A substrate comprising electrodes and an optical modulator with reduced diffraction.

Abstract

To provide a substrate for use in a light modulator.SOLUTION: A substrate may comprise at least one driving electrode applied thereto. The driving electrode is arranged in a pattern across the substrate. The pattern of multiple driving electrodes across the substrate comprises multiple repeated building blocks. Electrodes in the building blocks form the at least one driving electrode.SELECTED DRAWING: Figure 12c

Description

Technical Field

[0001] The subject of the present disclosure relates to an optical modulator, a substrate, an optical modulation method, and a computer-readable medium.

Background Art

[0002] Optically active glazing is known in the art. Typically, an optically active glazing system comprises two parallel plates made of a transparent dielectric material such as glass or plastic material. The internal volume defined between the plates may be subdivided into a plurality of small separate volumes or individual cells filled with a dielectric fluid. The fluid comprises a suspension of particles of dielectric, charged or chargeable material. Opposite faces of the two plates carry electrodes facing each other. The electrodes are connected to a power supply associated with a control means.

[0003] The electrodes of each plate are formed by combs interdigitated with each other in pairs. The two interdigitated comb electrodes can be supplied with voltages of the same or opposite polarity. With an appropriate voltage on the electrodes, the particles can concentrate at different locations between the electrodes, giving the system either a transparent appearance or an opaque appearance.

[0004] There are various drawbacks associated with known systems. When the known glazing is in its transparent configuration, the electrodes applied to the plates cause diffraction effects. Diffraction effects are undesirable for glazing. In some situations, the presence of diffraction effects may also be harmful to safety. For example, when optically active glazing is applied in a vehicle such as an automobile, the presence of diffraction may be confusing or distracting for the operator of the vehicle.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

[0006] [Non-licensed Document 1] Leutenegger,M.,Rao,R.,Leitgeb,RAおよびLasser,T. Fast focus field calculations.Opt.Express 14,11277-11291(2006) [Non-licensed Document 2] Hu, Y. et al. Efficient full-path optical calculation of scalar and vector diffraction using the Bluestein method. Light Sci.Appl.9,1-11(2020) [Non-licensed Document 3] Murray, Ian B., Densmore, V., Bora, V., Pieratt, WM, Hibbard, DL, and Milster TD Numerical comparison of grid pattern diffraction effects through measurement and modeling with OptiScan software. Proc.SPIE 8016, Window and Dome Technologies and Materials XII,80160U (2011) [Non-Patent Document 4] Yonghe, L. et al. (2013). “A Simple Sweep-line Delaunay Triangulation Algorithm” In: Journal of Algorithms and Optimization (JAO) 1.1, pp.30-38 [Non-Patent Document 5] Alan Mathison Turing “The chemical basis of morphogenesis” [Overview of the project] [Problems that the invention aims to solve]

[0007] It would be advantageous to provide an improved substrate equipped with electrodes and an optical modulator equipped with such an improved substrate to address these and other problems. The inventors have found that electrode designs in known systems result in diffraction. Addressing this concern provides a substrate that can be applied with less diffraction. [Means for solving the problem]

[0008] A substrate for use in an optical modulator may have multiple interdigitated drive electrodes applied to the substrate, each of which is arranged in a pattern across the substrate, and the multiple interdigitated drive electrodes are arranged alternately on the substrate. The drive electrodes are electrically isolated from each other so that the voltage on the drive electrodes can be controlled independently.

[0009] When such substrates are used in an optical modulator, the fluctuating voltage applied to the electrodes may cause electrophoretic motion of particles within the optical layer between two such substrates. This motion, in turn, causes modulation of the light shining through the substrates. Typically, at least two such substrates, each having at least two driving electrodes, are used, but additional substrates and / or driving electrodes may be used. The optical modulator is preferably electrophoretic, but can be dielectrophoretic. The substrates according to embodiments may also be used in other technologies, e.g., OLEDs or electrowetting. The substrates according to embodiments may be combined with another substrate according to embodiments, but this is not required; one or both of the substrates may be transparent. In glazing applications, typically both substrates are transparent.

[0010] Optically active glazing, particularly so-called smart glazing, is an important application of optical modulators, for example, in embodiments of substrates on which multiple inter-mating electrodes are applied. Typically, all substrates within an optical modulator are transparent; this is especially true in glazing applications. In embodiments, one or more substrates may be translucent. In embodiments, one substrate may be opaque, while the opposing substrate is transparent or translucent. Such an optical modulator will alter the appearance of incident light. The substrates may be reflective.

[0011] A significant issue for applications such as glazing is diffraction. Preferably, diffraction is reduced to a small number. Diffraction can be calculated using a number called the pixelated noise metric, which is the ratio of the maximum intensity of all non-zeroth-order peaks to the maximum intensity of the zeroth-order peak from the magnitude spectrum. See, for example, the paper Murray, Ian B., Densmore, V., Bora, V., Pieratt, WM, Hibbard, DL, and Milster TD, “Numerical comparison of grid pattern diffraction effects through measurement and modeling with OptiScan software.” Proc. SPIE 8016, Window and Dome Technologies and Materials XII, 80160U (2011), included herein by reference. It has been found that further reduction of pixelated diffraction values ​​is difficult using conventional electrode line patterning. However, we have found a way to overcome this obstacle and create a design that breaks existing barriers. In the embodiment, the calculated pixelation noise metric of the substrate drive electrode pattern is less than 6.05%, less than 5%, or less than 4%. In particular, the pixelation noise metric of the building block may be below these thresholds.

[0012] In an embodiment, the pattern of drive electrodes is formed by a plurality of repeating building blocks. The building blocks comprise interdigitated electrodes. By repeating the building blocks adjacent to each other, the electrodes on the building blocks are formed into the drive electrodes. For example, the building blocks may be merged into a pattern using a mask layouting tool before the entire pattern is deposited on the substrate. The building blocks may partially overlap. For example, if an electrode line of a first building block coincides with an electrode line of a neighboring building block, and these both belong to the same drive electrode, these electrode lines of the two building blocks may be merged. In an embodiment, the building blocks are surrounded by drive buses, and the drive buses are advantageously merged with buses for the same drive electrode of a neighboring building block.

[0013] In an embodiment, a drive bus is arranged at an edge of the substrate for each drive electrode to drive the drive electrode. The drive bus may also connect otherwise insulated electrodes to the drive electrode. The drive bus may then be connected to a controller.

[0014] The drive bus may be arranged only at the edge of the substrate, but may for example also extend across the substrate between building blocks or as part of building blocks. For example, a plurality of straight drive buses may extend across the building blocks, and arms may extend from the drive buses to further connect electrodes to the drive electrode. Preferably, two drive buses are prevented from extending across the substrate adjacent to each other. This is because this would form a narrow furrow which may adversely affect diffraction. When two drive electrodes are used, the drive buses are advantageously alternated between building blocks.

[0015] In an embodiment, the building block may comprise a plurality of interdigitated electrodes extending in at least two directions across the building block. The inventors have found that using electrodes of relatively long length relative to the size of the building block is advantageous for reducing diffraction. For example, for at least one electrode among the plurality of interdigitated electrodes in the building block, the maximum length between any two points on the electrode, measured along said electrode in the building block, is at least twice the diagonal length of the building block unit.

[0016] In an embodiment, the building block may comprise a plurality of branch nodes where electrodes branch. For example, at least three electrode lines may be connected to a branch node. Introducing clusters of branch nodes increases the local variability of electrodes and increases the electrode length compared to the building block diagonal. For example, a cluster of branch nodes may comprise at least a first branch node, and the first node is directly connected to a second branch node and a third branch node through electrode lines. In an embodiment, the cluster may be larger, for example, the first branch node is directly connected to two further branch nodes, which in turn are directly connected to four branch nodes.

[0017] A cluster of nodes together with the electrode lines connecting the nodes may form a tree. More generally, the drive electrode may be a tree.

[0018] Such clusters of branching nodes may be introduced into electrode patterns manually, but the inventors have found algorithms that can generate patterns with a large number of branching nodes. For example, driving electrodes may be found by computing the spanning tree of the Voronoi pattern. Complementary electrode patterns may be formed by placing edges that extend across edges removed from the Voronoi pattern. Other tessellations may be used instead of the Voronoi pattern. For example, regular tessellations may be used, perhaps using one or more polygon shapes. Tessellations may be randomized by randomly shifting the edges of the tessellation. The spanning tree of the randomized tessellation can be used as electrodes; complementary electrodes may be formed from the dual graph.

[0019] Building blocks may be repeated across the substrate by copying and translating the blocks without mirroring or rotation. However, in embodiments, isometry, such as mirroring, rotation, and / or point reflection, is applied to the building blocks. Multiple building blocks may be used, but using isometry has the advantage that the arrangement of building blocks can be improved without the need to optimize multiple blocks. For example, if a drive bus traversing the substrate is used, for example, between building blocks, isometry can be used to avoid the drive buses being placed adjacent to each other on the substrate. For example, an entire row or column of building blocks may be mirrored along its longitudinal direction to form the next row or column of building blocks, etc. Mirroring building blocks in this way has the advantage that drive buses can be merged between different building blocks and thus avoid gaps between building blocks. Mirroring building blocks has the advantage that a symmetric electrode design for the substrate may be established, which is advantageous when manufacturing optical modulators.

[0020] In embodiments, the tiles are arranged in a checkerboard pattern, and individual tiles may be mirrored or point-reflected. In embodiments, the tiles are not arranged in a checkerboard pattern, and the edges of the tiles are parallel or perpendicular to each other.

[0021] The substrates according to the embodiment may be used in optical modulators, also known as optical modulators. For example, two such substrates may be arranged facing each other so that charged particles suspended in a fluid between the substrates can move by applying a voltage to the electrodes. Typically, the electrode designs for the lower and upper substrates are identical, but this is not required. Similarly, the two designs are typically aligned with each other, but this is not required. The particles may absorb or reflect light. The reflection may be specular, diffusive, or intermediate between the two. The particles may emit light that has, for example, phosphorescence or fluorescence.

[0022] A light modulator provides a panel whose transparency or reflectivity can be modified. In embodiments, the color or color intensity may be altered. Light modulators may be used as covers, for example, containers, closets, cabinets, and similar items. Depending on the specific application, a light modulator may also be called an ambient light modulator, dynamic light modulator, light modulator, color modulator, IR modulator, UV modulator, IR active filter, UV active filter, or dynamic color filter.

[0023] Particularly advantageous applications lie in optically active glazing, also known in this field as smart glazing, smart windows, controllable glazing, optical panels, electronic signage, dynamic light panels, dynamic color panels, active color panels, active light panels, active light surfaces, active color surfaces, dynamic light surfaces, or dynamic color surfaces.

[0024] In embodiments, the controller is configured to apply a potential to electrodes on the substrate of the optical modulator to obtain an electromagnetic field between the electrodes. The electromagnetic field causes electrophoretic motion of particles toward or away from the electrodes. As the particles change position, the optical properties of the panel, e.g., transparency or reflectivity, change. If the particles are colored, the color of the panel may also change. By changing the pair of electrodes between which the electromagnetic field is established, the particles can be moved in a desired direction. We have found that the control of the optical modulator does not have to be limited to changing between which electrodes the electromagnetic field is applied, but can also include changing the maximum amplitude. It should be noted that, advantageously, alternating current is used. For example, by driving with a lower maximum amplitude, the rate of change of the optical modulator is changed. This is advantageous, for example, when the maximum amplitude may be reduced to avoid overshoot while driving toward a desired target transparency or reflectivity. The maximum amplitude may be increased as well, or instead, when starting to drive toward a target transparency or reflectivity. For example, a controller may be configured to obtain one of several levels of transmittance or reflectivity of an optical modulator by using one of several maximum amplitude AC currents or voltages. This relationship may be represented by an algorithm or similar mechanism. The relationship between the transmittance or reflectivity level and the maximum amplitude may be governed, for example, by a lookup table showing a sequence of maximum amplitudes for driving toward transmittance or reflectivity. Note that AC voltages are also possible.

[0025] In addition to changing the electrodes to which the signal is applied, varying the maximum amplitude of the drive signal can also be used to improve balanced driving. For example, the power applied to some electrodes, such as the maximum amplitude, may differ from that applied to others. For instance, a controller may be configured to apply a potential difference between consecutive electrodes on the same substrate and simultaneously between opposing electrodes on opposite substrates.

[0026] In embodiments, at least one of the two substrates conforms to the embodiment. The other substrate may have one or more electrodes or may not have electrodes. In embodiments, the superposition of electrodes on the substrates satisfies a limit relating to the ratio of the electrode length to its diameter within the building block, or a limit relating to the pixelation noise ratio, for example, such limits are shown herein. Instead of diameter, other measures of the size of the building block may commonly be used. For example, in the case of a rectangular building block, the average of the building block sides, such as the harmonic mean of the building block sides, may be used.

[0027] In embodiments, at least two electrodes are present on each substrate, but there may be three or more electrodes. For example, at least three electrodes may be applied to at least one of the first and second substrates. For example, in embodiments, two electrodes may be applied to the first substrate and three electrodes to the second substrate. Typically, opposing substrates are mirrored so that the electrode lines face each other; this is not necessary, and different effects are possible when the electrodes are not arranged in this manner.

[0028] A further aspect of the present invention is a structure comprising an optical modulator according to an embodiment. A further aspect of the present invention is a vehicle comprising an optical modulator according to an embodiment. For example, a vehicle and / or structure may comprise an optical modulator and a controller configured to control the transparency or reflectivity of the optical modulator by controlling the voltage to the electrodes of the optical modulator, the controller being electrically connected to or connectable to the optical modulator.

[0029] An optical modulator is an electronic device that may be driven by a power supply, for example, under the control of a controller. For example, the controller may instruct the power supply to apply a specific waveform to a specific electrode in order to achieve various transparency or reflectivity effects, or their absence.

[0030] Embodiments of the method may be implemented on a computer as a computer implementation method, in dedicated hardware, or a combination of both. Executable code for embodiments of the method may be stored on a computer program product. Examples of computer program products include memory devices, optical storage devices, integrated circuits, servers, and online software. Preferably, the computer program product includes non-temporary program code stored on a computer-readable medium to perform embodiments of the method when the program product is executed on a computer.

[0031] In embodiments, the computer program includes computer program code adapted to perform all or part of the steps of the embodiment of the method when the computer program is executed on a computer. Preferably, the computer program is embodied on a computer-readable medium.

[0032] Further details, aspects, and embodiments are described by reference to the drawings, merely as examples. Elements in the drawings are shown for simplification and clarity and are not necessarily drawn according to a constant proportional scale. In the drawings, elements corresponding to elements already described may have the same reference numerals. [Brief explanation of the drawing]

[0033] [Figure 1a] This diagram schematically shows an example of a building block embodiment. [Figure 1b] This figure schematically shows an example of a substrate embodiment. [Figure 1c] This figure schematically shows an example of a substrate embodiment. [Figure 1d] This figure schematically shows an example of a substrate embodiment. [Figure 1e] This diagram schematically shows an example of a building block embodiment. [Figure 1f] This diagram schematically shows an example of a building block embodiment. [Figure 1g]This figure schematically shows an example of a substrate embodiment. [Figure 1h] This figure schematically shows an example of a substrate embodiment. [Figure 2a] This is a schematic diagram showing an example of an electrode embodiment. [Figure 2b] This is a schematic diagram showing an example of an electrode embodiment. [Figure 2c] This is a schematic diagram showing an example of an electrode embodiment. [Figure 3] This figure schematically shows an example of a substrate embodiment. [Figure 4a] This figure schematically shows an example of a substrate embodiment. [Figure 4b] This figure schematically shows an example of a substrate embodiment. [Figure 4c] This figure schematically shows an example of a substrate embodiment. [Figure 4d] This figure schematically shows an example of a substrate embodiment. [Figure 4e] This figure schematically shows an example of a substrate embodiment. [Figure 4f] This figure schematically shows an example of a substrate embodiment. [Figure 4g] This figure schematically shows an example of a substrate embodiment. [Figure 4h] This figure schematically shows an example of a substrate embodiment. [Figure 4i] This figure schematically shows an example of a substrate embodiment. [Figure 5a] This figure schematically shows an example of a substrate embodiment. [Figure 5b] This figure schematically shows an example of a substrate embodiment. [Figure 6a] This diagram schematically shows an example of a building block embodiment. [Figure 6b] This figure schematically shows an example of a substrate embodiment. [Figure 6c] This figure schematically shows an example of a substrate embodiment. [Figure 6d] This figure schematically shows an example of a substrate embodiment. [Figure 7a]This figure schematically shows an example of an embodiment of an optical modulator. [Figure 7b] This figure schematically shows an example of an embodiment of an optical modulator. [Figure 7c] This is a schematic diagram illustrating an example of a vehicle embodiment. [Figure 8a] This is a schematic diagram showing an embodiment of an optical modulator. [Figure 8b] This is a schematic diagram showing an embodiment of an optical modulator. [Figure 8c] This is a schematic diagram showing an embodiment of an optical modulator. [Figure 9a] This figure schematically illustrates a computer-readable medium having a writable portion containing a computer program, according to an embodiment. [Figure 9b] This figure schematically illustrates a representation of a processor system according to an embodiment. [Figure 10a] This is a schematic diagram illustrating an embodiment of an optical modulator. [Figure 10b.1] This is a schematic diagram illustrating an embodiment of an optical modulator. [Figure 10b.2] This is a schematic diagram illustrating an embodiment of an optical modulator. [Figure 10c] This is a schematic diagram illustrating an embodiment of an optical modulator. [Figure 10d] This is a schematic diagram illustrating an embodiment of an optical modulator. [Figure 11] This is a schematic diagram showing a cross-section of an embodiment of an optical modulator. [Figure 12a] This is a schematic diagram showing an embodiment of an optical modulator. [Figure 12b] This is a schematic diagram showing an embodiment of an optical modulator. [Figure 12c] This is a schematic diagram showing an embodiment of an optical modulator. [Figure 13a] This diagram schematically shows an example of a building block embodiment. [Figure 13b] This figure schematically shows an example of a substrate embodiment. [Figure 14a] This is a schematic diagram showing an embodiment of the substrate. [Figure 14b] This is a schematic diagram showing an embodiment of the substrate. [Figure 14c] This is a schematic diagram showing an embodiment of the substrate. [Figure 14d] This is a schematic diagram showing an embodiment of the substrate. [Figure 14e] This is a schematic diagram showing an embodiment of the substrate. [Figure 14f] This is a schematic diagram showing an embodiment of the substrate. [Figure 14g] This is a schematic diagram showing an embodiment of the substrate. [Figure 14h] This is a schematic diagram showing an embodiment of the substrate. [Modes for carrying out the invention]

[0034] List of reference symbols The following list of references and abbreviations is provided to facilitate the interpretation of the drawings and shall not be construed as limiting the claims. 10 Optical modulator 11. First substrate 12 Second substrate 13, 13a, 13b electrode 14, 14a, 14b electrode 15 Fluid 16 Controllers 30 particles 20 cars 21 Optical modulator 40 Optical modulators 41 First substrate 42 Second substrate 43 Third substrate 46 controllers 100-102 circuit board 111-114 Main line 121-124 Main Line 131-134 Mutually mated electrodes 140 Building Blocks 141-144 Building Blocks 110, 120 drive bus 110', 120' drive bus 119, 129 connection zones 151-157 Points on the edges of building blocks 160 building blocks 161, 162 Partial building blocks Building blocks 171 and 172 191, 192 direction Nodes 201-207 Nodes 210-218 α1-α7 angle 221-222 Electrode Line 180 circuit boards 181 points on the substrate 182 The first shortest distance 183 The second shortest distance 188 First drive electrode 189 Second drive electrode 601 Building Block 602-604 circuit board 640 Groove 611-622 Building Blocks 651-662 Building Blocks 720 First electrode 730 Second electrode 740 Edge Seal 750 Spacer 760 Semiconductor Ink 772, 774 circuit boards 812 First drive bus 814 Second drive bus 820 Building Blocks 902-906 Drive bus section 912 Drive electrode 1000, 1001 Computer-readable media 1010 Writable portion 1020 Computer Programs 1110 Integrated circuits (multiple possible) 1120 Processing Units 1122 memory 1124 Dedicated Integrated Circuit 1126 Communication elements 1130 Interconnect 1140 Processor System

[0035] While the subject matter of this disclosure can take many different forms, one or more specific embodiments will be shown in the drawings and described herein in detail, with the understanding that this disclosure is intended to be an illustrative example of the principles of the subject matter of this disclosure and is not intended to limit the disclosure to any particular embodiment shown and described.

[0036] In the following, for the sake of understanding, the elements of the embodiments will be described in terms of their operation. However, it will be clear that each element is configured to perform the function described as being carried out by that element. Furthermore, the subject matter of this disclosure is not limited to the embodiments alone, but also includes all other combinations of features described herein or described in dependent claims that differ from each other.

[0037] For example, a substrate for use in an optical modulator is disclosed. The substrate may comprise a plurality of inter-mating drive electrodes applied to the substrate, each of which is arranged in a pattern across the substrate, and the plurality of inter-mating drive electrodes are arranged alternately to one another on the substrate. The pattern of the plurality of drive electrodes across the substrate comprises a plurality of repeating building blocks.

[0038] Figure 1b schematically shows an example of a substrate embodiment. The substrate is particularly useful for use in, for example, an optical modulator of the type described herein. Multiple interlocking drive electrodes are applied to the substrate across it.

[0039] An exemplary use of substrate motivation is in an electrophoretic optical modulator. Typically, an electrophoretic optical modulator comprises at least two substrates, each having at least two driving electrodes; however, although not required, an electrophoretic optical modulator may also comprise, for example, a single substrate having two electrodes and a counter substrate having one electrode. In either case, preferably, at least one of the substrates in the optical modulator follows the embodiment.

[0040] An embodiment of the optical modulator comprises a first substrate and a second substrate according to the embodiment. The first and second substrates are arranged so that their inner surfaces face each other. At least one drive electrode is applied to the inside of the first substrate. An optical layer is placed between the first and second substrates. A controller is configured to apply a potential to at least one drive electrode that causes modulation of the optical properties of the optical modulator. One or both of the first and second substrates are transparent and / or translucent.

[0041] There are many different types of optical modulators that use at least one driving electrode applied to a substrate. Interference is a common problem in the field of optical modulators, as light passes through the substrate. Optical layers and controllers may be arranged to modulate optical properties using potential-dependent effects on the driving electrode; examples include dielectrophoretic and electrophoretic effects. For example, optical modulation may involve the modulation of particles placed within the optical layer. The number of driving electrodes can range from one on a single substrate to multiple driving electrodes on one or both substrates.

[0042] The optical layer placed between the first and second substrates may, for example, contain particles suspended in a fluid. The controller may be configured to apply a potential to the driving electrode, causing the particles to move and thus modulating the optical properties of the optical modulator.

[0043] In embodiments, the particles include electrically charged or chargeable particles, and the controller is configured to apply a potential to the driving electrodes to obtain an electromagnetic field that causes the electrophoretic motion of the particles. In embodiments, the electromagnetic field is configured between at least two driving electrodes located on the same substrate or on different substrates.

[0044] In the embodiment, the particles include dielectric particles, and the controller is configured to apply a potential to the driving electrode to apply an electric field gradient to the particles, thereby enabling the particles to move under the action of dielectrophoretic force.

[0045] The controller may apply an electrical signal to one or more of the drive electrodes. Embodiments controlling electrophoretic force may use a signal that includes DC and / or AC signals. Embodiments controlling electrophoretic force may use a signal that includes DC and / or AC signals.

[0046] Below, several known optical modulators are reviewed, and some of the options in terms of technology and electrodes are presented.

[0047] U.S. Patent No. 1,0921678, which is included herein by reference and has the title “Electrophoretic device,” describes an electrophoretic device having only one patterned electrode on one of two substrates. For example, one substrate having an electrode in U.S. Patent No. 1,0921678 may be replaced with a substrate in an embodiment having one single electrode. U.S. Patents No. 8,054535B2 (included herein by reference) and No. 8,384659B2 (included herein by reference) provide examples of alternatives to an electrophoretic optical modulator in which one of two substrates has two patterned electrodes.

[0048] Patterned electrodes are also used in dielectrophoretic photomodulators. For example, U.S. Patent Application No. 2005185104A1 (included herein by reference) and U.S. Patent Application No. 20180239211A1 (included herein by reference) illustrate dielectrophoretic photomodulators having a substrate with patterned electrodes. Any of these cited electrophoretic or dielectrophoretic photomodulators may be adapted by patterning electrodes on a substrate according to the embodiment.

[0049] In an embodiment, the optical modulator comprises a first substrate and a second substrate. At least one of the first and second substrates may be according to the embodiment. For example, the first and second substrates may be arranged so that their inner surfaces face each other. Using substrates according to the embodiment has the effect of reducing optical interference, for example. An optical layer is placed between the first and second substrates. A driving electrode is placed to modulate the electric field in the optical layer. The optical layer contains a fluid containing particles, which are electrically charged or rechargeable. The particles may move under the control of the electric field. For example, a controller may be configured to apply a potential to the driving electrode to obtain an electromagnetic field at the driving electrode, resulting in electrophoretic motion of particles toward or from one of the at least one driving electrodes that causes modulation of the optical properties of the optical modulator.

[0050] The paper “Reversible Metal Electrodeposition Devices: An Emerging Approach to Effective Light Modulation and Thermal Management,” included by reference, also shows a substrate on which patterned electrodes are applied. The patterned electrodes may be configured according to the embodiment, for example, to reduce interference.

[0051] The substrate embodiment may be used in electrochromic devices (ECDs). Electrochromic devices (ECDs) continuously but reversibly control optical properties such as optical transmission, absorption, reflection, and / or emittance by applying voltage (electrochromism). This property allows electrochromic devices to be used for applications such as smart glass, electrochromic mirrors, and electrochromic display devices.

[0052] Electrochromic devices are described, for example, in the paper "Silver grid electrodes for faster switching ITO-free electrochromic devices" by Antonio California et al., which is included herein by reference. That paper describes the fabrication of electrochromic devices, in this case, ITO-free electrochromic devices.

[0053] Electrochromic devices use electrically conductive electrodes applied to a substrate. The cited paper uses a silver grid made with silver ink as the electrically conductive electrode. Electrochromic devices may contain electrochromic materials. The cited paper uses poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS). In an electrochromic device, at least one driving electrode, such as an electrically conductive electrode, is applied to the substrate. The driving electrode is arranged in a pattern across the substrate. The cited paper discloses two different grid patterns, regular hive and regular ladder designs. See Table 1 and Figure 3 of the cited paper.

[0054] In the cited paper, electrodes may be applied to the substrate by screen printing onto polyethylene terephthalate (PET). Electrodes are typically electrically conductive materials, such as metals or metal oxides. In the cited paper, silver ink was used to screen print a grid onto the PET using a RokuPrint RP 2.2 instrument and a 180-wired mesh. The samples were dried in an oven at 130°C for 15 minutes. One or two layers of PEDOT:PSS SV3 were subsequently screen printed on top of these silver grids.

[0055] Electrochromic devices are subject to interference due to regular patterns, such as the hive or ladder pattern in the cited paper, and the combination of transmitted light. One way to avoid interference is to use patterns according to the embodiment, such as electrodes, that are longer than other repeating elements, such as building blocks.

[0056] For example, the metal grid used in the cited paper may be replaced by drive electrodes applied to a substrate, the drive electrodes arranged in a pattern across the substrate, the pattern of drive electrodes across the substrate comprising a plurality of repeating building blocks, each building block comprising one or more electrodes extending in at least two directions across the building block, the electrodes within the building block forming at least one drive electrode, and for at least one electrode within the electrodes within the building block, the maximum length between any two points on the electrode, measured along the electrode within the building block, is at least twice the length of the diagonal of the building block unit. Instead of requiring a minimum electrode length, the pattern may use other features that reduce interference, such as a high degree of branching, for example, branching of the electrode into two or more paths, the branching repeating multiple times, for example, at least two, three, four, or more times, resulting in a branching of the initial electrode into at least four, eight, sixteen, or more electrodes.

[0057] Another example of an electrochromic device is given in U.S. Patent No. 5,161,048, titled “Electrochromic window with metal grid counter electrode and acidic polyelectrolyte,” which is incorporated herein by reference. For example, an electrochromic device may comprise a transparent electrochromic film and an ion-conducting layer disposed between pairs of electrodes. A metal grid electrode is provided for the electrode. Figure 1 of the patent shows a metal grid according to the cited patent. To form a counter electrode, the metal grid is disposed adjacent to a second glass substrate.

[0058] For example, in an embodiment of an electrochromic device, the electrochromic device may comprise a transparent substrate, an electrically conductive electrode member, a transparent electrochromic film in contact with the electrically conductive electrode member, an ion-conducting polymer in contact with the electrochromic film, and a patterned conductive electrode in contact with the ion-conducting polymer. The patterned conductive electrode may vary depending on the embodiment.

[0059] The substrates according to the embodiments may be advantageously applied in several other technologies. For example, the optical modulator may be a dielectrophoretic optical modulator, as shown, for example, in U.S. Patent Application No. 20050185104(A1), which is included herein by reference. Substrates like those in the embodiments may also be used in other electrowetting and OLED applications.

[0060] In OLEDs and electrowetting, electrodes are required on only one of several substrates. The substrate having the electrodes may vary depending on the embodiment.

[0061] In applications such as glazing optical modulators, both substrates are typically transparent. In other applications, such as televisions and e-readers, only one substrate may be transparent.

[0062] Figure 1b shows two drive electrodes on the same surface. The two drive electrodes are shown in Figure 1b with two different dashed line styles. For example, there may be three or more electrodes on the same side of the substrate to facilitate finer control of the voltage difference across the substrate. The drive electrodes are applied to the same side of the substrate. Applying electrodes to a substrate may be done by lithography, for example, using a mask that represents the electrode pattern. Electrodes may also be applied by embedding them in the substrate.

[0063] The drive electrodes are electrically connected and, for example, have the same potential everywhere. The drive electrodes may include a drive bus and a main line. At a minimum, the main line mates with the main lines of further drive electrodes. Typically, the drive electrodes extend in substantially straight lines across the substrate, while the main lines are intricate.

[0064] In an embodiment, each of the two substrates of the optical modulator has two electrodes located on its inner surface. However, as stated, multiple electrodes on one or both substrates are not required. For example, an embodiment of the optical modulator comprises a first substrate and a second substrate. For example, the first substrate may have one drive electrode, and the second substrate may not have a drive electrode. For example, the first substrate may have two drive electrodes, and the second substrate may have one drive electrode. For example, the first substrate may have two drive electrodes, and the second substrate may have two drive electrodes. For example, the first substrate may have three or more drive electrodes, and the second substrate may have two or more drive electrodes.

[0065] Optical modulators, however, with each substrate having two drive electrodes, are used as a motivational example. A substrate design featuring two drive electrodes may be adapted to have a single drive electrode, for example, by connecting the two drive electrodes or by removing one of the multiple drive electrodes. Adapting the substrate in this way may make it suitable for use in different technologies.

[0066] Each of the multiple drive electrodes is arranged in a pattern that crosses the substrate. The multiple drive electrodes are arranged alternately on the substrate relative to each other. Typically, each drive electrode has multiple main lines that extend across the substrate. The main lines of the drive electrodes are alternating, for example, interlocking. For example, in Figure 1b, the first drive electrode has main lines 111-114, and the second drive electrode has main lines 121-124. Each drive electrode is driven by its drive bus. Figure 1b shows two drive buses: drive bus 110 and drive bus 120. The drive electrodes also serve to connect the main lines together. For example, in Figure 1b, drive bus 110 drives and connects main lines 111-114; drive bus 120 drives and connects main lines 121-124. There can be more than four main lines than shown in this example. The use of main lines is advantageous because it reduces the length of the electrodes, but it is not necessary. While a design using only one main line per drive electrode is not impossible, having multiple main lines is advantageous.

[0067] Multiple main lines of the first and second electrodes are arranged alternately with respect to each other on the substrate.

[0068] Motivational applications for substrates such as substrate 100 may be applied in homes, offices, greenhouses, cars, and similar devices, such as smart glazing, for example, in optical modulators. The level of transparency or reflectivity of smart glazing can be electrically matched. For example, in smart glazing, two substrates such as substrate 100 are stacked such that the surfaces on which two electrodes are applied face each other. A fluid containing particles is confined between the two substrates. Embodiments of smart glazing are discussed further below. In embodiments, electrodes, for example, two or more electrodes, are applied to one surface of each substrate. For example, to facilitate the stacking of three or more substrates, one, two, or more electrodes may be present on other surfaces of substrate 100.

[0069] The following embodiments illustrate examples of modulating transparency or reflectivity levels. The optical modulator may be adapted for other optical effects. For example, if desired, the embodiments may be modified for different levels of translucency instead of different levels of transparency. If desired, the type of particles used in the embodiments may be varied, for example, for particles that absorb or reflect at different wavelengths and how specular or diffuse the reflection is. For example, in the embodiments, the optical modulator can modulate different levels of reflection. The particles may also emit light. Stacking multiple optical layers further increases the possibilities.

[0070] Having two sets of alternating main lines is sufficient to provide electrically adaptable glazing; the two alternating sets allow the electric field in any part of the substrate to be controlled because the two opposing electrodes demarcate that part from two opposing edges.

[0071] Interestingly, the pattern of the drive electrodes extending across the substrate is created by multiple repeating building blocks. As shown in Figure 1b, the drive electrodes on the substrate 100 show four blocks: blocks 141, 142, 143, and 144, all of which are substantially identical. The number of building blocks may be greater than four. The building blocks repeat across the substrate in both directions, for example, a first direction 191, e.g., the x-direction shown horizontally in the figure, and a second direction 192, e.g., the y-direction shown vertically in the figure.

[0072] For example, Figure 1a schematically shows an example of an embodiment of building block 140. Building block 140 comprises a plurality of inter-mating electrodes extending in at least two directions across the building block. Four electrodes: electrodes 131-134 are shown in Figure 1a. When the building block is repeated across the substrate in two directions, the electrodes within the building block will form drive electrodes, for example, forming multiple main lines of drive electrodes. Note that building blocks are typically connected in a substrate electrode design tool. Typically, a building block has five or more electrode lines. For example, within the scope of the embodiment, between eight and twelve main lines are used. The number of electrode lines can, however, be much larger. For example, a building block may have many short electrode lines near the edges that connect to lines of other building blocks when the block is repeated. Taking such short derivatives into account, the number of lines can increase to, for example, 50. Obviously, using larger building blocks may also increase the number of electrode lines. In this embodiment, the number of electrode lines within the building block is between 8 and 50, or between 8 and 25, and so on.

[0073] The drive electrodes, formed by repeating building blocks, are connected to the drive bus. Typically, electrode lines within a building block are connected to electrode lines in neighboring blocks by merging the corresponding electrode lines; however, connection zones connecting the corresponding electrode lines may be inserted between repeating building blocks, although this is not necessary.

[0074] This step allows multiple main lines to be connected together, thus forming a single drive electrode. Figure 1b shows two connection zones 119 and 129, where main lines belonging to the same drive electrode are connected to drive bus 110 and drive bus 120, respectively.

[0075] The electrodes shown in Figure 1a are alternately marked with dashed lines in the same dashed line style as in Figure 1b. In practice, it happens in this example that certain electrodes of the building blocks in Figure 1a always end up either within the first drive electrode or within the second electrode, for example, as indicated by the dashed line style in this case. This, however, is not always the case. Electrodes within a building block may end up as part of the first drive electrode or as part of the second drive electrode. This can change, for example, the repeating pattern of the building blocks as a result of the even or odd number of electrodes within the building block.

[0076] For example, a particular pattern of repeating building blocks may be used for an optical modulator having two drive electrodes, in which alternating main lines may be assigned to the two drive electrodes. However, the same pattern of repeating building blocks may be used for an optical modulator having three drive electrodes, in which all adjacent sets of the three main lines may be assigned to the three drive electrodes.

[0077] Furthermore, although the building blocks shown in Figure 1a are square, this is not required. For example, the building blocks may be rectangular. In embodiments, the building block shape(s) may form a so-called tessellation. For example, the building blocks may be triangular, hexagonal, or even a combination of planar tessellations.

[0078] As stated, Figures 1a and 1b are schematic. This is especially true for the depiction of electrodes. The electrodes shown in Figure 1a are straight, and their length is equal to the length of the side of the building block. However, in embodiments, electrodes on a building block are more interlocked with respect to at least one electrode in a plurality of inter-mating electrodes within the building block, and the maximum length between any two points on the electrode, measured along the electrode within the building block, is at least twice the length of the diagonal of the building block unit.

[0079] For example, considering the electrode shown schematically in Figure 1a, the maximum possible length along the same electrode is the length of the side of the building block. The ratio of the maximum length to the diagonal of Figure 1a (shown schematically) is:

number

[0080] Typically, two or more electrode lines within a building block satisfy this condition. For example, in an embodiment, a building block comprises multiple electrode lines that are not electrically connected within the building block, and the longest path on each electrode of the multiple electrodes is longer than twice the diagonal length of the building block. The number of these multiple electrodes could be at least two, at least four, at least ten, and so on.

[0081] Undesirable diffraction effects can be altered by adapting the shape of the electrodes. Reducing diffraction effects is particularly important for transparent substrates because, for example, in diffuse reflective displays, which may be applied in e-readers, the effect is less noticeable. However, specular reflective displays, such as dimmable mirrors, are affected by diffraction effects. The inventors have found that optical diffraction in an optical modulator can be reduced by orienting the electrode line shape at multiple different angles, spreading the diffraction in space and thus reducing the intensity of the strongest diffraction spots. For example, reducing diffraction is important in the case of dimmable mirrors.

[0082] In embodiments, the dimmable mirror comprises an optical modulator according to the embodiment. For example, the dimmable mirror comprises a transparent substrate, an optical layer, and a reflective substrate. One or both of the substrates are according to the embodiment. The dimmable mirror may be electrophoretic. Typically, each substrate has two electrodes, but this is not necessary.

[0083] Figure 1c schematically shows an example of an embodiment of substrate 101. Substrate 101 is similar to substrate 100, except that the main lines formed from electrodes on the building blocks are connected to the drive bus. In Figure 1a, a connection zone is inserted between the repeating building blocks and the drive buses 110 and 120. In the connection zone, main lines belonging to the same drive electrode are connected to the same drive bus. In Figure 1c, the drive bus is directly adjacent to the building block. Part of the building block is modified to avoid the drive bus connecting to the main lines of different drive electrodes.

[0084] For example, building block 141 may be a copy of building block 140, but electrode 134 is shortened so that the main line 122, of which line 134 is part, does not connect to bus 110. In Figure 1c, the building blocks are substantially the same except that a disconnection is introduced in some electrodes of the building block adjacent to the drive bus to avoid connecting the main line to the drive bus. All building blocks shown in Figure 1c are thus modified, but in the embodiment, the majority of building blocks, such as those not adjacent to drive buses 110, 120, are not modified.

[0085] Figure 1d schematically shows an example of an embodiment of the substrate 102.

[0086] In this embodiment, each electrode within the building block is connected to the same opposing edge of the building block. This results in the main line formed by the electrodes on the building block connecting opposing edges of the substrate. In such a situation, having only two drive buses, each extending along opposing edges of the substrate, is sufficient to connect and drive the drive electrodes.

[0087] However, electrodes within a building block do not need to connect opposite edges of the building block. Typically, all electrodes within a building block will connect two edges of the building block, but these two edges do not need to be opposite. The reason for this is that electrodes may be continued by the next building block. In such situations, most main lines will still connect the same two opposite edges, but this may not happen at the edges of the substrate because there are no further building blocks to carry the electrodes forward. To allow for more complex electrode designs with respect to building blocks, main lines may connect to the drive bus from two edges, for example, two adjacent edges of the substrate at the same corner of the substrate.

[0088] Figure 1d shows a drive bus 110' extending along two sides of the substrate and a drive bus 120' extending along the other two sides of the substrate.

[0089] The advantage of this configuration is that the drive bus can be made in the same plane. However, this is not necessary. The drive bus can be connected from all three or four sides, if desired, to further increase the design freedom for the building block, for example. Various examples are shown herein.

[0090] It should be noted that drive electrodes, such as drive buses and / or main lines, can overlap. This is possible, for example, by creating a portion of dielectric material between the electrodes. For example, such overlapping electrodes may be partially or completely located in different planes of the substrate.

[0091] For example, in an embodiment, the first drive electrode may be deposed. Then, the dielectric is locally deposed, and finally, the second drive electrode is deposed. The dielectric is positioned to cover at least the points where the first and second electrodes intersect. Vias may be used for lower first drive electrodes, for example, to connect to a lower first drive electrode. Deposing of the drive electrodes may include deposing the drive bus.

[0092] Figure 1e schematically shows an example of a building block embodiment. Two electrodes are schematically shown in Figure 1e. In actual implementations, the track of the electrodes shown will typically be much more intricate.

[0093] The building block in Figure 1e shows four electrode lines connected to at least two sides of the building block, respectively. In this case, the electrode lines do not directly connect to opposite sides of the building block. Connections to opposite sides of the building block are not required because the drive electrodes only need to be driven from one side. However, to cover the substrate, it is convenient if at least one of the electrodes reaches the opposite side from where the electrodes are driven. This is not necessary; there may be main line electrodes that reach only a portion of the substrate, and they may be driven from two sides.

[0094] Figure 1e shows that a main electrode into which a particular electrode line of a building block is incorporated can still reach across the substrate even if the electrode line does not connect to an opposing side. For example, an electrode line starting at 151 on the left side connects to the non-opposite upper side of the building block at 157. If the same building block is repeated on the shown building block, the main line formed by this line continues at point 154 of the repeating building block and reaches the opposing side of the repeating building block at 152. Similarly, an electrode line that will become part of a second drive electrode starts at 155 on the left side of the building block. This electrode line connects to the upper side at 153 and continues in the repeating block at 154. Thus, an electrode line starting on the left side of a building block may not connect to an opposing side of that building block, but the electrode line can still travel its distance in the x direction and reach the right side of a different building block, for example, a building block above or below the shown building block. The same is possible in the y-direction, and vice versa. In embodiments, the main line connects the sides of the substrate opposite to the first direction 191, e.g., x-direction, extending through multiple blocks in the first direction 191, e.g., x-direction, and extending through at least two blocks in the cross-sectional direction, e.g., y-direction. Typically, the first direction 191 and the second direction 192 are orthogonal; however, this is not strictly necessary, and the two directions may be inclined relative to each other.

[0095] Figure 1f shows that two electrode lines within a building block do not need to be connected within the building block, but can still be connected within the substrate through connections in neighboring building blocks. For example, consider an electrode starting on the left side at point 151. The electrode exits at the top side of the building block. Unlike the example in Figure 1e, the main line into which the electrode line starting at 151 is incorporated connects to the opposing part of the building block shown in Figure 1f.

[0096] At point 151, the electrode line, starting on the left edge of the building block, connects to the top edge of the building block at point 157. If the same building block is repeated on the top of the shown building block, the electrode line will connect to the bottom edge at point 156 and to the same edge as the bottom edge at point 154. Returning to the building block shown in Figure 1f, the electrode line continues on its top edge at point 153 and connects to the right edge at point 152, i.e., the edge opposite the edge at point 151.

[0097] In this embodiment, the main line of the drive electrode connects a first point on the first side of a first building block to a second point on the opposite side of the same building block, and between the first and second points, the main line intersects at least the second building block following the first building block.

[0098] In this example, the longest path between two points on the same electrode line is formed by a path starting at 155. According to the embodiment, the length of the longest path is a multiple of the size of the building block, e.g., a side or diagonal; for example, the longest path may be at least twice the length of the diagonal. In this example, only one path of that length exists, but there may be multiple such long paths.

[0099] An alternative requirement might be to consider paths extending through neighboring building blocks. For example, the longest path starting on an edge, e.g., the left edge, and connecting to an opposite edge of the same building block might be a multiple of the building block's diagonal, and this path might extend through neighboring building blocks. Using this definition, a somewhat higher threshold, e.g., 2, might be used, but an even higher threshold, e.g., 3, is also possible.

[0100] In this embodiment, the electrode line on the building block connects two points on the same side.

[0101] In this embodiment, the electrode line on the building block connects two points on different, non-opposing sides of the building block.

[0102] Figure 1f also shows electrode lines connecting two opposing sides of a building block. In this embodiment, all electrode lines on a building block connect opposing sides of the building block. However, as shown, this is not necessary. Typically, the drive bus is straight, while the main lines are intricate.

[0103] Figure 1g schematically shows an example of a substrate embodiment. Figure 1g illustrates a modification method for tiling the substrate using building blocks. In Figure 1g, the building blocks are staggered. For example, in a first direction 191, for example in the x-direction, the building blocks 160 are aligned in rows. At the top of the building blocks, the building blocks are similarly aligned in rows, but the building blocks are offset relative to the rows below. The offset is shown as half the width of the block, but this could be another proportion of the building block width, for example, one-third of the building block width.

[0104] If a rectangular substrate is desired, partial building blocks may be added to the rows to fill the substrate. Figure 1g shows two half-width building blocks: building block 161 and building block 162. Building blocks 161 and 162 may be identical to half of the substrate 160, but more typically, both are designed to connect drive electrodes and for substrate coverage. As shown, each row has partial building blocks, e.g., building block 161 in odd rows and building block 162 in even rows. However, it is also possible to have a staggered design, but with both partial building blocks at the beginning and end of even rows, for example, and full building blocks used only in alternating odd rows.

[0105] Other tessellations, such as substrate-filled tiling, may be used to create electrode patterns. For example, in embodiments, building blocks may be parallelograms, rhombuses, or similar shapes. In embodiments, building blocks may be aligned in rows, and in odd-numbered rows, blocks may be mirrored, for example, flipped; sometimes referred to as glide reflection symmetry. In addition to mirroring, building blocks may also be point-reflected or inverted.

[0106] Figure 1h schematically shows an example of a substrate embodiment. As in Figure 1b or Figure 1c, the building blocks repeat across the substrate in at least two directions. However, in Figure 1h, multiple different building blocks are used; Figure 1h shows two building blocks 171 and 172. Both blocks 171 and 172 repeat in two directions, for example, a first direction 191 and a second direction 192. In Figure 1h, building block 171 is not directly adjacent to building block 171; for example, two building blocks form a checkerboard fill. This is not necessary, but for example, a first building block may connect to a copy of the first building block on two opposing sides, but to a second building block on the other two opposing sides. There may be three or more different building blocks.

[0107] For example, using different tiles that are adjacent and alternating in different directions increases design flexibility, and this may be used, for example, to ensure continuity of supply to tiles within the substrate, while connections to controllers may be made at the edges of the substrate.

[0108] In electrode schemes, it should be noted that tiles may be powered by adjacent tiles. For example, in checkerboard stitching of building blocks, one building block may power the next building block. This may involve different tile layouts. For example, vertically adjacent and / or horizontally adjacent tiles may be different. In embodiments, parts of the checkerboard are repeated, while parts consist of different tiles. For example, consider five adjacent tiles, e.g., center, left, right, top, and bottom; such tiles may be different or repeated, but preferably the electrode lines are configured to connect to electrode lines in adjacent tiles and / or the entire drive bus.

[0109] Figure 2a schematically illustrates an example of an electrode embodiment; within the substrate, the electrode is part of a single drive electrode. For example, the electrode shown in Figure 2a may be part of an electrode line within a single building block. The shown electrode may similarly be formed from multiple adjacent building blocks. For example, the cluster shown in Figure 2a or 2b may be part of main lines 111-114, 121-124, or electrode line 131-134.

[0110] The electrode comprises multiple nodes from which the electrode branches. Branch nodes 201, 202, and 203 are shown. The nodes are electrically directly connected through the electrode line. One such electrode line between branch node 201 and branch node 203 is indicated by reference numeral 221.

[0111] It has been found that having multiple branching nodes within an electrode is advantageous in increasing the ratio of electrode length to building block diagonal, which in turn is advantageous in reducing diffraction. The presence of clusters of branching nodes causes the electrode to form various angles, which contributes to reducing diffraction.

[0112] In embodiments, the main line or further the drive electrode forms a tree, for example, an undirected and acyclic graph. Preferably, the tree comprises many branching nodes. Branching nodes have the advantage of allowing the introduction of angles between electrode lines. For example, Figure 1a shows branching node 201 directly connected to two further branching nodes: nodes 202 and 203. At all three nodes 201-203, the electrodes branch.

[0113] Figure 2b schematically shows an example of an electrode embodiment. This example elaborates on the example in Figure 2a. Seven branching nodes of the electrode are shown. Branching node 201 is directly connected to branching nodes 202 and 203. Branching nodes 202 and 203 are similarly connected to two further branching nodes, respectively. Branching node 202 is connected to branching nodes 204 and 205. Branching node 203 is connected to branching nodes 206 and 207. The direct connection between branching nodes 203 and 206 is indicated by reference numeral 222.

[0114] The branching patterns in Figure 2a or Figure 2b increase the ratio of electrode length to building block diameter or diagonal. These branching patterns also increase the variety of electrode line orientations and reduce the long extension of parallel electrode lines. Such improvements are equally valuable without any contribution to the ratio. For example, in one embodiment, a substrate is provided for use in an optical modulator, and the substrate is: - The device comprises a plurality of mutually mated drive electrodes (111-114, 121-124) applied to a substrate, each of the plurality of drive electrodes arranged in a pattern across the substrate, the plurality of mutually mated drive electrodes arranged alternately with respect to each other on the substrate, the electrodes on the substrate comprising a plurality of nodes from which the electrodes branch, the nodes being electrically connected through electrode lines, the plurality of nodes and connecting electrode lines forming a tree, the electrodes comprising at least a first node (201) from which the electrodes branch into at least three electrode lines, the first node (201) being directly connected to a second node (202) and a third node (203) through electrode lines, the electrodes branching into at least three electrode lines at the second node and at the third node.

[0115] Figure 2c schematically illustrates an example of an electrode embodiment; within a substrate, the electrode is part of a single drive electrode. For example, the electrode shown in Figure 2c may be part of an electrode line within a single building block. The electrode shown may similarly be formed from multiple adjacent building blocks.

[0116] Eight nodes directly connected to the electrode lines are shown: nodes 210-218. Figure 2c does not show branching for all of these nodes. In fact, not all nodes need to be branching nodes. For example, a node may connect two electrode lines at a certain angle.

[0117] For example, the path from 210 to 218 may be the longest path between any two points on the electrode, for example, from point 210 to 218. Along the path from node 210 to node 218, the subsequent electrode lines form certain angles. These angles are denoted as α1 to α7. For example, α1 is the angle between the electrode line from node 210 to 211 and the electrode line from node 211 to node 212.

[0118] To reduce diffraction, it is preferable that the angles in the design be non-uniform. For example, the angles along the path, e.g., the longest path, may be selected randomly, or they may be selected to uniformly sample a range of possible angles within the range of 0 to 360 degrees. For example, in an embodiment, the angles are selected so that one angle is selected from at least all blocks of 30 degrees. For example, the angles may be selected from the respective ranges of 1-30, 31-60, ..., 331-360. Longer paths affect diffraction; having many angles within a long path can make the path less uniform and thus reduce diffraction. Measurements may also be performed by first reducing all angles modulo 180.

[0119] Instead of limiting the angles to those along the path, all angles within a node in a building block may be included. For example, a node connecting n electrode lines defines n-1 angles between consecutive electrode lines. Similarly, it is preferable that these angles are uniform and represent the full range of angles. For example, they may be randomly selected, or selected to sample the full range of angles, for example, from 0-180 degrees.

[0120] Nodes are preferably selected to cover building blocks, and therefore the substrate. For example, nodes may be randomly selected across the building blocks.

[0121] Note that electrode lines between nodes may be straight or curved. Having straight lines simplifies calculations for the design, while curved designs offer greater flexibility that can be used to combat diffraction. In the case of curved designs, such as Figure 3 below, the consideration of angles may be limited to branching nodes. In embodiments, the substrate is curved, and multiple repeating building blocks have at least two different shapes.

[0122] Figure 3 schematically shows an example of an embodiment of the substrate 180. Details of the two drive electrodes: electrode 188 and electrode 189 are shown. The details shown may, for example, be part of a building block. Details may also arise because the two building blocks are aligned adjacent to each other.

[0123] Figure 3 shows an example of an electrode with a curved electrode line. The following considerations also apply to designs using straight electrode lines.

[0124] Figure 3 shows a point 181 on the substrate that is not on an electrode. At such a point, control of the electric field is desired so that the electrophoretic motion of particles in the optical layer adjacent to the substrate 180 can be controlled. Point 181 is shown as a small disk for clarity.

[0125] For a point such as point 181, the distance to the two nearest electrodes can be calculated. The nearest distance between an electrode and point 181 can be considered as the minimum distance between any point on the electrode and point 181. For example, for point 181 and electrode 189, the nearest distance is 183. For example, for point 181 and electrode 188, the nearest distance is 182. The distance is calculated as a Euclidean distance.

[0126] For example, the desired objectives for electrode patterns are as follows:

[0127] The nearest distance from any point in the substrate, for example, point 181, to the first drive electrode and the nearest distance to the second drive electrode should both be less than a threshold. For example, distances 183 and 182 should both be less than the threshold. Such a threshold is preferably effective across the entire substrate, for example, across the entire portion where particle motion is controlled. Limiting the distance from which a point can be removed from the electrode limits the attenuation of the electric field at that point from that electrode. The value for the threshold depends on the strength of the electric field and the desired uniformity of the optical effects, speed, and uniformity of the transitions between different optical states. As an example, the threshold may be set to 50 micrometers.

[0128] Another way to limit the distance between electrodes is to limit the sum of the closest distances to the first and second driving electrodes, for example, requiring that these be less than a first threshold. For example, the sum of distances 182 and 183 is less than the first threshold. If the two electrodes are too far apart, there may be a slow region between the two electrodes where neither electrode has much influence, for example, where both electric fields are extremely attenuated. An appropriate threshold, again, depends on the specific application, but as an example, 100 micrometers could be taken as the first threshold.

[0129] At the same time, it may be desirable to avoid electrodes being too close to each other. For example, if electrodes on a substrate are too close to each other, the chance of accidental short circuits increases. For instance, the sum of distances 182 and 183 may be required to be at least a second threshold. An appropriate value for the second threshold depends on the application. As an example, a second threshold of 10 micrometers may be taken.

[0130] Upper and lower limits for the distance between electrodes can be calculated for any point on the substrate, and appropriate limits can be set for them as shown. To simplify the calculation, it may be required that the distance from a point on the first drive electrode to a point on the second drive electrode is at least the second threshold. For example, this distance may be taken as 10 micrometers.

[0131] For electrode patterns where the electrode lines are lines, the calculation can be further simplified by limiting the calculation to the nodes containing the endpoints of the electrode lines.

[0132] In embodiments, the horizontal size of the building block, for example in a first direction 191, e.g., the x-direction, is at least 10 times the sum of the electrode line width and the electrode distance, also called the line gap. For example, the electrode distance may be taken as the sum of the maximum nearest distances to the two nearest electrodes, e.g., the sum of distances 183 and 182. The electrode line width and electrode distance depend on the application. For example, the electrode line width may be considered to be 5 micrometers. The electrode line width may be 1 micrometer, 10 micrometers, or a value in between, etc. Other values ​​are possible. For the vertical size of the building block, for example in a second direction 192, e.g., the y-direction, the same lower limit as for the x-direction may be taken. For example, the building block may be rectangular or square, and the side dimensions may be at least 500 micrometers, e.g., at least 1000 micrometers, etc.

[0133] In embodiments, the electrode line width is not constant when measured along the electrode line. For example, the electrode line width may be measured perpendicular to the side of the electrode line. A constant electrode line width tends to result in a more constant inter-line distance, which in turn has the disadvantage of contributing to diffraction. In actual designs, the electrode width is typically kept below a maximum value. As an example value, the maximum inter-line distance of the electrodes may be taken so that the electrode line is not thicker than the space between the electrodes anywhere.

[0134] The line gap, for example, the distance between electrodes, does not need to be constant. For example, in spiral designs such as the spiraling design in Figure 5b, it is possible to have a low diffraction design with a substantially constant line gap. However, in more randomized designs, such as the Waal design, the line gap is typically not constant but can vary, for example, within a certain range.

[0135] Making building blocks too small can lead to diffraction due to the repetition of similar building blocks. Making building blocks too large can lead to optimization and evaluation problems in production. For example, the sides of building blocks may be 0.5 mm, 1 mm, 1 cm, and 10 cm, but may extend to values ​​such as 100 cm or larger. For example, one or both sides of a building block may be between 0.5 mm and 10 cm.

[0136] In embodiments, the building block is square, but it can be rectangular. In embodiments, the sides of the building block have the same ratio as the substrate. In embodiments, the building block may not be square, but may be any one or more planar tiling shapes. For the diameter, for example, the maximum distance between two points on the building block, the same lower limit as for the x-direction may be taken.

[0137] The electrode pattern may be optimized for various constraints. For example, the length of the electrodes is preferably short to maintain low electrical resistance. In embodiments, for a given point on the substrate, the lengths of the two closest electrodes to that point are approximately equal, for example, having a ratio within a threshold of 1.

[0138] Preferably, optical diffraction below a threshold is of particular importance. Further information regarding diffraction for various example designs is given herein.

[0139] Optical diffraction The following methods were used to estimate optical diffraction.

[0140] 1. Prepare the design drawing: - Crop to 1024 x 1024 microns (unit cell size); - Normalize the pixel values ​​to 255 (black=0; white=255);

[0141] 2. Use the Bluestein method [1, 2] to calculate the magnitude and angle without scaling.

[0142] Since optical diffraction can be formulated as a Fourier transform, conventional methods involve using the Fast Fourier Transform (FFT) algorithm. However, the use of the FFT requires a fixed sampling relationship between the discretization of the input field and the discretization of the output field. The Bluestein method is efficient and flexible in the selection of the sampling grid and uses the chirp z-transform (CZT) algorithm instead of the FFT algorithm.

[0143] 3. Zero-order (main) peak (I) from the magnitude spectrum main Find the maximum intensity of );

[0144] 4. I in the magnitude spectrum mainIgnore pixels that have signals from the peak;

[0145] 5. All other higher-order peaks (I higher Find the maximum intensity within that range;

[0146] 6. The resulting diffraction metric value is calculated in the same way as in reference [3]:

number

[0147] The experiment confirmed that the calculated pixelation noise metric matched the apparent actual diffraction in the test setup.

[0148] Multiple designs were used to test the noise metric parameters. Table 1 summarizes these tests. Column 1 lists the informal design names. Column 2 indicates the figure number in which the design is shown. Columns 7 and 8 present estimated intensity values ​​for zero- and higher-order peaks from the magnitude spectrum. Column 9 shows the resulting pixelation metric value in percentage for all designs. A lower value indicates a better diffraction level for the corresponding design.

[0149] Column 3 gives the longest length of the electrode within the building block. Columns 4 and 5 give the width (x-direction) and height (y-direction) of the building block. Column 6 gives the ratio of the longest electrode length to the diameter within the building block.

[0150] The references cited above are as follows. References are included by reference.

[0151] [1]Leutenegger, M., Rao, R., Leitgeb, RA and Lasser, T. Fast focus field calculations.Opt.Express 14,11277-11291(2006) [2] Hu, Y. et al. Efficient full-path optical calculation of scalar and vector diffraction using the Bluestein method. Light Sci.Appl.9,1-11(2020) [3] Murray, Ian B., Densmore, V., Bora, V., Pieratt, WM, Hibbard, DL, and Milster TD Numerical comparison of grid pattern diffraction effects through measurement and modeling with OptiScan software. Proc.SPIE 8016, Window and Dome Technologies and Materials XII, 80160U (2011)

[0152] Therefore, the pixelated noise metric can be calculated as follows:

[0153] First, black and white design drawings are generated for specific dimensions, with the electrode lines being black and the substrate background being white. The results herein are calculated using a common 8-bit byte to represent one pixel. In this case, 255 is used to represent white and 0 is used to represent black. The Bluestein method is then used to calculate the magnitude and angle for the chirp z-transform (CZT) without scaling. The Bluestein method is a Fourier-like transform but gives computational characteristics. Finally, the pixelated noise metric can be calculated as the ratio of the higher peak value to the principal peak value. The principal peak value is determined as the maximum intensity in the magnitude spectrum of the chirp z-transform (CZT) of the design drawing, while the higher peak value is determined as the second maximum intensity in the magnitude spectrum chirp z-transform (CZT), excluding the principal peak.

[0154] [Table 1]

[0155] Figures 4a-4i schematically show examples of substrates with a low ratio. Figures 5a and 5b schematically show examples of embodiments of substrates with a high ratio. Note that high-ratio designs have low diffraction. The ratio is calculated as the quotient of the longest length and diagonal length of a rectangle having the dimensions shown in columns 4 and 5. Column 9 is calculated as the quotient of columns 8 and 7. Columns 3, 4, and 5 are in micrometers.

[0156] Previous experimental designs have shown that it is difficult to obtain a low pixelation noise metric. However, it has been found that the design according to this embodiment makes it possible to obtain an even lower pixelation noise metric.

[0157] In embodiments, the ratio is at least 2, at least 3, at least 5, or at least 10. In embodiments, the pixelation noise metric is less than 6.10, less than 6.07, less than 6.05, less than 6, less than 5, or less than 4. In embodiments, the ratio is at least 2 and the pixelation noise metric is less than 6.07. In embodiments, the ratio is at least 3 and the pixelation noise metric is less than 6.07. In embodiments, the ratio is at least 10 and the pixelation noise metric is less than 4. Designs with high ratios can be rapidly generated and therefore easily tested and selected for any other requirements.

[0158] Figures 5a and 5b show designs with two drive electrodes on the surface of the substrate. Both designs can be modified to have only a single drive electrode on the surface of the substrate, for example, by removing one of the two drive electrodes. Such a modified design could, for example, be used in an optical modulator using a substrate with a single electrode.

[0159] The designs shown in Figures 4a-4i and 5a-5b can be realized in a single plane without intersecting electrodes. In particular, when these designs are connected to two drive buses, intersecting electrodes are not required. When three or more drive electrodes are used, or when more complex electrode patterns are used, electrode intersections may be used or may be required. However, such intersections are possible, for example, where two electrode lines intersect, and dielectric material may be placed between the electrodes. For example, such an insulator may be deposited at the intersection site. For example, the first drive electrode is in a first plane of the substrate, and the second drive electrode is in a second plane of the substrate.

[0160] Figure 6a schematically shows an example of an embodiment of the building block 601. Figure 1d shows an L-shaped drive bus for a substrate, and the building block 601 is similar in that respect, except that the drive bus is applied to building blocks that are repeated across the substrate. This offers further advantages.

[0161] Figure 6a shows the drive buses for each of the two drive electrodes. Schematically, the configuration of the drive electrodes is shown inside the building block 601. The two drive buses are patterned to indicate that they drive different drive electrodes. Each of the two drive buses has two arms; the two arms extend along two sides of the building block, which meet at the corner of the building block. In this example, the building block is square, but this is not necessary. One of the two arms extends along the entire length of the side, while the other arm is shortened to avoid electrical contact with the other drive bus. For example, the gap remaining between the two drive buses could be the same size as the gap between the drive electrodes, e.g., 50 micrometers. Note that the drive electrodes are partially connected through the drive buses. Part of the drive electrode connects to the drive bus in the x-direction, while the other part connects to the side in the y-direction.

[0162] The building blocks 601 formed in this manner can be repeated across the substrate in various ways.

[0163] Figure 6b schematically shows an example of an embodiment of the substrate 602. In Figure 6b, the building blocks of Figure 6a have been copied multiple times. To obtain the substrate 602, the building blocks are copied by repeated translation in the x and y directions. Each of the building blocks shown in Figure 6b can be obtained by the direct translation of any other building block.

[0164] A drawback of this configuration is that the drive buses of different drive electrodes ultimately face each other. To avoid short circuits, a small amount of space is left between the drive electrodes, for example, a width equivalent to 50 micrometers. Although not shown in Figure 6b, the various parts of the translated drive bus need to be connected together, for example, by electrode lines.

[0165] For example, as indicated by arrow 640, a vertical groove is formed; that is, two parallel electrode lines are close to each other. Similar grooves exist in the horizontal direction. Such grooves have been found to adversely affect diffraction. While a design with low diffraction may still be better than a pattern using inferior building blocks, it is desirable to avoid these grooves.

[0166] Figure 6c schematically shows an example of an embodiment of substrate 603. In substrate 603, the building blocks are repeated across the substrate but are positioned to avoid grooves, as in Figure 6b. In this embodiment, the building blocks are translated and mirrored in two directions.

[0167] Building block 611 is mirrored in the y-direction to form building block 621. Building block 621 is positioned directly below building block 611. Building block 611 is mirrored in the x-direction to form building block 612. Building block 612 is positioned directly to the right of building block 611. Building block 611 is mirrored in both the x-direction and the y-direction to form building block 622. For example, the mirroring may have the edges of the building block as the mirroring axis.

[0168] By mirroring the building blocks, it is ensured that the drive buses of the same drive electrode end up adjacent to each other on the substrate. Merging these drive buses avoids grooves and reduces diffraction.

[0169] In embodiments, at least the drive electrodes on the substrate have mirror symmetry; in embodiments, the drive electrodes and drive bus have mirror symmetry. For example, the substrate is symmetrical with respect to the x-axis and / or y-axis. This is a significant advantage during manufacturing because it allows the upper and lower substrates to be equal. Eliminating the need to produce separate substrates for the upper and lower parts of the optical modulator also eliminates the need to monitor separate types of substrates. Furthermore, having symmetry in the substrate allows a broken upper substrate to be replaced by a lower substrate, and vice versa, because they are the same. A straight line along the axis of mirror symmetry, for example, the drive bus, is useful because the design can be mirrored around that axis. Using building blocks in mirrored or non-mirrored forms helps to create a mirror-symmetric design.

[0170] This is particularly advantageous when manufacturing using a photolithography step for patterning the electrodes, because the same substrate patterning can be used for both substrates of the optical modulator, limiting production costs. The presence of straight busbars attached to the building blocks or parts of each building block facilitates this effect. Having a symmetrical design in one direction to use the same electrode pattern for all substrates is possible without straight busbars, for example, by local modifications of the electrode design at the edges of the symmetric lines. In embodiments, the driving electrode pattern has at least one symmetry in one direction, for example, by tiling the building blocks with a mirroring and / or rotatable electrode pattern design across the substrate.

[0171] Figure 6d schematically shows an example of an embodiment of substrate 604. In substrate 604, the building blocks are repeated across the substrate but are positioned to avoid grooves, as in Figure 6b. In this embodiment, the building blocks are translated, mirrored, and rotated over 180 degrees.

[0172] Building block 651 is mirrored in the y-direction to form building block 661. Building block 661 is positioned directly below building block 651. Building block 651 is point-reflected, for example, rotated by 180 degrees, to form building block 652. Building block 652 is positioned directly to the right of building block 651. Building block 651 is mirrored in the x-direction to form building block 662.

[0173] Note that the odd-numbered rows on board 604 are the same as the odd-numbered rows on board 603. The even-numbered rows on board 604 are the same as the even-numbered rows on board 603, except that they are translated in the y-direction across the building blocks.

[0174] By mirroring the building blocks, it is ensured that the drive buses of the same drive electrode end up adjacent to each other on the substrate. Merging these drive buses avoids grooves and reduces diffraction.

[0175] The advantage of the patterns in Figures 6c and 6d is that both reduce diffraction. The disadvantage of the pattern in Figure 6c is that the connection point of one of the drive electrodes at the top and bottom of the substrate is much smaller than the connection point of the other electrode. This is not necessarily a problem, as such electrical connections can be easily made, however this problem is avoided in Figure 6d, where both electrodes can be easily connected at the top and bottom of the substrate 604. Note that the far right drive bus of the substrate 604 may extend to the right at the top and / or bottom if so desired.

[0176] Another way to obtain the drive bus pattern in Figure 6d is to translate building block 651 one block to the right and invert its electrodes, so that, for example, a drive bus that previously drove the first electrode now drives the second electrode, and vice versa. The next row, starting with block 661, may be obtained by mirroring row 651. This transformed pattern will give the same pattern for the drive bus, but will produce a difference when applied to the main line. When the pattern of the main line is inverted rather than point-reflected, it will probably look quite different.

[0177] However, it should be noted that while the drive electrode pattern may follow the same mirroring and translation pattern as the drive bus, this is not required. The drive electrode may follow a different pattern, for example, a translation similar to that in Figure 6b, or something similar. This would mean that the drive bus could look like, for example, Figure 6c or 6d, but the main line is identical from block to block.

[0178] The advantage of a drive bus extending across the substrate is that the length along the drive electrode to a point on the substrate is shorter. Furthermore, the length is more uniform, meaning there is less difference between the length of a first electrode near a certain point and the length of a second electrode near a certain point.

[0179] A drive bus is not required. One or more or all of the drive electrodes on the board may be powered from a drive bus applied on the same edge of the board and from a separate source. For example, the drive electrodes may be connected via vias from one surface of the board, e.g., the inner surface, and a second surface of the board, e.g., the outer surface. The vias on the outer surface may be connected to the same or similar power supply that may be used for the drive bus. For example, the drive bus may be applied on the outer surface from the edge of the board to the vias; other configurations are possible. The connection to the power supply may be through a controller.

[0180] For example, drive electrodes may be insulated from the edges of the substrate; for example, an insulated drive electrode may be surrounded on all sides by other drive electrodes. Using insulated electrodes significantly simplifies pattern design because it is no longer necessary to ensure that each drive electrode can reach the drive bus. For example, an insulated drive electrode may be connected from the inside to the outside using vias, and the vias may be connected to a controller.

[0181] Vias may also be used to connect one portion of a drive electrode to another portion of the same drive electrode. For example, a drive electrode may have two portions that are insulated from each other, for example, two portions that are insulated from each other because another drive electrode extends between them. Connecting two portions across their inner surfaces may cause an electrical short circuit. In embodiments, two or more portions are each connected from the inside to the outside by vias. On the outside, the vias are electrically connected to each other; thus, they form a drive electrode from that portion.

[0182] Returning to Figure 5a, this type of electrode design can be constructed from tessellations. Particularly useful sources for electrode designs are Delaunay triangulations and their corresponding Voronoi duals. These triangulations are a direct method for quickly generating a large number of tessellations, for example, to optimize the design. However, other planar tilings, such as randomization of regular tiling, or even aperiodic tilings like Penrose tiling, may be used instead.

[0183] The inventors refer to Yonghe, L. et al. (2013). "A Simple Sweep-line Delaunay Triangulation Algorithm." In: Journal of Algorithms and Optimization (JAO) 1.1, pp. 30-38. The paper is included by reference.

[0184] For example, the following algorithm may be followed. While the embodiment is described for covering a substrate, it may be similarly used for covering building blocks.

[0185] I: Generate a semi-randomized point distribution within a specific area. A first set of points covering the substrate is obtained. For example, to obtain a semi-randomized distribution of points crossing the substrate, the following may be done:

[0186] Step 1 - All points are initially distributed at equal intervals within the area.

[0187] Step 2 - Next, for each point, create small random variations in the x and y coordinates. For example, the range of random variation may be set so that it does not exceed 30% of the initial distance between equally spaced points. Another way to obtain such a pattern is to pick points from a suitable distribution.

[0188] II: Calculate the first and second networks

[0189] Step 3 - Calculate the triangulation. For example, a point may be triangulated, and each point is connected to 6 neighboring points: perhaps excluding the edges and corners of the substrate. Delaunay triangulation was found to work well for this step. Delaunay triangulation is an example of tiling.

[0190] The Voronoi pattern or Voronoi-like pattern is then calculated from the triangulation, for example, as follows: Step 4 - Create a second set of points corresponding to the center of the triangle.

[0191] Step 5 - Optionally, create small random variations in the x and y coordinates for each triangle center point. For example, the random variation may be similar to that for the first set of points, and for example, the variation may not be greater than 30% of the initial distance between the points.

[0192] Step 6 - Connect together the second set of points that cross the boundary of the triangle; for example, calculate the dual graph for the triangulation. For example, the center point is connected to its direct neighbor.

[0193] If the tiling used is a Delaunay triangulation and the shifting of an optional second set of points is skipped, the resulting second network is a Voronoi network. If a different type of tiling or triangulation is used, or if the center point is shifted, the resulting grid of polygons will not be strictly a Voronoi network, but it will resemble such a network and be suitable for use in an optical modulator.

[0194] III: Creation of the first and second electrode patterns At this point, two networks are created: a second network, a Voronoi-like pattern of polygons, and a first network, for example, a Delaunay triangulation. The two patterns are, respectively, the other dual or nearly dual, depending on the randomization.

[0195] From a second network, for example, a Voronoi network, the pattern for the second electrode can be obtained by breaking selected edges of the Voronoi polygon, for example, walls. From the first network, for example, a triangulation, the electrode for the first electrode can be obtained.

[0196] Step 7 - Remove edges from the second network (e.g., a Voronoi-like network) until the network is reduced to a tree. This can be done by a path-finding search algorithm for the first network, e.g., a triangulation, starting from a point in the first set of points, e.g., the center in a Voronoi polygon. The path-finding algorithm attempts to find a path to each node of the first network. Such an algorithm is also known as a spanning tree-finding algorithm for a graph.

[0197] Such search algorithms can be depth-first search or breadth-first search. Breadth-first search provides long, very straight patterns, while depth-first search provides short, non-straight patterns. The best results were obtained by following a mixture of depth-first and breadth-first search algorithms. For example, the depth-first or breadth-first search steps may be selected by a probability distribution, which may depend, for example, on the depth of the search. A suitable distribution is the gamma distribution.

[0198] When an edge in the first network is included in the spanning tree, the dual edge in the second network that intersects the added edge in the first network is removed. Therefore, the resulting spanning tree of the first network may produce a tree or forest in the second network, such as a Voronoi network. If the second network is not completely reduced to a tree or forest, this can be achieved by removing further edges within the second network.

[0199] In this way, two trees are created that cover the substrate and interlock as needed for the optical modulator. The pattern in Figure 5a was obtained using the algorithm described above.

[0200] Once a suitable graph is obtained, it can be translated into an actual electrode design by assigning thickness to all path segments. For example, a thickness of 10 micrometers may be used. A mask layout tool may be used, for example.

[0201] Further modifications that may be made to the design include: - This includes screening design units to eliminate shortcuts between electrode 1 and electrode 2. Increased thickness may introduce shortcuts. These can be avoided by iterating the process, moving edges or nodes, and iterating the generation process. - Including the possibility of additional drive buses. - This includes integrating the second electrode. It may occur that the second electrode is a forest rather than a tree. This can be resolved by adding an edge, typically connecting to the drive bus, and thus integrating the forest into a tree. - This includes correcting the point coordinates of the electrodes to maintain, for example, a minimum line gap of 20 μm between electrodes, and / or to maintain, for example, an average line gap of 50 μm between electrodes. - In particular, when a cover drive bus is not used, this includes shifting electrodes to allow the design to be stitched together and to ensure the continuity of electrodes from one unit to another. - This includes shifting electrodes to reduce optical diffraction, refraction, scattering, or moiré patterns. - This includes improving or optimizing the randomization of short segment orientations to reduce light diffraction, refraction, scattering, or moiré effects. This allows for less confusion when viewing through a display. - Further randomization may be achieved by transforming straight segments between points into curved segments. For example, splines may be used between points.

[0202] It has been found that further design optimization can be advantageously carried out in several optimization loops. For example, after generating the first and second electrode segments using the above tessellation-based procedure or a Turing pattern-based procedure or similar, the segments can be transformed into paths that give width to the segments. For example, the segments may represent the center lines of polygons of a certain width. While this procedure will work well most of the time, it may have undesirable effects, so further optimization may be possible.

[0203] For example, (A) it can be verified that the first path does not come into contact with the second path. If this condition is violated, one or both of those paths, for example, the first path, may be modified so that the first path no longer comes into contact with the second path.

[0204] For example, (B) it can be verified that all first paths are connected to a single first electrode. If this condition is violated, paths may be created and / or deleted in order to connect all first paths to the first electrode.

[0205] For example, (C) it can be verified that all second paths are connected to a single second electrode. If this condition is violated, paths may be created and / or deleted in order to connect all first paths to the first electrode.

[0206] Parts B and C may be repeated in the loop until both electrodes are fully connected. Note that, for example, adding a drive bus to the design, as described herein, may help in integrating the electrodes. Part A may also be repeated in this loop if necessary.

[0207] Once the first and second electrodes are fully connected and no longer short-circuit, the next optimization loop can be performed.

[0208] For example, (D) it can be verified that the distance between the first electrode and the second electrode is always within a predetermined range. If this condition is violated, the paths of the first and / or second electrodes can be modified to maintain the distance within that range.

[0209] Part D may be repeated until no points are found where the electrodes are too close or too far apart.

[0210] These optimizations may be performed in a computer-implemented method for optimizing the electrode pattern. Further or alternative optimizations may be added herein, for example, as proposed above. For example, the design may be iterated for optical performance, for length ratio, and so on. For example, since the cost of generating initial patterns for the first and second paths is low using tessellation or similar, the optimization process has the option to terminate the optimization and start from a new pattern if insufficient progress is made. In embodiments, the paths are modified not by themselves, but by a first set of points and a second set of points, and generation is iterated from that point onward.

[0211] The electrode obtained through this procedure has a large number of branch nodes and typically has many different angles. These factors are advantageous for low diffraction. For example, an advantageous substrate for use in an optical modulator comprises a plurality of interdigitated drive electrodes applied to the substrate, each of the plurality of drive electrodes is arranged in a pattern across the substrate, the plurality of interdigitated drive electrodes are arranged alternately with respect to each other on the substrate, and at least one of the first and second drive electrodes is a spanning tree of the tessellation.

[0212] A computer-implemented method for obtaining a first electrode design and a second electrode design for use on a substrate of an optical modulator, wherein both the first and the second electrode cover the substrate to provide a configurable electric field within the optical modulator, the method comprising: - obtaining a tessellation (100) of the substrate, the tessellation comprising a plurality of cells (101; 102; 103) that cover the substrate without overlapping, - obtaining a center point (111) within each cell of the tessellation, - calculating a spanning tree (Figure 1c) for the center points, wherein edges of the spanning tree represent two neighboring cells of the tessellation, - deriving a first electrode design (121) from the spanning tree, - deriving a second electrode design (122) from the tessellation, wherein said deriving comprises removing portions of the tessellation where edges of the spanning tree intersect boundaries of cells of the tessellation which comprises the above steps.

[0213] Several variant embodiments are contemplated. For example, in the above embodiments, any one of the following variants may be added.

[0214] 1. Tessellation a. the tessellation is aperiodic and / or randomized, b. Tessellation is a Voronoi diagram and / or a perturbed Voronoi diagram. c. An initial set of randomized points covering the substrate is selected, the triangulation of the set of points is calculated, and the tessellation is obtained as the dual of the triangulation. i. Triangulation may be a Delaunay triangulation. ii. A set of points may be obtained by perturbing a uniform set of points taken from a distribution, such as a Poisson distribution. iii. The dual may be calculated from a selected point within the triangle, such as the circumcenter. d. The maximum diameter of each cell is less than the threshold, e.g., 50 μm.

[0215] 2. Spanning trees a. Spanning tree computation iteratively constructs a spanning tree by selecting cells from a tessellation that have unvisited neighborhoods visited by a partial spanning tree, and the spanning tree is extended by visiting one of several unvisited neighborhoods. i. The selection of visited cells may be a combination of depth-first and breadth-first classifications, for example, a gamma distribution.

[0216] 3. Correct electrodes a. Integrate the electrodes i. Determine the components and combine them. 1. For example, by connecting subplanes, or by assigning a separate subplane to each electrode and connecting within those subplanes. Components can also be joined along the edges of planes, by tiling the design, or by drive buses between building blocks. 2. Select two neighboring components, reinsert the removed portion of the tessellation, and connect them by removing the corresponding edges of the spanning tree, and / or vice versa. b. Destroy the circular part of the second electrode. c. Correct the shortcut between the first and second electrodes caused by giving width to the electrodes by moving the portions of the first and / or second electrodes. d. Verify and correct the optical properties. i. The distance from any point in the plane to the first electrode and the distance to the second electrode should both be less than a threshold (e.g., 50 μm), or their sum should be less than a threshold (50 μm). ii. The distance from a point on the first electrode to the second electrode should be at least the second threshold (20 μm), and vice versa.

[0217] 4. Optimal modulator a. An optical modulator according to a conventional claim, wherein the first and second electrode designs are made by the design method described in any one of the preceding claims.

[0218] It should be emphasized that the above method is not the only way to obtain a design with a low pixelation noise metric or a high ratio of electrode length to diagonal. For example, instead of using a Voronoi network, a Turing pattern-based network may be used; see, for example, the paper "The chemical basis of morphogenesis" by Alan Mathison Turing, included herein by reference.

[0219] The design in Figure 5b was not obtained from tessellation, but still yields good values. For example, the design in Figure 5b includes a spiral. In the spiral, the first and second electrode lines, belonging to the first and second drive electrodes respectively, are spiral on the substrate. Even if some electrical lines are roughly parallel in the area between the spirals, the pattern as a whole yields good values. The pattern may be further improved by making the spirally configured lines undulate, particularly in the other turns of the spiral, e.g., turns 1-3. Such undulation may be, for example, by adding protrusions that disrupt the pattern to the electrode lines, as shown in Figure 4e or Figure 4f. For example, all lines within the spiral may undulate, having an amplitude of undulation, e.g., protrusions that decrease toward the center of the spiral.

[0220] The two substrates according to the embodiment may be combined to form an optical modulator. The optical modulator is particularly suitable for glazing. An exemplary embodiment of the optical modulator is shown below.

[0221] Figure 7a schematically shows an embodiment of the optical modulator 10 that may be applied in smart glazing.

[0222] References are made to patent application PCT / EP2020 / 052379, which is incorporated herein by reference; this application includes, for example, advantageous designs for optical modulators that can be further improved by including electrodes, buildable blocks, and / or substrates as described herein.

[0223] The optical modulator 10 can be electronically switched between a transparent state and a non-transparent state, and vice versa, or between a reflective state and a non-reflective state, and vice versa. The optical modulator 10 comprises a first substrate 11 and a second substrate 12 arranged opposite each other. At least two electrodes are applied to the inside of the first substrate 11: electrodes 13a and 13b are shown. These at least two electrodes together are called electrodes 13. At least two electrodes are applied to the inside of the second substrate 12: electrodes 14a and 14b are shown. These at least two electrodes together are called electrodes 14.

[0224] The fluid 15 is provided between the substrates. The fluid contains particles 30, such as nanoparticles and / or microparticles, which are electrically charged or can be charged. For example, particles may inherently have an electric charge on their surface. For example, particles may be surrounded by charged molecules.

[0225] The electrodes are positioned to drive the particles 30 to move toward or away from the electrodes, depending on the applied electric field. The optical properties of the optical modulator, in particular its transparency or reflectivity, depend on the location of the particles 30 in the fluid. For example, connections may be provided to apply an electromagnetic field to the electrodes.

[0226] At least one electrode, but preferably both electrodes 13 and 14, are shown schematically in the figures, according to the embodiment.

[0227] In an embodiment, at least one of the electrode pattern on the first substrate and the electrode pattern on the second substrate has a calculated low pixellation noise metric that contributes to diffraction. Interestingly, the electrode patterns on the substrates may not individually meet the limit for their pixellation noise metric, but their combination, that is, their superposition, may meet the limit. Since this is the pattern that will be visible when viewed through the light modulator, a low pixellation noise metric in the superposition will contribute to similarly low diffraction. Suitable limits for the pattern on the first and / or second substrate or for the superposition include: less than 6.05% or 5% or 4%.

[0228] In an example, the substrate 11 and the substrate 12 may be optically transparent outside the electrodes, typically >95% transparent at the relevant wavelength, for example >99% transparent. Considering the electrodes, the transparency can be much lower, for example 70%. The term "optical" may relate to wavelengths visible to the human eye (about 380nm to about 750nm) where applicable, and may relate to a broader range of wavelengths including infrared (about 750nm to 1 μm) and ultraviolet (about 10nm to 380nm) and subselections thereof where applicable. In an exemplary embodiment of the light modulator, the substrate material is selected from glass and polymer.

[0229] In another example, one substrate, such as the lower substrate 12, may be reflective or partially reflective, while the upper substrate 11 is transparent. The optical properties of the light modulator, in particular the reflectivity, depend on the location of the particles 30 within the fluid. When the panel is in an open state (vertical driving), the particles will be located approximately between the opposite electrodes of the two substrates, whereby incident light can pass through the transparent upper substrate and optical layer relatively unobstructed and be reflected or partially reflected on the lower substrate.

[0230] The distance between the first substrate and the second substrate is typically less than 30 μm, for example, 15 μm. In an exemplary embodiment of the optical modulator, the distance between the first substrate and the second substrate is less than 500 μm, preferably less than 200 μm, preferably less than 100 μm, and more preferably less than 50 μm, for example, less than 30 μm.

[0231] In the example, the modulator may be made of a flexible polymer, and the rest of the device may be made of glass. The glass may be hard glass or flexible glass. If required, a protective layer may be provided on the substrate. If two or more colors are provided, two or more layers of flexible polymer may be provided. The polymer may be polyethylene naphthalate (PEN), polyethylene terephthalate (PET) (optionally having a SiN layer), polyethylene (PE), etc. In further examples, the device may be made of at least one flexible polymer. Thus, the modulator may be attached to any surface by means of an adhesive, for example.

[0232] Particle 30 may be adapted to absorb light, thereby preventing certain wavelengths from passing through. Particle 30 may reflect light; for example, the reflection may be specular, diffuse, or somewhere in between. Particles may absorb some wavelengths and reflect others. Particles may emit light, either similarly or instead, using, for example, phosphorescence, fluorescence, or similar phenomena. Even fluids may emit light whose emittance is modulated by changing the location of particles.

[0233] In exemplary embodiments of the optical modulator, the size of the nanoparticles ranges from 20–1000 nm, preferably 20–300 nm, and more preferably less than 200 nm. In exemplary embodiments of the optical modulator, the nanoparticles / microparticles include a pigment coating and may preferably include a core. In exemplary embodiments of the optical modulator, the particle coating is made from a material selected from conductive and semiconducting materials.

[0234] In an exemplary embodiment of the optical modulator, the particles are adapted to absorb light having wavelengths of 700 nm–1 μm and 10–400 nm, such as 10 nm–1 mm, 400–800 nm, and / or to absorb (filter) a portion of light having a wavelength range that falls within 10 nm–1 mm, and combinations thereof.

[0235] In an exemplary embodiment of the optical modulator, the particles are electrically charged or can be charged. For example, the charge on a particle is 0.1e to 10e per particle (5 * 10 -7 It may be -0.1C / m2.

[0236] In an exemplary embodiment of the optical modulator, the fluid is present in amounts such as 1-1000 g / m², preferably 2-75 g / m², more preferably 20-50 g / m², for example 30-40 g / m². A major advantage of this layout is that much less fluid and similar particles can be used.

[0237] In an exemplary embodiment of the optical modulator, the particles are present in amounts such as 0.01–70 g / m², preferably 0.02–10 g / m², for example, 0.1–3 g / m².

[0238] In an exemplary embodiment of the optical modulator, the particles have colors selected from cyan, magenta, and yellow, and from black and white, and combinations thereof.

[0239] In an exemplary embodiment of the optical modulator, the fluid comprises one or more surfactants, emulsifiers, polar compounds, and compounds capable of forming hydrogen bonds.

[0240] The fluid 15 may be a nonpolar fluid having a dielectric constant less than 15. In an exemplary embodiment of the optical modulator, the fluid has a relative permittivity εr less than 100, preferably less than 10, for example less than 5. In an exemplary embodiment of the optical modulator, the fluid 15 has a dynamic viscosity greater than 10 mPa·s.

[0241] Electrodes 13a, 13b and electrodes 14a, 14b are in fluid contact with a fluid. The fluid may be in direct contact with the electrodes, or indirectly, for example, the fluid may be in contact with a second medium having electrodes, such as through a porous layer. In embodiments, the electrodes cover about 1-30% of the substrate surface. In embodiments, the electrodes have an electrical conductivity > 1 (at 20°C). * 10 7 The materials include electrically conductive materials having a resistivity less than 100 nΩm (at 273 K; for comparison, ITO, which is typically used, has 105 nΩm), similar to S / m. In embodiments of the optical modulator, the electrodes include copper, silver, gold, aluminum, graphene, titanium, indium, and combinations thereof, preferably copper. The electrodes may be in the form of microwires embedded in a polymer-based substrate; for example, copper microwires.

[0242] A connection for applying an electromagnetic field to electrodes may be provided, where the applied electromagnetic field to the electrodes results in the movement of nanoparticles and microparticles from a first electrode to a second electrode and vice versa. For example, in an exemplary embodiment of an optical modulator, the current is between -100 and +100 μA, preferably -30 and +30 μA, and more preferably -25 and +25 μA. For example, a power supply may be electrically connected to at least two electrodes. The power supply may be adapted to provide waveform power. At least one of amplitude, frequency, and phase may be adaptable to provide different states within the optical modulator. For example, the power mode may be adapted by a controller.

[0243] The optical modulator 10 may have one or more segments, each segment being a single optically switchable entity whose size may vary. The substrate at least partially confines the volume that may be the segment.

[0244] This device may include driver circuits for changing the appearance of (individual) segments by applying an electromagnetic field. Therefore, similarly, the appearance of the optical modulator or one or more parts thereof may change. For example, the segments may be at least 1 mm in diameter. 2 This design may have an area of ​​[a certain size]. This design allows for stacking to enable more colors; for example, in a full-color application, stacking two or three modulators may provide most or all of the colors, respectively.

[0245] Having one or more segments allows for localized control of the optical modulator; this is advantageous for some applications, but not always necessary. In smart glazing, optical modulators may be used with or without segments. For example, when applied in smart glazing, transparency or reflectivity can be locally controlled, for instance, to prevent sun-patch without reducing the overall transparency or reflectivity of the window. Segments can be relatively large, for example, having a diameter of at least 1 mm or at least 1 cm.

[0246] In an exemplary embodiment of the optical modulator, the substrates (11, 12) are aligned and / or the electrodes (13, 14) are aligned. For example, electrodes 13a, 13b and electrodes 14a, 14b may be aligned so that they face each other. In aligned substrates, electrodes on different substrates are behind each other when viewed in a direction perpendicular to the substrates. When the optical modulator is disassembled and the substrates are together with the electrodes facing upward, the electrode patterns are mirror images of each other.

[0247] Aligning substrates may increase the maximum transparency or reflectivity of an optical modulator, while in some cases, when selecting an optical modulator for more criteria, such as a range of transparency or reflectivity, it may be better not to align the two substrates or to not align them completely. Optical modulators can be stacked. For example, two stacked optical modulators may be made from three substrates, with the central substrate having electrodes on both of its surfaces. In embodiments of the optical modulator, optionally, at least one substrate 11, 12 of the first optical modulator is the same as the substrate 11, 12 of at least one second optical modulator. In the case of stacked modulators, alignment may increase the maximum transparency or reflectivity, but it may be detrimental to other considerations, such as diffraction.

[0248] Figure 7b schematically shows an example of an embodiment of the optical modulator 40. The optical modulator 40 is similar to the optical modulator 10, except that it comprises multiple optical layers; two optical layers are shown in the example. Three or more optical layers may be present. Each optical layer is located between two substrates. The optical modulator 40 can be considered a laminate of two-substrate optical modulators, as shown in Figure 7a. As shown, the optical modulator 40 comprises three substrates: a first substrate 41, a second substrate 42, and a third substrate 43. There is an optical layer between substrates 41 and 42, and an optical layer between substrates 42 and 43. The optical layers may be similar to the optical layers of the optical modulator 10. The controller 46 is configured to control the current on the electrodes of the substrates. For example, in Figure 7b, the controller 46 may be electrically connected to at least 4 × 2 = 8 electrodes.

[0249] Interestingly, particles within multiple optical layers may differ, so that multiple layers can be used to control more optical properties of the optical modulator. For example, particles in different optical layers may absorb or reflect at different wavelengths, and may have different colors, for example. This can be used by the controller 46 to create different colors and / or different color intensities on the panel. For example, a four-substrate panel may have three optical layers, each with different colored particles, e.g., cyan, yellow, and magenta. By controlling the transparency or reflectivity of different colors, a broad color spectrum can be created.

[0250] The surface of a substrate facing another substrate may be supplied with two or more patterns, for example, as in the embodiment. For example, the outer substrates 41 and 43 may receive electrodes only on their inner surfaces, while the inner substrate, for example, substrate 42, may have electrodes on both sides.

[0251] Substrates 41 and 42 may both be considered embodiments of an optical modulator. Similarly, substrates 42 and 43 may both be considered embodiments of an optical modulator.

[0252] Figure 7c schematically shows an example of an embodiment of a car 20 having smart glazing for a window 21. This is a particularly advantageous embodiment because the level of incident light can be changed frequently and rapidly while driving. Using smart glazing in a car has the advantage that the light level can be maintained at a constant level by adjusting the transparency of the car's windows. Furthermore, the reduced diffraction effect improves safety by reducing driver distraction. The car 20 may include a controller configured to control the transparency or reflectivity of the window 21.

[0253] Smart glazing can be used in other glazing applications where the amount of incident light is variable, such as in buildings, offices, homes, greenhouses, and skylights. A skylight is a window placed in the ceiling to allow sunlight to enter a room.

[0254] An optical modulator may have two optical states, for example, a transparent state and an opaque state or a reflective state and an antireflective state. An optical modulator, for example, optical modulator 10 or optical modulator 40, - By creating an alternating current voltage on at least one of the first and second substrates, and applying an alternating current between at least a first electrode and a second electrode on the first substrate, and / or between a first electrode and a second electrode on the second substrate, a second optical state, for example, an opaque state or an anti-reflective state, - Switch to a first optical state, e.g., a transparent state or a reflective state, by creating an alternating voltage between the first substrate and the second substrate, and applying an alternating current between the first electrode on the first substrate and the first electrode on the second substrate, and / or between the second electrode on the first substrate and the second electrode on the second substrate. It may be configured in this way.

[0255] The electrode pattern on the first substrate is at least partially arranged in the same pattern as the second electrode on the second substrate. Typically, the electrodes face each other, but the patterns of the first and second electrodes may be shifted relative to each other.

[0256] A protective coating may be provided on at least a portion of the inner surface area of ​​at least one of the first and second substrates.

[0257] The drive signal applied to the drive electrode typically has a varying voltage. For example, a power supply may operate at an AC frequency to switch between a transparent and an opaque state. Such a signal may have a frequency between, for example, 1-1000 Hz. A balanced electrolytic current may be obtained by continuously switching the polarity of oppositely charged electrodes on and / or between the first and second substrates.

[0258] Figures 8a-8b schematically show side views of an embodiment of an optical modulator in use. Applying an electric field to electrodes on a substrate induces an electric force on particles. Using this effect, particles can move around, so different transparency or reflectivity states can be induced within the optical modulator. A controller may control the electric field, for example, its amplitude, frequency, and phase. In embodiments, the controller is connected to at least four electrodes: two electrodes for each substrate. However, more electrodes may be used and connected to the controller; for example, three or more electrodes may be used for a substrate to better fine-tune grayscale and drive it into an opaque or non-reflective state. Multiple electrodes may also be used to support multiple segments on a substrate.

[0259] Figure 8a shows an optical modulator in a state where no electric field is applied. In Figure 8a, no electric force is yet applied to the particles 30 suspended in the fluid 15.

[0260] In the configuration shown in Figure 8a, the conductive electrode pattern on the upper substrate is perfectly or substantially aligned with the conductive electrode pattern on the lower substrate. The conductive electrode pattern may be deposited on a transparent or (partially) reflective glass substrate, or embedded in a plastic substrate or the like.

[0261] Alignment between the upper and lower electrode patterns contributes to a wider range of achievable levels of transparency or reflectivity. However, alignment is not necessary, as similar effects can be obtained without alignment. A similar range of transparency or reflectivity can be obtained without alignment.

[0262] Note that in these examples, references to the upper and lower boards refer to the board that is higher or lower on the page. The same board may also be referred to as, for example, the front board and the rear board, because in glazing applications, the boards will be aligned vertically rather than horizontally.

[0263] Figure 8b shows an optical modulator, for example in instance P1, where a potential +V1 is applied to each microwire electrode on the upper substrate, while a negative voltage, for example -V1, is applied to each microwire electrode on the lower substrate. Therefore, in this case, the same positive potential is applied to all electrodes 13, and the same negative potential is applied to electrode 14. The potential difference causes negatively charged particles to flow near the electrodes on the upper substrate, where the particles substantially align with the upper electrodes. As a result, if both the upper and lower substrates are transparent, the transparency of the optical modulator 10 will increase. Similarly, for example, if the upper substrate is transparent and the lower substrate is reflective, the reflectivity of the optical modulator 10 will increase if the solution contains positively charged particles that flow near the electrodes on the lower substrate, where these particles substantially align with the lower electrodes.

[0264] Similar transparency or reflectivity can be achieved in a second instance P2 in the ON state, where the voltages of the upper and lower electrodes are inverted in contrast to instance P1. In instance P2, the voltage of each electrode on the upper substrate is supplied with a negative potential -V1, while the voltage of the aligned electrodes on the lower substrate is supplied with a positive potential. This state is similar to the state shown in Figure 8b, but the upper and lower substrates are inverted. Similarly, in this configuration, the transparency or reflectivity of the optical modulator 10 is high.

[0265] Interestingly, transparency or reflectivity can be maintained while reducing corrosion damage to the electrodes by switching between, for example, the positive potential of the electrode on the upper substrate (and the negative potential on electrode 14), shown as electrode 13 in Figure 8b, and the positive potential of the electrode on the lower substrate, shown as electrode 14 in Figure 8b. This alternating electric field can be achieved by applying an alternating potential to the upper and lower electrodes.

[0266] Applying a waveform is optional but a useful measure to increase the lifespan of the optical modulator by reducing corrosion. Corrosion can form, for example, when using copper electrodes, because copper ions dissolve in the ionic fluid on one substrate and flow to the electrode on the opposing substrate, where the copper ions deposit. By applying a waveform, the direction of copper ion transport is frequently reversed, thus reducing corrosion damage. Between two instances P1 and P2, the corrosion currents between the two substrates are balanced, or substantially balanced, for example, >95%, for example, when a corrosion rate occurs on the electrode of the upper plate, there is a balanced deposition of copper on the lower electrode between instances P1 and in the same way between instances P2. Thus, particles continuously migrate or move between the upper and lower electrodes, the optical modulator or smart window is always on, while the dynamic electrolytic current between the upper and lower electrodes is constant, and therefore the net loss of electrode material on the upper and lower electrodes is zero or negligible.

[0267] Figure 8c illustrates how a reduced transparency or reflectivity state can be obtained. An AC voltage is applied to the same substrate. For example, in an embodiment, as shown in Figure 8c, a potential +V2 is applied to the first electrode, and the next immediately adjacent electrode has the opposite potential -V2, and so on. This can be achieved by applying a potential +V2 to electrode 13a and the opposite potential -V2 to electrode 13b. On the opposing substrate, a potential +V2 may be applied to electrode 14a and the opposite potential -V2 to electrode 14b. For example, the electrodes may be arranged so that the electrodes on the substrate are aligned; an electrode on the upper substrate has a counter electrode on the lower substrate, and vice versa. For example, to reduce transparency or reflectivity, the counter electrodes may receive the same potential, while the neighboring electrodes receive the opposite potential. An embodiment is shown in Figure 8c, where four electrodes are indicated by reference numerals 13a, 13b, 14a, and 14b, and the rest of the electrodes follow in an alternating manner.

[0268] By using AC drive cycles between the upper and lower substrates, oblique and transverse electric fields are generated between the two substrates, thereby causing random diffusion of particles and creating a closed state of the optical modulator. As a result of this configuration, particles move obliquely and transversely between the upper and lower substrates, and the diffusion of particles into the visible aperture of the optical modulator contributes to the closed opaque state of the optical modulator.

[0269] Regarding the transparent state shown in Figure 8b, the waveform may be applied to the electrodes such that, for example, the electrode shown in Figure 8b becomes negative when it has a positive potential, and vice versa. Similar to the case of Figure 8b, applying the waveform between electrodes 13a and 13b, and between 14a and 14b, for example, reduces corrosion damage to the electrodes.

[0270] The AC drive cycle may be implemented by using an interlocking line configuration that combines upper and lower electrode configurations, as shown in the plan view in Figures 5, 6a-6d, etc.

[0271] The degree to which transparency or reflectivity increases or decreases in Figures 8b and 8c depends on the voltage and frequency difference. By changing the voltage difference, the amount by which transparency or reflectivity increases or decreases, respectively, can be controlled. For example, a curve representing light transmittance versus voltage may be determined, for example, by measurement. A corresponding voltage, such as an AC voltage, may be applied to obtain a specific level of light transmittance, for example, a specific level of transparency, for example, a specific grayscale level. A level between transparent and opaque may be obtained by interpolating the signal for transparent or opaque states. Similarly, a curve representing light reflectance versus voltage may be determined, for example, by measurement. A corresponding voltage, such as an AC voltage, may be applied to obtain a specific level of reflectivity. A level between reflective and non-reflective may be obtained by interpolating the signal for reflective or non-reflective states.

[0272] Different electrode patterns may be used for optical modulators. Each electrode pattern may provide a certain range of grayscale, e.g., levels of transparency or reflectivity, that the optical modulator can achieve. However, the specific range of grayscale for any given electrode pattern may differ from that of another electrode pattern. In other words, different patterns may give an increase in transparency or reflectivity or an increase in opacity, but the precise response to the drive signal depends on many factors, including the specific pattern used. Variations in the optical properties of an optical modulator can have fine resolutions, for example, less than 1 mm. Note that pixilation of the optical modulator is not required to achieve different visible optical patterns in the optical modulator, e.g., a logo.

[0273] This effect can be used to embed visible images into an optical modulator by locally altering the electrode pattern on the substrate of the optical modulator. For example, different electrode patterns may locally have grayscales with a permanent grayscale offset from each other. For example, maximum transparency or reflectivity may be altered by locally changing the electrode pattern or its pitch.

[0274] The result is areas on the optical modulator having different intensities of grayscale, e.g., different grayscales, or different intensities of coloration. The areas may, however, have the same color point. In embodiments, they may switch together with the rest of the window, albeit at different speeds. For example, even if the same voltage is applied to electrodes in two different areas, they will cause different transparency states, e.g., different transmission levels, due to different electrode patterns. For example, the curve representing transmittance versus voltage may be shifted. For example, if voltage control is changed in the same way in both areas, the light transmittance in both areas may change, but by different amounts. Areas may also be made less responsive to the drive signal by reducing the density of electrodes; in particular, areas may be made not to switch at all, for example, by not applying electrodes within the area.

[0275] For example, electrode materials may include copper, aluminum, gold, and indium-tin oxide (ITO). ITO is transparent, while Cu / Al is reflective; therefore, different electrode materials may be used to obtain different appearances, regardless of the driving voltage. Similarly, different materials with different resistances will produce different electric fields. For example, ITO will have a smaller electric field even when driven by the same voltage.

[0276] An embodiment of the method for modulating light includes applying a potential to a plurality of drive electrodes applied to two opposing substrates to obtain an electromagnetic field between the plurality of drive electrodes that causes electrophoretic motion of particles toward or from one of the plurality of drive electrodes, resulting in modulation of light shining through the substrates, the two opposing substrates being as in the embodiment.

[0277] Many different ways of carrying out the method are possible, as will be apparent to those skilled in the art. For example, the order of the steps may be as shown, but the order of the steps may change, or some steps may be performed in parallel. Furthermore, other method steps may be inserted between the steps. The inserted steps may represent improvements to the method as described herein, or they may not be related to the method. For example, some steps may be performed in parallel, at least partially. Furthermore, a given step may not be completely completed before the next step begins.

[0278] Driving the electrodes may involve using a signal with a selected maximum amplitude corresponding to one of several levels of transparency or reflectivity of the optical modulator. The signal may be an alternating current or an alternating voltage.

[0279] Embodiments of the method may be executed using software that includes instructions for a processor system to perform the method. The software may consist only of steps taken by a specific sub-entity of the system. The software may be stored on a suitable storage medium such as a hard disk, floppy disk, memory, or optical disk. The software may be transmitted as a signal along a wired or wireless connection, or using a data network, such as the Internet. The software may be made available for download to a server and / or for remote use on the server. Embodiments of the method may be executed using programmable logic that performs the method, such as a bitstream configured to constitute a field-programmable gate array (FPGA).

[0280] It will be recognized that the subject matter of this disclosure extends similarly to computer programs adapted to implement the subject matter of this disclosure, particularly computer programs on or within a carrier. The program may be in the form of object code, such as source code, object code, code intermediate source, and partially compiled forms, or in any other form suitable for use in implementing embodiments of the method. Embodiments relating to a computer program product include computer executable instructions corresponding to each step of the processing steps of at least one of the described methods. These instructions may be stored in one or more files, which may be subdivided into subroutines and / or linked statically or dynamically. Another embodiment relating to a computer program product includes computer executable instructions corresponding to each of the devices, units, and / or parts for at least one of the systems and / or products described.

[0281] Figure 9a shows a computer-readable medium 1000 having a writable portion 1010 containing a computer program 1020, and also a computer-readable medium 1001 having a writable portion containing a computer program. The computer program 1020 includes instructions for causing a processor system to perform an optical modulator method, according to the embodiment. For example, the processor system may be connected to an optical modulator panel. The computer program 1020 may be embodied as a physical mark on the computer-readable medium 1000 or by magnetization of the computer-readable medium 1000. However, any other suitable embodiment is conceivable. Furthermore, although the computer-readable medium 1000 is shown here as an optical disc, it will be recognized that the computer-readable medium 1000 may be any suitable computer-readable medium such as a hard disk, solid memory, flash memory, etc., and may be non-recordable or recordable. The computer program 1020 includes instructions for causing a processor system to perform the optical modulator method.

[0282] Figure 9b shows a schematic diagram of a processor system 1140 according to an embodiment of a controller for an optical modulator. The processor system comprises one or more integrated circuits 1110. The architecture of one or more integrated circuits 1110 is schematically shown in Figure 9b. Circuit 1110 includes a processing unit 1120, e.g., a CPU, for executing computer program components to perform the method according to the embodiment and / or implement a module or unit thereof. Circuit 1110 includes a memory 1122 for storing programming code, data, etc. Part of the memory 1122 may be read-only. Circuit 1110 may include communication elements 1126, e.g., an antenna, a connector, or both, and similar. Circuit 1110 may include a dedicated integrated circuit 1124 for performing some or all of the processing defined in the method. The processor 1120, memory 1122, dedicated IC 1124, and communication elements 1126 may be connected to each other via an interconnect 1130, e.g., a bus. The processor system 1110 may be configured for contact and / or contactless communication using antennas and / or connectors, respectively.

[0283] For example, in an embodiment, the processor system 1140, for example, the device, may comprise a processor circuit and a memory circuit, the processor being configured to execute software stored in the memory circuit. For example, the processor circuit may be an Intel Core i7 processor, an ARM Cortex-R8, etc. In an embodiment, the processor circuit may be an ARM Cortex-M0. The memory circuit may be a ROM circuit or non-volatile memory, such as flash memory. The memory circuit may be volatile memory, such as SRAM memory. In the latter case, the device may comprise a non-volatile software interface configured to provide software, such as a hard drive, a network interface, etc.

[0284] For example, a controller for an optical modulator that controls the voltage applied to an electrode may include a processor circuit, or similarly, or instead, a state machine.

[0285] Figures 10a–10d schematically illustrate embodiments of an optical modulator. The modulator is illustrative and non-limiting. Figures 10a–10d correspond to the same embodiment of the optical modulator. The modulator may be advantageously combined with other features described herein. Parts of the modulator may be advantageous in an isolated state, with or without combinations of other features described herein. In particular, Figures 10a–10d provide advantageous examples such as building blocks, drive electrodes, drive buses, and bus electrode connections, each of which may be considered in an isolated state.

[0286] In an embodiment of a building block, the building block 820 in Figure 10a is an example, and the building block comprises a pattern of multiple electrodes arranged in a mating pattern. As the building block is repeated across the substrate, the electrodes terminating at the left and right edges of the building block, and the drive electrodes terminating at the top and bottom edges of the building block, match up to form multiple drive electrodes for an optical modulator. The drive electrodes are arranged in a mating pattern. It may or may not be necessary to connect the electrodes at the ends of the repeating building block in order to couple the electrodes to the drive electrodes. In the building block 820, the number of drive electrodes is two, for example, a first drive electrode and a second drive electrode. However, three or more drive electrodes are possible.

[0287] The building block 820 shown has several advantageous properties that help reduce interference in an optical modulator that includes the building block, for example, as shown in Figures 10b-10d.

[0288] For example, a first characteristic that the building block 820 satisfies is that, for at least one electrode among a plurality of inter-mating electrodes within the building block 820, the maximum length between any two points on the electrode, measured along the electrode within the building block 820, is at least twice the length of the diagonal of the building block. In practice, in this example, this characteristic is valid for multiple electrodes of the building block 820.

[0289] For example, a second characteristic that the building block 820 satisfies is that the building block 820 has electrodes that branch at nodes to form a tree. The building block 820 represents a highly branching tree, for example, where there is a first node, and at the first node, the electrodes branch into at least three lines, each of which is connected to at least three second nodes, each of which similarly branches into at least three lines. In practice, there may be three more second nodes connected to a third node, each of which the electrodes similarly branch.

[0290] For example, a third characteristic fulfilled by electrodes within a building block is that the angles at the electrode nodes are well distributed over a range of 0 to 360. For instance, the building block exhibits several angles within the range of 0-30, several angles within the range of 30-60, and several angles within the range of 330-360. In practice, any range from x to x+30 is represented by the angles in Figure 10a. In practice, this characteristic is valid for multiple electrodes within building block 820.

[0291] In building block 820, electrode lines are constructed from connected straight line segments. These line segments may be curved, or alternatively. In this example, the electrode line width within building block 820 is constant along the electrode line; this is not necessary.

[0292] For example, a fourth characteristic that a building block can satisfy is that it has a calculated low pixelation noise metric; in this case, less than 4%.

[0293] Any one of the above characteristics may be used to address interference, and they do not need to be combined, as is done in building block 820. For example, there may be characteristic 1 alone, or characteristic 2 alone, or characteristic 3 alone, or characteristic 4 alone, or a combination, e.g., 1 and 2, or 2 and 3, 2 and 4, 3 and 4, 1 and 2 and 3 and 4, 2 and 4 and 4, or any other combination possibly combined with other characteristics described herein.

[0294] Building block 820 also satisfies the constraint that the distance between two neighboring lines is greater than a minimum and less than a maximum. Building block 820 is an example of a building block in which electrodes are in the same plane and do not intersect. Note that if intersecting electrodes are desired, this is not a problem. For example, two electrodes may intersect by having an insulator between the two electrodes at the intersection. The insulator may be the substrate itself, and for example, one of the electrodes may be reoriented via two vias to extend along the back of the substrate.

[0295] Figure 10b.1 schematically shows the substrate 810 and the drive buses. Drive buses 812 and 814 are shown. To create the substrate for the optical modulator, building blocks 820 are repeated within the area bounded by the drive buses. The drive buses are positioned to drive the drive electrodes. In this example, the first drive electrode 812 is positioned on two neighboring edges of the substrate, while the second drive electrode 814 is positioned on two opposing neighboring edges of the substrate. Electrodes 812 and 814 do not contact each other. During use, a fluctuating voltage is applied to electrodes 812 and 814 to create a voltage distribution that produces an optical effect between the substrate 810 and the opposing substrate (not shown in Figure 10b.1).

[0296] In particular, the drive bus 812 or edge electrode extends along the left and top edges. At one point, a connection point is provided to connect bus 812 to the controller, as shown here in the upper left. In particular, the drive bus 814 or edge electrode extends along the right and bottom edges. At one point, a connection point is provided to connect bus 814 to the controller. Bus 814 extends along the top edge outside of bus 812. The advantage of having one electrode, such as bus 814, extend along three edges is that both electrodes can be connected to form the same edge. That is, the entire optical modulator may be powered from a single edge of the substrate. Bus 814 extends here over a limited portion, e.g., less than a quarter of the edge. Bus 814 may also extend further to almost the connection point of bus 812.

[0297] The resulting substrate may be combined, for example, with a mirror image of the substrate (e.g., by flipping the design with respect to the horizontal axis or the vertical axis).

[0298] Figure 10b.2 schematically shows the deformation of the substrate 810 and the drive bus. Drive buses 812 and 814 are shown. As in Figure 10b.1, the building block 820 is repeated within the area bounded by drive buses 812 and 814.

[0299] In addition to the drive bus along the edge of the substrate 810, further drive buses are shown extending within and across the substrate 810.

[0300] Figure 10b.2 shows additional drive buses 815-819 extending across the substrate. Parts of these additional drive buses, in this example, buses 815 and 816, connect to drive bus 814. Parts of these additional drive buses, in this example, buses 817 and 819, connect to drive bus 812. Optional projections extend from these additional drive buses to extend along the edges of copies of the building block. Thus, every building block may have drive buses extending along each edge of its edge, for example, a first drive bus for two edges connected at a vertex of the building block, and a second drive bus for two other edges connected at diagonally opposite vertices. The substrate in Figure 10b.2 may also be combined with a mirror image.

[0301] The advantage of the arrangement shown in Figure 10b.2 is that power is distributed more evenly across the devices. As a result, the transition is more uniform and completes faster.

[0302] The building blocks shown in Figures 10b.1 and 10b.2 are square building blocks, but generally speaking, building blocks can have any shape. In particular, one or more shapes that tile a plane, such as repeatable shapes, can be used. In particular, building blocks can have rectangular, for example, non-square shapes. For example, one side may be at least 1.5 times the length of the other sides. The shape of the building block may be the same as the shape of the optical modulator, and for example, they may have the same relative dimensions.

[0303] Building blocks may be patterned using one or more building block stepper masks. Additional steppers may be used for the drive bus. Steppers may also be used when connections are made by overlapping metal deposits. For example, when a stepper is processing the metal of drive bus 812, there may be overlap with where the placement of 820 was located. Connections from the outside to electrodes, for example, 812, may use conventional foil bolding or clips.

[0304] It should be noted that while one type of building block may be repeated, multiple types of building blocks may also be used. For example, the shape may be triangular. The shape of the building block may affect the overall shape of the device. This is advantageous, for example, for adapting the form factor of an optical modulator. Furthermore, various shapes of building blocks may be combined within a single substrate. For example, the substrate may have a square or rectangular shape in the center and triangular shapes on the edges.

[0305] Using different shapes and / or dimensions is useful for substrates without straight edges, as will be discussed further herein. Using different shapes and / or dimensions is also useful for curved substrates, such as non-flat substrates. While not strictly necessary, using different shapes for building blocks allows the building blocks to better conform to the shape of the substrate. A curved substrate may be combined with another curved substrate to form a curved optical modulator. For example, in an embodiment, the drive buses are arranged along a triangulation of the curved substrate, the drive buses follow the triangulation, and the building block shapes are positioned between the drive buses. For example, in an embodiment, the building blocks surrounding the center of the substrate are square or rectangular, while the building blocks at the edges are triangular. The latter configuration can be achieved using two or more shapes. While a curved substrate may be supported by building blocks of a single shape, it should be noted that using multiple shapes is advantageous. In general, building blocks of different shapes can be applied to a curved substrate, similarly without long electrodes. An example of such a substrate is a substrate for use in an optical modulator, the substrate comprising a plurality of mated drive electrodes applied to the substrate, each of the plurality of drive electrodes arranged in a pattern across the substrate, the plurality of mated drive electrodes arranged alternately with respect to one another on the substrate, the pattern of the plurality of drive electrodes across the substrate comprising a plurality of repeating building blocks, the building blocks comprising a plurality of mated electrodes extending in at least two directions across the building blocks, the mated electrodes within the building blocks forming drive electrodes, the substrate is curved, and the plurality of repeating building blocks comprises at least two different shapes.

[0306] Figure 10c schematically shows the details of the corner of Figure 10d, which will be discussed below. Figure 10c shows the corner of building block 820 and parts of drive buses 812 and 814. Figures 10d-10d schematically show building block 820 repeating across the substrate. Figure 10d corresponds to the lower left corner of Figure 8b. Figure 10d corresponds to the lower right corner of Figure 8b. Building block 820 repeats across the substrate in two directions by translation. The repeating may be a glide translation, for example, a translation followed by a reflection.

[0307] Figure 10c illustrates how electrodes formed by iterative building blocks may be connected to a drive bus. For example, electrode lines may extend from the drive bus to the electrodes within the building block.

[0308] Figure 10d schematically shows the details of the iteration of building block 820 between buses 812 and 814. Figure 10d shows four copies of the building block. The edges between the building blocks are indicated by the capital letters A, B, C, and D. An electrode on one side of a building block is connected to an electrode on the opposite side of the electrode; in this case, note that the electrodes in the design coincide so that aligning the building blocks is sufficient to create a continuous electrode.

[0309] In this example, Figure 10a is drawn such that, when repeated across the substrate as can be seen in Figure 10d, the blocks slightly overlap. Having overlap is advantageous, although it can be avoided if desired. The overlap in this example is 3%. That is, 3% of the x-direction dimension of one building block overlaps with 3% of the x-direction dimension of the next block. The amount of overlap is preferably small, for example, between 1% and 5%. Larger or smaller overlaps are possible. It is also possible to have no overlap at all, in which case the building blocks will align directly next to each other. The same is true for the y-direction, where possible overlaps are, for example, between 3%, 1%, and 5% in some embodiments.

[0310] In this example, building block 820 repeats across the substrate in two orthogonal directions by translation. The repeating could be a glide translation, for example, a translation followed by a reflection.

[0311] Figure 11 schematically shows a cross-section of an embodiment of the optical modulator 700. Figure 11 shows two substrates: substrate 772 and substrate 774. Mutually mated drive electrodes and drive buses are applied to their surfaces, for example, according to the embodiment. A spacer 750 is positioned between substrates 772 and 774 to maintain the substrates at a predetermined distance. The space between the two substrates is filled with semiconductor ink 760, for example, as described herein, while an edge seal is applied around the edges of the two substrates. By selecting different types of ink, the panel can be configured to modulate, for example, from transparent to opaque, or between reflective and non-reflective.

[0312] Figure 12a schematically shows an embodiment of an optical modulator. In Figure 12a, the corners of the substrate according to the embodiment are shown. The drive bus or edge connector is located along the top and right edges of the substrate. The drive electrodes corresponding to the drive bus are connected to the drive bus at multiple points, for example, at a first point and a second point. For some parts of the electrode, two connections may be required to integrate the electrode, for example, to ensure that the entire electrode is connected. However, it may be arranged so that the electrode is connected to the drive bus multiple times, even when it is not required to connect to the first electrode. For example, the first and second points may be connected along the drive bus, but also through an electrode that crosses the substrate. In that case, a portion of the drive bus between the first and second points may be removed. Removing this portion of the drive bus does not disconnect the drive bus from the power supply, because the drive bus remains connected through the electrode. Figure 12b shows an example where a portion of the drive bus is removed. Figure 12c shows the same portion of the substrate, but highlights the electrodes connecting portions 902, 904, and 906.

[0313] Interrupting long electrode lines, especially straight lines, is beneficial in reducing diffraction. If the edge connector is located only on the edge of the device, for example, as shown in the embodiment of Figures 10a-10d, this will make only a slight difference. However, in embodiments with a drive bus surrounding a building block, the impact is considerable. There, straight lines around the building block will significantly increase diffraction and optical artifacts. Here, these straight lines can be interrupted in multiple locations, thus reducing diffraction or optical artifacts. For example, a drive bus as shown in Figures 6a-6d benefits from removing a portion of the drive bus.

[0314] Figure 13a schematically shows an example of a building block embodiment. Figure 13b schematically shows an example of a substrate embodiment for use in an optical modulator. The building block in Figure 13a is repeated across the substrate in Figure 13b in two directions, in this case parallel to the edges of the substrate. The mated electrodes within the building block in Figure 13a are connected in Figure 13b to form two mated drive electrodes that extend across the building block in at least two directions.

[0315] Note that the electrodes shown in Figures 13 and 13b are highly intricate. This can be seen, for example, from their high degree of branching, or from the high ratio (greater than 2) between the maximum distance between any two points on the electrodes within the building block and the diagonal of the building block.

[0316] In Figure 13b, the drive electrodes within the substrate are in the same plane and do not intersect. Note that this design fully connects the electrodes without any floating electrodes on the edges. Note that some electrodes on the edges of building blocks are connected through electrodes in adjacent building blocks.

[0317] The building blocks are based on the so-called Turing pattern. The Turing pattern has been found to be advantageous because it generates fewer but longer branches. As a result, the design is less likely to form floating electrodes, which may have to be handled separately. The Turing pattern is also known as a reaction-diffusion system—in this particular example, the Gray-Scott equation was used.

[0318] Figures 14a–14h schematically illustrate an embodiment of a substrate comprising multiple repeating building blocks with a pattern of multiple drive electrodes traversing the substrate. The repeating building blocks form multiple interlocking electrodes extending in at least two directions across the substrate. Electrodes within a building block may have various advantageous properties, such as a high ratio between electrode length and diagonal; however, this is not required. One or more types of building blocks may be used. The blocks may be rotated, mirrored, and / or translated to fill the substrate. A drive bus may be located between the building blocks to distribute power; instead or even further, the building blocks may be connected to each other to distribute power. The building blocks may have the same shape, but their electrode patterns may or may not be different.

[0319] Figure 14a schematically shows an embodiment of a substrate where the building block is rectangular, in this case, square.

[0320] Figures 14b and 14c schematically show an embodiment of a substrate where the building block is triangular, in this case a right triangle. Any other triangular shape is also possible.

[0321] The advantage of having building blocks of different shapes is that substrates of different shapes can be supported more easily. For example, a square-shaped substrate can be supported by square building blocks or by triangular building blocks, as shown in Figures 14 and 14b. However, with triangular building blocks, a triangular substrate can be easily tiled without the need to support, for example, at the edges, with partial building blocks or different types of building blocks.

[0322] Figure 14d schematically shows an embodiment of a substrate in which the building block is hexagonal, in this case a regular hexagon.

[0323] Figure 14e schematically shows an embodiment of a substrate in which the building block is trapezoidal.

[0324] Figure 14f schematically shows an embodiment of a substrate where the building blocks are polygons, in this case, rectangular polygons having right angles. Note that the polygons do not need to be convex, as shown in Figure 14f. The polygons may be polyominoes; for example, polygons constructed from integer squares. In the example shown, trominos are used. Other examples of polyominoes include tetrominos and pentominoes. The polygons may also be isothetic polygons, for example, rectilinear polygons.

[0325] Figure 14g schematically shows an embodiment of a substrate where the building blocks are square. Figure 14h schematically shows an embodiment of a substrate where the building blocks are triangular. Note that substrates of various shapes can be supported by combining building blocks. Note that different shapes are possible for the substrate using triangular building blocks.

[0326] The substrate shape in Figure 14h can also be supported by rectangular building blocks, but partial building blocks or edge-type building blocks may be used to support sloped edges of the substrate, etc.

[0327] Supporting substrates of different shapes is advantageous for supporting different applications. For example, in cars, windows are often not rectangular. Having building blocks of various shapes makes it easier to support desired shapes.

[0328] Supporting substrates of different shapes is also advantageous for supporting non-planar substrates.

[0329] The following numbered clauses represent the intended embodiments.

[0330] Clause 1. A substrate for use in an optical modulator, - The substrate comprises a plurality of inter-mating drive electrodes (111-114, 121-124) applied thereto, each of the plurality of drive electrodes arranged in a pattern across the substrate, the plurality of inter-mating drive electrodes arranged alternately with respect to each other on the substrate, and the pattern of the plurality of drive electrodes across the substrate comprises a plurality of repeating building blocks, the building blocks are, - A substrate comprising a plurality of inter-mating electrodes extending in at least two directions across a building block, wherein the inter-mating electrodes within the building block form a driving electrode, and for at least one electrode among the plurality of inter-mating electrodes within the building block, the maximum length between any two points on the electrode, measured along the electrode within the building block, is at least twice the length of the diagonal of the building block unit.

[0331] Clause 2. The substrate described in Clause 1, wherein the calculated pixelation noise metric of the drive electrode pattern of the substrate is less than 6.05%, less than 5%, or less than 4%.

[0332] Clause 3. The substrate according to Clause 1 or 2, wherein the electrodes on the substrate comprise a plurality of nodes from which the electrodes branch, the nodes being electrically connected through electrode lines, the plurality of nodes and the connecting electrode lines forming a tree, and the electrodes comprise at least a first node (201) from which the electrodes branch into at least three electrode lines, the first node (201) being directly connected to a second node (202) and a third node (203) through electrode lines, and the electrodes branch into at least three electrode lines at the second node and at the third node.

[0333] Article 4. - The angle between the two directly connected electrode lines is randomly selected, and / or, - Directly connected electrode lines within a building block form multiple angles, with angles covering intervals from 0 to 360 degrees, and in particular, for each specific interval of at least 30 consecutive angles, there is at least one angle among the multiple angles that fall within that particular interval, and / or - Multiple nodes are randomly selected to cover the area of ​​the building block, and / or - The electrode lines are straight or curved, and / or - A substrate as described in Clause 3, wherein the electrode line width is not constant along the electrode line.

[0334] Article 5. - The shortest distance from any point on the substrate to the first drive electrode and the shortest distance to the second drive electrode should both be less than a threshold, and / or, - The sum of the shortest distances from any point on the substrate to the first drive electrode and to the second drive electrode is less than the first threshold and / or greater than the second threshold and / or - The distance from a point on the first drive electrode to a point on the second drive electrode is at least the second threshold, and / or - A substrate according to any one of the clauses 1 to 4, wherein the horizontal and / or vertical size of the building blocks is at least 10 times the sum of the electrode line width and electrode distance.

[0335] Article 6. - The driving electrodes are located in the same plane and do not intersect, or - A substrate according to any one of clauses 1 to 5, wherein the drive electrodes intersect within the substrate, and the dielectric separates the intersecting drive electrodes at least at the point of intersection.

[0336] Article 7. - The building blocks repeat across the substrate in at least two directions, and / or, - Multiple different building blocks repeat across the substrate in one or two directions, and / or, - Two different building blocks repeat in a checkerboard pattern across the board, and / or, - A substrate according to any one of clauses 1 to 6, wherein the substrate comprises a non-repeating electrode line connected to a drive electrode.

[0337] Article 8. - Two electrodes within a building block that are not connected within the building block are connected within the substrate through a connection in a neighboring building block, and / or - A substrate according to any one of clauses 1 to 7, wherein electrodes within the building block are connected to at least two sides of the building block.

[0338] Article 9. - The building blocks are translated with and without mirroring and / or point reflection, and / or - A substrate according to any one of clauses 1 to 8, wherein a row or column of building blocks is mirrored with respect to its longitudinal direction to form the next row or column of building blocks.

[0339] Clause 10. At least one drive bus is provided on the substrate for each drive electrode to drive the drive electrodes. - At least one drive bus is located on the edge of the substrate for each drive electrode to drive the drive electrode, and / or, - The drive bus is simply located on the edge of the board, and / or - A circuit board as described in any one of clauses 1 to 9, wherein the drive bus is located between building blocks covering the circuit board.

[0340] Clause 11. A substrate according to any one of Clauses 1 to 10, wherein at least one drive bus is located on the substrate for each drive electrode to drive the drive electrode, and at least one drive bus is located on the edge of the substrate and / or the edge of a building block, the drive bus comprises a discontinuity portion, the discontinuity portion being connected through the drive electrode driven by the drive bus.

[0341] Clause 12. A substrate according to any one of Clauses 1 to 11, wherein at least one of the first and second driving electrodes is a spanning tree of tessellation.

[0342] Clause 13. A substrate according to any one of Clauses 1 to 12, wherein the driving electrode has mirror symmetry.

[0343] Clause 14. A substrate as described in any one of Clauses 1 to 13, wherein the substrate is non-rectangular.

[0344] Article 15. An optical modulator, - A first substrate and a second substrate, wherein at least one of the first and second substrates is as described in any one of clauses 1-14, the first and second substrates are arranged so that their inner surfaces face each other, and a plurality of drive electrodes (111-114, 121-124) are applied to the inside of at least one of the first and second substrates, - Optical layer between the first substrate and the second substrate The optical layer is equipped with - A fluid containing particles, wherein the particles are electrically charged or can be charged. - An optical modulator comprising a controller configured to obtain an electromagnetic field between multiple drive electrodes, which applies a potential to multiple drive electrodes to cause modulation of the optical properties of the optical modulator, resulting in electrophoretic motion of particles toward or from one of the multiple drive electrodes.

[0345] Article 16. - An optical modulator according to Clause 15, having a calculated pixelation noise metric such that the overlap of the electrode patterns on the first substrate, the electrode patterns on the second substrate, and / or the electrode patterns on the first and second substrates is less than 6.05%, 5%, or 4%.

[0346] Article 17. A method for modulating light, A method for modulating light, comprising applying a potential to a plurality of drive electrodes applied to two opposing substrates to obtain an electromagnetic field between the plurality of drive electrodes, which causes electrophoretic motion of particles toward or from one of the plurality of drive electrodes, resulting in modulation of light shining through the substrates, wherein the two opposing substrates are the substrates described in any one of Clauses 1 to 16.

[0347] Clause 18. A computer-implemented method for calculating a pixelated noise metric for an electrode pattern for an optical modulator, - Preparing black and white design drawings for specific dimensions, where the electrode lines are black and the substrate background is white. - Calculating magnitude and angle for the chirp z-transform (CZT) without scaling using the Bluestein method, - The principal peak value is determined as the maximum intensity in the chirp z-transform (CZT) magnitude spectrum of the design drawing, - The higher peak value is determined as the second maximum intensity in the magnitude spectral chirp z-transform (CZT), excluding the primary peak. - The pixelation noise metric is calculated as the ratio of the higher peak value to the principal peak value. A computer implementation method that includes this.

[0348] Clause 19. A method for calculating the pixelation noise metric described in Clause 18, wherein the design drawing is an 8-bit drawing, with black set to 0 and white set to 255. The following numbered clauses represent the intended embodiments. Clause 1. A substrate for use in an optical modulator, - The substrate comprises at least one drive electrode (111-114, 121-124) applied thereto, the drive electrode arranged in a pattern across the substrate, the pattern of the drive electrode across the substrate comprises a plurality of repeating building blocks, the building blocks are - A substrate comprising one or more electrodes extending in at least two directions across a building block, wherein the electrodes within the building block form at least one driving electrode, and for at least one electrode within the electrodes within the building block, the maximum length between any two points on the electrode, measured along the electrode within the building block, is at least twice the length of the diagonal of the building block unit. Clause 2. The substrate described in Clause 1, wherein the calculated pixelation noise metric of the drive electrode pattern of the substrate is less than 6.05%, less than 5%, or less than 4%. Clause 3. The substrate according to Clause 1 or 2, wherein the electrodes in the building block comprise a plurality of nodes from which the electrodes branch, the nodes being electrically connected through electrode lines, the plurality of nodes and the connecting electrode lines forming a tree, and the electrodes comprise at least a first node (201) from which the electrodes branch into at least three electrode lines, the first node (201) being directly connected to a second node (202) and a third node (203) through electrode lines, and the electrodes branch into at least three electrode lines at the second node and the third node. Clause 4. - The angle between the two directly connected electrode lines is randomly selected, and / or, - Directly connected electrode lines within a building block form multiple angles, with angles covering intervals from 0 to 360 degrees, and in particular, for each specific interval of at least 30 consecutive angles, there is at least one angle among the multiple angles that fall within that particular interval, and / or - Multiple nodes are randomly selected to cover the area of ​​the building block, and / or - The electrode lines are straight or curved, and / or - A substrate as described in Clause 3, wherein the electrode line width is not constant along the electrode line. Clause 5. - The building blocks repeat across the substrate in at least two directions, and / or, - Multiple different building blocks repeat across the substrate in one or two directions, and / or, - Two different building blocks repeat in a checkerboard pattern across the board, and / or, - A substrate according to any one of the clauses 1 to 4, wherein the substrate comprises a non-repeating electrode line connected to a drive electrode. Clause 6. - Two electrodes within a building block that are not connected within the building block are connected within the substrate through a connection in a neighboring building block, and / or - A substrate according to any one of clauses 1 to 5, wherein electrodes within the building block are connected to at least two sides of the building block. Clause 7. - Building blocks are translated with and without mirroring and / or point reflection, and / or - A substrate according to any one of the clauses 1 to 6, wherein a row or column of building blocks is mirrored with respect to its longitudinal direction to form the next row or column of building blocks. Clause 8. At least one drive bus is provided on the substrate for each drive electrode of at least one drive electrode to drive the drive electrode. - At least one drive bus is located on the edge of the substrate for each drive electrode to drive the drive electrode, and / or, - The drive bus is simply located on the edge of the board, and / or - A circuit board as described in any one of clauses 1 to 7, wherein the drive bus is located between building blocks covering the circuit board. Clause 9. A substrate according to any one of Clauses 1 to 8, wherein at least one drive electrode is isolated from the edge of the substrate, powers the isolated drive electrode, and / or a via is connected from the surface of the substrate facing the drive electrode to the isolated drive electrode in order to connect the isolated drive electrode to another portion of the drive electrode on the substrate. Clause 10. A substrate according to any one of Clauses 1 to 9, wherein at least one drive bus is located on the substrate for each drive electrode to drive the drive electrode, and at least one drive bus is located on the edge of the substrate and / or the edge of a building block, the drive bus comprises a discontinuity portion, the discontinuity portion being connected through the drive electrode driven by the drive bus. Clause 11. A substrate according to any one of Clauses 1 to 10, wherein at least one of the driving electrodes is a spanning tree of tessellation. Clause 12. A substrate according to any one of Clauses 1 to 11, wherein the driving electrode has mirror symmetry. Clause 13. A substrate as described in any one of Clauses 1 to 12, wherein the substrate is non-rectangular. Clause 14. At least one drive electrode is multiple drive electrodes, - Multiple drive electrodes (111-114, 121-124) are mated to each other, each of the multiple drive electrodes is arranged in a pattern that crosses the substrate, the multiple mated drive electrodes are arranged alternately to each other on the substrate, and the pattern of multiple drive electrodes crossing the substrate comprises multiple repeating building blocks, the building blocks are, - A substrate for use in an optical modulator according to any one of the clauses 1 to 13, comprising a plurality of inter-mated electrodes extending in at least two directions across a building block, wherein the inter-mated electrodes within the building block form a driving electrode, and for at least one electrode among the plurality of inter-mated electrodes within the building block, the maximum length between any two points on the electrode, measured along the electrode within the building block, is at least twice the length of the diagonal of the building block unit. Clause 15. A plurality of drive electrodes comprises a first drive electrode and a second drive electrode, - The shortest distance from any point on the substrate to the first drive electrode and to the second drive electrode is less than a threshold, and / or - The sum of the shortest distances from any point on the substrate to the first drive electrode and to the second drive electrode is less than the first threshold and / or greater than the second threshold and / or - The distance from a point on the first drive electrode to a point on the second drive electrode is at least the second threshold, and / or - The substrate according to Clause 14, wherein the horizontal and / or vertical size of the building blocks is at least 10 times the sum of the electrode line width and electrode distance. Clause 16. - The drive electrodes are located in the same plane and do not intersect, or - A substrate according to clause 14 or 15, wherein the drive electrodes intersect within the substrate, and the dielectric separates the intersecting drive electrodes at least at the point of intersection. Article 17. Optical modulator, - A first substrate and a second substrate as described in any one of clauses 1 to 16, wherein the first and second substrates are arranged so that their inner surfaces face each other, and at least one drive electrode (111-114, 121-124) is applied to the inner surface of at least one of the first and second substrates, - Optical layer between the first substrate and the second substrate The optical layer is equipped with - An optical modulator comprising a controller configured to apply an electric potential to a driving electrode to cause modulation of the optical properties of the optical modulator. Clause 18. The optical modulator according to Clause 16, wherein the optical layer comprises particles, the particles are electrically charged or can be charged, and the controller is configured to apply a potential to a driving electrode to obtain an electromagnetic field that causes electrophoretic motion of particles toward or away from the driving electrode, thereby causing modulation of the optical properties of the optical modulator. Clause 19. An optical modulator according to Clause 17 or 18, wherein the first and second substrates are in accordance with Clause 14, and the controller is configured to obtain an electromagnetic field between the multiple drive electrodes, which causes electrophoretic motion of particles toward or from one of the multiple drive electrodes, by applying a potential to the multiple drive electrodes to cause modulation of the optical properties of the optical modulator. Clause 20. An optical modulator according to any one of Clauses 17 to 19, wherein the superposition of the electrode patterns on the first substrate, the electrode patterns on the second substrate, and / or the electrode patterns on the first and second substrates has a calculated pixelation noise metric of less than 6.05%, 5%, or 4%. Article 21. A method for modulating light, A method for modulating light, comprising applying a potential to driving electrodes applied to two opposing substrates to obtain an electromagnetic field between driving electrodes, which causes electrophoretic motion of particles toward or from one of a plurality of driving electrodes, resulting in modulation of light shining through the substrates, wherein at least one or both of the two opposing substrates are substrates as described in any one of Clauses 1 to 16. Clause 22. A computer-implemented method for calculating a pixelated noise metric for an electrode pattern for an optical modulator, - Preparing black and white design drawings for a specific dimension, where the electrode lines are black and the substrate background is white, - Calculating magnitude and angle for the chirp z-transform (CZT) without scaling using the Bluestein method, - The principal peak value is determined as the maximum intensity in the chirp z-transform (CZT) magnitude spectrum of the design drawing, - The higher peak value is determined as the second maximum intensity in the magnitude spectral chirp z-transform (CZT), excluding the primary peak. - The pixelation noise metric is calculated as the ratio of the higher peak value to the principal peak value. A computer implementation method that includes this. Clause 23. A method for calculating the pixelation noise metric described in Clause 22, wherein the design drawing is an 8-bit drawing, with black set to 0 and white set to 255.

Claims

1. A substrate for use in an optical modulator, wherein the substrate is - comprising at least one drive electrode (111-114, 121-124) applied to a substrate, the drive electrode arranged in a pattern across the substrate, the pattern of the drive electrode across the substrate comprising a plurality of repeating building blocks, the building blocks are, - comprising one or more electrodes extending in at least two different directions across the building block, The electrodes within the building block form at least one drive electrode. A substrate for use in an optical modulator, wherein, for at least one electrode within an electrode in a building block, the maximum length between any two points on the electrode, measured along the electrode in the building block, is at least twice the length of the maximum distance between two points in the building block.

2. The substrate according to claim 1, wherein the calculated pixelation noise metric of the drive electrode pattern of the substrate is less than 6.05%, and the pixelation noise metric is defined as the ratio of the maximum intensity of non-zeroth-order peaks to the maximum intensity of zero-order peaks from the magnitude of the Fourier spectrum.

3. The substrate according to claim 1, wherein at least two different directions are orthogonal or oblique to each other.

4. The substrate according to claim 1, wherein the building block is rectangular and the maximum distance between any two points is the diagonal.

5. The substrate according to claim 1, wherein the calculated pixelation noise metric of the drive electrode pattern of the substrate is less than 6.05%, and the pixelation noise metric is defined as the ratio of the maximum intensity of all non-zeroth-order peaks to the maximum intensity of zeroth-order peaks from the magnitude of the Fourier spectrum.

6. The substrate according to claim 1, wherein the calculated pixelation noise metric of the drive electrode pattern of the substrate is less than 5%, and the pixelation noise metric is defined as the ratio of the maximum intensity of all non-zeroth-order peaks to the maximum intensity of zeroth-order peaks from the magnitude of the Fourier spectrum.

7. The substrate according to claim 1, wherein the calculated pixelation noise metric of the drive electrode pattern of the substrate is less than 4%, and the pixelation noise metric is defined as the ratio of the maximum intensity of all non-zeroth-order peaks to the maximum intensity of zeroth-order peaks from the magnitude of the Fourier spectrum.

8. The substrate according to claim 1, wherein the electrodes in the building block comprises a plurality of nodes from which the electrodes branch, the nodes are electrically connected through electrode lines, the plurality of nodes and the connecting electrode lines form a tree graph, the electrodes comprises at least a first node (201) from which the electrodes branch into at least three electrode lines, the first node (201) is directly connected to a second node (202) and a third node (203) through electrode lines, the electrodes branch into at least three electrode lines at the second node and at least three electrode lines at the third node.

9. - The angle between the two directly connected electrode lines is randomly selected, or - Directly connected electrode lines within the building block form multiple angles, The angles cover intervals from 0 to 360 degrees, are selected uniformly within the range of 0 to 360 degrees, and the angles are selected so that the angles are chosen from at least all building blocks of 30 degrees, and / or - Multiple nodes are randomly selected to cover the area of ​​the building block, and / or - The electrode line is straight or curved, and / or - The substrate according to claim 1, wherein the electrode line width is not constant along the electrode line.

10. - The building blocks repeat across the substrate in at least two directions, or - Multiple different building blocks repeat across the substrate in one or two directions, or - The substrate according to claim 1, wherein the substrate comprises a non-repetitive electrode line connected to a drive electrode.

11. - The substrate according to claim 1, wherein two different building blocks are repeated in a checkerboard pattern across the substrate.

12. - Two electrodes within a building block that are not connected within the building block are connected within the substrate through a connection in a neighboring building block, and / or - The substrate according to claim 1, wherein electrodes within the building block are connected to at least two sides of the building block.

13. - The building blocks are translated without mirroring and without point reflection, and / or - The building blocks are mirrored, translated without point reflection, and / or - The building blocks are point-reflected, translated without mirroring, and / or - The substrate according to claim 1, wherein a row or column of building blocks is mirrored with respect to its longitudinal direction to form the next row or column of building blocks.

14. At least one drive bus is provided on the substrate for each drive electrode of at least one drive electrode to drive the drive electrode, The substrate according to claim 1, wherein at least one drive bus is arranged on the edge of the substrate for each drive electrode to drive the drive electrode.

15. The substrate according to claim 14, wherein the drive bus is located only on the edge of the substrate.

16. At least one drive bus is provided on the substrate for each drive electrode of at least one drive electrode to drive the drive electrode, The substrate according to claim 1, wherein at least one drive bus is located across the substrate and between building blocks.

17. At least one drive electrode is isolated from the edge of the substrate, The substrate according to claim 1, wherein vias are connected from the surface of the substrate facing the drive electrode to the insulated drive electrode for supplying power to the insulated drive electrode and / or for connecting the insulated drive electrode to another portion of the drive electrode on the substrate.

18. The substrate according to claim 1, wherein at least one drive bus is disposed on the substrate for each drive electrode to drive the drive electrode, and at least one drive bus is disposed on the edge of the substrate and / or the edge of a building block, the drive bus comprises a discontinuity portion, the discontinuity portion is connected through the drive electrode driven by the drive bus.

19. The substrate according to claim 1, wherein at least one of the driving electrodes includes a shape formed by a spanning tree of the substrate tessellation, the tessellation includes a plurality of cells covering the substrate without overlapping, the edges of the spanning tree represent two adjacent cells of the tessellation, and thereby the spanning tree connects each center point of each of the plurality of cells in the tessellation.

20. The substrate according to claim 1, wherein the driving electrode has mirror symmetry.

21. The substrate according to claim 1, wherein the substrate is non-rectangular.

22. At least one drive electrode is multiple drive electrodes, - Multiple drive electrodes (111-114, 121-124) are inter-mating, each of the multiple drive electrodes is arranged in a pattern that crosses the substrate, the multiple drive electrodes are arranged alternately with respect to each other on the substrate, and the pattern of multiple drive electrodes crossing the substrate comprises multiple repeating building blocks, the building blocks are, - comprising a plurality of interlocked electrodes extending across a building block in at least two different directions, wherein the interlocked electrodes within the building block form a driving electrode, and for at least one electrode among the plurality of interlocked electrodes within the building block, the maximum length between any two points on the electrode, measured along the electrode within the building block, is at least twice the length of the maximum distance between two points on the building block. The substrate according to claim 1.

23. Multiple drive electrodes comprise a first drive electrode and a second drive electrode, - The shortest distance from any point on the substrate to the first drive electrode and to the second drive electrode is less than a threshold of 50 micrometers, and / or - The sum of the shortest distances from any point on the substrate to the first drive electrode and to the second drive electrode is less than a first threshold of 100 micrometers and / or greater than a second threshold of 10 micrometers, and / or - The distance from a point on the first drive electrode to a point on the second drive electrode is a second threshold of at least 10 micrometers, and / or - The substrate according to claim 22, wherein the horizontal and / or vertical size of the building block is at least 10 times the sum of the electrode line width and the electrode distance.

24. - The driving electrodes are located in the same plane and do not intersect, or - The substrate according to claim 22, wherein the drive electrodes intersect within the substrate, and the dielectric separates the intersecting drive electrodes at least at the point of intersection.

25. It is an optical modulator, - A first substrate and a second substrate according to any one of claims 1 to 24, wherein the first and second substrates are arranged so that their inner surfaces face each other, and at least one drive electrode (111-114, 121-124) is applied to the inner surface of at least one of the first and second substrates, - An optical layer between the first substrate and the second substrate, - A controller configured to apply an electric potential to the drive electrode to cause modulation of the optical properties of the optical modulator, An optical modulator equipped with the following features.

26. The optical layer contains particles, The optical modulator according to claim 25, wherein the particles are electrically charged or can be charged, and the controller is configured to apply a potential to a driving electrode to obtain an electromagnetic field that causes electrophoretic motion of particles toward or away from the driving electrode, thereby causing modulation of the optical properties of the optical modulator.

27. The optical modulator according to claim 25, wherein the first and second substrates are according to claim 19, and the controller is configured to apply potentials to a plurality of drive electrodes to obtain an electromagnetic field between the plurality of drive electrodes, which causes electrophoretic motion of particles toward or away from one of the plurality of drive electrodes, thereby causing modulation of the optical properties of the optical modulator.

28. - The calculated pixelation noise metric has an overlay of less than 6.05% of the electrode pattern on the first substrate, the electrode pattern on the second substrate, and / or the electrode patterns on the first and second substrates. The optical modulator according to claim 25, wherein the pixelation noise metric is defined as the ratio of the maximum intensity of all non-zero-order peaks to the maximum intensity of the zero-order peak, from the magnitude of the Fourier spectrum.

29. - The calculated pixelation noise metric has an overlap of less than 5% between the electrode pattern on the first substrate, the electrode pattern on the second substrate, and / or the electrode patterns on the first and second substrates. The optical modulator according to claim 25, wherein the pixelation noise metric is defined as the ratio of the maximum intensity of all non-zero-order peaks to the maximum intensity of the zero-order peak, from the magnitude of the Fourier spectrum.

30. - The calculated pixelation noise metric has an overlap of less than 4% between the electrode pattern on the first substrate, the electrode pattern on the second substrate, and / or the electrode patterns on the first and second substrates. The optical modulator according to claim 25, wherein the pixelation noise metric is defined as the ratio of the maximum intensity of all non-zero-order peaks to the maximum intensity of the zero-order peak, from the magnitude of the Fourier spectrum.

31. A method of modulating light, A method for modulating light, comprising applying a potential to driving electrodes applied to two opposing substrates to obtain an electromagnetic field between driving electrodes that causes electrophoretic motion of particles toward or away from one of a plurality of driving electrodes, thereby causing modulation of light shining through the substrates, wherein at least one or both of the two opposing substrates are the substrates described in any one of claims 1 to 24.

32. A method for calculating the pixelation noise metric of an electrode pattern on a substrate according to any one of claims 1 to 24, the method comprising: - Prepare black and white design drawings, where the electrode lines are black and the substrate background is white. - Calculating magnitude and angle for the chirp z-transform (CZT) without scaling using the Bluestein method, - The principal peak value is determined as the maximum intensity within the magnitude of the Fourier spectrum of the chirp z-transform (CZT) of the design drawing, - The higher peak value is determined as the second maximum intensity within the magnitude of the Chirp Z-Transform (CZT) Fourier spectrum, excluding the primary peak value. - The pixelation noise metric is calculated as the ratio of the higher peak value to the principal peak value. A method of implementation in a computer, including

33. The method according to claim 32, wherein the design drawing is an 8-bit drawing, black is set to 0, and white is set to 255.

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