Layered element made of transparent layers providing directional diffuse reflection

Abstract

A transparent layered element includes two transparent external layers having substantially the same refractive index and each having a smooth external main surface, and a central layer intermediate between the external layers, the central layer including at least one transparent layer of refractive index different from that of the external layers or a metal layer. All the contact surfaces between two adjacent layers of the layered element, one of the two layers of which is a metal layer, or that are two transparent layers of different refractive indices, being textured and parallel to one another, the diffuse light reflection of the layered element on the side of at least one of the external layers having at least one maximum in a direction different from the direction of specular reflection. In addition, the surface of the layered element is divided into a plurality of pixels of same size.

Claims

1. A transparent layered element comprising: two transparent external layers having substantially the same refractive index and each having a smooth external main surface, and a central layer intermediate between the external layers, the central layer including at least one transparent layer of refractive index different from that of the external layers or a metal layer, all the contact surfaces between two adjacent layers of the layered element, one of the two layers of which is a metal layer, or that are two transparent layers of different refractive indices, being textured and parallel to one another, wherein, for radiation incident on one side of the layered element, the diffuse light reflection of the layered element has at least one maximum in a direction different from the direction of specular reflection, and wherein a surface of the layered element is divided into a plurality of pixels of same size, each pixel having at least one side of length smaller than or equal to 500 m, the texture of each textured contact surface within each pixel having a slope distribution f.sub.pix having a correlation coefficient r with the slope distribution f.sub.tot of the texture of the total textured contact surface, the layered element being such that, for a sample of N pixels, the average of the correlation coefficients r of each pixel of the sample is higher than or equal to 0.8.

2. The transparent layered element as claimed in claim 1, wherein the layered element is intended to be used, by an observer, lying substantially parallel to a plane Oxy of a coordinate system (O, x, y, z) in which the axis Ox is in a horizontal direction and the axis Oy is in a vertical direction with respect to the observer, the texture of each of said textured contact surfaces between two adjacent layers of the layered element, one of the two layers of which is a metal layer, or that are two transparent layers of different refractive indices, being of equation z=f(x, y) and having, at each point of coordinates (X.sub.0, Y.sub.0) of the contact surface, a first directional slope .sub.x and a second directional slope .sub.y such that: ${}_x\left(X_0,Y_0\right)=\arctan \frac{\mathrm{dz}}{\mathrm{dx}}{|}_{X_0,Y_0}\mathrm{and}$ ${}_y\left(X_0,Y_0\right)=\arctan \frac{\mathrm{dz}}{\mathrm{dy}}{|}_{X_0,Y_0},$ the slope distribution of the texture of each of said textured contact surfaces, which corresponds to the frequency of each pair of slopes (.sub.x, .sub.y), not having axial symmetry about at least one of the axes (O.sub.x, O.sub.y) of a first orthogonal coordinate system (O, .sub.x, .sub.y) where O corresponds to the pair of slopes (0, 0), or not having axial symmetry about at least one of the axes (O.sub.x, O.sub.y) of a second orthogonal coordinate system (O, .sub.x, .sub.y) obtained by rotating by 45 the first orthogonal coordinate system (O, .sub.x, .sub.y).

3. The transparent layered element as claimed in claim 2, wherein the slope distribution of the texture of each of said textured contact surfaces, which corresponds to the frequency of each pair of slopes (.sub.x, .sub.y), does not have axial symmetry about at least one of the axes of an orthogonal coordinate system centered on O.

4. The transparent layered element as claimed in claim 2, wherein the slope distribution of the texture of each of said textured contact surfaces, which corresponds to the frequency of each pair of slopes (.sub.x, .sub.y), has, excluding a potential peak centered on O, a single peak not centered on O.

5. The transparent layered element as claimed in claim 2, wherein the slope distribution of the texture of each of said textured contact surfaces, which corresponds to the frequency of each pair of slopes (.sub.x, .sub.y), has, excluding a potential peak centered on O, at least two peaks not centered on O.

6. The transparent layered element as claimed in claim 5, wherein all the peaks of the slope distribution of the texture of each of said textured contact surfaces are aligned along a single axis of an orthogonal coordinate system centered on O.

7. The transparent layered element as claimed in claim 5, wherein the slope distribution of the texture of each of said textured contact surfaces, which corresponds to the frequency of each pair of slopes (.sub.x, .sub.y), has two peaks that are symmetric to each other with respect to one of the axes of an orthogonal coordinate system centered on O.

8. The transparent layered element as claimed in claim 2, wherein the slope distribution of the texture of each of said textured contact surfaces, which corresponds to the frequency of each pair of slopes (.sub.x, .sub.y), has, excluding a potential peak centered on O, at least one peak not centered on O and for which the aspect ratio, which is a ratio between the width of the peak along the axis O.sub.x and the width of the peak along the axis O.sub.y, is different from 1.

9. The transparent layered element as claimed in claim 1, wherein an average of the correlation coefficients r (f.sub.pix, f.sub.tot) of each pixel of the sample is higher than or equal to 0.9.

10. The transparent layered element as claimed in claim 1, wherein each pixel has at least one side of length smaller than or equal to 150 m.

11. The transparent layered element as claimed in claim 10, wherein the length is smaller than or equal to 100 m.

12. The transparent layered element as claimed in claim 1, wherein the sample of N pixels is chosen from N+2 pixels, the pixel having the highest correlation coefficient and the pixel having the lowest correlation coefficient being removed.

13. The transparent layered element as claimed in claim 1, wherein the layered element is a flexible film.

14. A transparent glazing, comprising a layered element as claimed in claim 1.

15. The transparent glazing as claimed in claim 14, further comprising at least one additional layer positioned against the layered element, chosen from: transparent substrates chosen from polymers, glasses or ceramics comprising two smooth main surfaces, setable materials initially in a viscous, liquid or pasty state suitable for forming operations, polymer-based interlayer sheets.

16. The transparent glazing as claimed in claim 15, wherein the least one additional layer is a sol-gel layer, or a thermoformable or pressure-sensitive interlayer sheet.

17. The transparent glazing as claimed in claim 14, further comprising at least one antireflection coating at the interface between the air and the material from which the layer forming an external main surface of the glazing is made, said surface being intended to be opposite with respect to a projector during the projection of images onto the glazing.

18. The transparent glazing as claimed in claim 14, wherein the transparent glazing is a transparent projection screen.

19. The transparent layered element as claimed in claim 1, wherein the length is smaller than or equal to 200 m.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) Features and advantages of the invention will become apparent from the following description of a plurality of embodiments of a layered element and of a transparent projection screen or glazing according to the invention, which description is given merely by way of example with reference to the appended drawings, in which:

(2) FIG. 1 is a schematic view showing diffuse and specular reflection of radiation incident on a layered element according to the prior art.

(3) FIG. 2 is a schematic cross section of a layered element according to the invention, the position of a projector also being shown in this figure.

(4) FIG. 2a is a larger-scale view of a detail of the layered element of FIG. 2, according to a first alternative.

(5) FIG. 2b is a larger-scale view of a detail of the layered element of FIG. 2, according to a second alternative.

(6) FIG. 3 is a schematic cross section of a projection system, comprising a projector and a glazing including the layered element of FIG. 2, for a first structural variant of the glazing.

(7) FIG. 4 is a cross section analogous to FIG. 3 of a projection system, comprising a projector and a glazing including the layered element of FIG. 2, for a second structural variant of the glazing.

(8) FIG. 5a is a topology of a textured contact surface of a layered element according to a first embodiment of the invention.

(9) FIG. 5b schematically shows the slope distribution of the textured contact surface of FIG. 5a.

(10) FIG. 6a is a topology of a textured contact surface of a layered element according to a second embodiment of the invention.

(11) FIG. 6b schematically shows the slope distribution of the textured contact surface of FIG. 6a.

(12) FIG. 7a is a topology of a textured contact surface of a layered element according to a third embodiment of the invention.

(13) FIG. 7b schematically shows the slope distribution of the textured contact surface of FIG. 7a.

(14) FIG. 8 schematically shows the slope distribution of a textured contact surface of a layered element according to a fourth embodiment of the invention.

(15) FIG. 9 schematically shows the slope distribution of a textured contact surface of a layered element according to a fifth embodiment of the invention.

(16) FIG. 10 schematically shows the slope distribution of a textured contact surface of a layered element according to a sixth embodiment of the invention.

(17) FIG. 11 schematically shows the slope distribution of a textured contact surface of a layered element according to a seventh embodiment of the invention.

(18) FIG. 12 is a schematic view showing diffuse and specular reflection of radiation incident on a layered element according to the invention.

DETAILED DESCRIPTION

(19) Unless specified otherwise, a given element appearing in various figures has been referenced with a single reference. For the sake of clarity of the drawings, the relative thicknesses of the various layers have not been rigorously respected in FIGS. 2 to 4. In addition, the possible variation in the thickness of the or each constituent layer of the central layer as a function of the slope of the texture has not been shown in these figures, it being understood that this possible variation in thickness does not affect the parallelism of the textured contact surfaces. Specifically, for each given slope of the texture, the textured contact surfaces are parallel to one another. Moreover, it will be noted that the contact surfaces are shown only schematically in FIGS. 2 to 4, it being understood that their texture respects the slope-distribution criterion of the invention.

(20) FIG. 1, which schematically shows diffuse and specular reflection of radiation incident on a layered element according to the prior art, was described above.

(21) FIGS. 2a and 2b show a layered element 1 according to the invention, including two external layers 2 and 4 that are made of transparent dielectric materials having substantially the same refractive index n2, n4. Each external layer 2 or 4 has a smooth main surface, 2A and 4A, respectively, directed toward the exterior of the layered element, and a textured main surface, 2B and 4B, respectively, directed toward the interior of the layered element.

(22) The textures of the internal surfaces 2B and 4B are complementary to each other. The textured surfaces 2B and 4B are positioned facing each other, in a configuration in which their textures are strictly parallel to each other. The layered element 1 also comprises a central layer 3, intermediate between and in contact with the textured surfaces 2B and 4B.

(23) FIG. 2a shows a variant embodiment in which the central layer 3 is a monolayer made of a transparent material that is either metallic, or dielectric of refractive index n3 different from that of the external layers 2 and 4. FIG. 2b shows a variant embodiment in which the central layer 3 is formed by a transparent stack of a plurality of layers 3.sub.1, 3.sub.2, . . . , 3.sub.k, in which at least one of the layers 3.sub.1 to 3.sub.k is either a metal layer, or a dielectric layer of refractive index different from that of the external layers 2 and 4. Preferably, at least each of the two layers 3.sub.1 and 3.sub.k located at the ends of the stack is a metal layer or a dielectric layer of refractive index n3.sub.1 or n3.sub.k different from that of the external layers 2 and 4.

(24) In FIGS. 2a and 2b, the contact surface between the external layer 2 and the central layer 3 has been denoted S.sub.0, and the contact surface between the central layer 3 and the external layer 4 has been denoted S.sub.1. In addition, in FIG. 2b, the internal contact surfaces of the central layer 3 have been successively denoted S.sub.2 to S.sub.k starting from the contact surface closest to the surface S.sub.0.

(25) In the variant of FIG. 2a, because of the arrangement of the central layer 3 in contact between the textured surfaces 2B and 4B that are parallel to each other, the contact surface S.sub.0 between the external layer 2 and the central layer 3 is textured and parallel to the contact surface S.sub.1 between the central layer 3 and the external layer 4. In other words, the central layer 3 is a textured layer having a uniform thickness e3, measured perpendicular to the contact surfaces S.sub.0 and S.sub.1.

(26) In the variant of FIG. 2b, each contact surface S.sub.2, . . . , S.sub.k between two adjacent layers of the constituent stack of the central layer 3 is textured and strictly parallel to the contact surfaces S.sub.0 and S.sub.1 between the external layers 2, 4 and the central layer 3. Thus, all the contact surfaces S.sub.0, S.sub.1, . . . , S.sub.k between adjacent layers of the layered element 1 that are either of different, dielectric or metallic, natures or made of dielectric materials of different refractive indices, are textured and parallel to one another. In particular, each layer 3.sub.1, 3.sub.2, . . . , 3.sub.k of the constituent stack of the central layer 3 has a uniform thickness e3.sub.1, e3.sub.2, . . . , e3.sub.k, measured perpendicular to the contact surfaces S.sub.0, S.sub.1, . . . , S.sub.k.

(27) According to one aspect of the invention, the thickness e3 or e3.sub.1, e3.sub.2, . . . , e3.sub.k of the or each constituent layer of the central layer 3 is smaller than the average height of the features of each textured contact surface S.sub.0, S.sub.1 or S.sub.0, S.sub.1, . . . , S.sub.k of the layered element 1. This condition is important as it increases the probability that the entrance interface of radiation into a layer of the central layer 3 and the exit interface of the radiation from this layer will be parallel, and thus increases the percentage of radiation specularly transmitted through the layered element 1. In order make the various layers easier to see, this condition has not been strictly respected in the figures. In practice, when the central layer 3 is a thin layer or a stack of thin layers, the thickness e3 or e3.sub.1, e3.sub.2, . . . , e3.sub.k of each layer of the central layer 3 is about, or smaller than, 1/10 of the average height of the features of each textured contact surface of the layered element.

(28) Each of FIGS. 3 and 4 is a schematic cross section of a projection system comprising a projector P and a glazing 10 including the layered element 1 of FIG. 2. FIGS. 3 and 4 illustrate two possible structures for the glazing 10, by way of nonlimiting example.

(29) In the first example glazing 10 shown in FIG. 3, the first external layer 2 is a textured substrate made of clear or extra-clear glass, and the second external layer 4 is formed by an interlayer sheet (for example made of PVB) that has substantially the same refractive index as the substrate 2 and that conforms to the texture of the textured surface of the central layer 3. The interlayer sheet 4 is calender-rolled via its external surface 4A onto a planar substrate 6 made of clear or extra-clear glass, for example made of the glass SGG Planilux sold by Saint-Gobain Glass, which forms an additional layer. In addition, the glazing 1 comprises an antireflection coating 7 on the external main surface of the planar substrate 6, which is intended to be opposite with respect to a projector P during the projection of images onto the glazing 10. The presence of the antireflection coating 7 allows multiple reflections in the interior of the layered element 1 to be decreased and thus the quality of the projected images to be improved.

(30) In the second example glazing 10 shown in FIG. 4, the first external layer 2 is not a textured glass substrate but an interlayer sheet (for example made of PVB) that has substantially the same refractive index as the interlayer sheet 4. In this second example, the central layer 3 comprises a flexible film 3.sub.1, for example a film of polymethyl methacrylate (PMMA) having a thickness of about 50 to 250 m, on which has been deposited a thin layer 3.sub.2 made of dielectric material or made of metal material, for example a thin layer of TiO.sub.2 having a thickness of about 50 to 75 nm. The assembly consisting of the flexible film 3.sub.1 and of the thin layer 3.sub.2 is given a corrugated or accordion shape in order to create the textured central layer 3, which is then sandwiched between the interlayer sheets 2 and 4, such that the contact surfaces between the layers 2, 3.sub.1, 3.sub.2 and 4 remain parallel to one another. Each of the interlayer sheets 2, 4 is calender-rolled via its external surface 2A, 4A onto a planar substrate 5 or 6 made of clear or extra-clear glass, for example made of the glass SGG Planilux sold by Saint-Gobain Glass, which substrates form additional layers. In addition, as in the example of FIG. 3, the glazing 1 comprises an antireflection coating 7 on the external main surface of the planar substrate 6, which is intended to be opposite with respect to a projector P during the projection of images onto the glazing 10.

(31) The layered element 1 or a glazing incorporating it is able to be used as a projection screen. Such as shown in FIG. 2, the first and second external layers 2, 4 and the central layer 3 of the layered element 1 lie parallel to a plane Oxy of a coordinate system (O, x, y, z), where the axis Ox is in a horizontal direction and the axis Oy is in a vertical direction with respect to an observer. In the example of FIG. 2, the observer is located on the side of the projector P, facing this smooth main surface 2A of the layered element 1.

(32) The texture of each textured contact surface S.sub.0, S.sub.1, S.sub.k of the layered element 1 is of equation z=f(x, y) and has, at each point of coordinates (X.sub.0, Y.sub.0) of the contact surface, a first directional slope .sub.x and a second directional slope .sub.y such that:

(33) ${}_x\left(X_0,Y_0\right)=\arctan \frac{\mathrm{dz}}{\mathrm{dx}}{|}_{X_0,Y_0}\mathrm{and}$${}_y\left(X_0,Y_0\right)=\arctan \frac{\mathrm{dz}}{\mathrm{dy}}{|}_{X_0,Y_0}.$

(34) According to the invention, the slope distribution of the texture of each textured contact surface S.sub.0, S.sub.1, . . . , S.sub.k, which corresponds to the frequency of each pair of slopes (.sub.x, .sub.y), does not have axial symmetry about at least one of the axes O.sub.x, O.sub.y of a first orthogonal coordinate system (O, .sub.x, .sub.y) where O corresponds to the pair of slopes (0, 0), or does not have axial symmetry about at least one of the axes O.sub.x, O.sub.y of a second orthogonal coordinate system (O, .sub.x, .sub.y) obtained by rotating by 45 the first orthogonal coordinate system (O, .sub.x, .sub.y). A plurality of examples of slope distributions of textures according to embodiments of the invention are described below.

(35) The texture according to the invention of each textured contact surface S.sub.0, S.sub.1, . . . , S.sub.k is advantageously obtained by texturing a main surface of a first external layer among the two external layers 2 and 4, in particular by embossing or 3D printing, preferably on the basis of a computationally generated texture, and depositing the central layer 3 conformally on the textured main surface of the first external layer. The central layer 3 is considered to be deposited conformally on the textured main surface of the first external layer if, following the deposition, the top surface of the central layer 3 is textured and parallel to the textured main surface of the first external layer. The conformal deposition of the central layer 3, or the conformal deposition of the constituent layers of the stack of the central layer 3, on the textured main surface of the first external layer is preferably achieved by cathode sputtering, in particular cathode sputtering assisted by a magnetic field.

(36) The second external layer among the two external layers 2 and 4 may be formed by depositing, on the textured main surface of the central layer 3 opposite the first external layer, a layer that has substantially the same refractive index as the first external layer and that is initially in a viscous state suitable for forming operations. The second external layer may thus be formed, for example, by a process comprising depositing a layer of photocurable and/or photopolymerizable material initially in fluid form then irradiating this layer, or by a sol-gel process. As a variant, the second external layer may be formed by positioning, against the textured main surface of the central layer 3 opposite the first external layer, a layer based on polymer material having substantially the same refractive index as the first external layer, then forming this layer based on polymer material against the textured main surface of the central layer 3 by compression and/or heating at least to the glass transition temperature of the polymer material.

(37) FIG. 5a shows a topology of a textured contact surface of a layered element 1 according to a first embodiment of the invention. FIG. 5b schematically shows the distribution of the slopes of the texture of the textured contact surface of FIG. 5a. In this first embodiment, the distribution of the slopes has an axial symmetry about the axis O.sub.x, but does not have axial symmetry about the axes O.sub.y, O.sub.x and O.sub.y.

(38) FIG. 6a shows a topology of a textured contact surface of a layered element 1 according to a second embodiment of the invention. FIG. 6b schematically shows the distribution of the slopes of the texture of the textured contact surface of FIG. 6a. In this second embodiment, the distribution of the slopes has an axial symmetry about the axis O.sub.x, but does not have axial symmetry about the axes O.sub.x, O.sub.y and O.sub.y.

(39) FIG. 7a shows a topology of a textured contact surface of a layered element 1 according to a third embodiment of the invention. FIG. 7b schematically shows the distribution of the slopes of the texture of the textured contact surface of FIG. 7a. In this third embodiment, the distribution of the slopes does not have axial symmetry about any one of the axes O.sub.x, O.sub.y, O.sub.x and O.sub.y.

(40) As may clearly be seen in FIGS. 5b, 6b and 7b, in the first, second and third embodiments, the slope distribution of the texture of each of the textured contact surfaces of the layered element 1, which corresponds to the frequency of each pair of slopes (.sub.x, .sub.y), has a single peak not centered on O. This peak not centered on O corresponds to a privileged direction of specular reflection of radiation incident on the layered element 1, which is different from the direction of specular reflection. Thus, there is a privileged angle of observation for observing an image projected onto the layered element 1, or onto a glazing 10 incorporating it, this privileged angle of observation being different from the angle of specular reflection. Thus, an observer positioned with the privileged angle of observation may observe the projected image with a high brightness, and without being dazzled or discomforted by specular reflection from the smooth external surface of the layered element 1 or of a glazing 10.

(41) FIG. 8 schematically shows the slope distribution of the texture of a textured contact surface of a layered element according to a fourth embodiment of the invention. In this fourth embodiment, the slope distribution has an axial symmetry about the axes O.sub.x and O.sub.y, but does not have axial symmetry about the axes O.sub.x and O.sub.y. In addition, as shown by the oval shape of each peak in FIG. 8, the width of the peak is asymmetric and larger along the axis O.sub.x than along the axis O.sub.y, this indicating an angular range of observation for an observer that is larger along the axis Ox than along the axis Oy. In practice, for each peak of the slope distribution, an aspect ratio is defined, the aspect ratio being the ratio of the largest width of the peak, among the width along the axis O.sub.x and the width along the axis O.sub.y, to the smallest width of the peak, among the width along the axis O.sub.x and the width along the axis O.sub.y. Advantageously, when it is desired to have a larger angular range of observation in one of the directions Ox or Oy, for example when the layered element forms a screen integrated into an environment in which the ability to observe the screen is limited in one of these two directions, it is possible to choose a value for the aspect ratio different from 1 for at least one peak. Advantageously, the aspect ratio is comprised between 1 and 20.

(42) FIG. 9 schematically shows the slope distribution of the texture of a textured contact surface of a layered element according to a fifth embodiment of the invention. In this fifth embodiment, the slope distribution has an axial symmetry about the axes O.sub.x and O.sub.y, but does not have axial symmetry about the axes O.sub.x and O.sub.y.

(43) FIG. 10 schematically shows the slope distribution of the texture of a textured contact surface of a layered element according to a sixth embodiment of the invention. In this sixth embodiment, the slope distribution does not have axial symmetry about any one of the axes O.sub.x, O.sub.x, O.sub.y and O.sub.y.

(44) FIG. 11 schematically shows the slope distribution of the texture of a textured contact surface of a layered element according to a seventh embodiment of the invention. In this seventh embodiment, the slope distribution has an axial symmetry about the axes O.sub.y, but does not have axial symmetry about the axes O.sub.x, O.sub.x and O.sub.y.

(45) As may clearly be seen in FIGS. 8 to 11, in the fourth, fifth, sixth and seventh embodiments, the slope distribution of the texture of each of the textured contact surfaces of the layered element 1, which corresponds to the frequency of each pair of slopes (.sub.x, .sub.y), has two peaks not centered on O. These two peaks not centered on O correspond to two privileged directions of specular reflection of radiation incident on the layered element 1, which are different from each other and different from the direction of specular reflection. Thus, there are two privileged angles of observation for observing an image projected onto the layered element 1, or onto a glazing 10 incorporating it, each of these two privileged angles of observation being different from the angle of specular reflection. Thus, for an observer positioned with either of these two privileged angles of observation, the projected image is seen with a high brightness, and without any risk of being dazzled by specular reflection from the smooth external surface of the layered element 1 or of the glazing 10.

(46) Other embodiments (not illustrated in the figures) are also envisionable for a layered element according to the invention, in particular embodiments in which the slope distribution of the texture of each of the textured contact surfaces of the layered element, which corresponds to the frequency of each pair of slopes (.sub.x, .sub.y), has a number n of peaks not centered on O, with n3, this corresponding to n privileged directions of specular reflection of radiation incident on the layered element, each one being different from the others and different from the direction of specular reflection. There are then n privileged angles of observation for observing an image projected onto the layered element or a glazing incorporating it. The number of peaks not centered on O has an impact on the brightness of each peak, which decreases as the number of peaks increases. A compromise between the number of angles of observation desired for the screen-forming layered element and the brightness at each angle of observation is therefore to be found, also depending on the luminous power of the employed projector.

(47) It will be noted that in practice, the slope distribution of the texture of each textured contact surface of the layered element according to any one of the embodiments described above also has a peak centered on O, corresponding to the pair of slopes (0, 0), as schematically shown in FIGS. 5b, 6b, 7b and 8 to 11. Specifically, the actual textured features obtained, for example, by embossing glass or polymeric material on the basis of a computationally generated perfect texture, generally have ridges and extrema that are not perfectly sharp but slightly rounded.

(48) FIG. 12 schematically shows the diffuse and specular reflection of radiation R.sub.i incident on a layered element 1 according to the invention. A first portion of the incident radiation is transmitted by the smooth external surface 2A and is then reflected diffusely, in a plurality of directions R.sub.d, by the central layer 3 (not shown in FIG. 12). A second portion of the incident radiation is reflected by the smooth external surface 2A specularly, in the manner of a mirror, in a direction R.sub.s. As the plurality of directions R.sub.d is not centered on the direction R.sub.s of specular reflection, the angle .sub.v of observation of an observer ideally placed relative to the plurality of directions R.sub.d of diffuse reflection to observe a projected image is different from the angle .sub.s of specular reflection. An observer thus positioned is therefore not dazzled or discomforted by undesirable specular reflection from the smooth external surface 2A.

(49) Consider now that the smooth external surface 2A of the layered element 1 is divided into a plurality of pixels of given size, and that each pixel is projected orthogonally onto each textured contact surface plumb with said pixel. The texture of each contact surface is thus defined for said pixel. A pixel is typically of rectangular shape. The texture of each contact surface within each pixel has a slope distribution .sub.pix(.sub.x, .sub.y) having a certain correlation coefficient r with the slope distribution .sub.tot(.sub.x, .sub.y) of the texture of the total contact surface. The correlation coefficient r is defined by the following relationship:

(50) $r=\frac{{}_{{}_x}{}_{{}_y}\left[f_{\mathrm{pix}}\left({}_x,{}_y\right)-\stackrel{\_}{f_{\mathrm{pix}}}\right]\left[f_{\mathrm{tot}}\left({}_x,{}_y\right)-\stackrel{\_}{f_{\mathrm{tot}}}\right]}{\sqrt{\begin{array}{c}\left({}_{{}_x}{}_{{}_y}{\left[f_{\mathrm{pix}}\left({}_x,{}_y\right)-\stackrel{\_}{f_{\mathrm{pix}}}\right]}^2\right)\\ \left({}_{{}_x}{}_{{}_y}{\left[f_{\mathrm{tot}}\left({}_x,{}_y\right)-\stackrel{\_}{f_{\mathrm{tot}}}\right]}^2\right)\end{array}}}$
where .sub.pix is the average of the function .sub.pix over all of the slopes, and .sub.tot is the average of the function .sub.tot over all of the slopes.

(51) Advantageously, according to the invention, each pixel is a rectangle having at least one side of length smaller than or equal to 500 m, and preferably smaller than or equal to 200 m, and, for a sample of N pixels, the average of the correlation coefficients r of each pixel of the sample is higher than or equal to 0.8, and preferably higher than or equal to 0.9. Each pixel is thus sufficiently representative of the texture of the total contact surface, i.e. of the slope distribution of the texture of each of said textured contact surfaces of the layered element, to ensure a satisfactory resolution in particular when the layered element or a glazing incorporating it is used as projection screen. The need for a sufficient resolution is particularly great in the case of a layered element providing directional diffuse reflection, as if the resolution is not sufficient the surface of the layered element or of a glazing incorporating it will not uniformly redirect the radiation in the one or more privileged directions corresponding to the privileged angles of observation.

(52) The number N of pixels in each sample is preferably such that N3. The pixels of each sample are preferably randomly chosen. In addition, preferably, the sample of N pixels is chosen from N+2 pixels, the pixel having the highest correlation coefficient and the pixel having the lowest correlation coefficient being removed.