessary or desirable to use a controller capable of updating any area of ​​the display, and the present invention provides such a controller, which, for convenience, may be referred to below as the "arbitrary area allocation" or "ARA" controller of the present invention.

[0063] In all methods of the present invention, the display can utilize any of the aforementioned types of electro-optic media. Thus, for example, the electro-optic display can include a rotating dual-color component or an electrochromic material. Alternatively, the electro-optic display can include an electrophoretic material comprising a plurality of charged particles disposed in a fluid and capable of moving through the fluid under the influence of an electric field. These charged particles and the fluid can be confined within a plurality of capsules or microcells. Alternatively, these charged particles and the fluid can exist in the form of a plurality of discrete droplets surrounded by a continuous phase comprising a polymeric material. The fluid can be a liquid or a gas. Simple Explanation of the Diagram

[0064] Figures 1A and 1B of the accompanying drawings show voltage-to-time curves of two balanced pair waveforms that can be used in the GCMDS method of the present invention; Figure 1C shows a graph of the reflectivity of the display against time, where the same number of pixels are driven using the waveforms shown in Figures 1A and 1B; Figures 2, 3, 4, and 5 schematically illustrate the GCMDS method of the present invention performed through intermediate images; Figures 6A and 6B illustrate the differences in L* values ​​for various grayscale levels implemented using the BPPWWTDS of this invention and the conventional Global Limited driving scheme, respectively; Figures 7A and 7B are similar to Figures 6A and 6B, but illustrate overcorrection that may occur in some BPPWWTDS of the present invention; Figures 8A to 8D are graphs similar to those in Figure 7A, but show the effects of using 1, 2, 3, and 4 balanced pulse pairs in the BPPWWTDS of this invention, respectively. Figure 9 schematically illustrates the various transfers that occur in the combined WWTOPDS / IBDS of the present invention; Figures 10A and 10B are curves similar to those in Figures 6A and 6B, respectively, but show the grayscale error achieved using the combined WWTOPDS / IBDS of the present invention as shown in Figure 9; Figures 11A and 11B are graphs similar to those in Figures 10A and 10B, respectively, but show the grayscale error achieved using the WWTOPDS method of this invention, wherein a top cutoff pulse is applied without considering DC imbalance; Figures 12A and 12B illustrate, in a slightly schematic manner, the transfers that occur in the prior art driving method and the SEEPDS driving scheme of the present invention, achieving the same overall changes in the display; Figure 13 schematically illustrates the controller architecture required by SEEPDS, which allows updating regions of arbitrary shape and size compared to conventional controllers that only allow selection of rectangular areas; Figure 14 shows a flowchart of an exemplary driving method incorporating a residual voltage management state machine algorithm; and Figure 15 shows a flowchart of an exemplary driving method that includes a residual voltage management state machine algorithm. Implementation

[0065] As is apparent from the foregoing, the present invention provides a plurality of separate inventions relating to the driving of electro-optic displays and devices used in such methods. These different inventions will be described individually below; however, it should be understood that a single display may incorporate more than one of these inventions. For example, it is apparent that a single display may use the selective general update and straight-edge extra pixel driving scheme method of the present invention and the arbitrary region allocation controller of the present invention. [A] [Partial: The Selective General Update Method of the Invention]

[0066] As described above, the Selective General Update (SGU) method of the present invention is intended for use in an electro-optical display having a plurality of pixels. This method utilizes a first driving scheme and a second driving scheme; in the first driving scheme, all pixels are driven at each transition, while in the second driving scheme, pixels undergoing some transitions are not driven. In the SGU method, during the first update of the display, the first driving scheme is applied to a smaller proportion of non-zero pixels, while the second driving scheme is applied to the remaining pixels during the first update. During the second update following the first update, the first driving scheme is applied to a different smaller proportion of non-zero pixels, while the second driving scheme is applied to the remaining pixels during the second update.

[0067] In a preferred form of the SGU method, the first driving scheme is a GC-driven scheme, and the second driving scheme is a GL-driven scheme. In this case, the SGU method essentially replaces conventional techniques where a (relatively flicker-free) GL-driven scheme is used for most updates, while a (relatively flicker-free) GC-driven scheme is used for occasional updates; one approach where a smaller proportion of pixels use the GC-driven scheme on each update, while a larger proportion uses the GL-driven scheme. By carefully selecting the distribution of pixels using the GC-driven scheme, each update using the SGU method of this invention can be implemented in a manner that is not perceived as significantly more flicker-free than pure GL updates (to non-expert users), while avoiding infrequent, flickering, and distracting pure GC updates.

[0068] For example, suppose a particular display is found to require a GC-driven scheme for one update out of every four updates. To implement the SGU method of this invention, the display can be divided into multiple 2×2 groups of pixels. During the first update, the GC-driven scheme is used to drive one pixel in each group (e.g., the top-left pixel), while the GL-driven scheme is used to drive the remaining three pixels. During the second update, the GC-driven scheme is used to drive a different pixel in each group (e.g., the top-right pixel), while the GL-driven scheme is used to drive the remaining three pixels. The pixels driven by the GC-driven scheme rotate with each update. Theoretically, the flicker per update is one-quarter that of a pure GC update, but the increase in flicker is not particularly noticeable, and it avoids the distracting pure GC update that occurs every fourth update in conventional methods.

[0069] A tessellating pattern, as discussed above in the 2×2 grouping configuration, can be used to systematically or statistically determine which pixels receive the GC-driven scheme in each update, or by randomly selecting an appropriate proportion of pixels at each update (e.g., selecting 25% of the pixels at each update). It will be apparent to those skilled in visual psychology that certain "noise patterns" (i.e., the distribution of the selected pixels) may be more effective than others. For example, if the goal is to select one pixel from each adjacent 3×3 group to use the GC-driven scheme at each update, it may be advantageous not to set a corresponding pixel in each group at each update, as this produces a regular array of "flickering" pixels, which may be more pronounced than the at least pseudo-random array of "flickering" pixels resulting from selecting different pixels in each group.

[0070] At least in some cases, it may be desirable to configure a number of groups of pixels on a parallelogram or pseudo-hexagonal mesh using a GC-driven scheme on each update. Then, repeating in both directions, an example of pixels providing such a parallelogram or pseudo-hexagonal mesh as square or rectangular "tiles" is shown below (the numbers indicate the update number to which the GC-driven scheme is implemented on the pixel):

[0071] More than one pattern can be used for selected pixels to illustrate different usage styles. More than one pattern with different intensities can be used (e.g., a 2x2 block in a pixel using a GC-driven scheme compared to a 3x3 block in a pixel using a GC-driven scheme) to lightly imprint a watermark pattern on the page during updates. This watermark can be changed in real-time. These patterns can be moved relative to each other in a way to produce other desired watermark patterns.

[0072] The SGU method of this invention is not limited to a combination of GC and GL driving schemes, but can be used with other driving schemes, as long as one driving scheme is less flickering than another, and the second driving scheme provides better performance. Furthermore, similar effects can be achieved by using two or more driving schemes and varying the pixels undergoing partial updates and those undergoing full updates.

[0073] The SGU method of this invention can be effectively combined with the BPPWWTDS or WWTOPDS methods of this invention, which are described in detail below. Implementing the SGU method does not require extensive development and modification of the driver scheme (because this method can use combinations of known driver schemes), but allows for a significant reduction in noticeable display flicker. [B] [Partial: The Overall Complete Multi-Drive Scheme Method of the Invention]

[0074] As described above, the overall fully multi-drive scheme or GCMDS method of the present invention is a second method for driving an electro-optic display having multiple pixels, each pixel being driven using either a first or a second drive scheme. When an overall full update is required, the pixels are divided into two (or more) groups, and each group uses a different drive scheme, such that for at least one transition, pixels in different groups having the same transition between optical states do not experience the same waveform.

[0075] Part of the flickering in conventional whole-collected (GC) updates is due to the fact that a large number of pixels are typically subjected to the same waveform simultaneously. For this reason, in many cases this is a white-to-white waveform, but in other cases (e.g., when displaying white text on a black background), a black-to-black waveform may account for a large proportion of the flicker. In the GCMDS method, instead of driving (and thus flickering) every pixel of the display that simultaneously undergoes the same transition with the same waveform, each pixel is assigned a group value such that for at least some transitions, different waveforms are applied to different groups of pixels undergoing the same transition. Therefore, pixels undergoing the same image state transition will not (necessarily) experience the same waveform, and thus will not flicker simultaneously. Furthermore, the pixel grouping and / or waveform used can be adjusted between image updates.

[0076] Using the GCMDS method, perceived flicker during full global updates can be significantly reduced. For example, suppose pixels are divided into a checkerboard grid, with one class of equal pixels assigned to class A and another class of equal pixels assigned to class B. Then, white-to-white waveforms for both classes can be selected such that they are time-shifted so that neither class is ever simultaneously in a black state. One way to configure such waveforms is to use a conventional balanced pulse pair waveform (i.e., a waveform containing two rectangular voltage pulses of equal but opposite polarities) for both waveforms, but delaying one waveform by the duration of a single pulse. This type of waveform pair is illustrated in Figures 1A and 1B. Figure 1C shows the reflectivity of the display over time, where half of the pixels are driven using the waveform of Figure 1A, and the other half using the waveform of Figure 1B. As can be seen from Figure 1C, the reflectivity of the display will never approach black; for example, it might approach black if the waveform of Figure 1A were used alone.

[0077] Other waveform pairs (or more multivariates – using more than two pixel classes) can provide similar benefits. For example, for a mid-gray to mid-gray transition, two "single rail bounce" waveforms can be used, one driving from the mid-gray level to white and then from black to the mid-gray level, and the other driving from the mid-gray level to black and then from black to the mid-gray level. Furthermore, spatial configurations of other pixel classes are possible, such as horizontal or vertical stripes or random white noise.

[0078] In a second form of the GCMDS method, pixels are divided into several categories, allowing more than one temporary monochrome image to be displayed during the update. This reduces noticeable flicker on the display by drawing the user's attention to the intermediate image rather than any flickering that occurs during the update, much like a magician immediately diverting the audience's attention away from an elephant entering the stage. Examples of intermediate images that can be used include monochrome checkerboards, company logos, stripes, clocks, page numbers, or Escher prints. For example, Figure 2 of the accompanying drawings illustrates a GCMDS method in which two temporary horizontal stripe images are displayed during the transition; Figure 3 illustrates a GCMDS method in which two temporary checkerboard images are displayed during the transition; Figure 4 illustrates a GCMDS method in which two temporary random noise patterns are displayed during the transition; and Figure 5 illustrates a GCMDS method in which two temporary Escher images are displayed during the transition.

[0079] The two concepts mentioned above (the use of multiple waveforms and the use of temporary intermediate images) can be used simultaneously to reduce flickering during transitions and to distract the user by drawing attention to images of interest.

[0080] It will be apparent that implementations of the GCMDS method typically require a controller capable of maintaining a pixel class map; such a map can be hardwired into the controller or loaded via software, the latter offering the advantage of allowing for arbitrary changes to the pixel map. To obtain the waveform required for each transition, the controller retrieves the pixel class of the relevant pixel from this map and uses it as an additional index to define a lookup table of various possible waveforms; see the aforementioned MEDEOD application, particularly U.S. Patent No. 7,012,600. Alternatively, if the waveforms used for various pixel classes are merely delayed variations of a single basic waveform, a simpler structure can be used; for example, to update two different classes of pixels, a single waveform lookup table can be referenced, where the two pixel classes begin updating with a time shift, which may be equal to a multiple of the length of the basic driving pulse. It will be apparent that in classifying pixels into categories, the map may be unnecessary, as the class of any pixel can be simply calculated based on its number of columns and rows. For example, in the striped pattern flashing shown in Figure 2, a pixel can be assigned to its category based on whether its column number is even or odd, while in the checkerboard pattern shown in Figure 3, a pixel can be assigned to its category based on whether the sum of its column number and row number is odd or even.

[0081] The GCMDS method of this invention provides a relatively simple mechanism to reduce the visual impact of flicker during the update of bistable displays. The use of the GCMDS method with delayed waveforms for various pixel categories greatly simplifies the implementation of the GCMDS method at the cost of overall update time. [C] [Partial: Balanced Pulse Wave Approach to White in this Invention] [ / ] [White Transfer Driven Solution Method]

[0082] As described above, the Balanced Pulse Pair White / White Transfer Drive Scheme (BPPWWTDS) of the present invention aims to reduce or eliminate edge artifacts when driving a bistable electro-optic display. BPPWWTDS requires the application of one or more balanced pulse pairs (a balanced pulse pair, or "BPP", is a pair of drive pulses of opposite polarity such that the net pulse of the balanced pulse pair is substantially zero) during the white-to-white transfer of pixels that are likely to cause edge artifacts in the spatiotemporal configuration, so that the balanced pulse pairs effectively eliminate or reduce edge artifacts.

[0083] BPPWWTDS attempts to reduce the visibility of accumulated errors in a way that avoids distracting appearance during the transition and by having a limited DC imbalance. This is achieved by applying more than one balanced pulse pair to a subset of pixels on the display, where the proportion of pixels in the subset is small enough that the application of the balanced pulse pair does not visually distract. Visual distraction caused by the application of BPP can be reduced by selecting pixels adjacent to other pixels undergoing easily visible transitions to which BPP is applied. For example, in one form of BPPWWTDS, BPP is applied to any pixel undergoing a white-to-white transition, and at least one of its eight neighboring pixels undergoes a (non-white)-to-white transition. The (non-white)-to-white transition may create a visible edge between the pixel undergoing this transition and its neighboring pixels undergoing a white-to-white transition, and this visible edge can be reduced or eliminated by the application of BPP. This scheme for selecting pixels to be BPP applied to has the advantage of simplicity, but other, more conservative pixel selection schemes can also be used. A conservative approach (i.e., one that ensures only a small percentage of pixels have BPP applied during any given transfer) is desirable because such an approach has the least impact on the overall display of the transfer.

[0084] As shown, the BPP used in the BPPWWTDS of this invention can include more than one balanced pulse pair. Each half of a balanced pulse pair can consist of a single or multiple driving pulses, as long as each half has the same magnitude. The voltage of a BPP can be different, as long as the two halves of a BPP have the same amplitude but opposite signs. A zero-voltage period may occur between the two halves of a BPP or between consecutive BPPs. For example, in one experiment, the results are as follows: a balanced BPP consists of a series of six pulses: +15V, -15V, +15V, -15V, +15V, -15V, each lasting 11.8 milliseconds. Empirically, it has been found that the longer the sequence of BPPs, the greater the edge reduction obtained. When a BPP is applied to a pixel adjacent to a pixel undergoing a (non-white) to white transition, it has also been found that the temporal shift of the BPP relative to the (non-white) to white waveform also affects the degree of edge reduction obtained. There is currently no complete theoretical explanation for these findings.

[0085] The experiments mentioned earlier showed that BPPWWTDS is effective in reducing the visibility of accumulated edges compared to the conventional finite overall (GL) driving scheme. Figure 6 shows the difference in L* values ​​at different gray levels between the two driving schemes, and it can be seen that the L* difference of BPPWWTDS is closer to zero (ideally) than that of the GL driving scheme. Microscopic examination of the edge areas after implementing BPPWWTDS reveals two types of responses to this improvement. In some cases, the actual edges appear to be eroded by the implementation of BPPWWTDS. In other cases, the edges do not appear to be eroded much, but another bright edge is formed near the dark edge. When viewed from a normal user distance, these edge pairs cancel each other out.

[0086] In some cases, it has been found that the implementation of BPPWWTDS may actually overcorrect edge effects (as shown by the L* differences assumed to be negative in those curves of Figure 6). See Figure 7, which shows such overcorrection in an experiment with four BPPs. If such overcorrection occurs, it has been found that it can be reduced or eliminated by decreasing the number of BPPs used or by adjusting the timing of the BPPs relative to the (non-white) to white transition. For example, Figure 8 shows the results of experiments using one to four BPPs to correct for edge effects. For the specific medium tested, two BPPs appear to provide optimal edge correction. The number of BPPs and / or the timing of the BPPs relative to the (non-white) to white transition can be adjusted in a time-varying manner (i.e., instantaneously) to provide optimal correction for predicting edge visibility.

[0087] As discussed, driving schemes for bistable electro-optic media should generally be DC balanced; that is, the nominal DC imbalance of the driving scheme should be limited. While BPP is inherently DC balanced and therefore should not affect the overall DC balance of the driving scheme, a sudden voltage reversal on the pixel capacitors used to drive the bistable electro-optic media, typically present in the backplane (e.g., see U.S. Patent No. 7,176,880), can cause incomplete charging of the capacitors during the latter half of the BPP, which can actually cause some DC imbalance. Applying a BPP to a pixel that does not have a neighboring pixel undergoing a non-zero transition can cause the pixel to whiten or undergo other changes in optical state, and applying a BPP to a pixel that has a neighboring pixel undergoing a transition that is not to white can cause the pixel to darken somewhat. Therefore, the rules for selecting pixels to receive BPP should be carefully considered.

[0088] In one form of the BPPWWTDS of this invention, a logical function is applied to the initial and final images (i.e., the images before and after the transition) to determine whether a particular pixel should have more than one BPP applied during the transition. For example, various forms of BPPWWTDS may explicitly state that a pixel undergoing a white-to-white transition will have a BPP applied if all four major neighboring pixels (i.e., pixels sharing a common edge (not just a corner) with one of the pixels under discussion) have a final white state, and at least one major neighboring pixel has an initial non-white state. If this condition does not apply, a null transition is performed on the pixel, meaning no driving pixel is applied during the transition. Of course, other logical selection rules can be used.

[0089] Another variation of BPPWWTDS actually combines BPPWWTDS with the SGU driving scheme of the present invention by applying the overall full driving scheme to certain selected pixels undergoing white-to-white transitions, thereby further increasing edge cleanup. As mentioned above in the discussion of the SGU driving scheme, the GC waveform used for white-to-white transitions is often very flickering, so it is important that this waveform is applied to only a small proportion of pixels during any transition. For example, a logical rule might be implemented: when three of a pixel's major neighboring pixels are undergoing non-zero transitions during a relevant transition, only the GC white-to-white waveform is applied to that pixel; in this case, the flickering of the GC waveform is hidden in the activity of the three major neighboring pixels that are transitioning. Furthermore, if a fourth major neighboring pixel is undergoing a zero transition, the GC white-to-white waveform applied to the relevant pixel may trim an edge in the fourth major neighboring pixel, so that it may be desirable to apply BPP to the fourth major neighboring pixel.

[0090] Other variations of BPPWWTDS include the implementation of GC white-to-white (hereinafter referred to as "GCWW") transitions to select regions of the background, i.e., regions that are white both initially and ultimately. This is done to visit each pixel once during a predetermined number of updates, thereby eliminating the display of edges and drift artifacts over time. The main difference from the variations discussed earlier is that the decision of which pixels should receive GC updates is based on spatial location and the number of updates, rather than the activity of neighboring pixels.

[0091] In one variation, GCWW transfer is performed on the dithered sub-population of background pixels on a rotating basis with each update. As discussed in Part A above, this reduces the effects of image drift because all background pixels are updated after a predetermined number of updates, with only slight flickering or dips occurring during the update process when the background is white. However, this method may generate its own edge artifacts around the updated pixels, which persist until the surrounding pixels themselves are updated. According to BPPWWTDS, a reduced edge BPP can be applied to the neighboring pixels of the pixel undergoing GCWW transfer, so that background pixels can be updated without introducing noticeable edge artifacts.

[0092] In another variation, the pixel subpopulation driven by the GCWW waveform is further divided into sub-subpopulations. At least some of the resulting sub-subpopulations receive a delayed version of the GCWW waveform, such that only a portion of them are in a dark state at any given time during the transition. This further reduces the effect of flicker, which has already been reduced during the update. A delayed version of the BPP signal is also applied to the neighboring pixels of these sub-subpopulations. In this way, noticeable background flicker can be reduced to steadily decrease the exposure of image drift. The number of sub-subpopulations is limited by the considered acceptable increase in update time (caused by the use of a delayed signal). Typically, two sub-subpopulations are used, which superficially increases the update time by a basic driving pulse width (typically about 240 ms at 25°C). Furthermore, having excessively sparse sub-subpopulations can also make individual updated background pixels more noticeable psychologically, increasing a potentially undesirable type of distraction.

[0093] Modifications to display controllers used for implementing various forms of BPPWWTDS (e.g., those described in the aforementioned U.S. Patent No. 7,012,600) are straightforward. One or more buffers store grayscale data representing the initial and final images of the transition. Based on this data, along with other information such as temperature and driving scheme, the controller selects the correct waveform from a lookup table to apply to each pixel. To implement BPPWWTDS, a mechanism must be provided to select between several different transitions of the same initial and final grayscale state (particularly representing a white state), depending on the transitions experienced by adjacent pixels, the subgroup to which each pixel belongs, and the number of updates (when pixels in different subgroups are updated in different updates). For this purpose, the controller can store additional "quasi-states," as if they were additional grayscale levels. For example, if the display uses 16 grayscale levels (numbered 0 to 15 in the lookup table), states 16, 17, and 18 can be used to represent the type of desired white transition. These quasi-state values ​​can be generated in the system at various different levels (e.g., at the major level when provided to the display buffer, or at a lower level in the controller when generating LUT addresses).

[0094] Several variations of the BPPWWTDS of this invention are conceivable. For example, the balanced pulse pair can be replaced by any short DC balanced or even DC unbalanced sequence of drive pulses. The balanced pulse pair can be replaced by a top cutoff pulse (see Section D below), or the BPP and top cutoff pulse can be used in combination.

[0095] Although the above description mainly concerns the BPPWWTDS of the present invention for reducing bright-state edges, it can also be applied to reducing dark-state edges, which can be achieved simply by reducing the polarity of the driving pulse used in BPPWWTDS.

[0096] The BPPWWTDS of the present invention can provide a "flicker-free" driving solution that does not require periodic full system updates, which are considered offensive by many users. [D] [Partial: White in this invention] [ / ] [White Top Cutoff Pulse Drive Scheme Method]

[0097] As described above, the fourth method of the present invention for reducing or eliminating edge artifacts is similar to the aforementioned BPPWWTDS in that a "special pulse" is applied during the white-to-white transition of a pixel identified as likely to cause edge artifacts and in a spatiotemporal configuration, such that the special pulse is effective in eliminating or reducing the edge artifacts. However, the fourth method differs from the third method in that the special pulse is not a balanced pulse pair, but a "top-off" or "update" pulse. The terms "top-off" or "update" pulse are used herein in the same manner as in the aforementioned U.S. Patent No. 7,193,625 to refer to a pulse applied to a pixel in or near an extreme optical state (typically white or black) that drives the pixel toward that extreme optical state. In this case, the terms "top-off" or "update" pulse mean applying a driving pulse to a white or near-white pixel, wherein the driving pulse has a polarity that drives the pixel to its extreme white state. For convenience, the fourth driving method of the present invention may be referred to in the following as the "white / white top cutoff pulse driving scheme" or the "WWTOPDS" method of the present invention.

[0098] The criteria for selecting pixels to be subjected to a top cutoff pulse in the WWTOPDS method of this invention are similar to those for pixel selection in the BPPWWTDS method described above. Therefore, the proportion of pixels to which a top cutoff pulse is applied during any transition should be small enough that the application of the top cutoff pulse does not visually distract. By selecting pixels with applied top cutoff pulses adjacent to other pixels undergoing easily visible transitions, visual distraction caused by the application of the top cutoff pulse can be reduced. For example, in one form of WWTOPDS, a top cutoff pulse is applied to any pixel undergoing a white-to-white transition and at least one of its eight neighboring pixels undergoing a (non-white)-to-white transition. A (non-white)-to-white transition is likely to create a visible edge between the pixel with the applied top cutoff pulse and its neighboring pixels undergoing a white-to-white transition, and this visible edge can be reduced or eliminated by the application of the top cutoff pulse. This scheme for selecting pixels to which a top cutoff pulse is applied has the advantage of simplicity, but other, particularly more conservative, pixel selection schemes can be used. A conservative approach (i.e., ensuring that only a small percentage of pixels are subjected to a top cutoff pulse during any given transition) is desirable because such an approach has minimal impact on the overall display of the transition. For example, a typical black-to-white waveform is unlikely to produce edges in adjacent pixels, so there is no need to apply a top cutoff pulse to adjacent pixels if no other predicted edges accumulate in the pixel. For example, consider two adjacent pixels (denoted as P1 and P2) displaying the following sequence: P1:W->W->B->W->W; and P2:W->B->B->B->W. Although P2 is likely to cause an edge in P1 during its white-to-black transition, this edge is subsequently eliminated during the black-to-white transition of P1, so that the final black-to-white transition of P2 should not trigger the application of the top cutoff pulse in P1. Many more complex and conservative schemes can be developed. For example, edge generation can be predicted on a per-neighbor pixel basis. Furthermore, if a small number of edges are below a certain predetermined threshold, it can be expected that they remain intact. Alternatively, edge elimination may not be necessary unless the pixel is surrounded only by white pixels, because edge effects tend to be less noticeable when they are adjacent to edges between two pixels with very different gray levels.

[0099] It has been empirically observed that when a top cutoff pulse is applied to a pixel in conjunction with at least one of its eight neighboring pixels undergoing a (non-white) to white transition, the timing of the top cutoff pulse relative to the transition on that neighboring pixel has a significant impact on the achieved edge reduction. Optimal results are obtained when the top cutoff pulse occurs simultaneously with the end of the waveform applied to that neighboring pixel. The reasons for this empirical finding are not yet fully understood.

[0100] In one form of the WWTOPDS method of this invention, a top cutoff pulse is applied in conjunction with an impulse banking drive scheme (see section F below for details). In this combined WWTOPDS / IBDS, in addition to applying the top cutoff pulse, a clearing slideshow waveform (i.e., a waveform that repeatedly drives the pixel to its extreme optical state) is occasionally applied to the pixel when DC balance is restored. This type of drive scheme is illustrated in Figure 9 of the accompanying drawings. The top cutoff and clearing (slideshow) waveforms are applied only when the pixel selection criteria are met; in all other cases, zero transition is used. Such a slideshow waveform removes edge artifacts from the pixel, but it is a visible transition. The results of one type of drive scheme are shown in Figure 10 of the accompanying drawings; these results can be compared with those of Figure 6, but it should be noted that the vertical scales in the two sets of graphs are different. Due to the periodic application of the clearing pulse, the sequence is not monotonic. Because the application of the slideshow waveform occurs infrequently and can be controlled, it only occurs in proximity to other visible activities, so that it is rarely noticed. The waveform shown in the slide has the advantage of essentially completely clearing pixels, but it has the disadvantage of causing edge artifacts in adjacent pixels that need to be cleared. These adjacent pixels can be marked as likely to contain edge artifacts and therefore need to be cleared in the next available opportunity, but it should be understood that this combined driving scheme leads to the complex development of edge artifacts.

[0101] In another form of the WWTOPDS method of this invention, a top cutoff pulse is applied without considering DC imbalance. This introduces some risk of long-term damage to the display, but such a small DC imbalance, potentially diffused across the frame over a long period, should not be significant, and in fact, commercial displays have experienced DC imbalances of the same order of magnitude due to uneven charging of the TFTs by the storage capacitors in the positive and negative voltage directions. The results of one type of driving scheme are shown in Figure 11 of the accompanying drawings; these results can be compared with those in Figure 6, but it should be noted that the vertical scales are different in the two sets of graphs.

[0102] The WWTOPDS method of this invention can be implemented such that the top-off pulses are statistically DC balanced without mathematically restricted DC imbalance. For example, a "payback" transition can be implemented in a manner that is typically balanced for electro-optical media to counteract the "top-off" transition, but without tracking the net pulse count of individual pixels. It has been found that top-off pulses applied in spatiotemporal environments that reduce edge visibility are useful regardless of the exact mechanism by which they operate; in some cases, edges appear to be significantly eliminated, while in others, the center of the pixel appears bright enough to locally compensate for the darkness of edge artifacts.

[0103] The top cutoff pulse can include more than one drive pulse, and a single drive voltage or a series of different voltages can be used in different drive pulses.

[0104] The WWTOPDS method of the present invention can provide a "flicker-free" driving scheme that does not require periodic full global updates, which are considered offensive by many users. [E] [Partial: The method for driving additional pixels at straight edges in this invention]

[0105] As described, the "Straight Edge Extra Pixel Driving Scheme" or "SEEPDS" method of this invention attempts to reduce or eliminate edge artifacts that occur along the straight edge between driven and undriven pixels. The human eye is particularly sensitive to straight edge artifacts (especially those extending along columns or rows of a display). In the SEEPDS method, some pixels adjacent to the straight edge between the driven and undriven areas are actually driven, such that any edge effects caused by the transfer not only extend along the straight edge but also include edges perpendicular to that straight edge. It has been found that driving a limited number of extra pixels in this way significantly reduces the visibility of edge artifacts.

[0106] The basic principle of the SEEPDS method is illustrated in Figures 12A and 12B. Figure 12A illustrates a conventional method in which a region or partial update is used to transfer a first image, which is black at the top and white at the bottom, to a second image that is entirely white. Because the update uses a region or partial driving scheme and only rewrites the black upper half of the first image, edge artifacts are likely to be generated along the boundary between the original black and white regions. Such long horizontal edge artifacts are often easily seen by the viewer of the display and are offensive. According to the SEEPDS method, as shown in Figure 12B, the update is divided into two separate steps. The first step of the update turns some white pixels on the nominally "non-driving" side of the original black / white boundary (i.e., the side where pixels have the same color (i.e., white) in both the initial and final images) into black; the white pixels thus driven to black are set in a series of roughly triangular regions adjacent to the original boundary, making the boundary between the black and white regions meandering, and the original straight boundary has many line segments extending perpendicular to the original boundary. The second step turns all black pixels (including the "extra" pixels driven black in the first step) white. Even though the second step leaves edge artifacts along the boundary between the white and black areas present after the first step, these edge artifacts will be distributed along the curved boundary shown in Figure 12B, and their visibility to the viewer is much less than that of similar artifacts extending along the straight boundary shown in Figure 12A. In some cases, edge artifacts can be further reduced because some electro-optic media only exhibit less visible edge artifacts when held in an optical state for a short time, as if at least most black pixels were adjacent to the curved boundary established after the first step.

[0107] When selecting the mode to execute in the SEEPDS method, care should be taken to ensure that the frequency of the curved boundaries shown in Figure 12B is not too high. A frequency that is too high compared to the pixel pitch will cause the edges perpendicular to the original boundaries to have a blurred and darker appearance, thus enhancing rather than reducing edge artifacts. In this case, the boundary frequency should be reduced. However, a frequency that is too low will also make the artifacts very noticeable.

[0108] In the SEEPDS method, the update scheme can follow the following pattern: - Region -> Standard Image [Any Time Amount] – Region (slightly expanded to obtain new edges) -> Image with modified edges – Region -> Next Image; or - Part -> Standard Image [Any Time Amount] – Part -> Image with Modified Edges – Part -> Next Image Alternatively, if a full update is used in a specific region, the pattern could be: -Full area -> Standard image [Any time amount] - Area (slightly expand to obtain new edges) -> Next image.

[0109] If there is no unacceptable interference with the electro-optical characteristics of the display, the display may always use the SEEPDS method according to the following mode: -Part -> Standard image with modified edges [any time amount] –Part -> Next image.

[0110] To reduce edge artifacts during multiple updates, the SEEPDS method can be configured to change the position of the curved boundary curve, as shown in Figure 12B, in order to reduce repeated edge growth during repeated updates.

[0111] The SEEPDS method can significantly reduce visible edge artifacts in the used area and / or parts of a newly updated display. This method does not require changes to the overall driver scheme used, and some forms of the SEEPDS method can be implemented without changing the display controller. This method can be implemented through hardware or software.

[0112] [F] [Partial: Pulse Group Driving Scheme and Method of the Invention]

[0113] As described, in the pulse group drive scheme (IBDS) method of the present invention, pixels are "allowed" to borrow or return pulse units from a "pulse group" that records pulse "debts". Generally, when a goal needs to be achieved, a pixel borrows pulses (positive or negative) from the pulse group, and returns pulses when a smaller pulse than required by a fully DC balanced drive scheme can be used to achieve the next desired optical state. In practice, the pulse return waveform may include zero net-impulse tuning elements (e.g., balanced pulse pairs) and zero voltage period to achieve the desired optical state with reduced pulses.

[0114] Clearly, the IBDS method requires the display to maintain a "pulse group register," which contains a value for each pixel of the display. When a pixel needs to deviate from the normal DC-balanced drive scheme, the pulse group register of the relevant pixel is adjusted to represent the deviation. When the register value of any pixel is non-zero (i.e., when the pixel has deviated from the normal DC-balanced drive scheme), at least one subsequent transfer of the pixel is performed using a reduced pulse waveform, wherein the reduced pulse waveform differs from the corresponding waveform of the normal DC-balanced drive scheme and reduces the absolute value of the register. The maximum amount of pulses that any pixel can borrow should be limited to a predetermined value, as excessive DC imbalance can adversely affect pixel performance. Application-specific methods should be developed to handle cases where the predetermined pulse limit is reached.

[0115] A simplified form of the IBDS method is shown in Figure 9 of the accompanying drawings. This method uses a commercial electrophoretic display controller designed for controlling a 16-grayscale display. To implement the IBDS method, the 16 controller states, normally assigned to the 16 grayscale levels, are reassigned to 4 grayscale levels and 4 pulse liability levels. It should be understood that a commercial implementation of the IBDS controller will allow for additional storage so that the full number of grayscale levels can be used for some pulse liability levels; see section H below.

[0116] In the IBDS method shown in Figure 9, a single pulse unit (15V drive pulse) is used to execute a top cutoff pulse (which is typically a zero transition with zero net pulse) during a white-to-white transition under predetermined conditions. The pulse is compensated by performing a black-to-white transition that lacks a drive pulse toward white. Without any correction, the removal of this drive pulse often results in a slightly darker white state than a white state using the full number of drive pulses. However, several known "adjustment" methods, such as pre-pulse balancing pulse pairs or zero-voltage intermediate periods, can achieve a satisfactory white state.

[0117] If the maximum pulse borrowing (3 units) is reached, a clean transition will be implemented that is 3 pulse units shorter than the all-white to white slide display transition; naturally, the waveform used for this transition must be adjusted to remove the visual effect of insufficient pulses. Such a clean transition is undesirable because it has greater visibility. Therefore, it is important to design the rules for IBDS with conservative pulse borrowing and fast pulse repayment.

[0118] Other forms of the IBDS method can utilize additional transfers for pulse compensation, thereby reducing the number of forced clear transfers required. Other forms of the IBDS method can utilize pulse groups, where the pulse deficit or surplus decays over time, maintaining DC balance only within a short time scale; there is some empirical evidence that at least some types of electro-optic media require only this short-term DC balance. Clearly, allowing the pulse deficit or surplus to decay over time reduces the number of times the pulse limit is reached, and thus reduces the number of clear transfers required.

[0119] The IBDS method of the present invention can reduce or eliminate several practical problems in bistable displays, such as edge ghosting in flicker-free driving schemes, and fully provide subject-dependent adaptation of the driving scheme at the individual pixel level, while still maintaining limitations on DC imbalance. [G] [Partial: The Mode Update Request Cancellation Driver Scheme Method of the Invention]

[0120] As described above, the Mode Update Request Relief Drive Scheme (MURODS) method uses a state machine algorithm to calculate the number of stress levels experienced by the display device and switches between update schemes as needed to manage the accumulation of residual voltage. Figure 14 shows a flowchart of an exemplary drive method 1400 that includes a residual voltage management state machine algorithm.

[0121] When an update to the display has been requested, method 1400 begins at step 1405, and the display controller for controlling method 1400 selects a drive waveform to be applied to the display pixels.

[0122] There are many events that can trigger update requests. For example, update requests can be triggered by user interaction with the display (such as swiping the screen to advance a page or scrolling the screen). As another example, if the display device is rendering an animation, each consecutive displayed image will trigger an update request.

[0123] In step 1410, a fast-mode update scheme is used to apply the drive waveform to the display pixels. The fast-mode update scheme prioritizes update time over color accuracy. For example, by using a fast-mode update scheme combined with interrupting the PDD routine after each update and providing no or virtually no dwell time after each update, the update time on a display device, including a full-color e-ink system with four color pigments, can be compressed to approximately 500-650 ms. This makes the fast-mode update scheme well-suited for use cases where users frequently interact with the display device. However, fast-mode update schemes typically include DC unbalanced drive waveforms, which can lead to the accumulation of residual voltage and result in display artifacts such as ghosting.

[0124] In step 1415, the number of stress levels experienced by the display device is calculated. For example, the display controller used in control method 1400 can calculate the stress level based on several variables and parameters of the system being tracked for each update. For each update n, the stress level or "LOS" value x(n) is calculated. An exemplary equation for calculating x(n) is shown below:

[0125] In some embodiments, x(n) is an approximation of the residual voltage expected to accumulate on the display pixels of the electro-optical display based on update n and all previous updates. In some embodiments, x(n) is a fraction of the residual voltage or a number one order of magnitude larger than the residual voltage. In some embodiments, x(n) is a scalar quantity that can be used as an exponent or indicator of the growth or decay of the residual voltage, but is not an approximation of the actual residual voltage expected to have accumulated based on update n and all previous updates.

[0126] In the first term of the LOS quantification equation, e represents the exponential function, UT(n) represents the update time (in milliseconds) of the update mode used by the most recently completed update, and DT(n) represents how many milliseconds of PDD are applied after the most recently completed update.

[0127] TAU represents the time constant for the decay of stress level number x(n). TAU is determined before an update begins to be applied to the display and remains constant throughout all updates. In some embodiments, TAU directly corresponds to the RC time constant of the residual voltage decay on a production batch of a particular display system or electrophoretic material. For example, instant display systems are characterized by measuring the amount of residual voltage generated by several different update sequences and the decay time of the residual voltage. Therefore, the TAU value can be calculated from the curve generated by the residual voltage measurement over time.

[0128] In some embodiments, the ink system can be represented as a parametric mathematical model, and the TAU can be roughly estimated based on one or more simulations of the aforementioned updates and measurements. In some embodiments, the TAU is not specific to a particular display system or production batch of electrophoretic material. For example, the time constant of the stress level x(n) decay can be calculated based on several different production batches of display systems and / or electrophoretic materials, and a value can be selected for the TAU that is typically approximated by the time constant of the stress level x(n) decay for several ink platforms and display systems.

[0129] Finally, x(n-1) is the stress level calculated after updating n-1. Those familiar with this technique will understand that some initial conditions are set so that x(n) can be calculated after the first update.

[0130] The second term in the LOS equation, DT(n) and TAU, represent the same quantities as the first term, while B is a quantity that varies depending on the driving mode used to update n. For example, if a fast-mode update is used to update n, B can be a non-zero positive value or an increase in the value of x(n), since a fast-mode update is likely to increase the residual voltage. Alternatively, if a standard-mode update is used to update n, B is set to zero, and the second term becomes zero.

[0131] The non-zero value of B used after a fast mode update remains unchanged across all updates, and the value of B is always set to zero after a standard mode update. In some embodiments, if a fast mode update is used to update n, the value of B used is a factor representing the worst-case residual voltage increase, based on an evaluation of the update sequence with the maximum DC imbalance and resulting in the maximum residual voltage increase. In some embodiments, if a fast mode update is used to update n, the value of B used is a factor representing the average amount of the residual voltage increase, based on an evaluation of the update sequence with the maximum DC imbalance and resulting in the maximum residual voltage increase.

[0132] From the stress level equation, it can be understood that increasing the update time UT(n) has the effect of reducing the growth of x(n) after each update. Similarly, increasing the post-drive discharge time DT(n) has the effect of reducing the growth of x(n) after each update. Conversely, it can be understood that updating in fast mode and interrupting each PDD routine has the effect of increasing the growth of x(n) after each update.

[0133] Once x(n) is calculated, method 1400 proceeds to step 1417, which includes receiving a subsequent update request. For example, one or more events described above with respect to step 1405 may result in the receipt of a subsequent request for updating the optical state of the display pixels of the electro-optical display.

[0134] Next, method 1400 proceeds to step 1420, which determines whether update n is a fast mode update or a standard mode update. If update n is a fast mode update, method 1400 proceeds to step 1425, where it determines whether x(n) is greater than a first threshold. If update n is a standard mode update, method 1400 proceeds to step 1435, where it determines whether x(n) is less than a second threshold.

[0135] The first threshold indicates the limit of the stress level that the display device can withstand. As shown in step 1425, if x(n) does not exceed the first threshold, the algorithm returns to step 1410 and performs another fast mode update. However, if x(n) has exceeded the first threshold, the algorithm cancels the next requested fast mode update and proceeds to step 1430 instead, where a standard mode update with lower stress on the display is used.

[0136] The standard mode update scheme is one that prioritizes update time and color accuracy in a similar manner. For example, using a standard mode update scheme combined with interrupting the PDD routine after each update and providing or substantially not providing a dwell time after each update, the update time on a display device, including a full-color e-ink system with four color pigments, can be as long as 1000 ms. However, the waveform used for standard mode updates is DC balanced, and it has been observed that residual voltage is reduced even when the PDD routine is immediately interrupted. This makes the standard mode update scheme well-suited for reducing stress levels on the display device with only a slight impact on the user experience, as standard mode updates would take 350-500 ms longer. In some embodiments, the drive waveform of the standard mode update scheme is approximately 30% to 55% longer in duration than that of the fast update scheme. In some embodiments, the drive waveform of the standard mode update scheme is approximately 50% to 70% longer in duration than that of the fast update scheme.

[0137] Once the algorithm has abandoned the fast mode update and the update n is the standard mode update, method 1400 proceeds from step 1420 to step 1435, in which it is determined whether x(n) is less than the second critical value.

[0138] This second, lower threshold is incorporated into the algorithm to allow for hysteresis, enabling the display to operate only in a low-stress mode until the stress level calculated and tracked by the algorithm decreases to a level that the display device can withstand. The first and second thresholds can be set to reduce the average stress level caused by residual charge accumulation, while also reducing the frequency with which the display device switches between operating modes under specific usage conditions.

[0139] As shown in step 1435, if x(n) is not yet less than the second threshold, the algorithm returns to step 1430 and performs another standard mode update. However, if x(n) is less than the second threshold, the algorithm returns to step 1410 and performs a fast mode update again.

[0140] Figure 15 shows a flowchart of another exemplary driving method 1500 that includes a residual voltage management state machine algorithm. The steps constituting method 1500 are generally similar to those of method 1400. Therefore, the steps of method 1500 are numbered in a manner consistent with similar steps in method 1400 as much as possible.

[0141] Method 1500 begins by determining (1505) a stress level of the display pixel of the electro-optic display based on at least one previous update to the optical state of the display pixel. For example, an algorithm using the exemplary equation described with respect to step 1415 of method 1400 can be used to calculate the stress level based on previous updates (e.g., n, n-1). As described above, initial conditions can be set such that x(n) can be calculated when there are no previous updates to the optical state of the display pixel, making x(n) undefined and / or undeterminable.

[0142] Method 1500 then includes receiving (1518) a request for updating the optical state of the display pixels. For example, one or more events described above with respect to step 1405 of method 1400 may result in the receipt of a request for updating the optical state of the display pixels of the electro-optical display.

[0143] Next, in step 1520, method 1500 determines whether the driving waveform used for the previous update of the display pixel comes from a first update scheme (e.g., a fast mode update scheme) or a second update scheme (e.g., a standard update scheme). If the driving waveform used for the previous update comes from the first update scheme, method 1500 proceeds to step 1525, in which it determines whether the stress level quantity x(n) is greater than a first stress level threshold. If the driving waveform used for the previous update comes from the second update scheme, method 1500 proceeds to step 1535, in which it determines whether the stress level quantity x(n) is less than a second stress level threshold.

[0144] From step 1520 to step 1525, method 1500 includes applying the driving waveform from the first update scheme to the display pixel when the driving waveform from the first update scheme is used for the previous update of the display pixel and the stress level is not greater than the first stress level threshold. Alternatively, method 1500 includes applying the driving waveform from the second update scheme to the display pixel when the driving waveform from the first update scheme is used for the previous update of the display pixel and the stress level is greater than the first stress level threshold.

[0145] For example, similar to step 1425 of method 1400, if the stress level does not exceed a first stress level threshold, the algorithm proceeds to step 1510 and applies a drive waveform from a first update scheme (e.g., fast mode update) to the display pixel. However, if the stress level has exceeded the first stress level threshold, the algorithm cancels the next requested fast mode update and proceeds to step 1530 instead, in which a drive waveform from a second update scheme with lower stress (e.g., standard mode update) is applied to the display pixel. After updating the optical state of the display pixel by applying a drive waveform from either the first update scheme (1510) or the second update scheme (1530), method 1500 returns to step 1515, in which the stress level is determined based on the update just completed, in preparation for any subsequent update request (e.g., step 1518).

[0146] When the driving waveform from the second update scheme was used in the previous update of the display pixel, method 1500 proceeds from step 1520 to step 1535, in which it is determined whether the stress level is less than a second stress level threshold. From step 1520 to step 1535, method 1500 includes applying the driving waveform from the first update scheme to the display pixel when the driving waveform from the second update scheme was used in the previous update of the display pixel and the stress level is less than the second stress level threshold. Alternatively, method 1500 includes applying the driving waveform from the second update scheme to the display pixel when the driving waveform from the second update scheme was used in the previous update of the display pixel and the stress level is not less than the second stress level threshold.

[0147] For example, similar to step 1435 of method 1400, if the stress level is not less than the second stress level threshold, the algorithm proceeds to step 1530 and applies a driving waveform from the second update scheme (e.g., standard mode update) to the display pixel. However, if the stress level is less than the second stress level threshold, the algorithm proceeds to step 1510, in which a driving waveform from the first update scheme (e.g., fast mode update) is applied to the display pixel. After updating the optical state of the display pixel by applying a driving waveform from either the first update scheme (1510) or the second update scheme (1530), method 1500 returns to step 1515, in which the stress level is determined based on the update just completed, in preparation for any subsequent update request (e.g., step 1518).

[0148] The overall application of the stress management state machine method described above enables the device to remain responsive to the user during continuous use. Users may not want to implement long display updates, but this is better than the device being locked and unresponsive for a period of time (even if the device provides the user with a notification, such as a pop-up window saying, "Please wait, I am relaxing...").

[0149] Implementing longer and / or DC balancing updates in this alternating state also has the advantage of accelerating the reduction of residual voltage and helping to reduce stress on the display.

[0150] Implementing DC unbalanced drive schemes has several advantages (such as enhanced performance), but residual voltage control becomes more important. The state machine approach described above allows these types of drive schemes to be implemented in the device by monitoring and managing stress on the display, while maintaining the device's responsiveness to the user. [H] [Partial: Display Controller]

[0151] As will be readily apparent from the foregoing description, many methods of the present invention require or provide desired modifications to display controllers of the prior art. For example, in the form of the GCMDS method described in Section B above, where an intermediate image flashes on the display between two desired images (this variant is referred to below as "Intermediate Image GCMDS" or "II-GCMDS" method), pixels experiencing the same overall transition (i.e., having the same initial and final grayscale) may undergo more than two different waveforms, depending on the grayscale of the pixels in the intermediate image. For example, in the II-GCMDS method shown in Figure 5, pixels that are white in both the initial and final images will experience two different waveforms, depending on whether they are white in the first intermediate image and black in the second intermediate image, or black in the first intermediate image and white in the second intermediate image. Thus, a display controller used to control such a method must typically map each pixel to one of the available transitions according to an image map associated with the transition image. Obviously, more than two transitions may be associated with the same initial and final states. For example, in the II-GCMDS method shown in Figure 4, a pixel may be black in both intermediate images, white in both intermediate images, or black in one intermediate image and white in another intermediate image, such that the white-to-white transition between the initial image and the final image may be associated with four different waveforms.

[0152] Various modifications to the display controller can be used to allow for the storage of transfer information. For example, the image data table, typically used to store the grayscale of each pixel in the final image, can be modified to store more than one additional bit to identify the category to which each pixel belongs. For instance, an image data table that previously stored 4 bits per pixel to indicate which of the 16 grayscale levels the pixel would represent in the final image might be modified to store 5 bits per pixel, where the most significant bit of each pixel specifies which of the two states (black or white) the pixel would represent in the monochrome intermediate image. Obviously, if the intermediate image is not monochrome, or if more than one intermediate image is used, it may be necessary to store more than one additional bit per pixel.

[0153] Alternatively, different image transitions can be encoded into different waveform patterns based on the transition state diagram. For example, waveform pattern A causes a pixel to undergo a transition where it is in a white state in the intermediate image, while waveform pattern B causes a pixel to undergo a transition where it is in a black state in the intermediate image.

[0154] Clearly, it is desirable for both waveform modes to begin updating simultaneously so that the intermediate image can be displayed smoothly, and for this purpose, the structure of the display controller needs to be changed. The main processor (i.e., the device that provides the image to the display controller) must instruct the display controller that the pixels loaded into the image buffer are associated with waveform mode A or B. This capability does not exist in controllers of the prior art. However, a reasonable approximation is to utilize the current controller's area update function (i.e., the function that allows the controller to use different driving schemes in different areas of the display) and initiate two modes with a single scan frame offset. For the intermediate image to be displayed correctly, this single scan frame offset must be taken into account when constructing waveform modes A and B. Furthermore, the main processor needs to load two images into the image buffer and control two area updates. Image 1 loaded into the image buffer must be a composite of the initial and final images, where only the pixels affected by the area of ​​waveform mode A are changed. Once the composite image is loaded, the main processor must instruct the controller to begin area updates using waveform mode A. The next step is to load image 2 into the image buffer and control the overall update using waveform mode B. Because the pixels controlled by the first region update command are already locked into the update process, only the pixels in the dark areas of the intermediate image of waveform mode B will undergo a full update. For current controller architectures, only controllers with a pipeline-per-pixel architecture and / or without restrictions on the size of the rectangular region can complete this procedure.

[0155] Because each individual transition in waveform pattern A and waveform pattern B is identical, only delayed by the length of their respective first pulse, the same result can be achieved using a single waveform. Here, the second update (the overall update in the previous section) is delayed by the length of the first waveform pulse. Then, image 2 is loaded into the image buffer and updated overall using the same waveform. It is necessary that the rectangular regions have the same degrees of freedom.

[0156] The BPPWWTG method of the present invention described in Section C above requires further modifications to the display controller. As stated, the BPPWWTG method requires applying balanced pulse pairs to certain pixels based on rules that take into account the transitions experienced by neighboring pixels of the pixel to which the balanced pulse pair can be applied. To achieve this, at least two additional transitions (not transitions between gray levels) are required, but the current 4-bit waveform cannot accommodate these additional states, thus necessitating a new method. Three options are discussed below.

[0157] The first option is to store at least one additional bit for each pixel in the same manner as described in the GCMDS method above. For such a system to operate, the next state information must be calculated for each pixel upstream of the display controller itself. The main processor must evaluate the initial and final image state of each pixel, as well as the image state of its nearest neighbor pixels, to determine the correct waveform for the pixel. An algorithm for this method has already been proposed above.

[0158] The second option for implementing the BPPWWTG method is similar to the option for implementing the GCMDS method, namely, encoding additional pixel states (beyond the normal 16 states representing grayscale) into two separate waveform patterns. An example is waveform pattern A and waveform pattern B, where waveform pattern A is a traditional 16-state waveform encoding transitions between optical grayscale levels, while waveform pattern B is a new waveform pattern encoding two states (states 16 and 17) and their transitions to state 15. However, this does create a potential problem: the pulse potentials of specific states in pattern B will not be the same as those in pattern A. One solution is to have as many patterns as white-to-white transitions and use only that transition in each pattern, resulting in patterns A, B, and C, but this is highly inefficient. Alternatively, a null waveform can be passed down, mapping the pixel undergoing the mode B to mode A transition to state 16 first, and then transitioning from state 16 in subsequent mode A transitions.

[0159] To implement a dual-mode waveform system like this, a similar approach to option 3 could be considered. First, the controller must determine how to change the next state of each pixel by performing a pixel-wise examination of the initial and final image states of the pixel along with the initial and final image states of its nearest neighbor pixels. For pixels transitioning to waveform mode A, the new states of those pixels must be loaded into the image buffer, and then the region updates of those pixels must be controlled to use waveform mode A. One frame later, for pixels transitioning to waveform mode B, the new states of those pixels must be loaded into the image buffer, and then the region updates of those pixels must be controlled to use waveform mode B. With current controller architectures, only controllers with a per-pixel pipeline architecture and / or no limit on the size of the rectangular region can complete the above procedure.

[0160] The third option is to use a new controller architecture with separate final and initial image buffers (which are loaded with consecutive images in turn) and additional storage for optional state information. This provides a pipelined operator that can perform various operations on each pixel, taking into account the initial, final, and additional states of each pixel's nearest neighbors and their effects on the pixel being considered. The operator calculates the waveform table index for each pixel and stores it in an individual memory location, and can selectively modify the stored state information for each pixel. Alternatively, a memory format can be used to chain all memory buffers into a single large character for each pixel. This reduces the number of reads from different storage locations for each pixel. Furthermore, a 32-bit character with a frame count timestamp field is proposed to allow arbitrary access to the waveform lookup table for any pixel (per-pixel pipeline). Finally, a pipeline structure for the operator is proposed, in which three image columns are loaded into a fast access register to allow data to be efficiently shifted to the operator structure.

[0161] The frame count timestamp and mode field are used to establish unique identifiers in the mode lookup table, providing the illusion of a pipeline for each pixel. These two fields allow each pixel to be assigned to one of 15 waveform mode differences (allowing a mode state to indicate no operation on the selected pixel) and one of 8196 frames (currently far exceeding the number of frames required to update the display). The trade-off for this increased flexibility—extending the waveform index from 16-bit in conventional controller designs to 32-bit—is the display scan speed. In a 32-bit system, twice the number of bits per pixel must be read from memory, and the controller has limited memory bandwidth (the rate at which data can be read from memory). This limits the panel scan rate because the entire waveform table index (currently consisting of 32-bit characters per pixel) must be read for each scan frame.

[0162] Operators can be general-purpose arithmetic logic units (ALUs) that can perform simple operations on the examined pixel and its nearest neighbor, such as: bitwise logical operations (AND, NOT, OR, XOR); integer arithmetic operations (addition, subtraction, and optional multiplication and division); and bitwise shift operations.

[0163] The nearest neighbor pixels are identified within the dashed boxes of pixels in the bounding box inspection. Instructions for the ALU can be hard-coded or stored in the system's non-volatile memory and loaded into the ALU instruction cache at startup. This architecture allows for great flexibility in designing new waveforms and algorithms for image processing.

[0164] The image preprocessing required by various methods of the present invention will now be considered. For dual-mode waveforms or waveforms using balanced pulse pairs, it may be necessary to map an n-bit image to an n+1-bit state. Several methods can be used for this operation: (a) Alpha blending allows for double transitions based on the transition map / mask. If a 1-bit alpha mask is maintained per pixel, and regions associated with transition mode A and transition mode B are identified, this map can be blended with the next n-bit image to produce an n+1-bit transition map image that can therefore use an n+1-bit waveform. A suitable algorithm is as follows: DP = αIP + (1-α)M {If M=0, then DP=0.5IP, which means the IP data is shifted 1 bit to the right. If M=1, then DP=IP, which means no data is shifted.} Where DP = display pixels IP = Image Pixels M = pixel mask (1 or 0) α=0.5 For the 5-bit example with 4-bit grayscale image pixels mentioned above, this algorithm sets the pixels located in the transfer mode A region (represented by 0 in the pixel mask) in the range of 16-31, and sets the pixels located in the transfer mode B region in the range of 0-15. (b) Simple raster operations can be demonstrated to be easier to implement. The same result can be achieved by performing an OR operation on only the mask bits to obtain the most significant bits of the image data. (c) The problem can also be solved by adding an additional 16 to the image pixels associated with one of the transfer areas based on a transfer map / mask.

[0165] For waveforms using balanced pulse pairs, the above steps may be necessary but insufficient. In the case of dual-mode waveforms with a fixed mask, BPP requires some significant calculations to generate the unique mask needed for correct conversion. This calculation step can eliminate the need for individual masking steps, where image analysis and display pixel calculations may include masking steps.

[0166] The SEEPDS method described in Section E above introduces additional complexity into the controller architecture, namely, the generation of "artificial" edges—edges that do not appear in the initial or final image but are defined as required for intermediate images that occur during transfer (e.g., as shown in Figure 12B). Conventional controller architectures only allow region updates to be performed within a single continuous rectangular boundary; however, as shown in Figure 13, SEEPDS (and potentially other driving methods) requires a controller architecture that allows simultaneous updates of multiple discontinuous regions of arbitrary shape and size.

[0167] A memory and controller architecture that meets this requirement reserves a (region) bit in the image buffer memory to indicate any pixel contained within a region. This region bit serves as a "gatekeeper" for updating buffer modifications and allocating lookup table numbers. In fact, this region bit can include multiple bits to represent individual, simultaneously updatable, and arbitrarily shaped regions that can be allocated different waveform patterns, thus allowing the selection of arbitrary regions without creating a new waveform pattern.

[0168] Those skilled in the art will readily recognize that many changes and modifications can be made to the specific embodiments of the invention described above without departing from the scope of the invention. Therefore, the entire foregoing description should be interpreted as illustrative rather than restrictive.

[0169] 1400: Method 1405: Steps 1410: Steps 1415: Steps 1417: Steps 1420: Steps 1425: Steps 1430: Steps 1435: Steps 1500: Method 1510: Steps 1515: Steps 1518: Steps 1520: Steps 1525: Steps 1530: Steps 1535: Steps

Claims

1. An electro-optical display, comprising: An electrophoretic material is coupled between a common front electrode and a display pixel electrode, the display pixel electrode being associated with a display pixel; A display controller is configured to change the optical state of one of the display pixels using one or more drive waveforms applied between the display pixel electrode and the common front electrode. The display controller is configured to perform the following steps: applying a drive waveform from a first update scheme to the display pixel; determining a stress level of one of the display pixels based on at least one previous update of the optical state of the display pixel; receiving a request to update the optical state of the display pixel; applying a drive waveform from a first update scheme to the display pixel when: (i) the drive waveform from the first update scheme was used for a previous update of the display pixel, and the stress level is not greater than a first stress level threshold; or (ii) the drive waveform from a second update scheme was used for a previous update of the display pixel, and the stress level is less than a second stress level threshold; and applying a drive waveform from a second update scheme to the display pixel when: (i) the drive waveform from the first update scheme was used for a previous update of the display pixel, and the stress level is greater than the first stress level threshold; or (ii) The driving waveform from the second update scheme is used for the previous update of the display pixel, and the stress level is not less than the second stress level threshold.

2. The electro-optical display as requested in item 1, wherein the request for updating the optical state of the display pixel of the electro-optical display is triggered by interaction with a user of the electro-optical display.

3. The electro-optical display as claimed in claim 2, wherein the user interaction includes swiping the screen surface of the electro-optical display.

4. The electro-optical display as requested in item 2, wherein the user interaction includes displaying animation on the electro-optical display.

5. The electro-optical display as requested in item 1, wherein the first update scheme includes a DC unbalanced drive waveform.

6. The electro-optical display as requested in item 1, wherein the second update scheme includes a DC-balanced drive waveform.

7. The electro-optical display as claimed in claim 1, wherein the second update scheme includes a drive waveform that is longer in duration than the drive waveform of the first update scheme.

8. The electro-optical display as claimed in claim 7, wherein the driving waveform of the second update scheme is approximately 350 ms to 500 ms longer in duration than the driving waveform of the first update scheme.

9. The electro-optical display of claim 7, wherein the driving waveform of the second update scheme is about 30% to 55% longer in duration than the driving waveform of the first update scheme.

10. The electro-optical display of claim 7, wherein the driving waveform of the second update scheme is about 50% to 70% longer in duration than the driving waveform of the first update scheme.

11. The electro-optical display of claim 1, wherein the stress level is an approximation of the actual residual voltage accumulated on the display pixel.

12. The electro-optical display of claim 1, wherein the stress level quantity comprises a pure quantity indicating an index of the increase or decrease of the amount of residual voltage accumulated on the display pixel.

13. The electro-optical display of claim 1, wherein determining the stress level of the display pixel includes calculating the following equation: where, x(n) represents the stress level of an update n, UT(n) represents the duration (in milliseconds) of the drive waveform used for the previous update of the display pixel, DT(n) represents the number of milliseconds of the subsequent drive discharge routine applied after the previous update of the display pixel, TAU represents the decay time constant of the stress level x(n), e represents the exponential function, x(n-1) is a stress level calculated based on the previous update of the display pixel, and B has a value that changes according to the drive mode used for the update n.

14. The electro-optical display of claim 13, wherein B is set to a non-zero positive value after the driving waveform from the first update scheme is applied to the display pixel.

15. The electro-optical display of claim 13, wherein after the driving waveform from the second update scheme is applied to the display pixel, the value of B is set to zero.

16. The electro-optical display as claimed in claim 1 further includes interrupting a post-drive discharge routine after applying the drive waveform from the first update scheme.

17. The electro-optical display as claimed in claim 1 further includes substantially not performing a dwell time after applying the drive waveform from the first update scheme.

18. The electro-optical display as claimed in claim 1 further includes interrupting a post-drive discharge routine after applying the drive waveform from the second update scheme.

19. The electro-optical display as claimed in claim 1 further includes substantially not performing a dwell time after applying the drive waveform from the second update scheme.

20. The electro-optic display of claim 1, wherein the first stress level critical value represents the limit of the stress level that the electro-optic display can withstand.

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