ANTI-REFLECTION COATINGS AND COATED ARTICLES

Abstract: Coated optical substrates and a method of coating optical substrates with anti-reflective (AR) coatings are described. The composition of the coating is determined by material constraints such as adhesion, durability, ease of manufacture, and cost. The thickness of one or more layers of AR material is determined by minimizing the product of the Fresnel reflection coefficients for the coated article with the angle- and wavelength-dependent sensitivity of the human visual system. Preferred designs have a value of perceived reflectance, F, less than or equal to 1.25 Fmin is the minimized perceived reflectance for the coated article. Coatings which have minimal perceived reflection while maintaining reflections with desired visually perceived colors are also described.

Description: ANTI -REFLECTION COATINGS AND COATED ARTICLES BACKGROUND OF THE INVENTION The present invention generally relates to improving the transmission of light through optical materials, such as spectacle lenses and, at the same time, reducing reflection of stray light that leads to glare from optical materials. The invention further relates to controlling the perceived color of light reflected from the surface of optical materials. All uncoated, optically transparent materials reflect a portion of incident light. The amount of reflection varies with the wavelength, polarization, and angle of incidence of the light as well as the wavelength-dependent refractive index, n, of the material. This Fresnel reflection is described by Maxwell's equations for electromagnetic radiation, as known to those practiced m the art of optics and described, for example, by M. Born and E. Wolf m Principles of Opti cs , New York, Pergammon Press (1980; . It is also known that layers of transmissive materials with refractive indices different from that of the substrate can reduce the amount of reflection. The amount of this reduction depends on the wavelength-dependent refractive index of the coating materials and their thickness as well as the wavelength, polarization, and angle of incidence of the light. The design and manufacture of these anti- reflection (AR) coatings is thoroughly described m Chapters 3 and 9 of H.A. McLeod, Thin Film Optical Fil ters, New York, McGraw-Hill (1989) . The sensitivity of the human visual system also varies with the wavelength of light and the angle with which it enters the eye, as described, for example, m Color Sci ence : Concepts and Methods , Quanti ta tive Da ta and Formulae £>y Gunter Wyszecki and W.S. Stiles 'New York: Wiley) (1982) and Vi sual Perception by Nicholas Wade ana Micnael Swanston (London : Routledge) '1991^ . A proolem therefore s tc choose tne coating thickness and composition so that the angular and wavelength variation of Fresnel reflection from the coated article as perceived by the human visual system is minimized. Known AR coatings use one or more thin layers of inorganic oxides, nitrides, or fluorides to achieve a reduction m reflection. Common thm-film materials used for such AR coatings are described m chapter 9 and Appendix I of Mcleod and include oxides of Al , Sb, Be, Bi, Ce, Hf, La, Mg, Nd, Pr, Sc, Si, Ta, Ti , Th, Y, and Zr. Mcleod's tabulation also includes fluorides of Bi, Ca, Ce, Al , La, Na, Pb, Li, Mg, Nd, Na, and Th, as well as a few sulphides and selenides . A similar tabulation is found m table 4.1 on page 179 of Opti cs of Mul tilayer Systems (Sh. A. Furman and A.V. Tikhonravov, Editions Frontieres : Gif -sur Yvette Cedex- France, 1992) . The number of layers and their compositions are generally chosen based on auxilliary constraints including hardness or scratch resistance, adhesion, durability, ease of deposition, cost, and other factors familiar to those practiced m the art of optical coatings. However the layer thicknesses are generally adjusted to minimize the proportion of incident light that is reflected (reflectance) at normal incidence and one or more specified wavelengths. A problem therefore is to choose a set of layer thicknesses that minimize or significantly reduce the amount of reflected light that can be perceived by the human visual system over all relevant angles and wavelengths . As described above, the amount of reflectance from a coated article varies with angle and wavelength. When uncoated spectacle lenses are worn, a person looking at the wearer perceives a reflection of light from the environment, i.e., "glare." The color of this reflection is, for uncoated lenses, typically that of the ambient light source (s) because the variation of reflection with wavelength from an uncoated spectacle is quite small. This result is generally true for mildly dispersive optical materials such as glass, polycarbonate, polymethylmethacrylate, and other spectacle lens materials. A plot of the wavelength and angle dependent reflectance for glass is shown m FIG. 1. The amount of reflected light from an AR coated article varies more dramatically with wavelength and angle, so that the perceived color of the reflection may differ from that of the light source. As this color influences the cosmetic quality of a spectacle lens, and other optical substrates, it is therefore, desirable to reduce reflection while controlling the perceived color of reflected light. SUMMARY OF THE INVENTION In accordance with the present invention, an anti- reflection (AR) coating is designed using the wavelength and angle dependent refractive properties of one or more thin layers on an optical substrate. The number and ordering of the layers is determined by non-optical constraints such as adhesion, durability, cost, ease of deposition, and the like. A perceived reflectance, F, which weights the angle- and wavelength-dependent Fresnel reflectance by the angle and wavelength sensitivity of the human visual system, is computed for each combination of layer thicknesses. In one embodiment, the value of F is calculated to obtain a minimum value unique to the combination of optical substrate and layers of coated material, for any specified viewing conditions. In an alternative embodiment, the thicknesses of the one or more layers of material are such that perceived reflectance of the coated substrate is not completely minimized, but is close to, and preferably within 25% of the minimum value of F, for the specified viewing conditions. The advantage of this approach is that one obtains a coated substrate having the absolute lowest value of perceived reflectance over a range of wavelengths and angles for a given geometry of viewing conditions. Alternatively, where absolute minimization is not required, perceived reflectance is reduced to within 25% or less of the minimum value -- still far lower than the value of oerceived reflectance otherwise obtainable. In one embodiment of the invention, the layer or layers (also referred to as "coatings" or "films") are formed by plasma-enhanced chemical vapor deposition (PECVD) of volatile precursors, non-limitmg examples of which include organic and organometallic compounds. Alternatively, one or more layers are formed by sputtering or evaporation, using techniques and materials well known m the art. The McLeod reference provides a good description of such techniques and materials. The resulting layers may be optically dispersive (i.e., have a variation of refractive index with wavelength) . Alternatively, the resulting layer (s) may not be optically dispersive. The layers have refractive properties that depend on the precursor, the deposition conditions, and the film thickness. Both single and multiple layer AR coatings are prepared m this manner. A further aspect of the present invention is the control of the perceived color of light reflected by the coated article. For each set of film thicknesses the color perceived by reflection of standard lllummants, (e.g. daylight, fluorescent, incandescent, or arc lamps) is computed using standard coloπmetric methods. The perceived color and its variation with angle are then used as constraints while the perceived reflectance is minimized. This process leads to a coated article that exhibits a minimum perceived reflectance (or a value within 25% or less of minimum) of desired color. BRIEF DESCRIPTION OF THE DRAWINGS These and other features and advantages of the present invention will be better understood by reference to the following detailed description when considered m conjunction with the accompanying drawings, wherein: FIG. 1 is a plot of the human photopic response showing the total sensitivity as well as the response for sets of cone cells with red, green, and blue photoreceptors , after Wyszecki and Stiles, Table 3.1.1. The scotopic (rod- photoreceptor) response curve has its maximum 49 nm to the blue (507 nm) and has a full width at half maximum of 100 nm. FIG. 2(a) is a plot of the angular variation of cone and rod photoreceptors m a human eye taken from Wandell, op . a t . , FIG. 3.1b, PAGE 46. The photopic (cone) response is responsible for color vision and is active at moderate to bright illumination levels. Scotopic vision is dominated by rod photoreceptors and s active only at low light levels (night vision) . These factors are combined with the geometry of the viewing situation to yield the angular part of S(λ,θ). FIG. 2 (b) is a schematic view of the geometry for viewing through spectacle lens. The 8 dioptre piano lens is 12 mm from the sαπace of the cornea. Rays that travel from left to right impinge on tne cornea at 0 'blue, , 10 degrees (green) and 20 degrees (red) are snown propagating through a 3 mm diameter pupil and onto the retina. Note that 20 degree rays normally impinge on regions of the retina for which the cone sensitivity is low. The eye therefore rotates in its orbit by +/- 25 degrees horizontally and vertically in order to image this angular range with high fidelity on the fovea. As the eye executes this saccadic motion the range of angles at wnich light strikes the spectacle lens depend on its refracting power ana orientation with respect to the eye socket m ways that are straightforwardly computer from geometric optics. FIG. 3 is a plot of the human response function 3 (λ,θ) for an observer looking through a set of spectacle lenses as a function or viewing angle ana optical wave_ength. The wavelength dependent sensitivity is governed by the photopic retinal response, while the angular dependence ^ ε set DV saccadic eye movement and the variation of cone αensit it angular separation from central fixation. FIG. 4 is a plot reflectance from a glass substrate coated with a three layer antireflection coating as described on page 110 of McLeod : 72.4 nanomemters (nm) of PrO (n=192) , 68.4 nm of TiO (n=2.06), and 100 nm of MgF (n=1.38) . The perceived reflectance of this design is 141, or 24.5% of that for the uncoated glass substrate. FIG. 5 is a plot of Fresnel reflectance from a single, uncoated glass surface (n(λ)=1.50) as a function of wavelength and angle computed by solution of equation 1. Although independent of wavelength, the amount of reflection increases from 4% at normal incidence to 9% at 60 degrees. FIG.6 (a) is a plot of reflectance R(λ,θ) for the PrO:TιO:MgF coated glass article with minimal perceived reflectance using the response function snown in figure 3. FIG.c ,D) IS a comparison of R(λ,θ=0)for the articles of Figures J (o) and 6(a) (x) . The photopic response curve is also shown. FIG. 7 is an illustration of the geometry for considering the color of light reflected from a spectacle lens at an angle φ and perceived by an observer, the child. The perceived color is computed using the wavelength dependent intensity of the source (sunlight filtered by window) , the reflectance of the physician' s coated spectacle lens (R(λ,θ)), and the color response of the child observer. FIG. 8 is a plot of CIE color trajectories for the coatings shown in FIG. 2 ("x") and FIG. 4 ("o") from 0 to 60 degrees m 5 degree increments presuming spectrally flat, broadband illumination such as is proviαed by a xenon arc ^ .arnp. The wn.-.te point is shown by a diamond, and dominant wavelengths are shown at the boundary of the plot. To compute the dominate wavelength one extends a line from the white point through the computed CIE coordinate to the boundary. The point of intersection is the dominant wavelength. FIG. 9(a) is a plot of spectral irradiances of three typical lightsources : daylight at sea level ( o ) , an incandescent tungsten lamp ( + ), and a fluorescent lamp [ ■ * ) . FIG. 9(b) is a plot of CIE Chromaticity coordinates for the coated article (Ex 1, table I for each of the three illummants at angles from 0 to 60 degrees in 5 degree increments. Plotting symbols correspond to daylight at sea level (o) , an incandescent tungsten lamp ( + ), and a fluorescent ±amD '*) . FIG. 11 is a plot of CIT trajectory for reflection from each of the 18 AR coatings for whicn F<140 at angles of incidence from 0 to 60 degrees. (Coating thicknesses shown m Table I) . FIG. 12 is a plot of S (λ,θ) for a video display screen with light reflected by overhead illumination. FIG. 13 is a plot of reflectance from the minimal Fa design of a three-layer PrO:TιO:MgF AR coating on a glass video display terminal. FIG. 14 is a plot of CIE chromatically coordinates for the video display with minimal Fa from 0 degrees to 60 degrees m 5 degree increments. DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention provides new, single and multilayer AR coatings on optical substrates. As used herein, the terms "optical materials," "optical substrates," and "optical articles" refer to normally transparent or translucent materials such as glass and plastic, and articles made of such materials. Nonlimitmg examples of such articles include lenses, windows, television and computer monitor screens, and automotive windshields. Reflectance, R, is the ratio of the intensity of the reflected portion of light, I r , to the intensity of the incident probe light, I : The reflectance varies with the wavelength of light, λ,the angle of incidence, θ,and the light's polarization P. It is equal to the product of the Fresnel reflection coefficient, p, and its complex conjugate p\ which can also be expressed m terms of optical admittances for the substrate medium y 0 and the incident medium y_ . The optical admittance is y =2. 6544 x 10 (n - κ) = (C/B) (2) where n is the real part of the refractive index, k is the absorptive (imaginary) part of the refractive index, and the constant is a conversion factor for SI units. The optical admittance when one or more thin layers is added to a substrate whose admittance is η m becomes \y - (C I B)\ where C and B are computed by solving the matrix equation (3) CH^ - ' ^IW ) <3) In equation (3) the argument of the trigonometric functions for each layer r whose physical thickness is d ^ is δ =2 π(n -ιk)d r cos(θ r )/ λ (4) At normal incidence, (θ=0) , the admittance is the same for any polarization. At other angles of incidence one splits the incident wave into two polarizations, p and s, and defines tilted optical admittances η p ~ tk) I cos(θ) η = 2 6544x 10 n -ιk) \ cos(θ) (5) leading to general reflectance R, transmission T, and absorption A via the formulae: T: (6) (η n B +C)(η 0 B +Q- where the subscripts 0 and m refer to the incident medium and substrate, respectively. The derivation of these equations is described m chapter 1 by H.A. McLeod, op . ci t . The sensitivity of human vision varies both with optical wavelength and angle of incidence as discussed, for example m Color Science : Concepts and Methods , Quanti tative Data and Formulae by Gunter Wyszecki and W.S. Stiles (New York:Wιley) (1982) and Visual Perception by Nicholas Wade and Michael Swanston (London: Routledge) (1991) . It is not, however, sensitive to polarization. The variation of human visual sensitivity with wavelength, S (λ) , is graphically presented m FIG. 1, wnicn shows the sensitivity for each cone pigment (nominally red, green, and blue) , as well as the sum of the cone responses. This sum is referred to as the photopic response. The variation of visual response with angle depends on the geometry of the viewing situation as well as on the physiological and optical constraints imposed by the human eye. When viewing through spectacle lenses one can construct an angular function S (θ) that accounts for the distribution of cone pigments as well as normal saccadic eye movement. FIG. 2(a) shows a plot of the a real density of cones and rods for the human eye. The cones are heavily concentrated m a solid angle of less than 5 degrees. During normal vision, the eyeball moves m its socket at angles up to about 25 degrees from central fixation m saccadic movements. When viewing at more extreme angles, the natural physiological response is to initiate head movement. Saccadic movements allow the region of maximum photoreceptor sensitivity, the fovea, which subtends a small solid angle, to cover a wider range of angles without head movement. The foveal response and saccadic motion are then combined with the geometrical optics of a spectacle lens to produce S(λ,θ). As can be seen m figure 2B, from each optical ray that enters the pupil there are corresponding locations and angles at both the retina and the surfaces of the ophthalmic lens. The angles with which light strikes the coated article and is suosequently imaged on the fovea over the range of saccadic eyeoall motions is αirectly converted to the angular variation of S(λ,θ). The visual response function S (λ,θ) shown m FIG. 3 combines the human response functions for wavelength and angle appropriate to viewing through a spectacle lens. The particular form of S (λ,θ) may vary m a manner consistent with the viewing conditions. For example, the rod photoreceptors are primarily active m low light conditions, resulting m an angular sensitivity that is dramatically different than for photopic vision, as can be inferred from the rod photoreceptor density shown m FIG. 2. The chromatic (wavelength-dependent) response of the rods is also different, having a maximum at 507 nm and a full-width at half maximum of 100 nm as described more fully m Wyszecki, p. 258 FIG. 4.3.2. Another example for use of different S (λ,θ) is obtained for humans with partial color blindness or retinal damage such as is caused by macular degeneration. The angular component of S (λ,θ) also varies with the geometry of the optical viewing condition. When viewing reflections off of a monitor screen or a spectacle lens worn by another person, the angular variation of S depends on the geometric relationship between the observer, the coated article, and the position of the illumination source, rather than on the observer's saccadic eye movements. Similarly, the angular dependence of reflection from an automotive windshield will depend on its distance from the driver's head and its angle m the frame of the automobile. Although the coating materials, number of layers, and ordering of layers may be the same for two applications, say a windshield and a spectacle lens, the layer thicknesses computed for minimal Fa according to the invention may be different for each application. An example of the solution to the Fresnel equations using wavelengths between 390 and 710 nm and angles up to 60 degrees for a glass substrate coated with 72 nm of Pr0 2 68 nm of TιO x , and 100 nm of MgF is shown m FIG. 4. This arrangement of layers and thicknesses is described as an anti-reflection (AR) coating m McLeod, op.cit., p. 110. The plot m FIG. 4 shows the average of s- and p- polarized reflectance, which is appropriate for human visual performance since human vision does not sense optical polarization. Changes to the substrate, the refractive properties of layers, or the order m which they are coated onto the substrate lead to complex but calculable changes m the reflectance R(λ,θ,P) . According to the present invention, the design of an AR coating is based on perceived reflectance. The perceived reflectance, F, of light from a surface by a human observer is defined as the integral of the product of the reflectance, R(λ,-Θ-), with the human sensitivity function, S (λ,-Θ : F =ffi(λ, θ)R(λ, θ)dMΘ (7) R(λ,-Θ-) is the average of the p- and s- polarized reflectances and s used here because the human visual system is not sensitive to polarization. (In some cases, it is convenient to refer to the perceived reflectance of an uncoated article as "Fαncoated" or "Fo", and perceived reflectance of an AR coated substrate as "FAR" (The latter is sometimes referred to as "F".j The value of F depends on the wavelength-dependent refractive indices of the substrate and layer media, on the thickness of the layers, and also on the angular and wavelength dependent visual response as described above . In the ideal case, and as described m Application Serial No. 08/990,003, equation 7 is solved for the absolute minimum value of F (denoted Fmm) for a given stack of coatings or layers on a substrate, for a given geometry of viewing conditions. The result is unique for the particular combination and composition of AR layers or coatings, the physical thickness of which are such that F=Fmm. In an alternate embodiment, equation 7 is solved for a range of values close to, but not necessarily equal to, Fmin. That is, good results are obtained when the value of F is small, but not necessarily an absolute minimum. In one such embodiment, the value of F for the coated substrate is within 25% of Fmm, i.e., F < to 1.25 Fmm. For some applications, where extremely low amounts of perceived reflectance are desired, equation 7 is solved for values of F within 20%, 15%, or even 10% of Fmm, i.e., F < 1.20 Fmm, F <. 1.15 Fmm, or F <. 1.10 Fmm. In each case, the solution to F enables one to identify the combination of physical thicknesses of layers of anti-reflection coatings that satisfy the desired range or value of F. The following non- limiting examples are illustrative of the invention. Starting with the McLeod three-layer AR coating (FIG. 4) applied to a spectacle lens, one uses the response function shown m FIG. 3 and computes a baseline value of perceived reflectance F=141. The value of perceived reflectance from an uncoated glass lens (FIG. 5) has a value of 575 for the same S (λ,θ) , and the McLeod design reduces the perceived reflection to 25% of that for the uncoated lens. Example 1 According to the present invention, the perceived reflectance, F, is computed for all combinations of layer thicknesses and the set of thicknesses for which F is minimized is selected. Beginning with the glass : PrO :TιO :MgF system described above, this calculation was performed and the minimum perceived reflectance Fmm, was calculated to be 104, which is 18% that of the uncoated article and a 35% reduction from that of the textbook coating. This absolute minimum value of perceived reflectance (shown in FIG. 6) for these materials corresponds to the following physical thicknesses: lOOnm of PrO, 25nm of TiO, and 87nm of MgF . Examples 2-19 Using the approach of the present invention, and solving equation 7 by altering the magnitude of physical thicknesses of the three layers m lOnm increments, yielded over 16,000 combinations. Of these, eighteen were found to have perceived reflectances less than that of the textbook coating, m addition to the case where F=Fmm (Ex. 1) . Twelve examples (plus Ex. 1) satisfy the desired parameter that F < . 1.25Fmm The results are presented m the following table: Table I Perceived Reflectance for Coated and Uncoated Spectacle Lenses 2 % Within F mιn = (F/F mιn - 1 )100 The thickness combinations reported m Table I do not preclude other combinations for which the value of F is within 25% (or some other desirably low percentage) of its minimum value of 104. However, of the 16000+ permutations that were examined, only Examples 1-13 were found to meet this criterion. One skilled m the art will appreciate that equation 7 can be solved (for F, Fmm, 1.25Fmm, or any other desired value or range of F) using linear algebra and calculus. As an alternative to manual computation, linear algebra software can be used. Non-limitmg examples of such software include Mathematica (Wolfram Research, Champaign- Urbana, ID, Matlab 'The MathWorks, Inc., Natick, MA), Macsyma (Macsyma Inc., Arlington, MA), and Maple (Waterloo Maple, Inc., Waterloo, Ontario, Canada) . Computational analysis of F is also possible using spreadsheet software, for example Excel (Microsoft, Redmond, WA) and Lotus 1-2-3 (Lotus Development Corp., Cambridge MA) . It will be apparent from Table I that discrete values of thicknesses were selected for each layer of material m computing F (namely, lOnm intervals) . One could, of course, choose a different interval, for example 5nm, 2nm, etc. In general, for small departures m the value of a given layer's physical thickness the effect on the computed value of F will also be small, and F will often lie within 25% of Fmm. For example, the value of F corresponding to the layer thicknesses for PrO:TιO:MgF of 40, 80, and 80nm, respectively, is 127 (Ex. 13 m Table I) . The value of F corresponding to thicknesses 42, 80 and 80nm, respectively, is 121, as is the value for a 40, 82, and 80nm system. When the thicknesses are 40, 80, and 82nm, F becomes 122. In each case, the value F is within 25% of Fmm. However, when the thicknesses are set to 40, 80, and 78nm, the value of F rises to 136, which is 31% higher than Fmm. A further aspect of the present invention concerns constraints on the perceived color of light reflected from the coated article. As an example of this embodiment we consider the AR coatings summarized m Table I from the point of view of an observer looking at a person wearing the spectacle lens. Light from overhead lamps, windows, or other sources of illumination strike the surface of the lens and are reflected into the eye of an observer at an angle (φ) as shown schematically m FIG. 7. The color of this reflection depends on the wavelength-dependent intensity of the lllummant (sunlight filtered by the window) , the wavelength and angle dependent reflectance of the coated article (the coated spectacle lens) , and the physiology of color vision as described, for example, m Wandell, Foundations of Vision , Smauer Associates : Sunderland MA, 1995, or Wyszecki and Stiles op ci t . The perceived color of an object is quantitatively defined by coordinates m color space such as the CIE 1931 or 1964 colorimetπc coordinates or the uniform 1976 CIE (L*,u*,v*) color space described m Wyszecki and Stiles m chapter 3. FIG. 8 shows the color coordinates (denoted ="x") in the CIE 1931 representation for the McLeod textbook AR PrO:TιO:MgF coating as a function of angle for illumination by a xenon arc lamp. Also shown m FIG. 8 are the color coordinates (denoted "o") for the (Fmxn) minimal coating prepared m accordance with the present invention. The location marked by a diamond corresponds to white, that is, no perceived color. The dominant wavelength, which is defined as the wavelength at which a monochromatic stimulus produces the same perceived color, is found by tracing a line from the white point (diamond) to the periphery of the plot through the computed CIE color point. For example, both the textbook coating at a viewing angle of 50 degrees and the minimal Fmm coating at 0 degrees have a dominant wavelength of about 480 nm, that is, blue-green. Not all points m CIE color space have a dominant wavelength, however, the dominant wavelength provides a qualitative label with which to compare various hues . The perceived color of light reflected from the surface of an AR coated article varies with both the angle of incidence and the source of illumination. FIG 9(a) shows the spectra of three standard llluminats: daylight at sea level, an incandescent tungsten lamp, and a fluorescent lamp. The color coordinates for reflection of these lights from a coated article corresponding to Ex. 1 (table 1, F=Fmιn) according to the present invention is shown m Fig. 9(b) for angles from 0 to 60 degrees m intervals of 5 degrees. The perceived color, as quantified by the CIE chromaticity coordinates, is a function of both the angle and the lllummant. Both the actual location and the variation of CIE color location with angle are of practical interest for the design of AR coated articles. It is known to those practiced m the art of optometry that certain colors and hues are cos etically preferable to others. Furthermore, the variation of hue with viewpoint is a factor m the cosmetic acceptance of a spectacle lens product . It is also clear from FIG 1 that the absolute visual sensitivity for the reflected image is more acute for some wavelengths, say 550 nm (green) than for blue (450 nm) or deep red (750 nm) . One of the advantages of the present invention is that it allows minimization of the reflectance perceived by a spectacle lens wearer (e.g. the physician m FIG. 7) while at the same time controlling the color of reflections perceived by an external observer (the child m FIG. 7) . FIG. 10 shows the perceived color for sunlight reflected from each of the Examples 2-19 summarized in Table I at normal incidence. As the angle between the lllummant, lens, and observer is increased, there is a shift m the perceived color as shown m FIG. 11, where the chromaticity coordinate trajectories are plotted in five degree intervals from 0 to 60 degrees. In one embodiment of the present invention, these calculated colors are used in connection with cosmetic or other color criteria to produce an article that has minimal perceived reflectance while maintaining a predefined color. For example, if one desires to minimize the appearance of the reflection one might match the hue to that of the wearer's skin color. Alternatively, one might constrain the color to within a range of hues that are minimally perceptible baed on their proximity to the white point or the photopic sensitivity toward blue or red hues implied by figure 1. In a third embodiment color control one might elect the AR coating that has the smallest change m hue as it is tipped through a predetermined angular range under a predetermined source of llllumination . This range can be quantified by computing the length of the curves shown in figure 11 after the coordinates are transformed from the 1931 CIE color space to the 1976 CIE uniform (L*,u*,v*) color space. According to one aspect of the invention, the empirically determined average values of S (λ,θ) (see Wyszecki, Ch.5) are used to determine the preferred response factor to be used m designing an AR coating. However, construction of individual profiles for individuals with peculiar constraints on S (θ) , such as would occur, for example, m individuals that are blind m one eye or that suffer from macular degeneration, are also encompassed by the invention. The perceived reflectance, F, is numerically evaluated for one or more layers on an optical substrate as a function of the thickness, composition, and order in which they are coated on the substrate. The composition and order may be constrained by other material issues such as adhesion, surface energy, chemical resistance, etc. According to the present invention, the preferred thickness of the layer (s) m an AR coating brings the value of F to within 25% of its absolute minimum, subject to these constraints . According to the present invention, the thickness of the layer (s) may also be constrained by the color perceived for light reflected from the article and into the eyes of an observer. This auxiliary optical constraint yields an AR coated article that is at once minimally reflective while having cosmetically desirable appearance. Examples 20-30 A second embodiment of an AR coated article according to the present invention is a computer monitor or video screen that has a glass surface. Anti-reflection coatings for these articles are desirable because overhead or window illumination causes reflected images that impair the visibility of the images projected onto the display screen. The photopic response, S (λ) , for the human observer is as shown m FIG. 1. However, the angular component of S (λ,θ) is substantially different than for the spectacle lens. Presuming overhead illumination m a typical workplace environment, and using simple geometry, a sample S (λ.θ) is shown m FIG. 12. The perceived reflectance of the uncoated screen is 717, while that found for the textbook PrO:TιO:MgF coating is 258, or 36% of that for the uncoated display. Using the method described above, the layer thicknesses that reduce F to 191, its minimal value (26.6% that of the uncoated display) , are found to oe 60 nm PrO, 80 nm TiO, and 120 nm MgF . A plot showing Fmm for this embodiment is presented m FIG. 13. It will be appreciated that this combination of layer thicknesses for these three materials is not ideal for the spectacle lens. Using the human response function for the spectacle lens (FIG. 3) leads to a value of F=252, substantially greater than even the textbook coating. The chromaticity coordinates for this AR coated display terminal are shown m FIG. 14. As before, a series of computations is undertaken and yields values within a desired percentage of the minimum value of F, I.e., 25%, while the hue of the reflected light is separately computed for relevant angles using the colorimetry formulae. After evaluating the chromaticity coordinates of each design m Table II, the cobmmation of hue and minimally perceived reflectance can be selected based on cosmetic or visual function constraints. For example, if the video display background is a preset color it is desirable to make the reflected hue blend with this background color to further reduce the reflections' visual impacts. It will be seen to those practiced m the art of vision science that the selction of particular hues for articles with F<1.25 Fmm will vary with illumination, the geometric optics of the display, and the color background of the environment m which the AR coated article is to be employed. Table II presents a partial set of the solutions to equation 7 for this AR coated display terminal, where computations were carried out by varying the magnitude of physical thicknesses of the layers m the lOnm increments, yielding over 16,000 combinations. Of these, 165 had values of perceived reflectance within 30% of Fmm, and approximately 125 had values of perceived reflectance within 25% of Fmm. The results for the uncoated lens, the textbook (McLeod) coating, Ex. 20 (FTΠ) , and Ex. 21-30 are presented below. Table II Perceived Reflectance for Coated and Uncoated Video Display Screens 2 % Within F mιn = (F/F mιn - 1 )100 It will be apparent to those practiced in the art of colorimetry that the perceived color depends quantitatively on the spectral distribution of the lllummant, as shown FIGS. 9(A) and (B) . Incandescent, fluorescent, and arc lamps have different spectral outputs than sunlight. Furthermore, the spectral content of sunlight varies with time of day and weather conditions. The present invention can incorporate the lllummant ' s spectral features into the computation of perceived reflectance or perceived color by including the wavelength dependent intensity of the source explicitly m the computation of S (λ,θ) . One skilled the art will appreciate that the details of which form or weignted average of forms should be applied will, of course, take into account the viewing conditions under which the article is to be employed. The invention provides unique articles of manufacture, characterized by low reflectance. Generally, the articles are transparent, for example, ophthalmic lenses, windows, windshields, television and computer screens, etc. Transparent articles have no absorption of light over the region of the spectrum sensed by the human visual system, that is between about 350 and about 750 nm. In some embodiments, however, the article may be translucent. Translucent articles transmit light at some visible wavelengths but absorb some or all of the light at one or more visible wavelengths. Nonlimit g examples of translucent articles include tinted and shaded sunglasses, stained-glass windows, and tinted windshields. In one embodiment, a transparent, low reflection article comprises an optical substrate and one or more layers of AR material. It will be readily appreciated that low reflection articles having more than two layers of material deposited on an underlying optical substrate are also within the scope of the present invention. The invention has been described preferred and exemplary embodiments, but is not limited thereto. A variety of modifications, modes of operations and embodiments, all within the ability and skill of those skilled m the art, can be made without departing from the present invention. For example, the AR coatings and methods of designing and applying them can be used on a variety of optical substrates addition to ophthalmic lenses. Even large articles, like automotive windshields, can be given an AR coating if a suitably large reactor is built. All references herein are incorporated by reference as if set forth herein m their entirety. In both the text and the claims, use of the word "about" relation to a range of numbers is intended to modify both the high and low values stated.

Claims: WHAT IS CLAIMED: 1. A transparent or translucent coateo article having a perceived reflectance F, wherein where λ s wavelength, θ is incident angle, S(λ,θ) s human sensitivity function as a function of the wavelength and the incident angle, and R(λ,θ) is an average of p- and s-polarized reflectances, the coated article comprising: an optical substrate; and one or more layers of anti-reflection material coated on at least a portion of the optical substrate, said one or more layers of anti-reflection material having a thickness such that the perceived reflectance of the coated article is less than or equal to 1.25F mιr , where F mιr is a minimized perceived reflectance of the coateo article. 2. An article as recited m claim 1, wherein the optical substrate is an ophthalmic lens. 3. An article as recited claim 2, wherein the ophthalmic lens is coateo with the anti-reflection material on at least a portion of one or both lens surfaces and/or its edge. 4. An article as recited m claim 1, wherein the optical substrate is a window. 5. An article as recited m claim 1, wherein the optical substrate is a television screen or computer monitor. 6. A coated article as recited m claim 1, wherein at least one layer of anti-reflection material comprises a fluorocarbon film. -97- 7. An article as recited m claim 6, wherein the fluorocarbon film is a plasma deposition product of a perfluormated organic compound. 8. An article as recited m claim 7, wherein the perfluormated organic compound is a perfluoroaliphatic or perfluorocycloaliphatic compound. 9. An article as recited m claim 8, wherein the perfluormated organic compound is selected from the group consisting of perfluorocyclobutane, hexafluoroethane , tetrafluoroethylene, perfluoropropene, and mixtures thereof. 10. An article as recited m claim 6, wherein the fluorocarbon film comprises polytetrafluoroethylene . 11. A coated article as recited in claim 1, wherein at least one layer of anti-reflection material comprises an organic or organosilicon film. 12. A coated article as recited m claim 1, wherein at least one of layer of anti-reflection material comprises a plasma- enhanced chemical vapor deposition product of one or more precursors selected from the group consisting of Sι(CH 3 ) 4 , HSι(CH 3 ) 3 , thiophene, furan, benzene, Ti (OC 2 H 5 ) „, Tι(OC,H,),, Ti (N (C 2 H S ) 2 ) 4 , and perfluormated organic compounds. 13. An article as recited in claim 1, wherein each layer of anti-reflection material has a physical thickness greater than about 5nm and less than about 1 micron. 14. An article as recited in claim 1, further comprising an optically thin metal layer deposited on the optical substrate and/or on a layer of anti-reflection material. 15. An article as recited claim 1, further comprising a laver of material. 16. An article as recited in claims 1, having a color, when viewed at a specified angle or angles, under a specified illumination, that is perceived to lie within a specified volume element of color space defined by the color's CIE chromaticity coordinates. 17. An article as recited in class 16, wherein the illumination is selected from normal or spectrally filtered daylight, tungsten lamps, fluorescent lamps, and arc lamps. 18. An article as recited m claim 16, where the volume element is defined by a circle of radius 0.1 centered at (1/3, 1/3) in 1931. 19. An article as recited m claim 16, where the volume element is selected to match a background color and thereby decrease the visibility of reflected light. 20. A transparent or translucent coated article, comprising: an optical substrate; ano one or more layers of anti-reflection material coated on at least a portion of the optical substrate, said one or more layers having a thickness se_ected to maintain chromaticity coordinates contained with a volume element defined by a circle or radius 0.1 centereα at (1/3, 1/3) in 1931 CIE color space . 21. A method for making a transparent or translucent coated article in which an optical suostrate s coated with one or more ^ ayers of anti-reflecticn material, said coated article having a perceived reflectance F, wherein F =Jβ(λ, θ)R( θ)dλdθ where λ _s waveienαtn, θ s incident angle, 3 λ,θ) is human sensιtιv_t_ function as a function of the wavelength and the incident ang_e, and R(λ,θ) is an average of p- ano s-po aπzed reflectances, the method comprising: initiating deposition of one or more layers of anti- reflection material on the suostrate; and terminating deposition wnen said one or more layers reach a desired thickness such that the perceived reflectance of the coated article is less than or equal to 1.25Fmm, where Fm is a minimum perceived reflectance of the coated article. 22. The method of claim 21, wherein the layer is deposited by plasma-enhanced cnemical vapor deposition.

Inventors: HAALAND PETER D, MICKOY B VINCENT, HAALAND, PETER, D., MICKOY, B., VINCENT
Applicants: HAALAND PETER D, MICKOY B VINCENT, HAALAND, PETER, D., MICKOY, B., VINCENT
Application year: 2000
Main classification: G02B1
IPC codes: B32B7, C03C17, G02B1, G02C7