Continuous waveform driving in multicolor electrophoresis displays

Abstract

Providing continuous waveform driving for multicolor electrophoretic displays. [Solution] A continuous waveform for driving a four-particle electrophoresis medium comprising four different types of particles, e.g., a set of scattering particles and three sets of subtractive color mixing particles. A method for identifying a preferred waveform for a target color state or target transition when using a continuous or quasi-continuous voltage driver / controller. In one embodiment, the waveform comprises at least 32 distinct voltage levels over 500 ms. In one embodiment, the at least four types of particles comprise two particles of a first polarity and two particles of a second polarity.

Description

[Background technology]

[0001] (Related applications) This application claims priority to U.S. Provisional Patent Application No. 63 / 147,465, filed on 9 February 2021. All patents and published documents disclosed herein are incorporated together by reference.

[0002] Electrophoretic displays (EPDs) change color by modifying the position of charged colored particles on a light-transmitting viewing surface. Such electrophoretic displays are typically referred to as "electronic paper" or "e-paper" because the resulting display has high contrast, much like ink on paper, and is readable in sunlight. Electrophoretic displays are widely used in e-readers such as Amazon Kindle® because they provide a book-like reading experience, use less power, and allow users to carry a library of hundreds of books in a lightweight, handheld device.

[0003] For many years, electrophoretic displays have contained only two types of charged colored particles: black and white (to be clear, “color” as used herein includes black and white). White particles are often light-scattering and may consist of titanium dioxide, for example, while black particles are absorbent across the visible spectrum and may consist of carbon black or absorbent metal oxides such as copper chromite. In its simplest sense, a monochrome electrophoretic display requires only a light-transmitting electrode on the viewing surface, a back electrode, and an electrophoretic medium containing conversely charged white and black particles. When a voltage of one polarity is applied, white particles move to the viewing surface, and when a voltage of the opposite polarity is applied, black particles move to the viewing surface. If the back electrode contains controllable regions (pixels) (segmented electrodes controlled by transistors, or active matrices of pixel electrodes), a pattern can be fabricated to appear electronically on the viewing surface. This pattern could be, for example, the text of a book.

[0004] In recent times, a variety of color options, including three-color displays (black, white, red; black, white, yellow) and four-color displays (black, white, red, yellow), are becoming commercially available for electrophoretic displays. Similar to the operation of a monochrome electrophoretic display, an electrophoretic display with three or four reflective pigments operates similarly to a simple monochrome display, as the desired color particles are driven relative to the viewing surface. While the driving scheme is far more complex than that of black and white alone, ultimately, the optical functionality of the particles remains the same. Furthermore, it is noteworthy that such displays can show only a single color at a time (i.e., only one set of colors of particles being driven relative to the viewing surface).

[0005] Advanced Color Electronic Paper (ACeP) TMAlthough it contains four particles, the cyan, yellow, and magenta particles are not reflective but subtractive, thereby allowing thousands of colors to be produced in each pixel. The color process is functionally equivalent to the printing method that has long been used in offset and inkjet printers. A given color is produced by using the correct ratio of cyan, yellow, and magenta on a bright white paper background. In the case of ACeP, the relative positions of the cyan, yellow, magenta, and white particles to the viewing surface will determine the color in each pixel. While this type of electrophoretic display allows thousands of colors in each pixel, it is crucial to carefully control the position of each pigment (50-500 nanometers in size) within a working space of approximately 10-20 microns in thickness. Obviously, variations in the position of the pigments will result in the display of the wrong color in a given pixel. Therefore, precise voltage control is required for such a system. Further details of the system are available in the following U.S. Patents, namely U.S. Patent No. 9,361,836 (Patent Document 1), No. 9,921,451, No. 10,276,109, No. 10,353,266, No. 10,467,984, and No. 10,593,272 (all of which are incorporated as a whole by reference).

[0006] For the most part, electrophoretic media, such as those described above, are designed to be driven using low-voltage square waves, such as those produced by driver circuits from thin-film transistor backplanes. Such driver circuits can be mass-produced inexpensively because they are very closely related to the driver networks and fabrication methods used to create liquid crystal display panels, such as those found in smartphones, laptop monitors, and televisions. Conventionally, even when electrophoretic media are driven directly by insulating electrodes (e.g., segmented electrodes), the driving pulse is delivered as a square wave having a certain amplitude and a certain time width. See, for example, U.S. Patent No. 7,012,600 (Patent Document 2) (which is incorporated as a whole by reference). In this form of driving, the electrical impulse, i.e., the amount of time the charged particles are exposed to a field of a given size, determines the final "state" observed on the viewing surface.

[0007] The term “gray state” is used herein in its conventional sense in the field of imaging technology and refers to an intermediate state between the two extreme optical states of a pixel, and does not necessarily imply a black-white transition between these two extreme states. For example, some of the E Ink patents and published applications referenced below describe electrophoretic displays where the extreme states are white and dark blue, so that the intermediate gray state would actually be light blue. In fact, as already described, a change in optical state may not be a change in color at all. The term “black and white” may hereafter be used herein to refer to the two extreme optical states of a display and should generally be understood to include extreme optical states that are not strictly black and white, e.g., the aforementioned white state and the dark blue state.

[0008] The terms “bistable” and “bistable” are used herein to refer to a display having a display element having a first and second display state having at least one different optical property, such that any given element is driven with a finite-duration address pulse to exhibit either its first or second display state, and after the address pulse has terminated, the state persists for at least several times, e.g., at least four times, the minimum duration of the address pulse required to change the state of the display element. U.S. Patent No. 7,170,670 demonstrates that some grayscale-enabled particle-based electrophoretic displays are stable not only in their extreme black-and-white state but also in their intermediate gray state, and that the same is true for some other types of electro-optic displays. While this type of display is appropriately called “multistable” rather than “bistable,” for convenience, the term “bistable” may be used herein to include both bistable and multistable displays.

[0009] The term "impulse," when used herein to refer to driving an electrophoretic display, refers to the integral of the applied voltage over time during the period in which the display is driven. The term "waveform," when used to refer to driving an electrophoretic display, refers to a series of voltages, or a pattern thereof, applied to the electrophoretic medium over a given period (seconds, frames, etc.) in order to produce a desired optical effect in the electrophoretic medium.

[0010] Particles that absorb, scatter, or reflect light in a broadband or selected wavelength range are referred to herein as coloring or pigment particles. Various materials other than pigments (in the strict sense of the term, meaning insoluble coloring materials), such as dyes or photonic crystals, that absorb or reflect light may also be used in the electrophoretic media and displays of the present invention.

[0011] Numerous patents and applications, assigned to or in the name of the Massachusetts Institute of Technology (MIT) and E Ink Corporation, describe various techniques used in encapsulated electrophoretic media and other electro-optical media. Such encapsulated media comprise numerous small capsules, each of which comprises an inner phase containing electrophoretically mobile particles in a fluid medium and a capsule wall surrounding the inner phase. Typically, the capsules themselves are held within a polymer binder to form a coherent layer positioned between two electrodes. The techniques described in these patents and applications include: (a) Electrophoretic particles, fluids, and fluid additives (see, for example, U.S. Patent Nos. 7,002,728 and 7,679,814) (b) Capsules, binders, and encapsulation processes (see, for example, U.S. Patent Nos. 6,922,276 and 7,411,719) (c) Microcell structures, wall materials, and methods for forming microcells (see, for example, U.S. Patent Nos. 7,072,095 and 9,279,906) (d) Methods for filling and sealing microcells (see, for example, U.S. Patent Nos. 7,144,942 and 7,715,088) (e) Films and subassemblies containing electro-optical materials (see, for example, U.S. Patent Nos. 6,982,178 and 7,839,564) (f) Backplanes, adhesive layers, and other auxiliary layers, and methods used in displays (see, for example, U.S. Patents No. 7,116,318 and 7,535,624) (g) Color formation and color adjustment (e.g., U.S. Patent Nos. 6,017,584, 6,545,797, 6,664,944, 6,788,452, 6,864,875, 6,914,714, 6,972,893, 7,038,656, 7,038,670, 7,046,228, 7,052,571, 7,075,502, 7,167,155, 7,385,751, 7,492,505, 7,667,684, No. 7,684,108, No. 7,791,789, No. 7,800,813, No. 7,821,702, No. 7,839,564, No. 7,910,175, No. 7,952,790, No. 7,956,841, No. 7,982,941, No. 8,040,594, No. 8,054,526, No. 8,098,418, No. 8,159,636, No. 8,213,076, No. 8,363,299, No. 8,422,116, No. 8,441,714, No. 8,441,716, No. 8,466,852, No. 8,503,063, No. 8,576,470, No. 8,576,475, No. 8,593,721, No. 8,605,354, No. 8,649,084, No. 8,670,174, No. 8,704,756 , No. 8,717,664, No. 8,786,935, No. 8,797,634, No. 8,810,899, No. 8,830,559, No. 8,873,129, No. 8,902,153, No. 8,902,491, No. 8,917,439 , Nos. 8,964,282, 9,013,783, 9,116,412, 9,146,439, 9,164,207, 9,170,467, 9,170,468, 9,182,646, 9,195,111, 9,199,441, 9,268,191, 9,285,649, 9,293,511, 9,341,916, 9,360,733, 9,361,836, 9,383,623, and 9,423,U.S. Patent Application Publication No. 666, and U.S. Patent Application Publication Nos. 2008 / 0043318, 2008 / 0048970, 2009 / 0225398, 2010 / 0156780, 2011 / 0043543, 2012 / 0326957, 2013 / 0242378, 2013 / 0278995, 2014 / 0055840, 2014 / 0078576, 2014 / 0340430, 2014 / 0340736, and 2014 / 0362 See issues 213, 2015 / 0103394, 2015 / 0118390, 2015 / 0124345, 2015 / 0198858, 2015 / 0234250, 2015 / 0268531, 2015 / 0301246, 2016 / 0011484, 2016 / 0026062, 2016 / 0048054, 2016 / 0116816, 2016 / 0116818, and 2016 / 0140909). (h) Methods for driving the display (e.g., U.S. Patent Nos. 5,930,026, 6,445,489, 6,504,524, 6,512,354, 6,531,997, 6,753,999, 6,825,970, 6,900,851, 6,995,550, 7,012,600, 7,023,420, 7,034,783, 7,061,166, 7,061,662, 7,116,466, 7,119,772, 7,177,066, 7,193,625, 7,202,84 No. 7, No. 7,242,514, No. 7,259,744, No. 7,304,787, No. 7,312,794, No. 7,327,511 , No. 7,408,699, No. 7,453,445, No. 7,492,339, No. 7,528,822, No. 7,545,358, No. 7 , No. 583,251, No. 7,602,374, No. 7,612,760, No. 7,679,599, No. 7,679,813, No. 7,6 No. 83,606, No. 7,688,297, No. 7,729,039, No. 7,733,311, No. 7,733,335, No. 7,787, No. 169, No. 7,859,742, No. 7,952,557, No. 7,956,841, No. 7,982,479, No. 7,999,78 No. 7, No. 8,077,141, No. 8,125,501, No. 8,139,050, No. 8,174,490, No. 8,243,013, No. 8,274,472, No. 8,289,250, No. 8,300,006, No. 8,305,341, No. 8,314,784, No. 8 ,373,649, No.8,384,658, No.8,456,414, No.8,462,102, No.8,514,168, No.8,53 No. 7,105, No. 8,558,783, No. 8,558,785, No. 8,558,786, No. 8,558,855, No. 8,576, No. 164, No. 8,576,259, No. 8,593,396, No. 8,605,032, No. 8,643,595, No. 8,665,206 No. 8,681,191, No. 8,730,153, No. 8,810,525, No. 8,928,562, No. 8,928,641, No. 8,976,444, No. 9,013,394, No. 9,019,197, No. 9,019,198, No. 9,019,318, No. 9,Nos. 082,352, 9,171,508, 9,218,773, 9,224,338, 9,224,342, 9,224,344, 9,230,492, 9,251,736, 9,262,973, 9,269,311, 9,299,294, 9,373,289, 9,390,066, 9,390,661, and 9,412,No. 314, and U.S. Patent Application Publications No. 2003 / 0102858, 2004 / 0246562, 2005 / 0253777, 2007 / 0091418, 2007 / 0103427, 2007 / 0176912, 2008 / 0024429, 2008 / 0024482, 2008 / 0136774, 2008 / 0291129, 2008 / 0303780, 2009 / 0174651, 2009 / 0195568, No. 2009 / 0322721, No. 2010 / 0194733, No. 2010 / 0194789, No. 2010 / 0220121, No. 2010 / 0265561, No. 2010 / 0283804, No. 2011 / 0063314, No. 2011 / 0175875, 2011 / 0193840, 2011 / 0193841, 2011 / 0199671, 2011 / 0221740, 2012 / 0001957, 2012 / 0098740, 2 No. 013 / 0063333, No. 2013 / 0194250, No. 2013 / 0249782, No. 2013 / 0321278, No. 2014 / 0009817, No. 2014 / 0085355, No. 2014 / 0204012, No. 20 No. 14 / 0218277, No. 2014 / 0240210, No. 2014 / 0240373, No. 2014 / 0253425, No. 2014 / 0292830, No. 2014 / 0293398, No. 2014 / 0333685, No. 201 See issues 4 / 0340734, 2015 / 0070744, 2015 / 0097877, 2015 / 0109283, 2015 / 0213749, 2015 / 0213765, 2015 / 0221257, 2015 / 0262255, 2015 / 0262551, 2016 / 0071465, 2016 / 0078820, 2016 / 0093253, 2016 / 0140910, and 2016 / 0180777). (i) Uses of the display (see, for example, U.S. Patent Nos. 7,312,784 and 8,009,348) (j) Non-electrophoretic displays as described in U.S. Patent No. 6,241,921, and U.S. Patent Application Publication No. 2015 / 0277160, and U.S. Patent Application Publication Nos. 2015 / 0005720 and 2016 / 0012710.

[0012] Many of the aforementioned patents and applications recognize that the walls surrounding individual microcapsules within an encapsulated electrophoretic medium may be replaced by a continuous phase, and thus the electrophoretic medium may produce a so-called “polymer-dispersed electrophoretic display” comprising multiple individual droplets of electrophoretic fluid and a continuous phase of polymer material, and that individual droplets of electrophoretic fluid within such a polymer-dispersed electrophoretic display may be considered capsules or microcapsules, even though no individual capsule membrane is associated with each individual droplet (see, for example, U.S. Patent No. 6,866,760). Therefore, for the purposes of this application, such polymer-dispersed electrophoretic media are considered a variant of encapsulated electrophoretic media.

[0013] A related type of electrophoretic display is the so-called "microcell electrophoretic display." In microcell electrophoretic displays, charged particles and fluids are not encapsulated within microcapsules, but instead are held within a carrier medium, typically a polymer film, in multiple cavities formed within it. See, for example, U.S. Patents 6,672,921 and 6,788,449.

[0014] Electrophoretic media are often impermeable (for example, in many electrophoretic media, the particles substantially block the transmission of visible light through the display) and operate in reflective mode. However, many electrophoretic displays can be manufactured to operate in a so-called "shutter mode," where one display state is substantially impermeable and the other is light-transmitting. See, for example, U.S. Patents 5,872,552, 6,130,774, 6,144,361, 6,172,798, 6,271,823, 6,225,971, and 6,184,856. Dielectrophoretic displays are similar to electrophoretic displays but can operate in a similar mode, depending on the variation in electric field strength (see U.S. Patent 4,418,346). Other types of electro-optical displays may also be capable of operating in shutter mode. An electro-optical medium operating in shutter mode can be used in a multilayer structure for a full-color display, in which at least one layer adjacent to the viewing surface of the display operates in shutter mode, exposing or obscuring a second layer that is further away from the viewing surface.

[0015] Encapsulated electrophoretic displays typically do not suffer from the clustering and sedimentation failure modes of conventional electrophoretic devices and offer additional advantages such as the ability to print or coat displays on a wide variety of flexible and rigid substrates (the use of the term "print" is intended to include, without limitation, pre-metered coating, such as patch die coating, slot or extrusion coating, slide or cascade coating, curtain coating, etc., roll coating, such as knife over roll coating, forward and reverse roll coating, etc., gravure coating, dip coating, spray coating, meniscus coating, spin coating, brush coating, air knife coating, silk screen printing process, electrostatic printing process, thermal printing process, inkjet printing process, electrophoretic deposition (see U.S. Patent No. 7,339,715), and any other similar techniques). Thus, the resulting display can be flexible. Further, since the display medium can be printed (using a variety of methods), the display itself can be manufactured at a low cost. In addition, as described in U.S. Patent Application No. 17 / 088,762, encapsulated electrophoretic media can be incorporated into non-planar surfaces, which can then be incorporated into consumer goods. As a result, the surfaces of products, building materials, etc. can be designed to change color when a suitable electric field is supplied.

Prior Art Documents

Patent Documents

[0016]

Patent Document 1

Patent Document 2

Summary of the Invention

Means for Solving the Problems

[0017] An improved method for driving an electrophoretic medium comprising four types of particles is disclosed herein, each particle having different optical properties from one another, and each type of particle having different combinations of charge polarity and charge magnitude from one another. One embodiment of such an electrophoretic medium is commercially known as high-grade color electronic paper or ACEP®, however other suitable electrophoretic media are described herein, and the method described herein is generally applicable to four-particle (or more) electrophoretic systems. In one aspect, the method comprises providing a continuous drive waveform for at least 500 ms, wherein the continuous drive waveform has at least 16 distinct voltage levels during the 500 ms. The resulting waveform in the transition is less like a “flash” to the viewer and less likely to be visually unpleasant. The resulting waveform also allows for controlled transitions, which can be, for example, abrupt, smooth, sloped, or pulsating / vibrating. In one embodiment, this waveform has a rate of change of less than 3V / ms for at least 500ms, while simultaneously the change in the rate of change (second derivative) is -1V / ms. 2 ~1V / ms 2 In one embodiment, this waveform includes at least 32 distinct voltage levels within 500 ms. In one embodiment, the continuous drive waveform lasts for at least 1 second. In one embodiment, at least four types of particles include two particles of a first polarity and two particles of a second polarity. In one embodiment, at least four types of particles include three particles of a first polarity and one particle of a second polarity. In one embodiment, the optical property is color, which is selected from the group consisting of white, red, magenta, orange, yellow, green, cyan, blue, purple, and black. In one embodiment, at least two types of particles include a surface polymer, and each of the two types of particles has a different type of surface polymer.

[0018] In another aspect, a method for driving an electrophoretic medium comprising at least four types of particles, each particle having different optical properties from one another, and each type of particle having different combinations of charge polarity and charge magnitude from one another. The method comprises providing a continuous drive waveform over at least 500 ms, the continuous drive waveform as a function of time, and the waveform as a whole having the following forms:

number

[0019] In another aspect, a display system is disclosed, the display system comprising: a first light-transmitting electrode; an electrophoretic medium comprising at least four types of particles, each particle having different optical properties from one another, and each type of particle having different combinations of charge polarity and charge magnitude from one another; a second electrode, the electrophoretic medium being positioned between the first light-transmitting electrode and the second electrode; a controller; and a power source operably connected to the first light-transmitting electrode and the second electrode and configured to provide at least 16 distinct voltage levels, wherein the controller provides at least three of the distinct voltage levels between the first light-transmitting electrode and the second electrode when the electrophoretic medium is changed from a first display state to a second display state. In one embodiment, the power source provides at least two voltage levels that differ by more than 20 volts. In one embodiment, the at least four types of particles include two particles of a first polarity and two particles of a second polarity. In one embodiment, at least four types of particles include three particles of a first polarity and one particle of a second polarity. In one embodiment, the optical property is color, which is selected from the group consisting of white, red, magenta, orange, yellow, green, cyan, blue, purple, and black.

[0020] In another aspect, a method is disclosed for determining a continuous waveform for driving an electrophoretic medium placed between a first light-transmitting electrode and a second electrode, wherein the electrophoretic medium comprises at least four types of particles, each type of particle having different optical properties, and each type of particle having different combinations of charge polarity and charge magnitude, and the method comprises determining a first optical state with respect to the electrophoretic medium, determining a second optical state with respect to the electrophoretic medium, propagating a repetitive drive voltage with respect to frame width in the reverse direction over a desired time range from the second optical state to the first optical state while minimizing a cost function based on a differentiable surrogate model of the electrophoretic medium between the first light-transmitting electrode and the second electrode, and assembling a repetitive drive voltage with respect to frame width to produce a continuous waveform. In some embodiments, the cost function is as follows:

number

[0021] In some embodiments, the desired time range is at least 500 ms, and the frame width is less than 50 ms.

[0022] In another aspect, a method is disclosed for determining a continuous waveform for driving an electrophoretic medium placed between a first light-transmitting electrode and a second electrode, wherein the electrophoretic medium comprises at least four types of particles, each type of particle having different optical properties, and each type of particle having different combinations of charge polarity and charge magnitude, and the method comprises determining a first optical state with respect to the electrophoretic medium, determining a second optical state with respect to the electrophoretic medium, propagating a repetitive drive voltage in reverse with respect to frame width over a desired time range from the second optical state to the first optical state, wherein the transition between frames does not involve a voltage change greater than ±40V, and assembling the repetitive drive voltage to produce a continuous waveform. In one embodiment, the continuous waveform between the first optical state and the second optical state is -1V / ms2 Less than or 1 V / ms 2 It does not exhibit a change in the rate of change of voltage as a function of time exceeding a certain threshold. The present invention provides, for example, the following: (Item 1) A method for driving an electrophoretic medium comprising at least four types of particles, wherein each particle has different optical properties from one another, and each type of particle has different combinations of charge polarity and charge magnitude from one another, and the method is This includes providing a continuous drive waveform for at least 500ms, The continuous drive waveform has at least 16 unique voltage levels within the 500ms, the continuous drive waveform has a measurable rate of change in V / ms, and the time-dependent change of the rate of change is -1V / ms 2 ~1V / ms 2 The method. (Item 2) The method according to item 1, wherein the waveform includes at least 32 unique voltage levels within the 500ms. (Item 3) The method according to item 1, wherein the at least four types of particles include two particles of a first polarity and two particles of a second polarity. (Item 4) The method according to item 1, wherein the at least four types of particles include three particles of a first polarity and one particle of a second polarity. (Item 5) The method according to item 1, wherein the optical property is a color, and the color is selected from the group consisting of white, red, magenta, orange, yellow, green, cyan, blue, purple, and black. (Item 6) The method according to item 1, wherein at least two types of particles contain a surface polymer, and each of the two types of particles has a different type of surface polymer. (Item 7) A method for driving an electrophoretic medium comprising at least four types of particles, wherein each particle has different optical properties from one another, and each type of particle has different combinations of charge polarity and charge magnitude from one another, and the method is This includes providing a continuous drive waveform for at least 500ms, The continuous drive waveform as a function of time has the following form within the waveform as a whole:

number

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Brief Description of the Drawings

[0023] The patent or application file includes at least one drawing executed in color. Copies of this patent or patent application publication document with color drawings will be provided by the Patent Office upon request and payment of the required fees.

[0024] [Figure 1A] FIG. 1A is a representative cross-section of a four-particle electrophoretic display, in which the electrophoretic medium is encapsulated within a capsule.

[0025] [Figure 1B] Figure 1B shows a typical cross-section of a four-particle electrophoresis display in which the electrophoretic medium is encapsulated within a microcell.

[0026] [Figure 2A] Figure 2A illustrates an exemplary equivalent circuit for a single pixel in an electrophoretic display using an active matrix backplane with a storage capacitor.

[0027] [Figure 2B] Figure 2B illustrates an exemplary equivalent circuit of the simplified electrophoretic display of the present invention, in which the power source is configured to provide multiple voltage levels.

[0028] [Figure 3A] Figure 3A illustrates the preferred positions of each of the four sets of particles for producing eight standard colors in a white-cyan-magenta-yellow (WCMY) four-particle electrophoretic display, where the white particles are reflective and the cyan, magenta, and yellow particles are absorbent.

[0029] [Figure 3B] Figure 3B illustrates the preferred positions of each of the four sets of particles for producing eight standard colors in a black-red-yellow-blue (KRYB) four-particle electrophoretic display, where the black particles are absorbent and the red, yellow, and blue particles are reflective.

[0030] [Figure 4] Figures 4A and 4B show a simple (prior art) push-pull waveform that could be used to achieve a specific color in an EPD system containing one reflective (white) particle and three subtractive color-mixing (cyan, yellow, and magenta) particles.

[0031] [Figure 5A]Figure 5A illustrates a color space that can be defined for a four-particle electrophoresis system and a method by which the transition from the first color to the second color can proceed along two or more paths.

[0032] [Figure 5B] Figure 5B illustrates a method in which a waveform can be repeatedly propagated in reverse from a second optical state to a first optical state and then assembled to produce a desirable waveform.

[0033] [Figure 6] Figure 6A illustrates the predicted color transition from the first color state to the second color state as a function of the continuous voltage delivered over several frames in the WCMY EPD system, and Figure 6B shows experimental results of providing the predicted waveform to the system.

[0034] [Figure 7] Figure 7A illustrates the predicted color transition from the first color state to the second color state as a function of the continuous voltage delivered over several frames in the WCMY EPD system, and Figure 7B shows experimental results of providing the predicted waveform to the system.

[0035] [Figure 8] Figure 8A illustrates the predicted color transition from the first color state to the second color state as a function of the continuous voltage delivered over several frames in the WCMY EPD system, and Figure 8B shows experimental results of providing the predicted waveform to the system. [Modes for carrying out the invention]

[0036] The present invention details a method for identifying enhanced continuous waveforms for driving a multi-particle color electrophoretic medium when it has at least four different electrophoretic particle sets (for example, at least three of the particle sets are colored and subtractively color-mixable and at least one of the particles is scattering / reflective, or at least three of the particle sets are colored and reflective and at least one of the particles is subtractively color-mixable). Typically, such a system includes reflective white particles and primary colored particles of subtractive mixing of cyan, yellow, and magenta, or red, yellow, and blue reflective particles and absorbent black particles. Naturally, alternative color options can be used, provided that suitable primary colors are selected. In addition, the method for developing continuous waveforms for driving such multi-particle systems is applicable to electrophoretic display systems containing more types of particles, such as 5-particle, 6-particle, 7-particle, and 8-particle systems.

[0037] Continuous voltage waveforms possess a unique characteristic: they exhibit tunable transitions in ways not found in conventional push-pull or rectangular pulse-based waveforms. This is particularly important for applications where controllers with many voltage levels (high bit depth) are available, and where the expression of transitions and the final color are paramount. Access to minute amounts of color within the model allows for the incorporation of complex and differentiable costs associated with color states.

[0038] Methods for manufacturing electrophoretic displays containing four (or more) particles have been discussed in the prior art. The electrophoretic fluid is encapsulated in microcapsules or incorporated into a microcell structure, which may then be sealed using a polymer layer. The microcapsules or microcell layers may be coated or laminated onto a plastic substrate or film supporting a transparent coating of conductive material. Alternatively, the microcapsules may be coated onto a light-transmitting substrate or other electrode material using a spraying technique (see U.S. Patent No. 9,835,925, incorporated herein by reference). The resulting assembly may be laminated onto a backplane supporting pixel electrodes using a conductive adhesive. The assembly may, alternatively, be mounted to one or more segmented electrodes on the backplane, which are directly driven. In another embodiment, an assembly that may include a non-planar light-transmitting electrode material is spray-coated together with the capsules and then overcoated with a back electrode material (see U.S. Patent Application No. 17 / 088,762). Alternatively, the electrophoretic fluid can be dispensed directly onto a thin open-cell grid positioned on a backplane, containing the active matrix of the pixel electrodes. The filled grid can then be top-sealed with an integrated protective sheet / light-transmitting electrode.

[0039] Electrophoretic displays typically comprise an electrophoretic material layer and at least two other layers positioned opposite the electrophoretic material, one of which is an electrode layer. In most such displays, both layers are electrode layers, and one or both of the electrode layers are patterned to define pixels on the display. For example, one electrode layer may be patterned into elongated row electrodes, and the other into elongated column electrodes extending perpendicular to the row electrodes, with pixels defined by the intersections of the row and column electrodes. Alternatively, and more commonly, one electrode layer may have the form of a single continuous electrode, and the other electrode layer may be patterned into a matrix of pixel electrodes, each of which defines one pixel on the display. In another type of electrophoretic display intended for use with a separate stylus, print head, or similar movable electrode, only one of the layers adjacent to the electrophoretic layer contains the electrode, while the layer opposite the electrophoretic layer is typically a protective layer intended to prevent the movable electrode from damaging the electrophoretic layer.

[0040] The electrophoretic media used herein include charged particles that vary in color, reflectance or absorption properties, charge density, and mobility in an electric field (measured as zeta potential). Particles that absorb, scatter, or reflect light in a broadband or selected wavelength are referred to herein as colored or pigmented particles. A variety of materials other than pigments (in the strict sense of the term meaning insoluble coloring materials), such as dyes or photonic crystals, that absorb or reflect light may also be used in the electrophoretic media and displays of the present invention. For example, the electrophoretic medium may include a fluid and a plurality of first particles and a plurality of second particles dispersed in the fluid, wherein the first particles and second particles are charged with opposite polarity, the first particles are light-scattering particles, and the second particles have one of the primary colors of subtractive mixing, and a plurality of third particles and a plurality of fourth particles dispersed in the fluid, wherein the third particles and fourth particles are charged with opposite polarity, and each of the third and fourth particles has a primary color of subtractive mixing that is different from that of the second particles, and the electric field required to separate aggregates formed by the third and fourth particles is greater than that required to separate aggregates formed by any two other types of particles.

[0041] The electrophoretic media of the present invention may include, for example, any of the additives used in conventional electrophoretic media, such as those described in the E Ink and MIT patents and applications described above. Thus, for example, the electrophoretic media of the present invention typically includes at least one charge control agent for controlling the charge on various particles, as described in U.S. Patent No. 7,170,670 above, the fluid having a polymer dissolved or dispersed therein, the polymer having a number-average molecular weight of more than about 20,000, and being essentially non-absorbent on particles to improve the bistability of the display.

[0042] In one embodiment, the present invention uses light-scattering particles, typically white particles, and three substantially non-light-scattering particles. Naturally, there are no such things as perfectly light-scattering particles or perfectly non-light-scattering particles, and the minimum light scattering degree of the light-scattering particles used in the electrophoresis of the present invention, and the maximum acceptable light scattering degree of the substantially non-light-scattering particles, can vary somewhat depending on factors (such as the pigments used, their colors, and the user's or application's ability to tolerate some deviation from the ideal desired color). The scattering and absorption properties of the pigments can be assessed by measuring the diffuse reflectance of a sample of the pigment dispersed in a suitable matrix or liquid against a white and dark background. The results from such measurements can be interpreted according to several models well known in the art, e.g., the one-dimensional Kuberkamung process. In the present invention, it is preferable that when the pigment is dispersed substantially isotropically at a volume ratio of 15% in a 1 μm thick layer comprising the pigment and a liquid with a refractive index of less than 1.55, the white pigment exhibits a diffuse reflectance of at least 5% at 550 nm, measured against a black background. Yellow, magenta, and cyan pigments preferably exhibit a diffuse reflectance of less than 2.5% at 650, 650, and 450 nm, respectively, measured against a black background under the same conditions (the wavelengths selected above for the measurement of yellow, magenta, and cyan pigments correspond to the spectral regions of the minimum absorbance of these pigments). Coloring pigments that meet these criteria will hereafter be referred to as “non-scattering” or “substantially non-light-scattering.” Specific examples of suitable particles are disclosed in U.S. Patent No. 9,921,451 (incorporated herein by reference).

[0043] Alternative particle sets may also be used, including four sets of reflective particles, or one absorbent particle accompanied by three or four sets of different reflective particles (i.e., those described in U.S. Patents 9,922,603 ​​and 10,032,419, which are incorporated herein by reference). For example, white particles may be formed from inorganic pigments such as TiO2, ZrO2, ZnO, Al2O3, Sb2O3, BaSO4, and PbSO4, and black particles may be formed from CI pigment black 26 or 28 (e.g., manganese ferrite black spinel or copper chromite black spinel), or carbon black. Third / fourth / fifth types of particles may be colors such as red, green, blue, magenta, cyan, or yellow. Pigments for this type of particle may include, but are not limited to, CI pigments PR254, PR122, PR149, PG36, PG58, PG7, PB28, PB15:3, PY138, PY150, PY155, or PY20. Specific examples include Clariant Hostaperm Red D3G 70-EDS, Hostaperm Pink E-EDS, PV fast red D3G, Hostaperm red D3G 70, Hostaperm Blue B2G-EDS, Hostaperm Yellow H4G-EDS, Hostaperm Green GNX, BASF Irgazine red L 3630, Cinquasia Red L 4100 HD, and Irgazine Red L 3660 HD, and Sun Chemical phthalocyanine blue, phthalocyanine green, diarylide yellow, or diarylide AAOT yellow.

[0044] As shown in Figures 1A and 1B, an electrophoretic display (101, 102) typically comprises an upper transparent electrode 110, an electrophoretic medium 120, and a bottom electrode 130, the bottom electrode 130 being a pixel electrode of an active matrix of pixels controlled by thin-film transistors (TFTs). However, for the displays of the present invention in particular, the bottom electrode 130 can be a larger, standalone electrode such as a graphite backplane, a PET / ITO film, a metallized film, or a conductive coating. In the electrophoretic medium 120 described herein, there are four different types of particles, 121, 122, 123, and 124, however, more particle combinations can be used in conjunction with the methods and displays described herein. The electrophoretic medium 120 is typically divided into compartments, such as by the walls of microcapsules 126 or microcells 127. An optional adhesive layer 140 can be positioned adjacent to any of the layers, however it is typically adjacent to an electrode layer (110 or 130). Two or more adhesive layers 140 may be present in a given electrophoretic display (105, 106), however only one layer is more common. The entire display stack is typically positioned on a substrate 150, which can be rigid or flexible. The displays (101, 102) also typically include a protective layer 160, which may simply protect the upper electrode 110 from damage or enclose the entire display (101, 102) to prevent the ingress of water, etc. The electrophoretic displays (101, 102) may also include a sealing layer 180, if necessary. In some embodiments, the adhesive layer 140 may contain a primer component to improve adhesion to the electrode layer 110, or a separate primer layer (not shown in Figure 1B) may be used.The structure of electrophoretic displays, as well as their components, pigments, adhesives, electrode materials, etc., are described in numerous patents and patent applications published by E Ink Corporation, including U.S. Patents No. 6,922,276, No. 7,002,728, No. 7,072,095, No. 7,116,318, No. 7,715,088, and No. 7,839,564 (all of which are incorporated herein by reference as a whole).

[0045] In some embodiments, for example, as shown in Figure 1A, the electrophoretic display may comprise only a first light-transmitting electrode, an electrophoretic medium, and a second (rear) electrode, the second electrode also being light-transmitting. However, to create a high-resolution display (e.g., to display an image), individual pixels are used to control color across the image. Naturally, each pixel must be addressable without interference from neighboring pixels so that the image file is faithfully reproduced on the display. One way to achieve this objective is to create an "active matrix" display by providing an array of nonlinear elements, such as transistors or diodes, with at least one nonlinear element associated with each pixel. The address or pixel electrode addressing a single pixel is connected to a suitable voltage source through the associated nonlinear element. Typically, when the nonlinear element is a transistor, the pixel electrode is connected to the drain of the transistor, and this arrangement will be assumed in the following description, but is essentially arbitrary, and the pixel electrode may also be connected to the source of the transistor. Conventionally, in high-resolution arrays, pixels are arranged in a two-dimensional array of rows and columns such that any particular pixel is uniquely defined by the intersection of one defined row and one defined column. The sources of all transistors in each column are connected to a single column electrode, while the gates of all transistors in each row are connected to a single row electrode (again, the assignment of sources to rows and gates to columns is conventional but essentially arbitrary and can be reversed as desired). The row electrodes are connected to a row driver, which essentially ensures that, at any given moment, a selection voltage is applied to the selected row electrode such that only one row is selected, i.e., all transistors in the selected row are conductive, while a deselection voltage is applied to all other rows such that all transistors in those unselected rows remain nonconductive.The column electrodes are connected to a column driver, which applies selected voltages to the various column electrodes to drive the pixels in the selected row to their desired optical states (the aforementioned voltages are conventionally provided on the opposite side of the nonlinear array of the electro-optic medium and are relative to a common front electrode that extends across the entire display). After a pre-selected interval known as the "line address time," the selected row is deselected, the next row is selected, and the voltage on the column driver is changed so that the next line of the display is written. The process is repeated so that the entire display is written in a line-by-line manner. The time between addresses in the display is known as a "frame." Thus, a display updated at 60 Hz has a frame of 16 milliseconds.

[0046] However, the term "frame" is not limited to its use with active matrix backplanes, and many of the drive waveforms described herein are described with reference to a frame as a unit of time. While it is possible to drive the electrophoretic medium using analog voltage signals, such as those produced by power sources and voltage dividers, the use of digital controllers discretizes the waveform into blocks, typically of about 10 ms (however, shorter or longer frame widths are also possible). For example, frames can be 0.5 ms or longer, such as 1 ms, 5 ms, 10 ms, 15 ms, 20 ms, 30 ms, or 50 ms. In most cases, frames are less than 100 ms, such as 250 ms, 200 ms, 150 ms, or 100 ms. In most applications described herein, frames have a width of 10 ms to 30 ms. Suitable controllers are available, for example, from Digi-Key and other electronic component suppliers.

[0047] In conventional electrophoretic displays using an active matrix backplane, each pixel electrode has an associated capacitor electrode (storage capacitor), thereby the pixel electrode and the capacitor electrode form a capacitor (see, for example, International Patent Application No. WO01 / 07961). In some embodiments, an N-type semiconductor (e.g., amorphous silicon) may be used to form a transistor, and the “selective” and “deselective” voltages applied to the gate electrode can be positive and negative, respectively.

[0048] Figure 2A of the accompanying drawings depicts an exemplary equivalent circuit of a single pixel in an electrophoretic display. As shown, the circuit includes a capacitor 10 formed between the pixel electrode and the capacitor electrode. The electrophoretic medium 20 is represented as a capacitor and resistor in parallel. In some cases, direct or indirect coupling capacitance 30 (commonly referred to as “parasitic capacitance”) between the gate electrode of the transistor associated with the pixel and the pixel electrode can introduce undesirable noise into the display. Typically, the parasitic capacitance 30 is much smaller than that of the storage capacitor 10, and when a pixel row of the display is selected or deselected, the parasitic capacitance 30 can introduce a small negative offset voltage to the pixel electrode, also known as a “kickback voltage,” which is typically less than 2 volts. [In some embodiments, to compensate for the undesirable “kickback voltage,” a common potential V com However, this can be supplied to the top plane electrode and capacitor electrode associated with each pixel, thereby V com The kickback voltage (V KBWhen set to a value equal to ), all voltages supplied to the display are offset by the same amount, and net DC unbalance may not be experienced. It has been found that the drive waveform for separating the pigments of a four-particle system into the appropriate configuration and producing these colors requires at least five voltage levels (high positive, low positive, zero, low negative, high negative). For further details, see U.S. Patent Application No. 17 / 088,762. However, as described below, when a continuous range of voltage levels (or approximate) is used to drive such a four-particle system, a much wider variety of colors and color transitions are achievable.

[0049] The equivalent circuit in Figure 2A represents a "typical" method for driving a four-particle electrophoresis system, particularly when used to display high-resolution images such as photographs and text. However, it is also possible to drive the electrophoresis medium using a simpler equivalent circuit, such as that shown in Figure 2B. This simpler circuit simply represents a voltage source coupled to a first electrode adjacent to the electrophoresis medium and a second electrode on the other side of the electrophoresis medium, which is grounded. If the voltage source is capable of providing any arbitrary voltage waveform, this simpler circuit can produce any possible display color and any possible transitions between display colors. Similar to Figure 2A, the electrophoresis medium 20 itself can be represented in parallel as a capacitor and resistor. Of course, the second electrode itself does not need to be grounded, but it can be set to an arbitrary voltage level. A suitable voltage capable of providing an arbitrary waveform can be obtained from Tektronix, however, in many cases, combining the power source with a digital controller is more cost-effective.

[0050] As shown in Figure 3A, in the case of a four-particle system including subtractive color-mixing cyan, yellow, and magenta particles paired with reflective white particles, each of the eight primary colors (red, green, blue, cyan, magenta, yellow, black, and white) corresponds to a different arrangement of the four pigments. For example, three particles providing three subtractive color primary colors for an advanced color electronic paper (ACeP) display may be substantially non-light scattering ("SNLS"). The use of SNLS particles allows for color mixing and provides more color results than can be achieved using the same number of scattering particles. These thresholds must be sufficiently separated relative to the voltage-driven level to avoid crosstalk between particles, and this separation necessitates the use of high address voltages for some colors. In addition, addressing a colored particle with the highest threshold also moves all other colored particles, which must then be switched to their desired positions at lower voltages.

[0051] As shown in Figure 3A, the system operates similarly to printing on bright white paper, in principle, that only the colored pigments on the viewing side of the white pigment (i.e., the only pigment that scatters light) are visible to the viewer. In Figure 3A, it is assumed that the viewing surface of the display is at the top (as shown), i.e., the user views the display from this direction, and light is incident from this direction. As already stated, in a preferred embodiment, only one of the four particles used in the electrophoretic medium of the present invention substantially scatters light, and in Figure 3A, it is assumed that the particle is the white pigment. This light-scattering white particle forms a white reflector, and any particle above the white particle is visible to it (as shown in Figure 3A). Light entering the viewing surface of the display passing through these particles is reflected from the white particle, passes back through these particles, and emerges from the display. Thus, particles above the white particle may absorb various colors, and the color that appears to the user is the result of the combination of particles above the white particle. Any particle positioned below (behind from the user's perspective) the white particle is masked by the white particle and does not affect the displayed color. The second, third, and fourth particles are substantially non-light-scattering, so their relative order or arrangement to each other is not important; however, for the reasons already stated, their order or arrangement relative to the white (light-scattering) particle is important.

[0052] More specifically, when cyan, magenta, and yellow particles are located below the white particle (situation [A] in Figure 3A), no particles are located above the white particle, and the pixel simply displays white. When a single particle is located above the white particle, the color of that single particle is displayed as yellow, magenta, and cyan in situations [B], [D], and [F] in Figure 3A, respectively. When two particles are located above the white particle, the displayed color is a combination of those two particles; in Figure 3A, in situation [C], the magenta and yellow particles display red; in situation [E], the cyan and magenta particles display blue; and in situation [G], the yellow and cyan particles display green. Finally, when all three colored particles are located above the white particle (situation [H] in Figure 3A), all incident light is absorbed by the three subtractive colored particles, and the pixel displays black.

[0053] An alternative particle set using reflective colored particles is shown in Figure 3B. In the embodiment of Figure 3B, the reflective particles are red, yellow, and blue; however, alternative color sets may be used, provided that the color combinations suitably extend to a useful color spectrum. In the system of Figure 3B, the cause of the color visible on the surface lies in the direct reflection of the colored particles, and an absorbent black layer is typically placed between the displaying particles and the particles that should not be displayed, in an attempt to keep the color as true as possible. Since the viewer is primarily seeing light interacting with only one pigment surface, the image produced using the system of Figure 3B appears more saturated. However, the overall color gamut using the system of Figure 3B is reduced because it is difficult to achieve precise control over the amount of specific particles mixed together to create secondary colors (e.g., orange, green, purple). In applications such as digital signage, saturation is often more important than color gamut, and many users are satisfied with the eight "standard" color sets.

[0054] Different combinations of light-scattering and light-absorbing particles are also possible. For example, a primary color of a subtractive mixture may be rendered by light-scattering particles, and thus the display may have two types of light-scattering particles, one of which is white and the other is colored. However, in this case, the position of the light-scattering colored particles relative to the other colored particles covering the white particles will be important. For example, in rendering black (when all three colored particles are present covering the white particles), the scattering colored particles cannot be present covering the non-scattering colored particles (otherwise, the non-scattering colored particles would be partially or completely hidden behind the scattering particles, and the color rendered would be that of the scattering colored particles, not black). Naturally, if two or more types of colored particles scatter light without the presence of light-absorbing black particles, rendering black will not be easy.

[0055] Figures 3A and 3B illustrate the ideal scenario where the colors are uncontaminated (i.e., in Figure 3A, light-scattering white particles completely mask any particles behind them, or in Figure 3B, light-absorbing black particles shield light-scattering particles that should not be visible). In practice, masking by white particles can be imperfect, and therefore there may be some slight absorption of light by particles that would ideally be completely masked. Such contamination typically reduces both the brightness and saturation of the rendered colors. In the case of Figure 3B, the presence of light-absorbing particles often causes the entire image to appear darker, due to imperfect scattering by reflective particles. In addition, because it is difficult to create pigments that are precisely equidistant on the color spectrum, the colors combined in Figure 3B, such as orange, green, and purple, may not achieve the desired colors. This is particularly problematic with respect to green, as the human eye is very sensitive to different shades of green, while different shades of red are not as easily noticed. In some embodiments, this can be corrected by including additional particles with different steric or charge properties, such as green scattering particles; however, adding additional particles may complicate the driving scheme and require a wider range of driving voltages. Obviously, in the electrophoretic media described herein, such color contamination should be minimized to the extent that the resulting color is suitable for industrial standards for color rendering. A particularly preferred standard is SNAP (Standard for Newspaper Advertising Production), which has L for each of the eight primary colors referenced above. * a * , and b * Defines the value.

[0056] Waveforms for driving four-particle electrophoretic media have been described previously, but they differ considerably from the waveforms of the present invention. A set of waveforms for driving a color electrophoretic display having four particles is described in U.S. Patent No. 9,921,451 (incorporated herein by reference). Most commercial electrophoretic displays use amorphous silicon-based thin-film transistors (TFTs) in the construction of the active matrix backplane (202 / 024) due to the wider availability of fabrication equipment and the cost of various starting materials. Amorphous silicon thin-film transistors become unstable when supplied with a gate voltage that would allow switching of voltages higher than about + / -15V. Therefore, improved performance is achieved by additionally changing the bias of the upper light-transmitting electrode to the bias on the backplane pixel electrode, a technique known as top-plane switching, as described in previous patents / applications for such systems. Therefore, if a voltage of +30V (relative to the backplane) is required, the top plane may be switched to -15V, while the appropriate backplane pixels are switched to +15V. A method of driving a four-particle electrophoresis system using top-plane switching is described in detail, for example, in U.S. Patent No. 9,921,451.

[0057] In a previous embodiment of advanced color electronic paper (ACeP), the waveform (voltage-time curve) applied to the pixel electrodes of the backplane of the display of the present invention is described and plotted, but the front electrode is assumed to be grounded (i.e., at zero potential). The electric field experienced by the electrophoretic medium is, of course, determined by the potential difference between the backplane and the front electrode and the distance separating them. The display is typically viewed through its front electrode, thereby controlling the color displayed by the pixels, and it is sometimes easier to understand the accompanying optical transitions when the potential of the front electrode relative to the backplane is considered, which can be done simply by inverting the waveform discussed below. Two exemplary waveforms of this type are shown in Figures 4A and 4B, which are equivalent to Figures 7A and 7B of U.S. Patent No. 9,921,451. In particular, these types of “push-pull” waveforms are not continuous in terms of the general mathematical definition of “continuous.” In other words, when the waveform changes from push to pull (see the dotted circle), the waveform does not satisfy equation 1.

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[0058] Theoretically, there is no reason why discontinuous drive waveforms must be used. In particular, when there is independent control of the voltage across the medium (see Figure 2A) and fewer constraints on the number of voltage levels and update lengths, there are virtually an unlimited number of different ways to transition from the first color to the second color. As a necessary consequence, it is possible to select the "appearance" of a particular transition (e.g., a very slow transition, a very sharp transition, or oscillation between colors or accumulation up to a particular color). As shown in Figure 5A, the full color space can be obtained using a four-particle system including reflective white particles and subtractive mixed particles of cyan, yellow, and magenta. For standardization purposes, the vertices of this color space, corresponding to Figure 3A, are labeled with commonly used RGB values, namely [255,0,0], [0,255,0], [0,0,255], [0,255,255], [255,0,255], [255,255,0], [255,255,255], and [0,0,0]. Therefore, any color transition from the first color to the second color can be visualized within this color space as a path from start to finish, as shown in Figure 5A.

[0059] The voltage response of the display is ultimately a function of the type of electrophoresis medium, the capacitance and resistance of the electrophoresis stack (see Figure 2A).

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[0060] Naturally, many solutions exist for equation (2), some of which are very expensive (due to system refresh or wear time), and some do not reflect the physical reality of the final display. The goal is to identify a waveform that achieves a target optical state with an acceptable number of flashes, duration, etc. This is a difficult optimization problem because the inversion process is not symmetric: for any V(t), there exists a unique optical state, but for any optical state, there exists a list of multiple / infinite input voltages. The inverse problem (i.e., from the desired optical state to the list of voltages (i.e., waveforms)) is described here in the context of a continuous voltage waveform.

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[0061] The cost function in equation (4) is expressed as a function of the input voltage list V(t) in an arbitrarily high-dimensional space, and the target color and model

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[0062] During the ceremony,

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[0063] Ultimately, the waveform needs to be analyzed into frames for digital storage and execution (e.g., by a voltage controller). Waveforms can be arbitrarily long, but are typically around 500ms to 5 seconds, e.g., 1 second. The frame size can be suitably adjusted depending on the desired time frame for the transition. For use on a controller, these voltages can be discretized to match the available bit depth, but practically, the method is suitable for applications where the provided bit depth is sufficient to eliminate large quantization artifacts (i.e., >8 bits). However, in most cases, a bit depth of 4 (16 voltage levels) is sufficient, but 32 or more voltage levels improve the correlation between the calculated color state and the actual final color state. The current passing through the device is

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[0064] A preferred method for constructing functions in color space is to use a differentiable model that is a surrogate representing the final display construct. A specific electrophoretic display construct can be represented by a transfer function. Its simplest form is as follows:

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[0065] (Examples) Examples of continuous voltage waveforms are shown in Figures 6A, 6B, 7A, 7B, 8A, and 8B. A microencapsulated electrophoretic medium containing reflective white particles and three subtractive color (C, M, Y) particles was placed on glass between a PET-ITO layer and a graphite backplane. The top and bottom electrodes were programmed via a computer using a special controller (LUCY) that produced at least 256 unique voltage levels between 0 and 50V. TMThe controller (E Ink Corporation) was coupled to the display. The display was mounted on a workbench of a spectrophotometric optical measurement device of the type described in the literature (see D. Hertel, “Application of the Optical Measurement Methodologies of IEC and ISO Standards to Reflective E-Paper Displays,” Society for Information Display, International Symposium Digest of Technical Papers, Volume 49, No. 1, pp. 161–164 (May 2018) (incorporated herein by reference)). A series of measurements were used to build a training model that was ultimately well-stocked to predict the display color for specific waveforms, as shown in Figures 6A, 7A, and 8A. The image-driven panels in Figures 6A, 6B, 7A, 8A, and 8B roughly show the color state observed in each frame (Figures 6B, 7B, and 8B) and the progression from the first state (frame 0) to the second state (frame 85) as a function of frame number. Since the total waveform was 2 seconds, each frame is roughly 20 μs. The actual waveform is represented as a dark line. In Figure 6B, the cyan, magenta, and yellow lines indicate the relative positions of their colored particle sets with respect to the viewing side of the display (see Figure 3A). In effect, the "voltage" values ​​for the cyan, magenta, and yellow lines represent the relative positions between the upper (viewing) electrode and the counter electrode below the electrophoretic medium. Larger positive voltages indicate proximity to the viewing surface, while larger negative voltages indicate the furthest distance from the viewing surface. The cyan, magenta, and yellow lines are not waveforms.

[0066] As shown in the measured traces, 6B, 7B, and 8B, when the predicted waveforms were executed on the actual display, the final state was (roughly) achieved in each case, and the overall transitions were quite close to the predicted values. Figure 6B illustrates a sharp optical transition, Figure 7B illustrates a smooth optical transition, and Figure 8B illustrates a transition oscillating with an irregular period. Thus, this new waveform structure performs at least as well as a standard push-pull drive and comes with the advantage of expressing different transitions that may be considered more preferable or desirable for specific applications.

[0067] While some aspects and embodiments of the present invention have been described above, it should be understood that various modifications, alterations, and improvements will be readily conceivable to those skilled in the art. Such modifications, alterations, and improvements are intended to be within the spirit and scope of the art described herein. For example, those skilled in the art will readily conceive of various other means and / or structures for performing the functions described herein and / or obtaining one or more of the results and / or benefits, and each of such modifications and / or alterations will be considered within the scope of the embodiments described herein. Those skilled in the art will be able to recognize or confirm many equivalents of the specific embodiments described herein by mere everyday experimentation. Therefore, it should be understood that the embodiments described herein are presented only as examples, and embodiments of the present invention may be practiced in ways different from those specifically described within the scope of the appended claims and their equivalents. In addition, any combination of two or more features, systems, articles, materials, kits, and / or methods described herein is also included within the scope of this disclosure, provided that such features, systems, articles, materials, kits, and / or methods are not inconsistent with each other.

Claims

1. A method for determining a continuous waveform for driving an electrophoretic medium disposed between a first light-transmitting electrode and a second electrode, wherein the electrophoretic medium comprises at least four types of particles, each type of particle having different optical properties, each type of particle having different combinations of charge polarity and charge magnitude, and the method is To determine the first optical state for the electrophoretic medium, To determine the second optical state for the electrophoretic medium, Based on a differentiable surrogate model of the electrophoretic medium between the first light-transmitting electrode and the second electrode, the repeating drive voltage with respect to the frame width is propagated in reverse over a desired time range from the second optical state to the first optical state, while minimizing the cost function, such that the transitions between frames do not involve voltage changes greater than ±40V. By assembling the aforementioned repeating drive voltages, a continuous waveform is created. Methods that include...

2. The method according to claim 1, wherein the continuous waveform between the first optical state and the second optical state does not have a change in the rate of change of voltage as a function of time less than -1 V / ms² or as a function of time greater than 1 V / ms².

3. The method according to claim 1, wherein the first optical state is the current color displayed by the electrophoretic medium.

4. The method according to claim 1, wherein the second optical state is a target color displayed by the electrophoretic medium.

5. The method according to claim 1, wherein the desired time range is at least 500 ms and the frame width is less than 50 ms.

6. The method according to claim 1, wherein the transition between repeated drive voltages during the period of each frame width is 50V or less.

7. The method according to claim 1, further comprising determining a transfer function of the electrophoretic medium to an optical state as a function of time based on the output of a differentiable surrogate model to each iterative drive voltage used to transition from the first optical state to the second optical state, wherein the differentiable surrogate model is a model of the electrophoretic medium between the first light-transmitting electrode and the second electrode.

8. The method according to claim 7, wherein the transfer function is based on the voltage applied to the electrophoretic medium as a function of time, given the initial state of the system.

9. The method according to claim 8, wherein the transfer function is further based on one or more of ambient temperature, relative humidity, and incident light spectrum.

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