Non-dichroic thin film coating

Abstract

We provide a thin-film coating that includes a gradient refractive index layer. [Solution] A non-dichroic coating thin film structure consisting of a Bragg reflector structure and a gradient refractive index layer is deposited on a substrate. The Bragg reflector structure comprises several pairs of layers, each pair having a first layer of a first material having a first refractive index and a thickness of a quarter wavelength determined by the target wavelength, positioned adjacent to a second layer of a second material having a second refractive index and a thickness of a quarter wavelength. The first refractive index is at least 0.5 higher than that of the second. A gradient refractive index layer having a continuously changing refractive index that transitions from a third refractive index to a first refractive index is deposited on top of the Bragg reflector structure. The thickness of the gradient refractive index layer is selected such that the reflection coefficient for light in the visible spectrum from 400 to 700 nanometers does not change by more than 25 percent over this wavelength range.

Description

[Technical Field]

[0001] This disclosure relates to non-dichroic thin film coatings, and more specifically, to thin film coatings including a gradient refractive index layer. [Background technology]

[0002] Thin films are crucial in many optical applications and are used to control surface reflectivity to achieve specific optical effects. These films often consist of layered structures with optical properties finely tuned to satisfy optical requirements. Common film structures include dielectric multilayer structures, which can enhance or reduce reflectivity depending on their structure. Thin films are typically deposited using advanced techniques such as physical vapor deposition (PVD) or chemical vapor deposition (CVD). These systems have precise control characteristics, such as mass flow controllers and accurate temperature setpoints, enabling the precise deposition of thin films with specific optical qualities. This precision allows for the fabrication of thin films with specific optical properties for various optical applications in different industries. [Overview of the project] [Means for solving the problem]

[0003] This disclosure introduces a novel method using a gradient refractive index composition film to substantially conceal or reduce substrate coloration. This technique offers significant advantages over conventional coating methods in addressing their inherent limitations. Applying a gradient refractive index film to a substrate significantly reduces the influence of the substrate color on the final appearance. By controlling the refractive index profile within the film, this technique enables precise manipulation of light transmission and reflection properties. As a result, undesirable substrate hues are suppressed, leading to a uniform and aesthetically pleasing color across the entire coated surface.

[0004] Furthermore, the addition of a gradient refractive index film can achieve non-dualistic properties for the substrate color, further enhancing the visual consistency of the coated surface. This means that the color appearance is maintained consistently regardless of the viewing angle.

[0005] One embodiment of this disclosure involves converting all substrate colors to various shades of gray, depending on the type of gradient film used. By strategically adjusting the composition and thickness of the gradient refractive index layer, this process can facilitate the transformation of the substrate hue into grayscale tones. Such a method not only neutralizes the substrate coloration but also enhances the overall visual consistency and appearance of the coated surface.

[0006] The primary advantage of this disclosure is its ability to achieve superior color control and consistency. By adjusting the thickness and composition of the gradient refractive index layer, variations in color perception are minimized, resulting in a more uniform and visually pleasing appearance. In addition, the tunable manipulation of optical behavior enables the realization of specific color effects desired for various applications, thereby enhancing the versatility of the coated substrate.

[0007] Furthermore, the gradient refractive index composition film provides an additional protective layer for the underlying substrate, improving its durability and resistance to environmental factors. This protective function not only maintains the integrity of the substrate but also extends the lifespan of the coated surface, ensuring a long-lasting aesthetic appearance. Combined with its optical properties, this aspect highlights the multifaceted benefits of using gradient refractive index coatings in a wide range of industrial contexts.

[0008] The use of solid inorganic materials instead of solvent-based organic paints offers several advantages. Inorganic materials have optical properties that are easier to adjust and can be made to be more chemically and environmentally durable. In addition, they avoid the release of volatile organic compounds, reducing environmental harm.

[0009] Other technical advantages will be readily apparent to those skilled in the art from the following figures, descriptions, and claims. Furthermore, while specific advantages have been listed above, various embodiments may include, include, or not include all, some, of the listed advantages.

[0010] Without being inconsistent with various other embodiments, the appended claims can contribute as yet another summary of the disclosure of the present invention.

[0011] The embodiments described herein relate to non-dichroic coating thin film structures and systems for forming such structures.

[0012] In certain non-limiting embodiments, the structure is deposited on a substrate, and this non-dichroic coating thin film structure includes a Bragg-reflector structure deposited on the substrate. The Bragg-reflector structure includes a plurality of pairs of layers, each pair having a first layer and a second layer. The first layer comprises a first material with a first refractive index and has a first thickness of one-quarter of the target wavelength determined within the first layer, and the first layer is positioned adjacent to the second layer. The second layer comprises a second material with a second refractive index and has a second thickness of one-quarter of the target wavelength determined within the second layer, and the first refractive index is at least 0.5 higher than the second refractive index. A gradient refractive index layer with a continuously changing gradient refractive index is deposited on top of a Bragg reflector structure, where the gradient refractive index changes continuously from a third refractive index to a first refractive index, and the thickness of the gradient refractive index layer is selected such that the reflection coefficient for visible wavelength light changes by no more than 25 percent over the visible wavelength range of 400-700 nanometers.

[0013] In certain non-limiting embodiments, a system for depositing a non-dichroic coating thin film is provided. The system includes a control system having a processor, which executes commands to cause the control system to send signals to activate a mass flow controller for the deposition of a precursor gas, and for maintaining temperature and pressure control within the reaction chamber, the commands causing the processor to execute operations including receiving optical properties of the substrate, including the color of the substrate, obtained from spectrophotometer measurements, receiving reflectance requirements for the substrate, and selecting a formulation for depositing a non-dichroic coating thin film on the substrate based on the received optical properties and reflectance requirements, the formulation selection step including determining a set of parameters for the non-dichroic coating thin film. The non-dichroic coating thin film includes a Bragg-reflector structure deposited on the substrate, the Bragg-reflector structure having a plurality of pairs of layers, each pair having a first layer and a second layer. The first layer comprises a first material with a first refractive index and has a first thickness of one-quarter of a target wavelength determined within the first layer, and the first layer is adjacent to the second layer. The second layer comprises a second material with a second refractive index and has a second thickness of one-quarter of the target wavelength determined within the second layer, and the first refractive index is at least 0.5 higher than the second refractive index. Furthermore, the non-dichroic coating thin film comprises a gradient refractive index layer with a continuously changing gradient refractive index deposited on the Bragg-reflector structure, where the gradient refractive index changes continuously from a third refractive index to a first refractive index. Furthermore, the step of determining the parameter set includes the step of determining the target wavelength and the step of determining the thickness of the gradient refractive index layer.

[0014] The embodiments disclosed in this specification are merely examples, and the scope of this disclosure is not limited thereto. Some embodiments may include all, some, or none of the components, elements, features, functions, operations, or steps of the embodiments disclosed herein. The dependencies or superordinate references in the appended patent claims are only selected for formal reasons. However, any subject matter resulting from an intentional superordinate reference (especially multiple dependencies) to any preceding patent claim can equally be claimed, and thus any combination of the patent claims and their features is disclosed and can be claimed regardless of the dependencies selected in the appended patent claims. The subject matter that can be claimed includes not only combinations of features as listed in the appended patent claims but also any other combination of features in the patent claims, and each feature mentioned in the patent claims can be combined with any other feature or combination of features in the patent claims. Furthermore, any of the embodiments and features described or depicted herein can be claimed in an individual patent claim and / or in any combination with any of the embodiments or features described or depicted herein or with any of the features of the appended patent claims.

Brief Description of the Drawings

[0015] [Figure 1A] It is a schematic diagram illustrating a non-dichroic coating thin film structure according to an embodiment. [Figure 1B] It is another schematic diagram illustrating a non-dichroic coating thin film structure according to an embodiment. [Figure 2A] It is a diagram showing an exemplary refractive index profile regarding a gradient refractive index layer according to an embodiment. [Figure 2B] It is a diagram showing an exemplary refractive index profile regarding a gradient refractive index layer according to an embodiment. [Figure 3] It is an exemplary reflectivity graph regarding different non-dichroic coating thin film structures according to an embodiment. [Figure 4] It is a diagram showing an exemplary structure of a gradient refractive index layer according to an embodiment. [Figure 5] This figure shows the possible rates and material profiles for the deposition of a non-dichroic coating thin film structure according to the embodiment. [Figure 6] This figure shows an exemplary system for depositing a non-dichroic coating thin film structure according to an embodiment. [Figure 7] This figure shows an exemplary method for depositing a non-dichroic coating thin film structure according to an embodiment. [Figure 8A] This figure shows an exemplary method for determining the parameters used to obtain a deposition formulation for depositing a non-dichroic coating thin film structure according to the embodiment. [Figure 8B] This figure shows an exemplary method for determining the parameters used to obtain a deposition formulation for depositing a non-dichroic coating thin film structure according to the embodiment. [Figure 8C] This figure shows an exemplary method for determining the parameters used to obtain a deposition formulation for depositing a non-dichroic coating thin film structure according to the embodiment. [Figure 8D] This figure shows an exemplary method for determining the parameters used to obtain a deposition formulation for depositing a non-dichroic coating thin film structure according to the embodiment. [Figure 8E] This figure shows an exemplary method for determining the parameters used to obtain a deposition formulation for depositing a non-dichroic coating thin film structure according to the embodiment. [Figure 9] This figure shows an exemplary computer system for controlling the deposition of a non-dichroic coating thin film structure according to an embodiment. [Modes for carrying out the invention]

[0016] The following description reveals many specific details for illustrative purposes to provide a complete understanding of this disclosure. However, it will be apparent that embodiments of this disclosure can be carried out without using these specific details. Furthermore, to avoid unnecessarily obscuring the description of this disclosure, known structures and devices are described only in a schematic form.

[0017] This document, together with the accompanying drawings, aims to clearly communicate the design and method at a level of detail consistent with the standard methods of communication among those skilled in the art in the relevant trade. This level of detail reflects the customary methods of communication among those skilled in the art in the relevant trade and substantially represents the structure and function of the various designs outlined in this disclosure.

[0018] This disclosure may describe various embodiments to illustrate different aspects. Other embodiments may be used without departing from the scope of the embodiments described, and structural, logical, software, and other modifications may be made. Various modifications and changes are possible and within the scope of expectation. Some features may be described with reference to one or more embodiments or drawings, but such features are not limited to their use in the one or more embodiments or drawings referenced in their description. Accordingly, this disclosure is neither a verbatim description of all embodiments nor a list of features that must be present in all embodiments.

[0019] Section headings and titles are provided for convenience only and are not intended to limit this disclosure in any way or to serve as a basis for interpreting the claims.

[0020] Descriptions of embodiments with several components do not necessarily imply that all such components are required. Optional components may be described to illustrate various possible embodiments and to more fully illustrate one or more aspects of this disclosure. Similarly, while processing steps, method steps, or algorithms may be described in sequence, unless specifically stated otherwise, such steps, methods, and algorithms can generally be configured to function in different orders. No order or sequence of steps described in this disclosure is mandatory. The steps of a described process can be performed in any practical order. Furthermore, some steps can be performed simultaneously. Exemplification of processes in the drawings does not preclude variations and modifications, imply that such process or any of its steps is required, or imply that further illustrated processes are preferable. While steps may be described once per embodiment, these steps do not necessarily have to be performed only once. Some embodiments or implementations may omit some steps, or some steps may be performed more than once in each embodiment or implementation. When describing a single device or article, more than one device or article may be used instead of a single device or article. When describing more than one device or article, you may use "single device or article" instead of "more than one device or article."

[0021] The functions or features of a device may be embodied by one or more other devices not explicitly described as having such functions or features. Therefore, other embodiments do not need to include such devices themselves. Multiple technologies and mechanisms described or referenced herein are described below in singular form for potentially clarifying purposes. However, unless otherwise noted, embodiments may involve multiple iterations of a technology or multiple appearances of a mechanism.

[0022] definition

[0023] In various embodiments of the disclosure of the present invention, terms such as “approximate,” “about,” “similar,” “equal,” “equivalent,” or “same” are used to indicate the degree of flexibility or tolerance in the disclosed numerical values, measurements, and eigenvalues. The scope of the disclosure of the present invention should not be limited to strict numerical precision, and the above terms are used to allow for variations within acceptable limits.

[0024] The terms “approximate,” “about,” and “similar” are interchangeable terms used to indicate that a given value, parameter, or eigenvalue may deviate within a reasonable range from the value it describes. This range may include minor variations that do not substantially affect the function or performance of the systems and methods described in the disclosure of the present invention. For example, the terms “approximate,” “about,” and “similar” may mean a 10 percent variation from a particular value.

[0025] The terms “equal,” “equivalent,” or “same” are used to indicate that the values, parameters, or eigenvalues ​​described in this way are substantially identical or sufficiently close in magnitude, without necessarily requiring absolute precision. For example, such terms may mean a deviation of a few percent from a particular value, such as one percent or two percent.

[0026] Furthermore, the term “similar” can be used to describe similarity or alike that allows for variations among two or more elements, aspects, or features that do not impair the fundamental nature or purpose of the disclosure of the present invention.

[0027] In various embodiments of the disclosure of the present invention, the term “set” is used to describe a group or collection of objects, elements, components, or entities. The flexibility in the interpretation of the term “set” provides adaptability in situations where a single object satisfies the intended function or purpose of the disclosure of the present invention, enabling practical applications. Thus, the disclosure of the present invention is not limited to cases where the “set” should consist of multiple objects, in other words, it also considers scenarios where the “set” may include a single object.

[0028] Non-dichroic thin film structure

[0029] Conventionally, the design of thin-film anti-reflective (AR) coatings and Bragg reflectors has involved one or more layers composed of multiple thin films, each made of a material with a low refractive index and a material with a high refractive index. The limitation of this multilayer approach is that it provides unique anti-reflective or reflective properties only within a certain range of wavelengths and viewing angles. At angles greater than the normal incidence to such a thin film or beyond the design angle of incidence (AOI), a phenomenon known as dichroism occurs, which is an optical phenomenon in which the material provides two different colors or absorbs light differently when viewed from different angles or under different light polarizations. In some cases, the number of layers in the multilayer thin film structure may exceed 100, increasing the complexity of the coating process.

[0030] The disclosure of this invention describes a process for depositing a continuous layer having a gradually increasing refractive index (generally greater than 2.0) using various techniques such as physical vapor deposition (PVD) (thermal deposition, such as sputtering), chemical vapor deposition (CVD), or plasma-enhanced chemical vapor deposition (PECVD). The deposited material undergoes a chemical reaction with a reaction gas (such as nitrogen or oxygen) in the CVD process or interacts with a gas in the PVD process, at a ratio that gradually increases from 0 to a value slightly below the stoichiometric equilibrium value or to a value approximately equal to the stoichiometric value. For example, the layer of deposited material can be silicon mononitride represented as Si1N1 or stoichiometric silicon nitride Si3N4. a Nb Therefore, the value of "a" can be in the range between 1 and 3, and the value of "b" can be in the range between 1 and 4.

[0031] During the deposition process, the mass flow controller is configured to adjust the gas flow rate. In some cases, the mass flow controller can be adjusted by a suitable control system having a processor configured to execute commands to control the gas flow rate. In addition to or instead of this, manual adjustment of the gas flow rate is also possible during deposition. By adjusting the mass flow rate of the precursor gas, films with varying compositions can be formed. Such films have a stepwise variation in refractive index and can form gradient refractive index layers. As an example, a deposited thin film has a refractive index and absorption coefficient that vary continuously throughout its thickness and can act as a "neutral density" filter. This filter appears uniformly darker without any color shift (dichroism) regardless of the viewing angle.

[0032] One characteristic of the deposition process for producing optical films with gradient refractive indices is its ability to achieve a desired gray area of ​​"neutral density." This is achieved by stopping the deposition process at some point before the elements or compounds reach a balanced stoichiometric ratio. In addition, this process is fully compatible with web-based or roll-to-roll thin-film coating methods commonly used to coat various surfaces, including aircraft surfaces.

[0033] The present invention discloses a non-dichroic coating thin film structure deposited on a substrate. The substrate may include any suitable material, including metals, ceramics, plastics, cloths, or similar materials. The substrate may have substrate-related optical properties, including substrate color, substrate reflectivity, and light scattering. Such substrate-related optical properties can determine the properties or parameters of the non-dichroic coating thin film structure deposited on such a substrate, as will be discussed in more detail below.

[0034] The non-dichroic coating thin film structure is a Bragg reflector structure deposited on a substrate, and may include a plurality of pairs of layers, each having a first layer and a second layer. The first layer may be formed from a first material having a first refractive index n1. The first layer may have a first thickness d1, which can be one-quarter of the target wavelength determined within it. For example, if the target wavelength of light in a vacuum is λ0, the wavelength of light in the first layer having the first refractive index n1 is given by λ0 / n1. Thus, the first layer may have a thickness of d1 = 1 / 4·λ0 / n1.

[0035] A second layer follows the first layer. The second layer is formed from a second material with a second refractive index n2 and has a second thickness d2 which is one-quarter of the target wavelength determined within the second layer. For example, the second thickness is d2 = 1 / 4·λ0 / n2. In exemplary embodiments, the first refractive index is at least 0.5 higher than the second refractive index (e.g., n1-n2≧0.5).

[0036] In addition to Bragg reflector structures, non-dichroic coating thin-film structures feature a gradient refractive index layer deposited on top of the Bragg reflector, having a continuously changing refractive index. This gradient refractive index is designed to transition smoothly from a third refractive index to a first refractive index. In various cases, the parameters of the gradient refractive index layer can be adjusted to enhance overall transparency and provide reflective properties that are less dependent on the angle of incidence of the illuminating light. Such parameters can include, for example, the thickness of the gradient refractive index layer. Specifically, the thickness of this layer can be optimized so that the reflection coefficient for visible light wavelengths does not change by more than 25 percent within the range of 400 nanometers (nm) to 700 nanometers (nm). Depending on the material used for the gradient refractive index layer, the thickness of this layer can range from 0.1 microns to about 1 micron. In some scenarios, with materials that have high transparency to visible light, the gradient refractive index layer can be several microns thick.

[0037] Figure 1A shows a non-dichroic coating thin film structure 100 including a gradient refractive index layer 120 and a Bragg-reflector structure 130. The non-dichroic coating thin film structure 100 extends in the x and y directions as shown in Figure 1A. As depicted, a ray 110 strikes a surface 121 of the gradient refractive index layer 120, and thereafter, the ray 110 follows a path 111 that is influenced by the gradient refractive index of the layer 120. In addition to this, as shown by the reflected ray 114, some of the light is reflected at surface 121. The degree of reflection at this surface is determined by Fresnel's equation and depends on the angle of incidence of the ray 110 and the refractive index n3 of the gradient refractive index layer 120 near surface 121. Thus, by selecting the material for surface 121, it is possible to select the refractive index n3, which can be used to control the reflective properties of the non-dichroic coating thin film structure 100. In exemplary embodiments, the refractive index n3 can be selected to be in the range between 1.5 and 2.5.

[0038] Figure 1A shows that the gradient refractive index layer 120 has a refractive index n3 at surface 121 and a refractive index n4 at surface 122, which is the interface between the gradient refractive index layer 120 and the Bragg reflector structure 130. The refractive index n4 is configured to be greater than the refractive index n3. Furthermore, the gradient refractive index layer 120 has a continuously changing refractive index n g Formed from a material having (x). Refractive index n g (x) is configured to increase continuously along the direction x from the value of n3 to the value of n4. In some cases, the refractive index n g (x) can be changed to a linear function as shown in Figure 2A. Alternatively, the refractive index n g (x) can be changed in any appropriate way. For example, Figure 2B shows the refractive index n g This illustrates how (x) changes parabolicly. In many cases, the values ​​of the refractive indices n1, n2, n3, and n4 are specified with respect to visible wavelengths. These wavelengths fall within the range of 400 nm to 800 nm.

[0039] In some cases, the gradient refractive index layer 120 can be formed from a binary compound such as silicon nitride (SiN), which can be represented by the stoichiometric formula Si3N4. In various embodiments, the gradient refractive index layer 120 can be selected from composite materials containing a variable mole fraction of silicon and nitrogen. It should be noted that any suitable silicon-to-nitrogen ratio can be used such that the refractive index of the material can vary from substantially about 1.5 or 2 near surface 121 to a value ranging from about 3.5 to 2.5 near surface 122. For example, in a high-concentration silicon-containing layer, the refractive index can be substantially high, reaching a value of about 3.5, and in a high-concentration nitrogen-containing layer, the refractive index can be about 2 or less. It should be noted that other materials other than silicon or nitrogen can be used. For example, such materials can include TiO2, GaN, AlGaN, AlN, SiO2, MgO, Al2O3, ZnS, ZnO, Ga2O3, BN, InN, InGaN, GaP, diamond, and combinations thereof.

[0040] In various embodiments, composite materials such as SiN can be deposited using any suitable method, such as PVD, CVD, PECVD, and sputtering. For example, a gradient refractive index layer 120 containing a silicon nitride layer can be deposited using chemical vapor deposition, where the variable mole fraction of silicon and nitrogen can be determined by the mass flow rates of silane and ammonia gases. In some cases, not only the gradient refractive index layer but the entire non-dichroic coating thin film structure 100 can be deposited using PVD, CVD, PECVD, and sputtering. In some cases, for example, a portion of a structure, such as a Bragg-reflector structure, can be deposited using a first method such as PVD, and a second portion of the structure can be deposited using a different method such as CVD. In exemplary embodiments, when using CVD, the process can be plasma-enhanced (e.g., using PECVD) to reduce the substrate temperature to a suitable temperature (e.g., several hundred degrees Celsius). It should be noted that a specific deposition process can be selected based on the type of substrate being used. For example, CVD can be selected when the substrate has the capability to withstand high temperatures, and PVD can be selected when the substrate cannot be heated to several hundred degrees Celsius.

[0041] In various embodiments, the Bragg reflector structure 130 is designed to reflect light incident on the surface 122 from various angles. Optimal reflection occurs when there is only a relatively small deflection angle from the normal direction to the surface 122. It should be noted that the gradient refractive index layer 120 is designed to bend the optical path as shown by path 111. As a result, the rays traveling along this path exhibit only a small deflection angle from the normal compared to the rays 110 at surface 121.

[0042] As shown in Figure 1A, the Bragg reflector structure 130 includes multiple pairs of layers, such as a second layer 132 following a first layer 131. The first layer 131 is configured to be adjacent to a gradient refractive index layer 120. In an exemplary embodiment, the refractive index of the first layer 131 can be n1, which is the same as the refractive index n4 of the gradient refractive index layer 120 near the surface 122. Alternatively, in some cases, n1 can be different from n4. For example, the absolute difference |n1-n4| can be as large as 0.5 or greater. In some cases, n1 can be greater than n4, and in other cases, n1 can be less than n4.

[0043] In various embodiments, the second layer 132 follows the first layer 131. The first layer 131 and the second layer 132 form a pair that can be repeated multiple times. For example, the Bragg reflector structure 130 may include several pairs of layers 131 and 132, dozens of pairs of layers 131 and 132, or even about 100 pairs of layers 131 and 132. As shown in Figure 1A, the thickness of the first layer 131 is represented by D1, and the thickness of the second layer is represented by D2, and the thicknesses D1 and D2 are selected such that the ratio D2 / D1 is equal to n1 / n2. In an exemplary embodiment, D1 may be selected such that D1 = λ0 / n1.

[0044] In various embodiments, the material for the first layer 131 can be selected such that n1 is greater than n2. The greater the difference between n1 and n2, the more effective the Bragg reflector structure 130 is. In some cases, n1 can be in the range of about 2.5 to about 3.5, and n2 can be in the range of about 1.5 to 2.5.

[0045] Figure 1A illustrates that a ray along path 111 is reflected from the Bragg reflector structure 130 and substantially follows a non-linear path 112, similar to path 111, due to the gradient refractive index of the gradient refractive index layer 120. This ray is configured to be emitted from the gradient refractive index layer 120 as a reflected ray 113.

[0046] In various embodiments, the Bragg reflector structure 130 can be deposited on a substrate. In an exemplary embodiment, a second layer 132 is deposited on the substrate following the first layer 131. In some cases, a buffer layer can be deposited on the substrate before depositing the second layer 132. The buffer layer can be used to provide a layer with a low roughness or a layer that allows for good adhesion of the second layer 132.

[0047] In various embodiments, the thicknesses of the first and second layers 131 and 132 may be influenced by the peak wavelengths at which reflection from the Bragg reflector structure 130 is desirable. For example, when the substrate is red, to prevent the reflected light from having prominent red wavelengths (e.g., wavelengths in the range of approximately 650-800 nm), the Bragg reflector structure 130 can reflect the complementary color of red (e.g., green wavelengths in the range of approximately 490-570 nm) while transmitting at least a portion of the red wavelengths. That is, the Bragg reflector structure 130 can be designed to substantially reflect green light.

[0048] The Bragg reflector structure 130 can utilize tens or hundreds of layers. In some cases, the thickness of the Bragg reflector structure 130 is approximately 1 / 10th of a micron, 1 / 2 micron, 1 micron, or 1 and 1 / 2 microns.

[0049] Furthermore, the thickness and composition of the gradient refractive index layer 120 can be determined based on the reflectivity requirements of the non-dichroic coating thin film structure 100. For films with higher reflectivity, the thickness of the gradient refractive index layer 120 can be less than 1 micron (approximately 0.1 to 1 micron, including all intermediate values), while for films with lower reflectivity, the gradient refractive index layer 120 can be thicker than 1 micron (e.g., 1 to 3 microns). The reflectivity of the non-dichroic coating thin film structure 100 can be selected to have any appropriate value based on the additional requirements of such a film. For example, in some cases, the reflectivity of the non-dichroic coating thin film structure 100 can be higher than 10 percent. In some cases, the composition of the gradient refractive index layer 120 can be selected such that the film has a reflectivity of approximately 50 percent at a thickness of approximately 0.1 microns.

[0050] It should be noted that in some cases, a Fabry-Perot structure can be used instead of having a Bragg-reflector structure 130. An example of a Fabry-Perot structure 140 is shown in Figure 1B. Such a structure can be similar to the Bragg-reflector structure 130, but allows peak wavelengths to pass through while almost reflecting other wavelengths. The Fabry-Perot structure 140 is characterized by several pairs of layers formed from a second layer 142 and a first layer 141, each of which can be similar in structure and material to the second layer 132 and the first layer 131, respectively. It should be noted that the second layer 142 of the Fabry-Perot structure 140 is configured to be adjacent to the surface 122 of the gradient refractive index layer 120. The second layer 142 is a layer with refractive index n2, followed by a first layer 141 with refractive index n1.

[0051] Furthermore, the Fabry-Perot structure 140 includes a third layer 143 with refractive index n1 sandwiched between multiple pairs of layers 142 and 141. In exemplary embodiments, the Fabry-Perot structure 140 can be configured based on a specific peak wavelength of light that can be transmitted. For example, if it is necessary to transmit light of wavelength λ0 (measured in a vacuum), the second layer 142 may have a thickness D2 = 1 / 4·λ0 / n2, and the first layer 141 may have a thickness D1 = 1 / 4·λ0 / n1. In the Fabry-Perot structure 140, the third layer 143 has a thickness D3 that is twice the thickness of the first layer. In exemplary embodiments, when the substrate is a specific color, such as red, the Fabry-Perot structure 140 can be configured to transmit only light of wavelengths corresponding to that color and reflect most of the other colors.

[0052] In various cases, as described above, the thicknesses of the first and second layers 131 and 132 in the Bragg-reflector structure 130, the first and second layers 141 and 142 in the Fabry-Perot structure 140, and the third layer 143 in the Fabry-Perot structure 140 are determined based on the target wavelength that needs to be reflected (in the case of the Bragg-reflector structure 130) or transmitted (in the case of the Fabry-Perot structure 140). In some cases, the target wavelength can be determined based on the color of the substrate. For example, the target wavelength can correspond to the complementary color of the substrate in the case of the Bragg-reflector structure 130, and to the color of the substrate in the case of the Fabry-Perot structure 140 (for example, if the color of the substrate is red, the wavelength can be about 650 nm or 800 nm).

[0053] Figure 1A shows a Bragg-reflector structure 130 and Figure 1B shows a Fabry-Perot structure 140, but it should be noted that other structures can be combined with the gradient refractive index layer 120 to form a non-dichroic coating thin film structure. For example, in some cases, the non-dichroic coating thin film structure may include a first Bragg-reflector structure and a second Bragg-reflector structure deposited between the substrate and the first Bragg-reflector structure. In some embodiments, the first Bragg-reflector structure may be similar to or identical to the Bragg-reflector structure 130, but the second Bragg-reflector structure may be configured to reflect light of a second target wavelength different from the target wavelength of the first Bragg-reflector structure (referred to herein as the first target wavelength for clarity). For example, the second target wavelength may differ from the first target wavelength by at least 100 nanometers, and in some cases, the difference between the first and second target wavelengths may be several hundred nanometers.

[0054] It should be noted that not only can two Bragg-reflector structures be combined, but other combinations are also possible; for example, several Fabry-Perot structures can be combined, or a Bragg-reflector structure can be combined with a Fabry-Perot structure.

[0055] It should be noted that in some embodiments, a gradient refractive index layer, such as a gradient refractive index layer 120, can be deposited directly over the substrate without the presence of a Bragg-reflector structure, such as a Bragg-reflector structure 130, or a Fabry-Perot structure 140. In exemplary embodiments, such a gradient refractive index layer can be less than 1 micron thick and have a composition that allows for a reflectance of about 10 to 30 percent. In some cases, when the gradient refractive index layer is about half the thickness of 1 micron, the reflectance can be about 50 percent.

[0056] FIG. 3 illustrates examples of reflectance from a substrate with and without a gradient refractive index structure. In FIG. 3, graph 210 illustrates the reflection coefficient R as a function of wavelength when a Bragg - reflector structure having 14 layers is deposited on the substrate. The Bragg - reflector structure has a thickness of about 1.5 microns. As shown, the reflection coefficient R varies by only about 20% or more when such a film is deposited on the substrate. The graph 220 shown in FIG. 3 illustrates the reflection coefficient R as a function of wavelength when a gradient refractive index layer having a thickness of about 0.7 microns is deposited on the substrate. As shown by graph 220, the variation of the reflection coefficient R as a function of wavelength is significantly smaller than that for graph 210. For example, the variation of the reflection coefficient R for graph 220 is less than 10 percent for the wavelength range from 400 nm to 700 nm.

[0057] FIG. 4 shows a gradient refractive index layer 420 that can include sub - layers 421, 423, and 425. These sub - layers can further finely control the optical and / or mechanical properties of the gradient refractive index layer 420. For example, some of the sub - layers can be used to reduce the mechanical stress within the gradient refractive index layer 420, thereby reducing the number of defects and / or cracks in the layer. In addition to this, some sub - layers can be configured to control light scattering. For example, sub - layer 423 presents a lateral variation in refractive index and can be developed under conditions that result in light scattering. This sub - layer is thought to be formed by first creating islands of a first material having a particular refractive index and then depositing a second material having a different refractive index. These islands are thought to be formed during the deposition process. For example, during deposition, sub - layer 425 made from a binary compound can be deposited to have a refractive index ranging from n g (x1) to n g (x2). Adjacent to sub - layer 425, sub - layer 423 has a refractive index ranging from n g (x2) to n gThe material can be deposited to have a refractive index over the range of (x3) and to have morphological properties that further induce scattering. These properties may include islands of the first material surrounded by the second material. For example, the sublayer 423 can be deposited by using CVD, PECVD, or PVD under predetermined temperature and pressure conditions to promote island formation using a specific combination of precursor gas or precursor material, and then continuing deposition to fill the gaps between the islands under different temperature and pressure conditions using a different combination of precursor gas or precursor material. In one example, the first material can be a high-concentration nitrogen-containing SiN composition, while the second material can be a high-concentration silicon-containing SiN composition. Alternatively, the first material can be a high-concentration silicon-containing SiN and the second material can be a high-concentration nitrogen-containing SiN. In certain implementations, sublayers 423 may have length scales of 50 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 600 nm, 700 nm, and similar scales, and may include lateral non-uniformity of refractive index with a change in refractive index of about 10% or more. In some cases, these changes can be as large as 1 micron or more. Multiple islands within sublayers 423 can be spaced apart by proper distances of 50 to 1000 nm and can be formed from materials having refractive indices that differ from the surrounding material by at least 10%. Proper distances can be measured as the diameter of the island at its widest point or as the square root of the island's area. Potentially, the proper distance between islands can be similar to the proper size of the islands. In various cases, these proper distances are statistics determined by averaging the diameters (or square roots of the areas) of various islands. Similarly, the proper distance between islands is a statistic determined by averaging the distances between islands.

[0058] In some cases, specific sublayers can be deposited to reduce lateral non-uniformity within the sublayer. By achieving greater uniformity, these sublayers enhance the overall durability of the gradient refractive index layer 420 and improve stress management. This reduction in non-uniformity helps prevent crack initiation and propagation by generating a stress field that counteracts crack formation and growth. In addition, such sublayers can be optimized to control diffusive optical scattering, ensuring better optical performance by maintaining transparency and reducing unintended light dispersion.

[0059] Figure 4 shows that another layer 421 can be deposited further. This layer may include a superlattice composed of materials having various compositions. For example, the sublayer 421 could include alternating thin layers in which a thin layer of a first material having a specific refractive index is followed by a thin layer of a second material having a different refractive index. These layers can be formed to be several tens of nanometers thick and can be used to further fine-tune the refractive index of the gradient layer and / or introduce scattering. In one embodiment, the difference in refractive index between the first and second materials can be at least 10% or greater.

[0060] It should be noted that various changes in the layer growth conditions can result in specific optical properties of the deposited layers, such as their refractive index and light scattering characteristics. Furthermore, various deposition techniques can affect the mechanical or optical properties of such layers. In some cases, to achieve better mechanical / optical performance, at least a portion of the gradient refractive index layer can be annealed by increasing the temperature during the deposition process. In some cases, changes in pressure can be applied.

[0061] Temperature can play a crucial role in thin-film deposition processes, particularly in how it affects the mobility of atoms on the surface. Increasing the temperature increases the surface mobility of deposited atoms, allowing these atoms to diffuse more easily through the substrate. This increased mobility helps to produce more densely packed sublayers (also referred to herein as films) with fewer voids and defects. Essentially, a certain deposition temperature range can result in thin films with better structural uniformity, higher density, and potentially enhanced optical and mechanical properties.

[0062] However, in many cases, thin film deposition, especially that involving polymer substrates, can be limited to lower temperatures (e.g., around room temperature). Polymer substrates generally have only low heat resistance, and exposure to high temperatures can lead to deformation or other forms of degradation. As a result, room temperature processes are often used, which have limited functionality in maximizing the effect of temperature on surface mobility and film density.

[0063] Pressure during the deposition process provides another means of controlling the properties of the thin film. By adjusting the deposition pressure, the true stress within the film can be substantially controlled. Different pressure ranges can induce changes in stress properties. For example, depending on the specific material and deposition technique, some pressures may deposit films with low internal stress, while other pressures may deposit films with compressive or tensile stress. Controlling these stresses is particularly important to ensure the mechanical stability of the film in applications where the film may be exposed to thermal circulation or mechanical loads over long periods. In certain cases, selecting an appropriate pressure range can facilitate the scattering of incident atoms (adsorbed atoms), enhance the distribution of these atoms across the substrate surface, and induce more uniform film deposition.

[0064] For various elements or compounds, there may be a specific pressure at which a "neutral" stress (neither tensile nor compressive stress) is obtained at a given film thickness. However, as the film thickness increases, this neutral pressure shifts due to changes in the film's structure. Generally, tensile stress occurs at lower pressures (<3 milliliters) and can lead to delamination, while compressive stress occurs at higher pressures (>10 milliliters) and can lead to blistering or buckling. It is important to determine the pressure value during the deposition process and the degree of adjustment required to achieve desired effects such as increased voids or correction of stress levels. For example, for gradient refractive indices in the visible spectral range of 400–700 nm, a thickness of 3,500 Å is generally sufficient to produce the desired optical effect. At this thickness, a stable deposition pressure between 2–4 milliliters can be maintained without causing significant stress-related problems.

[0065] In addition, reducing the pressure during deposition (to less than approximately 3 milliliters) can increase the density of the deposited film by shortening the mean free path for adsorbed atoms at lower temperatures. Conversely, higher pressures (greater than approximately 5 milliliters) result in lower density films. In some cases, alternating the pressure between these two ranges (less than approximately 3 milliliters and greater than 5 milliliters) can induce density changes within the film and substantially adjust the internal stress. These pressure changes can be applied to sublayers with thicknesses encompassing all values ​​in the range from tens of angstroms (e.g., 10–90 Å) to hundreds of angstroms (e.g., 100–900 Å). Furthermore, if it is determined that the film presents tensile stresses greater than a predetermined threshold (e.g., based on deposition parameters), the deposition can be shifted toward compressive stress conditions, thereby adjusting the pressure to balance the overall stress within the film.

[0066] Pressure also has a significant effect on the optical properties of thin films, particularly their refractive index. By adjusting the deposition pressure or selecting a specific pressure range, microscopic voids or shielding can be introduced into the film. These shieldings lower the refractive index, which can be advantageous in applications requiring a lower refractive index to achieve enhanced optical performance. However, in some cases, these voids can reduce the adhesion of the film to the substrate, lowering the overall density of the substrate and resulting in a more fragile and less durable film. Therefore, while pressure adjustment is a valuable tool for tuning optical properties, it requires a delicate balance to avoid compromising the mechanical integrity of the thin film.

[0067] In one implementation, a cost function can be introduced to represent this balance between optical performance and mechanical integrity. A possible cost function could be a weighted sum in which one score corresponds to the optical properties of the film (e.g., desired refractive index, transparency, or light scattering properties) and the other score corresponds to the mechanical integrity of the film (e.g., adhesion, density, and stress resistance). The cost function can be based on a pressure parameter, and the goal is to optimize this function to achieve an optimal compromise between optical and mechanical properties. For example, if C(p) is the cost function and p is the deposition pressure, then C(p) = w1·f optical (p+w2·f mechanical It is thought that it can take the form (p), and in the above equation f optical (p) represents the score for optical properties, and f mechanical (p) represents a score for the mechanical properties, and w1 and w2 are weighting coefficients that reflect the importance of each property for a given application. Next, the function C(p) can be optimized with respect to pressure p to find the pressure range that yields the optimal balance between these conflicting factors.

[0068] f optical (p) and f mechanicalThe example in (p) can include any suitable function. For example, to perform a cost function that takes into account the deviation from the target gradient refractive index, the optical part of the cost function f optical (p) is the actual refractive index profile n(z,p) and the target gradient profile n T A function can be defined to evaluate the amount that deviates from (z). Such a function can be expressed as follows, for example, when d is the total thickness of the gradient refractive index layer: JPEG2026086357000002.jpg16156 This integral captures how much the actual refractive index deviates from the target at each point in the film. The goal is to minimize this function so that the actual refractive index faithfully follows the desired gradient profile. It should be noted that the function shown is only one possible example, and any other suitable function can be determined.

[0069] Similarly, f mechanical (p) can also be any appropriate function. Such a function is thought to be able to measure the mechanical integrity of the film by taking into account factors such as the adhesion strength, density, and internal stress of the film. One way to determine this function is by using a model that penalizes some outlier mechanical properties, such as high internal stress, low density, and insufficient adhesion strength. For example, if the stress in the film is σ(p), the film density is ρ(p), and the adhesion strength is A(p), then this function is f mechanical (p) = β1·σ(p) 2 It is possible that the expression looks like -β2·ρ(p)+β3·1 / A(p). Using such a function, it is possible to minimize stress σ(p) and density ρ(p) and maximize the adhesive force A(p). In the above equation, β1, β2, and β3 are weights that balance the importance of stress, density, and adhesive force. mechanical It should be noted that (p) is merely one possible example of a function, and any other suitable function can be used.

[0070] Deposition system and method for gradient refractive index layers

[0071] Figure 5 shows graphs 510 and 520 illustrating the material composition and deposition rate as functions of time and film thickness during the deposition process of a gradient refractive index layer, such as gradient refractive index layer 120. As shown in Figure 5, the material composition represented by graph 520 can be largely linearly changed as a function of time when depositing the gradient refractive index layer. For example, graph 520 shows silicon oxynitride Si x O y N z This illustrates the percentage of nitrogen deposited while substituting oxygen in the composition. For example, when nitrogen is absent (z=0), the composition of the material is SiO2, and when 100 percent nitrogen is present (z=4), the composition of the material is Si3N4. Generally, the relationship between x, y, and z is determined by the valence (bonding function) of the atoms involved, particularly silicon, oxygen, and nitrogen. Silicon generally forms four bonds in a compound, oxygen forms two bonds, and nitrogen generally forms three bonds. Stoichiometry must balance these bonding requirements, and stable compounds generally require 4x = 2y + 3z. This equation can result in silicon oxynitride such as SiO2 (x=1,y=2,z=0), Si3N4 (x=3,y=0,z=4), Si2O1N2 (x=2,y=1,z=2), and Si3O3N2 (x=3,y=3,z=2). As shown in Figure 5, during the initial deposition, nitrogen is not deposited or only a small amount of nitrogen is deposited. However, at the end of deposition, most of the integration is deposited. In the exemplary embodiment, the linear form in Graph 520 represents a refractive index layer with a linear gradient.

[0072] Furthermore, Graph 510 illustrates the deposition rate. In the exemplary embodiment, the deposition rate can be relatively linear over the initial period (e.g., over a period of about 14 minutes) and thereafter become nearly constant at a few angstroms per second. In some cases, if the deposition is greater than the stoichiometric ratio, an excess of one element (such as silicon) may result in a non-stoichiometric material that introduces undesirable optical effects such as dichroism, which results in gradient layers that provide different colors or absorb light differently when viewed from different angles or under different polarizations of light. This effect occurs when the refractive index of the material is configured to exhibit anisotropy (direction-dependent), leading to variable optical performance depending on the viewing angle.

[0073] Figure 6 shows a system 600 designed to deposit a non-dichroic coating thin film, such as the non-dichroic coating thin film structure 100 shown in Figure 1A. System 600 can be used to deposit gradient refractive index layers, Bragg-reflector structures, and / or Fabry-Perot structures. System 600 includes a control system 610 equipped with a processor 612 that executes instructions stored in memory 614. These instructions enable the control system 610 to send signals to manage the mass flow controller to deposit a precursor gas and maintain the temperature and pressure in the reaction chamber. Figure 6 exemplifies a reaction chamber 630 having a gas injection nozzle 632 that releases a precursor gas 634. These gases physically and / or chemically interact over the substrate 640 to form a non-dichroic coating thin film 636. In various embodiments, the control system 610 executes operations, including data acquisition and deposition stages, through the processor 612. As part of data acquisition, the control system 610 can be configured to receive optical properties of the substrate 640, including the substrate color determined from spectrophotometer measurements. This information regarding the substrate color can suggest specific structures to be deposited on the substrate. Furthermore, as part of data acquisition, the control system 610 can make reflectance requirements for the substrate available to the user of system 600. For example, these reflectance requirements may specify that the substrate reflects 10–30 percent of light in the visible wavelength range, and that the change in the reflectance coefficient with respect to the reflected wavelength in the visible spectrum remains below a specified threshold. Specifically, the change in the reflectance coefficient may be less than 20 percent or even less than 10 percent for the wavelength range of 400–700 nm. In some cases, the reflectance requirements may be provided in tabular format, as shown in the table below.

[0074] (Table 1) JPEG2026086357000003.jpg26147 Table 1: Reflectance Requirements Table for Non-Dichroic Coating Thin Films

[0075] Subsequently, the control system 610 is configured to select a formulation for depositing a non-dichroic coating thin film on the substrate based on the received optical properties and reflectance requirements. This selection step includes determining a set of parameters for the non-dichroic coating thin film. In one exemplary embodiment, the non-dichroic coating thin film includes a Bragg-reflector structure deposited on a substrate similar to or identical to the Bragg-reflector structure 130 shown in Figure 1A. This Bragg-reflector structure includes a plurality of pairs of layers, each containing a first layer and a second layer. The first layer is made of a material having a first refractive index and has a thickness equal to one-quarter of the target wavelength determined within this layer. The first layer is followed by a second layer, the second layer is made of a second material having a second refractive index and also has a thickness equal to one-quarter of the target wavelength determined within the second layer, in this case the first refractive index is at least 0.5 higher than the second refractive index. Furthermore, the non-dichroic coating thin film includes a gradient refractive index layer having a continuously changing gradient refractive index similar to or identical to that of the gradient refractive index layer 120. As illustrated in Figure 1A, this gradient refractive index layer can be deposited on top of a Bragg-reflector structure, where the gradient refractive index transitions continuously from a third refractive index to a first refractive index. In various cases, the step of determining the parameter set for the non-dichroic coating thin film includes identifying a target wavelength to which the Bragg-reflector structure will reflect most of the light, and determining at least the thickness of the gradient refractive index layer.

[0076] It should be noted that in some embodiments, the Bragg reflector structure may not be deposited, and the gradient refractive index layer can be deposited directly on the substrate. In such cases, the step of determining the parameter set for the non-dichroic coating thin film includes the step of determining the optical properties such as the thickness and gradient refractive index for the gradient refractive index layer.

[0077] Furthermore, when a Bragg reflector structure exists, the step of determining the parameter set includes determining the type of first material and the type of second material that can be used to form the Bragg reflector structure. For example, the first and second materials can be SiN having various mole fractions of silicon and nitrogen. For example, the first material can have a first mole fraction of silicon, and the second material can have a second mole fraction of silicon. For example, the first material may have the compositional formula Si a1 N b1 This can be done, and in contrast, the second material is Si a2 N b2 This can be done, in which case a1≠a2 and b1≠b2. In addition to or instead of this, other materials can be used for the first and second materials. For example, any suitable material can be used, such as TiO2, GaN, AlGaN, AlN, SiO2, MgO, Al2O3, ZnS, ZnO, Ga2O3, BN, InN, InGaN, GaP, diamond, and combinations thereof.

[0078] In addition, the step of determining the parameter set includes determining the type of third material that can be used with the first material to form a gradient refractive index layer. For example, the gradient refractive index layer can be formed from a combination of the third material and the first material. For example, as shown in Figure 1A, near surface 121, the gradient refractive index layer 120 is formed from a third material having a refractive index n3, and near surface 122, the gradient refractive index layer 120 is formed from a first material having a refractive index n1. For example, the third and first materials can be SiN having various mole fractions of silicon and nitrogen. For example, the first material can have a first mole fraction of silicon, and the third material can have a third mole fraction of silicon. In some cases, the first material is of the compositional formula Si a1 N b1 This can be done, and the third material is composed of Si a3 N b3This can be done, in which case a3≠a2 and b3≠b1. In addition to or instead of this, other materials can be used to form the first and third materials. For example, any suitable material can be used, such as TiO2, GaN, AlGaN, AlN, SiO2, MgO, Al2O3, ZnS, ZnO, Ga2O3, BN, InN, InGaN, GaP, diamond, and combinations thereof. Furthermore, the step of determining the parameter set includes not only determining the type of third material that can be used with the first material to form the gradient refractive index layer, but also determining the gradient profile for the gradient refractive index layer. In some cases, the gradient refractive index layer may have a linear gradient profile, for example, as shown in Figure 2A.

[0079] Referring to Figure 6, the control system 610 is configured to determine the time-dependent mass flow rate m1~mN for releasing the precursor gas, as shown by arrow 621 in Figure 6, and to further select the time-dependent pressure (shown by arrow 622) and time-dependent temperature (shown by arrow 623) for the reaction chamber. In some cases, the time-dependent temperature can be applied to the substrate holder 642. Furthermore, the control system 610 can be configured to determine the duration for the deposition of the precursor gas.

[0080] Figure 7 illustrates an example of a method 700 for selecting a deposition formulation for depositing a non-dichroic coating thin film on a substrate. Method 700 includes, in an optional step 710, a step of receiving optical properties of the substrate, such as the substrate's color, the substrate's reflectance to visible light in the wavelength range of 400 nm to 700 nm, and the substrate's scattering optical properties. These properties are available by a spectrometer. In some cases, in addition to optical properties, mechanical and / or material properties of the substrate can be obtained. For example, the raw materials used to fabricate the substrate can provide guidance for selecting a temperature at which the non-dichroic coating thin film can be deposited, and surface properties such as roughness can provide guidance for determining how the non-dichroic coating thin film will be deposited (e.g., a specific temperature and deposition rate as a function of time and the thickness of the non-dichroic coating thin film).

[0081] After the completion of step 710, method 700 includes an optional step in which a reflectance requirement is received in step 715. The reflectance requirement expresses, for example, the amount of light expected to be reflected from the non-dichroic coating thin film, as well as the variation in reflectance as a function of wavelength, as described above in Table 1. In certain cases, the reflectance requirement may generally include a specified range for the reflectance coefficient over visible light wavelengths that fall in the range of 400 nanometers to 700 nanometers.

[0082] After the completion of step 720, a deposition formulation can be selected based on the data obtained in steps 710 and 715, and method 700 can be completed. The deposition formulation can be selected based on known non-dichroic coating thin films having known reflectivity properties when deposited on a known substrate having specific optical and / or mechanical properties, and further having specific surface properties. A database of various non-dichroic coating thin films can be compiled for various substrates having various surface properties that result in specific reflectivity properties, and a specific formulation for the non-dichroic coating thin film can be selected based on such a database. In some cases, when the optical properties and / or reflectivity requirements of the substrate do not exactly match the parameters in the database, an appropriate interpolation method can be used to determine the deposition formulation. Such interpolation methods are schematically illustrated in Figures 8A to 8C.

[0083] Figure 8A illustrates an exemplary interpolation method. This method uses a linear function 801, given the reflectance from a non-dichroic coating thin film, to determine the thickness of the non-dichroic coating thin film based on the reflectance requirement. For example, if the reflectance requirement is 25%, a thickness D1 can be used. In certain embodiments, the thickness D1 can be approximately 1 micron. Figure 8A provides an embodiment of interpolation when a single parameter P1 determines the reflective properties of a non-dichroic coating thin film.

[0084] However, typically, there are several parameters that can affect the reflective properties of a non-dichroic coating thin film. Interpolation in a multidimensional parameter space can be performed as shown in Figure 8B. In Figure 8B, surface 802 shows the dependence of reflectance on several parameters (e.g., parameters P1 and P2). A constant reflectance contour 812 for a required reflectance value R1 is shown along with contours 811 and 813 for reflectance values ​​R0 and R2. Figure 8C shows such contours 811 to 813 for different reflectance values ​​R0 to R2. Specific points on contour 812 can be selected for the values ​​V1 and V2 of the relevant parameters P1 and P2. This selection may be based on other requirements unrelated to reflectance, such as the desired thickness, composition, or structure of the non-dichroic coating thin film.

[0085] In some cases, such selections can be based on specific requirements for the variation in reflectance from the average reflectance value as a function of the wavelength of visible light. For example, the plane 803 shown in Figure 8D illustrates the dependence of such a maximum reflectance change on multiple parameters (e.g., parameters P1 and P2). Contour 822 of the maximum reflectance change for the required maximum reflectance change with value ΔR1 is shown, along with similar contours 821 and 823 for the maximum reflectance changes with values ​​ΔR0 and ΔR2. Figure 8E shows both contours 811-813 for different reflectance values ​​R0-R2 and contours 821-823 for different maximum reflectance changes. It should be noted that when it is necessary to select values ​​for parameters P1 and P2 such that a reflectance of value R1 is desirable and a maximum reflectance change ΔR1 is required, such parameters can be obtained at the intersection of contours 822 and 812, and are given by values ​​V3 and V4.

[0086] It should be noted that the exemplary interpolation methods described in Figures 8A to 8E are merely illustrative, and various other methods can be used to determine the deposition formulation based on the optical properties and reflective requirements of the substrate. For example, a machine learning model can be run that outputs a desirable deposition formulation based on inputs of the optical properties and reflective requirements of the substrate. Such a machine learning model can be trained on historical training data associated with inputs including the optical properties and reflective requirements of the substrate and a desired output including non-dichroic coating thin film parameters.

[0087] When considering machine learning to determine deposition formulations based on the optical properties and reflection requirements of the substrate, various techniques can be applied. One approach is to use regression-based methods such as linear regression, polynomial regression, or support vector regression. These methods aim to establish a relationship between input features (optical properties and reflection requirements of the substrate) and output parameters (parameters of the non-dichroic coating thin film).

[0088] In addition to this, other machine learning techniques such as neural networks can be used. Neural networks, such as feedforward neural networks (FNNs), are particularly well-suited to complex nonlinear relationships between inputs and outputs. These neural networks can learn intricate patterns and correlations within the data, allowing the neural network itself to potentially capture the nuances of the deposition process.

[0089] Furthermore, ensemble methods such as random forests or gradient boosting may also be effective. These techniques combine multiple models to make predictions, and these predictions often result in improved performance and robustness. In some cases, hybrid methods combining various machine learning techniques such as neural networks and random forests may be advantageous. These hybrid models can further improve prediction performance by leveraging the strengths of each individual method.

[0090] Ultimately, the choice of machine learning algorithm depends on factors such as the complexity of the problem, the quantity and quality of available data, computing resources, and the desired level of accuracy.

[0091] Example - Hardware Overview

[0092] In some embodiments, techniques described herein, such as monitoring the deposition of non-dichroic coating thin films, are carried out by at least one computer device. For example, such a computer device may be part of the control system 610 shown in Figure 6 and may include a processor 612 and a memory 614 that stores instructions that can be executed by it.

[0093] The technologies described above can be implemented in whole or in part using a combination of at least one computer and / or other computer devices coupled together using a network such as a packet data network. Computer devices can be wired together to implement these technologies, or these computer devices may include digital electronic devices such as at least one application-specific integrated circuit (ASIC) or field-programmable gate array (FPGA) persistently programmed to implement these technologies, or at least one general-purpose hardware processor programmed to implement these technologies according to program instructions stored in firmware, memory, other storage, or a combination thereof. Such computer devices can be combined with specially designed wired logic circuits, ASICs, or FPGAs and specially designed programs to bring the described technologies to life. Computer devices may be server computers, workstations, personal computers, portable computer systems, handheld devices, mobile computer devices, smartphones, internetworking devices, autonomous devices, or semi-autonomous devices, or any other electronic device incorporating wired logic circuits and / or programmable logic circuits, one or more virtual computer machines or virtual computer instances in a data center, and / or a network of server computers and / or personal computers to implement the described technologies.

[0094] Figure 9 is a block diagram illustrating an exemplary computer system that enables the implementation of an embodiment. In the example of Figure 9, the computer system 900 and instructions for performing the disclosed technology using hardware, software, or a combination of hardware and software are schematically represented, for example, as boxes or circles, at the same level of detail commonly used by those skilled in the art when communicating with a computer architecture and implementation of a computer system relating to the disclosure of the present invention.

[0095] The computer system 900 includes an input / output (I / O) subsystem 902 which may include buses and / or other communication mechanisms for communicating information and / or instructions between components of the computer system 900 through electronic signal paths. The I / O subsystem 902 may include an I / O controller, a memory controller, and at least one I / O port. In the drawings, electronic signal paths are schematically represented, for example, as lines, unidirectional arrows, or bidirectional arrows.

[0096] The I / O subsystem 902 is coupled to at least one hardware processor 904 for processing information and instructions. The hardware processor 904 may include, for example, a general-purpose microprocessor or microcontroller and / or embedded system, a graphics processing unit (GPU), a digital signal processor, or a dedicated microprocessor such as an ARM processor. The processor 904 may include an integrated arithmetic logic unit (ALU) or be coupled to a separate ALU.

[0097] The computer system 900 includes one or more units of memory 906, such as main memory, coupled to the I / O subsystem 902 for electronically digitally storing data and instructions executed by the processor 904. Memory 906 may include various forms of random access memory (RAM) or volatile memory such as other dynamic storage devices. Memory 906 can be used to store temporary variables or other intermediate information during the execution of instructions by the processor 904. When such instructions are stored in a non-temporary computer-readable storage medium accessible to the processor 904, the computer system 900 can be transformed into a special-purpose machine customized to perform the operations specified in those instructions.

[0098] The computer system 900 further includes non-volatile memory, such as read-only memory (ROM) 908 or another static storage device, coupled to the I / O subsystem 902 for storing information and instructions for the processor 904. The ROM 908 may include various forms of programmable ROM (PROM), such as erasable PROM (EPROM) or electrically erasable PROM (EEPROM). Units of persistent storage 910 may include various forms of volatile RAM (NVRAM), such as flash memory, solid-state storage, magnetic disks, or optical disks such as CD-ROMs or DVD-ROMs, and may be coupled to the I / O subsystem 902 for storing information and instructions. Storage 910 is an example of a non-temporary computer-readable medium that can be used to store instructions and data that cause a computer implementation method for performing the techniques described herein when executed by the processor 904.

[0099] Instructions in memory 906, ROM 908, or storage 910 may include one or more instruction sets organized as modules, methods, objects, functions, routines, or calls. Instructions may be organized as one or more computer programs, operating system services, or application programs including mobile applications. Instructions may include operating system and / or system software, one or more libraries supporting multimedia, programs, or other functions, data protocol instructions or stacks for executing TCP / IP, HTTP, or other communication protocols, file format processing instructions for parsing or translating files encoded using HTML, XML, JPEG, MPEG, or PNG, user interface instructions for translating or interpreting instructions relating to a graphical user interface (GUI), command line interface, or text user interface, and application software such as office suites, internet access applications, design and manufacturing applications, graphics applications, audio applications, software engineering applications, educational applications, games, or miscellaneous applications. Instructions may implement a web server, web application server, or web client. Instructions can be organized as a presentation layer, an application layer, and a data storage layer such as a relational database system using a structured query language (SQL) or noSQL, an object store, a graph database, a flat file system, or other data storage.

[0100] The computer system 900 can be coupled to at least one output device 912 through the I / O subsystem 902. In one embodiment, the output device 912 is a digital computer display. Examples of displays that can be used in various embodiments include touch screen displays, light-emitting diode (LED) displays, liquid crystal displays (LCDs), or electronic paper displays. The computer system 900 may include other types of output devices 912 instead of or in addition to the display device. Examples of other output devices 912 include printers, ticket printers, plotters, projectors, sound cards or video cards, speakers, buzzers or piezoelectric devices, or other audible devices, lamp indicators, LED indicators, or LCD indicators, tactile devices, actuators, or servos.

[0101] The I / O subsystem 902 is coupled to at least one input device 914 for communicating signals, data, command selections, or operations to the processor 904. Examples of input devices 914 include touch screens, microphones, still digital cameras and video digital cameras, alphanumeric and other keys, keypads, keyboards, graphic tablets, image scanners, joysticks, clocks, switches, buttons, dials, slides, various types of sensors, such as force sensors, motion sensors, thermal sensors, accelerometers, gyroscopes, and inertial measuring unit (IMU) sensors, and / or various types of transceivers, such as cellular, Wi-Fi, radio frequency transceivers, infrared (IR) transceivers, and Global Positioning System (GPS) transceivers.

[0102] Another type of input device is a control device 916 that, in place of or in addition to the input function, can perform other automatic control functions such as cursor control on a display screen or navigation on a graphical interface. The control device 916 can be a touchpad, mouse, trackball, or cursor directional keys for communicating directional information and command selection to the processor 904 and for controlling cursor movement on the output device 912. The control device 916 may have at least two degrees of freedom, allowing it to specify a position in a plane along two axes, such as a first axis (e.g., x) and a second axis (e.g., y). Another type of input device may be a wired control device, a wireless control device, or an optical control device, or other type of control device, such as a joystick, wand, console, steering wheel, pedal, or gear shift mechanism. The input device 914 may include a combination of several different input devices, such as a video camera and a depth sensor.

[0103] In another embodiment, the computer system 900 may include an Internet of Things (IoT) device in which one or more of the output device 912, input device 914, and control device 916 are excluded. Alternatively, in such an embodiment, the input device 914 may include one or more cameras, motion sensors, thermometers, microphones, seismic sensors, other sensors or detectors, measuring devices, or encoders, and the output device 912 may include a dedicated display such as a single-row LED or LCD display, one or more indicators, display panels, measuring instruments, valves, solenoids, actuators, or servos.

[0104] When the computer system 900 is a mobile computer device, the input device 914 may include a Global Positioning System (GPS) receiver coupled to a GPS module that has the capability to perform triangulation relative to multiple GPS satellites and to determine and generate a location or position on Earth, such as latitude-longitude values ​​relating to the geophysical location of the computer system 900. The output device 912 may include hardware, software, firmware, and interfaces for generating location reporting packets, notifications, pulse signals or heart rate signals, or other repetitive data transmissions that determine the location of the computer system 900, either alone or in combination with other application-specific data, directed toward the host 924 or server 930.

[0105] The computer system 900 may perform the techniques described herein using specially designed wired connection logic circuits, at least one ASIC or FPGA, firmware, and / or program instructions or logic that, when loaded and used or executed in combination with the computer system, cause or program the computer system to operate as a dedicated machine. In one embodiment, the techniques described herein are performed by the computer system 900 in response to a processor 904 executing at least one sequence of at least one instruction confined in main memory 906. Such instructions can be read into main memory 906 from another storage medium, such as storage 910. The execution of the instruction sequence confined in main memory 906 causes the processor 904 to perform the processing steps described herein. In alternative embodiments, wired connection circuits may be used instead of or in combination with software instructions.

[0106] As used herein, the term “storage medium” means any non-temporary medium that stores data and / or instructions that operate a machine in a particular manner. Such storage media may include non-volatile media and / or volatile media. Non-volatile media include, for example, optical disks or magnetic disks, such as storage 910. Volatile media include dynamic memory, such as memory 906. Common forms of storage media include, for example, hard disks, solid drives, flash drives, magnetic data storage media, optical or physical data storage media, or memory chips.

[0107] The storage medium is separate from the transmission medium but can be used in conjunction with it. The transmission medium is involved in transmitting information between storage media. For example, the transmission medium includes coaxial cables, copper wires, and optical fibers, which contain wires that make up the bus of the I / O subsystem 902. The transmission medium can take the form of acoustic waves or optical waves, such as those generated during radio frequency data communication and infrared data communication.

[0108] Various forms of media may be involved in transmitting at least one sequence of at least one instruction to the processor 904 for execution. For example, the instruction may initially be held on a magnetic disk or solid drive of a remote computer. The remote computer may load the instruction into its dynamic memory and send it through a communication link such as optical fiber, coaxial cable, or telephone line using a modem. A modem or router local to computer system 900 may receive data on the communication link and convert it into a format that computer system 900 can read. For example, a receiver such as a radio frequency antenna or infrared detector may receive data transmitted in a radio signal or optical signal, and appropriate circuitry may supply the data to the I / O subsystem 902, for example, by putting the data on a bus. The I / O subsystem 902 transmits the data to memory 906, from which the processor 904 retrieves and executes the instruction. The instruction received by memory 906 may optionally be stored in storage 910 either before or after execution by processor 904.

[0109] The computer system 900 further includes a communication interface 918 coupled to the I / O subsystem 902. The communication interface 918 enables mutual data communication coupled to a network link 920 directly or indirectly connected to at least one communication network, such as network 922 or a public or private cloud on the Internet. For example, the communication interface 918 could be an Ethernet network connection interface, an Integrated Services Digital Network (ISDN) card, a cable modem, a satellite modem, or a modem for enabling data communication connections to a corresponding type of communication line, such as an Ethernet cable, any type of metal cable, fiber optic cable, or telephone line. Network 922 comprehensively represents a local area network (LAN), a wide area network (WAN), a campus network, an interconnect network, or any combination thereof. The communication interface 918 may include a LAN card enabling data communication connections to a compatible LAN, a wired cellular radio phone interface for sending and receiving cellular data according to a cellular radio phone wireless network connection standard, or a wired satellite radio interface for sending and receiving digital data according to a satellite radio network connection standard. In any such implementation, the communication interface 918 transmits and receives electrical, electromagnetic, or optical signals through a signal path that carries digital data streams representing various types of information.

[0110] The network link 920 typically provides electrical, electromagnetic, or optical data to other data devices directly or through at least one network using technologies such as satellite technology, cellular technology, Wi-Fi technology, or Bluetooth technology. For example, the network link 920 can enable connection to host 924 through network 922.

[0111] Furthermore, network link 920 can enable connections to network 922 or other computer devices through interconnection devices and / or computers operated by an Internet Service Provider (ISP) 926. ISP 926 provides data communication services through a global packet data communication network represented as the Internet 928. Server 930 may be connected to the Internet 928. Server 930 comprehensively represents any computer, data center, virtual machine, or virtual computer instance. Server 930 may represent electronic digital services that are implemented using one or more computers or instances and accessed and used by sending web service requests, parameterized Uniform Resource Locator (URL) strings in HTTP payloads, API calls, application service calls, or other service calls. Computer system 900 and server 930 can form elements of a distributed computer system, including other computers, processing clusters, server farms, or other computer organizations that collaborate to perform tasks or run applications or services. Server 930 may include one or more instruction sets organized as modules, methods, objects, functions, routines, or calls. Instructions can be organized as one or more computer programs, operating system services, or application programs including mobile apps.The instructions may include an operating system and / or system software, one or more libraries supporting multimedia, programs, or other functions, data protocol instructions or stacks for executing TCP / IP, HTTP, or other communication protocols, file format processing instructions for parsing or translating files encoded using HTML, XML, JPEG, MPEG, or PNG, user interface instructions for translating or interpreting instructions relating to a graphical user interface (GUI), command line interface, or text user interface, and application software such as office suites, internet access applications, design and manufacturing applications, graphics applications, audio applications, software engineering applications, educational applications, games, or miscellaneous applications. Server 930 may include a presentation layer, an application layer, and a web application server hosting a data storage layer such as a relational database system using Structured Query Language (SQL) or noSQL, an object store, a graph database, a flat file system, or other data storage.

[0112] The computer system 900 can send messages and receive instructions, including data and program code, through the network, network link 920, and communication interface 918. In an internet embodiment, it is conceivable that the server 930 can send request code relating to an application program through the internet 928, ISP 926, network 922, and communication interface 918. The received code can be executed by the processor 904 immediately upon receipt and / or stored in storage 910 or other non-volatile storage for later execution.

[0113] The execution of instructions described in this section can be carried out in the form of an instance of a running computer program, which consists of program code and its current operational status. Depending on the operating system (OS), a process can include multiple execution threads that execute instructions simultaneously. In this context, a computer program can be a set of passive instructions, while a process can be the actual execution of these instructions. Several processes can be associated with the same program; for example, opening several instances of the same program often means that more than one process is running. Multitasking can be performed to allow multiple processes to share a processor 904. Each processor 904 or its core executes a single task at a time, but the computer system 900 can be programmed to perform multitasking and switch between running tasks without having to wait for each processor to complete each task. In some embodiments, switching can occur when a task performs an input / output operation, when a task indicates that it can switch itself, or during a hardware interrupt. Time division can be implemented by rapidly performing context switching to make it appear as if multiple processes are running in parallel simultaneously, enabling a quick response to interactive user applications. In some embodiments, to achieve security and reliability, the operating system may prevent direct communication between independent processes and provide strictly mediated and controlled inter-process communication functions.

[0114] The embodiments of the disclosure of the present invention have been described with reference to many specific details, which may vary from one embodiment to another. Therefore, this specification and the drawings should be understood as illustrative rather than restrictive. The sole limiting indicator of the scope of the disclosure of the present invention, and what this applicant intends as the scope of the disclosure of the present invention, is the verbatim scope and equivalent scope of the set, characterized by including any subsequent amendments arising out of this application in specific forms.

[0115] The scope of the disclosure of the present invention encompasses all substitutions, alternatives, variations, changes, and modifications to the exemplary embodiments described or illustrated herein, which will be recognized by those skilled in the art. The scope of the disclosure of the present invention is not limited to the exemplary embodiments described or illustrated herein. Furthermore, while the disclosure of the present invention describes and illustrates each embodiment herein as comprising a particular component, element, feature, function, operation, or stage, any of these embodiments may include any combination or rearrangement with any of the components, elements, features, functions, operations, or stages described or illustrated elsewhere in this specification, which will be recognized by those skilled in the art. Furthermore, the reference in the appended claims to an apparatus or system or component of an apparatus or system being adapted or positioned to perform a particular function, or having or being configured to have such a function, or being activated or operable or operating, includes such systems, apparatuses, or components, insofar as such systems, apparatuses, or components are adapted or positioned or having or being configured to have such a function, or being activated or operable or operating, regardless of whether such systems, apparatuses, components or their particular function are activated, started or unlocked. In addition, while the disclosure of the present invention describes or illustrates certain embodiments as providing certain advantages, certain embodiments may provide none of, some of, or all of these advantages.

[0116] In this specification, unless otherwise specified or the circumstances indicate otherwise, “or” is inclusive, not restrictive. Thus, in this specification, unless otherwise specified or the circumstances indicate otherwise, “A or B” means “A, B, or both.” Furthermore, unless otherwise specified or the circumstances indicate otherwise, “and” can mean both congruent and separate. Thus, in this specification, unless otherwise specified or the circumstances indicate otherwise, “A and B” means “A and B congruently or separately.” [Explanation of Symbols]

[0117] 100 Non-dichroic coating thin film structure 110 Rays 120 gradient refractive index layer 130 Bragg-Reflector Structure n3 refractive index

Claims

1. A non-dichroic coating thin film structure deposited on a substrate, A Bragg reflector structure deposited on the substrate, having a plurality of pairs of layers, each pair having a first layer and a second layer, The first layer comprises a first material having a first refractive index and has a first thickness of one-quarter of the target wavelength determined within the first layer, and the first layer is positioned adjacent to the second layer. The second layer comprises a second material having a second refractive index and has a second thickness of one-quarter of the target wavelength determined within the second layer, and the first refractive index is at least 0.5 higher than the second refractive index. The Bragg reflector structure and, A gradient refractive index layer having a continuously changing gradient refractive index deposited on the Bragg reflector structure, wherein the gradient refractive index changes continuously from a third refractive index to a first refractive index, and the thickness of the gradient refractive index layer is selected such that the reflection coefficient for visible wavelength light changes by no more than 25 percent over the visible wavelength range of 400 to 700 nanometers. A non-dichroic coating thin film structure including this.

2. The non-dichroic coating thin film structure according to claim 1, wherein the target wavelength is determined based on the color of the substrate.

3. The non-dichroic coating thin film structure according to claim 2, wherein the target wavelength corresponds to a color that is the complementary color of the color of the substrate.

4. The non-dichroic coating thin film structure according to claim 1, wherein the first refractive index is in the range between 2.5 and 3.

5.

5. The non-dichroic coating thin film structure according to claim 1, wherein the second refractive index is in the range between 1.5 and 2.

5.

6. The non-dichroic coating thin film structure according to claim 1, wherein the third refractive index is in the range between 1.5 and 2.

5.

7. The non-dichroic coating thin film structure according to claim 1, wherein the gradient refractive index layer is selected from a composite material containing a variable mole fraction of silicon and nitrogen.

8. The gradient refractive index layer includes a silicon nitride layer deposited using chemical vapor deposition. The variable mole fraction of silicon and nitrogen is determined by the mass flow rate of silane gas and ammonia gas. The non-dichroic coating thin film structure according to claim 1.

9. The non-dichroic coating thin film structure according to claim 8, wherein the chemical vapor deposition is plasma-enhanced to lower the substrate temperature to several hundred degrees Celsius.

10. The thickness of the Bragg reflector structure is approximately 1 and 1 / 2 microns. The thickness of the gradient refractive index layer is further determined based on the reflectivity requirements of the non-dichroic coating thin film structure. The non-dichroic coating thin film structure according to claim 1.

11. The non-dichroic coating thin film structure according to claim 1, having a reflectance higher than 10 percent.

12. The non-dichroic coating thin film structure according to claim 1, wherein the gradient refractive index has a linear profile.

13. The Bragg reflector layer is a first Bragg reflector layer, The aforementioned non-dichroic coating thin film structure is The system further comprises a second Bragg-reflector layer deposited between the substrate and the first Bragg-reflector layer, wherein the second Bragg-reflector layer is configured to reflect light at a second target wavelength that is at least 100 nanometers different from the target wavelength of the first Bragg-reflector layer. The non-dichroic coating thin film structure according to claim 1.

14. The non-dichroic coating thin film structure according to claim 1, wherein the composition of the gradient refractive index layer is selected to have a reflectance of about 50 percent with a thickness of about 0.1 microns.

15. A system for depositing non-dichroic coating thin films, A control system having a processor, Includes, The processor causes the control system to transmit a signal to activate the mass flow controller for the deposition of the precursor gas, and executes commands to maintain temperature and pressure control inside the reaction chamber. The aforementioned instruction is, Receiving the optical properties of the substrate, including the color of the substrate, obtained from measurements using a spectrophotometer, To receive the reflectance requirements for the said substrate, Selecting a formulation for the deposition of the non-dichroic coating thin film on the substrate based on the received optical properties and reflectance requirements, wherein the selection of the formulation includes determining a parameter set for the non-dichroic coating thin film. The processor is made to perform an operation that includes the following: The aforementioned non-dichroic coating thin film is A Bragg reflector structure deposited on the substrate, having a plurality of pairs of layers, each pair having a first layer and a second layer, The first layer comprises a first material having a first refractive index and has a first thickness of one-quarter of the target wavelength determined within the first layer, and the first layer is adjacent to the second layer. A Bragg reflector structure comprising a second layer containing a second material having a second refractive index and having a second thickness of one-quarter of the target wavelength determined within the second layer, wherein the first refractive index is at least 0.5 higher than the second refractive index, A gradient refractive index layer having a continuously changing gradient refractive index deposited on the Bragg reflector structure, wherein the gradient refractive index of the gradient refractive index continuously changes from a third refractive index to the first refractive index, Includes, Determining the aforementioned parameter set means Determining the target wavelength, Determining the thickness of the gradient refractive index layer, A system that includes this.

16. The system according to claim 15, wherein determining the parameter set further comprises determining the first material and the second material.

17. The system according to claim 15, wherein determining the parameter set includes determining a third material having the third refractive index and determining a gradient profile for the gradient refractive index layer.

18. The system according to claim 15, wherein determining the parameter set includes determining a time-dependent mass flow rate for releasing the precursor gas and selecting a time-dependent pressure and temperature for the reaction chamber.

19. The system according to claim 15, wherein determining the parameter set includes determining the duration for the deposition of the precursor gas.

20. The system according to claim 15, wherein the reflectance requirement includes a required range for the reflectance coefficient for a wavelength set in the range of 400 to 700 nanometers.

21. The system according to claim 15, wherein the optical properties of the substrate include the reflectance of the substrate for visible light in the range of 400 to 700 nanometers and the scattering of visible light from the substrate.

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