Continuous waveform driving in multi-color electrophoretic displays

Abstract

To provide continuous waveform driving in multi-color electrophoretic displays.SOLUTION: The invention provides continuous waveforms for driving a four-particle electrophoretic medium including four different types of particles, such as a set of scattering particles and three sets of particles of subtractive color mixing. Methods for identifying a preferred waveform for a target color state or a target transition when using a continuous or quasi-continuous voltage driver / controller. In one embodiment, the waveform includes at least 32 unique voltage levels during 500 ms. In one embodiment, the at least four types of particles include two particles of a first polarity and two particles of a second polarity.SELECTED DRAWING: Figure 1A

Description

[Background technology]

[0001] (Related Applications) This application claims priority to U.S. Provisional Patent Application No. 63 / 147,465, filed February 9, 2021. All patents and publications disclosed herein are incorporated by reference in their entirety.

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

[0003] For many years, electrophoretic displays have included only two types of charged colored particles: black and white (for clarity, "color" as used herein includes black and white). The white particles are often light scattering and comprise, for example, titanium dioxide, while the black particles are absorbing across the visible spectrum and may comprise carbon black or light absorbing metal oxides such as copper chromite. In the simplest sense, a black-and-white electrophoretic display requires only a light-transmissive electrode at the viewing surface, a back electrode, and an electrophoretic medium that includes oppositely charged white and black particles. When a voltage of one polarity is applied, the white particles move to the viewing surface, and when a voltage of the opposite polarity is applied, the black particles move to the viewing surface. If the back electrode includes controllable regions (pixels) (split electrodes controlled by transistors, or an active matrix of pixel electrodes), a pattern can be made to appear electronically at the viewing surface. This pattern can be, for example, the text of a book.

[0004] More recently, a variety of color options are becoming commercially available for electrophoretic displays, including three-color displays (black, white, red; black, white, yellow) and four-color displays (black, white, red, yellow). Similar to the operation of black-and-white electrophoretic displays, electrophoretic displays with three or four reflective pigments operate similarly to simple black-and-white displays, since the desired color particles are driven against the viewing surface. Although the driving scheme is much more complicated than just black and white, ultimately, the optical function of the particles is the same. In addition, it is worth noting that such displays can only show a single color at a time (i.e., only the color of one set of particles being driven against the viewing surface).

[0005] Advanced Color Electronic Paper (ACeP TM) also contains four particles, but the cyan, yellow, and magenta particles are subtractive rather than reflective, thereby allowing thousands of colors to be produced at each pixel. The color process is functionally equivalent to the printing method long used in offset and inkjet printers. A given color is produced by using the correct ratios of cyan, yellow, and magenta colors on a bright white paper background. In the case of ACeP, the relative positions of the cyan, yellow, magenta, and white particles with respect to the viewing surface will determine the color at each pixel. This type of electrophoretic display allows thousands of colors at each pixel, but careful control of the position of each of the pigments (50-500 nanometers in size) within a working space about 10-20 microns thick is critical. Obviously, variations in the position of the pigments will result in the wrong color being displayed at a given pixel. Hence, precise voltage control is required for such systems. Further details of the system are available in the following U.S. patents: U.S. Pat. Nos. 9,361,836, 9,921,451, 10,276,109, 10,353,266, 10,467,984, and 10,593,272, all of which are incorporated by reference in their entirety.

[0006] For the most part, electrophoretic media such as those described above are designed to be driven with low voltage square waves, such as those produced by driver circuits from a thin film transistor backplane. Such driver circuits are very closely related to the drive circuitry and fabrication methods used to produce liquid crystal display panels such as those found in smartphones, laptop monitors, and televisions, and can therefore be mass produced inexpensively. Traditionally, even when the electrophoretic medium is directly driven by isolated electrodes (e.g., split electrodes), the drive pulse is delivered as a square wave with a certain amplitude and a certain time width. See, for example, U.S. Pat. No. 7,012,600 (incorporated by reference in its entirety). With this form of drive, the amount of time that the electrical impulse, i.e., the charged particles, are exposed to a field of a given magnitude, determines the final "state" seen at the viewing surface.

[0007] The term "gray state" is used herein in its conventional sense in the imaging arts to refer to a state intermediate between 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 whose extreme states are white and dark blue, such that an intermediate gray state would actually be light blue. In fact, as already described, the change in optical state may not be a change in color at all. The term "black and white" may hereinafter 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, such as the white state mentioned above, and the dark blue state.

[0008] The terms "bistable" and "bi-stable" are used herein in their conventional meaning in the art to refer to displays with display elements having first and second display states differing in at least one optical property, such that after any given element has been driven with an address pulse of finite duration to exhibit either its first or second display state, the state will persist after the address pulse has been terminated 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. It is shown in U.S. Pat. No. 7,170,670 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 for some other types of electro-optic displays. Displays of this type are appropriately referred to as "multistable" rather than "bistable," although 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, is used to refer to the integral of an applied voltage with respect to time during the period that the display is driven. The term "waveform", when used to refer to driving an electrophoretic display, is used to describe a series, or pattern of voltages, provided to an electrophoretic medium over a given period (seconds, frames, etc.) to produce a desired optical effect in the electrophoretic medium.

[0010] Particles that absorb, scatter, or reflect light, either broadband or at selected wavelengths, are referred to herein as colored or pigment particles. A variety of materials other than pigments (in the strict sense of the term as meaning insoluble colored materials) that absorb or reflect light, such as dyes or photonic crystals, 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 Massachusetts Institute of Technology (MIT) and E Ink Corporation describe various techniques used in encapsulating electrophoretic and other electro-optic media. Such encapsulated media comprises a number of small capsules, each of which itself comprises an internal phase containing electrophoretically mobile particles in a fluid medium and a capsule wall surrounding the internal phase. Typically, the capsules are themselves held within a polymeric binder to form a coherent layer that is positioned between two electrodes. Techniques described in these patents and applications include: (a) Electrophoretic particles, fluids, and fluid additives (see, e.g., U.S. Pat. Nos. 7,002,728 and 7,679,814) (b) Capsules, binders, and encapsulation processes (see, e.g., U.S. Pat. Nos. 6,922,276 and 7,411,719) (c) Microcell structures, wall materials, and methods of forming the microcells (see, e.g., U.S. Pat. Nos. 7,072,095 and 9,279,906). (d) Methods of filling and sealing microcells (see, e.g., U.S. Pat. Nos. 7,144,942 and 7,715,088) (e) Films and subassemblies containing electro-optical materials (see, e.g., U.S. Pat. Nos. 6,982,178 and 7,839,564) (f) Backplanes, adhesive layers, and other auxiliary layers and methods used in displays (see, e.g., U.S. Pat. Nos. 7,116,318 and 7,535,624) (g) Color formation and color control (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 , No. 8,964,282, No. 9,013,783, No. 9,116,412, No. 9,146,439, No. 9,164,207, No. 9,170,467, No. 9,170,468, No. 9,182,646, No. 9,195,111, No. 9,199,441, No. 9,268,191, No. 9,285,649, No. 9,293,511, No. 9,341,916, No. 9,360,733, No. 9,361,836, No. 9,383,623, and No. 9,423,666, 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, 2014 / 0362 213, No. 2015 / 0103394, No. 2015 / 0118390, No. 2015 / 0124345, No. 2015 / 0198858, No. 2015 / 0234250, No. 2015 / 0268531, No. 2015 / 0301246, No. 2016 / 0011484, No. 2016 / 0026062, No. 2016 / 0048054, No. 2016 / 0116816, No. 2016 / 0116818, and No. 2016 / 0140909). (h) methods of driving displays (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. 9,082,352, No. 9,171,508, No. 9,218,773, No. 9,224,338, No. 9,224,342, No. 9,224,344, No. 9,230,492, No. 9,251,736, No. 9,262,973, No. 9,269,311, No. 9,299,294, No. 9,373,289, No. 9,390,066, No. 9,390,661, and No. 9,412,314, and U.S. Patent Application Publication Nos. 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 4 / 0340734, No. 2015 / 0070744, No. 2015 / 0097877, No. 2015 / 0109283, No. 2015 / 0213749, No. 2015 / 0213765, No. 2015 / 0221257, No. 2015 / 0262255, No. 2015 / 0262551, No. 2016 / 0071465, No. 2016 / 0078820, No. 2016 / 0093253, No. 2016 / 0140910, and No. 2016 / 0180777). (i) Display applications (see, e.g., U.S. Pat. Nos. 7,312,784 and 8,009,348) (j) Non-electrophoretic displays, such as those described in U.S. Pat. No. 6,241,921, and U.S. Patent Application Publication Nos. 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 the separate microcapsules in an encapsulated electrophoretic medium may be replaced by a continuous phase, thus creating so-called "polymer-dispersed electrophoretic displays" in which the electrophoretic medium comprises a plurality of separate droplets of electrophoretic fluid and a continuous phase of polymeric material, and that the separate droplets of electrophoretic fluid in such polymer-dispersed electrophoretic displays may be considered capsules or microcapsules, even though no separate capsule membrane is associated with each individual droplet (see, e.g., U.S. Pat. No. 6,866,760). Thus, for purposes of this application, such polymer-dispersed electrophoretic media are considered a subspecies of encapsulated electrophoretic media.

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

[0014] Electrophoretic media are often opaque (e.g., in many electrophoretic media, the particles substantially block the transmission of visible light through the display) and operate in a reflective mode, but 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, U.S. Pat. Nos. 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 rely on variations in electric field strength and can operate in similar modes (see U.S. Pat. No. 4,418,346). Other types of electro-optic displays may also be capable of operating in a shutter mode. Electro-optic media operating in shutter mode can be used in multi-layer structures for full color displays, in which at least one layer adjacent the viewing surface of the display operates in shutter mode to expose or conceal a second layer that is further from the viewing surface.

[0015] Encapsulated electrophoretic displays typically do not suffer from the clustering and settling failure modes of conventional electrophoretic devices, and offer additional advantages such as the ability to print or coat the display on substrates of a wide variety of flexibility and stiffness (the use of the term "printing" is intended to include all forms of printing and coating, including, but not limited to, pre-metered coating, e.g., patch die coating, slot or extrusion coating, slide or cascade coating, curtain coating, etc., roll coating, e.g., 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 processes, electrostatic printing processes, thermal printing processes, inkjet printing processes, electrophoretic deposition (see U.S. Pat. No. 7,339,715), and other similar techniques). Thus, the resulting display can be flexible. Furthermore, because the display medium can be printed (using a variety of methods), the display itself can be inexpensively made. Additionally, as described in U.S. Patent Application Serial No. 17 / 088,762, encapsulated electrophoretic media can be incorporated into non-planar surfaces which are then incorporated into everyday products. As a result, surfaces of products, construction materials, and the like can be engineered to change color when a suitable electric field is applied. [Prior art documents] [Patent documents]

[0016] [Patent Document 1] U.S. Pat. No. 9,361,836 [Patent Document 2] U.S. Patent No. 7,012,600 Summary of the Invention [Means for solving the problem]

[0017] Disclosed herein is an improved method for driving an electrophoretic medium comprising four types of particles, each particle having different optical properties and each type of particle having a different combination of charge polarity and charge magnitude. One embodiment of such an electrophoretic medium is commercially known as Advanced Color Electronic Paper or ACEP®, however, other suitable electrophoretic media are described herein, and the described method is generally applicable to four-particle (or more) electrophoretic systems. In one aspect, the method includes providing a continuous driving waveform for at least 500 ms, the continuous driving waveform having at least 16 unique voltage levels during the 500 ms. The resulting waveform in the transition is less "flash"-like and less visibly annoying to the viewer. The resulting waveform also allows for controlled transitions, which can be, for example, abrupt, smooth, ramped, or pulsating / vibrating. In one embodiment, the waveform has a rate of change of less than 3 V / ms for at least 500 ms, while at the same time the rate of change (second derivative) is less than -1 V / ms 2 ~1V / ms 2 In one embodiment, the waveform includes at least 32 unique voltage levels over 500 ms. In one embodiment, the continuous drive waveform lasts for at least 1 second. 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, the 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, the color being selected from the group consisting of white, red, magenta, orange, yellow, green, cyan, blue, purple, and black. In one embodiment, the 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 of driving an electrophoretic medium comprising at least four types of particles, each particle having a different optical property from the others, and each type of particle having a different combination of charge polarity and charge magnitude from the others, the method includes providing a continuous drive waveform over at least 500 ms, the continuous drive waveform as a function of time being of the following form throughout the waveform:

number

[0019] In another aspect, a display system is disclosed that includes a first light-transmissive electrode, an electrophoretic medium comprising at least four types of particles, each particle having a different optical property from the others, each type of particle having a different combination of charge polarity and charge magnitude from the others, a second electrode, the electrophoretic medium being disposed between the first light-transmissive electrode and the second electrode, a controller, and a power supply operatively connected to the first light-transmissive electrode and the second electrode and configured to provide at least 16 unique voltage levels, the controller providing at least three of the unique voltage levels between the first light-transmissive 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 supply 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, the at least four types of particles include three particles of a first polarity and one particle of a second polarity, hi one embodiment, the optical property is color, the color being 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 disposed between a first light-transmissive electrode and a second electrode, the electrophoretic medium comprising at least four types of particles, each type of particle having a different optical property from the others, each type of particle having a different combination of charge polarity and charge magnitude from the others, the method including: determining a first optical state for the electrophoretic medium; determining a second optical state for the electrophoretic medium; propagating frame-wide repetitive driving voltages backwards 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-transmissive electrode and the second electrode; and assembling the frame-wide repetitive driving voltages to create the continuous waveform. In some embodiments, the cost function is:

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 disposed between a first light-transmissive electrode and a second electrode, the electrophoretic medium comprising at least four types of particles, each type of particle having a different optical property from the others, each type of particle having a different combination of charge polarity and charge magnitude from the others, the method including: determining a first optical state for the electrophoretic medium; determining a second optical state for the electrophoretic medium; propagating a repeating drive voltage for a frame width in a reverse direction over a desired time range from the second optical state to the first optical state, the transition between frames not involving a voltage change of more than ±40V; and assembling the repeating drive voltage to create a continuous waveform. In one embodiment, the continuous waveform between the first optical state and the second optical state has a voltage change of less than -1V / ms.2 Less than or equal to 1V / ms 2 does not have a change in the rate of change of voltage as a function of time greater than The present invention provides, for example, the following: (Item 1) 1. A method of driving an electrophoretic medium comprising at least four types of particles, each type of particle having a different optical property, each type of particle having a different combination of charge polarity and charge magnitude, the method comprising: providing a continuous drive waveform for at least 500 ms; The continuous drive waveform has at least 16 unique voltage levels during the 500 ms period, the continuous drive waveform having a measurable rate of change in V / ms, and the time dependent change in the rate of change is less than -1 V / ms 2 ~1V / ms 2 That is, the method. (Item 2) 2. The method of claim 1, wherein the waveform comprises at least 32 unique voltage levels during the 500 ms. (Item 3) 2. The method of claim 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) 2. The method of claim 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) 2. The method of claim 1, wherein the optical property is color, and the color is selected from the group consisting of white, red, magenta, orange, yellow, green, cyan, blue, purple, and black. (Item 6) 2. The method of claim 1, wherein at least two types of particles comprise a surface polymer, and each of the two types of particles has a different type of surface polymer. (Item 7) 1. A method of driving an electrophoretic medium comprising at least four types of particles, each type of particle having a different optical property, each type of particle having a different combination of charge polarity and charge magnitude, the method comprising: providing a continuous drive waveform for at least 500 ms; The continuous drive waveform as a function of time has the following form throughout the waveform:

number

number

[0023] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[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] FIG. 1B is a representative cross-section of a four-particle electrophoretic display in which the electrophoretic medium is encapsulated within microcells.

[0026] [Figure 2A] FIG. 2A illustrates an exemplary equivalent circuit of a single pixel of an electrophoretic display using an active matrix backplane with a reservoir capacitor.

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

[0028] [Figure 3A] FIG. 3A illustrates the preferred positions of each of the four sets of particles to produce 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 absorbing.

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

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

[0031] [Figure 5A]FIG. 5A illustrates a color space that may be defined for a four-particle electrophoretic system and how the transition from a first color to a second color may proceed along two or more paths.

[0032] [Figure 5B] FIG. 5B illustrates how waveforms can be iteratively propagated back from a second optical state to a first optical state and then assembled to create a desired waveform.

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

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

[0035] [Figure 8] FIG. 8A illustrates a predicted color transition from a first color state to a second color state as a function of continuous voltage delivered over several frames in a WCMY EPD system, and FIG. 8B shows experimental results of providing the predicted waveforms to the system. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0036] The present invention details a method for identifying enhanced continuous waveforms for driving multi-particle color electrophoretic media when the medium has at least four different electrophoretic particle sets (e.g., at least three of the particle sets are colored and subtractive, 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 subtractive). Typically, such systems include reflective white particles and subtractive primary color particles of cyan, yellow, and magenta, or red, yellow, and blue reflective particles and absorbing black particles. Of course, 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 that include more types of particles, such as 5-particle, 6-particle, 7-particle, and 8-particle systems.

[0037] Continuous voltage waveforms have the unique property of having adjustable transition appearances in a way that traditional push-pull or rectangular pulse based waveforms do not. This is especially important for applications where controllers with many voltage levels (high bit depth) are available and the appearance of the transitions and final color are paramount. Access to minute amounts of color in the model allows the incorporation of complex and differentiable costs associated with color states.

[0038] Methods for producing 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 can then be sealed with a polymer layer. The microcapsules or microcell layer can be coated or laminated onto a plastic substrate or film carrying a transparent coating of conductive material. Alternatively, the microcapsules can be coated onto a light-transmitting substrate or other electrode material using spraying techniques (see U.S. Patent No. 9,835,925, incorporated herein by reference). The resulting assembly can be laminated to a backplane carrying pixel electrodes using a conductive adhesive. The assembly can alternatively be attached to one or more split electrodes on the backplane, which are directly driven. In another embodiment, the assembly, which may include a non-planar light-transmitting electrode material, is spray-coated 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 that is disposed on a backplane containing the active matrix of pixel electrodes. The filled grid can then be top-sealed with an integrated protective sheet / light-transparent electrode.

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

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

[0041] The electrophoretic medium of the present invention may contain any of the additives used in prior art electrophoretic media, for example, as described in the E Ink and MIT patents and applications mentioned above.Thus, for example, the electrophoretic medium of the present invention typically contains at least one charge control agent for controlling the charge on the various particles, as described in the aforementioned U.S. Patent No. 7,170,670, the fluid has a polymer dissolved or dispersed therein, the polymer having a number average molecular weight of greater than about 20,000, and being essentially non-light absorbing on the 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. Of course, there is no such thing as a completely light scattering particle or a completely non-light scattering particle, and the minimum light scattering degree of the light scattering particles used in the electrophoresis of the present invention, and the maximum light scattering degree acceptable for the substantially non-light scattering particles, may vary somewhat depending on factors such as the exact pigments used, their color, and the ability of the user or application 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, such as the one-dimensional Kubelka-Munk process. In the present invention, it is preferred that the white pigment exhibits at least 5% diffuse reflectance at 550 nm measured against a black background when the pigment is dispersed substantially isotropically at 15% by volume in a 1 μm thick layer comprising the pigment and a liquid with a refractive index less than 1.55. The yellow, magenta, and cyan pigments preferably exhibit a diffuse reflectance of less than 2.5% at 650, 650, and 450 nm, respectively, measured on a black background under the same conditions (the wavelengths selected above for measuring the yellow, magenta, and cyan pigments correspond to the spectral regions of minimum light absorption by these pigments). Colored pigments that meet these criteria are hereinafter referred to as "non-scattering" or "substantially non-light-scattering". Specific examples of suitable particles are disclosed in U.S. Pat. No. 9,921,451, which is incorporated herein by reference.

[0043] Alternative particle sets including four sets of reflective particles, or one absorbing particle with three or four sets of different reflective particles (i.e., such as those described in U.S. Pat. Nos. 9,922,603 ​​and 10,032,419, which are incorporated herein by reference) may also be used. For example, the white particles may be TiO 2 , ZrO 2 , ZnO, Al 2 O 3 , Sb2 O 3 , BaSO 4 , PbSO 4 The third / fourth / fifth type particles may be formed from inorganic pigments such as CI pigment black 26 or 28 (e.g., manganese ferrite black spinel or copper chromite black spinel), or carbon black. The third / fourth / fifth type particles may be red, green, blue, magenta, cyan, or yellow, or other colors. 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 are Clariant Hostaperm Red D3G 70-EDS, Hostaperm Examples of pigments that may be used include: 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 Irgazin 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 includes a top transparent electrode 110, an electrophoretic medium 120, and a bottom electrode 130, which is often a pixel electrode of an active matrix of pixels controlled using thin film transistors (TFTs). However, for displays of the present invention in particular, the bottom electrode 130 can be a single larger electrode such as a graphite backplane, a film of PET / ITO, a metallized film, or a conductive paint. In the electrophoretic medium 120 described herein, there are four different types of particles, 121, 122, 123, and 124, however, many more particle sets can be used with the methods and displays described herein. The electrophoretic medium 120 is typically divided into compartments, such as by walls of microcapsules 126 or microcells 127. An optional adhesive layer 140 can be disposed adjacent to any of the layers, however, it is typically adjacent to the electrode layer (110 or 130). There can be more than one adhesive layer 140 in a given electrophoretic display (105, 106), however, only one layer is more common. The entire display stack is typically disposed 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 top electrode 110 from damage or may encapsulate the entire display (101, 102) and prevent ingress of water and the like. The electrophoretic displays (101, 102) may also include a sealing layer 180, if desired. In some embodiments, the adhesive layer 140 may include a primer component to improve adhesion with the electrode layer 110, or a separate primer layer (not shown in FIG. 1B) may be used.The structure of electrophoretic displays, as well as their component parts, pigments, adhesives, electrode materials, and the like, are described in many patents and patent applications published by E Ink Corporation, such as U.S. Pat. Nos. 6,922,276, 7,002,728, 7,072,095, 7,116,318, 7,715,088, and 7,839,564, all of which are incorporated herein by reference in their entireties.

[0045] In some embodiments, for example as shown in FIG. 1A, an electrophoretic display may include only a first light-transmissive electrode, an electrophoretic medium, and a second (rear) electrode, and the second electrode may also be light-transmissive. However, to create a high-resolution display (e.g., to display an image), individual pixels are used to control the color across the image. Of course, 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 goal is to provide an array of nonlinear elements, such as transistors or diodes, with at least one nonlinear element associated with each pixel, creating an "active matrix" display. The address or pixel electrode that addresses a pixel is connected to an appropriate 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 although this arrangement will be assumed in the following description, it 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, while conventional, is essentially arbitrary and can be reversed as desired). The row electrodes are connected to row drivers, which essentially ensure that at any given moment, only one row is selected, i.e., a select voltage is applied to the selected row electrode to ensure that all transistors in the selected row are conductive, while a non-select voltage is applied to all other rows to ensure that all transistors in these non-selected rows remain non-conductive.The column electrodes are connected to column drivers, which apply selected voltages to the various column electrodes so as to drive the pixels in a selected row to their desired optical state (the aforementioned voltages are relative to a common front electrode which is conventionally provided opposite the nonlinear array of electro-optic medium and extends across the entire display). After a preselected interval known as the "line address time", the selected row is deselected, the next row is selected and the voltages on the column drivers are changed so that the next line of the display is written. The process is repeated so that the entire display is written in a row-by-row fashion. The time between addresses in a display is known as a "frame". Thus a display updated at 60 Hz has a frame which is 16 milliseconds.

[0046] However, frames are not limited to use with active matrix backplanes, and many of the drive waveforms described herein are described with reference to frames as a unit of time. Although it is possible to drive the electrophoretic medium with analog voltage signals, such as those produced by a power supply and a voltage divider, the use of digital controllers discretizes the waveform into blocks that are typically about 10 ms (although shorter or longer frame widths are possible). For example, a frame may 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, a frame is less than 100 ms, such as 250 ms, 200 ms, 150 ms, or 100 ms. In most applications described herein, a frame is 10 ms to 30 ms wide. Suitable controllers are available, for example, from Digi-Key and other suppliers of electronic components.

[0047] In conventional electrophoretic displays that use an active matrix backplane, each pixel electrode has a capacitor electrode (a reservoir capacitor) associated with it, whereby the pixel electrode and the capacitor electrode form a capacitor (see, for example, International Patent Application No. WO 01 / 07961). In some embodiments, N-type semiconductors (e.g., amorphous silicon) may be used to form the transistors, and the "select" and "deselect" voltages applied to the gate electrodes can be positive and negative, respectively.

[0048] FIG. 2A of the accompanying drawings depicts an exemplary equivalent circuit of a single pixel of an electrophoretic display. As shown, the circuit includes a capacitor 10 formed between a pixel electrode and a capacitor electrode. An electrophoretic medium 20 is represented as a parallel capacitor and resistor. In some cases, a direct or indirect coupling capacitance 30 between the gate electrode of a transistor associated with the pixel and the pixel electrode (commonly referred to as "parasitic capacitance") may 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 may introduce a slight negative offset voltage, also known as a "kickback voltage", to the pixel electrode, which is typically less than 2 volts. [In some embodiments, to compensate for the undesirable "kickback voltage", a common potential V com may be supplied to the top plane and capacitor electrodes associated with each pixel, thereby providing V com is the kickback voltage (V KB), all voltages supplied to the display are offset by the same amount and no net DC imbalance may be experienced.] It has been found that the drive waveforms to separate the pigments of a four-particle system into the appropriate configurations to create these colors require at least five voltage levels (high positive, low positive, zero, low negative, high negative). For further details, see U.S. Patent Application Serial No. 17 / 088,762. However, as explained below, when a continuous range of voltage levels (or a close approximation) is used to drive such a four-particle system, a much wider variety of colors and color transitions are achievable.

[0049] The equivalent circuit of FIG. 2A represents a "typical" way to drive a four-particle electrophoretic system, especially when used to display high resolution images such as photographs and text. However, it is also possible to drive the electrophoretic medium using a simpler equivalent circuit, such as that shown in FIG. 2B. This simple circuit simply represents a voltage source coupled to a first electrode adjacent to the electrophoretic medium and a second electrode on the other side of the electrophoretic medium, which is grounded. If the voltage source is capable of providing any arbitrary voltage waveform, this simple circuit can create any possible display color, and any possible transition between display colors. As in FIG. 2A, the electrophoretic medium 20 can itself be represented as a capacitor and resistor in parallel. Of course, the second electrode does not itself have 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, it is often more cost-effective to combine a power supply with a digital controller.

[0050] In the case of a four-particle system, including subtractive cyan, yellow, and magenta particles paired with reflective white particles, as shown in FIG. 3A, 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, the three particles providing the three subtractive primary colors for an advanced color electronic paper (ACeP) display can be substantially non-light scattering ("SNLS"). The use of SNLS particles allows for color mixing and provides more color results than can be achieved with the same number of scattering particles. These thresholds must be well separated relative to the voltage drive levels to avoid crosstalk between particles, which necessitates the use of high address voltages for some colors. In addition, addressing the colored particle with the highest threshold also displaces all other colored particles, which must then be switched to their desired positions at a lower voltage.

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

[0052] More specifically, when cyan, magenta, and yellow particles are present below the white particle (situation [A] in FIG. 3A), there are no particles above the white particle, and the pixel simply displays white. When a single particle is above the white particle, the color of the single particle is displayed as yellow, magenta, and cyan in situations [B], [D], and [F] in FIG. 3A, respectively. When two particles are above the white particle, the displayed color is a combination of those two particles, and in situation [C] in FIG. 3A, 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 above the white particle (situation [H] in FIG. 3A), all the incident light is absorbed by the three subtractive primary colored particles, and the pixel displays black.

[0053] An alternative particle set using reflective color particles is shown in FIG. 3B. In the embodiment of FIG. 3B, the reflective particles are red, yellow, and blue, however, alternative color sets can be used, provided that the color combinations suitably span the useful color spectrum. In the system of FIG. 3B, the color seen at the surface is due to direct reflection of the colored particles, and a light-absorbing black layer is typically placed between the display particles and those that should not be displayed in an attempt to keep the color as true as possible. Images produced using the system of FIG. 3B appear more saturated, since the viewer primarily sees light interacting only with one pigment surface. However, the overall color gamut using the system of FIG. 3B is reduced because it is difficult to achieve fine 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 a set of eight "standard" colors.

[0054] Different combinations of sets of light-scattering and light-absorbing particles are also possible. For example, one subtractive primary color may be rendered by light-scattering particles, and thus the display comprises 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 over the white particles), the scattering colored particles cannot be present over the non-scattering colored particles (otherwise the non-scattering colored particles will be partially or completely hidden behind the scattering particles and the color rendered will be that of the scattering colored particles, not black). Of course, if two or more types of colored particles scatter light without the presence of light-absorbing black particles, it will not be easy to render black.

[0055] 3A and 3B show an ideal situation where there is no color contamination (i.e., in FIG. 3A, the light-scattering white particles completely mask any particles present behind the white particles, or in FIG. 3B, the light-absorbing black particles shield the light-scattering particles that should not be visible). In practice, the masking by the white particles may be imperfect, and thus 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 color being rendered. In the case of FIG. 3B, the presence of the light-absorbing particles often causes the entire image to appear darker due to the incomplete scattering of the reflective particles. In addition, since it is difficult to make pigments that are strictly equidistantly spaced on the color spectrum, the colors combined in FIG. 3B, such as orange, green, and purple, may not achieve the desired color. This is particularly problematic for the color green, since the human eye is very sensitive to different shades of green, whereas different shades of red are not so easily noticed. In some embodiments, it may be compensated for by including additional particles with different spatial or charge properties, e.g., green scattering particles; however, adding additional particles may complicate the drive scheme and require a wider range of drive voltages. Clearly, in the electrophoretic media described herein, such color contamination should be minimized to the point that the colors formed meet industry standards for color rendering. A particularly preferred standard is SNAP (Standard for Newspaper Advertising Production), which specifies L for each of the eight primary colors referenced above. * , a * , and b * Specify the value.

[0056] Waveforms for driving four-particle electrophoretic media have been described previously, but they are significantly different from the waveforms of the present invention. A set of waveforms for driving a color electrophoretic display with four particles is described in U.S. Pat. No. 9,921,451, which is incorporated herein by reference. Most commercial electrophoretic displays use amorphous silicon-based thin film transistors (TFTs) in the construction of active matrix backplanes (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 gate voltages that would allow switching voltages higher than about + / -15V. Therefore, improved performance is achieved by additionally altering the bias of the top light-transmitting electrode relative to the bias on the backplane pixel electrodes, a technique known as top-plane switching, as described in previous patents / applications for such systems. Thus, if a voltage of +30 V (relative to the backplane) is required, the top plane can be switched to −15 V while the appropriate backplane pixels are switched to +15 V. Methods of using top-plane switching to drive four-particle electrophoretic systems are described in more detail in, for example, U.S. Patent No. 9,921,451.

[0057] In the previous embodiment of Advanced Color Electronic Paper (ACeP), waveforms (voltage vs. time curves) applied to the pixel electrodes of the backplane of the display of the present invention are described and plotted, with the front electrode 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. A display is typically viewed through its front electrode, whereby particles adjacent to the front electrode control the color displayed by a pixel, and it is sometimes easier to understand the optical transitions involved when the potential of the front electrode relative to the backplane is taken into account, which can be done simply by inverting the waveforms 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. Pat. No. 9,921,451. Notably, these types of "push-pull" waveforms are not continuous in terms of the common mathematical definition of "continuous." That is, when the waveform switches from push to pull (see dotted circle), the waveform does not satisfy Equation 1.

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[0058] Theoretically, there is no reason why a discontinuous drive waveform must be used. In particular, when there is independent control of the voltage across the medium (see FIG. 2A) and there are fewer constraints on the number of voltage levels and the length of the update, there is a virtually unlimited number of different ways to transition from a first color to a second color. As a corollary, it is possible to choose a particular transition "look" (e.g., a very slow transition, a very sharp transition, or an oscillation between colors or a build-up to a particular color). As shown in FIG. 5A, a full color space can be obtained using a four-particle system that includes reflective white particles and subtractive cyan, yellow, and magenta particles. For standardization, the vertices of this color space corresponding to Figure 3A are labeled with the typically used RGB values, i.e., [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]. Hence, any color transition from a first color to a second color can be visualized in this color space as a path from start to finish, i.e., as shown in Figure 5A.

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

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

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

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[0062] During the ceremony,

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[0063] Finally, the waveform needs to be parsed into frames for digital storage and execution (e.g., by a voltage controller). The waveforms can be arbitrarily long, but are typically about 500 ms to 5 seconds, e.g., 1 second. Depending on the desired time frame for the transition, the size of the frames can be suitably adjusted. For use on the controller, these voltages can be discretized to match the available bit depth, but in practice the method is geared towards applications where the bit depth provided 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 through the device is

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

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[0065] (Example) 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 the glass between a PET-ITO layer and a graphite backplane. The top and bottom electrodes were connected to a special controller (LUCY) that could be programmed via computer to create at least 256 unique voltage levels from 0 to 50V. TM The display was coupled to a 32-bit display controller (E Ink Corporation). The display was mounted on the platform of a spectrophotometric optical measurement device of the type described in the literature (D. Hertel, "Applications of the Optical Measurement See “Methodologies of IEC and ISO Standards to Reflective E-Paper Displays,” Society for Information Display, International Symposium Digest of Technical Papers, Volume 49, Issue 1, pp. 161-164 (May 2018) (incorporated herein by reference). A series of measurements was used to build a training model that was ultimately sufficient to predict the display color for a specific waveform, as shown in Figures 6A, 7A, and 8A. The image driving panels of Figures 6A, 6B, 7A, 8A, and 8B roughly show the color state observed in each frame (Figures 6B, 7B, 8B) as a function of frame number, and the progression from a first state (frame 0) to a second state (frame 85). Each frame is roughly 20 μs long, since the total waveform was 2 seconds. 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 top (viewing) electrode and the counter electrode below the electrophoretic medium. Large positive voltages are closer to the viewing surface, while large negative voltages are furthest away from the viewing surface. The cyan, magenta, and yellow lines are not wavy.

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

[0067] Although several aspects and embodiments of the technology of the present application have been described above, it should be understood that various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be within the spirit and scope of the technology described herein. For example, one skilled in the art will readily envision various other means and / or structures for performing the functions and / or obtaining one or more of the results and / or advantages described herein, and each of such variations and / or modifications is deemed to be within the scope of the embodiments described herein. One skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments described herein. Thus, the foregoing embodiments are presented by way of example only, and it should be understood that within the scope of the appended claims and their equivalents, the embodiments of the present invention may be practiced otherwise than as specifically described. 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 the present disclosure, if such features, systems, articles, materials, kits, and / or methods are not mutually inconsistent.

Claims

[Claim 1] The invention described in this specification.

Images