EP1614097A4

EP1614097A4 - Methods for driving bistable electro-optic displays

Info

Publication number: EP1614097A4
Application number: EP04758742A
Authority: EP
Inventors: Karl R Amundson; Robert W Zehner; Ara Knaian; Benjamin Zion
Original assignee: E Ink Corp
Current assignee: E Ink Corp
Priority date: 2003-03-31
Filing date: 2004-03-31
Publication date: 2009-08-12
Also published as: HK1175579A1; JP2012133380A; EP1614097A1; JP2014063185A; KR100857745B1; WO2004090857A1; KR20050116160A; CN102768822B; JP4599349B2; CN102074200B; CN102074200A; JP2011008271A; JP5734395B2; CN102768822A; JP5005800B2; HK1128809A1; HK1157925A1; JP5632861B2; JP2014059577A; JP2006522372A

Abstract

A gray scale bistable electro-optic display is driven by storing a look-up table containing data representing the impulses necessary for transitions, storing data representing at least an initial state of each pixel of the display, receiving an input signal representing a desired final state of at least one pixel of the display; and generating an output signal representing a pixel voltage to be applied to the pixel. Compensation voltage data representing a compensation voltage is stored for each pixel, the compensation voltage for each pixel being calculated dependent upon at least one impulse previously applied to that pixel, and the pixel voltage is the sum of a drive voltage determined from the initial and final states of the pixel and the look-up table, and a compensation voltage determined from the compensation voltage data for the pixel. Other similar methods for driving such displays are also disclosed.

Description

METHODS FOR DRIVING BISTABLE ELECTRO-OPTIC

DISPLAYS

[0001] This application is related to International Application No.

PCT/US02/37241. Publication No. WO 03/044765, the entire contents of which are herein incorporated by reference.

[0002] This invention relates to methods for driving electro-optic displays, especially bistable electro-optic displays; this application also related to apparatus for use in such methods. More specifically, this invention relates to driving methods and apparatus (controllers) which are intended to enable more accurate control of gray states of the pixels of an electro-optic display. This invention also relates to a method which enables long-term direct current (DC) balancing of the driving impulses applied to an electrophoretic display. This invention is especially, but not exclusively, intended for use with particle-based electrophoretic displays in which one or more types of electrically charged particles are suspended in a liquid and are moved through the liquid under the influence of an electric field to change the appearance of the display.

[0003] The term "electro-optic" as applied to a material or a display, is used herein in its conventional meaning in the imaging art to refer to a material having first and second display states differing in at least one optical property, the material being changed from its first to its second display state by application of an electric field to the material. Although the optical property is typically color perceptible to the human eye, it may be another optical property, such as optical transmission, reflectance, luminescence or, in the case of displays intended for machine reading, pseudo-color in the sense of a change in reflectance of electromagnetic wavelengths outside the visible range.

[0004] The term "gray state" is used herein in its conventional meaning in the imaging art to refer to a state intermediate two extreme optical states of a pixel, and does not necessarily imply a black-white transition between these two extreme states. For example, several of the patents and published applications referred to below describe electrophoretic displays in which the extreme states are white and deep blue, so that an intermediate "gray state" would actually be pale blue. Indeed, as already mentioned the transition between the two extreme states may not be a color change at all.

[0005] The terms "bistable" and "bistability" are used herein in their conventional meaning in the display art to refer to displays comprising display elements having first and second display states differing in at least one optical property, and such that after any given element has been driven, by means of an addressing pulse of finite duration, to assume either its first or second display state, after the addressing pulse has terminated, that state will persist for at least several times, for example at least four times, the minimum duration of the addressing pulse required to change the state of the display element. It is shown in published U.S. Patent Application No. 2002/0180687 that some particle-based electrophoretic displays capable of gray scale are stable not only in their extreme black and white states but also in their intermediate gray states, and the same is true of some other types of electro-optic displays. This type of display is properly called "multi-stable" rather than bistable, although for convenience the term "bistable" may be used herein to cover both bistable and multi-stable displays. [0006] The term "gamma voltage" is used herein to refer to external voltage references used by drivers to determine voltages to be applied to pixels of a display. It will be appreciated that a bistable electro-optic medium does not display the type of one-to-one correlation between applied voltage and optical state characteristic of liquid crystals, the use of the term "gamma voltage" herein is not precisely the same as with conventional liquid crystal displays, in which gamma voltages determine inflection points in the voltage level/output voltage curve. [0007] The term "impulse" is used herein in its conventional meaning of the integral of voltage with respect to time. However, some bistable electro-optic media act as charge transducers, and with such media an alternative definition of impulse, namely the integral of current over time (which is equal to the total charge applied) may be used. The appropriate definition of impulse should be used, depending on whether the medium acts as a voltage-time impulse transducer or a charge impulse transducer. [0008] Several types of electro-optic displays are known. One type of electro-optic display is a rotating bichromal member type as described, for example, in U.S. Patents Nos. 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 as more accurate since in some of the patents mentioned above the rotating members are not spherical). Such a display uses a large number of small bodies (typically spherical or cylindrical) which have two or more sections with differing optical characteristics, and an internal dipole. These bodies are suspended within liquid-filled vacuoles within a matrix, the vacuoles being filled with liquid so that the bodies are free to rotate. The appearance of the display is changed to applying an electric field thereto, thus rotating the bodies to various positions and varying which of the sections of the bodies is seen through a viewing surface. This type of electro-optic medium is typically bistable. [0009] Another type of electro-optic display uses an electrochromic medium, for example an electrochromic medium in the form of a nanochromic film comprising an electrode formed at least in part from a semi-conducting metal oxide and a plurality of dye molecules capable of reversible color change attached to the electrode; see, for example O'Regan, B., et al., Nature 1991, 353, 737; and Wood, D., Information Display, 18(3), 24 (March 2002). See also Bach, U., et al., Adv. Mater., 2002, 14(11), 845. Nanochromic films of this type are also described, for example, in U.S. Patent No. 6,301,038, International Application Publication No. WO 01/27690, and in U.S. Patent Application 2003/0214695. This type of medium is also typically bistable.

[0010] Another type of electro-optic display, which has been the subject of intense research and development for a number of years, is the particle-based electrophoretic display, in which a plurality of charged particles move through a suspending fluid under the influence of an electric field. Electrophoretic displays can have attributes of good brightness and contrast, wide viewing angles, state bistability, and low power consumption when compared with liquid crystal displays. Nevertheless, problems with the long-term image quality of these displays have prevented their widespread usage. For example, particles that make up electrophoretic displays tend to settle, resulting in inadequate service-life for these displays.

[0011] Numerous patents and applications assigned to or in the names of the Massachusetts Institute of Technology (MIT) and E Ink Corporation have recently been published describing encapsulated electrophoretic media. Such encapsulated media comprise numerous small capsules, each of which itself comprises an internal phase containing electrophoretically-mobile particles suspended in a liquid suspending medium, and a capsule wall surrounding the internal phase. Typically, the capsules are themselves held within a polymeric binder to form a coherent layer positioned between two electrodes. Encapsulated media of this type are described, for example, in U.S. Patents Nos. 5,930,026 5,961,804; 6,017,584; 6,067,185; 6,118,426; 6,120,588; 6,120,839; 6,124,851 6,130,773; 6,130,774; 6,172,798; 6,177,921; 6,232,950; 6,249,721; 6,252,564 6,262,706;^' 6,262,833; 6,300,932; 6,312,304; 6,312,971; 6,323,989; 6,327,072 6,376,828; 6,377,387; 6,392,785; 6,392,786; 6,413,790; 6,422,687; 6,445,374 6,445,489; 6,459,418; 6,473,072; 6,480,182; 6,498,114; 6,504,524; 6,506,438 6,512,354; 6,515,649; 6,518,949; 6,521,489; 6,531,997; 6,535,197; 6,538,801 6,545,291; 6,580,545; 6,639,578; 6,652,075; 6,657,772; 6,664,944; 6,680,725 6,683,333; and 6,704,133; and U.S. Patent Applications Publication Nos

2002/0019081; 2002/0021270; 2002/0053900; 2002/0060321 2002/0063661 2002/0063677; 2002/0090980; 2002/0106847; 2002/0113770 2002/0130832 2002/0131147; 2002/0145792; 2002/0171910; 2002/0180687 2002/0180688 2002/0185378; 2003/0011560; 2003/0011868; 2003/0020844 2003/0025855 2003/0034949; 2003/0038755; 2003/0053189; 2003/0096113 2003/0102858 2003/0132908; 2003/0137521; 2003/0137717; 2003/0151702 2003/0189749 2003/0214695; 2003/0214697; 2003/0222315; 2004/0008398 2004/0012839 2004/0014265; and 2004/0027327; and International Applications Publication Nos. WO 99/67678; WO 00/05704; WO 00/38000; WO 00/38001; WO00/36560; WO 00/67110; WO 00/67327; WO 01/07961; WO 01/08241; WO 03/092077; and WO 03/107,315. [0012] Many of the aforementioned patents and applications recognize that the walls surrounding the discrete capsules in an encapsulated electrophoretic medium could be replaced by a continuous phase, thus producing a so-called "polymer-dispersed electrophoretic display" in which the electrophoretic medium comprises a plurality of discrete droplets of an electrophoretic fluid and a continuous phase of a polymeric material, and that the discrete droplets of electrophoretic fluid within such a polymer-dispersed electrophoretic display may be regarded as capsules or microcapsules even though no discrete capsule membrane is associated with each individual droplet; see for example, the aforementioned 2002/0131147. Accordingly, for purposes of the present application, such polymer-dispersed electrophoretic media are regarded as subspecies of encapsulated electrophoretic media.

[0013] An encapsulated electrophoretic display typically does not suffer from the clustering and settling failure mode of traditional electrophoretic devices and provides further advantages, such as the ability to print or coat the display on a wide variety of flexible and rigid substrates. (Use of the word "printing" is intended to include all forms of printing and coating, including, but without limitation: pre-metered coatings such as patch die coating, slot or extrusion coating, slide or cascade coating, curtain coating; roll coating such as knife over roll coating, forward and reverse roll coating; gravure coating; dip coating; spray coating; meniscus coating; spin coating; brush coating; air knife coating; silk screen printing processes; electrostatic printing processes; thermal printing processes; ink jet printing processes; and other similar techniques.) Thus, the resulting display can be flexible. Further, because the display medium can be printed (using a variety of methods), the display itself can be made inexpensively. [0014] A related type of electrophoretic display is a so-called "microcell electrophoretic display". In a microcell electrophoretic display, the charged particles and the suspending fluid are not encapsulated within capsules but instead are retained within a plurality of cavities formed within a carrier medium, typically a polymeric film. See, for example, International Application Publication No. WO 02/01281, and U.S. Patent Application Publication No. 2002/0075556, both assigned to Sipix Imaging, Inc.

[0015] Although electrophoretic media are often opaque (since, for example, in many electrophoretic media, the particles substantially block transmission of visible light through the display) and operate in a reflective mode, many electrophoretic displays can be made to operate in a so-called "shutter mode" in which one display state is substantially opaque and one is light-transmissive. See, for example, the aforementioned U.S. Patents Nos. 6,130,774 and 6,172,798, and U.S. Patents Nos. 5,872,552; 6,144,361; 6,271,823; 6,225,971; and 6,184,856. Dielectrophoretic displays, which are similar to electrophoretic displays but rely upon variations in electric field strength, can operate in a similar mode; see U.S. Patent No. 4,418,346.

[0016] The bistable or multi-stable behavior of particle-based electrophoretic displays, and other electro-optic displays displaying similar behavior, is in marked contrast to that of conventional liquid crystal ("LC") displays. Twisted nematic liquid crystals act are not bi- or multi-stable but act as voltage transducers, so that applying a given electric field to a pixel of such a display produces a specific gray level at the pixel, regardless of the gray level previously present at the pixel. Furthermore, LC displays are only driven in one direction (from non-transmissive or "dark" to transmissive or "light"), the reverse transition from a lighter state to a darker one being effected by reducing or eliminating the electric field. Finally, the gray level of a pixel of an LC display is not sensitive to the polarity of the electric field, only to its magnitude, and indeed for technical reasons commercial LC displays usually reverse the polarity of the driving field at frequent intervals.

[0017] In contrast, bistable electro-optic displays act, to a first approximation, as impulse transducers, so that the final state of a pixel depends not only upon the electric field applied and the time for which this field is applied, but also upon the state of the pixel prior to the application of the electric field. Furthermore, it has now been found, at least in the case of many particle-based electro-optic displays, that the impulses necessary to change a given pixel through equal changes in gray level (as judged by eye or by standard optical instruments) are not necessarily constant, nor are they necessarily commutative. For example, consider a display in which each pixel can display gray levels of 0 (white), 1, 2 or 3 (black), beneficially spaced apart. (The spacing between the levels may be linear in percentage reflectance, as measured by eye or by instruments but other spacings may also be used. For example, the spacings may be linear in L* (where L* has the usual CLE definition: [0018] L* = 116(R/Ro)^{1 3} - 16,

[0019] where R is the reflectance and Ro is a standard reflectance value), or may be selected to provide a specific gamma; a gamma of 2.2 is often adopted for monitors, and where the present displays are be used as a replacement for a monitor, use of a similar gamma may be desirable.) It has been found that the impulse necessary to change the pixel from level 0 to level 1 (hereinafter for convenience referred to as a "0-1 transition") is often not the same as that required for a 1-2 or 2-3 transition. Furthermore, the impulse needed for a 1-0 transition is not necessarily the same as the reverse of a 0-1 transition, hi addition, some systems appear to display a "memory" effect, such that the impulse needed for (say) a 0-1 transition varies somewhat depending upon whether a particular pixel undergoes 0-0-1, 1-0-1 or 3-0-1 transitions. (Where, the notation "x-y-z", where x, y, and z are all optical states 0, 1, 2, or 3 denotes a sequence of optical states visited sequentially in time, list from earlier to later.) Although these problems can be reduced or overcome by driving all pixels of the display to one of the extreme states for a substantial period before driving the required pixels to other states, the resultant "flash" of solid color is often unacceptable; for example, a reader of an electronic book may desire the text of the book to scroll down the screen, and may be distracted, or lose his place, if the display is required to flash solid black or white at frequent intervals. Furthermore, such flashing of the display increases its energy consumption and may reduce the working lifetime of the display. Finally, it has been found that, at least in some cases, the impulse required for a particular transition is affected by the temperature and the total operating time of the display, and by the time that a specific pixel has remained in a particular optical state prior to a given transition, and that compensating for these factors is desirable to secure accurate gray scale rendition.

[0020] Furthermore, as will readily be apparent from the foregoing discussion, the drive requirements of bistable electro-optic media render unmodified drivers designed for driving active matrix liquid crystal displays (AMLCD's) unsuitable for use in bistable electro-optic media-based displays. However, such AMLCD drivers are readily available commercially, with large permissible voltage ranges and high pin-count packages, on an off-the-shelf basis, and are inexpensive, so that such AMLCD drives are attractive for drive bistable electro-optic displays, whereas similar drivers custom designed for bistable electro-optic media-based displays would be substantially more expensive, and would involve substantial design and production time. Accordingly, there are cost and development time advantages in modifying AMLCD drivers for use with bistable electro-optic displays, and this invention seeks to provide a method and modified driver which enables this to be done.

[0021] Also, as already noted, this invention relates to methods for driving electrophoretic displays which enable long-term DC-balancing of the driving impulses applied to the display. It has been found that encapsulated and other electrophoretic displays need to be driven with accurately DC-balanced waveforms (i.e., the integral of current against time for any particular pixel of the display should be held to zero over an extended period of operation of the display) to preserve image stability, maintain symmetrical switching characteristics, and provide the maximum useful working lifetime of the display. Conventional methods for maintaining precise DC-balance require precision-regulated power supplies, precision voltage-modulated drivers for gray scale, and crystal oscillators for timing, and the provision of these and similar components adds greatly to the cost of the display.

[0022] (Strictly speaking, DC balance should be measured "internally" having regard to the voltages experienced by the electro-optic medium itself. However, in practice it is impracticable to effect such internal measurements in an operating display which may contain hundreds of thousands of pixels, and in practice DC balance is measured using an "external" measurement, namely the voltages applied to the electrodes disposed on opposed sides of the electro-optic medium. Furthermore, there are two assumptions normally made when discussing DC balance. Firstly, it is assumed, normally with good reason, that the conductivity of the electro-optic medium is not a function of polarity, so that pulse length is an appropriate way to track DC balance, when a constant voltage is applied. Secondly, it is assumed that the conductivity of the electro-optic medium is proportional to the applied voltage, so that one can use impulse to track DC balance.) [0023] Hereinafter the term "superframe" will be used to denote a sequence of successive display scan frames needed to effect all necessary gray level changes from an initial image to a final image. Typically, a display update is initiated only at the beginning of a superframe.

[0024] The aforementioned WO 03/044765 describes a method of driving a bistable electro-optic display having a plurality of pixels, each of which is capable of displaying at least three gray levels (as is conventional in the display art, the extreme black and white states are regarded as two gray levels for purposes of counting gray levels). The method comprises:

[0025] storing a look-up table containing data representing the impulses necessary to convert an initial gray level to a final gray level;

[0026] storing data representing at least an initial state of each pixel of the display;

[0027] receiving an input signal representing a desired final state of at least one pixel of the display; and

[0028] generating an output signal representing the impulse necessary to convert the initial state of said one pixel to the desired final state thereof, as determined from the look-up table.

[0029] This method may hereinafter for convenience be referred to as the

"basic look-up table method.

[0030] Depending upon the number of prior states stored, the look-up tables used in look-up table methods may become very large. To take an extreme example, consider a look-up table method for a 256 (2⁸) gray level display using an algorithm that takes account of initial, final and two prior states. The necessary four-dimensional look-up table has 2³² entries. If each entry requires (say) 64 bits (8 bytes), the total size of the look-up table would be approximately 32 Gbyte. While storing this amount of data poses no problems on a desktop computer, it may present problems in a portable device. In another aspect, this invention provides a method for driving a bistable electro-optic display which achieves results similar to those of the look-up table method but which does not require the storage of very large look-up tables.

[0031] One aspect of the present invention relates to methods and apparatus for driving a bistable electro-optic display in a manner which permits part of the display to operate at a different bit depth (i.e., different number of gray scale levels) from the remainder of the display. From the description of the sawtooth driving method illustrated in Figures 11A and 11B of the aforementioned WO 03/044765, it will be apparent to those skilled in the art that transitions between successive images in general image flow of bistable electro-optic displays having numerous gray scale levels can be substantially longer than transitions if the same displays were being driven in monochrome mode. Typically, gray scale transitions may be up to four times as long as the corresponding monochrome transitions. The relatively slow gray scale transitions may not be objectionable when the display is being used to present a series of images, such as a series of photographs or successive pages of an electronic book. However, there are times when it would be useful to achieve rapid updating of a limited area of such a display. For example, consider a situation where a user employs such a display to review of series of photographs stored in a database in order to enter for each photograph key words or other indexing terms intended to facilitate later retrieval of images from the database. In this situation, relatively slow transitions between successive photographs may be tolerable; for example, if the user spends one to two minutes studying each photograph and deciding on the indexing terms, a one to two second transition between successive photographs does not greatly affect the user's productivity. However, as is well known to anyone who has tried to run a word processing program on a computer with inadequate processing power, a one to two second delay in updating a dialog box, in which are displayed the indexing terms being entered by the user, is extremely frustrating and likely to lead to numerous typing errors. Accordingly, in this and similar situations, it would be advantageous to be able to run the dialog box in a monochrome mode to permit swift transitions, while continuing to run the remainder of the display in a gray scale mode to enable the images to be reproduced accurately, and this invention provides a method and apparatus to enable this to be done.

[0032] Another aspect of the present invention relates methods to achieve fine control of gray levels of an impulse drive imaging medium without the need for fine voltage control. Although as already indicated, electrophoretic and some other electro-optic displays exhibit bistability, this bistability is not unlimited, and images on the display slowly fade with time, so that if an image is to be maintained for extended periods, the image may have to be refreshed periodically, so as to restore the image to the optical state which it has when first written. [0033] However, such refreshing of the image may give rise to its own problems. As discussed in the aforementioned U.S. Patents Nos. 6,531,997 and 6,504,524, problems may be encountered, and the working lifetime of a display reduced, if the method used to drive the display does not result in zero, or near zero, net time-averaged applied electric field across the electro-optic medium. A drive method which does result in zero net time-averaged applied electric field across the electro-optic medium is conveniently referred to a "direct current balanced" or "DC balanced". If an image is to be maintained for extended periods by applying refreshing pulses, these pulses need to be of the same polarity as the addressing pulse originally used to drive the relevant pixel of the display to the optical state being maintained, which results in a DC unbalanced drive scheme. [0034] A challenge for achieving accurate gray scale levels in an impulse driven medium is applying the appropriate voltage impulse for achieving the desired gray tone. Satisfactory transitions between optical states can be achieved by fine control of the voltage of all or part of the drive waveform. The need for precision can be understood from the following example. Consider the case where a current image consists of a screen that is half black and half white, and the desired next image is a uniform gray intermediate between black and white. In order to achieve a uniform gray level, the impulses used to go from black to gray and white to gray have to be finely adjusted so that the gray level achieved coming from black matches the gray level coming from white. Fine tuning is further needed if the final gray level achieved is a function of prior gray level history of the display. For example, as already discussed, the optical state achieved when going from black to gray can be a function, not only of the waveform applied, but also of what state was visited before the current black state. It is then desirable to have the display module keep track of some aspects of the display history, such as prior image states, and allow fine tuning of the waveform to compensate for this prior state history (see below for more detailed discussions on this point). [0035] Fine tuning of the impulse can be achieved using only three voltage levels (0, +N, -N), by adjusting the width of the applied pulse with high accuracy. However, this is not desirable for an active matrix display, since the frame rate must be increased in order to achieve high pulse width resolution. A high frame rate increases the power consumption of the display, and puts more strenuous demands on the control and drive electronics. It is therefore not desirable to operate an active matrix display at frame rates substantially above 60-75 Hz. [0036] Fine tuning of the impulse can also be achieved if a number of finely-spaced voltages are available. In an active matrix drive, this requires source drivers that can output one of a numerous set of voltages available over at least a subset of the available voltages. For example, for a driver that outputs between -10 and +10 volts, it may be advantageous to have available 0 V, and two bands of voltages between -10 and -7 volts and between 7 and 10 volts, with 16 distinct voltage levels between -10 and -7 volts and 16 distinct voltage levels between 7 and 10 volts bringing the total number of required voltage levels to 33 (see Table 1). One could then achieve fine control of the optical final state, for example, by varying the voltage between +7 and +10 or between -10 and -7 volts for the last one or more scan frames of the addressing period. This method is an example of a voltage-modulated technique for achieving acceptable display performance. [0037] Table 1 : Example of voltages needed for voltage modulated drive

[0038] The disadvantage of using voltage-modulated techniques is that drivers must have some range of fine voltage control. Display module cost can be reduced by using drivers that offer only two or three voltages. [0039] In another aspect, this invention seeks to provide methods for achieving fine control of gray levels using drivers with only a small set of available voltages, specifically, where the control of impulse is too coarse to achieve the fine tuning necessary for acceptable display performance. Thus, this aspect of the present invention seeks to provide methods to achieve fine control of gray levels of an impulse driven imaging medium without the need for fine voltage control. This aspect of the invention can be applied, for example, to an active matrix display that has source drivers that can output only two or three voltages. [0040] In another aspect, this invention relates to a method of driving an electro-optic display using a drive scheme that contains at least some direct current (DC) balanced transitions. For reasons explained at length in the aforementioned copending applications, when driving an electro-optic display it is desirable to use a drive scheme that is DC balanced, i.e., on which has the property that, for any sequence of optical states, the integral of the applied voltage is zero whenever the final optical state matches the initial optical state. This guarantees that the net DC imbalance experienced by the electro-optic layer is bounded by a known value. For example, a 15V, 300 ms pulse may be used to drive an electro-optic layer from the white to the black state. After this transition, the imaging layer has experienced 4.5 N-s of DC-imbalance impulse. To drive the film back to white, if a -15N, 300ms pulse is used, then the imaging layer is DC balanced across the series of transitions from white to black and back to white.

[0041] It has also been found desirable to use a drive scheme in which at least some of the transitions are themselves DC balanced; such transitions are hereinafter termed "DC balanced transitions". A DC-balanced transition has no net voltage impulse. A drive scheme waveform that employs only DC-balanced transitions leaves the electro-optic layer DC balanced after each transition. For example, a -15N, 300ms pulse followed by a 15N, 300ms pulse might be used to drive the electro-optic layer from white to black. The net voltage impulse across the electro-optic layer across this transition is zero. One might then use a 15N, 300ms pulse followed by a -15N 300ms pulse to drive the electro-optic layer back to white. Again, the net voltage impulse is zero across this transition. [0042] A drive scheme composed of all DC-balanced transition elements is, by necessity, a DC-balanced waveform. It is also possible to formulate a DC- balanced drive scheme that contains DC-balanced transitions and DC-imbalanced transitions, as discussed in detail below.

[0043] In one aspect, this invention provides a method of driving a bistable electro-optic display having a plurality of pixels, each of which is capable of displaying at least three gray levels, the method comprising: [0044] storing a look-up table containing data representing the impulses necessary to convert an initial gray level to a final gray level; [0045] storing data representing at least an initial state of each pixel of the display;

[0046] storing compensation voltage data representing a compensation voltage for each pixel of the display, the compensation voltage for any pixel being calculated dependent upon at least one impulse previously applied to that pixel; [0047] receiving an input signal representing a desired final state of at least one pixel of the display; and [0048] generating an output signal representing a pixel voltage to be applied to said one pixel, said pixel voltage being the sum of a drive voltage determined from the initial and final states of the pixel and the look-up table, and a compensation voltage determined from the compensation voltage data for the pixel.

[0049] This method may hereinafter for convenience be referred to as the

"compensation voltage" method of the present invention.

[0050] In this compensation voltage method, the compensation voltage for each pixel may be calculated dependent upon at least one of a temporal prior state of the pixel and a gray level prior state of the pixel. Also, the compensation voltage for each pixel may be applied to that pixel both during a period when a drive voltage is being applied to the pixel and during a hold period when no drive voltage is being applied to the pixel.

[0051] For reasons explained in detail below, it is necessary periodically to update the compensation voltages used in the compensation voltage method of the present invention. The compensation voltage for each pixel may be updated during each superframe (the period required for a complete addressing of the display). The compensation voltage for each pixel may be updated by (1) modifying the previous value of the compensation voltage using a fixed algorithm independent of the pulse applied during the relevant superframe; and (2) increasing the value from step (1) by an amount determined by the pulse applied during the relevant superframe. hi a preferred variant of this updating procedure, the compensation voltage for each pixel is updated by (1) dividing the previous value of the compensation voltage by a fixed constant; and (2) increasing the value from step (1) by an amount substantially proportional to the total area under the voltage/time curve applied to the electro-optic medium during the relevant superframe.

[0052] In the compensation voltage method of the present invention, the compensation voltage may be applied in the form of an exponentially decaying voltage applied at the end of at least one drive pulse.

[0053] This invention also provides a device controller for use in such a compensation voltage method. The controller comprises: [0054] storage means arranged to store both a look-up table containing data representing the impulses necessary to convert an initial gray level to a final gray level, data representing at least an initial state of each pixel of the display; and compensation voltage data for each pixel of the display;

[0055] input means for receiving an input signal representing a desired final state of at least one pixel of the display;

[0056] calculation means for determining, from the input signal, the stored data representing the initial state of said pixel, and the look-up table, a drive voltage required to change the initial state of said one pixel to the desired final state, the calculation means also determining, from the compensation voltage data for said pixel, a compensation voltage for said pixel, and summing the drive voltage and the compensation voltage to determine a pixel voltage; and [0057] output means for generating an output signal representative of said pixel voltage.

[0058] In this controller, the calculation means may be arranged to determine the compensation voltage dependent upon at least one of a temporal prior state of the pixel and a gray level prior state of the pixel. Also, the output means may be arranged to apply the compensation voltage to the pixel both during a period when a drive voltage is being applied to the pixel and during a hold period when no drive voltage is being applied to the pixel.

[0059] Furthermore, in this controller, the calculation means may be arranged to update the compensation voltage for each pixel during each superframe required for a complete addressing of the display. For such updating, the calculation means may be arranged to update the compensation voltage for each pixel by (1) modifying the previous value of the compensation voltage using a fixed algorithm independent of the pulse applied during the relevant superframe; and (2) increasing the value from step (1) by an amount determined by the pulse applied during the relevant superframe. In a preferred variant of this procedure, the calculation means is arranged to update the compensation voltage for each pixel by (1) dividing the previous value of the compensation voltage by a fixed constant; and (2) increasing the value from step (1) by an amount substantially proportional to the total area under the voltage/time curve applied to the electro-optic medium during the relevant superframe.

[0060] The output means of the controller may be arranged to apply the compensation voltage in the form of an exponentially decaying voltage applied at the end of at least one drive pulse.

[0061] In another aspect, this invention provides a method for updating a bistable electro-optic display having a plurality of pixels arranged in a plurality of rows and columns such that each pixel is uniquely defined by the intersection of a specified row and a specified column, and drive means for applying electric fields independently to each of the pixels to vary the display state of the pixel, each pixel having at least three different display states, the method comprising:

[0062] storing region data representing a defined region comprising a part but less than all of said display;

[0063] determining for each pixel whether the pixel is within or outside the defined region;

[0064] applying a first drive scheme to pixels within the defined region and a second drive scheme, different from the first drive scheme, to pixels outside the defined region.

[0065] This method may hereinafter for convenience be referred to as the

"defined region" method of the present invention.

[0066] hi this defined region method, the first and second drive schemes may differ in bit depth; in particular, one of the first and second drive schemes may be monochrome and the other may be gray scale having at least four different gray levels. The defined region may comprise a text box used for entry of text on to the display.

[0067] In another aspect, this invention provides a method of driving a bistable electro-optic display having a plurality of pixels, each of which is capable of displaying at least three gray levels, the method comprising:

[0068] storing a look-up table containing data representing the impulses necessary to convert an initial gray level to a final gray level; [0069] storing data representing at least an initial state of each pixel of the display;

[0070] receiving an input signal representing a desired final state of at least one pixel of the display; and

[0071] generating an output signal representing the impulse necessary to convert the initial state of said one pixel to the desired final state thereof, as determined from the look-up table,

[0072] wherein for at least one transition from an initial state to a final state, the output signal comprises a DC imbalanced fine tuning sequence which:

[0073] (a) has a non-zero net impulse;

[0074] (b) is non-contiguous;

[0075] (c) results in a change in gray level of the pixel that is substantially different (typically differs by more than 50 per cent) from the change in optical state of its DC reference pulse, where the DC reference pulse is a pulse of voltage No, where No is the maximum voltage applied during the fine tuning sequence but with the same sign as the net impulse G of the fine tuning sequence, and the duration of the reference pulse is G/V₀; and

[0076] (d) results in a change in gray level of the pixel smaller in magnitude than (typically less than half of) the change in gray level caused by its time-reference pulse, where the time-reference pulse is defined as a monopolar voltage pulse of the same duration as the fine tuning sequence, but where the sign of the reference pulse is that which gives the larger change in gray level.

[0077] This method (and the similar method defined below) may hereinafter for convenience be referred to as the "non-contiguous addressing" method of the present invention; when it is necessary to distinguish between the two methods they may be referred to as the "DC imbalanced non-contiguous addressing" method and the "DC balanced non-contiguous addressing" method respectively.

[0078] In a preferred form of this non-contiguous addressing method, the fine tuning sequence results in a change in gray level of the pixel less than one half of the change in gray level caused by its time-reference pulse. [0079] This invention also provides a method of driving a bistable electro- optic display having a plurality of pixels, each of which is capable of displaying at least three gray levels, the method comprising:

[0080] storing a look-up table containing data representing the impulses necessary to convert an initial gray level to a final gray level; [0081] storing data representing at least an initial state of each pixel of the display;

[0082] receiving an input signal representing a desired final state of at least one pixel of the display; and

[0083] generating an output signal representing the impulse necessary to convert the initial state of said one pixel to the desired final state thereof, as determined from the look-up table,

[0084] wherein for at least one transition from an initial state to a final state, the output signal comprises a DC balanced fine tuning sequence which: [0085] (a) has substantially zero net impulse; and

[0086] (b) at no point in the fine tuning sequence, causes the gray level of the pixel to vary from its gray level at the beginning of the fine tuning sequence by more than about one third of the difference in gray level between the two extreme optical states of the pixel.

[0087] In both variants of the non-contiguous addressing method of the present invention, the output signal typically comprises at least one monopolar drive pulse in addition to the fine tuning sequence. The non-contiguous output signal may be non-periodic. For a majority of transitions in the lookup table, the output signal may have a non-zero net impulse and be non-contiguous. In the at least one transition using a non-contiguous output signal, the output signal may consist only of pulses having voltage levels of +N, 0 and -V, preferably consisting only of pulses having voltage levels of 0 and one of +V and -N. In a preferred variant of this method, for the at least one transition using a non-contiguous output signal, and preferably for a majority of transitions in the look-up table for which the initial and final states of the pixel are different, the output signal consists of a pulse having a voltage level of 0 preceded and followed by at least two pulses having voltage levels of the same one of +N and -N. Preferably, the transition table is DC balanced. Also, for the at least one transition using a non-contiguous output signal, the output signal may consist of a series of pulses which are integer multiples of a single interval.

[0088] The non-contiguous addressing method of the present invention may further comprise storing data representing at least one temporal prior state of said one pixel and/or at least one gray level prior state of said one pixel, and generating the output signal dependent upon said at least one temporal prior state and/or at least one gray level prior state of said one pixel.

[0089] The present invention also provides a method of driving a bistable electro-optic display having a plurality of pixels, each of which is capable of displaying at least three gray levels, the method comprising applying to each pixel of the display an output signal effective to change the pixel from an initial state to a final state, wherein, for at least one transition for which the initial and final states of the pixel are different, the output signal consists of a pulse having a voltage level of 0 preceded and followed at by least two pulses having voltage levels of the same one of +V and -N.

[0090] h another aspect, this invention provides a method of driving a bistable electro-optic display having a plurality of pixels, each of which is capable of displaying at least three gray levels, the method comprising applying to each pixel of the display an output signal effective to change the pixel from an initial state to a final state, wherein, for at least one transition, the output signal is nonzero but DC balanced.

[0091] This method may hereinafter for convenience be referred to as the

"DC balanced addressing" method of the present invention. [0092] hi this DC balanced addressing method, for the at least one transition, the output signal may comprise a first pair of pulses comprising a voltage pulse preceded by a pulse of equal length but opposite sign. The output signal may further comprise a period of zero voltage between the two pulses alternatively, at least one of the pulses may be interrupted by a period of zero voltage. The output signal may further comprise a second pair of pulses of equal length but opposite sign; the second pair of pulses may have a length different from that of the first pair of pulses. The first of the second pair of pulses may have a polarity opposite to that of the first of the first pair of pulses. The first pair of pulses may occur between the first and the second of the second pair of pulses. [0093] Also, in this DC balanced addressing method, for the aforementioned transition, the output signal may comprise at least one pulse element effective to drive the pixel substantially into one optical rail. [0094] As discussed in more detail below, the DC balanced addressing method of the present invention may make use of a combination of DC balanced and DC imbalanced transitions. For example, for each transition for which the initial and final states of the pixel are the same, the output signal may be non-zero but DC balanced, and for each transition in which the initial and final states of the pixel are not the same, the output signal may not be DC balanced. In this addressing method, for each transition in which the initial and final states of the pixel are not the same, the output signal may have the form -x/ALP/x, where ΔLP is the difference in impulse potential between the initial and final states of the pixel and -x and x are a pair of pulses of equal length but opposite sign. [0095] The DC balanced addressing method of the present invention may further comprise:

[0096] storing a look-up table containing data representing the impulses necessary to convert the initial gray level of a pixel to a final gray level; [0097] storing data representing at least an initial state of each pixel of the display;

[0098] receiving an input signal representing a desired final state of at least one pixel of the display; and

[0099] generating an output signal representing the impulse necessary to convert the initial state of said one pixel to the desired final state thereof, as determined from the look-up table.

[0100] This invention also provides a method of driving a bistable electro- optic display having at least one pixel which comprises applying to the pixel a waveform N(t) such that: _[oioi_] J = jV{t)M{T - t)dt ₍₁₎

0 [0102] (where T is the length of the waveform, the integral is over the duration of the waveform, N(t) is the waveform voltage as a function of time t, and

M(t) is a memory function that characterizes the reduction in efficacy of the remnant voltage to induce dwell-time-dependence arising from a short pulse at time zero) is less than about 1 volt sec. This method may hereinafter for convenience by referred to as the "DTD integral reduction" method of the present invention. Desirably J is less than about 0.5 volt sec, and most desirably less than about 0.1 volt sec. In fact J should be arranged to be as small as possible, ideally zero.

[0103] In a preferred form of this method, J is calculated by:

[0105] where T is a decay (relaxation) time, which preferably has a value of from about 0.7 to about 1.3 seconds.

[0106] Figures 1A-1E show five waveforms which can be used in the noncontiguous addressing method of the present invention.

[0107] Figure 2 illustrates a problem in addressing an electro-optic display using various numbers of frames of a monopolar voltage.

[0108] Figure 3 illustrates one approach to solving the problem shown in

Figure 2 using the non-contiguous addressing method of the present invention. [0109] Figure 4 illustrates a second approach to solving the problem shown in Figure 13 using the non-contiguous addressing method of the present invention. [0110] Figure 5 illustrates a waveform which may be used in the noncontiguous addressing method of the present invention.

[0111] Figure 6 illustrates a base waveform which can be modified in accordance with the present invention to produce the waveform shown in Figure 5. [0112] Figure 7 illustrates a problem in addressing an electro-optic display using various numbers of frames of a monopolar voltage while maintaining DC balance.

[0113] Figure 8 illustrates one approach to solving the problem shown in

Figure 7 using the non-contiguous addressing method of the present invention. [0114] Figure 9 illustrates a second approach to solving the problem shown in Figure 7 using the non-contiguous addressing method of the present invention. [0115] Figure 10 illustrates the gray levels obtained in a nominally four gray level electro-optic display without using the non-contiguous addressing method of the present invention, as described in the Example below. [0116] Figure 11 illustrates the gray levels obtained from the same display as in Figure 10 using various non-contiguous addressing sequences. [0117] Figure 12 illustrates the gray levels obtained from the same display as in Figure 10 using a modified drive scheme in accordance with the noncontiguous addressing method of the present invention.

[0118] Figure 13 illustrates a simple DC balanced waveform which may be used to drive an electro-optic display.

[0119] Figures 14 and 15 illustrate two modifications of the waveform shown in Figure 24 to incorporate a period of zero voltage.

[0120] Figure 16 illustrates schematically how the waveform shown in

Figure 13 may be modified to include an additional pair of drive pulses. [0121] Figure 17 illustrates one waveform produced by modifying the waveform of Figure 13 in the manner illustrated in Figure 16. [0122] Figure 18 illustrates a second waveform produced by modifying the waveform of Figure 24 in the manner illustrated in Figure 27. [0123] Figure 19 illustrates schematically how the waveform shown in

Figure 18 may be further modified to include a third pair of drive pulses. [0124] Figure 20 illustrates one waveform produced by modifying the waveform of Figure 18 in the manner illustrated in Figure 19. [0125] Figure 21 illustrates one preferred DC imbalanced waveform which may be used in conjunction with DC balanced waveforms to provide a complete look-up table for use in the methods of the present invention.

[0126] Figure 22 is a graph illustrating the reduced dwell time dependency which can be achieved by the compensation voltage method of the present invention.

[0127] Figure 23 is a graph illustrating the effect of dwell time dependence in an electro-optic display.

[0128] From the foregoing, it will be apparent that the present invention provides numerous different improvements in methods for driving electro-optic displays, and in device controllers or other apparatus for carrying out such driving methods, hi the description below, the various different improvements provided by the present invention will normally be described separately, although it will be understood by those skilled in the imaging art that in practice a single display may make may make use of more than one of these major aspects; for example, a display which uses the non-contiguous addressing method of the present invention may also make use of the defined region method.

[0129] It might at first appear that the ideal method for addressing an impulse-driven electro-optic display would be so-called "general grayscale image flow" in which a controller arranges each writing of an image so that each pixel transitions directly from its initial gray level to its final gray level. However, inevitably there is some error in writing images on an impulse-driven display. As already mentioned in part, some such errors encountered in practice include:

[0130] (a) Prior State Dependence; The impulse required to switch a pixel to a new optical state depends not only on the initial and desired optical state, but also on the previous optical states of the pixel.

[0131] (b) Dwell Time Dependence; The impulse required to switch a pixel to a new optical state depends on the time that the pixel has spent in its various optical states. The precise nature of this dependence is not well understood, but in general, more impulse is required that longer the pixel has been in its current optical state. [0132] (c) Temperature Dependence; The impulse required to switch a pixel to a new optical state depends heavily on temperature. [0133] (d) Humidity Dependence; The impulse required to switch a pixel to a new optical state depends, with at least some types of electro-optic media, on the ambient humidity.

[0134] (e) Mechanical Uniformity; The impulse required to switch a pixel to a new optical state may be affected by mechanical variations in the display, for example variations in the thickness of an electro-optic medium or an associated lamination adhesive. Other types of mechanical non-uniformity may arise from inevitable variations between different manufacturing batches of medium, manufacturing tolerances and materials variations.

[0135] (f) Voltage Errors; The actual impulse applied to a pixel will inevitably differ slightly from that theoretically applied because of unavoidable slight errors in the voltages delivered by drivers.

[0136] General grayscale image flow suffers from an "accumulation of errors" phenomenon. For example, imagine that temperature dependence results in a 0.2 L* error in the positive direction on each transition. After fifty transitions, this error will accumulate to 10 L*. Perhaps more realistically, suppose that the average error on each transition, expressed in terms of the difference between the theoretical and the actual reflectance of the display is ± 0.2 L*. After 100 successive transitions, the pixels will display an average deviation from their expected state of 2 L*; such deviations are apparent to the average observer on certain types of images.

[0137] This accumulation of errors phenomenon applies not only to errors due to temperature, but also to errors of other types. Compensating for such errors is possible, but only to a limited degree of precision. For example, temperature errors can be compensated by using a temperature sensor and a lookup table, but the temperature sensor has a limited resolution and may read a temperature slightly different from that of the electro-optic medium. Similarly, prior state dependence can be compensated by storing the prior states and using a multi-dimensional transition matrix, but controller memory limits the number of states that can be recorded and the size of the transition matrix that can be stored, placing a limit on the precision of this type of compensation, as discussed above. [0138] Thus, general grayscale image flow requires very precise control of applied impulse to give good results, and empirically it has been found that, in the present state of the technology of electro-optic displays, general grayscale image flow is typically infeasible in a commercial display.

[0139] Almost all electro-optic media have a built-in resetting (error limiting) mechanism, namely their extreme (typically black and white) optical states, which function as "optical rails". After a specific impulse has been applied to a pixel of an electro-optic display, that pixel cannot get any whiter (or blacker). For example, in an encapsulated electrophoretic display, after a specific impulse has been applied, all the electrophoretic particles are forced against one another or against the capsule wall, and cannot move further, thus producing a limiting optical state or optical rail. Because there is a distribution of electrophoretic particle sizes and charges in such a medium, some particles hit the rails before others, creating a "soft rails" phenomenon, whereby the impulse precision required is reduced when the final optical state of a transition approaches the extreme black and white states, whereas the optical precision required increases dramatically in transitions ending near the middle of the optical range of the pixel. Obviously, a pure general grayscale image flow drive scheme cannot rely upon using the optical rails to prevent errors in gray levels since in such a drive scheme any given pixel can undergo an infinitely large number of changes in gray level without ever touching either optical rail.

[0140] As discussed in the aforementioned U.S. Patents Nos. 6,504,524 and 6,531,997, in many elecfro-optic media, especially particle-based electrophoretic media, it is desirable that the drive scheme used to drive such media be direct current (DC) balanced, in the sense that, over an extended period, the algebraic sum of the currents passed through a specific pixel should be zero or as close to zero as possible, and the drive schemes of the present invention should be designed with this criterion in mind. More specifically, look-up tables should be designed so that any sequence of transitions beginning and ending in one extreme optical state (black or white) of a pixel should be DC balanced. From what has been said above, it might at first appear that such DC balancing may not be achievable, since the impulse, and thus the current through the pixel, required for any particular gray to gray transition is substantially constant. However, this is only true to a first approximation, and it has been found empirically that, at least in the case of particle-based electrophoretic media (and the same appears to be true of other electro-optic media), the effect of (say) applying five spaced 50 msec pulses to a pixel is not the same as applying one 250 msec pulse of the same voltage. Accordingly, there is some flexibility in the current which is passed through a pixel to achieve a given transition, and this flexibility can be used to assist in achieving DC balance. For example, the look-up table used in the present invention can store multiple impulses for a given transition, together with a value for the total current provided by each of these impulses, and the controller can maintain, for each pixel, a register arranged to store the algebraic sum of the impulses applied to the pixel since some prior time (for example, since the pixel was last in a black state). When a specific pixel is to be driven from a white or gray state to a black state, the controller can examine the register associated with that pixel, determine the current required to DC balance the overall sequence of transitions from the previous black state to the forthcoming black state, and choose the one of the multiple stored impulses for the white/gray to black transition needed which will either accurately reduce the associated register to zero, or at least to as small a remainder as possible (in which case the associated register will retain the value of this remainder and add it to the currents applied during later transitions). It will be apparent that repeated applications of this process can achieve accurate long term DC balancing of each pixel.

[0141] The following discussion of the various aspects of the present invention will assume familiarity with the entire contents of the aforementioned WO 03/044765, and in particular the various waveforms disclosed therein. It will be appreciated by those skilled in the display art that the various methods of the present invention may be modified to include the various optional features (for example, temperature compensation, operating lifetime compensation, humidity compensation, etc.) of the basic look-up table method described in the aforementioned WO 03/044765. The various methods of the present invention may also take advantage of the methods described in the aforementioned WO 03/044765 for reducing the amount of data which has to be stored for a look-up table. Furthermore, since the data comprising a look-up table can be treated as a general multi-dimensional data set, any standard functions, algorithms and encodings known to those skilled in the art of data storage and processing may be employed to reduce one or more of (a) the size of the storage required for the data set, (b) the computational effort required to extract the data, or (c) the time required to locate and extract a specific element from the set. These storage techniques include, for example, hash functions, loss-less and lossy compression, and representation of the data set as a combination of basis functions. [0142] Non-contiguous addressing method

[0143] Fine control of gray scale levels in the methods of the present invention may be achieved by using the non-contiguous addressing method of the present invention. As mentioned above, the non-contiguous addressing method has two principal variants, a DC imbalanced variant and a DC balanced variant. The DC imbalanced variant effects at least one transition between gray levels using an output signal which has a non-zero net impulse (i.e., the length of positive and negative segments is not equal), and therefore is not internally DC balanced, and is non-contiguous, (i.e. the pulse contains portions of zero voltage or opposite polarity). The output signal used in the non-contiguous addressing method may or may not be non-periodic (i.e., it may or may not consist of repeating units such as +/-/+/- or ++/--/++/--).

[0144] Such a non-contiguous waveform (which may hereinafter be referred to as a "fine tuning" or "FT" waveform) may have no frames of opposite polarity, and/or may include only three voltage levels, +N 0, and -N with respect to the effective front plane voltage of the display (assuming, as is typically the case, an active matrix display having a pixel electrode associated with each pixel and a common front electrode extending across multiple pixels, and typically the whole display, so the electric field applied to any pixel of the electro-optic medium is determined by the voltage difference between its associated pixel electrode and the common front electrode). Alternatively, an FT waveform may include more than three voltage levels. An FT waveform may consist of any one of the types of waveforms described above (such n-prepulse etc), with a non-contiguous waveform appended.

[0145] An FT waveform may (and typically will) be dependent on one or more prior image states, and can be used in order to achieve a smaller change in optical state than can be achieved using standard pulse width modulation (PWM) techniques. (Thus, the exact FT waveform employed will vary from one transition to another in a look-up table, in contrast to certain prior art waveforms in which pulses of alternating polarity are employed, for example, allegedly to prevent sticking of electrophoretic particles to surfaces such as capsule walls.) hi a preferred variant of the non-contiguous addressing method, there is provided a combination of all waveforms required to achieve all allowed optical transitions in a display (a "transition matrix"), in which at least one waveform is an FT waveform of the present invention and the combination of waveforms is DC- balanced. In another preferred variant of the non-contiguous addressing method, the lengths of all voltage segments are integer multiples of a single interval (the "frame time"); a voltage segment is a portion of a waveform in which the voltage remains constant.

[0146] The non-contiguous addressing method of the present invention is based upon the discovery that, in many impulse driven electro-optic media, a waveform which has zero net impulse, and which thus might theoretically be expected to effect no overall change in the gray level of a pixel, can in fact, because of certain non-linear effects in the properties of such media, effect a small change in gray level, which can be used to achieve finer adjustment of gray levels than is possible using a simple PWM drive scheme or drivers with limited ability to vary the width and/or height of a pulse. The pulses which may up such a "fine tuning" waveform may be separate from the "major drive" pulses which effect a major change in gray level, and may precede or follow such major drive pulses. Alternatively, in some cases, the fine adjustment pulses may be intermingled with the major drive pulses, either a separate block of fine tuning pulses at a single point in the sequence of major drive pulses, or interspersed singly or in small groups at multiple points in the sequence of major drive pulses.

[0147] Although the non-contiguous addressing method has very general applicability, it will primarily be described using as an example drive schemes using source drivers with three voltage outputs (positive, negative, and zero) and waveforms constructed from the following three types of waveform elements (since it is believed that the necessary modifications of the present invention for use with other types of drivers and waveform elements will readily be apparent to those skilled in the technology of electro-optic displays):

[0148] 1) Saturation pulse: A sequence of frames with voltages of one sign or one sign and zero volts that drives the reflectance approximately to one extreme optical state (an optical rail, either the darkest state, here called the black state, or the brightest state, here called the white state);

[0149] 2) Set pulse: A sequence of frames with voltages of one sign or one sign and zero volts that drives the reflectance approximately to a desired gray level (black, white or an intermediate gray level); and

[0150] 3) FT sequence: A sequence of frames with voltages that are individually selected to be positive, negative, or zero, such that the optical state of the ink is moved much less than a single-signed sequence of the same length. Examples of FT drive sequences having a total length of five scan frames are: [ + - + - -] (here, the voltage of each frame is represented sequentially by a + for positive voltage, 0 for zero voltage, and - for a negative voltage), [- - 0 + +], [ 0 0 0 0 0], [0 0 + - 0], and [0 - + 0 0]. These sequences are shown schematically in Figures 1A-1E respectively of the accompanying drawings, in which the circles represent the starting and end points of the FT sequence, and there are five scan frames between these points.

[0151] An FT sequence may be used either to allow fine control of the optical state, as previously described, or to produce a change in the optical state similar to that for a sequence of monopolar (single-signed) voltages but having a different net voltage impulse (where impulse is defined as the integral of the applied voltage over time). FT sequences in the waveform can thus be used as a tool to achieve DC balance.

[0152] The use of an FT sequence to achieve fine control of the optical state will first be described. In Figure 2, the optical states achievable using zero, one, two, three, or more frames of a monopolar voltage are indicated schematically as points on the reflectivity axis. From this Figure, it will be seen that the length of the monopolar pulse can be chosen to achieve a reflectance represented by its corresponding point on this axis. However, one may wish to achieve a gray level, such as that indicated by "target" in Figure 2, that is not well approximated by any of these gray levels. An FT sequence can be used to fine-tune the reflectance to the desired state, either by fine tuning the final state achieved after a monopolar drive pulse, or by fine-tuning the initial state and then using a monopolar drive sequence. [0153] A first example of an FT sequence, shown in Figure 3, shows an FT sequence being used after a two-pulse monopolar drive. The FT sequence is used to fine-tune the final optical state to the target state. Like Figure 2, Figure 3 shows the optical states achievable using various numbers of scan frames, as indicated by the solid points. The target optical state is also shown. The optical change by applying two scan frames is indicated, as is an optical shift induced by the FT sequence.

[0154] A second example of an FT sequence is shown in Figure 4; in this case, the FT sequence is used first to fine tune the optical state into a position where a monopolar drive sequence can be used to achieve the desired optical state. The optical states achievable after the FT sequence are shown by the open circles in Figure 4.

[0155] An FT sequence can also be used with a rail-stabilized gray scale

(RSGS) waveform, such as that shown in Figures 11A and 11B of the aforementioned WO 03/044765. The essence of an RSGS waveform is that a given pixel is only allowed to make a limited number of gray-to-gray transitions before being driven to one of its extreme optical states. Thus, such waveforms use frequent drives into the extreme optical states (referred to as optical rails) to reduce optical errors while maintaining DC balance (where DC balance is a net voltage impulse of zero and is described in more detail below). Well resolved gray scale can be achieved using these waveforms by selecting fine-adjust voltages for one or more scan frames. However, if these fine-adjust voltages are not available, another method must be used to achieve fine tuning, preferably while maintaining DC balance as well. FT sequences may be used to achieve these goals.

[0156] First, consider a cyclic version of a rail-stabilized grayscale waveform, in which each transition consists of zero, one, or two saturation pulses

(pulses which drive the pixel into an optical rail) followed by a set pulse as described above (which takes the pixel to the desired gray level). To illustrate how

FT sequences can be used in this waveform, a symbolic notation will be used for the waveform elements: "sat" to represent a saturation pulse; "set" to represent a set pulse; and "N" to represent an FT drive sequence. The three basic types of cyclic rail-stabilized grayscale waveforms are:

[0157] set (for example, transition 1104 in Figure 11A of WO 03/044765)

[0158] sat - set (for example, transition 1106/1108 in Figure 11A of WO

03/044765)

[0159] sat - sat' - set (for example, transition 1116/1118/1120 in Figure

HAof WO 03/044765) where sat and sat' are two distinct saturation pulses.

[0160] Modification of the first of these types with an FT sequence gives the following waveforms:

[0161] N - set

[0162] set - N

[0163] that is, an FT sequence followed by a set pulse or the same elements in reverse order.

[0164] Modification of the second of these types with one or more FT sequences gives, for example, the following FT-modified waveforms:

[0165] N - sat - set

[0166] sat - N - set

[0167] sat - set - N

[0168] sat - N - set - N' [0169] N - sat - set - N'

[0170] N - sat - N' - set

[0171] N - sat - N' - set - N"

[0172] where N, N', and N" are three FT sequences, which may or may not be different from one another.

[0173] Modification of the second of these types can be achieved by interspersing FT sequences between the three waveform elements following essentially the previously described forms. An incomplete list of examples includes:

[0174] N - sat - sat' - set

[0175] N - sat - sat' - set - N*

[0176] sat - N - saf - N' - set - N"

[0177] N - sat - N - sat* - N" - set - N'".

[0178] Another base waveform which can be modified with an FT sequence is the single-pulse slide show gray scale with drive to black (or white). In this waveform, the optical state is first brought to an optical rail, then to the desired image. The waveform of each transition can be symbolically represented by either of the two sequences: [0179] sat - set

[0180] set.

[0181] Such a waveform may be modified by inclusion of FT drive sequence elements in essentially the same manner as already described for the rail- stabilized gray scale sequence, to produce sequences such as: [0182] sat - set - N

[0183] sat - N - set

[0184] etc.

[0185] The above two examples describe the insertion of FT sequences before or after saturation and set pulse elements of a waveform. It may be advantageous to insert FT sequences part way through a saturation or set pulse, that is the base sequence: [0186] sat - set [0187] would be modified to a form such as:

[0188] {sat, part I } - N - {sat, part II } -set

[0189] or

[0190] sat - {set, part I } - N - {set, part II } .

[0191] As already indicated, it has been discovered that.the optical state of many electro-optic media achieved after a series of transitions is sensitive to the prior optical states and also to the time spent in those prior optical states, and methods have been described for compensating for prior state and prior dwell time sensitivities by adjusting the transition waveform accordingly. FT sequences can be used in a similar manner to compensate for prior optical states and/or prior dwell times.

[0192] To describe this concept in more detail, consider a sequence of gray levels that are to be represented on a particular pixel; these levels are denoted Ri,

R₂, R₃, P , and so on, where Ri denotes the next desired (final) gray level of the transition being considered, R is the initial gray level for that transition, R₃ is the first prior gray level, is the second prior gray level and so on. The gray level sequence can then be represented by:

[0193] R_n R_n-ι R_n_₂ R₃ R₂ R,

[0194] The dwell time prior to gray level i is denoted D;. D; may represent the number of frame scans of dwell in gray level i.

[0195] The FT sequences described above could be chosen to be appropriate for the transition from the current to the desired gray level. In the simplest form, these FT sequences are then functions of the current and desired gray level, as represented symbolically by:

[0196] N = N(R₂, Rι)

[0197] to indicate that the FT sequence N depends upon R and Ri .

[0198] To improve device performance, and specifically to reduce residual gray level shifts correlated to prior images, it is advantageous to make small adjustments to a transition waveform. Selection of FT sequences could be used to achieve these adjustments. Various FT sequences give rise to various final optical states. A different FT sequence may be chosen for different optical histories of a given pixel. For example, to compensate for the first prior image (R₃), one could choose an FT sequence that depends on R₃, as represented by:

[0199] N = N(R₃, R₂, Rι)

[0200] That is, an FT sequence could be selected based not only on Ri and

R , but also on R₃.

[0201] Generalizing this concept, the FT sequence can be made dependent on an arbitrary number of prior gray levels and/or on an arbitrary number of prior dwell times, as represented symbolically by:

[0202] N = N(D_m, D_m.ι, . . . D₃, D₂; R_n, R„._l3 . . .R₃, R₂, Rj) where the symbol D represents the dwell time spent in the gray level R_k and the number of optical states, n, need not equal the number of dwell times, m, required in the FT determination function. Thus FT sequences may be functions of prior images and/or prior and current gray level dwell times.

[0203] As a special case of this general concept, it has been found that insertion of zero voltage scan frames into an otherwise monopolar pulse can change the final optical state achieved. For example, the optical state achieved after the sequence of Figure 5, into which a zero voltage scan frame has been inserted, will differ somewhat from the optical state achieved after the corresponding monopolar sequence of Figure 6, with no zero voltage scan frame but the same total impulse as the sequence of Figure 5.

[0204] It has also been found that the impact of a given pulse on the final optical state depends upon the length of delay between this pulse and a previous pulse. Thus, one can insert zero voltage frames between pulse elements to achieve fine tuning of a waveform.

[0205] The present invention extends to the use of FT drive elements and insertion of zero-volt scan frames in monopolar drive elements in other waveform structures. Other examples include but are not limited to double-prepulse

(including triple-prepulse, quadruple-prepulse and so on) slide show gray scale waveforms, where both optical rails are visited (more than once in the case of higher numbers of prepulses) in going from one optical state to another, and other forms of rail-stabilized gray scale waveforms. FT sequences could also be used in general image flow gray scale waveforms, where direct transitions are made between gray level.

[0206] While insertion of zero voltage frames can be thought of as a specific example of insertion of an FT sequence, where the FT sequence is all zeros, attention is directed to this special case because it has been found to be effective in modifying final optical states.

[0207] The preceding discussion has focused on the use of FT sequences to achieve fine tuning of gray levels. The use of such FT sequences to achieve DC balance will now be considered. FT sequences can be used to change the degree of DC imbalance (preferably to reduce or eliminate DC imbalance) in a waveform. By DC balance is meant that all full-circuit gray level sequences (sequences that begin and end with the same gray level), have zero net voltage impulse. A waveform can be made DC balanced or less strongly DC imbalanced by use of one or more FT sequences, taking advantage of the fact that FT sequences can either (a) change the optical state in the same way as a saturation or set pulse but with a substantially different net voltage impulse; or (b) result in an insubstantial change in the optical state but with a net DC imbalance.

[0208] The following illustration shows how FT sequences can be used to achieve DC balance. In this example, a set pulse can be of variable length, namely one, two, three or more scan frames. The final gray levels achieved for each of the number of scan frames are shown in Figure 7, in which the number next to each point represents the number of scan frames used to achieve the gray level. [0209] Figure 7 shows the optical states available using scan frames of positive voltage, monopolar drive where the number labels specify the number of monopolar frames used to produce the final gray level. Suppose that, in order to maintain DC balance in this example, a net voltage impulse of two positive voltage frames need to be applied. The desired (target) gray level could be achieved by using three scan frames of impulse; however, in doing so, the system would be left DC imbalanced by one frame. On the other hand, DC balance could be achieved by using two positive voltage scan frames instead of three, but the final optical state will deviate significantly from the target. [0210] One way to achieve DC balance is to use two positive voltage frames to drive the electro-optic medium to the vicinity of the desired gray level, and also use a DC balanced FT sequence (an FT sequence that has zero net voltage impulse) to make the final adjustment sufficiently close to the target gray level, as illustrated symbolically in Figure 8, in which the target gray level is achieved using two scan frames followed by an FT sequence of zero net voltage impulse chosen to give the proper change in optical state.

[0211] Alternatively, one could use three positive voltage scan frames of monopolar drive to bring the reflectance to the target optical state, then use an FT sequence that has a net DC imbalance equivalent to one negative voltage scan frame. If one chooses an FT sequence that results in a substantially unchanged optical state, then the final optical state will remain correct and DC-balance will be restored. This example is shown in Figure 9. It will be appreciated that typically use of FT sequences will involve some adjustment of optical state along with some effect on DC balance, and that the above two examples illustrate extreme cases. [0212] The following Example is now given, though by way of illustration only, to show experimental uses of FT sequences in accordance with the present invention.

[0213] Example : Use of FT sequences in cyclic RSGS waveform

[0214] This Example illustrates the use of FT sequences in improving the optical performance of a waveform designed at achieve 4 gray level (2-bit) addressing of a single pixel display. This display used an encapsulated electrophoretic medium and was constructed substantially as described in Paragraphs [0069] to [0076] of the aforementioned 2002/0180687. The single- pixel display was monitored by a photodiode.

[0215] Waveform voltages were applied to the pixel according to a fransition matrix (look-up table), in order to achieve a sequence of gray levels within the 2-bit (4-state) grayscale. As already explained, a transition matrix or look-up table is simply a set of rules for applying voltages to the pixel in order to make a transition from one gray level to another within the gray scale. [0216] The waveform was subject to voltage and timing constraints. Only three voltage levels, -15V, 0V and +15V were applied across the pixel. Also, in order to simulate an active matrix drive with 50 Hz frame rate, voltages were applied in 20 ms increments. Tuning algorithms were employed iteratively in order to optimize the waveform, i.e. to achieve a condition where the spread in the actual optical state for each of the four gray levels across a test sequence was minimized. [0217] In an initial experiment, a cyclic rail-stabilized grayscale (cRSGS) waveform was optimized using simple saturation and set pulses. Consideration of prior states was limited to the initial (R₂) and desired final (Ri) gray levels in determining the transition matrix. The waveform was globally DC balanced. Because of the coarseness of the minimum impulse available for tuning (20 ms at 15 V), and the absence of states prior to R₂ in the transition matrix, quite poor performance was anticipated from this waveform.

[0218] The performance of the transition matrix was tested by switching the test pixel through a "pentad-complete" gray level sequence, which contained all gray level pentad sequences in a random arrangement. (Pentad sequence elements are sequences of five gray levels, such as 0 - 1 - 0 - 2 - 3 and 2 - 1 - 3 - 0 - 3, where 0, 1, 2 and 3 represent the four gray levels available.) For a perfect transition matrix, the reflectivity of each of the four gray levels is exactly the same for all occurrences of that gray level in the random sequence. The reflectivity of each of the gray levels will vary significantly for realistic transition matrices. The bar graph of Figure 10 indeed shows the poor performance of the voltage and timing limited transition matrix. The measured reflectivity of the various occurrences of each of the target gray levels is highly variable. The cRSGS waveform optimized without FT sequences developed in this part of the experiment is hereinafter referred to as the base waveform.

[0219] FT sequences were then incorporated into the cRSGS waveform; in this experiment, the FT sequences were limited to five scan frames, and included only DC balanced FT sequences. The FT sequences were placed at the end of the base waveform for each transition, i.e., the waveform for each transition had one of the following forms: [0220] set - N

[0221] sat - set - N

[0222] sat - sat' - set - N.

[0223] Successful incorporation of FT sequence elements into the waveform required two steps; first, ascertaining the effect of various FT sequences on the optical state at each gray level and second selecting FT sequences to append to the various waveform elements.

[0224] To ascertain the effect of various FT sequences on the optical state of each gray level, an "FT efficacy" experiment was performed. First, a consistent starting point was established by switching the electrophoretic medium repeatedly between black and white optical rails. Then, the film was taken to one of the four gray levels (0, 1, 2, or 3), here referred to as the optical state R₂. Then, the base waveform appropriate to make the transition from R₂ to one of the other gray levels (here called Ri) with an appended FT sequence was applied. This step was repeated with all of the 51 DC balanced, 5-frame FT sequences. The final optical state was recorded for each of the FT sequences. The FT sequences were then ordered according to their associated final reflectivity. This process was repeated for all combinations of initial (R ) and final (Ri) gray levels. The ordering of FT sequences for the final gray level 1 (Rι=l) and the current gray level 0, 2 and 3 (R₂

= 0, 2, 3) are shown in Tables 2-4, respectively, where the columns labeled "Frame

1" to "Frame 5" show the potential in volts applied during the five successive frames of the relevant FT sequence. The final optical states achieved for the waveform using the various FT sequences are plotted in Figure 11. From this

Figure, it will be seen that FT sequences can be used to affect a large change in the final optical state, and that the choices of five-scan-frame FT sequences afforded fine control over the final optical state, all with no net voltage impulse difference.

[0225] Table 2 : Final optical states for gray level 0 to 1 for various FT sequences.

[0228] Next, a cRSGS waveform was constructed using FT sequences chosen using the results represented in Tables 2 to 4 and Figure 11 (specifically Sequence 33 from Table 2, Sequence 49 from Table 3 and Sequence 4 from Table 4), and their analogs for the other final gray levels. It is noted that the region between -36.9 and -37.5 L* on the y-axis in Figure 11 shows the overlap between optical reflectance of the same final (Ri) state with different initial (R ) states made available by using DC balanced FT sequences. Therefore, a target gray level for Rι=l was chosen at 37.2 L*, and the FT sequence for each R₂ that gave the final optical state closest to this target was selected. This process was repeated for the other final optical states (Ri = 0, 2 and 3). [0229] Finally, the resultant waveform was tested using the pseudo-random sequence containing all five-deep state histories that was described earlier. This sequence contains 324 fransitions of interest. The cRSGS waveform modified by the selected FT sequences was used to achieve all the transitions in this sequence, and the reflectivity of each of the optical states achieved was recorded. The optical states achieved are plotted in Figure 12. It is apparent by comparing Figure 12 with Figure 10 that the spread in reflectivity of each of the gray levels was greatly reduced by incorporation of the FT sequences.

[0230] In summary, the non-contiguous addressing aspect of this invention provides FT sequences which either (i) allow changes in the optical state or (ii) allow a means of achieving DC balance, or at least a change in the degree of DC imbalance, of a waveform. As already noted, it is possible to give a rather mathematical definition of an FT sequence, for example, for the DC imbalanced variant of the method:

[0231] (a) Application of a DC imbalanced FT sequence that results in a change in optical state that is substantially different from the change in optical state of its DC reference pulse. The "DC reference pulse" is a pulse of voltage Vo, where V₀ is the voltage corresponding to the maximum voltage amplitude applied during the FT sequence but with the same sign as the net impulse of the FT sequence. The net impulse of a sequence is the area under the voltage versus time curve, and is denoted by the symbol G. The duration of the reference pulse is T = G/Vo. This FT sequence is utilized to introduce a DC imbalance that differs significantly from the net DC imbalance of its reference pulse. [0232] (b) Application of a DC imbalanced FT sequence that results in a change in optical state that is much smaller in magnitude than the optical change one would achieve with its time reference pulse. The "time-reference pulse" is defined as a single-signed- voltage pulse of the same duration as the FT sequence, but where the sign of the reference pulse is chosen to give the largest change in optical state. That is, when the electro-optic medium is near its white state, a negative voltage pulse may drive the electro-optic medium only slightly more white, whereas a positive voltage may drive the electro-optic medium strongly toward black. The sign of the reference pulse in this case is positive. The goal of this type of FT pulse is to adjust the net voltage impulse (for DC balancing, for example) while not strongly affecting the optical state.

[0233] The non-contiguous addressing aspect of the present invention also relates to the concept of using one or more FT sequences between or inserted into pulse elements of a transition waveform, and to the concept of using FT sequences to balance against the effect of prior gray levels and prior dwell times One specific example of the present invention is the use of zero voltage frames inserted in the middle of a pulse element of a waveform or in between pulse elements of a waveform to change the final optical state.

[0234] The non-contiguous addressing aspect of the present invention also allows fine tuning of waveforms to achieve desired gray levels with desired precision, and a means by which a waveform can be brought closer to DC balanced (that is, zero net voltage impulse for any cyclic excursion to various gray levels), using source drivers that do not permit fine tuning of the voltage, especially source drivers with only two or three voltage levels. [0235] DC balanced addressing method

[0236] It should be noted that the sawtooth drive scheme shown in Figures

11 A and 11B of the aforementioned WO 03/044765 is well adapted for use in DC balancing, in that this sawtooth drive scheme ensures that only a limited number of transitions can elapse between successive passes of any given pixel though the black state, and indeed that on average a pixel will pass through the black state on one-half of its transitions.

[0237] However, as already indicated, DC balancing according to the present invention is not confined to balancing the aggregate of the impulses applied to the electro-optic medium during a succession of transitions, but also extends to making at least some of the fransitions undergone by the pixels of the display "internally" DC balanced, in accordance with the DC balanced addressing method of the present invention; this method will now be described in detail. [0238] The DC balanced addressing method of the present invention relates to DC balanced transitions that are advantageous for driving encapsulated electrophoretic and other impulse-driven electro-optic media for display applications. This method can be applied, for example, to an active-matrix display that has source drivers that can output only two or three voltages. Although other types of drivers can be used, most of the detailed description below will focus on examples using source drivers with three voltage outputs (positive, negative, and zero).

[0239] In the following description of the DC balanced addressing method of the present invention, as in preceding description of other aspects of the invention, the gray levels of an elecfro-optic medium will be denoted 1 to N, where 1 denotes the darkest state and N the lightest state. The intermediate states are numbered increasing from darker to lighter. A drive scheme for an impulse driven imaging medium makes use of a set of rules for achieving fransitions from an initial gray level to a final gray level. The drive scheme can be expressed as a voltage as a function of time for each transition, as shown in Table 5 for each of the 16 possible transitions in a 2-bit (4 gray level) gray scale display. [0240] Table 5

[0241] hi Table 5, Vij(t) denotes the waveform used to make the fransition from gray level i to gray level j. DC-balanced fransitions are ones where the time integral of the waveform Vij(t) is zero.

[0242] The term "optical rails" has already been defined above as meaning the extreme optical states of an electro-optic medium. The phrase "pushing the medium towards or into an optical rail" will be employed below. By "towards", is meant that a voltage is applied to move the optical state of the medium toward one of the optical rails. By "pushing", is meant that the voltage pulse is of sufficient duration and amplitude that the optical state of the electro-optic medium is brought substantially close to one of the optical rails. It is important to note that "pushing into an optical rail" does not mean that the optical rail state is necessarily achieved at the end of the pulse, but that an optical state substantially close to the final optical state is achieved at the end of the pulse. For example, consider an electro- optic medium with optical rails at 1% and 50% reflectivities. A 300 msec pulse was found to bring the final optical state (from 1% reflectivity) to 50% reflectivity. One may speak of a 200 msec pulse as pushing the display into the high- reflectivity optical rail even though it achieves a final reflectivity of only 45% reflectance. This 200 msec pulse is thought of as pushing the medium into one of the optical rails because the 200 msec duration is long compared to the time required to traverse a large fraction of the optical range, such as the middle third of the optical range (in this case, 200 msec is long compared to the pulse required to bring the medium across the middle third of the reflectivity range, in this case, from 17% to 34% reflectance).

[0243] Three different types of DC balanced transitions in accordance with the DC balanced addressing method of the present invention will now be described, together with a hybrid drive scheme using both DC balanced and DC imbalanced transitions. In the following description for convenience pulses will a denoted by a number, the magnitude of the number indicating the duration of the pulse. If the number is positive, the pulse is positive, and if the number is negative, the pulse is negative. Thus, for example, if the available voltages are +15V, ON and -15V, and the pulse duration is measured in milliseconds (msec), then a pulse characterized by x=300 indicates a 300 msec, 15V pulse, and x=-60 indicates a 60 msec, -15V pulse. [0244] Type I:

[0245] In the first and simplest type of DC balanced transition of the present invention, a voltage pulse ("x") is preceded by a pulse ("-x") of equal length but of opposite sign, as illustrated in Figure 13. (Note that the value of x can itself be negative, so the positive and negative pulses may appear in the opposite order from that shown in Figure 13.) [0246] As mentioned above, it has been found that the effect of the waveform used to effect a transition is modified by the presence of a period of zero voltage (in effect a time delay) during or before any of the pulses in the waveform, in accordance with the non-contiguous addressing method of the present invention. Figures 14 and 15 illustrate modifications of the waveform of Figure 13. In Figure 14, a time delay is inserted between the two pulses of Figure 13 while in Figure 15 the time delay in inserted within the second pulse of Figure 13, or, which amounts to the same thing, the second pulse of Figure 13 is split into two separate pulses separated by the time delay. As already described, time delays can be incorporated into a waveform to achieve optical states not achievable without such delays. Time delays can also be used to fine-tune the final optical state. This fine-tuning ability is important, because in an active matrix drive, the time resolution of each pulse is defined by the scan rate of the display. The time resolution offered by the scan rate can be coarse enough that precise final optical states cannot be achieved without some additional means of fine tuning. While time delays offer a small degree of fine tuning of the final optical state, additional features such as those described below offer additional means of coarse and fine tuning of the final optical state. [0247] Type II:

[0248] A Type II waveform consists of a Type I waveform as described above with the insertion of a positive and negative pulse pair (denoted "y" and "-y" pulses) at some point into the Type I waveform, as indicated symbolically in Figure 16. The y and -y pulses do not have to be consecutive, but can be present at different places into the original waveform. There are two especially advantageous forms of the Type II waveform. [0249] Type II : Special case A:

[0250] In this special form, the "-y,y" pulse pair is placed before the "-x,x" pulse pair. It has been found that, when y and x are of opposite sign, as illustrated in Figure 17, the final optical state can be finely tuned by even moderately coarse adjustment of the duration y. Thus, the value of x can be adjusted for coarse control and the value of y for final control of the final optical state of the elecfro-optic medium. This is believed to happen because the y pulse augments the -x pulse, thus changing the degree to which the electro-optic medium is pushed into one of its optical rails. The degree of pushing into one of the optical rails is known to give fine adjustment of the final optical state after a pulse away from that optical rail (in this case, provided by the x pulse). [0251 ] Type II: Special case B:

[0252] For reasons indicated above, it has been found advantageous to use waveforms with at least one pulse element long enough to drive the electro-optic medium substantially into one optical rail. Also, for a more visually pleasing transition, it is desirable to arrive to the final optical state from the nearer optical rail, since achieving gray levels near an optical rail requires only a short final pulse. Waveforms of this type require at least one long pulse for driving into an optical rail and a short pulse to achieve the final optical state near that optical rail, and hence cannot have the Type I structure described above. However, special cases of the Type II waveform can achieve this type of waveform. Figure 18 shows one example of such a waveform, where the y pulse is placed after the -x,x pulse pair and the -y pulse is placed before the -x,x pulse pair, hi this type of waveform, the final y pulse provides coarse tuning because the final optical state is very sensitive to the magnitude of y. The x pulse provides a finer tuning, since the final optical state typically does not depend as strongly on the magnitude of the drive into the optical rail. [0253] Type III:

[0254] A third type (Type III) of DC balanced waveform of the present invention introduces yet another DC-balanced pulse pair (denoted "z", "-z") into the waveform, as shown schematically in Figure 19. A preferred example of such a Type LU waveform is shown in Figure 20; this type of waveform is useful for fine tuning of the final optical state, for the following reasons. Consider the situation without the z and -z pulses (i.e. the Type II waveform discussed above). The x pulse element is used for fine tuning, and the final optical state can be decreased by increasing x and increased by decreasing x. However, it is undesirable to decrease x beyond a certain point because then the electro-optic medium is not brought sufficiently close to an optical rail, as required for stability of the waveform. To avoid this problem, instead of decreasing x, one can (in effect) increase the -x pulse without changing the x pulse by adding the -z,z pulse pair as shown in Figure 20, with z having the opposite sign from x. The z pulse augments the -x pulse, while the -z pulse maintains the transition at zero net impulse, i.e., maintains a DC- balanced transition.

[0255] The Type I, II and III waveforms discussed above can of course be modified in various ways. Additional pairs of pulses can be added to the waveform to achieve more general structures. The advantage of such additional pairs diminishes with increasing number of pulse elements, but such waveforms are a natural extension of the Type I, II and III waveforms. Also, as already discussed, one or more time delays can be inserted in various places in any of the waveforms, in the same manner as illustrated in Figures 14 and 15. As mentioned earlier, time delays in pulses affect the final optical state achieved, and are thus useful for fine tuning. Also, the placement of time delays can change the visual appearance of transitions by changing the position of transition elements relative to other elements in the same transition as well as relative to fransition elements of other fransitions. Time delays can also be used to align certain waveform transition elements, and this may be advantageous for some display modules with certain controller capabilities. Also, in recognition of the fact that small changes in the ordering of the applied pulses may substantially change the optical state following the pulses, the output signal may also be formed by transposing all or part of one of the above-described pulse sequences, or by repeated transpositions of all or part of one of the above described sequences, or by the insertion of one or more 0 V periods at any location within one of the above-described sequences. In addition, these transposition and insertion operators can be combined in any order (e.g., insert 0 V section, then transpose, then insert 0 V section). It is important to note that all such pulse sequences formed by these transformations retain the essential character of having zero net impulse.

[0256] Finally, DC balanced transitions can be combined with DC imbalanced fransitions to form a complete drive scheme. For example, copending Application Serial No. 60/481,053, filed July 2, 2003 describes a preferred waveform of the type -TM(R1,R2) [LP(R1)-IP(R2)] TM(R1,R2). where [JT(R1)- LP(R2)] denotes a difference in impulse potential between the final and initial states of the fransition being considered, while the two remaining terms represent a DC balanced pair of pulse. For convenience this waveform will hereinafter be referred to as the -x/ΔLP/x waveform, and is illusfrated in Figure 21. While satisfactory for fransitions between differing optical states, this waveform is less satisfactory for zero transitions in which the initial and final optical states are the same. For these zero transitions there is used, in this example, a Type II waveform such as the ones shown in Figures 17 and 18. This complete waveform is shown symbolically in Table 6, from which it will be seen that the -x/ΔlP/x waveform is used for non-zero fransitions and the Type LT waveform for zero fransitions. [0257] Table 6

[0258] The DC balanced addressing method is not of course confined to transition matrices of this type, in which DC balanced transitions are confined to the "leading diagonal" transitions, in which the initial and final gray levels are the same; to produce the maximum improvement in control of gray levels, it is desirable to maximize the number of transitions which are DC balanced. However, depending upon the specific elecfro-optic medium being used, it may be difficult to DC balance transitions involving transitions to or from extreme gray levels, for example to or from black and white, gray levels 1 and 4 respectively. Furthermore, in choosing which transitions are to be DC balanced, it is important not to imbalance the overall fransition matrix, i.e., to produce a transition matrix in which a closed loop beginning and ending at the same gray level is DC imbalanced. For example, a rule that fransitions involving only a change of 0 or 1 unit in gray level are DC balanced but other transitions are DC imbalanced is not desirable, since this would imbalance the entire transition matrix, as shown by the following example; a pixel undergoing the sequence of gray levels 2-4-3-2 would experience transitions 2-4 (DC imbalanced), 4-3 (balanced) and 3-2 (balanced), so that the entire loop would be imbalanced. A practical compromise between these two conflicting desires may be to use DC balanced transitions in cases where only mid gray levels (levels 2 and 3) are involved and DC imbalanced fransitions where the transition begins or ends at an extreme gray level (level 1 or 4). Obviously, the mid gray levels chosen for such a rule may vary with the specific electro-optic medium and controller used; for example, in three-bit (8 gray level) display it might be possible to use DC balanced transitions in all transitions beginning or ending at gray levels 2-7 (or perhaps 3-6) and DC imbalanced transitions in all transitions beginning or ending at gray levels 1 and 8 (or 1, 2, 7 and 8). [0259] From the foregoing, it will be seen that the DC balanced addressing method of this invention allows fine tuning of waveforms to achieve desired gray levels with high precision, and a means by which a waveform transition can have zero net voltage, using source drivers that do not permit fine tuning of the voltage, especially source drivers with only two or three voltage levels. It is believed that DC balanced waveform fransitions offer better performance than DC imbalanced waveforms. This invention applies to displays in general, and especially, although not exclusively, to active-matrix display modules with source drivers that offer only two or three voltages. This invention also applies to active-matrix display modules with source drivers that offer more voltage levels. [0260] The DC balanced addressing method of this invention can provide certain additional advantages. As noted above, in some driving methods of the invention, the fransition matrix is a function of variables other than prior optical state, for example the length of time since the last update, or the temperature of the display medium. It is quite difficult to maintain DC balance in these cases with non-balanced transitions. For example, consider a display that repeatedly transitions from white to black at 25°C and then from black to white at 0°C. The slower response at low temperature will typically dictate using a longer pulse length. As a result, the display will experience a net DC imbalance towards white. On the other hand, if all transitions are internally balanced, then different fransition matrices can be freely mixed without introducing DC imbalance. [0261 ] Defined region method

[0262] The objectionable effects of reset steps, as described above, may be further reduced by using local rather than global updating, i.e., by rewriting only those portions of the display which change between successive images, the portions to be rewritten being chosen on either a "local area" or a pixel-by-pixel basis. For example, it is not uncommon to find a series of images in which relatively small objects move across a larger static background, as for example in diagrams illustrating parts in mechanical devices or diagrams used in accident reconstruction. To use local updating, the display controller needs to compare the final image with the initial image and determine which area(s) differ between the two images and thus need to be rewritten. The controller may identify one or more local areas, typically rectangular areas having axes aligned with the pixel grid, which contain pixels which need to be updated, or may simply identify individual pixels which need to be updated. Any of the drive schemes already described may then be applied to update only the local areas or individual pixels thus identified as needing rewriting. Such a local updating scheme can substantially reduce the energy consumption of a display.

[0263] Furthermore, as already mentioned, the defined region method of the present invention provides a defined region method which permits updating of a bistable electro-optic display using different updating methods in different regions of the display.

[0264] Elecfro-optic displays are known in which the entire display can be driven in a one-bit or in a grayscale mode. When the display is in one-bit mode, updates are effected using a one-bit general image flow (GLF) waveform, whereas when the display is in grayscale mode, updates are effected using a multi-prepulse slide show waveform, or some other slow waveform, even if, in a specific area of the display, only one-bit information is being updated. [0265] Such an elecfro-optic display may be modified to carry out the defined region method of the present invention by defining two additional commands in the controller, namely a "DEFINE REGION" command and a "CLEAR ALL REGIONS" command. The DEFINE REGION command typically takes as arguments locations sufficient to define completely a rectangular area of the display, for example the locations of the upper right and lower left corners of the defined region; this command may also have an additional argument specifying the bit depth to which the defined region is set, although this last argument is not necessary in simple forms of the defined region method in which the defined region is always monochrome. The bit depth set by the last argument of course overrides any bit depth previously set for the defined region. Alternatively, the DEFINE REGION command could specify a series of points defining the vertices of a polygon. The CLEAR ALL REGIONS command may take no arguments and simply reset the entire display to a single predefined bit depth, or might take a single argument specifying which of various possible bit depths is to be adopted by the entire display after the clearing operation.

[0266] It will be appreciated that the defined region method of the present invention is not restricted to the use of only two regions and more regions could be provided if desired. For example, in an image editing program it might be helpful to have a main region showing the image being edited at full bit depth, and both an information display region (for example, a box showing present cursor position) and a dialog box region (providing a dialog box for entry of text by the user) running in one-bit mode. The invention will primarily be described below in a two- region version, since the necessary modifications to enable use of more than two regions will readily be apparent to those skilled in the construction of display controllers.

[0267] i order to keep track of the depths of the different regions, the controller may keep an array of storage elements, one element being associated with each pixel in the display, and each element storing a value representing the current bit depth for the associated pixel. For example, an XVGA (800x600) display capable of operating in either 1-bit or 2-bit mode could use an 800 x 600 array of 1-bit elements (each containing 0 for 1-bit mode, 1 for 2-bit mode). In such a controller, the DEFINE REGION command would set the elements within the defined region of the display to the requested bit depth, while the CLEAR ALL

REGIONS command would reset all elements of the array to the same value (either a predetermined value or one defined by the argument of the command).

[0268] Optionally, when a region is defined or cleared, the controller could execute an update sequence on the pixels within that region to transfer the display from one mode to the other, in order to ensure DC balancing or to adjust the optical states of the relevant pixels, for example by using an FT sequence as described above.

[0269] When a display is operating in defined region mode, a new image is sent to the controller, and the display must be redrawn, there are three possible cases:

[0270] 1. Only pixels within the defined (say) one-bit region have changed. In this case, a one-bit (fast) waveform can be used to update the display;

[0271] 2. Only pixels within the non-defined (grayscale) regions have changed. In this case, a grayscale (slow) waveform must be used to update the display (note that since by definition not pixels are changed within the defined region, the legibility of the defined region, for example a dialog box, during the redrawing is not a problem); and

[0272] 3. Pixels in both the defined and non-defined regions have changed. In this case, the grayscale pixels are updated using the grayscale waveform, and the one-bit pixels are updated using the one-bit waveform (the shorter one-bit waveforms must be zero-padded appropriately to match the length of the grayscale update).

[0273] The controller may determine, before scanning thee display, which of these cases exists by performing the following logical tests (assuming a one-bit value associated with each pixel and storing the pixel mode, as defined above):

[0274] (Old_image XOR new_image) > 0: pixels are changed in the display [0275] (Old__image XOR new_image) AND mode_array > 0: grayscale pixels are changed

[0276] (Old_image XOR new_image) AND (NOT mode_array) > 0: monochrome pixels are changed

[0277] As the controller scans the display, for case 1 or case 2 it can use one waveform look-up table for all pixels, since the unchanged pixels will receive

0 V, assuming that a null transition in one-bit mode is the same as in grayscale mode (in other words, that both waveforms are local-update). If instead the grayscale waveform is global-update (all pixels are updated whenever the display is updated), then the controller will need to test to see if a pixel is within the appropriate region to determine whether to apply the global-update waveform or not. For Case 3, the controller must check the value of the mode bit array for each pixel as it scans to determine which waveform to use.

[0278] Optionally, if the lightness values of the black and white states achieved in one-bit mode are identical to those achieved in grayscale mode, in

Case 3 above the grayscale waveform can be used for all pixels in the display, thus eliminating the need for transfer functions between the one-bit and grayscale waveforms.

[0279] The defined region method of the present invention may make use of any of the optional features of the basic look-up table method, as described above.

[0280] The primary advantage of the defined region method of the present invention is that it enables the use of a fast one-bit waveform on a display that is displaying a previously written grayscale image. Prior art display controllers typically only allow the display to be in either grayscale or one-bit mode at any one time. While it is possible to write one-bit images in grayscale mode, the relevant waveforms are quite slow. In addition, the defined region method of the present invention is essentially transparent to the host system (the system, typically a computer) which supplies images to the confroller, since the host system does not have to advise the confroller which waveform to use. Finally, the defined region method allows both one-bit and grayscale waveforms to be used on the display at the same time, whereas other solutions require two separate update events if both kinds of waveforms are being used. [0281 ] Further general waveform discussion

[0282] The aforementioned drive schemes may be varied in numerous ways depending upon the characteristics of the specific electro-optic display used. For example, in some cases it may be possible to eliminate many of the reset steps in the drives schemes described above. For example, if the elecfro-optic medium used is bistable for long periods (i.e., the gray levels of written pixels change only very slowly with time) and the impulse needed for a specific transition does not vary greatly with the period for which the pixel has been in its initial gray state, a look-up table may be arranged to effect gray state to gray state transitions directly without any intervening return to a black or white state, resetting of the display being effected only when, after a substantial period has elapsed, the gradual "drift" of pixels from their nominal gray levels has caused noticeable errors in the image presented. Thus, for example, if a user was using a display of the present invention as an electronic book reader, it might be possible to display numerous screens of information before resetting of the display were necessary; empirically, it has been found that with appropriate waveforms and drivers, as many as 1000 screens of information can be displayed before resetting is necessary, so that in practice resetting would not be necessary during a typical reading session of an electronic book reader.

[0283] It will readily be apparent to those skilled in display technology that a single apparatus of the present invention could usefully be provided with a plurality of different drive schemes for use under differing conditions. For example, since in the drive schemes shown in Figures 9 and 10 of the aforementioned WO 03/044765, the reset pulses consume a substantial fraction of the total energy consumption of the display, a controller might be provided with a first drive scheme which resets the display at frequent intervals, thus minimizing gray scale errors, and a second scheme which resets the display only at longer intervals, thus tolerating greater gray scale errors but reduce energy consumption. Switching between the two schemes can be effected either manually or dependent upon external parameters; for example, if the display were being used in a laptop computer, the first drive scheme could be used when the computer is running on mains electricity, while the second could be used while the computer was running on internal battery power. [0284] Compensation voltage method

[0285] A further variation on the basic look-up table method and apparatus of the present invention is provided by the compensation voltage method and apparatus of the present invention, which will now be described in detail. [0286] As already mentioned, the compensation voltage method and apparatus of the present invention seek to achieve results similar to the basic lookup table methods described above without the need to store very large look-up tables. The size of a look-up table grows rapidly with the number of prior states with regard to which the look-up table is indexed. For this reason, as already discussed, there is a practical limitation and cost consideration to increasing the number of prior states used in choosing an impulse for achieving a desired transition in a bistable electro-optic display.

[0287] In the compensation voltage method and apparatus of the present invention, the size of the look-up table needed is reduced, and compensation voltage data is stored for each pixel of the display, this compensation voltage data being calculated dependent upon at least one impulse previously applied to the relevant pixel. The voltage finally applied to the pixel is the sum of a drive voltage, chosen in the usual way from the look-up table, and a compensation voltage determined from the compensation voltage data for the relevant pixel. In effect, the compensation voltage data applies to the pixel a "correction" such as would otherwise be applied by indexing the look-up table for one or more additional prior states.

[0288] The look-up table used in the compensation voltage method may be of any of the types described above. Thus, the look-up table may be a simple two- dimensional table which allows only for the initial and final states of the pixel during the relevant transition. Alternatively, the look-up table may take account of one or more temporal and/or gray level prior states. The compensation voltage may also take into account only the compensation voltage data stored for the relevant pixel but may optionally also take into account of one or more temporal and/or gray level prior states. The compensation voltage may be applied to the relevant pixel not only during the period for which the drive voltage is applied to the pixel but also during so-called "hold" states when no drive voltage is being applied to the pixel.

[0289] The exact manner in which the compensation voltage data is determined may vary widely with the characteristics of the bistable elecfro-optic medium used. Typically, the compensation voltage data will periodically be modified in a manner which is determined by the drive voltage applied to the pixel during the present and/or one or more scan frames. In preferred forms of the invention, the compensation voltage data consists of a single numerical (register) value associated with each pixel of the display.

[0290] In a prefeπed embodiment of the invention, scan frames are grouped into superframes in the manner already described so that a display update can be initiated only at the beginning of a superframe. A superframe may, for example, consist often display scan frames, so that for a display with a 50 Hz scan rate, a display scan is 20 ms long and a superframe 200 ms long. During each superframe while the display is being rewritten, the compensation voltage data associated with each pixel is updated. The updating consists of two parts in the following order:

[0291] (1) Modifying the previous value using a fixed algorithm independent of the pulse applied during the relevant superframe; and [0292] (2) Increasing the value from step (1) by an amount determined by the impulse applied during the relevant superframe.

' [0293] In a particularly preferred embodiment of the invention, steps (1) and (2) are carried out as follows:

[0294] (1) Dividing the previous value by a fixed constant, which is conveniently two; and [0295] (2) Increasing the value from step (1) by an amount proportional to the total area under the voltage/time curve applied to the electro-optic medium during the relevant superframe.

[0296] In step (2), the increase may be exactly or only approximately proportional to the area under the voltage/time curve during the relevant superframe. For example, as described in detail below with reference to Figure 22, the increase may be "quantized" to a finite set of classes for all possible applied waveforms, each class including all waveforms with a total area between two bounds, and the increase in step (2) determined by the class to which the applied waveform belongs.

[0297] The following example is now given. The display used was a two- bit gray scale encapsulated electrophoretic display, and the drive method employed used a two-dimensional look-up table as shown in Table 7 below, which takes account only of the initial and final states of the desired transition; in this Table, the column headings represent the desired final state of the display and the row headings represent the initial state, while the numbers in individual cells represent the voltage in volts to be applied to the pixel for a predetermined period. [0298] Table 7

[0299] To allow for practice of the compensation voltage method of the present invention, a single numerical register was associated with each pixel of the display. The various impulses shown in Table 7 were classified and a pulse class was associated with each impulse, as shown in Table 8 below. [0300] Table 8

[0301] During each superframe, the numerical register associated with each pixel was divided by 2, and then increased by the numerical value shown in Table 13 for the pulse being applied to the relevant pixel during the same superframe. The voltage applied to each pixel during the superframe was the sum of the drive voltage, as shown in Table 12 and a compensation voltage, V_comp, given by the formula:

[0302] V_comp = A*(pixel register)

[0303] where the pixel register value is read from the register associated with the relevant pixel and "A" is a pre-defined constant.

[0304] In a laboratory demonstration of this preferred compensation voltage method of the invention, single pixel displays using an encapsulated electrophoretic medium sandwiched between parallel elecfrodes, the front one of which was formed of ITO and light-transmissive, were driven by 300 millisecond +/- 15V square wave pulses between their black and white states. The display started in its white state, was driven black, then back to white after a dwell time. It was found that the lightness of the final white state was a function of dwell state, as shown in Figure 22 of the accompanying drawings. Thus, this encapsulated elecfrophoretic medium was sensitive to dwell time, with the L* of the white state varying by about 3 units depending upon dwell time.

[0305] To show the effect of the compensation voltage method of the present invention, the experiment was repeated, except that a compensation voltage, consisting of an exponentially decaying voltage starting at the end of each drive pulse, was appended to each pulse. The applied voltage was the sum of the drive voltage and the compensation voltage. As shown in Figure 22, the white state for various dwell times in the case with the compensation voltage was much more uniform than for the uncompensated pulses. Thus, this experiment demonstrated that use of such compensation pulses in accordance with the present invention can greatly reduce the dwell time sensitivity of an encapsulated electrophoretic medium. [0306] The compensation voltage method of the present invention may make use of any of the optional features of the basic look-up table method described above.

[0307] From the foregoing description, it will be seen that the present invention provides methods for controlling the operation of electro-optic displays, which are well adapted to the characteristics of bistable particle-based elecfrophoretic displays and similar displays.

[0308] From the foregoing description, it will also be seen that the present invention provides methods for controlling the operation of electro-optic displays which allow accurate control of gray scale without requiring inconvenient flashing of the whole display to one of its extreme states at frequent intervals. The present invention also allows for accurate control of the display despite changes in the temperature and operating time thereof, while lowering the power consumption of the display. These advantages can be achieved inexpensively, since the confroller can be constructed from commercially available components. [0309] DTD integral reduction method

[0310] As already mentioned, It has been found that, at least in some cases, the impulse necessary for a given transition in a bistable electro-optic display varies with the residence time of a pixel in its optical state, this phenomenon, which does not appear to have previously been discussed in the literature, hereinafter being referred to as "dwell time dependence" or "DTD". Thus, it may be desirable or even in some cases in practice necessary to vary the impulse applied for a given transition as a function of the residence time of the pixel in its initial optical state.

[0311] The phenomenon of dwell time dependence will now be explained in more detail with reference to Figure 23 of the accompanying drawings, which shows the reflectance of a pixel a function of time for a sequence of transitions denoted R₃ - R₂ -> Ri, where each of the R_k terms indicates a gray level in a sequence of gray levels, with R's with larger indices occurring before R's with smaller indices. The fransitions between R₃ and R₂ and between R₂ and Ri are also indicated. DTD is the variation of the final optical state Ri caused by variation in the time spent in the optical state R₂, referred to as the dwell time. The DTD integral reduction method of the present invention provides a method for reducing dwell time dependence when driving bistable elecfro-optic displays. [0312] Although the invention is in no way limited by any theory as to its origin, DTD appears to be, in large part, caused by remnant electric fields experienced by the elecfro-optic medium. These remnant electric fields are residues of drive pulses applied to the medium. It is common practice to speak of remnant voltages resulting from applied pulses, and the remnant voltage is simply the scalar potential coπesponding to remnant electric fields in the usual manner appropriate to electrostatic theory. These remnant voltages can cause the optical state of a display film to drift with time. They also can change the efficacy of a subsequent drive voltage, thus changing the final optical state achieved after that subsequent pulse. In this manner, the remnant voltage from one fransition waveform can cause the final state after a subsequent waveform to be different from what it would be if the two transitions were very separate from each other. By "very separate" is meant sufficiently separated in time so that the remnant voltage from the first fransition waveform has substantially decayed before the second transition waveform is applied.

[0313] Measurements of remnant voltages resulting from transition waveforms and other simple pulses applied to an electro-optic medium indicate that the remnant voltage decays with time. The decay appears monotonic, but not simply exponential. However, as a first approximation, the decay can be approximated as exponential, with a decay time constant, in the case of most encapsulated elecfrophoretic media tested, of the order of one second, and other bistable elecfro-optic media are expected to display similar decay times. [0314] Accordingly, the DTD integral reduction method of present invention provides a method of driving a bistable electro-optic display having at least one pixel which comprises applying to the pixel a waveform V(t) such that:'

T _[031_5] J = \V{t)M{T - t)it ₍₁₎

0 (where T is the length of the waveform, the integral is over the duration of the waveform, V(t) is the waveform voltage as a function of time t, and M(t) is a memory function that characterizes the reduction in efficacy of the remnant voltage to induce dwell-time-dependence arising from a short pulse at time zero) is less than about 1 volt sec. Desirably J is less than about 0.5 volt sec, and most desirably less than about 0.1 volt sec. In fact J should be arranged to be as small as possible, ideally zero.

[0316] Waveforms can be designed that give very low values of J and hence very small DTD, by generating compound pulses. For example, a long negative voltage pulse preceding a shorter positive voltage pulse (with a voltage amplitude of the same magnitude but of opposite sign) can result in a much- reduced DTD. It is believed (although the invention is in no way limited by this belief) that the two pulses provide remnant voltages with opposite signs. When the ratio of the lengths of the two pulses are correctly set, the remnant voltages from the two pulses can be caused to largely cancel each other. The proper ratio of the length of the two pulses can be determined by the memory function for the remnant voltage.

[0317] In a presently preferred embodiment of the present invention, J is calculated by:

[0319] where τ is a decay (relaxation) time best determined empirically.

[0320] For some encapsulated electrophoretic media, it has been found experimentally that waveforms that give rise to small J values also give rise to particularly low DTD, while waveforms with particularly large J values give rise to large DTD. hi fact, good correlation has been found between J values calculated by

Equation (2) above with τ set to one second, roughly equal to the measured decay time of the remnant voltage after an applied voltage pulse.

[0321] Thus, it is advantageous to apply the methods described in the aforementioned patents and applications with waveforms where each transition (or at least most of the transitions in the look-up table) from one gray level to another is achieved with a waveform that gives a small value of J. This J value is preferably zero, but empirically it has been found that, at least for the encapsulated electrophoretic media described in the aforementioned patents and application, as long as J had a magnitude less than about 1 volt sec. at ambient temperature, the resulting dwell time dependence is quite small.

[0322] Thus, this invention provides a waveform for achieving transitions between a set of optical states, where, for every transition, a calculated value for J has a small magnitude. The J is calculated by a memory function that is presumably monotonically decreasing. This memory function is not arbifrary but can be estimated by observing the dwell time dependence of the display film to simple voltage pulse or compound voltage pulses. As an example, one can apply a voltage pulse to the display film to achieve a transition from a first to a second optical state, wait a dwell time, then apply a second voltage pulse to achieve a transition from the second to a third voltage pulse. By monitoring the shift in the third optical state as a function of the dwell time, one can determine an approximate shape of the memory function. The memory function has a shape approximately similar to the difference in the third optical state from its value for long dwell times, as a function of the dwell time. The memory function would then be given this shape, and would have amplitude of unity when its argument is zero. This method yields only an approximation of the memory function, and for various final optical states, the measured shape of the memory function is expected to change somewhat. However, the gross features, such as the characteristic time of decay of the memory function, should be similar for various optical states. However, if there are significant differences in shape with final optical state, then the best memory function shape to adopt is one gained when the third optical state is in the middle third of the optical range of the display medium. The gross features of the memory function should also be estimable by measuring the decay of the remnant voltage after an applied voltage pulse.

[0323] Although, the methods discussed here for estimating the memory function are not exact, it has been found that J values calculated from even an approximate memory are a good guide to waveforms having low DTD. A useful memory function expresses the gross features of the time dependence of the DTD as described above. For example, a memory function that is exponential with a decay time of one second has been found to work well in predicting waveforms that gave low DTD. Changing the decay time to 0.7 or 1.3 second does not destroy the effectiveness of the resulting J values as predictors of low DTD waveforms. However, a memory function that does not decay, but remains at unity indefinitely, is noticeably less useful as a predictor, and a memory function with a very short decay time, such as 0.05 second, was not a good predictor of low DTD waveforms. [0324] An example of a waveform that gives a small J value is the waveform shown in Figures 19 and 20 described above, where the x, y, and z pulses are all of durations much smaller than the characteristic decay time of the memory function. This waveform functions well when this condition is met because this waveform is composed of sequential opposing pulse elements whose remnant voltages tend to approximately cancel. For x and y values that are not much smaller than the characteristic decay time of the memory function but not larger than this decay time, it is found that that waveforms where x and y are of opposite sign tend to give lower J values, and x and y pulse durations can be found that actually permit very small J values because the various pulse elements give remnant voltages that cancel each other out after the waveform is applied, or at least largely cancel each other out.

[0325] It will be appreciated that the J value of a given waveform can be manipulated by inserting periods of zero voltage into the waveform, or adjusting the lengths of any periods of zero voltage already present in the waveform. Thus a wide variety of waveforms can be used while still maintaining a J value close to zero.

[0326] The DTD integral reduction method of this invention has general applicability. A waveform structure can be devised described by parameters, its J values calculated for various values of these parameters, and appropriate parameter values chosen to minimize the J value, thus reducing the DTD of the waveform.

Claims

Claims 1. A method of driving a bistable electro-optic display having a plurality of pixels, each of which is capable of displaying at least three gray levels, the method comprising: storing a look-up table containing data representing the impulses necessary to convert an initial gray level to a final gray level; storing data representing at least an initial state of each pixel of the display; receiving an input signal representing a desired final state of at least one pixel of the display; and generating an output signal representing a pixel voltage to be applied to said one pixel, the method being characterized by: storing compensation voltage data representing a compensation voltage for each pixel of the display, the compensation voltage for any pixel being calculated dependent upon at least one impulse previously applied to that pixel; and said pixel voltage being the sum of a drive voltage determined from the initial and final states of the pixel and the look-up table, and a compensation voltage determined from the compensation voltage data for the pixel. 2. A method according to claim 1 wherein the compensation voltage for each pixel is calculated dependent upon at least one of a temporal prior state of the pixel and a gray level prior state of the pixel. 3. A method according to claim 1 wherein the compensation voltage for each pixel is applied to that pixel both during a period when a drive voltage is being applied to the pixel and during a hold period when no drive voltage is being applied to the pixel. 4. A method according to claim 1 wherein the compensation voltage for each pixel is updated during each superframe required for a complete addressing of the display.

5. A method according to claim 4 wherein the compensation voltage for each pixel is updated by (1) modifying the previous value of the compensation voltage using a fixed algorithm independent of the pulse applied during the relevant superframe; and (2) increasing the value from step (1) by an amount determined by the pulse applied during the relevant superframe.

6. A method according to claim 5 wherein the compensation voltage for each pixel is updated by (1) dividing the previous value of the compensation voltage by a fixed constant; and (2) increasing the value from step (1) by an amount substantially proportional to the total area under the voltage/time curve applied to the electro-optic medium during the relevant superframe.

7. A method according to claim 1 wherein the compensation voltage is applied in the form of an exponentially decaying voltage applied at the end of at least one drive pulse.

8. A device controller comprising: storage means arranged to store both a look-up table containing data representing the impulses necessary to convert an initial gray level to a final gray level, data representing at least an initial state of each pixel of the display; and compensation voltage data for each pixel of the display; input means for receiving an input signal representing a desired final state of at least one pixel of the display; calculation means for determining, from the input signal, the stored data representing the initial state of said pixel, and the look-up table, a drive voltage required to change the initial state of said one pixel to the desired final state, the calculation means also determining, from the compensation voltage data for said pixel, a compensation voltage for said pixel, and summing the drive voltage and the compensation voltage to determine a pixel voltage; and output means for generating an output signal representative of said pixel voltage.

9. A device controller according to claim 8 wherein the calculation means is arranged to determine the compensation voltage dependent upon at least one of a temporal prior state of the pixel and a gray level prior state of the pixel.

10. A device controller according to claim 8 wherein the output means is arranged to apply the compensation voltage to the pixel both during a period when a drive voltage is being applied to the pixel and during a hold period when no drive voltage is being applied to the pixel.

11. A device confroller according to claim 8 wherein the calculation means is arranged to update the compensation voltage for each pixel during each superframe required for a complete addressing of the display.

12. A device confroller according to claim 11 wherein the calculation means is arranged to update the compensation voltage for each pixel by (1) modifying the previous value of the compensation voltage using a fixed algorithm independent of the pulse applied during the relevant superframe; and (2) increasing the value from step (1) by an amount determined by the pulse applied during the relevant superframe.

13. A device controller according to claim 12 wherein the calculation means is arranged to update the compensation voltage for each pixel by (1) dividing the previous value of the compensation voltage by a fixed constant; and (2) increasing the value from step (1) by an amount substantially proportional to the total area under the voltage/time curve applied to the electro-optic medium during the relevant superframe.

14. A device controller according to claim 8 wherein the output means is arranged to apply the compensation voltage in the form of an exponentially decaying voltage applied at the end of at least one drive pulse.

15. A method for updating a bistable electro-optic display having a plurality of pixels arranged in a plurality of rows and columns such that each pixel is uniquely defined by the intersection of a specified row and a specified column, and drive means for applying electric fields independently to each of the pixels to vary the display state of the pixel, each pixel having at least three different display states, the method comprising: storing region data representing a defined region comprising a part but less than all of said display; determining for each pixel whether the pixel is within or outside the defined region; applying a first drive scheme to pixels within the defined region and a second drive scheme, different from the first drive scheme, to pixels outside the defined region.

16. A method according to claim 15 wherein the first and second drive scheme differ in bit depth.

17 A method according to claim 16 wherein one of the first and second drive schemes is monochrome and the other is gray scale having at least four different gray levels.

18. A method according to claim 15 wherein the defined region comprises a text box used for entry of text on to the display.

19. A method of driving a bistable electro-optic display having a plurality of pixels, each of which is capable of displaying at least three gray levels, the method comprising: storing a look-up table containing data representing the impulses necessary to convert an initial gray level to a final gray level; storing data representing at least an initial state of each pixel of the display; receiving an input signal representing a desired final state of at least one pixel of the display; and generating an output signal representing the impulse necessary to convert the initial state of said one pixel to the desired final state thereof, as determined from the look-up table, wherein for at least one transition from an initial state to a final state, the output signal comprises a DC imbalanced fine tuning sequence which:

(a) has a non-zero net impulse;

(b) is non-contiguous; (c) results in a change in gray level of the pixel that is substantially different from the change in optical state of its DC reference pulse, where the DC reference pulse is a pulse of voltage V₀, where V₀ is the maximum voltage applied during the fine tuning sequence but with the same sign as the net impulse G of the fine tuning sequence, and the duration of the reference pulse is G/V₀; and

(d) results in a change in gray level of the pixel smaller in magnitude than the change in gray level caused by its time-reference pulse, where the time-reference pulse is defined as a monopolar voltage pulse of the same duration as the fine tuning sequence, but where the sign of the reference pulse is that which gives the larger change in gray level.

20. A method according to claim 19 wherein the fine tuning sequence results in a change in gray level of the pixel less than one half of the change in gray level caused by its time-reference pulse.

21. A method according to claim 19 wherein for said at least one transition, the output signal comprises at least one monopolar drive pulse in addition to the fine tuning sequence.

22. A method according to claim 19 wherein, for said at least one fransition, the output signal is non-periodic.

23. A method according to claim 19 wherein, for a majority of fransitions in the lookup table, the output signal has a non-zero net impulse and is non-contiguous.

24. A method according to claim 19 wherein, for said at least one transition, the output signal consists only of pulses having voltage levels of +V, 0 and -V

25. A method according to claim 23 wherein, for said at least one fransition, the output signal consists only of pulses having voltage levels of 0 and one of +V and -V.

26. A method according to claim 25 wherein, for said at least one transition, the output signal consists of a pulse having a voltage level of 0 preceded and followed by at least two pulses having voltage levels of the same one of +V and -V

27. A method according to claim 26 wherein, for a majority of fransitions in the lookup table for which the initial and final states of the pixel are different, the output signal consists of a pulse having a voltage level of 0 preceded and followed by at least two pulses having voltage levels of the same one of +V and -V.

28. A method according to claim 19 wherein the transition table is DC balanced.

29. A method according to claim 19 wherein, for said at least one transition, the -output signal consists of a series of pulses which are integer multiples of a single interval.

30. A method according to claim 19 further comprising storing data representing at least one temporal prior state of said one pixel and/or at least one gray level prior state of said one pixel, and wherein the output signal is generated dependent upon said at least one temporal prior state and/or at least one gray level prior state of said one pixel.

31. A method of driving a bistable electro-optic display having a plurality of pixels, each of which is capable of displaying at least three gray levels, the method comprising applying to each pixel of the display an output signal effective to change the pixel from an initial state to a final state, wherein, for at least one transition for which the initial and final states of the pixel are different, the output signal consists of a pulse having a voltage level of 0 preceded and followed at by least two pulses having voltage levels of the same one of +V and -V

32. A method of driving a bistable elecfro-optic display having a plurality of pixels, each of which is capable of displaying at least three gray levels, the method comprising: storing a look-up table containing data representing the impulses necessary to convert an initial gray level to a final gray level; storing data representing at least an initial state of each pixel of the display; receiving an input signal representing a desired final state of at least one pixel of the display; and generating an output signal representing the impulse necessary to convert the initial state of said one pixel to the desired final state thereof, as determined from the look-up table, wherein for at least one transition from an initial state to a final state, the output signal comprises a DC balanced fine tuning sequence which:

(a) has substantially zero net impulse; and

(b) at no point in the fine tuning sequence, causes the gray level of the pixel to vary from its gray level at the beginning of the fine tuning sequence by more than about one third of the difference in gray level between the two extreme optical states of the pixel.

33. A method according to claim 32 wherein for said at least one transition, the output signal comprises at least one monopolar drive pulse in addition to the fine tuning sequence.

34. A method of driving a bistable electro-optic display having a plurality of pixels, each of which is capable of displaying at least three gray levels, the method comprising applying to each pixel of the display an output signal effective to change the pixel from an initial state to a final state, wherein, for at least one transition, the output signal is non-zero but DC balanced.

35. A method according to claim 34 wherein, for said at least one transition, the output signal comprises a first pair of pulses comprising a voltage pulse preceded by a pulse of equal length but opposite sign.

36. A method according to claim 35 wherein the output signal further comprises a period of zero voltage between the two pulses.

37. A method according to claim 35 wherein at least one of the pulses is interrupted by a period of zero voltage.

38. A method according to claim 35 wherein, for said at least one transition, the output signal further comprises a second pair of pulses of equal length but opposite sign.

39. A method according to claim 38 wherein the second pair of pulses having a length different from that of the first pair of pulses.

40. A method according to claim 38 wherein the first of the second pair of pulses has a polarity opposite to that of the first of the first pair of pulses.

41. A method according to claim 38 wherein the first pair of pulses occur between the first and the second of the second pair of pulses.

42. A method according to claim 34 wherein, for said at least one fransition, the output signal comprises at least one pulse element effective to drive the pixel substantially into one optical rail.

43. A method according to claim 34 wherein, for each transition for which the initial and final states of the pixel are the same, the output signal is non-zero but DC balanced, and for each transition in which the initial and final states of the pixel are not the same, the output signal is not DC balanced.

44. A method according to claim 43 wherein, for each transition in which the initial and final states of the pixel are not the same, the output signal has the form -x/ΔEP/x, where ΔLP is the difference in impulse potential between the initial and final states of the pixel and -x and x are a pair of pulses of equal length but opposite sign.

45 A method according to claim 34 further comprising: storing a look-up table containing data representing the impulses necessary to convert the initial gray level of a pixel to a final gray level; storing data representing at least an initial state of each pixel of the display; receiving an input signal representing a desired final state of at least one pixel of the display; and generating an output signal representing the impulse necessary to convert the initial state of said one pixel to the desired final state thereof, as determined from the look-up table.

46. A method of driving a bistable elecfro-optic display having at least one pixel which comprises applying to the pixel a waveform V(t) such that:

0

(where T is the length of the waveform, the integral is over the duration of the waveform, V(t) is the waveform voltage as a function of time t, and M(t) is a memory function that characterizes the reduction in efficacy of the remnant voltage to induce dwell-time-dependence arising from a short pulse at time zero) is less than about 1 volt sec.

47. A method according to claim 46 wherein J is less than about 0.5 volt sec.

48. A method according to claim 47 wherein J is less than about 0.1 volt sec.

49. A method according to claim 46 wherein J is calculated by:

where T is a decay (relaxation) time.

50. A process according to claim 49 wherein τ has a value of from about 0.7 to about 1.3 seconds.