Methods and apparatus for ultra wide entrance angle reflective articles for use with autonomous vehicle machine vision systems

Abstract

A two-layer retroreflective article construction is enabled that produces higher wide-entrance-angle performance for signs and pavement markings. A single-layer overlay is enabled for existing signs and pavement markers that improve their entrance angle performance. Materials used in the construction of an article or an overlay are transparent to radiation in the range of 400 to 1000 nanometers and utilize TIR (total internal reflection). Minimum performance specifications are proposed that extend sign sheeting retroreflectivity specifications to entrance angles of 60 degrees. An innovative traffic sign design is enabled that increases the positioning performance of safety systems and automated navigation systems.

Claims

1. An ultrawide angle retroreflective sheeting comprising: a body layer presenting a front surface; a base layer retroreflective material having an array of cube corner elements each with an apex axis having an orientation generally parallel to a normal of the front surface proximate the cube corner element; and a mezzanine layer retroreflective material between the body layer and the base layer and having an array of cube corner elements configured with at least some of the cube corner elements having an apex axis having an orientation generally tilted relative to a normal of the front surface proximate the cube corner element such that the mezzanine layer is reflective for electromagnetic radiation striking the front surface at higher entrance angles above a critical angle but is bi-directionally transmissive for electromagnetic radiation striking the front surface at lower entrance angles below the critical angle.

2. The sheeting of claim 1, wherein the body layer is transparent to wavelengths from 400-1000 nanometers.

3. The sheeting of claim 1, wherein the base material cube corner elements produce high total internal reflection (TIR) for entrance angles from −10 degrees to +10 degrees.

4. The sheeting of claim 1, wherein the mezzanine material is transparent to wavelengths from 400-1000 nanometers.

5. The sheeting of claim 1, wherein the mezzanine material cube corner elements produce high total internal reflection (TIR) for entrance angles from −60 degrees to −15 degrees and 15 degrees to 60 degrees.

6. The sheeting of claim 1, wherein the body layer and the mezzanine layer retroreflective material have relatively lower indices of refraction of less than 1.7.

7. A retroreflective sheeting overlay article comprising: a body layer presenting a front surface; a backing layer having an adhesive surface; and an intermediate layer material of retroreflective material between the body layer and the backing layer having a texturized array of cube corner elements configured with at least some of the cube corner elements having an apex axis having an orientation generally tilted relative to a normal of the front surface proximate the cube corner element such that the mezzanine layer is reflective for electromagnetic radiation striking the front surface at higher entrance angles above a critical angle but is bi-directionally transmissive for electromagnetic radiation striking the front surface at lower entrance angles below the critical angle.

8. The article of claim 7, wherein the intermediate layer material is transparent to wavelengths from 400-1000 nanometers.

9. The article of claim 7, wherein the intermediate layer material cube corner elements produce high total internal reflection (TIR) for entrance angles from −60 degrees to −15 degrees and 15 degrees to 60 degrees.

10. The article of claim 7, wherein the body layer and the intermediate layer material have relatively lower indices of refraction of less than 1.7.

11. A retroreflective sign article, comprising: a backing material; and an approved sign sheeting material applied to the backing material; and an overlay material applied to the sign sheeting material constructed with a layer of texturized cube corner elements configured with at least some of the cube corner elements having an apex axis having an orientation generally tilted relative to a normal of the front surface proximate the cube corner element such that the mezzanine layer is reflective for electromagnetic radiation striking the front surface at higher entrance angles above a critical angle but is bi-directionally transmissive for electromagnetic radiation striking the front surface at lower entrance angles below the critical angle.

12. The article of claim 11, wherein the overlay material is transparent to wavelengths from 400-1000 nanometers.

13. The article of claim 11, wherein the overlay material cube corner elements produce high total internal reflection (TIR) for entrance angles from −60 degrees to −15 degrees and 15 degrees to 60 degrees.

14. The article of claim 11, wherein the approved sign sheeting material is selected from the standard sheeting types as defined in ASTM D4956 consisting of the set of: Type I, Type II, Type III, Type IV, Type VIII, Type IX, Type X, and Type XI.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 illustrates a plan view of a prior art cube corner retroreflective sheeting.

(2) FIG. 2 illustrates a cross-sectional view of the prior art sheeting of FIG. 1.

(3) FIG. 3 illustrates paths of light travel for TIR reflected rays for the prior art sheeting of FIG. 2.

(4) FIG. 4 illustrates paths of light travel for mixed TIR and specular reflected rays for the prior art sheeting of FIG. 2.

(5) FIG. 5 illustrates entrance angle performance for a cube corner design for the prior art sheeting of FIG. 2.

(6) FIG. 6 illustrates sign sheeting performance of a prior art cube corner retroreflective sheeting at various entrance angles.

(7) FIG. 7 illustrates the retroreflectivity response for a prior art cube corner article.

(8) FIG. 8 illustrates a cross-sectional view for a reflective article in accordance with an embodiment of the present invention having a base retroreflective layer and a mezzanine retroreflective layer.

(9) FIG. 9A illustrates a plan view for tilted apex axis cube corner retroreflective features for an embodiment of the mezzanine reflective layer as shown in FIG. 8.

(10) FIG. 9B illustrates a more detailed plan view of a single tilted apex axis cube corner retroreflective feature for FIG. 9A.

(11) FIG. 9C illustrates a first cross-sectional view of a single tilted apex axis cube corner retroreflective feature for FIG. 9B.

(12) FIG. 9D illustrates a second cross-sectional view of a single tilted apex axis cube corner retroreflective feature for FIG. 9B.

(13) FIG. 10 illustrates a cross-sectional view of reflective sheeting in accordance with an embodiment of the present invention with a normal apex axis cube corner base layer and a tilted apex axis cube corner mezzanine layer.

(14) FIG. 11 illustrates the mezzanine layer retroreflectivity response for the sheeting of FIG. 10.

(15) FIG. 12 illustrates the combined base layer and mezzanine layer retroreflectivity response for the sheeting of FIG. 10.

(16) FIG. 13 illustrates a sign construction with a backing material, a sheeting material, and a mezzanine layer overlay in accordance with an embodiment of the present invention.

(17) FIG. 14 illustrates improved entrance angle performance for four sheeting materials with mezzanine layer overlays in accordance with embodiments of the present invention.

(18) FIG. 15 illustrates prior art definition of entrance angle for pavement markings.

(19) FIG. 16 illustrates a sign or pavement marking embodiment with a tilted apex axis cube corner construction.

(20) FIG. 17 illustrates pavement marking entrance angle performance for a TIR article for the embodiment in FIG. 16.

(21) FIG. 18 illustrates the pavement marking retroreflectivity response for the embodiment in FIG. 16.

(22) FIG. 19 illustrates wet article pavement marking retroreflectivity response.

(23) FIG. 20 illustrates an embodiment of a proposed traffic sign design for safety systems and machine vision systems.

(24) FIG. 21 illustrates a positioning of the proposed traffic sign of FIG. 20 along a roadway.

(25) FIG. 22 illustrates a roadway with horizontal roadway elements obscured by snow.

(26) FIG. 23 illustrates a heads-up display that projects obscured roadway elements.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(27) FIGS. 1 and 2 illustrate a portion of a typical replicated cube corner retroreflective sheet 10 known in the prior art. Referring to both FIGS. 1 and 2, reference 12 generally designates one of the minute cube corner elements of formations prism features disposed in an array on one side of sheeting 10. Each retroreflective element 12 has the shape of a trihedral prism with three exposed planar faces, substantially perpendicular to one another, and an apex axis defined by a line intersecting the apex of the trihedral prism that is equidistant to each of the planar faces. The angle between the faces of the trihedral prism is the same for each cube corner element in the array and will be about 90 degrees.

(28) As is illustrated in FIG. 2, cube corner elements 12 in sheet 10 can be all of the same dimensions and aligned in an array or pattern of rows and columns, the bases being in the same plane, and adjacent elements being contiguous at the edges of their bases such that there are no margins or flats between adjacent elements or spaced apart as desired. If desired, different elements in the array may have varying dimensions and orientations.

(29) Body portion 16 is preferably integral with cube corner optical elements 12, constituting what is referred to as a land that defines a front surface 18 into which electromagnetic radiation enters. The dimensions of the land portion of the sheeting relative to the individual cube corner optical elements will vary depending on the material of the medium of the sheeting, the method chosen for manufacture and, ultimately, the end purpose of the sheeting.

(30) It is helpful to note that the trihedral prism elements 12 in cross-sectional FIG. 2 are shown as effectively being upside-down from a conventional pyramid in that the apex 13 is below the base 14 which is operably connected to the body portion 16. The triangular structure of the trihedral prism element 12 that provides the total internal reflection (TIR) phenomenon is the inverted shaded shape shown in this cross-section as the figure portion of a figure-ground representation, and not the corresponding unshaded upright triangular shape that is effectively the ground portion in this representation.

(31) Cube corner elements of the prior art produce retroreflection due to TIR. Faces of cube corner elements will produce TIR when rays, beams, or electromagnetic waves strike the internal boundaries of the medium forming the retroreflective elements at an angle of incidence greater than the critical angle. The critical angle is measured from the normal vector to each boundary. For retroreflective articles and materials, it is common to refer to the angle of the incoming rays, beams or electromagnetic waves that strike the front surface of the material or article as being the entrance angle, whereas the angles of the ray, beam or wave as it propagates internally within the medium and encounters one or more additional boundaries, such as the face of a cube corner, are referred to as the incidence angles or angles of incidence.

(32) FIG. 3 shows two examples of incoming light rays 20, 34 that experience total internal reflection (TIR) at the surfaces of the cube corner elements of prior art retroreflective articles. The first ray 20 enters the front surface of the reflective material essentially parallel to the normal vector of the reflective material surface and travels through a medium 22 with a higher index of refraction than the backing material 24 at a point 26 on the boundary of the backing material. Because the incident angle is greater than the critical angle, TIR projects the reflected ray 28 toward a second face of the cube corner element. Upon meeting the second face of the cube corner element, the ray 28 experiences TIR at point 30 and is completely reflected along ray 32. Rays 20 and 32 are essentially parallel and in opposite directions, thus providing TIR retroreflectivity.

(33) In contrast to light ray 20 which was perpendicular to the front surface, light ray 34 is non-parallel to the normal vector for the point at which light ray 34 intersects the front surface of the reflective material. Because light ray 34 encounters the cube corner boundary at point 36 at an incidence angle greater than the critical angle, light ray 34 also experiences TIR. The reflected ray 38 encounters the second cube corner face at point 40 at an incidence angle greater than the critical angle, also experiencing TIR. Rays 34 and 42 are essentially parallel and in opposite directions, thus providing TIR retroreflectivity.

(34) FIG. 4 shows examples of rays 50, 62, 74 that experience retroreflective loss due to incident angles that are less than the critical angle and therefore do not conform to the geometry of TIR in prior art retroreflective articles.

(35) In a first example, ray 50 strikes the front surface of the medium at an entrance angle that is less than the critical angle and so enters the medium. After ray 50 enters the medium it encounters the first cube corner face at point 52 at an incidence angle greater than the critical angle and experiences complete internal reflection off of the first cube corner face. The reflected ray 54 encounters the subsequent cube corner face at point 56 at an incidence angle that is less than the critical angle. Unlike the interaction with the first cube corner face, the internal interaction with the second cube corner face causes a portion of the reflected ray 54 to refract through the barrier along ray 58 and a portion of the reflected ray 54 to experience specular reflection along ray 60. As a result, even though there was complete reflection caused by the interaction with the first cube face, there is not TIR because the interaction with the second cube face did not result in complete internal reflection.

(36) As a second example in FIG. 4, incoming ray 62 strikes the front surface of the medium at an entrance angle that is less than the critical angle and so enters the medium. After ray 62 enters the medium it encounters the cube corner face at point 64 at an incidence angle that is less than the critical angle. A portion of the incident ray 62 refracts through the barrier along ray 66 and a portion of the incident ray 62 experiences specular reflection along ray 68. Reflected ray 68 encounters the cube corner at point 70 and experiences complete internal reflection along ray 72 because the angle is greater than the critical angle. The retroreflected ray 72 is parallel to and in the opposite direction of the incident ray. Its intensity, however, is less than the intensity of a full TIR path because of the loss due to specular refraction that occurred at point 64.

(37) As a third example in FIG. 4, incident ray 74 strikes the front surface of the medium at an entrance angle that is less than the critical angle and so enters the medium. After ray 74 enters the medium it encounters a cube corner surface at point 76 at an angle that is less than the critical angle. A portion of the incident ray 74 refracts through the barrier along ray 78 and a portion of the reflected ray 54 experiences specular reflection along ray 80. Because the reflected ray does not encounter a second surface of the cube corner, the direction of the ray 80 as it exits the medium is non-parallel to the incident ray 74 and produces little or no retroreflectivity.

(38) TIR retroreflectivity for an article with a flat front surface and a cube corner back surface will be defined by the indexes of refraction of the medium that contains the article (typically air), the index of refraction of the material used to produce the article, and the index of refraction of the material behind the cube corner elements (also typically air). FIG. 5 shows the geometry for TIR for a typical prior art retroreflective article. The critical angle at the cube corner surface is referenced from the cube corner normal vector 92 and is defined by Snell's law:
η.sub.1*sin θ.sub.1=η.sub.2*sin θ.sub.2  Eq. 1

(39) where η.sub.1 is the index of refraction of medium 1 θ.sub.1 is the angle of the wave in medium 1 η.sub.2 is the index of refraction of medium 2 θ.sub.2 is the angle of the wave in medium 2

(40) For a medium 104 made of a material having an index of refraction of 1.6 and with a cube corner backing 106 interfacing with air having an index of refraction 1.0, the critical angle at the cube corner surface equates to 38.7 degrees from the cube corner normal vector 92. The angle 91 between the cube corner normal 92 and the surface normal 90 is 45 degrees, so the internal range of TIR angles 94, 96 within the medium is defined as:
+/−(cube-corner-normal−critical angle) or +/−6.3 degrees.  Eq. 2

(41) Incoming waves will be refracted when entering the front surface 102 of the medium 104 if the entrance angles are less than the critical angle. Using Eq. 1 and the index of refraction of the medium 104 and air as the medium interfacing with the front surface 102, the range 95 of TIR angles 98, 100 entering the medium 104 from air is +/−10.1 degrees.

(42) To summarize FIG. 5 and the TIR geometry of a typical prior art cube corner-type of retroreflective article or material, a trihedral prism with three exposed planar faces in which an apex axis of the prism is parallel to the surface normal 90 will produce TIR when light waves have entrance angles relative to the surface normal 90 that are smaller than the range defined by ray 98 and ray 100.

(43) FIG. 6 shows images 110, 112, 114, 116 collected from a sign panel utilizing conventional retroreflective materials at four different entrance angles. The panel contains various colors of sheeting types, with white sheeting in the leftmost column of the panel. Images were collected with an 850 nm active camera, and the lower four rows of samples contain sheeting types that conform to TIR geometries produced with vertically-aligned prism apexes in a conventional retroreflective material. Sample 118 is ASTM Type IV white sheeting, sample 120 is ASTM Type VIII white sheeting, sample 122 is ASTM Type IX white sheeting, and sample 124 is ASTM Type XI white sheeting. Image 110 was collected at a 0-degree entrance angle and shows the baseline intensity levels. Image 112 was collected at a 20-degree entrance angle and shows reduced intensity levels. Image 114 at a 40-degree entrance angle and image 116 at a 60-degree entrance angle show dramatic reduction of intensity levels at these higher entrance angles in conventional retroreflective materials.

(44) FIG. 7 shows a graph 130 of reflected intensity value 132 versus entrance angle 134 for a retroreflective element of a conventional retroreflective material having an apex axis that is parallel to the surface normal. The narrow, central part of the curve 136 shows intensity values for the range 138 of smaller entrance angles that produce TIR retroreflectance. The intermediate entrance angle ranges 140, 141 produce intensity curves 142, 143 that are a result of a combination of TIR retroreflectance and internal spectral reflectance. The outer entrance angle zones 134, 135 representing larger entrance angles produce intensity values 144, 145 that are a result of dramatically lower levels of TIR and internal spectral reflectance.

(45) For purposes of describing the various embodiments, the following terminology and references may be used with respect to retroreflective articles or materials in accordance with one or more embodiments as described.

(46) “Surface” means an exterior boundary of an article or material. In some embodiments, a surface may interface with air or vacuum at least partially surrounding the article or material. In other embodiments, a surface may interface with another object, such as a lens or coating. A surface may be comprised of one or more facets, and may be either rigid or flexible in form, smooth or rough in texture, and homogeneous or heterogeneous in composition.

(47) “Front surface” means a surface of an article or material exposed to electromagnetic waves, beams, or rays that strike the article or material and may be reflected or refracted by the article or material.

(48) “Back surface” means a surface of an article or material generally opposite from a front surface.

(49) “Layer” means a region of an article or material having thickness relative to a front surface of the article or material. In some embodiments, a layer may be a region of a medium of generally uniform thickness presenting an area that is substantially parallel in orientation to an orientation of the front surface of the article or material, and in some embodiments a layer may have varying thickness and present an area that is not of generally uniform thickness or substantially parallel in orientation to an orientation of the front surface of the article or material. In some embodiments, a layer may be coextensive with an area of the front surface of the article or material, and in other embodiments, a layer may not be coextensive with an area of the front surface. In some embodiments, a layer may be generally rigid and planar, and in other embodiments, a layer may be generally flexible. In some embodiments, a layer may be a medium that is homogenous in composition or construction, and in other embodiments, a layer may be of a medium that is non-homogenous and non-uniform in composition or construction.

(50) “Normal” describes a direction that intersects a surface or boundary at right angles.

(51) “Entrance angle” is defined as the angle relative to normal of a ray, beam, or wave of electromagnetic radiation as it strikes the front surface.

(52) “Boundary” is a change of medium defined by a face, facet, surface, and/or material having a different index of refraction.

(53) “Incidence angle” or “angle of incidence” is defined as the angle relative to normal of a ray, beam, or wave of electromagnetic radiation as it strikes a boundary within an article or material.

(54) “Cube corner element” describes a TIR retroreflective element, such as a trihedral pyramid, having multiple faces of the pyramid oriented at 90 degrees with respect to each other.

(55) “Apex” means the tip of a cube corner pyramid as defined by the intersection of the edges of the faces of the pyramid other than the edges of the base of the pyramid.

(56) “Apex axis” means a line intersecting the apex of a cube corner pyramid that is equidistant from each face of the pyramid.

(57) “Near-normal TIR range” means a range of entrance angles which produce TIR based only on a retroreflection by a single layer of retroreflective elements for a given type of medium and retroreflective elements.

(58) “Net retroreflectivity” means a combined retroreflectivity produced by retroreflective elements arranged in more than a single layer of a reflective article or material.

(59) “Ultrawide angle” means a range of angles for which TIR retroreflectivity occurs as a result of net retroreflectivity that is greater than a near-normal TIR range for a given type of medium and retroreflective elements. In various embodiments, ultrawide angle may mean +/−35 degrees, +/−40 degrees, +/−45 degrees, and +/−60 degrees.

(60) “ASTM D4956” means the ASTM International (formerly the American Society for Testing and Materials) standard ASTM D4956-19, Standard Specification for Retroreflective Sheeting for Traffic Control, ASTM International, West Conshohocken, Pa., 2019, www.astm.org. ASTM D4956 defines minimum retroreflectivity performance requirements for commonly-used ASTM sheeting types like I, II, III, IV, VII, VIII, IX, X and XI. Retroreflectivity requirements are established based on the observer's or sensor's observation angle and entrance angle, and minimum retroreflectivity levels are expressed in units of candelas*lux.sup.−1*m.sup.−2. For ultrawide angle performance versions of ASTM sheeting types that meet enhanced performance specifications for retroreflectivity at larger entrance angles, the units of measure for retroreflectivity can be expressed in units other than candela or lux (which are used based on the response of the human eye to light in the visible spectrum) such that the units are valid for light sources and sensors in the range of 400-1000 nanometers that includes the near infrared spectrum.

(61) “Transparent” means a degree of clarity of a material as measured by the ability to transmit image-forming light through the material. The measure of light transmission expressed in terms of transparency or transmissivity is a ratio of the light intensity measured with a sample of the material present in the light beam versus with the sample of the material not present in the light beam. For various embodiments, a material is considered to be transparent if the transmissivity is at least 95% for light at 550 nm as measured according to ASTM International standard ASTM D1746-17, Standard Test Method for Transparency of Plastic Sheeting, ASTM International, West Conshohocken, Pa., 2019, www.astm.org. For other embodiments with more transparency, a material is considered to be transparent if the transmissivity is at least 97% for light at 550 nm as measured according to ASTM D1746. For even more transparency for other embodiments, a material is considered to be transparent if the transmissivity is at least 99% for light at 550 nm as measured according to ASTM D1746. Like retroreflectivity, standards for measuring transparent materials are measured in the visible spectrum. Given that the ultrawide angle performance in embodiments includes light spectrums beyond the visible spectrum that include near-infrared wavelengths of light, the measure of transparency or transmissivity for visible light frequencies and for frequencies beyond those of the visible spectrum would be made consistent with the standards for measuring transparency. For the present disclosure a material is considered a transparent sheet-type material in the wavelengths beyond 700 nm if the transmissivity as measured consistent with ASTM D1746 for light at 850 nm is at least set forth in the at least 90% of the transmissivity as measured for light at 550 nm, and the transmissivity as measured consistent with ASTM D1746 for light at 1000 nm is at least set forth in the at least 85% of the transmissivity as measured for light at 550 nm.

(62) FIG. 8 illustrates an embodiment for a reflective article 150 in accordance with various aspects of the present inventions that contains a mezzanine retroreflective layer 152 operably connected to a base retroreflective layer 154.

(63) The properties of the base retroreflective layer 154 of various embodiments are similar to prior art retroreflective articles that utilize TIR from cube corner elements 155, for example, utilizing a material or materials that result in TIR reflectance within a near-normal TIR range 158 of angles 164, 166 that is relative to a surface normal shown at 156.

(64) There are various properties of the mezzanine retroreflective layer 152 in various embodiments that may differ from the properties of a conventional base retroreflective layer 154. First, the mezzanine retroreflective layer 152 produces a substantially unmodified internal path for incident and reflected rays having an entrance angle in the range 158 of angles for TIR reflectance 164, 166 such that the mezzanine retroreflective layer 152 propagates these rays with entrance angle within the near-normal TIR range 158 to the base retroreflective layer 154. Second, the mezzanine retroreflective layer 152 produces TIR reflectance for some, most, or all of rays that have entrance angles in the range of angles 160, 162 that lie outside the near-normal TIR range 158 for the base retroreflective layer 154. Third, the mezzanine retroreflective layer 152 produces an increase of entrance angles which are outside of the near-normal TIR range 158 for rays entering the front surface from all directions, not just a particular dimensional direction.

(65) FIG. 9A shows geometry of a cube corner architecture of embodiments wherein the apex axis of the faces of the trihedral prism used as the retroreflective element in the mezzanine layer is tilted relative to normal of a front surface of the article or material. As shown, for example, in FIG. 9B, each repeating structure of a cube corner feature in this embodiment consists of 18 faces organized as six groups of three cube corner faces 174, with each of the faces 174 of the cube corner groups aligned generally 90 degrees from each other. The apex angle 184 relative to a vector directly opposite the normal vector is determined by the high point 170 of the cube corner structure and the low points 172 of the cube corner structure. The cube corner geometry of the high point 170, low points 172 and the refractive indexes of the interfacing materials will determine the TIR incident angles at the surface of retroreflective articles in accordance with these embodiments. The apex angle 184 as indicated along an apex axis 185 that is tilted relative to a vector directly opposite a normal vector entering the front surface indicates the relative tilt for the set of faces intersecting at that apex of the trihedral cube corner for the base retroreflective layer. Cross-sectional representations of different aspects of the cube corner structure are shown in FIG. 9C and FIG. 9D. FIG. 9C shows what can be characterized as a double bottom W shape indicating the angles of the faces at the cross-sectional line taken at the bottom of FIG. 9B. FIG. 9D shows what can be characterized as a single bottom W shape (shown rotated 90 degrees) and indicating the angles of the faces at the cross-sectional line taken at the right side of FIG. 9B.

(66) FIG. 10 illustrates a two-layer article 180 produced from a single article material with a structured embedded air mezzanine layer 182 and a structured base layer 186. The mezzanine layer 182 is configured as a trihedral prism with three planes, substantially perpendicular to one another, with the apex angle 184 of the prism having a tilted apex axis orientation as described in FIG. 9. The base layer 186 is configured as a trihedral prism with three planes, substantially perpendicular to one another, with the apex axis of the prism 198 in a non-tilted orientation and parallel to the surface normal of the article or material. In the embodiment shown, the angle between the faces 183 at the mezzanine layer 182 and the faces 185 at the base layer 186 are roughly the same for each cube corner element in each array, and in this embodiment are shown at about 90 degrees. In the cross-sectional view of this embodiment as shown in FIG. 10, the mezzanine layer 182 is depicted as a series of generally W-shaped figures and the base layer 186 is depicted as a series of generally V-shaped figures. Alternatively, constructions of the mezzanine retroreflective layer 182 in other embodiments may utilize a material other than air that has a low index of refraction sufficient for TIR for the higher entrance angle rays to be retroreflected by the mezzanine layer 182.

(67) Ray 188 enters the article 180 at an angle that is sufficiently small (near normal) and will thus be within the near-normal TIR range for the cube corner base layer 186. Upon interaction with the near-horizontal face of the prism of mezzanine layer 182 the path of the ray 188 is essential unmodified as it passes through the embedded air gap associated with the mezzanine layer 182. The light experiences TIR at the faces of the base layer 186 cube corner structure 174 and is directed back through the face 189 of the prism of mezzanine layer 182. The exiting ray is refracted at the article surface and produces a TIR ray 190 that is essentially parallel to and in the opposite direction of the ray 188.

(68) Ray 192 enters the medium at an angle that is beyond the near-normal TIR range and is refracted at the surface of medium 180. The refracted ray 194 encounters a near-horizontal face 195 of the prism in the mezzanine 182 layer at an angle that is greater than critical angle, thus experiencing TIR. The reflected ray encounters a face 197 of the mezzanine 182 layer at an angle that is greater than the critical angle and also experiences TIR. The resulting ray 196 is refracted at the article 180 surface and is projected in a direction that is essentially parallel to and in the opposite direction of the ray 192.

(69) The width of the gaps 199 of air or other material that form the faces of the trihedral prisms of the mezzanine layer 182 can be as small as one micron. In various embodiments, the width of the gap 199 should be sufficiently large to produce TIR at the surface of the article 180 for ultrawide angle rays. A completely connected trihedral prism structure could, in practice, result in structural integrity issues of the article when the prism material is air. In practice, and to increase manufacturability and structural integrity, in various embodiments the intersection points of the trihedral prisms of the mezzanine layer 182 can be filled with the article material without appreciable loss in TIR performance. In other embodiments, face connection vias can be provided between the material faces of the gap 199 to further improve structural integrity.

(70) FIG. 11 illustrates the response of the mezzanine layer and the side lobes produced by an embodiment of a tilted apex axis cube corner geometry. For FIG. 11, the cube corner parameters are:

(71) η.sub.0—index of refraction of air at article surface=1.0

(72) η.sub.1—index of refraction of article medium=1.6

(73) η.sub.2—index of refraction of mezzanine air gap=1.0

(74) η.sub.3—index of refraction of base layer air gap=1.0

(75) base layer cube corner apex angle=180°

(76) mezzanine layer cube corner apex angle=162°

(77) Utilizing Eq. 1 and the indices of refraction (η.sub.1 and η.sub.2) the critical angle for the mezzanine faces equates to 38.7°. In embodiments, the relatively lower indices of refraction of the body layer and/or the mezzanine layer are relatively lower. In some embodiments, the indices of refraction are less than 1.7. In other embodiments, the indices of refraction are less than 1.5. The equations for the minimum and maximum angles in the medium for the side lobes for TIR reflectivity for the various tilted apex axis are:
TIR-negative-lobe-min=(θ.sub.apex−180)−(45−θ.sub.crit)  Eq. 3
TIR-negative-lobe-max=(θ.sub.apex−180)+(45−θ.sub.crit)  Eq. 4
TIR-positive-lobe-min=−(θ.sub.apex−180)−(45−θ.sub.crit)  Eq. 5
TIR-positive-lobe-max=−(θ.sub.apex−180)+(45−θ.sub.crit)  Eq. 6

(78) Where θ.sub.apex is the angle of the apex of the cube corner elements θ.sub.crit is the critical angle relative to the normal of the cube corner faces

(79) Utilizing a cube corner apex angle of 162 degrees equates to side lobes with TIR ranges of −24.3 to −11.7 degrees and 11.7 degrees to 24.3 degrees. Because these angular ranges are within the article medium, they must be converted to in-air angles by utilizing Eq. 1 with the indexes of refraction for air and the medium. Eq. 1 determines the in-air TIR angular limits as −61.5 to −34.4 degrees and 34.4 to 61.5 degrees. The table below shows some side lobe behavior based on varying some geometry and material parameters. For the table headings, η.sub.0 is the index of refraction of the air layer above the medium, η.sub.1 is the index of refraction of the medium, η.sub.2 is the index of refraction of the material that forms the gap at the mezzanine layer, and η.sub.3 is the index of refraction of the material that forms the gap at the base layer. The Mezz layer apex angle is the tilt of the particular cube corner element configuration as measured relative to a vector directly opposite a normal vector entering the front surface.

(80) TABLE-US-00001 Base Base Mezz Mezz Mezz Mezz layer layer layer layer layer layer crit. TIR apex crit. TIR TIR η.sub.0 η.sub.1 η.sub.2 η.sub.3 Angle max angle Angle min max 1 1.6 1 1 38.7 10.1 162 38.7 34.4 61.5 1 1.6 1 1 38.7 10.1 164 38.7 38.1 67.7 1 1.6 1 1 38.7 10.1 167.36 38.7 44.6 89.2 1 1.7 1 1.1 40.3 8 158 36 24.3 64.2 1 1.7 1 1.1 40.3 8 160 36 28 71.8 1 1.7 1 1.1 40.3 8 162.06 36 31.9 89.2 1 1.8 1.1 1.2 41.8 5.7 156 37.7 25.2 58.7 1 1.8 1.1 1.2 41.8 5.7 158 37.7 29.1 65.4 1 1.8 1.1 1.2 41.8 5.7 161.41 37.7 36 88.8

(81) The article response 210 for the mezzanine layer in FIG. 11 shows the TIR range for negative angles 200, the TIR range for positive angles 202, and the three ranges 204, 206, 208 that exhibit combinations of net retroreflectivity due to TIR and specular reflection.

(82) FIG. 12 shows the combined response 220 for the mezzanine layer and the base layer for a combined article. The response 220 has a middle lobe 221 that is due to TIR for the base layer cube corner geometry and has two side lobes 222, 223 that are due to TIR for the mezzanine layer cube corner geometry.

(83) FIG. 13 shows a traffic sign 225 construction utilizing standard sign sheeting material 227 with an ultrawide-entrance-angle overlay 228. The backing 226 for the sign is made from a material like aluminum, to which a standard sign sheeting 227 material is affixed. The base sign material 227 is selected from products that include, but are not limited to, embedded glass beads or retroreflective cube corners. The overlay 228 exhibits the properties of TIR over ultrawide entrance angle ranges due to side-lobe geometry while passing through low-entrance-angle rays for optical processing by the base sheeting 227 material.

(84) FIG. 14 shows the effect of adding an ultrawide overlay that contains tilted apex axis, cube corner structures to the face of existing sign sheeting materials. Images 230, 231, 233, 233 show the effect of a modified sign panel at four different entrance angles. The panel contains various colors of sheeting types, with white sheeting in the leftmost column of the panel. Sample 234 depicts ASTM Type IV white sheeting with a tilted apex angle cube corner overlay as a mezzanine layer, sample 235 depicts ASTM Type VIII white sheeting with a tilted apex angle cube corner overlay as a mezzanine layer, sample 122 depicts ASTM Type IX white sheeting with a tilted apex angle cube corner overlay as a mezzanine layer, and sample 124 depicts ASTM Type XI white sheeting with a tilted apex angle cube corner overlay as a mezzanine layer. Image 230 depicts a 0-degree entrance angle and shows the baseline intensity levels. Image 231 depicts a 20-degree entrance angle and shows appreciably similar intensity levels to the baseline levels. Image 232 at 40-degree entrance angle and image 233 at 60-degree entrance angle show no appreciable reduction of intensity levels.

(85) The ASTM D4956 minimum requirements for three commonly-used sheeting types are:

(86) TABLE-US-00002 Observation Angle Entrance Angle R.sub.A Type IV White 0.1°  −4° 500 0.1° +30° 240 Type VIII White 0.1°  −4° 1000 0.1° +30° 460 Type IX White 0.1°  −4° 660 0.1° +30° 370

(87) Candela is a measure of luminous intensity and lux is measure of luminance. Both measures are based on the response of the human eye to light. As a result, both measures do not have utility outside the visible spectrum (400-700 nm). With the advent of NIR sensors for vehicle safety systems and autonomous vehicle navigation, new performance measures are required for road-based markers. One measure of retroreflectivity can utilize milliwatts (mW) for reflected intensity and watts per square meter (W/m.sup.2) for incident intensity. Restating the ASTM D4956 requirements for Types IV, VIII and IX sheeting and using the conversion factors of 1 W/m.sup.2=683 lux at 555 nm and 1 candela=18.399 mW, the minimum performance table can be restated as follows, with retroreflectivity expressed in units of milliwatts per watt per meter squared, or mW*W.sup.−1*m.sup.−2:

(88) TABLE-US-00003 Observation Angle Entrance Angle R.sub.A Type IV White 0.1°  −4° 13.5 0.1° +30° 6.5 Type VIII White 0.1°  −4° 26.9 0.1° +30° 12.4 Type IX White 0.1°  −4° 17.8 0.1° +30° 10.0

(89) In embodiments, ultrawide angle performance versions of ASTM sheeting types are enabled that meet enhanced performance specifications for retroreflectivity at larger entrance angles. In embodiments, the units of measure for retroreflectivity are expressed in units that are valid for light sources and sensors in the range of 400-1000 nanometers. The table below shows minimum proposed performance levels for ultrawide angle versions of three popular ASTM sheeting types:

(90) TABLE-US-00004 Observation Angle Entrance Angle R.sub.A Type IV-WA White 0.1°  −4° 21.1 0.1° +30° 9.7 0.1° +60° 7.3 Type VIII-WA White 0.1°  −4° 24.2 0.1° +30° 19.4 0.1° +60° 14.5 Type IX-WA White 0.1°  −4° 16.0 0.1° +30° 12.8 0.1° +60° 9.6

(91) Ultrawide angle versions of ASTM sheeting types I, II, III, VII, X, and XI are enabled in embodiments. Suggested minimum performance specifications for each ultrawide-angle type will utilize a base performance level of something less than a base performance of a similar non-ultra wide angle type of sheeting to account for the potential loss of reflection through the mezzanine retroreflective layer. Performance level of at least about 90% of the base performance level as the non-ultrawide angle type for −4 degree entrance angles. Performance levels for +30 degrees for ultrawide angle sheeting may be established at a base level of at least about 80% of the −4 degree retroreflectivity level. Performance levels for +60 degrees for ultrawide angle sheeting may be established at a base level of at least about 60% of the −4 degree retroreflectivity level. Other performance level percentages for ultrawide angle retroreflective articles may be utilized and would be in accordance with other embodiments.

(92) FIG. 15 shows a prior art description of pavement marking 242 geometry. A sensor is shown as vehicle 246 whereby the headlamps function as the sensor illuminator. The entrance angle 244 is defined as the angle formed by the vector from the illuminator to a point on the pavement marker 242 and the normal vector to the same point on the pavement marking 240. In the United States, pavement markers are typically evaluated utilizing a 30-meter geometry, consisting of a measurement distance 248 of 30 meters and an entrance angle 244 of 88.76 degrees.

(93) FIG. 16 shows a cross section of a pavement marking embodiment that utilizes embedded TIR structures for increased retroreflectivity at ultrawide angles. The pavement marker 250 is produced from a material 254 that contains a structured air gap 252 formed as a tilted apex axis cube corner construction forming a mezzanine retroreflective layer. The angle of the apex axis is selected appropriately to produce a TIR angle zone that extends to +/−90 degrees from the marker 250 normal. Light ray 257 at a near-horizontal direction encounters the surface and is refracted toward the structured air gap 252. Upon experiencing TIR at the three faces of the cube corner, the resulting retroreflected ray is refracted at the surface and the refracted ray 258 is roughly parallel to and in the opposite direction of the ray 257. Ray 255 enters the medium 250 at an angle that is outside the near-normal TIR range for the article. Because the refracted ray encounters the air gap at an angle that is not greater than the critical angle, the ray passes through the air gap to the lower layer of the marker 250 where it experiences specular reflection. The reflected ray 256 exits the medium 250 at an angle that is near-parallel to and generally in the opposite direction of the incident ray 255.

(94) FIG. 17 illustrates the relationship between the tilted apex axis cube corner construction 266 of a pavement marker 250 and the range of angles 260 that produce TIR reflectivity. The smallest negative TIR angle 262 is near surface normal and the largest negative TIR angle 264 is at an angle that is well above the incident ray of any vehicle-based sensor on a roadway. Utilizing an air gap constructed from a tilted apex axis cube corner geometry will require an apex angle that is selected based on the index of refraction of the material that comprises the medium 250. Utilizing Equations 1, 3 and 4, the following table displays apex angles and various materials that yield near horizontal TIR angles for the pavement marker 250. For the table headings, the index of refraction of the air layer above the medium is 1.0, η.sub.1 is the index of refraction of the medium, and η.sub.2 is the index of refraction of the material that forms the gap at the cube corner structure.

(95) TABLE-US-00005 Min Max. Min Max. Apex Neg. TIR Neg. TIR Neg. TIR Neg. TIR η.sub.1 η.sub.2 Angle Angle Angle Angle Angle 1.5 1.0 173.62 −89.7 −60.4 60.4 89.7 1.6 1.0 167.36 −89.2 −44.6 44.6 89.2 1.7 1.0 162.06 −89.2 −31.9 31.9 89.2

(96) FIG. 18 illustrates the response 270 of the pavement marker and the side lobes produced by the tilted apex axis cube corner geometry utilizing a medium index of refraction of 1.6 and an apex angle of 167.36 degrees. The negative TIR lobe angular range 272 extends from essentially −90 degrees to −44.6 degrees, and the positive TIR lobe angular range 274 extends from 44.6 degrees to near 90 degrees. The middle range 276 of angles produce a lower response because incident rays in this range do not experience TIR in the marker medium.

(97) Pavement marker manufacturers will utilize techniques and materials at the surface of their products to establish good performance in both dry environments and on wet roadways. Manufacturers will typically include two types of materials with varying geometries to account for different indexes of refraction between dry surface elements and water-covered road surface elements. FIG. 19 illustrates an embodiment with a pavement marker 250 with a flat surface that includes a non-vertical apex cube corner TIR embedded structure with a lower index of refraction than the marker 250 medium. A layer of water 280 rests upon the marker 250.

(98) Utilizing a medium index of refraction of 1.6, a structured air gap index of refraction of 1.0, and an apex angle of 167.36 degrees, the medium exhibits a minimum negative TIR angle 282 of −38.68 degrees and a maximum negative TIR angle of −26.04 degrees. Utilizing an index of refraction of 1.33 for water, Eq. 1 produces a minimum negative TIR angle 286 of −48.74 degrees in water 280 and a maximum negative TIR angle 288 of −31.88 degrees in water 280. Utilizing an index of refraction of 1.0 for air, Eq. 1 produces a minimum negative TIR angle 292 of −89.21 degrees in air and a maximum negative TIR angle 294 of −44.62 degrees in air. As shown by the computations for a water-covered pavement marker 250, the minimum and maximum TIR angles 292, 294 for the pavement marker 250 are not affected by surface water on a medium with a flat surface.

(99) Ultrawide angle reflective sign sheeting based on TIR described in embodiments enables new capabilities in automotive safety applications. FIG. 20 displays a proposed new “fiducial” traffic sign 360 design and layout. The sign is produced with a white, wide-angle TIR sheeting material 362 with a structured, non-reflective overlay 364. Proposed dimensions for a U.S. version of the fiducial sign 360 are:

(100) TABLE-US-00006 Reference Description Dimension (inches) 366 sign height 12 368 sign base to overlay top 10 370 sign base to overlay cutout top 8 372 sign base to overlay cutout bottom 4 374 sign base to overlay bottom 2 376 sign width 12 378 sign edge to right overlay edge 10 380 sign edge to right overlay cutout 8 382 sign edge to left overlay cutout 4 384 sign edge to start of overlay 2

(101) FIG. 21 displays a use of a fiducial sign 360 along a roadway 362. Signs are placed on each side of the road 362 and are at sufficient density so at least two consecutive signs on a side of the road are simultaneously available within the field of view of a typical machine vision sensor on board a vehicle traversing the roadway. The ultrawide angle TIR property of the sign sheeting type allows the vehicle to be closer to the near-range signs and still exhibit high-intensity sensing. A wide-angle sensor viewing of the ultrawide angle retroreflective signs will, as a result, enhance the spatial accuracy of roadway elements that are referenced relative to the fiducial signs.

(102) FIG. 22 illustrates the roadway with visible fiducial signs 360 and a non-visible roadway due to snow 364 cover. The vehicle sensor detects a sufficient number of fiducial 360 signs, thus allowing the vehicle processing system to determine the relative location of necessary roadway elements.

(103) FIG. 23 illustrates a use for the relatively-positioned roadway elements contained within the vehicle's high-definition map containing previously mapped locations of each roadway element. The vehicle windshield 370 acts as a heads-up display (HUD) whereby the vehicle positioning system can accurately display messages and information. In this view the roadway signs are viewed through the windshield or are obscured by an attenuating environment like snowfall. The vehicle sensor, however, maintains optical contact with the fiducial signs and displays them on the HUD 370. Other important roadway elements a like pavement surface 372, edge lines 374 and centerlines 376 are displayed in proper orientation to a driver or communicated to an autonomous control system that can accurately and safely navigate the roadway based on the added roadway elements after corresponding the sensed roadway elements with the high-definition map.

(104) Persons of ordinary skill in the relevant arts will recognize that embodiments may comprise fewer features than illustrated in any individual embodiment described above. The embodiments described herein are not meant to be an exhaustive presentation of the ways in which the various features of the embodiments may be combined. Accordingly, the embodiments are not mutually exclusive combinations of features; rather, embodiments can comprise a combination of different individual features selected from different individual embodiments, as understood by persons of ordinary skill in the art. Moreover, elements described with respect to one embodiment can be implemented in other embodiments even when not described in such embodiments unless otherwise noted. Although a dependent claim may refer in the claims to a specific combination with one or more other claims, other embodiments can also include a combination of the dependent claim with the subject matter of each other dependent claim or a combination of one or more features with other dependent or independent claims. Such combinations are proposed herein unless it is stated that a specific combination is not intended. Furthermore, it is intended also to include features of a claim in any other independent claim even if this claim is not directly made dependent to the independent claim.

(105) Any incorporation by reference of documents above is limited such that no subject matter is incorporated that is contrary to the explicit disclosure herein. Any incorporation by reference of documents above is further limited such that no claims included in the documents are incorporated by reference herein. Any incorporation by reference of documents above is yet further limited such that any definitions provided in the documents are not incorporated by reference herein unless expressly included herein.

(106) For purposes of interpreting the claims, it is expressly intended that the provisions of Section 112, sixth paragraph of 35 U.S.C. are not to be invoked unless the specific terms “means for” or “step for” are recited in a claim.