Transmissive optical systems with limited ghost visibility, systems and methods for evaluating ghost visibility of transmissive optical systems

Abstract

The invention relates to a transmissive optical system (1) having at least a first surface (11) and a second surface (12) having different curvatures and / or being arranged to provide a dioptric power. According to the invention, a first coating (21) and a second coating (22) are configured such that the optical system (1) has a chromaticity evaluation parameter of ghost visibility below a predetermined threshold, said chromaticity evaluation parameter being based on a total ghost transmission factor of at least one ghost formed by an internal reflection of a light beam (30) from a light source (5) between the at least first surface (11) and the second surface (12) and by a transmission through the optical system (1), the light beam from the light source being incident on the first surface with a non-zero angle of incidence, the total ghost transmission factor being integrated over the visible spectral band and depending on a spectrum of the light source.

Description

Technical Field

[0001] This invention relates to a transmission optical system with low ghosting visibility, and a system and method for evaluating ghosting visibility in a transmission optical system.

[0002] The present invention also relates to apparatus and methods for reducing ghosting visibility in optical systems comprising one or more lenses.

[0003] The present invention also relates to a method for optimizing at least one antireflective coating in a transmission optical system to reduce ghosting visibility. Background Technology

[0004] Ghosting is a physical phenomenon typically caused by internal reflections within one or more lenses. It is visible when viewing a light source through an optical system comprising at least one lens. Ghosting is only visible with lenses or prisms that have a refractive power, as it separates the ghost image from the direct image of the light source angularly. Ghosting can also occur when the first lens is sandwiched between another lens, due to virtual reflections between the surfaces of the first and second lenses.

[0005] Depending on the color and intensity of the double image, double images can be a cause of discomfort for the wearer.

[0006] Many documents describe apparatus and methods for manufacturing optical systems with anti-reflective coatings to provide comfort under specific conditions (such as night driving) and to limit or avoid ghosting of light sources.

[0007] However, the visibility of ghosting depends on several parameters, such as the reflectivity and transmittance characteristics of convex and concave surfaces, as well as the absorbance of the substrate and the spectrum of the light source.

[0008] Patent document US 5,193,028 discloses a transmission optical system comprising a plurality of transmission optical elements having at least two boundary reflective surfaces, which create ghosting when light is reflected by the at least two boundary reflective surfaces. The two boundary reflective surfaces are coated with two antireflective coatings having complementary reflectance spectral profiles to eliminate ghosting over a broad wavelength band.

[0009] The publication "Ophthalmic lenses and dispensing," pp. 75-87, January 1, 2008, Elsevier, XP055039205, discloses multilayer and broadband antireflective coatings to prevent ghosting from interfering with vision through an optical system, based on a reflectance spectrum calculated or measured in the 400-700 nm range, where light is incident and reflected at a normal angle of incidence. Document US 2020 / 0284962 relates to methods, systems, and compositions that reduce actual and perceived glare when viewing through a partially transparent material by incorporating an optical absorber into the material.

[0010] For lenses with anti-reflective coatings, each anti-reflective coating can be defined using chromaticity parameters in CIE color coordinates (C, h°, Rv), where C represents chromaticity, h represents hue angle, and Rv represents color luminance based on human eye sensitivity to a CIE 1931 photopic observer and a D65 standard reference illuminance.

[0011] Ghosting visibility is related to the phenomenon of few or many internal reflections. Moreover, for optical systems with more than two surfaces, each additional surface causes additional ghosting.

[0012] Empirically, applying an anti-reflective coating to at least one surface of an optical system can reduce ghosting visibility. However, using conventional anti-reflective coatings on all surfaces is insufficient to prevent ghosting in a predictable manner.

[0013] There is no method for numerically evaluating ghost visibility in transmission optical systems with two or more surfaces.

[0014] There is no method for optimizing one or more coatings in a transmission optical system to minimize ghosting visibility.

[0015] Therefore, there is a need for standards, systems, and / or methods to evaluate ghost visibility in transmission optical systems with two or more surfaces.

[0016] Similarly, a method is needed to optimize anti-reflective coatings in optical systems with two or more surfaces to avoid or limit ghosting visibility. Summary of the Invention

[0017] Therefore, one object of the present invention is to provide a transmission optical system having at least a first surface and a second surface, the first surface and the second surface having different curvatures and / or the first surface and the second surface being configured to provide refractive power, wherein the transmission optical system has a chromaticity evaluation parameter for ghost visibility below a predetermined threshold for ghost visibility, the chromaticity evaluation parameter being based on the total ghost transmission coefficient of at least one ghost, the at least one ghost being formed by the internal reflection of a light beam from a light source between at least the first surface and the second surface and by transmission through the optical system, the light beam from the light source being incident on the first surface at a non-zero angle of incidence, the total ghost transmission coefficient being generated by the integral of the ghost transmittance of the at least one ghost in the visible spectral band and depending on the spectrum of the light source and the spectral luminous efficiency of a CIE 1964 photopic observer.

[0018] According to specific and advantageous aspects, the transmission optical system has exactly two surfaces with different curvatures, and each ghost image formed by the internal reflection of the light beam between the two surfaces of the optical system and by the transmission through the optical system has a ghost transmittance calculated using the following formula:

[0019] T(λ, 15°) = T Cx (λ, 15°).R BCc (λ, α).R BCx (λ, α).T Cc (λ,α).(T int (λ,α)) 3

[0020] Wherein, λ represents the wavelength in the visible spectrum, the incident angle of the light source is set to 15 degrees and corresponds to the refraction angle α within the substrate supporting the first and second surfaces, T Cx (λ, 15°) represents the spectral transmittance of the first surface at the incident angle, R BCc (λ, α) represents the spectral reflectance of the second surface at the refraction angle α for reflections occurring within the medium of the substrate, R BCx (λ, α) represents the spectral reflectance of the first surface for reflections occurring within the medium of the substrate, T Cc (λ, α) represents the spectral transmission of the second surface, and T int (λ, α) represents the spectral transmittance between the first surface and the second surface.

[0021] According to a specific embodiment, the total ghost transmission coefficient is calculated using the following formula:

[0022]

[0023] Wherein, the visible spectral band extends between 380 nm and 780 nm, S(λ) represents the spectral brightness of the light source, and This indicates the spectral luminous efficiency of a photopic observer as defined in CIE 1964.

[0024] Depending on a particular aspect, the first surface includes a first coating, and the second surface includes a second coating.

[0025] In a particular embodiment, the transmission optical system further includes at least one other surface having another coating, wherein each pair of two different surfaces with different curvatures among the first surface, the second surface, and the at least one other surface forms a specific ghost image, and each specific ghost image has a specific ghost image transmittance, and wherein the first coating, the second coating, and the other coating are configured such that each specific ghost image has a total ghost image transmittance coefficient below the predetermined threshold.

[0026] Depending on the specific aspect, the transmittance of the total ghost image formed by the superposition of different ghost images is calculated using the following formula:

[0027]

[0028]

[0029]

[0030] Where XY represents any pair of surfaces X and Y with the same combination of two radii of curvature, Z represents any substrate between surfaces X and Y, and W represents every other surface between surfaces X and Y that is different from surfaces X and Y, R represents the reflectivity of the interface under consideration, T represents the surface transmittance, and T0 represents the surface transmittance. int This indicates the transmittance of the substrate.

[0031] Alternatively, according to another specific embodiment, the transmission optical system further includes at least one other surface having another coating, each pair of two different surfaces having the same curvature pair among the first surface, the second surface, and the at least one other surface forming a component of the same specific ghost with component ghost transmittance, and wherein the first coating, the second coating, and the other coating are configured such that, for the same specific ghost, the total ghost transmittance coefficient is calculated based on the sum of the different components of the same specific ghost transmittance and is below the predetermined threshold.

[0032] Specifically, the total ghosting transmission coefficient for each ghost image is calculated using the following formula:

[0033]

[0034] Wherein, the visible spectral band extends between 380 and 780 nanometers, S(λ) represents the spectral brightness of the light source, and Let denot be the spectral light efficiency of a CIE 1964 photopic observer, and ∑T(λ, 15°) represent the sum of all ghost transmittance components of two surfaces with the same curvature pair.

[0035] Depending on the specific aspect, the total ghosting transmission coefficient is further based on the number of surfaces of the transmission optical system, the transmission coefficient of each surface, and the transmission coefficient of each substrate supporting the surface of the transmission optical system.

[0036] For example, the light source is a light-emitting diode with a color temperature ranging from 2700 Kelvin to 6000 Kelvin.

[0037] Depending on the specific aspect, the predetermined threshold for ghost visibility is less than 0.010%, preferably 0.007%.

[0038] Preferably, the transmission optical system includes at least one anti-reflective coating on the first surface and / or the second surface.

[0039] According to a specific embodiment, at least one antireflective coating comprises a pair of coatings consisting of a first antireflective coating on a first surface and a second antireflective coating on a second surface, wherein the pair of coatings is selected from the following pairs: a blue antireflective coating and a copper-colored antireflective coating; a blue antireflective coating and a green antireflective coating; an orange mirror coating and a blue antireflective coating; a blue mirror coating and a copper-colored antireflective coating; a green antireflective coating and a copper-colored antireflective coating; and a copper-colored antireflective coating and a copper-colored antireflective coating.

[0040] According to a specific embodiment, the at least one antireflective coating comprises a pair of coatings consisting of a first antireflective coating on the first surface and a second antireflective coating on the second surface, wherein the pair of coatings comprises at least one of the following: a copper-colored antireflective coating, a green antireflective coating, and an orange mirror coating.

[0041] Advantageously, the copper-colored antireflective coating comprises a multilayer stack having at least six layers, the multilayer stack comprising, along a direction away from the substrate, a silicon dioxide layer with a thickness of approximately 150 nm, a zirconium dioxide layer with a thickness of 14 nm to 16 nm, a silicon dioxide layer with a thickness of 28 nm to 32 nm, a zirconium dioxide layer with a thickness of 87 nm to 93 nm, a tin oxide or indium tin oxide layer with a thickness of approximately 6.5 nm, and a silicon dioxide layer with a thickness of 71.7 nm to 77 nm.

[0042] According to a specific embodiment, the coating includes at least one of a copper-colored anti-reflective coating and a blue mirror or blue anti-reflective coating.

[0043] Another object of the present invention is to provide a method for evaluating the ghost visibility of a transmission optical system having at least a first surface and a second surface, the first surface and the second surface having different curvatures and / or the first surface and the second surface being configured to provide refractive power.

[0044] According to the present invention, the above-mentioned object is achieved by providing a method for evaluating ghost visibility, the method comprising the step of determining a chromaticity evaluation parameter of ghost visibility, the chromaticity evaluation parameter being based on the total ghost transmission coefficient of at least one ghost, the at least one ghost being formed by the internal reflection of a light beam from a light source between a first surface and a second surface and by transmission through the optical system, the light beam from the light source being incident on the first surface at a non-zero incident angle, the total ghost transmission coefficient being generated by the integral of the ghost transmittance of the at least one ghost in the visible spectral band and depending on the spectrum of the light source and the spectral luminous efficiency of a CIE 1964 photopic observer.

[0045] According to the present invention, the above-mentioned objective is achieved by providing a method for optimizing at least one antireflective coating of a transmission optical system having at least a first surface and a second surface, the first surface including a first coating and the second surface including a second coating, wherein at least one of the first coating and the second coating is an antireflective coating, the first surface and the second surface having different curvatures and / or the first surface and the second surface being configured to provide refractive power.

[0046] According to the present invention, the above-mentioned objective is achieved by providing a method for optimizing at least one antireflective coating, the method comprising the following steps:

[0047] a) Determine the chromaticity evaluation parameters for ghost visibility, the chromaticity evaluation parameters being based on the total ghost transmission coefficient of at least one ghost, the at least one ghost being formed by the internal reflection of a beam of light from a light source between the first surface and the second surface and by transmission through the optical system, the beam of light from the light source being incident on the first surface at a non-zero incident angle, the total ghost transmission coefficient being generated by the integral of the ghost transmittance of the at least one ghost in the visible spectral band and depending on the spectrum of the light source and the spectral luminous efficiency of a CIE 1964 photopic observer;

[0048] b) Modify the structure and / or composition of the first and / or second coatings, and

[0049] c) Repeat steps a) and b) until the chromaticity evaluation parameter of the ghost visibility of the transmission optical system is lower than the predetermined threshold of ghost visibility.

[0050] Another object of the present invention is to provide a system for evaluating the ghost visibility of a transmission optical system having at least a first surface and a second surface, the first surface and the second surface having different curvatures and / or the first surface and the second surface being configured to provide refractive power.

[0051] According to this disclosure, the system for evaluating ghost visibility includes a processor configured to determine chromaticity evaluation parameters for ghost visibility, the chromaticity evaluation parameters being based on the total ghost transmittance coefficient of at least one ghost formed by the internal reflection of a beam of light from a point source between a first surface and a second surface and by transmission through an optical system, the beam of light from the source being incident on the first surface at a non-zero angle of incidence, the total ghost transmittance coefficient being generated by the integral of the ghost transmittance of the at least one ghost in the visible spectral band and depending on the spectrum of the source and the spectral luminous efficiency of a CIE 1964 photopic observer.

[0052] According to a particular aspect, the transmission optical system has a third surface and / or a fourth surface, and the system for evaluating ghost visibility includes a processor configured to determine the total ghost transmission coefficient for each ghost, each ghost being formed by the internal reflection of the light beam between all surface pairs having the same pair of two different curvatures, the total ghost transmission coefficient depending on the sum of the ghost transmission components of each ghost transmissivity component of all surface pairs having the same pair of two different curvatures.

[0053] According to another aspect, the transmission optical system has a third surface and / or a fourth surface, and the system for evaluating ghost visibility includes a processor configured to determine the ghost transmission coefficient of each ghost, each ghost being formed by the internal reflection of the light beam between each pair of surfaces having two different curvatures, the total ghost transmission coefficient depending on the sum of the ghost transmission coefficients of each ghost.

[0054] Detailed explanation of the example

[0055] The following description, given with reference to the accompanying drawings, will make the scope of the invention and the manner in which it is implemented clear. The invention is not limited to the embodiments shown in the drawings. Accordingly, it should be understood that where features mentioned in the claims are followed by reference numerals, such reference numerals are included only for the purpose of enhancing the comprehensibility of the claims and are in no way intended to limit the scope of the claims.

[0056] The following brief description now refers to the accompanying drawings and detailed description, wherein the same reference numerals denote the same parts.

[0057] In the attached diagram:

[0058] -Figure 1 A cross-sectional view of an ophthalmic lens and the internal reflection of the incident beam at the origin of the ghosting;

[0059] - Figure 2 A system for observing ghosting of a light source through an optical system is shown;

[0060] - Figure 3 Examples of direct images and ghosting of the same light source as seen through an optical system are shown;

[0061] - Figure 4 A cross-sectional view of a two-lens optical system and multiple internal reflections of the incident beam at the origin of the ghosting;

[0062] - Figures 5A to 5C This shows each ghosting formed by internal reflection between a pair of surfaces of a dual-lens optical system; Figure 5D The internal reflection between surfaces with the same radius of curvature is shown, which does not produce a separate ghosting;

[0063] - Figure 6 An example of ray tracing simulation of ghosting in a dual-lens optical system is shown;

[0064] - Figure 7 Different parameters (incident angle, refraction angle, transmission and reflection coefficients of a double-surface optical system) are shown for determining ghost transmittance.

[0065] - Figure 8 This represents the spectral luminous efficiency of different types of observers under daytime and nighttime visual conditions.

[0066] - Figure 9 The results of the evaluation of ghost visibility as a function of the logarithm of the total ghost transmittance of various dual-surface optical systems are shown.

[0067] - Figure 10 The correlation curves between contrast and the logarithm of total ghost transmittance for various dual-surface optical systems are shown.

[0068] - Figure 11 The diagram schematically illustrates the four surfaces of the optical system and the ghosting formed by internal reflection between the first surface (denoted as A) and the fourth surface (denoted as D);

[0069] - Figure 12 The diagram schematically illustrates the four surfaces of the optical system and the ghosting formed by internal reflection between the second surface (denoted as B) and the fourth surface (denoted as D);

[0070] - Figure 13The diagram schematically illustrates the four surfaces of the optical system and the ghosting formed by internal reflection between the third surface (denoted as C) and the fourth surface (denoted as D);

[0071] - Figures 14 to 17 Different dual-lens optical systems according to this disclosure are shown, wherein at least one coating is optimized to reduce ghosting visibility.

[0072] In the following description, the accompanying drawings are not necessarily drawn to scale, and some features may be shown in generalized or schematic form for clarity and brevity or for informational purposes. Furthermore, although several different embodiments of manufacture and use are discussed in detail below, it should be understood that many inventive concepts that can be practiced in a variety of contexts are provided as described herein. The embodiments discussed herein are merely illustrative and do not limit the scope of the invention. It will also be apparent to those skilled in the art that all technical features defined relative to the method can be transposed individually or in combination to the apparatus, and conversely, all technical features defined relative to the apparatus can be transposed individually or in combination to the method.

[0073] Apparatus and Method

[0074] Figure 1 An optical system is shown in cross-section, comprising a single ophthalmic lens 1 having a first surface 11 and a second surface 12. The first surface 11 and the second surface 12 have different curvatures, and / or the first surface 11 and the second surface 12 are configured to provide refractive power. Generally, for an ophthalmic lens, the first surface 11 is convex, and the second surface 12 is concave. Figure 1 The diagram also shows a point light source 5 that generates an incident beam 30 pointing towards the ophthalmic lens 1, and two main optical paths through the lens 1. A directly transmitted beam 40 is formed when the transmitted light passes directly through the first and second surfaces 11 of the lens, thus passing through the lens substrate once. A first-order reflected beam 41 is formed when the incident light undergoes internal reflection at the second surface 12, then internal reflection at the first surface 11, and then passes through the second surface 12 again, thus passing through the lens substrate twice. Under certain conditions, ghosting occurs. Specifically, for the point light source 5, when the incident angle of the incident beam 30 at the first surface 11 is not zero or non-zero, the directly transmitted beam 40 and the first-order reflected beam 41 propagate in angularly separated directions, easily forming two different images of the light source 5. The direct image 6 is formed along the direction of the directly transmitted beam 40. The ghosting 7 of the light source 5 is formed along the direction of the first-order reflected beam 41. Therefore, the formation of ghosting is a physical phenomenon caused by internal reflection within the lens 1. Ghosting is only visible for lenses or prisms with refractive power because it separates the ghost image 7 from the direct image 6 of the light source at an angle through the optical system.

[0075] Figure 2 A system for observing ghosting is shown. When viewing point light source 5 through lens 1, ghosting 7 is visible. Point light source 5 is, for example, a light-emitting diode or LED. Depending on the color and intensity of the ghosting, its presence may be a cause of discomfort for the wearer.

[0076] Figure 3 Examples of direct image 6 and ghost image 7 are shown, formed using an LED light source and lenses with a high-chromaticity blue coating on both sides. Direct image 6 appears sharp and intense against a dark background. Ghost image 7 appears less intense and is colored, for example, blue in this case.

[0077] Because light bounces off both sides of the lens, the chromaticity characteristics of the coatings deposited on both sides affect ghosting. Let us represent the first coating 21 on the first surface 11 and the second coating 22 on the second surface 12, respectively. Each of the first and second coatings is selected from the following coatings: anti-reflective coating, specular coating, and hard coating. Each coating may consist of a single layer or multiple stacks.

[0078] The goal is to maximize the visible transmittance of the direct image while minimizing the visibility of ghosting.

[0079] However, the relationship between the chromaticity of the first and second coatings and the visibility of ghosting is not obvious. The chromaticity of a coating can be defined using 3D chromaticity coordinates, such as (Rv, C, h), where h represents the hue angle, C represents the chromaticity, and Rv represents the brightness of the color based on human eye sensitivity (Rv from CIE 1931, chromaticity and hue from CIE 1964, and the D65 illuminant). When considering a combination of two antireflective coatings, there are many chromaticity parameters: Rv, chromaticity, and hue angle for each coating.

[0080] Based on experience, it has been observed that different combinations of anti-reflective coatings on the convex and concave surfaces of a single lens produce significantly different ghosting visibility.

[0081] According to the first approximation, for a single lens, ghosting visibility is related to Rv on the first (convex) surface 11 and Rv on the second (concave) surface 12. However, there are lens configurations with the same coating on the convex side and two different coatings with the same Rv value on the concave side, which result in significantly different ghosting.

[0082] For example, let's consider a lens with a first coating 21 consisting of a high-chromaticity blue coating and a second coating on the back side. When the second coating 22 consists of a blue anti-reflective coating with an Rv of 0.96, the ghosting appears as a deep blue. However, when the second coating 22 consists of a green anti-reflective coating with an Rv of 0.96, the ghosting is much darker and almost disappears on a dark background.

[0083] Similarly, this paper observes that antireflective colors are typically calculated using a D65 standard illuminator corresponding to daylight illumination. However, the D65 standard illuminator does not appear to be suitable for observing ghosting, which is typically formed by point sources on a dark background.

[0084] When the ophthalmic system has two or more surfaces (N≥2) and one of the surfaces has a different curvature, multiple ghost images can easily occur due to the multiple internal reflections between these surfaces.

[0085] For an ophthalmic system with two surfaces, there exists a single, or first-order, ghosting caused by double reflections within the system. From there, each additional surface results in an additional ghosting. Therefore, in a system with N ≥ 2 surfaces, there are (N-1)! potential first-order ghostings.

[0086] Ophthalmic systems with two or more surfaces typically consist of, but are not limited to, a combination of a first lens 1 and a second lens 2. The first lens is usually a plano lens, and the second lens is a convex lens. This combination may be intended to prescribe plano lenses (electrochromic, sunglasses, etc.). Alternatively, this combination may be intended to provide additional functionality, whether temporary or permanent, on top of a refractive lens (such as a set of clip-on lenses for daytime or nighttime driving, or augmented reality lenses).

[0087] In ophthalmic systems with more than two surfaces, most systems have four surfaces arranged in a specific combination of their radii of curvature. Generally, all surfaces except one are parallel to each other or have the same (or nearly the same) radius of curvature. The use of the same radius of curvature at the interface between the two clamped lenses is dictated by mechanical constraints.

[0088] For example, such as Figure 4 As shown, the ophthalmic system consists of a first lens 1 and a second lens 2. The first lens 1 has a first convex surface 11 with a first radius of curvature (denoted as R1) and a second concave surface 12 with the same radius of curvature R1. The second lens 2 has a third convex surface 13 with the same first radius of curvature R1 and a fourth concave surface 14 with a second radius of curvature (denoted as R2) different from R1.

[0089] For ophthalmic systems with two or more surfaces, several ghost images are formed. Point light source 5 generates an incident beam 30 directed at the first lens 1 of the ophthalmic system at a non-zero incident angle. Figure 4The main optical path of the light beam passing through the first lens 1 and the second lens 2 is shown. When the transmitted light directly passes through the first surface 11 and the second surface 12 of the first lens 1, and then through the third surface 13 and the fourth surface 14 of the second lens 2, a directly transmitted beam 40 is formed. The directly transmitted beam 40 passes through the substrate of the first lens 1 once and through the substrate of the second lens 2 once. When the incident light undergoes internal reflection at the fourth surface 14 and the third surface 13 of the second lens 2, and then passes through the fourth surface 14, a first-order reflected beam 43 is formed, thus passing through the substrate of the first lens 1 once and through the substrate of the second lens 2 twice. Figure 5A When the incident light undergoes internal reflection at the fourth surface 14 of the second lens 2 and the second surface 12 of the first lens, and then passes through the third and fourth surfaces of the second lens 2, it forms another first-order reflected beam 42. Figure 5B Therefore, this other first-order reflected beam 42 passes through the substrate of the first lens 1 once and through the substrate of the second lens 2 three times. When the incident light undergoes internal reflection at the fourth surface 14 of the second lens 2 and the first surface 11 of the first lens 1, and then passes through the second, third, and fourth surfaces, another first-order reflected beam 41 is formed. Figure 5C Therefore, another first-order reflected beam 41 passes through the substrate of the first lens 1 three times and through the substrate of the second lens 2 three times. The first-order reflected beams 43, 42 and 41 are parallel to each other.

[0090] This particular configuration has several consequences regarding ghosting. It results from the same two different radii of curvature R1, R2 (… Figure 5A , Figure 5B , Figure 5C All the ghosting caused by the combination of ) are combined together to form a first-order ghosting. Figure 6 Therefore, it is more obvious than when they are independent.

[0091] Some ghosting merges with the direct image because they occur between parallel surfaces (with two identical radii of curvature R1), so the ghosting is not visible. For example (see...) Figure 5D The reflected beam 50 is formed by internal reflections on the second surface 12 and the first surface 11, and is transmitted through the second surface 12 of the first lens and the third and fourth surfaces of the second lens 2. The reflected beam 50 generates a ghost image. However, the directly transmitted beam 40 and the reflected beam 50 propagate in parallel directions, so this ghost image is superimposed on the direct image of the point light source 5.

[0092] Figure 6 It shows that in such Figure 4The example shown in Figure 5 illustrates a ray-tracing simulation of ghosting formation in an uncoated dual-lens optical system. The simulation software used here is Zemax OpticStudio. The light source used for the simulation is a 40mm square, placed at a 15-degree angle of incidence to the optical axis, 500mm from the eye. The light source has three equally weighted wavelengths: 486nm, 588nm, and 656nm. The light source has a color temperature of approximately 4000K LED. The three ghosts formed by internal reflections on a pair of surfaces with different radii of curvature (R1 = 193mm and R2 = 117mm) in the dual-lens optical system combine to form a single ghost 7 spatially offset relative to the primary image 6. Other stray light 8 is also generated. However, this residual stray light 8 is practically invisible to the human eye.

[0093] In the case of an ophthalmic system with a single lens, providing a conventional anti-reflective coating to both surfaces (N=2) may be sufficient to reduce ghosting visibility.

[0094] However, in ophthalmic systems with two lenses (as in the previous example, where three surfaces have the same radius of curvature R1 and one surface has a different radius of curvature R2), three ghost images of similar intensity are superimposed, resulting in a combined transmittance of approximately three times higher. However, simply applying a conventional anti-reflective coating to all surfaces is often insufficient to reduce the resulting ghost image visibility below the visibility threshold. More generally, different combinations of radii of curvature lead to different numbers of ghost images, which are superimposed in different ways.

[0095] Therefore, the purpose of this disclosure is to propose alternative criteria for assessing ghost visibility.

[0096] More specifically, we propose an appropriate chromaticity parameter for evaluating the visibility of ghosting. This new parameter is based on calculations of the ghosting spectrum, also incorporating the spectrum of the light source and the CIE 1964 observer, which has been found to be more relevant than the conventional CIE 1931 observer. The calculation method is specified below for ophthalmic systems with at least two surfaces.

[0097] New parameter, total ghost transmission coefficient (hereinafter referred to as T) GI The ghosting transmittance, representing the ghosting transmittance of a two-sided optical system or the total ghosting transmittance of an optical system with two or more surfaces, is supported by a strong correlation with perception, as demonstrated by the results of one study on untrained observers and another on trained observers. Based on the sensory data, criteria for the ghosting risk of antireflective coating combinations can be established and integrated into the antireflective design process for optical systems with at least two surfaces. We also determined a numerical threshold for ghosting visibility.

[0098] 1. In an optical system with two surfaces, T GI Definition and calculation

[0099] To calculate the chromaticity parameters, the transmittance spectrum of the ghost image is used in the first step. The transmittance spectrum provides descriptive information about the ghost image's color. From this, concise and accurate numerical parameters for describing and evaluating the ghost image are derived.

[0100] Currently, ghosting cannot be measured directly and requires very specific spectral equipment and acquisition conditions, so it is modeled.

[0101] Numerical simulation tools were developed in Matlab to calculate the transmittance spectrum of ghosting. The transmittance spectrum of ghosting can also be calculated using the vStack function in the Macleod software (available in the enhanced version of Macleod).

[0102] Numerical simulation is based on Figure 7 The following assumptions are illustrated schematically:

[0103] - An approximation of two parallel surfaces (without considering lens correction).

[0104] - The light absorption and thickness of the substrate were taken into account.

[0105] - Calculations are performed when the angle of incidence is 15 degrees.

[0106] The angle of incidence is set to 15 degrees to represent a general observation angle. However, if necessary, any non-zero angle of incidence (preferably between 5 and 30 degrees) can be used to match more specific sets of conditions.

[0107] The color of the ghost image is calculated using the transmittance of the ghost image in the 380-780nm spectral range.

[0108] The reference light source used for color calculations is typically D65 (the standard illuminance representing daylight). However, ghosting cannot be observed under daylight because a point light source is required, and "daylight" is not a point light source. Sunlight is also generally unsuitable because people do not usually look directly at the sun.

[0109] Therefore, the reference light source chosen here is a specific light source used for observation and that has been measured. For example, a reference light source is an LED with a color temperature between 2700 and 6000 Kelvin, specifically a 4000K LED, or any point light source such as a filament lamp, a halogen lamp, or even the sun. In this document, a point light source is a light source that appears very small compared to the observer's field of view through the lens. For example, the observer's total field of view is more than 5-10 times the angular size of the light source. According to the general definition in optics, the calculations performed in this disclosure approximate the light source as a point light source.

[0110] Colors are calculated using the following tools: the required color calculation functions have been implemented in Matlab (also available as a commercial toolkit), and Macleod has built-in color calculation functions.

[0111] In the CIE XYZ color coordinate system, the R of the antireflective coating V This corresponds to the Y trichromatic stimulus values ​​(representing brightness values) calculated using a 2-degree observer (CIE 1931 observer) based on antireflectivity. GI The Y tri-stimulus values, defined in this paper as ghost transmittance, are instead calculated using the 10-degree observer (or CIE 1964 observer). The 10-degree observer is an updated version of the 2-degree observer, providing correction in the blue wavelength range and is the CIE recommendation for color calculations. (Compared to R...) V Similarly, T GI Expressed as a percentage. In other words, T GI This corresponds to a chromaticity parameter representing the color brightness of ghosting based on the human eye sensitivity of a CIE 1964 photopic observer and the spectrum of a point light source (rather than the D65 standard reference).

[0112] Figure 8 The spectral luminous efficacy (SI, expressed in arbitrary units) for different types of observers under daytime (or photopic) and nighttime (or scotopic) visual conditions is shown. Curve 51 shows the spectral luminous efficacy of a CIE 1931 photopic observer, i.e., a 2-degree observer under daytime visual conditions. Curve 52 shows the spectral luminous efficacy of a CIE 1951 scotopic observer, i.e., a 2-degree observer under nighttime visual conditions. Curve 53 shows the spectral luminous efficacy of a CIE 1964 photopic observer, i.e., a 10-degree observer under daytime visual conditions, selected according to this disclosure for evaluating ghosting visibility.

[0113] In this case, the CIE 1964 observer is chosen for two reasons. First, ghosting has color (in most cases), and the CIE 1964 observer is the recommended observer for color calculations, while the CIE 1931 observer is used for standard values, such as R. V The second reason relates to the experimental results and will be described later.

[0114] For the ghosting visibility criterion, there is no pre-existing standard requiring the use of the 1931 observer. Therefore, we propose using the 1964 observer, which seems more appropriate for us for the reasons mentioned above.

[0115] The ghost transmittance, or ghost transmittance coefficient (denoted as T) of a two-sided optical system GI (I) is calculated using the following expression:

[0116]

[0117] Where S(λ) represents the spectrum of the light source depending on wavelength λ in the visible spectral range between 380 nm and 780 nm, and T(λ,15°) is the ghost transmittance depending on wavelength λ for an incident angle of 15 degrees. It is the spectral luminous efficiency of the CIE 1964 photopic observer (also known as the "10° observer").

[0118] The ghost transmittance of a two-sided optical system is calculated using the following expression (II):

[0119] T(λ, 15°) = T Cx (λ, 15°).R BCc (λ, α).R BCx (λ, α).T Cc (λ,α).(T int (λ,α)) 3

[0120] Among them, T Cx (λ, 15°) represents the spectral transmittance of the incident beam through the first (convex) surface 11, depending on the wavelength λ, with respect to an incident angle of 15 degrees. BCc (λ, α) represents the spectral reflectance of the light beam on the second (concave) surface 12, depending on the wavelength λ, for reflection occurring from within the substrate medium at the angle of refraction α. BCx (λ, α) represents the spectral reflectance of the light beam on the first (convex) surface 11, depending on the wavelength λ, for reflection occurring from within the substrate medium with respect to the refraction angle α. Cc (λ, α) represents the spectral transmittance of the light beam through the second (concave) surface 12, which is dependent on the wavelength λ and has a refraction angle α, for transmission from the substrate medium to air, and T int (λ, α) represents the spectral transmittance of the light beam through the substrate supporting the first and second surfaces, depending on the wavelength λ, with respect to the refraction angle α (see also...). Figure 7 ).

[0121] For an incident angle of 15 degrees, the angle of refraction α is derived from the Snell-Descartes formula:

[0122] n 空气 sin(15°)=n 基材 sin(α)

[0123] Where, n 空气 It is the refractive index of air, and n 基材 It is the refractive index of the lens substrate.

[0124] In the case of an optical system with two surfaces, the numerical threshold for ghost visibility has been determined to be 0.007%. In other words, with N=2, the numerical threshold for ghost visibility is determined to be T. GI =0.007%.

[0125] Using the above formula T GI (15°) can optimize the coating on the first and second surfaces to achieve a ghost transmittance of less than 0.007% below the ghost visibility threshold.

[0126] New parameter, ghost transmission coefficient, T GI Supported by a strong correlation with perception, this is demonstrated by the results of one study on untrained observers and another on trained observers. Based on sensory data, criteria for the ghosting risk of antireflective coating assemblies can be established and integrated into the antireflective design process of optical systems with at least two surfaces.

[0127] More precisely, the numerical threshold for ghost visibility was determined empirically using two independent methods: the first method was based on machine learning, and the second method was based on expert observer scoring and compared with T. GI Related.

[0128] 2. Determine T through machine learning GI threshold

[0129] A set of 28 lenses was prepared, each coated with a different combination of anti-reflective coatings (or AR combinations). All other lens parameters were identical (diopter: -2.00D, substrate: CR39, refractive index-matched hard coating of 1.5).

[0130] On one side, color data is associated with each lens / AR combination. The color coordinates (T) of the ghosting for each lens, as explained in the previous paragraphs, are calculated. GI The reflectance (Rv, a*, b*, C*, h) of the convex and concave lenses were observed using the light source spectrum S(λ) of a 4000K LED (neutral white). The AR colors (Rv, a*, b*, C*, h) (Cx and Cc colors) were calculated based on reflectance measurements of the exact same lens observed in the study and the spectrum of a 4000K LED. In this study, the reflectance was compared with that of a T… GI In the same way, Y 10 R was calculated using the 1964 observers (instead of the 1931 observers). V ).

[0131] On the other side, sensory data were collected. An intrasensory study was conducted using 28 lenses and 16 observers. Ghosting was observed under specific conditions. Specifically, these conditions involved a 4000K LED as the light source, a light gray background, and artificial lighting in the room being turned on. The conditions in this particular group were designed to more closely approximate real-life, everyday conditions, contrasting with the conditions in other groups, such as a “black background and dark environment” that make ghosting more noticeable.

[0132] Therefore, under these conditions, there are some lenses in which the observer cannot see any ghosting. The observer is asked to specify which lenses have no ghosting at all (or, in other words, the ghosting is not visible).

[0133] Using 16 observers and 39 lenses (some of the 28 lenses were presented twice), we have 16*39=624 data points, which are labeled as 0 (ghosting is visible) or 1 (ghosting is not visible).

[0134] The color data was then correlated with the sensory data to build a decision tree. The color data correlated with the sensory data were combined into four different datasets, which served as input to the decision tree algorithm. The algorithm works by predicting a 0 / 1 sensation (visible or invisible ghosting) solely from the input data (color data). Of the 624 sensory data points, 70% (randomly selected) were used to train the algorithm, and 30% were used for validation.

[0135] The dataset is as follows:

[0136]

[0137] The dataset that provides the most accurate and simplest results is the dataset covering all ghost chromaticity coordinates (T) GI The dataset contains ghost colors on (a*, b*, c*, h). The algorithm was executed 11 times. All attempts will result in T. GI As the most relevant parameter among all coordinates. In these 11 tests:

[0138] - Single-condition tree appears 5 times: T GI >0.0071%.

[0139] - Single-condition tree appears 4 times: T GI >0.0063%.

[0140] -3 appears twice in the condition tree, and its main condition is: T GI >0.0071%.

[0141] The predetermined threshold (0.0068%) was determined based on the rounded weighted average of the above results.

[0142] This predetermined threshold is defined as less than 0.010%, preferably less than 0.009%, more preferably less than 0.008%, and even more preferably less than 0.007%.

[0143] Each of the 11 trees correctly predicted 80 to 90% of all 0s and 1s in the validation data.

[0144] • CIE 1931 and CIE 1964

[0145] Another reason for choosing the CIE 1964 observer is that this non-visibility data shows that the CIE 1964 observer provides better observational relevance than the CIE 1931 observer.

[0146] Figure 9 The logarithm (log(T)) is shown as the ghost transmission coefficient. GI The percentage of people who did not see any ghosting in the internal study (the total number of '1' = 'invisible' in the total number of observations).

[0147] However, a similar chart using the 1931 observer reveals the main outliers, corresponding to samples that include a combination of a blue-violet cutoff coating on the convex side and a highly effective anti-reflective coating on the concave side. It is important to consider this sample as it is significant.

[0148] 3.T GI Correlation with expert observer ratings

[0149] The study of external observers replicated one of the conditions of the internal study: LED light source, observation against a black background in a dark environment (see also...). Figure 2 Twelve expert observers evaluated each of the 28 lenses on an absolute scale based on three descriptors characterizing ghosting: contrast, sharpness, and luminous intensity.

[0150] These three descriptors were generated by 12 observers over two one-hour sessions. The observers were trained on the descriptors from the two one-hour sessions to provide repeatable and accurate scale scores, which could later be correlated with chromaticity parameters. Each expert evaluated all 28 lenses twice.

[0151] In total, each lens received 24 individual scores for each descriptor.

[0152] The scores for each descriptor are highly correlated to the extent that they can be believed to describe the same quantity. The contrast descriptor appears to account for 99% of the variation. This means that each of the other two descriptors (sharpness and luminance) differs from the contrast descriptor by less than 1%, and using either of the other two descriptors would be equivalent to 99%. Therefore, Figure 10 Only the contrast score is used.

[0153] The data points appear in a logarithmic shape. Therefore, human perception of brightness has been shown to vary according to the logarithm of a physical quantity. The results indicate that the contrast score assessed by experts is related to T... GI There is indeed a strong correlation between the logarithms.

[0154] Figure 10 The contrast score and T are shown. GI The logarithmic relationship.

[0155] exist Figure 10 In the study, the contrast score was observed to correlate with the logarithm (T). GI The linear correlation between and the logarithm (T). Specifically, the linear correlation between and the logarithm (T). GI The correlation coefficient R between the two groups is greater than 0.85. 2 In sensory analysis, R 2 A coefficient exceeding 0.75 is considered good. The dashed line here corresponds to the 95% prediction interval: new data points will fall within the line 95% of the time.

[0156] With logarithm (R) vCx *R vCc The correlation between ) and T also appears to be good, but lower than that between T and T. GI The correlation coefficient is 0.75. It should be noted that the product R... vCx *R vCc The parameters do not take into account potential compensation from substrate absorbance or Cx / Cc reflectance. In the current case, the data comes only from Orma lenses, which have very low or even no absorbance; however, other substrates would result in R... vCx *R vCc Not entirely accurate.

[0157] To summarize these two independent methods (respectively, the machine learning-based method and the expert observer-based method, and T...), GI Related methods), ghost transmittance, or T GI The quantity (correlated with a threshold of 0.007%) provides a new standard for the visibility of ghosting suitable for human perception. This standard takes into account the spectrum of the light source. GI The light absorption of the substrate was also considered, but observations were only conducted on transparent lenses. The threshold was obtained through observations under specific conditions chosen to approximate real-life indoor conditions.

[0158] Then, in the coating design step, this standard is used to assess the risk of ghosting in any coating combination.

[0159] The TGI standard for optical systems with two surfaces has been extended to optical systems with more than two surfaces, as detailed in the following section.

[0160] 4. Calculation of systems with N>2 surfaces

[0161] Therefore, the chromaticity evaluation parameters for ghost visibility are suitable for multiple ghosts. These parameters can optimize coating combinations on different surfaces.

[0162] First, identify the curvature combination of the optical system. Each possible combination of the two curvatures is checked based on the following rules:

[0163] Combinations of different curvatures (R1, R2) or (R2, R3) are considered individually.

[0164] • All similar combinations of two curvatures (R1, R2) or (R2, R1) are considered together (unless there is another surface with a curvature radius of R3 between the surfaces of one of the combinations but not between the surfaces of the other combinations. In this case, that particular combination is excluded).

[0165] • All combinations of the same curvature (R1, R1) are ignored unless there is a prism between the two surfaces (in which case they are not parallel).

[0166] Considering the rules regarding curvature combinations mentioned above, this computational model needs to be applicable to systems with more than two surfaces.

[0167] When a system has more than two surfaces, but only combinations of the same two curvatures R1 and R2, the T value of each combination should not be considered individually. GI To accurately assess ghost visibility, the T values ​​for all these specific combinations should be considered. GI The sum of these values. This calculation excludes any ghosting caused by combinations of surfaces with the same curvature R1 and R2.

[0168] In this section, we explained a method for calculating the total ghosting transmission coefficient of an optical system with two lenses and four surfaces. However, those skilled in the art will apply this method to other optical systems with more than two surfaces.

[0169] We propose two alternative methods to calculate the total ghost transmission coefficient in the transmission formed by light reflected exactly from the two surfaces of the transmission optics system.

[0170] We consider, for illustrative purposes, that an optical system includes a first lens 1 and a second lens 2, such as... Figure 4 As shown. The first convex surface 11 has a first radius of curvature R1, the second concave surface 12 has the same radius of curvature R1, the third convex surface 13 has the same first radius of curvature R1, and the fourth concave surface 14 has a second radius of curvature (denoted as R2, which is different from R1).

[0171] The first method

[0172] Each pair of two different surfaces with different curvatures among the first surface, the second surface, and at least another surface forms a ghost image, and each ghost image has a ghost transmittance that depends on the wavelength and the angle of incidence.

[0173] like Figures 11 to 13 As illustrated, in an example of a dual-lens optical system, the first surface is denoted as A, the second surface as B, the third surface as C, and the fourth surface as D.

[0174] The transmittance of each ghost image is calculated individually as a function of the transmittance of each ghost image.

[0175] According to the first method, the total ghost transmission coefficient T of the obtained ghost is... GI,T The sum of the ghost transmission coefficients for each ghost is calculated according to the following expression:

[0176] T GI,T =T GI,AD +T GI,BD +T GI,CD (III)

[0177] in

[0178] Where X represents one of the surface pairs: AD, BD, or CD;

[0179] S(λ) represents the spectrum of a point source that depends on wavelength λ in the visible spectral range between 380 nm and 780 nm;

[0180] T G,X (λ, 15°) represents the ghost transmittance of the surface relative to X with respect to an incident angle of 15 degrees, and

[0181] It is the spectral luminous efficiency of a CIE 1964 diopter observer (or 10° observer).

[0182] Here, since surfaces A, B, and C have the same radius of curvature R1, the corresponding ghosting transmittance is not considered: T GI,AB T GI,AC : and T GI,BC .

[0183] We will now explain the ghost transmittance T for each of the following surfaces with respect to X. G,X Calculation of (λ, 15°): AD, BD, or CD.

[0184] ·T G,AD

[0185] We consider the combination of a first surface A with radius of curvature R1 and a fourth surface D with radius of curvature R2. First-order ghosting is produced by the internal reflection of the incident beam 30 on surfaces A and D that form the first-order reflected beam 41 (see...). Figure 11 ).

[0186] Ghost transmittance T G，AD It is calculated in series based on the following expression (V), taking into account the transmission and reflection coefficients of different interfaces and substrates on which the incident beam 30 is reflected, refracted, or transmitted:

[0187] T G，AD (λ, 15°) = T A (λ, 15°)*T intAB (λ,α)*T B (λ, 15°)*T C (λ, 15°)*T intCD (λ, β)*BR D (λ,β)*T intCD (λ,β)*T C (λ, 15°)*T B (λ, 15°)*T intAB (λ,α)*BR A (λ,α)*T intAB (λ,α)*T B (λ, 15°)*T C (λ, 15°)*T intCD (λ,β)*T D (λ, 15°)

[0188] The incident angle was set to 15 degrees.

[0189] T Y (λ, 15°) represents the transmission coefficient of surface Y (chosen from surfaces A, B, C, and D) at an incident angle of 15 degrees, which depends on the wavelength λ.

[0190] T intAB (λ, α) represents the transmission coefficient inside the first lens, which depends on the wavelength λ and the refraction angle α between surfaces A and B.

[0191] T intCD(λ, β) represents the transmission coefficient inside the second lens, which depends on the wavelength λ and the refraction angle β between surfaces C and D.

[0192] BR D (λ,β) represents the back reflection coefficient at surface D at refraction angle β, which depends on wavelength λ and the reflection occurring within the substrate of the second lens.

[0193] BR A (λ, α) represents the back reflection coefficient on surface A at the refraction angle α, which depends on the wavelength λ and the reflection that occurs inside the substrate of the first lens.

[0194] The angles of refraction α and β are determined by the Snell-Descartes law:

[0195] n 空气 sin(15°)=n AB sin(α)

[0196] n 空气 sin(15°)=n CD sin(β)

[0197] Where, n AB Let n represent the refractive index of the substrate supporting surfaces A and B, and n CD This represents the refractive index of the substrate supporting surfaces C and D.

[0198] Because the model assumes all surfaces are flat and parallel, the angle of incidence in air is always 15 degrees. Furthermore, the principle of the reversibility of light states that the path of light rays traveling in any direction is identical. Therefore, considering the 15-degree angle of incidence, all transmittance from the air medium to the substrate is correctly evaluated regardless of the actual direction.

[0199] Therefore, the ghost transmittance T G，AD It is calculated based on the following simplified expression:

[0200] T G，AD (λ, 15°) = T A (λ, 15°)*BR D (λ, β)*BR A (λ,α)*T D (λ,15°)*(T B (λ, 15°)) 3 *(T intAB (λ,α)) 3 *(T C (λ, 15°)) 3 *(T intCD (λ,β)) 3

[0201] If there is no air gap between surfaces B and C, but rather another medium, the angle of refraction γ within this medium is calculated according to the Snell-Descartes law. If this medium is absorbing, the above formula is updated to account for T at wavelength λ and angle of refraction γ. intBC .

[0202] These formulas do not take into account the polarization of light, so they are not entirely equivalent to ray tracing calculations. However, at low incident angles (i.e., less than 45 degrees), the effect of polarization is usually small.

[0203] Then, the ghost transmittance T of the first-order ghost formed by the internal reflection between surfaces A and D. G，AD With the ghost transmittance T of the double-surface optical system GI The same method is used based on the ghost transmittance T GI，AD To calculate: Ghost transmittance T GI，AD Corresponding to the ghost transmittance T in the CIE XYZ system G，AD The Y tri-color stimulus values ​​were obtained using an LED as the light source and a CIE 1964 observer (see the formula above in this section).

[0204] ·T G，BD

[0205] We consider the combination of a second surface B with radius of curvature R1 and a fourth surface D with radius of curvature R2. First-order ghosting is produced by the internal reflection of the incident beam 30 on surfaces B and D that form the first-order reflected beam 42 (see...). Figure 12 ).

[0206] Ghost transmittance T G，BD It is calculated in series according to the following expression (VI), using similar notation as described above, based on the transmission and reflection coefficients of different interfaces and substrates on which the incident beam 30 is reflected, refracted, or transmitted:

[0207] T G，BD (λ, 15°) = T A (λ, 15°)*T intAB (λ,α)*T B (λ, 15°)*T C (λ, 15°)*T intCD (λ, β)*BR D (λ,β)*T intCD (λ,β)*T C (λ, 15°)*R B (λ,15)*T C (λ, 15°)*T intCD (λ,β)*T D (λ, 15°)

[0208] Alternatively, in the simplified version:

[0209] T G，BD (λ, 15°) = T A (λ, 15°)*T intAB (λ,α)*T B (λ, 15°)*BR D (λ,β)*R B (λ,15)*T D (λ,15°)*(T C (λ, 15°)) 3 *(T intCD (λ,β)) 3

[0210] In these expressions, the angles of refraction α and β are determined by the Snell-Descartes law as described above.

[0211] Similarly, the ghost transmittance T of the first-order ghost formed by the internal reflection between surfaces B and D is... GI，BD With the ghost transmittance T of the double-surface optical system GI The same method is used based on the ghost transmittance T G，BD To calculate: Ghost transmittance T GI，BD Corresponding to the ghost transmittance T in the CIE XYZ system G，BD The Y tri-color stimulus values ​​were obtained using an LED as the light source and a CIE 1964 observer (see the formula above).

[0212] ·T G，CD

[0213] Similarly, we consider the combination of a third surface C with radius of curvature R1 and a fourth surface D with radius of curvature R2. The first-order ghosting is produced by the internal reflection of the incident beam 30 on surfaces C and D that form the first-order reflected beam 43 (see...). Figure 13 ).

[0214] Ghost transmittance T G，CD It is calculated in series according to the following expression (VII), using similar notation as described above, based on the transmission and reflection coefficients of different interfaces and substrates on which the incident beam 30 is reflected, refracted, or transmitted:

[0215] T G，CD (λ, 15°) = T A (λ, 15°)*T intAB (λ,α)*T B (λ, 15°)*T C (λ, 15°)*T intCD (λ, β)*BR D (λ,β)*TintCD (λ, β)*BR C (λ,β)*T intCD (λ,β)*T D (λ, 15°)

[0216] Alternatively, in the simplified version:

[0217] T G，CD (λ, 15°) = T A (λ, 15°)*T intAB (λ,α)*T B (λ, 15°)*T C (λ, 15°)*BR D (λ, β)*BR c (λ,β)*T D (λ,15°)*(T intcD (λ,β)) 3

[0218] Similarly, the ghost transmittance T of the first-order ghost formed by the internal reflection between surfaces C and D is... GI，CD With the ghost transmittance T of the double-surface optical system GI The same method is used based on the ghost transmittance T G，CD To calculate: Ghost transmittance T GI，CD Corresponding to the ghost transmittance T in the CIE XYZ system G，CD The Y tri-color stimulus values ​​were obtained using an LED as the light source and a CIE 1964 observer (see the formula above).

[0219] Then, the total ghost transmittance T of the ghost images formed by the superposition of the ghost images formed by beams 41, 42 and 43. GI，T Each ghost transmittance T determined according to the above expressions (V), (VI) and (VII) GI，AD T GI，BD and T GI，CD The sum (see formula (III)) is used to calculate.

[0220] The second method

[0221] Similar to the first method, each pair of two different surfaces with different curvatures among the first surface, the second surface, and at least another surface forms a ghost image, and each ghost image has a wavelength-dependent ghost transmittance for an incident angle of 15 degrees.

[0222] We consider a two-lens optical system, where the first surface is denoted as A, the second surface as B, the third surface as C, and the fourth surface as D (see [reference]). Figures 11 to 13 ).

[0223] According to the second method, the total ghost transmission coefficient T formed by the superposition of the ghosts produced by beams 41, 42, and 43 is... GI,T The calculation is based on the following expression (VIII), which depends on the sum of the transmittance of each ghost image:

[0224]

[0225] Where S(λ) represents the spectrum of a point source that depends on wavelength λ in the visible spectral range between 380 nm and 780 nm;

[0226] It is the spectral luminous efficiency of a CIE 1964 dichroic observer (or a 10° observer), and

[0227] Ghost transmittance T G，AD (λ, 15°), T G，BD (λ, 15°) and T G，CD (λ, 15°) is calculated in its full or simplified form using the expressions (V), (VI), and (VII) detailed in the previous section, respectively.

[0228] In another example, we consider an optical system with three surfaces. For instance, the optical system consists of a highly absorbent solar glass lens and a refractive lens; the solar glass lens is highly absorbent and has no specular coating. For example, the solar glass lens is sandwiched between the refractive lens. The first surface of the solar glass lens is denoted as A, the second surface as B, the third surface as C, and the fourth surface as D.

[0229] Because solar glass lenses are highly absorbent, the component related to surface A can be ignored. For example, the transmittance of a solar clip is Tint = 10% or 0.1. The contribution of this transmittance term is not significant because Tint... 2 Even less significant. Unless surface A is covered with a specular coating, its reflectivity is high enough to compensate for Tint. 2 .

[0230] Suppose surfaces A, B, and C have the same radius of curvature, while surface D has a different radius of curvature. In this case, T G,AD It is negligible, and there is only one ghost image; its transmittance is equal to:

[0231] T G =T G,BD +T G,CD

[0232] Among them, T G,BD and T G,CDCalculate using the full or simplified versions, respectively, the expressions (VI) and (VII) detailed in the previous section.

[0233] The total ghost transmission coefficient T is formed by the superposition of ghost images produced by light beams from surfaces B, C, and D. GI,T The calculation is based on the following expression (IX), which depends on the sum of the transmittance of each ghost image:

[0234]

[0235] Where S(λ) represents the spectrum of a point source that depends on wavelength λ in the visible spectral range between 380 nm and 780 nm, and It is the spectral luminous efficiency of a CIE 1964 diopter observer (or 10° observer).

[0236] The same method applies to optical systems with three surfaces, such as doublet lenses, where two lenses are attached by a common interface. This optical system has a first surface (denoted as A), a second surface (denoted as B) at the interface between the two lenses, and a third surface (denoted as C). The three surfaces A, B, and C have different radii of curvature, taking on their radii of curvature in pairs. Therefore, there are three pairs of radii of curvature. This optical system with three surfaces generates three separate total ghost images, denoted as AB, AC, and BC, respectively. The transmittance of each ghost image is calculated using the following formula:

[0237] T G，AB (λ)=T A (λ)*BR B (λ)*BR A (λ)*T B (λ)*T C (λ)*(T intAB (λ)) 3 *T intBC (λ)

[0238] T GAC (λ)=T A (λ)*BR C (λ)*BR A (λ)*(T B (λ)) 3 *T C (λ)*(T intAB (λ)) 3 *(T intBC (λ)) 3

[0239] T G，BC (λ)=T A (λ)*T B (λ)*BRc (λ)*BR B (λ)*T C (λ)*(T intBC (λ)) 3 *T intBC (λ)

[0240] The total ghost transmission coefficient is calculated for each of the three ghosts using the following formula:

[0241]

[0242]

[0243]

[0244] T GI，1 T GI，2 and T GI，3 Each of them must be below the predetermined threshold for ghost visibility.

[0245] In summary, for an optical system with two or more surfaces, each total ghost image is the sum of ghost components generated by pairs of identical radii of curvature. An optical system with two or more surfaces can generate more than one total ghost image. There exist as many total ghost images as there are pairs of different radii of curvature. Each total ghost image must have a Tg value that satisfies the given condition. GI Below the predetermined threshold (T) for ghost visibility GI <7.10 -3 ).

[0246] The transmittance of total ghosting is calculated using the following formula:

[0247]

[0248]

[0249]

[0250] Where XY represents surface pair X and Y with the same combination of two radii of curvature, Z is the substrate or glass sheet between surfaces X and Y, and W is every other surface different from A and B located between surfaces A and B; R represents the reflectivity of the interface under consideration with respect to a specific incident angle of the relevant array, T represents the surface transmittance with respect to a specific incident angle of the relevant array, and T int This represents the internal substrate transmittance for a specific incident angle of the relevant array. In the above formula, the surface transmittance and internal transmittance are squared because they correspond to the round trip of light.

[0251] T 总系统(λ) represents the direct transmittance of the light beam through all substrates and all surfaces, depending on the wavelength.

[0252] Total ghosting threshold of an optical system with two or more surfaces

[0253] The same threshold value of 0.010%, preferably 0.009%, more preferably 0.008%, and even more preferably 0.007% is applied to the total ghosting transmission coefficient T, as is the case for optical systems with only two surfaces. GI,T .

[0254] The third method

[0255] Even when ghosting occurs in a system with multiple centered surfaces (optically aligned surfaces) when the incident light is defined at a non-zero incident angle, an additional method involves calculating the aforementioned T for a 0° incident angle. G (λ), T 总系统 (λ) and T GI These calculations produce T corresponding to the ghosting. GI These values, calculated for an incident angle of 0°, should not physically exist, but they can be compared to determine the probability ranking of ghosting between several systems on more than two surfaces. Similarly, these values ​​can form approximations of those obtained for non-zero incident angles, while being less computationally complex.

[0256] 5. Applied to coating optimization

[0257] Therefore, systems and methods for evaluating ghost visibility are provided, which are capable of determining the ghost visibility of optical systems with two or more surfaces and of proposing new coating combinations to prevent ghosting from interfering with the user.

[0258] Total ghost transmission coefficient T GI,T It is optimized to be below a predetermined threshold, for example, below 7‰. In particular, the total ghost transmission coefficient is calculated using a database of known coatings.

[0259] The systems and methods for evaluating ghost visibility can also create anti-reflective coatings that enable the construction of optical systems with surfaces covered by these coatings, the total ghost transmission coefficient T of which... GI,T Below the predetermined threshold.

[0260] The system can also optimize the combination of antireflective coatings based on minimizing the total ghosting transmittance, so that T GI,T Below the predetermined threshold.

[0261] We consider an optical system consisting of two lenses (such as...) Figure 4), where three surfaces 11, 12, and 13 have the same radius of curvature R1, while a fourth surface 14 has a different radius of curvature R2. In this case, all possible combinations of the two surfaces are (a) (R1, R2) or (b) (R1, R1). As explained by the combination rules above, only combination (a) produces ghosting, and combination (b) can be ignored.

[0262] Each of the four surfaces includes a coating. However, the coating of the fourth surface 14, which has a different radius of curvature, is a first-order parameter of all individual ghostings. Therefore, in this configuration, the improvement is almost equivalent whether all coatings on all three parallel surfaces 11, 12, and 13 are optimized, or only the coatings on the surface 14 with different curvatures are optimized.

[0263] In the first example (see) Figure 14 The coatings on surfaces 11, 12, and 13 are fixed, and during optimization, only the coating on the fourth surface 14 varies according to the total ghosting transmission standard of the optical system. The coatings on surfaces 11, 12, and 13 can be fixed because the planar portion of the system (first lens 1) is provided as is (therefore the coating cannot be removed or altered); or the coating on the first lens 1 is severely constrained, so the coating on surface 14 of the second lens is the preferred means. This may occur on electrochromic lenses in a transparent state with attached refractive appendages (any prescription), or in cases where a transparent clip is used on a prescription lens (e.g., for nighttime driving conditions).

[0264] In the second example (see) Figure 15 In this particular configuration, the coating on the fourth surface 14 is fixed, while the coatings on surfaces 11, 12, and 13 vary during optimization according to the total ghosting transmission criterion of the optical system. In this specific configuration, the contribution of all three coatings on surfaces 11, 12, and 13 is as large as that of the coating on the fourth surface 14 in the first example. Therefore, here, changing only one or two coatings (11, 12, and / or 13) is less "efficient" than changing the coatings on the fourth surface as in the first example. This situation may correspond to optical systems similar to those in the first example but with different constraints on the coatings. For example, the coating on the fourth surface 14 could be fixed due to stringent E-SPF (eye protection factor) requirements or cracking issues.

[0265] In the third example (see) Figure 16 The entire system was designed simultaneously. The coatings on all four surfaces can be optimized concurrently according to the total ghosting transmission criterion of the optical system. This configuration allows for greater customization. This is the case when there are strong constraints on the optical objectives of some coatings, but at least one degree of freedom remains in the design of each coating.

[0266] In the fourth example (see) Figure 17 The first lens 1 has low transmittance (e.g., an added tinted lens or solar clip). In this case, due to the low transmittance of the sunglass lens, the ghosting reflected on the first surface 11 can be ignored. As a result, the corresponding ghosting transmittance is particularly reduced because internal reflections on the first surface pass through the tinted lens three times, compared to other ghosting and direct images passing through only once. This situation may correspond to the same optical system as in the previous example.

[0267] Application examples of antireflective (AR) coating selection for electrochromic units with air gaps and Rx additives.

[0268] Optical systems (such as) Figure 4 (As shown) includes a first lens 1 and a second lens 2. The first lens 1 includes an electrochromic unit, or electrochromic element, which can control light electrically. The first surface 11 and the second surface 12 of the electrochromic unit have the same radius of curvature R1. The second lens 2 includes a refractive appendage or Rx appendage, a surface 13 having a radius of curvature R1, and a fourth surface having a radius of curvature R2 different from R1. An air gap is located between the rear surface 12 of the first lens and the front surface 13 of the second lens.

[0269] The coatings on the first surface 11 and the second surface 12 of the electrochromic unit are fixed because they are supplied by the supplier. Moreover, the composition and materials of the electrochromic unit are mostly unknown, so the ghosting performance of the unit must be characterized.

[0270] The optical system has additional constraints. UV reflectivity should be very low on the fourth concave surface with the additions to maintain good E-SPF. The coatings on surfaces 13 and 14 should be four layers to reduce the total film thickness, thereby limiting cracking issues while exhibiting good AR optical performance (Rv < 1%).

[0271] The coating on the third surface 13 comprises a multilayer stack according to Table I below, wherein the number of layers is marked from 1 to 5 along the direction from air to substrate, and the thickness of each layer is in nanometers:

[0272] layer Material Refractive index @ 550nm thickness 1 SiO2 1,472563 86,3 2 SnO2 1,82448 6,5 3 ZrO2 1,996951 67 4 SiO2 1,472563 14,6 5 ZrO2 1,996951 35,9

[0273] Table I: Multilayer coatings on surface 13

[0274] The initial design of the coating on the fourth surface 14 includes a multilayer stack according to Table II below:

[0275] layer Material Refractive index @ 510nm thickness 1 SiO2 1,47409 77,4 2 ITO 2,0822 6,5 3 ZrO2 2,0038 96,1 4 SiO2 1,47409 11,6 5 ZrO2 2,0038 22,5

[0276] Table II: Initial Multilayer Coating on Surface 14

[0277] The optimized design of the coating on the fourth surface 14 includes a multilayer stack according to Table III below:

[0278] layer Material Refractive index @ 510nm thickness 1 <![CDATA[SiO2]]> 1,47409 82,01 2 <![CDATA[SnO2]]> 1,84321 6,5 3 <![CDATA[ZrO2]]> 2,0038 92,47 4 <![CDATA[SiO2]]> 1,47409 21,79 5 <![CDATA[ZrO2]]> 2,0038 16,82

[0279] Table III: Multilayer coatings on surface 14 optimized for ghosting

[0280] The simulation yielded the following performance:

[0281]

[0282] Table IV: Comparison of ghosting transmittance between initial coating design and optimized coating design

[0283] In Table IV, T GI1 This corresponds to T. GI,AD +T GI,BD And T GI2 Corresponding to T GI,CD .

[0284] Total T generated by initial coating design GI The value is 0.0178. According to simulations, the optimized coating on the concave side 14 can increase the total T... GI It is below the confirmed threshold of 0.007 while maintaining good E-SPF performance (approximately 25).

[0285] 6. System T GI Measurement

[0286] First, we consider an optical system consisting of only one lens, with a convex surface (Cx) and a concave surface (Cc).

[0287] Internal reflection ghosting cannot be measured directly and would require very specific spectroscopic equipment and acquisition conditions, so the method here is to independently measure each element required in the calculation (e.g., Figure 7 (as stated):

[0288] T GI，T (λ, 15°) = T Cx (λ, 15°).R BCx (λ, α).R BCc (λ, α).T Cx (λ, α).T int (λ, α) 3

[0289] The approximate values ​​and measurement methods are described below.

[0290]

[0291]

[0292] SMR stands for Reflectance Measurement System, and is typically based on a spectrometer suitable for measuring the reflectance of a lens at a given incident angle. The Cary50 is another device used to measure transmittance at a normal incident angle.

[0293] Assume that for a non-light-absorbing coating, the sum of the reflection (R) and transmission (T) coefficients is equal to 1 (R+T=1).

[0294] The back reflectance (R) of the lens was not measured. BCx or R BCc Therefore, an approximation is used: the back reflectance of a lens (i.e., inside the lens) is approximately equal to the front reflectance on the same surface of the lens (i.e., outside the lens).

[0295] For light-absorbing substrates, the sum of the reflection (R), transmission (T), and absorption (A) coefficients equals 1 (R + T + A = 1). Therefore, T int =1–A=R tot +T tot Here, T tot and R tot It refers to the transmittance and reflectance on both sides of the lens. T tot It can be measured, however, the reflectance at an incident angle of 0° cannot be measured, so it is approximated by the reflectance on both sides at an incident angle of 10°, which is the lowest possible incident angle for measuring using a multi-incident SMR.

[0296] Then, at an incident angle of 15°, the ghost transmittance as a function of wavelength is calculated using the following expression as a product of the spectral quantities measured in the previous table:

[0297] T G (λ, 15°) = T Cx *R Cx *T Cc *R Cc *T int 3

[0298] Using the described measurement method, the T0 of three commercially available lenses with ghosting visibility problems was estimated. GI The results are compiled into the table below.

[0299]

[0300] These examples demonstrate that T GI The calculated value is a quantitative representation of the most accurate perception (compared to expert scores) because it is based on complete and accurate information about the optical system, light source, and observer.

[0301] Then, T GIBased on this spectrum, the Y trichromatic stimulation values ​​were calculated using an LED light source and a 1964 observer.

[0302] The table below presents simulation results for several single-lens ophthalmic systems, validating the ghosting transmission coefficient T. GI Conditions for chromaticity parameters <0.007% and descriptions of each stack.

[0303] Cx Design Blue AR Blue AR Orange mirror Blue mirror Green AR Copper AR Cc design Copper AR Green AR Blue AR Copper AR Copper AR Copper AR <![CDATA[T GI ]]> 0.0028 0.0036 0.0036 0.0048 0.0052 0.0067

[0304] The structure and composition of the multilayer coating are detailed in the table below:

[0305]

[0306]

[0307] Other examples of copper-colored antireflective coatings (or copper-colored AR) correspond to Examples 9, 10, and 11 disclosed in patent application WO 2012 / 076714, and are incorporated herein by reference. More generally, a copper-colored antireflective coating comprises a multilayer stack having at least six layers, said multilayer stack comprising, along a direction away from the substrate, a silicon dioxide layer with a thickness of approximately 150 nm, a zirconium dioxide layer with a thickness of 14 nm to 16 nm, a silicon dioxide layer with a thickness of 28 nm to 32 nm, a zirconium dioxide layer with a thickness of 87 nm to 93 nm, a tin oxide or indium tin oxide layer with a thickness of approximately 6.5 nm, and a silicon dioxide layer with a thickness of 71.7 nm to 77 nm.

[0308] According to a specific and advantageous example, the optical system includes at least one of a copper-colored anti-reflective coating on a concave surface and a blue mirror or blue anti-reflective coating on a convex surface.

[0309] Finally, consider optical systems with more than two surfaces (N>2). Depending on the system, such systems can employ T... GI Measurement Method. For this purpose, measurement of each term in the equation is necessary (refer to expressions (III) to (VIII)). This requires disassembling the optical system (if it consists of two assembled lenses) to measure the reflectivity and transmittance of each surface or set of surfaces. For a two-surface system, the main concern is the internal transmittance of the substrate material. For a disassembled optical system, the internal transmittance can be approximated by the total transmittance and total reflectance of each lens.

[0310] Although representative methods and optical systems have been described in detail herein, those skilled in the art will recognize that various alternatives and modifications can be made without departing from the scope described and defined by the appended claims.

[0311] 8. Applied to optical systems with three or four surfaces

[0312] This method and system are applicable to optical systems with two or more surfaces, such as four surfaces.

[0313] In the first example, the optical system includes an electrochromic unit attached to a lens. The electrochromic unit has two surfaces (S1, S2) with the same radius of curvature. The lens has a first surface with the same radius of curvature S1 and a second surface with a different radius of curvature S2. This optical system generates a single ghost image, the total ghost transmittance of which is formed by three components S1S2.

[0314] In the second example, the optical system includes a clip attached to a lens. The lens includes a first surface having a first radius of curvature S1 and a second surface having a different radius of curvature S2. The clip, or plano lens, has two surfaces having the same radius of curvature (S3, S3), different from the nearest surface of the lens. This optical system generates three distinct ghost images, each with a total ghost transmittance formed by two components: a first total ghost image generated by the two surfaces of the lens; a second total ghost image (S1S3+S1S3) generated by the first surface of the lens and the two surfaces of the clip having the same radius of curvature, respectively; and a third total ghost image (S2S3+S2S3) generated by the second surface of the lens and the two surfaces of the clip having the same radius of curvature, respectively.

[0315] In the third example, the optical system includes a clip attached to a plano glass lens. The plano glass lens includes two surfaces having the same radius of curvature (S1, S1). The clip (also a plano clip) has two surfaces having the same radius of curvature (S3, S3), different from the surfaces of the lens. This optical system generates a single ghost image whose total ghost transmittance is formed by four components: a first component from the first surface S1 of the lens and the first surface S3 of the clip; a second component from the second surface S1 of the lens and the first surface S3 of the clip; a third component from the first surface S1 of the lens and the second surface S3 of the clip; and a fourth component from the second surface S1 of the lens and the second surface S3 of the clip.

Claims

1. A transmission optical system having a first surface and a second surface, wherein the first surface and the second surface have different curvatures and / or the first surface and the second surface are configured to provide refractive power, wherein, The transmission optical system has a total ghosting transmission coefficient for at least one ghost image, the at least one ghost image being formed by the internal reflection of a light beam from a light source between at least the first surface and the second surface and by transmission through the optical system, the light beam from the light source being incident on the first surface at a non-zero incident angle, the total ghosting transmission coefficient being generated by the integral of the ghosting transmittance of the at least one ghost image in the visible spectral band and depending on the spectrum of the light source and the spectral luminous efficiency of a CIE 1964 photopic observer, and wherein the total ghosting transmission coefficient is below a predetermined threshold for ghosting visibility. The ghost transmittance is calculated using the following formula: in, The wavelength in the visible spectrum is represented by the light source, the incident angle of which is set to 15 degrees and corresponds to the angle of refraction α within the substrate supporting the first and second surfaces. This represents the spectral transmittance of the first surface calculated at the incident angle. This represents the spectral reflectance of the second surface at the refraction angle α, calculated for reflections occurring within the medium of the substrate. This represents the spectral reflectance of the first surface calculated for reflections occurring within the medium of the substrate. This represents the calculated spectral transmittance of the second surface, and This represents the spectral transmittance calculated between the first surface and the second surface. The total ghost transmission coefficient is calculated using the following formula: Wherein, the visible spectral band extends between 380 nm and 780 nm, S(λ) represents the spectral brightness of the light source, and This indicates the spectral luminous efficiency of a photopic observer as defined in CIE 1964.

2. The transmission optical system according to claim 1, wherein, The first surface includes a first coating, and the second surface includes a second coating.

3. The transmission optical system according to claim 1, wherein, The predetermined threshold for ghost visibility is less than 0.010%.

4. The transmission optical system according to claim 1, wherein, The predetermined threshold for ghost visibility is 0.007%.

5. A transmission optical system having at least a first surface and a second surface, wherein the first surface and the second surface have different curvatures and / or the first surface and the second surface are configured to provide refractive power, wherein, The first surface includes a first coating, and the second surface includes a second coating, wherein the transmissive optical system has a total ghosting transmission coefficient for at least one ghost image, the at least one ghost image being formed by the internal reflection of a light beam from a light source between at least the first surface and the second surface and by transmission through the optical system, the light beam from the light source being incident on the first surface at a non-zero angle of incidence, the total ghosting transmission coefficient being generated by the integral of the ghosting transmittance of the at least one ghost image in the visible spectral band and depending on the spectrum of the light source and the spectral luminous efficiency of a CIE 1964 photopic observer, and wherein the total ghosting transmission coefficient is below a predetermined threshold for ghosting visibility, and wherein the transmissive optical system further includes at least another surface having another coating, wherein each pair of two different surfaces with different curvatures among the first surface, the second surface, and the at least another surface forms a specific ghost image, and each specific ghost image has a specific ghosting transmittance, and wherein the first coating, the second coating, and the other coating are configured such that each specific ghost image has a total ghosting transmission coefficient below the predetermined threshold. The total ghost transmittance is calculated using the following formula: Among them, T 总系统 T represents the direct transmittance of the light beam through all substrates and all surfaces, depending on the wavelength λ. GI Let S(λ) represent the total ghosting transmission coefficient, and S(λ) represent the spectral brightness of the light source. R represents the spectral luminous efficiency of a photopic observer as defined in CIE 1964, where XY represents any pair of surfaces X and Y having the same combination of two radii of curvature, Z represents any substrate between surfaces X and Y, and W represents every other surface between surfaces X and Y that is different from surfaces X and Y. X R represents the spectral reflectance of surface X. Y Let Y represent the spectral reflectance of surface Y, T represent the surface transmittance, and T0 represent the surface transmissivity. int This indicates the transmittance of the substrate.

6. The transmission optical system according to claim 5, wherein, The predetermined threshold for ghost visibility is less than 0.010%.

7. The transmission optical system according to claim 5, wherein, The predetermined threshold for ghost visibility is 0.007%.

8. A transmission optical system having at least a first surface and a second surface, wherein the first surface and the second surface have different curvatures and / or the first surface and the second surface are configured to provide refractive power, wherein, The transmission optical system further includes at least one other surface, wherein the transmission optical system has a total ghost transmission coefficient of at least one ghost image, the at least one ghost image being formed by an internal reflection of a beam of light from a light source incident at a non-zero incident angle on the first surface and by transmission through the optical system, wherein each pair of two different surfaces having the same curvature among the first surface, the second surface, and the at least one other surface forms a component of the same specific ghost image with a component ghost transmission coefficient, and wherein the total ghost transmission coefficient is calculated based on the sum of the ghost transmission coefficients of the different components of the same specific ghost image and is below a predetermined threshold for ghost visibility. The ghost transmittance of each component of the same specific ghost image is calculated using the following formula: Where X represents one of the different surface pairs that form the same specific ghosting; S(λ) represents the spectrum of a point source with wavelength λ depending on the visible spectral range between 380 nm and 780 nm; T G,X (λ, 15°) represents the ghost transmittance of the surface relative to X with respect to an incident angle of 15 degrees, and It is the spectral luminous efficiency of a CIE 1964 photopic observer (or 10° observer).

9. The transmission optical system according to claim 8, wherein, The total ghosting transmission coefficient is further based on the number of surfaces of the transmission optical system, the transmission coefficient of each surface, and the transmission coefficient of each substrate supporting the surface of the transmission optical system.

10. The transmission optical system according to claim 8, wherein, The predetermined threshold for the ghost visibility is less than 0.010%.

11. A method for evaluating the visibility of ghosting in a transmission optical system, the transmission optical system having two surfaces, a first surface and a second surface, the first surface and the second surface having different curvatures and / or the first surface and the second surface being configured to provide refractive power, the method comprising the step of determining a total ghosting transmission coefficient for at least one ghosting, the at least one ghosting being formed by the internal reflection of a light beam from a light source between the first surface and the second surface and by transmission through the optical system, the light beam from the light source being incident on the first surface at a non-zero angle of incidence, the total ghosting transmission coefficient being generated by the integral of the ghosting transmittance of the at least one ghosting in the visible spectral band and depending on the spectrum of the light source and the spectral luminous efficiency of a CIE 1964 photopic observer, wherein, The ghost transmittance is calculated using the following formula: in, The wavelength in the visible spectrum is represented by T, and the incident angle of the light source is set to 15 degrees, corresponding to the angle of refraction α within the substrate supporting the first and second surfaces. Cx (λ, 15°) represents the spectral transmittance of the first surface calculated at the incident angle, R BCc (λ, α) represents the spectral reflectance of the second surface at the refraction angle α, calculated for reflections occurring within the medium of the substrate, R BCx (λ, α) represents the spectral reflectance of the first surface calculated for reflections occurring within the medium of the substrate, T Cc (λ, α) represents the calculated spectral transmittance of the second surface, and T int (λ, α) represents the calculated spectral transmittance between the first surface and the second surface, and The total ghost transmission coefficient is calculated using the following formula: Wherein, the visible spectral band extends between 380 nm and 780 nm, S(λ) represents the spectral brightness of the light source, and This indicates the spectral luminous efficiency of a photopic observer as defined in CIE 1964.

12. A method for optimizing at least one antireflective coating of a transmissive optical system having two surfaces, the transmissive optical system having a first surface and a second surface, the first surface including a first coating and the second surface including a second coating, wherein, At least one of the first coating and the second coating is an anti-reflective coating, the first surface and the second surface have different curvatures and / or the first surface and the second surface are configured to provide refractive power, the method comprising the following steps: a) Determine the total ghost transmission coefficient of at least one ghost image formed by internal reflection of a light beam from a light source between the first and second surfaces and by transmission through the optical system, wherein the light beam from the light source is incident on the first surface at a non-zero angle of incidence, and the total ghost transmission coefficient is generated by the integral of the ghost transmittance of the at least one ghost image in the visible spectral band and depends on the spectrum of the light source and the spectral luminous efficiency of a CIE 1964 photopic observer, wherein the ghost transmittance of the ghost image is calculated using the following formula: in, The wavelength in the visible spectrum is represented by T, and the incident angle of the light source is set to 15 degrees, corresponding to the angle of refraction α within the substrate supporting the first and second surfaces. Cx (λ, 15°) represents the spectral transmittance of the first surface calculated at the incident angle, R BCc (λ, α) represents the spectral reflectance of the second surface at the refraction angle α, calculated for reflections occurring within the medium of the substrate, R BCx (λ, α) represents the spectral reflectance of the first surface calculated for reflections occurring within the medium of the substrate, T Cc (λ, α) represents the calculated spectral transmittance of the second surface, and T int (λ, α) represents the calculated spectral transmittance between the first surface and the second surface, and The total ghost transmission coefficient is calculated using the following formula: Wherein, the visible spectral band extends between 380 nm and 780 nm, S(λ) represents the spectral brightness of the light source, and Indicates the spectral luminous efficiency of a photopic observer as defined in CIE 1964; b) Modify the structure and / or composition of the first coating and / or the second coating, and c) Repeat steps a) and b) until the total ghost transmission coefficient of the transmission optical system is below a predetermined threshold for ghost visibility.

13. A system for evaluating the visibility of ghosting in a transmission optical system, the transmission optical system having a first surface and a second surface, the first surface and the second surface having different curvatures and / or the first surface and the second surface being configured to provide refractive power, the system for evaluating the visibility of ghosting comprising a processor configured to determine a total ghosting transmission coefficient for at least one ghosting, the at least one ghosting being formed by the internal reflection of a beam of light from a point light source between the first surface and the second surface and by transmission through the optical system, the beam of light from the light source being incident on the first surface at a non-zero angle of incidence, the total ghosting transmission coefficient being generated by the integral of the ghosting transmittance of the at least one ghosting in the visible spectral band and depending on the spectrum of the light source and the spectral luminous efficiency of a CIE 1964 photopic observer, wherein, The ghost transmittance is calculated using the following formula: in, The wavelength in the visible spectrum is represented by T, and the incident angle of the light source is set to 15 degrees, corresponding to the angle of refraction α within the substrate supporting the first and second surfaces. Cx (λ, 15°) represents the spectral transmittance of the first surface calculated at the incident angle, R BCc (λ, α) represents the spectral reflectance of the second surface at the refraction angle α, calculated for reflections occurring within the medium of the substrate, R BCx (λ, α) represents the spectral reflectance of the first surface calculated for reflections occurring within the medium of the substrate, T Cc (λ, α) represents the calculated spectral transmittance of the second surface, and T int (λ, α) represents the calculated spectral transmittance between the first surface and the second surface. The total ghost transmission coefficient is calculated using the following formula: Wherein, the visible spectral band extends between 380 nm and 780 nm, S(λ) represents the spectral brightness of the light source, and This indicates the spectral luminous efficiency of a photopic observer as defined in CIE 1964.

14. A system for evaluating the visibility of ghosting in a transmission optical system, the transmission optical system having at least a first surface and a second surface, the first surface and the second surface having different curvatures and / or the first surface and the second surface being configured to provide refractive power, the system for evaluating the visibility of ghosting comprising a processor configured to determine a total ghosting transmission coefficient of at least one ghosting, the at least one ghosting being formed by the internal reflection of a beam of light from a point light source between the first surface and the second surface and by transmission through the optical system, the beam of light from the light source being incident on the first surface at a non-zero angle of incidence, the total ghosting transmission coefficient being generated by the integral of the ghosting transmittance of the at least one ghosting in the visible spectral band and depending on the spectrum of the light source and the spectral luminous efficiency of a CIE 1964 photopic observer, wherein, The transmission optical system has a third surface and / or a fourth surface. The system for evaluating ghost visibility includes a processor configured to determine the total ghost transmission coefficient for each ghost, each ghost being formed by internal reflection of the light beam between all surface pairs having the same pair of two different curvatures. The total ghost transmission coefficient depends on the sum of the ghost transmission components of each ghost for all surface pairs having the same pair of two different curvatures, wherein the total ghost transmission coefficient is calculated using the following formula: Where XY represents any pair of surfaces X and Y having the same combination of two radii of curvature, Z represents any substrate between surfaces X and Y, and W represents every other surface between surfaces X and Y that is different from surfaces X and Y. 总系统 T represents the direct transmittance of the light beam through all substrates and all surfaces, depending on the wavelength λ. GI Let S(λ) represent the total ghosting transmission coefficient, and S(λ) represent the spectral brightness of the light source. R represents the spectral luminous efficiency of a photopic observer as defined in CIE 1964, where XY represents any pair of surfaces X and Y having the same combination of two radii of curvature, Z represents any substrate between surfaces X and Y, and W represents every other surface between surfaces X and Y that is different from surfaces X and Y. X R represents the spectral reflectance of surface X. Y Let Y represent the spectral reflectance of surface Y, T represent the surface transmittance, and T0 represent the spectral reflectance of surface Y. int This indicates the transmittance of the substrate.

15. A system for evaluating the visibility of ghosting in a transmission optical system, the transmission optical system having at least a first surface and a second surface, the first surface and the second surface having different curvatures and / or the first surface and the second surface being configured to provide refractive power, the system for evaluating the visibility of ghosting comprising a processor configured to determine a total ghosting transmission coefficient of at least one ghosting, the at least one ghosting being formed by the internal reflection of a beam of light from a point light source between the first surface and the second surface and by transmission through the optical system, the beam of light from the light source being incident on the first surface at a non-zero angle of incidence, the total ghosting transmission coefficient being generated by the integral of the ghosting transmittance of the at least one ghosting in the visible spectral band and depending on the spectrum of the light source and the spectral luminous efficiency of a CIE 1964 photopic observer, wherein, The transmission optical system has a third surface and / or a fourth surface. The system for evaluating ghost visibility includes a processor configured to determine the ghost transmission coefficient of each ghost, each ghost being formed by the internal reflection of the light beam between each pair of surfaces having two different curvatures. The total ghost transmission coefficient depends on the sum of the ghost transmission coefficients of each ghost, wherein the total ghost transmission coefficient of each ghost is calculated using the following formula: Wherein, the visible spectral band extends between 380 nm and 780 nm, and S(λ) represents the spectral brightness of the light source. This indicates the spectral luminous efficiency of a photopic observer according to CIE 1964, and It represents the sum of all ghost transmittance components of each pair of surfaces with the same curvature.

Images