CA2224001A1 - Retroreflective cube corner article having scalene base triangles - Google Patents

Abstract

The present invention provides improved cube corner retroreflective articles which exhibit a wide range of retroreflective entrance angularity in at least one plane, and preferably in two or more planes. An article in accordance with the present invention includes a structured surface having at least one array of cube corner elements formed by three intersecting sets of substantially parallel grooves. Each cube corner element includes a base triangle bonded by one groove from each of the three intersecting groove sets, the base triangle being scalene.

Description

WO 96/42024 PCTrUS~6~'~3232 RETROREFLECTIVE CUBE CORNER ARTICLE
HAVlNG SCALENE BASE TRIANGLES

S FIELD OF THE rNVENTION
The present invention relates to r~L,ul ~lective articles having structured sllrf~~es In particular, the present invention relates to r~l-olenective ~heetin~ having a sL~ ul~d surface that in~l~ldes cube corner I~I-ul~,nective e1P ~ having scalene base I ~ ;~n~IF~S and to molds for follluhl~, the sarne.

BACKGROUND
Retroreflective articles that rely upon cube corner leLIùr~:nective Pl~."~
have gained wide acc~pl~ce in applic~;or~c relating to traffic and pel~ol~al safety lll~l h~g,. Cube corner r~:tlur~flective ~heetin~ is widely used to f~nh~nce the visibility, lS or conspic~lity~ of road signs in poor lighting conditions and at night. Cube corner ul~;nective ~1-P~l;ng has also gained wvide ..ccepl~-ce in vehicle con~picuity ...~.L;.,~ related applic~tion~ For PY~mrle, in the United States, govellu~ t re~ tion~ require lelror~le~;live materials to be positio~ed on serni-truck trailers to iullplove the ce ~ ity ofthese vehicles. Other applic~tionc for cube corner 20 l~llul~flective ~l.re~ , include l~,llultinective ~ for use in high-visibility clothing.
The basic cube corner l~t~ûl~ective element is well knûwn in the illu~enective arts. This element is generally a trihedral structure having threemutually sul,~l~llially perpendicular lateral faces which intersect at a single ler~l ence 2~ point, or apex, and a base triangle opposite the apex. The symmetry axis, or optical axis of the element is the axis which extends through the cube apex and trisects the internal space of the cube corner ~ m~nt In operation, light inf id~nt upon the base ofthe cube corner ~l, .n--..l is r~flected from each ofthe three lateral faces and is l~.lh~;-;led toward the light source. Reflection from the lateral cube corner faces may 30 be achieved through specular reflection, in which case the lateral faces of a cube corner el~.nc~-l are coated with a spec~ rly reflective subst~nce such as, for ~'e, ~1.. ;~.. or silver. Alternatively, reflection may be achieved pursuant to principles of total internal reflection, in which case the faces of the cube corner W O 96/42024 PCTAJsgCo~232 ~lc~ are not coated with a specul~rly reflective material. Retroreflective ~eheeting generally h~col~,ul~les a structured surface inC~u~ing at least one array of cube corner reflective P~ to enh~nce the visibility of an object. The total light rc~ cflected by the ~he~l iug is the sum of the light r~,L~. ~ cnected by the individual cube corner S
The term 'c.l~ ce angularity' is commonly used to describe the re~orcnec~ e pc~ru~ ce of le~ ellective $heclin~ as a function ofthe elll,~lce angle of light inc;~Pnt on the eheeti~ and the oriPnt~tiQn of the ~hC~ p The e,lt~ ce angle of inridçnt light is typically measured with respect to an axis that 10 extends normal to the base surface ofthe eheetin~ The rellolcnective pc,ro"..ance of an article may be c,~ ssed as a pe.ccnlage of the total light inC;dpnt on the face of the article which is returned by the article at a particular entrance angle.
ConvPntis)n~l truncated cube corner lcllol~cflective rlr--~ ; exhibit poor c,ll~ ~lce angularity. The amount of light l cl, ~ nected by a conventional cube-5 corner el~ l drops sharply when the e.lLl~-ce angle of incidPnt light deviates from the optical axis ofthe Pl-omP!nt Similarly"cl,or~,llec~ e eheetinP which employs non-canted, trlmc~ted cube corner e1. .,.~ c exhibits poor rcllorcnective pc,r~,l,llance in ~SpOllSe, to light which is inrident upon the sheeting at high entrance angles.
Many app!i~tionc could benefit from rc~lorcnective cheeting that exhibits 20 broad e~ ulce angularity in ml-ltiple planes. One such applic~tion relates torclr(,lcIlective com~;c~;ly chP~ti~g for the trucking industry. Truck conspicuity She~ R. is typically placed on the rear and the sides of truck trailers in both a ho. ;,Ol.~i~l o,i~ ;on and a vertical orientation relative to the frame of the trailer. To fimr.tion c~cc~ ly, the cheeting must lcllolcflect light in~i~lçnt on the trailer at high 2s ~IIl~lncC angles when the sheeti~ is positioned in either orientation. Accordingly, it would be dw;l~ ble to provide rcllo,tIlective truck conspicuity !'hr~ which exhibits broad entrance angularity in two planes. Signing applications would also benefit from rcl~u~ ective cheeting having broad entrance angularity in multipleplanes. In particular, ~c~lulcnective cheeting having multiple planes of broad 30 ellllnllce angularity reduces the importance of positioning .cheesing at a particular o,ie.ll~lion on the sign.

WO 96/42024 PCT/U~CI~232 One method of producing, el, o, ~nective article having broad e.,l- ~ce angularity in mllltill~e planes, commonly known in the art as 'tiling', involves~-~-~ng a plurality of discrete tiles of canted cube corner arrays at di~er~
Ol;~n~ on the ChP.~ g, FY~mPt~e of p~blir~tions relating to tiling include s Tiling has the advantage of el~ ely producing an article with multiple planes of broad entrance angularity. However, tiling has the inherent disadvantage that, at any given o,ie~ lion, only a fraction of the tiled sections are oriented to ~ rOItllect the m~imllm amount of light ;..-,id~ on their surface. As a result, tiled cube corner ~hreting suffers an inherent loss in brightnrq~ at any given o~ l;ol~ to gain ~Illtirle planes of e"l,~nce ~ngnl~rity.
U.S. Patent 4,588,258 discloses a ltil,o~nective article which has two planes -of broad elll~ce angularity: a first plane which is substantially coinritlPnt with the plane which inrl~ldes the optical axes ofthe cube corner el~ ls and a second plane which is pe",~n~lir,lll~r to the first plane. However, this article exhibits sul;,~ ;ally 1S broader e.,l,~ce al~uLuily in the first plane than in the second plane.
It would be desirable to provide a rel,olenective ~heeting that has two broad planes of e.,l~lce angularity which exhibit ~Ubs~ ly similar rell ol enective p~lrul'.'allce at non-zero enl,ance angles. It would be ever more desirable to provide a sheeting which could achieve this optical prope. ly without sacrificing brightn~s~, as r~uiled by tiled cube corner .~he~ g The art neither discloses nor s~lg~est~ such an article or a manner of achieving such an optical pl ope, ly.

SI~IMARY OF THE INVENTION
The present invention is directed toward cube corner I~IOl~nective ~heeting 2~ that exhibits improved t;"h~ce angularity in one or more planes and toward master articles and molds for m~mlf~r.tllring the same. Briefly, according to one aspect of the invention the present invention provides a retroreflective cube cornem~l~e~
co.~ .g a ~u~ le having a base surface disposed in a base plane a structured surface .1i~ ~ced from the base surface The structured surface incll~des an array of ~ 30 cube corner elemrnt m~tçhed pairs formed by three inte, ~e~li"g sets of s~lbst~nti~lly parallel grooves. Only two groove sets intersect at an angle less than 60 degrees; and W O 96/42024 PCTrUS~5232 a pluratity of cube corner ele-ne"l~ in the array co",~.ise a base triangle bounded by one groove from each of the three inte. ~ec~il.g groove sets, the base triangle being scalene.
Acco,dillg to another aspect, the invention provides a lel,ol~neclive sl,c.,li"g5 formed from a s-~lJs~ l;AIIy optically l.~u,~,.,t l"aLe,ial co."~,.isi..g a substrate having a base surface disposed in a base plane and a structured surface di~aced from the base surface. The structured surface inrl~ldes an array of canted cube corner el~ m~t~hed pairs formed by three mutually i"~e,~ecling sets of ~ub~ lly parallel grooves, each .~t~l.ed pair in~ i~ a first cube corner clc.ne..l and an0 optically opposing second cube corner el~m~Pnt A plurality of cube corner Ple~ "~
in the array co-.-plise a base triangle bounded by one groove from each of the three inte.~e.;li..g groove sets that is sc~iene Additionally, a plurality of cube corner el- ...-..1~ in the array have their ~"...,~l.y axes canted in a first plane and the .~heetin~
exhibits its broadest range of enl-~lce angularity in a second plane that is angularly lS d ,'-~ed from the first plane.

BRIEF DESCRIPTION OF THE DRAWrNGS
Fig. 1 is a m~gnified plan view of a portion of one embodiment of a cube corner article in accold~lce with p~ 'r t~- of the present invention;
Fig. 2 is a cross-sectional view of the cube corner article depicted in Fig. l;
Fig. 3 is a graph of isob- ;yhl ~.css curves clepicting the predicted leL~ ort;~lective pe.r.,l--.~ce of a r~tl-,.t;nu,li~e article in accordance with the article depicted in Fig.
l;
Fig. 4 is a graph of isob.;gl.l..~s curves clepicting the measured ~t;llol~lective 2s p~,.r~,..l.~ce of a l~l.or~;ne.,~ e article in accordance with the article depicted in Fig.
l;
Fig. 5 is a graph ofthe total light return as a function ofthe elll-~ilce angle of inf~ nt light for the cube corner gPQmet~ depicted in Figs. 1-2;
Fig. 6 is a graph co---p~ ;--g the total light return as a function of the entrance 30 angle of in-~;dPnt light for the cube corner geometry depicted in Figs. 1-2 with a dirrt.cl.~ cube corner gec~ r,t~y;
-W O 96/42024 PcT/v~ 232 S

Fig. 7 is a sçhf~ ic view of one embodiment of cube corner Iellùrenective sl-P~ g in accoldance with plillciplos ofthe present invention;
Fig. g is a p~ . :.peclive view of a motor vehicle illustrating one application of the ~h9c~ g depicted in Fig. 7 as truck conspicuity eheetir~;
s Fig. 9 is a pel :".e~ e view of a rell ul enective ~hev~ which employs scalene base triangle cube corner Pl~mPntc;
Fig. 10 is a graph of isobri htness curves depicting the predicted rt;l.u.t;nective pc.~",-~ce of a ~~L~ùr~Ilective article in accordance with the article d-opicted in Fig. 9;
Fig. 1 1 is a pc~ ~,eclive view of a rell ùrenective ehPetin~ which employs scalene base triangle cube corner ~ e Fig. 12 is a graph of isobrightnees curves depicting the predicted ~el~u.t;nective l)t;.r~,-...ance of a r~l.o.enective article in accordallce with the article clepicted in Fig. 1 1;
Fig. 13 is a s~hPm~tic plan view of a cube corner rt;lru, t;nective eheetin~ in acco..l~ce with prin~irles of the present invention;
Fig. 14 is a srh~ ;c plan view of a co~ e~;;ally available cube corner r~llult;nective eh~eting;
Fig. 15 is a graph co,--pali,-g the optical pe,ro"llance ofthe eheeting 20 illustrated in Fig. 13 with the ~h-oetin~ illustrated in Fig. 14;
Figs. 16a-16j are isobrightnP-ee graphs illustrating isobrightness profiles of cube corner ~eL~olenective element m~t~hecl pairs over i"c,- a;,i~lg cant angles.
Figs. 1, 2, 7-9, 11, 13, and 14 are not drawn to scale.

DETAILED DESCRIPTION
The present invention provides cube corner ~Llul ~llective articles that exhibiti"~l)roved optical l)t;,ru",.ance characteristics. One embodiment ofthe present invention is directed toward providing a relrol~nective eheetinE that exhibits improved ~ allce angularity in at least one plane. While not neCçes~y~ it is 30 l~r~ rtied that an article in accordance with the present invention has at least two planes of broad ~ ance angularity. It is even more plert;ll~d that an article in W O 96/42024 PCTAUS96~3232 acco.dance with the present invention returns substantially the same amount of light at a given ~ cc angle in either plane of broad entrance angularity.
One aspect ofthe present invention lies in the ~ecogllllion that certain as~.. ~,lions implicit in prior cube corner terhnrJlogy do not hold true for all cube s corner geolllctl;cs. In particular, one important assumption implicit in prior cube corner technology is that canting the optical axes of cube corner el~m-F~nts through a given angle in a particular plane improves the entrance angularity of the article in a plane that is subs~ ly parallel to the plane that co..~ C the optical axes ofthecube corner _IF ~r ~ and p~ n~iaJ1~r to the base plane ofthe sheefing The 10 present t1i~rl~ s~lre demor~ les that this as~w.l~lion is not accurate for all classes of cube corner ge~ ias. A second aspect of the present invention lies in the recognition that the optical pel roll~dl-ce of retl ~renective articles that have planes of broad entrance all~,ul~lily that are not co;ncident with the plane in which the optical axes of cube corner el~ Iie may be improved by ~ligning the planes of broad lS C.lll~u~CF angularity at a particular O~ llalion angle relative to an edge ofthe F~eL;~ ~g P~,rel~bly, the broad planes of entrance angularity should be o-i~nledapprox;.~ P,ly parallel with one ofthe edges ofthe shp~eting Fig. 1 is a m~grlified s~ ic plan view of a portion of a structured surface 10 of an article that inrludes a plurality of cube corner plPmPnt~ 12, 14 formed by 20 three mutually i.lle.~e.;ti,-g groove sets in-~.lu-ling a primary groove set 30 and two sets of secondary grooves 36, 37. Cube corner elements 12, 14 have three a~,r~,.;...~ lely mutually perpen~lic~ r faces 16, 18, 20 and a base triangle bounded by one groove in each ofthe three groove sets in the ~ubsll~te. The .J;~ ce ~e~ n ~ cPnt grooves in each groove set preferably measures between less than 2~ about 600 microns and more preferably measures about 150-200 n.. cl~ ns, however it should be applc~;aled that the precise measuré---~,.-ls ofthe cube corner el- ~ are not critical. The inrhlded angles of the base triangles of the cube corner PlemPnt~ 12, 14 d~ te d in Fig. 1 measure app~ ely 65 degrees, 65 degrees, and 50 degrees,however, the particular geo---el- y of the base triangle of cube corner elements 12, 14 30 is not critical and it will be appreciated that the present invention is not limited to cube corner el~ s having these specific base triangle measult;..-enls.

W 096/42024 PCTAUS96~ 232 The deci~tion of groove set 30 as a pl hl~aly groove set and groove sets 36, 37 as secon~ y groove sets is f?~senti~lly an albill~ly convention. For cube corner x that have icoscPIP~ base trig~lec, such as the cube corner Pl~mP~nte depicted in Fig. 1, the second~ry groove sets 36, 37 have sub~ ly identi-f ~l groove angles s (e.g. 38.721~). By CO~llla~l, the groove angle al of the p.;.. a-y groove 30 (e.g.
27.795~) differs from the groove angle of second~y groove sets 36, 37. By adopting the co..~..lion of de~;gnA~ , one groove set as a p-in-~ly groove set, the oriP~nt~ti~?n of a cube corner array relative to the edge of the substrate upon which the array is disposed can be defined by the angle at which the plilllaly groove set 30 Lll~-se~ls 10 the edge of the substrate.
Fig. 2 is a cross-sectional view of a portion of an article 2 having a structured surface 10 as depicte(l in Fig. 1. Article 2 in~ des a s.~ lale 4 which, when laid flat, has a base surface 6 disposed in a base plane and a structured surface 10 d;~l - eed from base surface 6. The material from which ~ub~ll ale 4 is formed may 15 vary d~pP.~ P upon the particular application for which article 2 is suited. Suitable m~teTi~lc for di~re.~..l applic~tion~ are ~~ sed below. ~ ition~lly, in the embodiment illu~ led in Fig. 2, structured surface 10 is opposite ~orn, and ~ubsl~lially co-planar with, base surface 6, however, it will be applc;ciated that structured surface 10 need neither be directly opposite from, nor co-planar with, 20 base surface 6.
Refe..i.lg to Fig. 2, the syrnmetry axes 24, 26 of cube corner elP-~P~.Is 12, 14 are canted through a cant angle, a, of appro~i-,-a~ely 7.47 degrees from an axis 28 that extends ~ubsl~lially normal to base surface 6 and intersects the apex of the respective cube corner ~ 12, 14. It will be apple-,iated, however, that the precise cant angle, a, is not critical and the present invention co~lenlpla~es a range of cant angles ~ - k ~ from about 4 degrees to about 15 degrees. In the embodiment illustrated in Fig. 2, cube corner ~hPmPntC 12, 14 are canted in a plane that isapp,ox;~ y perpenrlic~ r to p,i,.,a,y groove 30. More precisely, cube corner e~ 12, 14 are canted such that the symmetry axes 24, 26 lie in a plane that is - 30 a~)~lox;~ ely perppn~liG~ r to primary groove 30 and to base surface 6. Canted cube corner elf -~f~ such as those depicted in Figs. 1-2 may be referred to as W O 96/42024 PCT~US9G~232 'backward' canted cube corner PIF-mPnt~ Bachvard canted cube corner PIPmPn may be further characterized in that only one in~luded angle of the cube corner ~1~n~. .11 base triangle measures less than 60 degrees; the other two int~lnded angles ."easure at least 60 degrees and, in the embodiment illustrated, measure about 65 s degrees. By co~ , rc,l w~ ~l canted cubes may be characterized in that two of the in~ de~ angles ofthe base triangle measure less than 60 degrees and a single base triangle included angle ",easures greater than 60 degrees.
Fig. 2 also shows that the groove side angle al of primary groove 30 measures al~p,~ ely 29.795degrees. ~Itho~lghnotshowninFig.2,thegroove side angle of second~y grooves 36, 37 measure a~,u~ hl ely 38.721 degrees.
Retroreflective eheeti~ inco,pG,~li"g cube corner ek-.~P,~ subst~nti~lly as depicted in Figs. 1 and 2 is disclosed in U.S. Patent No. 2,310,790 (Junge.se~
Fig. 3 is an isobri~htness contour graph illustrating the predicted total light return for a ,el,o,t;nective cube corner element m~t~hed pair formed by bac~w~d 15 canted cube corner ~l- ."- ."~j 12, 14 formed from a material having an index of refraction of 1.517 at varying enl,~nce angles and orientation angles. Predicted total light return for a cube corner m~t~hed pair array may be c~lc~ ted from a knowledge of percent active area and ray intensity. Total light return is defined as the product of percent active area and ray ",lensily. An PYCPllpnt diecusQ;on of total light return for 20 directly ...~ h;..~d cube corner arrays is presented by Stamm U.S. Patent No. 3,812,706.
For an initial unitary light ray intensity, losses may result from two pass l~ne...:,C on through the base surface of the ~I.Pe~ and from reflection losses at each of the three cube surfaces. Base surface tr~nemie~eion losses for near normal in-;~l.on~e and a eheeting refractive index of about 1.5 are roughly 0.92. l~eflectinn losses for cubes which have been reflectively coated depend for ~ )Ic on the type of coating and the angle of inc;dence relative to the cube surface normal. Typical r~fleGtior coefficients for alumimlm reflectively coated cube surfaces are roughly 0.85 to 0.9 at each of the cube surfaces. Reflection losses for cubes which rely on total internal reflection are ess~pnti~lly zero. However, if the angle of in(idence of a light ray relative to the cube surface normal is less than the critical angle, then total W O 96/42024 PCTAUS~.~J~g2~2 internal reflection can break down and a ~i~nificsnt amount of light may pass through the cube s~lrfs-ce. Critical angle is a function of the refractive index of the cube msterisl and of the index of the material behind the cube (typically air). Standard optics texts such as Hecht, "Optics", 2nd edition, Addison Wesley, 1987 explain s front surface 1~ cn losses and total internal reflection.
Effective area for a single or individual cube corner ~lem~nt may be dclelll..ned by, and is equal to, the topological intersection ofthe projection ofthe three cube corner surfaces on a plane normal to the re~acted in~;d.ont ray with the pr~je-~ion ofthe image surfaces ofthe third reflection on the same plane. One 0 procedure for dt:le----mi-lg effective ap~,.lu-~ is tlicc~ ed for example by Eckhardt, Applied Optics, v. 10 n. 7, July 1971, pg. 1559-1566. Straubel U.S. Patent No.
835,648 also ~iecusses the concel)l of effective area or aperture. Percent active area for a single cube corner elemt:.-l is then defined as the effective area divided by the total area ofthe proje~ion ofthe cube corner surfaces. Percent active area may be 5 r,~slr,nlsted using optical modelin~ terhniq-les known to those of or~ .a,y skill in the optical arts or may be detelll--lled numerically using conventional ray tracing te~ s Percent active area for a cube corner ....~14l~çd pair array may be e~lcl-lsted by averaging the percent active area ofthe two individual cube corner P1~rn~.nt~ in the ...~l~ hed pair. Allt~ ,ly stated, percent active apellu-e equals the 20 area of a cube corner array which is r1l,o-çnecting light divided by the total area of the array. Percent active area is ~ffected for eY~mple by cube geol.leLIy, refractive index, angle of inri~l-onr,~, and ~heetins~ orientation.
R~;~l-ill~, to Fig. 3 vector Vl l~plesel-ls the plane that inr.l.ldes the sy.l--lle~ly axes24, 26 of cubecorner~le~ 12, 14. Forexample, inFig. 1, vectorVl liesin 2s a plane s~L~Ilially perp~ontliclll~r to primary groove 30. The concentric isobrightness curves I cpl ese--l the predicted total light return as a ,oercenlage of the light inr;~Pnt on the base surfaces of cube corner ~1em~onts 12, 14 at various col..l)inalions of entrance angles and orientation angles. Radial movement from the center ofthe plot ~ s~ increasing entrance angles, while ch~;u.~c;nlial 30 r"ovt;.,.e.-l ~~ ;sellls r,h~nging the orientation ofthe cube corner elrmlont with respect to the light source. The innermost isobrightness curve de---a~ cales the set of WO 96/42024 PCTAJS9G~5232 e~ ce angles at which a m~tçhed pair of cube corner Fl~mFntc 12, 14 return applox;...~lF,ly 90% of light incjdent on their base triangles. .~lcc~csively outlying isob~ .e.ss curves d~."al~,ale c..~ ce angles which return s~lccçssively lower pclcl .I ~es of light inl~;dent on the base triangles of f ~ 12, 14.
s Fig. 4 is an isobrightnecq graph, similar to the graph pre~ellled in Fig. 3, that illustrates the measured total light return of a cube corner element m~t~ ed pair having the same ~eoln~tl~/ as the cube corner element ...A~çl-ed pair depicted in Figs.
1 and 2. The cube corner ~ " .1~ are formed from BK7 glass, which has a ~ia~ilive index of 1.517. ~Itho~gh slight variations in the plots exist due to lo m~nllf~ctllring i",p.,.reclions and meas-lle-n~.,l errors, the measured results illu~llaled in Fig. 4 confirm the shape of the isob, ;gl~ ess profile depicted in Fig. 3 .
Two aspects of the isobrightness plots illustrated in Figs. 3-4 should be noted.First, the plots dt;lllonsllale that a ~Atehed pair of cube corner cle-.~ 12, 14 has two planes of broad e.,l, ~lce ang~ ily that are s~lbsl ~ lly perpPnt~iC~ r to one another and that lie in a plane that is not coinr;dPnt with the plane in which the cube corner F~l~nnentc are canted, in~ir~ted by vector Vl. For the cube corner m~tched pair depicted in Figs. 1-2, the two broad planes of e~lllallce angularity are oriented at ~p~ux;i.~ltly 45 degrees relative to the plane in which the cube corner cl~ 15 are canted and may be identified on the isobri~htness graphs as two subsla"lially 20 pe.~endicular planes 40, 42 which are coincident with the broad lobes ofth isobrightness graph.
A second aspect of the isobrightnes~ curves depicted in Figs. 3-4 results from the fact that cubes 12, 14 are s~ lA~ lly symmetrical about plane V,. Accûldingly, a ~--~ -ed pair of cube corner ~le ~ having the ~.eQI~ y depicted in Figs. 1-2 will 25 return al)pl.)~ t~ly the same pe,ce.llage of light at a given entrance angle in either plane 40 or plane 42. This aspect is illustrated in greater detail in Fig. 5, which plots the predicted total light return of cube corner elem~nts 12, 14 as a function ofthe enl,~lce angle of light ineident on the base of elomentc 12, 14 in planes 40 and 42.
Curves 44 and 46 rel"ese"l the total light return of a I el~ulenective cube corner 30 ~ F..~ 1F,d pair formed from a material having an index of refraction of 1.6 The two curves are virtually superimposed across the entire range of entrance angles, W 096/42024 PCT~US3~'~232 in~ ?tin~ that the total light reflected by the .~A~çl-ed pair is app,o~..-ahly equ~ at a given c.~ ce angle in either plane 40 or plane 42. The slight di~.~nces above 60~
result from .. i~ Al errors in p,~U~ * p~,.ro--ll~lce for cubes at very high ~ ~n~ ce angles. Curves 48 and S0 are analogous curves for a .c~-urenective cube s corner c~ -hed pair formed from a material having an index of refraction of 1.5.
Fig. 6 cO~ S the r~lr~r~le~liv-e ptlr~"",~lce ofthe cube corner element l,fd pair geG~ y d., ~e~ in Figs. 1-2 with the ru. w~d canted cube corner e1/ -"~ C'l~p~d pair B~~~ dep--~ted in U.S. Patent 4,588,258 (the '258 patent).
0 Curve 52 plots the total light return as a function of entrance angle in the broadest plane of enl ~ ce angularity in the '258 patent ~omet~ This plane is id.-ntifi~d as the 'X' plane in the '258 patent. Curve 54 plots the total ligh~ return as a function of c~ ce angle in the second broadest plane of e.,~ ce angularity in 258 geometry.
This plane is identified as the 'Y' plane in the '258 patent. Curves 56 and 58 plot the lS total light return as a fimCtio~ of entrance angle for the two broad planes of e .I~ ce angularity for the ~.~o,..- I~y depiGted in Fig. 1. Fig. 6 d~ on~ tes that, at c.~ ce angles of greater than about 35-40 degrees, the cube corner F~ mAt~hed pair as dF~i~-1~1 in Fig. 1 retums a greater pel~,~,nl&ge of light in both planes of broad el,l,~ce Angl~lAnty 40, 42 than the peo...~y dep;cted in the '258 patent returns in 20 the 'Y' plane.
Fig. 7 is a srl~P ~A~ic plan view of a ,t;~lesenl~ re r~Lrort;nective ~heeting 60 that has two broad planes of e l-L-~ce angularity in acco,dance with p,inci~lcs ofthe present invention. ~heeti~ 60 inrludes first and second longit~ inAI edges 62 and a structured surface ~ n.,~;AIIy as desc~ ed in connection with the structured surface 2s depiA,ted in Figs. 1-2. The structured surface in~ludes an array of cube corner ,"A1~.hl~d pairs defined by three inte.:ie~Li-lg sets of substantially paraUel ~ooves incl~l~ing a plilllaly groove 66 and two sets of secondary grooves 68, 69.
neÇA~e the cube corner el~ nt~ have isosceles base triangles, two ofthe base in~ ded angles are the same. The primary groove set may be defined as the groove30 set joining the two equal angles of the base triangle. The re., ~ groove sets may be considered seconclaly groove sets. In the embodiment depicted in Fig. 7, the array W O 96/42024 PCTfUS~'03232 extends ~ubsl~lially entirely across the surface of the sheeting Each m~tched pair of cube corner çlFm~nt~ in~lu~les two opposing individual cube corner CIC~I~GIIIS 70, 72 canted in a plane s~ ;Ally perpen~lic~ r to plhll~y groove 66. Additionally, a major portion of subs~ Ally every primary groove 66, and preferably the entire s ~ y groove 66, lies in a plane that inl~ a lon~tu-linAl edge 62 of the article at an angle, a, that plt;rt;lably ~--eas-lrcs app-u~ lPly 45 degrees. It should be noted that the structured surface is greatly magnified in Fig. 7 for illustrative purposes. In practice, the ~ re between ~ cent grooves typically me&~ul es between about 60 and 600 m: Ol s.
o Although opposing cube corner el~ s 70, 72 of each m~tl hed pair del: cted in Fig. 7 are physically located directly opposite primary groove 66 from one another, it will be app- ec;aled that such relative physical location is not a r~uh~..~ of the present invention. In its broadest sense, the term 'opposing', as used herein may be construed to mean optically opposing Cube corner rl~ e~ may 15 be con~;~iered optically opposing when they generate 'mirror image' l~l-u~t;nection p&lle --s. It is well known in the cube corner ~ t;l~ u- t;nective arts that cube corner ~1F ~ I S which are physical mirror images of one another--that is, F 1~F~ C which are iAlly idFntic~l but are rotated 180 degrees relative to one another, yield mirror image ..,~-u.~nective patterns. Direct m~rhinin~ techn~ F ~ make it 20 ndv~ u.-~ to posil;on opposing cube corner elemPnts directly opposite a groove from one another, as depicted in Fig. 7. However, it will be app-ecialed that opposing cube corner el~-"~"l~ could be physically remote from one another one the ~,l,F,"~ Additionally, it will be apprccialed that opposing cube corner elF-"....l~
need not be perfect physical mirror images of one another to yield optically opposing 2s cube corner F~ Slight variations in the physical shape of opposing cube corner P~ will yield only slight variations in the l~l-u~t:nective pattern which are not ~letect~ble by the human eye under normal viewing conditions. Such cube corner F1FmPntS are still oppo5;,lgF1FmFnh: within the mF~nins~ ofthe term used as used herein.
A rel.urt;nective ~h-F,eting having a structured surface as depicted in Fig. 7 exhibits a theoretical isobrightn-F,ss proffle substantially the same shape as that -~lepict~Pd in Fig. 3. However, be~;~use the array of cube corner f lr ~ 1 S iS oliG.,led such that the plillla.y grooves 66 lie in a plane which intersects the edge ofthe ~hçeting at an angle of appl~ çly 45 degrees, one broad plane of c .,~ ce angularity, corresponding with plane 40 of Fig. 3, is a~p~o,~;...AIely parallel with the s longih~ n~l edges 62 of shp~eting 60. The other broad plane of entrance angularity, coll~ .polldill~ with plane 42 of Fig. 3, is applv~ .A~Pl~ perpen~iC~ r to the longitu~in~l edges of ~h~ g 60. One of or-lin&,y skill in the art will recognize that the .GllulGnective pc~r~ .ce of ~I~P~I;U~ 60 may vary from the theoretical p~;. rO~ ", a~.ct; ~ ,f- ~ r d in Fig. 3 as a result of factors such as m~mlf~ctllring 10 i l*clre.;lions and measurement errors. Such minor variations are considered within the scope of the present invention.
One applic~tion in which ~ u~enective ~I.ee~ g 60 is particularly advantageous is in the field of vehicle co~pic~ity ~hçeting Fig. 8 is a schPm~tiC .
depiction of a large vehide 82 having a strip of retroreflective .~hf~etin~ 60 disposed in lS a h~ ...l ,.l vl ;~ l ;oll and a strip of rGIlvl Gnective ~hçeting 60 disposed in a vertical O~ nl;Qn Retroreflective ~he~t;~g 60 ~ lulGnects light from the he~-llight~ Of passing aulvlllobiles to f .h~-ce the conspicuity of vehicle 82. To ...~,c;,..;,e the amount of light I Glullled by ho. ;,o..l ~lly oriented strip of I ~tl olGnective ~hpeting 60at high e.ltl~ce angles, its broadest plane of entrance angularity should be ~ubsl~lially 20 parallel with its lon~gitu-lin~l edge62. By contrast, to ...~x;..-;,e the amount of light returned by vertically oriented strip of ~ olenective sheeting 60 at high enl.~llce angles, its broadest plane of c ~ nce angularity should be ~lb~ lly perpPn~ir,lll~r to its lon~yt~ldin~l edge 62.
RetrOref1eCtiVe .~hFel;~g 60 is particularly well suited for such vehicle 2s co-~s~ ity appl;c~ti~m~ When ~heeting 60 is placed on vehicle 82 in the ho.i~o..l~l Oli~lnl;Qn~ one broad plane of entrance angularity is aligned subst~nti~lly parallel with the longitu~in~l edge 62 of rcll orc;nective sheeting 60, thereby . ~;1 x;~ ..;,;. .g the arnount of light relullled by holi~olll~l strip 84 at high entrance angles. Sirnilarly, when ~heeting 60 is placed on the vehicle in the vertical orientation, one broad plane - 30 of c.. L~Ice angularity is aligned s l,~ ially perpçn~1iC l1~r to the longit~ in~l edge 62 of-e~-olt;llective sheetin~ 60, thereby ,n~xi...;,.;..g the amount of light returned by W O 96142024 PCT/U'3G~0~232 vertical strip 86 at high entrance angles. The ability to supply a single ~1 e~ g product for this application yields savings in the design, m~m-f~cturing, and n process for such consp~ e~ g .~h~eting 60 is similarly adv~ntageo~lc in the highway sign ~h~eting S appl;rAti~n~ As ~I;c~ c~ed above, the ,.L,o.t;nective pelru""ance of most canted cube-corner ~I.eel;.~g products is ~~.o.p.on~l~nt upon the orientation ofthe ~heetin~r on the sign. For ~ ~ ~le, ~ g illu~llal~,d in the '258 patent has better e.,l,~nce angularity in the plane identified as the X-plane. To ensure the best optical p~;,f,~ ce from the ~h~eting ofthe '258 patent, the ~l~ee~ g must be oriented such 0 that the X-plane is coinrident with the entrance plane of inA.id~nt light. By conll~sL, the cl~e~ g depicted in Fig. 7 may be oriented such that either plane of broad e~ ce angularity is coin~ident with the enl,~llce plane of in- ident light.
For most applicaLions, ~I.eet;~.g 60 exhibits its best ~cl~urt;llective pe~ 1~" ~ e when one plane of broadest e"l~al,ce angularity is aligned s~"ially 15 parallel with the longitu~linAI edge 62 of sl.ee~ For the cube corner geometry depicted in Fig. 7, this co"cal,onds to a structured surface in which the major portion of the p".n~y grooves 66, and pl ~rer;~ly the entire length of each plilllaly groove 66, lies in a plane that inle. ~ecls a lon~tu~lin~l edge 62 of the ~heeting at an angle 45 degrees. However, it will be applc~;;aled by one of ordinary skill in the 20 art that the p,iln&,y grooves need not lie in planes which intersect the edge of a piece of sheelii~ at exactly 45 degrees. ~Ithough the rcllolcnective bri~htness ofthe article will de.;leasc as the angle at which primary groove 66 intersects the edge 62 of the article deviates from 45 degrees, the decl ~ asc will be gradual. De~uendi,,g upon the p~,.rull,~ance requ;r~,."enls, the advantages of the present invention may be 2S obl~ned with the geometry depicted in Fig. 7 provided primary groove 66 intersects the edge 62 at an angle that measures between about 35 and 55 degrees and more preferably bct~een about 40 and 50 degrees. Additionally, numerous other cube corner ~ . ies exist that have planes of broad entrance angularity angularly di~pl~ced from the plane in which the optical axis of the cube corner element is30 canted. One of ol dh~&~y skill in the rcl~ ul cnective arts will a~precidle that the pclfwlllal~ce of l~ ùlenective ~l.eel;~ incorporating such cube corner elem~nts may WO96/42024 PcT/u'~Gl~5232 lS
be improved by o-i~.. Led the cube corner ~ such that the broad planes of e ~ll~lce angularity are aligned sllhs~ l1y parallel with an edge of the ~hPPtit~g The optical fldvantages of the present invention may be achieved using cube corner PlP - "_.11 geo---~l ~ ;es other than the geome~ i y depicted in Fig. 1. A broad class s of cube corner el- -..-,-.l ~ that have scalene base triangles have isobrightness profiles that are s~it~h~-~ for ,.. ..-r, ,I...",g ~ u~enective ~ g in a cco~dance with aspects ofthe present invention. Scalene base triangle cube corner ~-IF..n~l.le may be characterized in that none ofthe three in~ ded angles ofthe cube corner element base triangle are the same.
One PY~mple of structured surface 100 employing a ~ .llali~e scalene base triangle cube corner element geon.cl~y is dep;cted in Fig. 9. The ;nrlllded angles of the base triangle of each cube corner ~el~lt;nective element Illeavule approx;~ ely 62.09 degrees, 67.91 degrees, ~nd 50.00 degrees (,BI, 132, and ,B3,especli~ely)~ The groove side angle of groove 102 (a 2) measures ~ro~;.n,-~ely 42.295 deg-ees, the groove side angle of groove 104 (a 1) measures apl,lo,.;in~ly 26.284 degrees; and the groove side ang1e of groove 106 (a 3)"~eavu~S
appro~ ly 36.334 degrees. The optical axis of each cube corner element is canted a~prox;...-lPly 8.38 degrees from an axis normal to the base surface ofthe vul,vl ale in a plane that is app~ ,x;~ ely parallel to groove 104 and pel~e~ cul~r to 20 the base surface of the m~t~ri~l Fig. 10 is a predicted isob,;gl~ s profile of a ,~,u,~nective ~hPetin~
employing cube corner element m~tr.lled pairs formed from a material having a refractive index of 1.590 and having the g~o...~ y depicted in Fig. 9. Vector Vlcoll.,v,.onds to the plane in which the cube corner PlPmPnt~ are canted (i.e. the plane 2s that col;.;~ the vyll~"~l,y axes ofthe cube corner Pl~mPnt~) The cube corner g~~ hy depicted in Fig. 9 exhibits two planes of broad entrance angularity, denoted by planes 110, 112, that are angularly ~ plrlced from the plane in which the cube corner c~ are canted by applù~ tply 30 degrees and 120 degrees, respectively. Additionally, planes 110 and 112 are app~uX;.~ ly perp~n~ic -l~r to - 30 one another. Accol.lh~gly, orienting the structured surface such that groove 104 intersects a lon~ih~lin~l edge of a lel, ~" t;nective ~I.eel ;,.g at either 30 degrees or 120 degrees wi11 align one broad planes of e,-l,~lce angularity parallel with the longit ~ edge of the chPetir~ and another broad plane of entrance angularity pe.~n~lic~llnr to the lon~h~ n~l edge ofthe sheeti~
Fig. 11 illu~ les a structured surface 120 inc~ i~ another scalene base s triangle cube corner gf.~O"'~ )r that has two broad planes of c .I~ ce angularity angularly rl;cp!~ced from the plane in which oppos;"g cube corner clenl~lls are canted. The included angles ofthe cube corner el~ f -.1 base triangles depicted in Fig. 11 Illea~ appru~ ely 68.71 degrees, 63.29 degrees, and 48.00 degrees (~1, and ~3, resl,e~ ely). The groove side angle of groove 122 (a 2)ll-c~i~iul~s 0 al~plu~ lf Iy 42.295 degrees; the groove side angle of groove 124 (a l )measures applo~ f l~/ 26.284 degrees; and the groove side angle of groove 126 (a 3 ) measures appr~ ,ly 36.334 degrees. The optical axes ofthe cube corner f~l. -... -.1~; are canted appro~-ll,alely 9.Sl degrees from an axis normal to the base surface ofthe substrate in a plane that intersects groove 122 at an angle of al)~,lu~ ely 45 degrees.
As illustrated in Fig. 12, a l~llolt;llective ~l.e~ g that incl~ldes an array ofcube corner e~ as c~epicted in Fig. 11 and having a refractive index of 1.590 has t~vo broad planes of entrance angularity 130, 132 angularly ~iepl~ced from the plane in which the ~ are canted Vl by about 26 degrees and 116 degrees, I~:~e~ ,ly. Accoldin~ly, ulie~ g the structured surface such that groove 124 intersects a longitutlin~l edge of a rtilr-,l c;nective cheetin~ at either 49 degrees or 139 degrees will align one broad planes of c.,ll~-ce angularity parallel with the longit l-lin~l edge of the cl.Pt ~ g and another broad plane of entrance angularity p~l~,.... ......,.lir,llls-r to the longjtll~in~l edge ofthe cheeti~
2s Cube corner elc.ll~.,l designs employing scalene base triangles have some additional ad~ gcs over cube corner elements having isosceles base triangles. One advantage is that a structured surface having scalene base triangle cube corner may allow a greater degree of canting of opposing cube corner PIPmPntc in the m~nllf~ctllring process without causing physical damage to ~dj~cPnt cube corner e,l~

WO 96/42024 PCT~US96109232 In directly m~-hined cubes using three sets of mutually i..~ e~,ling grooves, cube Cl;ppillg occurs when any one of the groove side angles c~ceeds 45~, causing the cutting tool to clip the edge of an ~jacent cube. A ~l~m~ged cube corner element results in losses in ~ tinectivity. For ~ , the cube corner element geo~ y s depicted in U.S. Pat. No. 4,S88,258 cannot be canted beyond a cant angle of 9.736 degrees in a co~ ;on~l array. In Table I, below, leplese.llali~e scalene ~,ec,...f~y values for base triangle in~ ded angles (13) and groove side (a) angles, are shown for canting opposing cube corner e~ k~lc in a plane which is roughly parallel to a groove and perpentliclll~r to the base plane.
10 Scalene geo---ell;es may permit greater ~mollntc oftilt prior to any groove side angle ~Yceeding 45 degrees, thereby allowing tilting of cube corner e1ementc beyond the known limit~tionc due to ...ec~ ;c~l clipping caused by a cutting tool. For; ,~le7' Table I df -~o~ les that a tilt or cant angle of up to roughly 13.376 degrees can be utilized without edge clipping.

W O 96/42024 PCT~US9G/~5232 Table I
~2 ~3 ~1 al a2 a3 Tilt A~n~e 40.0 73.321 66.679 36.695 21.063 45.789 14.912 S 41.0 72.84S 66.1SS 36.S77 21.677 45.485 14.305 42.0 72.3S8 6S.642 36.464 22.300 4S.161 13.689 42.5 72.110 6S.390 36.408 22.614 44.992 13.376 43.0 71.8S8 6S.142 36.354 22.931 44.818 13.061 44.0 71.34S 64.6SS 36.247 23.S71 44.4SS 12.421 4S.0 70.817 64.183 36.14S 24.221 44.071 11.769 46.0 70.274 63.727 36.047 24.881 43.666 ll.lOS
47.0 69.713 63.287 3S.953 2S.SS0 43.238 10.426 48.0 69.133 62.867 3S.864 26.230 42.787 9.733 49.0 68.533 62.467 35.780 26.921 42.313 9.025 lS S0.0 67.912 62.088 35.700 27.623 41.814 8.300 Sl.0 67.266 61.734 3S.626 28.336 41.289 7.SS9 S2.0 66.S9S 61.40S 3S.SS8 29.061 40.738 6.801 S3.0 6S.896 61.104 3S.49S 29.797 40.160 6.024 54.0 6S.167 60.833 3S.440 30.S4S 39.SS3 S.228 SS.0 64.40S 60.S9S 35.391 31.304 38.917 4.412 56.0 63.607 60.393 3S.349 32.075 38.250 3.574 S7.0 62.770 60.230 35.316 32.857 37.SS2 2.715 S8.0 61.892 60.109 3S.291 33.6S0 36.822 1.833 S9.0 60.967 60.033 3S.275 34.452 36.058 0.927 60.0 60.000 60.000 3S.264 3S.264 3S.264 0.000 In col..l.;.. ~I;on with the teaçhing.c ofthis invention relating to improved ple~ll ~d entrance angularity not in the plane of cant, scalene base gec l~,~lly cube comer clcll,e"l arrays also enable tilting beyond previously known limits at which total light retum breaks down for light incid~nt perpendicular or nommal to the base of the cubes. Total light retum (TLR) for reLI orenective ch~eting iS derived from the product of percent active aperture and rell ort:flected light ray intensity. For some co...l.;.-~l;on.c of cube geQ...~l~ies, entrance angles, and refractive index, significant red~lctiQn.c in ray inlt;l,~;ly may result in relatively poor total light return even though 3S percent active aperture is relatively high. One ~ ,le is lellu.enective cube comer W O 96J42024 PCTAUS96J'~323 f ~ arrays which rely on total internal reflection of the r e~-Ol~nected light rays.
Ray il.tenD;Iy is s~l..s~ ;Ally reduced if the critical angle for total internal reflection is ~Yceeded at one of the cube faces. ~lthough met~ 7çd or other reflective co~ting~
~ may be utilized adv~nt~geQusly in such sittl~tion~ these co~tings are not always s de~;l~lc due to cost, process, appeal~lce, or other factors. In such ~itl-~tion~, the use of scalene base triangle cube corner e1~mentc is prer~ d.
Table II shows limiting total light return geometries for normally inc;dçnt 1ight and cubes with a refractive index of 1.586. For a 52.2~-52.2~-74.6~ base angle cube comer el- ..- ~-~ the limiting tilt angle is 15.60~, for ~Y~mple as shown in U. S. Pat.
No. 4,588,258 (EIoopman). However, this limit~tion may be ~Yçeeded without totallight return breakdown using scalene base geometries, for example, 16.41~ (45.40~-58.57~-76.03~) or even 18.830~ (77.358~-65.642~-37.00~). Data in Table II l~iltiSe,lL
mlm~ric~l rather than analytical solutions.
Tuble II
1S ~1 B2 B,3 a, a2 a3 Tilt 7S.600 S2.200 S2.200 50.867 26.505 26.S05 lS.602 7S.749 48.900 S5.351 50.939 24.769 28.080 lS.8S7 76.030 4S.400 S8.S70 S0.924 22.949 29.689 16.408 76.623 41.400 61.977 S0.985 20.840 31.290 17.476 20 77.3S8 37.000 6S.642 S0.816 18.S82 33.064 18.830 Principles ofthe present invention may also be applied to tiled ~~;l-u-~nective .cl.e~l;..p. As used herein, a tiled structured surface in~ dçs a plurality of discrete arrays of cube corner elom~nt m~tched pairs positioned at di~rt;-ll oriçnt~tion~2S relative to the edge of the !~hee~ g Tiling is one :~tl~egy employed to produce ~ ,olene~ e ~heeting having multiple planes of broad entrance angularity. Tiled ~etl~l~;nective shçeti~ suffers some inherent loss of bri~htn~ss at high en~ ce angles because, by definition, only a portion of the arrays are oriented to r t:~- oleLlect the ..~ .~.h~ .. arnount of light at a given entrance angle and ~heeting orientation.
30 However, it is possible to ...;..i...;~-, or at least to reduce, the bri~htness loss inherent in tiled !~hf,~ h~B by orienting the arrays of cube corner Plom~nt~ on the structured surface in acco- d~ce with principles of the present invention.

W O 96/42024 PCT~US96~0~232 The utility oftiling may be ~Ypl~ined with .~.felence to the lel-u.~,nective cheeting d epicted in Fig. 7. As diccllcced above, the structured surface of thecl.olellective .c1.~ 2, d e~ ~ ted in Fig. 7 has a single array of cube corner cl~
m~tr.h~d pairs which results in two broad planes of entrance angularity: a first plane s s~ s~ ly parallel with a lnngitl~-lin~l edge 62 of ch~eting 60 and a second plane s~ ;AIlyperpen~lir,ul~to lon it~ in~l edge62 of shc~,Ling 60. Atiled olcllective ~he.,~ g inrl~ltling a structured surface having two distinct ,ositir~ned at two di~.~ ;onc relative to the edge ofthe ;~heel;n~ may have as many as four broad planes of c.~ ce angularity. Similarly, a ~cL-u~t~e-;live 0 .cheeting inr.l~l~ing a tiled structured surface having three distinct tiled arrays positiQ~d at three di~l ~.-l orientations relative to the edge of the she~ may have as many as six broad planes of e.,lr~1ce angularity. In general, for the cube corner ~eo---e~y d., i~ d in Fig. 7, a lel,orcnective cheeting having a number X broad planes of c.,l-~ce angularity may be produced by a structured surface having a lS plurality of tiled arrays positioned at X/2 distinct oriçn~tion~ relative to the edge of the ~h~etir~g In acco~dance with the present invention, at least one ofthe arrays of cube corner element m~trhed pairs should be oriented such that one broad plane of ~,.llla.~cc angularity is positioned appr~X;..~ Iy parallel with the edge ofthe shc~li"g.
20 Acco~.li-.~,ly, for the cube corner el~ment ~eomlo,try depicted in Fig. 7, one array of cube corner ~1~ .".-,~ .ed pairs should be oriented at such that the plilllaly groove i..lt;. ~c~,ls the edge of the article at an angle of ap,olox;. ~ .z~ely 45 degrees.
The o-ic..l~lion of the ~ 8 arrays depends upon the number of discrete arrays of cube corner ~ m~tched pairs in the structured surface. For the cube 25 corner geometry of Fig. 7, a~ 8 that the goal oftiling is to produce a more rot~tio. ~lly :,y~ ical ~t;l,."~nection pattern, the angular ~lif~,ence ~betweenarrays of cube corner e~ m~tched pairs may be e,~ ssed by the forrnula:
~ = 90/N
where N lt;~.~.se..ls the number of discrete arrays of cube corner f~ ment~ Thus, in a 30 .~;~.o.~flective !~I.edi,~g having four broad planes of entrance angularity (e.g. using N-2 arrays of cube corner elements) the angular di~,~,nce ~ in the orientation ofthe WO 96~42024 PCTAJS9~ 232 cube corner arrays should measure a~ Iy 4s degrees. Accoldill~ly, the second array of cube corner c~ should be oriented such that the p~h~&ly groove intersects the edge ofthe article at an angle of app,u,~;...~tely 90 degrees.
Similarly, in a rcl.o~cne~ e ~he~ having six broad planes of entrance ~ng~l1srity s the di~.~.~ce ~in the ori-P~ Qn ofthe cube corner arrays should ~"e&s.
appru~ fly 30 degrees. Acco,du,~ly, a second array of cube corner e1=.... ~
should be o. i-,-~led such that the p,h~a-y groove intersects the edge of the article at an ang1e of applv,.;~ y 15 degrees relative to a 1Ongitlldin~l edge of the ~l.cc~ p and a third array of cube corner elP -~nl ~ should be oriented such that the plhllaly 0 groove i~ e~,ls the edge of the article at an angle of ~y~u~ alely 75 degrees relative to a longit~l~lin~l edge ofthe ~he~;.lg This progression may be contin-led lhlo~h as many distinct orientations as desired.
Fig. 13 is a s~ l.- -~. l;c depiction of one embodiment of a tiled rGl~u,t;nective .d.fel;l~p 150 in accoldance with the present invention which has six arrays of cube corner fl~ .. lc r~ in six planes of broad entrance angularity. In a pler~"~,~embodimf nt, ret,ù~nective cheeting 150 is m~mlf~r~hlred as a contimlollc web ofthin, flexible l_holenective ~l.e~ g capable of being wound onto a roll. The structured surface of ~ urt;ne~ re cheeting 150 in~l~ldes six groups of cube corner P~ ed pair arrays po~ilioned at six distinct orientations relative to a lon~t~ edge 152 of .I.P~l;.~g 150: a first group of arrays 154 positioned such that the plUIl&ly groove intersects the edge 152 at an acute angle of 15 degrees, a second group of arrays 158 positioned such that the plilll&ly groove intersects the e dge 152 at an acute angle of 75 degrees, and a third group of arrays 162 positioned such that the plinlaly groove intersects the edge 152 at an acute angle of 45 degrees, a fourth group of arrays 155 positioned such that the plilll&ly groove intersects the edge 152 at an acute angle of 45 degrees, a fifth group of arrays 159 po~itioned such that the p~iUI&ly groove h~lf ,~e.ils the edge 152 at an acute angle of 75 degrees and a sixth group of arrays 163 oriented such that the plhn&ly groove intersects the edge 152 at an acute angle of 15 degrees. Each ofthe arrays is formed from cube corner 30 f IP .". ,1 ...~ ed pairs sul,sLal,lially id-Pnti~l to those desc-il,ed in comleclion with Figs. 1 and 2, above. Vectors 156, 160, and 164 l~,plesenl the directiûn ûfthe W O 96/42024 PCTAUS96J0~232 pliln&ly grooves of each array 154, 158, 162, rts~,ec;~ ely, of cube corner rl~ .I.F...~
Similarly, vectors 157, 161, and 165 r~lese,ll the direction ofthe pl;nlaly groove of arrays 155, 159, and 163, r~ s~e~ ely~ .Altho~-~h not nece~ y, it is p-Grt;llcd that each ofthe six distinct groups of arrays 154, 155, 158, 159, 162 and 163 cover 5 appro~ 3A I ~ one-s~ll- of the surface area of structured surface of sl-e~ 150.
~ hPPtirlg 150 has six broad planes of e.l~ ce angularity. Two broad planes of e.lll~lce S~ng~ rity~ COIl~Ollding to the group of arrays 162 and 155 are aligned at a~r~,~;...AlPly O degrees and 90 degrees relative to lor~itu-1inAl edge 152 of ~hP~ 1g 150. Two broad planes of e.~ ce angularity, colle~onding to the set of 0 arrays 154 and 159 are a1igned at ap~ ly 60 degrees and 150 degrees relative to an edge of ~heel;~g 150. Two broad planes of e.ll-~lce angularity, co..es~ondi~.g to the set of arrays 158 and 163 are aligned at appro~ ely 30 and 120 degrees relative to an edge of che~ p 150.
The ~I-P,~ P 150 d~F~ ~- d in Fig. 13 employs six arrays oriented at six lS distinct o~;v-.lAlinne to produce a l~ oltllective eheeting with six broad planes of e.-l-~cc angularity, one of which is aligned sllbstAntiAlly parallel with a lnngit~ldi edge 152 of sl-c~ 150. However, it will be apl)-cc,ialed that sl .P,~ g 150 could incorporate a greater or lesser number of arrays to produce a LeL-u-eflective ~he~ g with a correspor~di.lgly greater or lesser number of broad planes of e nll~lce 20 ~Igul~uily.
As ~iccll$sed above in co~ eclion with single-array embodimP,nte ofthe present invention, the arrays need not be p. ~;-,isely aligned to achieve the advantages ofthe invention. For many applications positioning the cube corner arrays withinabout five degrees of the p- ~r~ d o~;e.-l~lion will be sufficient to produce the 25 le~Uil ed b~ c~ at a given entrance angle.
Fig. 14 is a sc~ -A~ic rtprese~ ion of l~llulenective eheetin~ 170 which employs a plurality of tiled arrays of backward canted cube corner element mAAtAhec~
pairs similar to those depi~: o ~ in Figs. 1-2. The .eheeting depictecl in Fig. 14 is co.-....P-c;ally available from Sli-.-so- ile Corporation of Niles, Illinois and is 30 mAmlfrctured and di~ ibuled under the trade name STIMSONITE High P~.r~lllallce Grade Reflective ShP,eting ~Lot 1203W, Product Number 8432170). The structured W 096J42024 PCT~US96~2.',~

surface of .~l, ul ~nective SI~G~ g 170 inrl~ldes a pluralit,v of groups of cube corner Pl- ...f..-~ m~tr.hed pair arrays positioned at a plurality of distinct ori~ont~tir~ne relative to a k>ngiturlin~l edge 172 of sl.e~ 170. The cube corner arrays are oriented such that the p,;,n~ grooves of the arrays lie in planes that are positioned at oric- .~ e s of 0 degrees, 30 degrees, 60 degrees, and 90 degrees relative to lon~it~ldin~l edge 172 of sheet 170.
Pos;tioning the tiled sectionc of ~ ulellective eheeting to align the broad planes of ~..I. ~ce angularity at angles of app~ v~ çly 0 degrees and 90 degreesrelative to a longitu~in~l edge 152 of chçeti~ 150 in acco--lance with the present 0 invention a~ /cs signifir~nt p~;.ro"nallce gains over the tiled ~ ,ling depicted in Fig. 14. These p~;,ru"..ance gains are illustrated in Fig. 15, which depicts thel~....;nAI-ce (in r,~nrlel~e per square meter) of rel~"c;nective eheeting as a fi-nr,tinn of the J;~ ce (in rneters) for vA~ying G.;c"l~lions oftiles section~ on ~t;L-ur~nective ~l-e~ g (e.g. varying groove ~lignm~nt angles). The h .~ni~ r~e data in Fig. 15 is IS ~ s~ Li~e. of a sL~ dal d sedan approaching a semi-truck trailer which is parked at a 45 degree angle across the road. The lel~ol~nective ~h~ g is pneitioned ho,;,.oi~lly across the bottom edge ofthe semi-trailer. A detailed description ofthe testing environl"~ and methodology employed to generate Fig. 15 may be found in Sign T-~ ce as a Methodology for ~tchin~ Driver Needs, Roadway Variables, and Signing M~teri~l~, by Woltman and S7-'.7eÇll, T~ s~o, lalion Research Record, 1213, Human p~.rul"-~ce and IIigllway Visibility--Design Safety and Methods, T~ ,.oll~lion Research Board, National Research Council, pp. 21-26, (1989).
In Fig. lS, curve 180 co".sl)ollds to .~he~ g having cube corner arrays positioned at o.i~ ;ol~c of 0, 30, 60, and 90 degrees, as depicted in the rtl,u,.llective ~he~ of Fig. 14. Curve 182 col~ .ondsto sheeli"ghaving cube corner arrays posi~ioned at o,it;~ lions of 5, 35, and 65 degrees, curve 184 coll~ ollds to eheeting having cube corner arrays positioned at orientations of 10, 40, and 70 degrees, curve 186 coll~ onds to eheeting having cube corner arrays poeitioned at o nl;OI .e of 15, 45, and 75 degrees, and curve 188 corresponds to~ c~ g having cube corner arrays positioned at orientations of 20, 50, and 80 degrees. Fig. 15 d~ on~l~ales that ~heeting having cube corner arrays positioned at W O 96142024 PCT~US96/09232 u~ nc of appro,~ lely 15, 45 and 75 degrees exhibits the best r~ ult;nectivepe.ru~...ance at almost all ~ r.es from the cheeting Similarly, sheeting having cube corner arrays posilioned at orientations of 10, 40, and 70 degrees and .cl.e~ g having cube corner arrays po~;l;Qned at 20, 50, and 80degree ori~..laliolls exhibit 5 good r~_hu.-,nective ~.,.rù~ ance across the range of.l;~ ces modeled. A 0 degree o,;r~nl~l;on, cG11~3pOn~ling to ch~oeting 170, c~lubiled the poorest ~~l-ult;nective pe~ru..l.ancc. Tiled l~t-olenective ch~tin oriented in accol-lal-~ce with the present invention oul~lrulllls the ~1 e~ r ~ ted in Fig. 14 at all ~ nces d~ d on thecurve. ~lditiQn~lly~ ~he~ B in accGIdance with the present invention is nearly twice lO as bright in the critical range of ~ 5e~.on(1ing from about 50 meters to about 150 meters.
R~,ne~;live ~he~1;u~ in accoldance with the present invention may be made as one integral m~teri~l e.g., by embossing a preru.med sheet vvith a desw;l,ed array of cube-corner e~ or by casting a fluid material into a mold. Alternatively, such 5 ..il,ùrli;Ilc~,liv~ chP~ may be made as a layered product, e.g, by casting theP~ ; against a p.~fo--ned film as taught in U.S. Patent No. 3,684,348, or by a pr~,fo-~,-ed film over the front face of individual molded ~lc-~" -"c Useful tools for m~ fs~cl~ ~ ing r~l. ul enective .~ ec;l ;.~g in accorda,lce with the present invention include embossing molds which may be in the form of contin--ouC
20 belts or mandrills. Such continllol~c molds may be formed using a replic~tion process which begins with the direct m~rhining of a structured surface in a m~rhin~h~e ~ubsl~le using a precision m~rhining tool such as, for C~n?lC, a diamond ruling or turning rn~rhin~ to produce a master mold tool. The structured surface may r~lic~ted by electrolytic deposition of nickel onto a master article. A plurality of such rerlir,~trcl tools may be cc-nlle~,led into an embossing or casting mold. To the extent that the present invention deswibes articles having novel structured surface geo...~l~;ec, the claims ofthe present invention are intended to cover replicas, tooling and molds used in the m~nnf~ctllring process of-et-olenective sl.eel;~.g S ~- bl~ materials for rc;l~o,t;nective articles or cheel;l~g ofthis invention are 30 pr f~,. bl~ lll materials which are ~ n.c;onally stable, durable, ~w~all,e ~ble, and easily rep1ic~ed into the desired configuration. Illustrative e,.~"ples of suitable W O 96/42024 PCT~US9CJ'~232 m~t~ri~lc include glass; acrylics, which have an index of refraction of about 1.5, such as PLEXlGLAS brand resin m~mlf~ct~lred by Rohm and Haas Col.lpa -y, poly.i~l,ollales, which have an index of refraction of about 1.59; reactive materials such as taught in United King~lom Patent No. 2,027,441 and U. S. Patents Nos.
s 4,576,850, 4,582,885, and 4,668,558; materials ~ spalc~ll to the wavrle-~gll.C of actinic r~ tion used in curing cube corner Ple-~P~.ls formed ofthe material(s);
polymeric lllalelial selected from the group co~ g of poly(carbonate), poly(lnc;~ rlate), poly(ethylel1etel~ph~ lste), and crosclin~e~ polymers of multi-fi~nction~l acrylate Illonolll~ , polyethylene based ionomers, such as those 0 lll&l~led under the brand name of SURlYN by E. I. Dupont de Nemours and Co.,Inc.; polyesters, polyureth~n~c; and cellulose acetate butyrates. Polycarbonates are particularly suitable because of their tou~hn~cs and relatively high refractive index, which generally conl-il~ules to improved ll;l-ol~nective pe-rullllance over a widef range of c.lll~ulce angles. These materials may also include dyes, colorants, pigm~ntc, W stabilizers, or other additives. Colorants may include fluorescelll dyes or pi~ to improve daytime visibility and con.~pi~ ty of the cheetin~ T.~.s~ y of the materials ensures that the separation or truncated surfaces will h~lsllli~ light through those portions of the article or sllee~
The illCC,l~Olalioll oftruncated or separation surfaces does not ~ le the n,~.or-,nectivity of the article, but rather it renders the entire article partially l-~-~arenl. In some applications requiring partially l-~--~are--~ materials, lowindices of refraction ofthe article will improve the range of light ~n~ ed through the article. In these applications, the increased tr~n~miCsiQn range of acrylics (.er, - ve index of about 1.5) is desirable.
In fully le~-olenective articles, materials having high indices of refraction are pl~f~ cd. In these applic~tionc~ materials such as polycarbonates, with ~t;r a~i~ive indices of about 1.59, are used to increase the di~lei-ce between the indices ofthe material and air, thus h~c.easing r~tlult;nection. Polycarbonates are also generally pl~r~;;l-ed for their le,l,p~ re stability and impact reCiet~nce - 30 The invention also contemplates use of a cast and cure type of m~mlf~ctllring process using the cube corner element optical designs disclosed about to create a .~hee~ g having superior optical p~,lru~ al~ce and excellent flexibility. One embodiment of an article using this process co...p. ises a first polymeric composition for the cube corner el~ and a second polymeric overlay materials which is a thcl--.oplai,lic material. Plcrc~ bly, the overlay material is l.~l~arc..l to the S wa~ hq of actinic r~ tiQn used in curing the resin forming the cube corner ~l~.". .l~ Another p-cfc--cd characteristic ofthe materials ofthis embodiment is the relative elastic m~ llls for each COIllpOll~,.lt. High elastic mod~ s materials are p-cr~. ble for the cube corner el( .". ..lc due to their mech~n;c~l p~ùpc lies that impart distortion l -~ ql ~ ce The overlay material is p~ . ably a polymeric ..-alc ial of 10 SOlll~ ~ . Ldl lower relative elastic mo~ul lq During curing of the cube corner c~j-n~on~ .-l, ~lep~n~ing on the composition of the cube corner material, the individual cube corner el- -"~-~lC can experience a certain degree of sh-ii~ing. If the elas~ic mori-ll~lc ofthe overlay material is too high, torsional stresses can be applied to the cube corner ~1r . ,....l e as they shrink during curing If the stresses are sllffir;~ntly lS high, then the cube corner el~ .1 e can become distorted with a res--lting degradation in optical pe.rO....~nre When the elastic mndllllls ofthe overlay film is sllffir;~ntly lower than the modulus of the cube corner materials, the overlay can deform along with the shrinking of the cube corner element without eAcl Li.lg the type of dcîu-.. ~I;on~l stresses on the cube corner ele.--.,.-L to which it is adhered that 20 would lead to a deg-a~l~tion of optical characteristics.
Alternatively, the di~.clLal belwccn the elastic modulus ofthe cube corner el ..~ .1 and the overlay material need not be as great depending on the llimPncionc Of the cube corner el~ ~ .ls When the cube corner Pl~omPnts are of lower height, the di~c cn~ between the elastic mocllll~lc ofthe cube corner Plement and the overlay 2s film need not be as great, presumably because the smaller cube corner PlemPnte do not u..d~ as great a shrinkage during curing, as measured in absolute rlinnPn~;onal units, and the overlay film does not interact with the cube corner el~m~Pntc toward the cn,alion of torsional and l;,.. -nc;on~l stresses to as great an extent as with the larger cube corner e~ lc In general, it is possible to state that the modulus difrcn,.lLial 30 bcL~ n the overlay material and the cube corner element material should be on the order of 1.0 to 1.S x 107 pascals, or more As the height ofthe cube corner el~ le WO 9~42024 PCTAUS~ 232 .l;...;..~l.e5, it is possible for this mo~llllle dirre,enlial to reach the low end ofthe range given ;..~ ely above. However, it should be kept in mind that there is a practical lower limit to the modulllc of the cube corner cle~llGlll m~t~.ri~l Below a certain level, generally on the order of about 2.0 to 2.5 x 108 pascals, the cube corner s el~ ..f -1~ c becolllc too flexible and do not possess sufflcient . ~e~h~nic~l rigidity to plcJpf,ly L~lule upon applic~l;on of a stress. Fracturing is a feature which is d~ b!~ in some embo~ n~ to achieve discrete cube corner PlO-..~ ; Without such L~lu~ g, the de-c~-lylil~g ofthe individual cube corner Pl~-.-- ~-lc that is eccf-~ 1 to the fl/ .;l~ y and the s.lp~-;or optical p~,pc~Lies ofthe !~I.r,~ g under o stress cannot be ~tt~ine~
Aside from the c! - ~1erations conce,..mg the relative elastic modulus b~tweell the cube corner e~ c and the overlay film onto which the cube corner el- -..- - .l ~ are cast, there is a .~ui,~,..,- .,l of relatively low elastic mo~ lllc for the overlay film. This is i",l,o,l~,l if a goal ofthe m~mlf~r,tllring is to achieve a high lS degree of flexibility in the ,~,~. Ili,~ ,~l,u,t;nective ~1~ç~ g material. Pler~l~bly, the cube corner f~lP..~f ..~1 C are cast onto the overlay film with a minim~l amount of land.
Provided that the land can be suffir,iently ~ e~ elcllillg or other suitablee1astic distortion of the overlay fi1m results in the fracture of the cube corner m~teri~
b.,l~..~.~ the individual cube corner ~k ~ This can be accomrliehed by applic~tinn of elastic stress to the overlay/cube corner m~tçri~lc post-fabrication, or can result from the process of simply removing the m~tPri~ls from the fabrication appalalus. This r~plese.lLs considerable ~ffir;enry in fabrication in that cignifil;~nt post-casting op_.~lions to fracture more sul,slanLial lands to achieve the same effect are ~ ececc~y, with ~ulling savings in fabrication costs.
2s As a concequ~nre of the fracture of the minim~l land of the cube corner film, the individual cube corner optical rlP..~. .,lc are ecsenti~lly totally decoupled from each other and from the overlay material. Signific~nt advantages derive from this deco~plil-g The first of these is the ultra-flexibility that is sought for the m~t~ri~lc The decou~led optical el~mentC are no longer ",e~ ~ c~lly cons~,~ined by the effect - 30 ofthe land, regardless ofthe land's th;~l~ness This permits cignific~nt distortion of the elastic ove,lay/cube corner composite m~t~ri~l, while at the same time pelllliL~ing W 096/42024 PCT~US9G/~232 çcc~nti~lly complete ...cc.l.hl~ic~l recovery ofthe composite material post-distortion.
Also, the decoupling of the individual cube elements makes it possible to isolate any distortional stresses applied to the composite material. The direct benefit of this is that stresses applied to the rellol~lective material generally have minim~l degradative s effect on the optical p~upwlies ofthe materials. With less-flexible, prior art~licfi~;onc, localized stress applied to one area ofthe cube corner composition can bell~n~ edto~ c~ areaswiththeresultthatSig~ir~Cdnllossofoptical plup~,.ties is eYtl~n~ed to a much greater area ofthe ~el~u~nective material.
In another, ~l;c~ ---;l~r, process for achieving a certain degree of flexibility in a 0 rel,ur~nective article, the first step is to te~po~ily affix an array of cube comer I lr ~ to a sheet of base material. The cube corner Plem~ntC may be formed by casting a suitable material onto a release coating on the base material. Then, areflective layer on the cube corner ~l~om~nte is formed by met~li7ing or other means.
A sul~sllate is then affixed to the reflective layer side of the cube corner ~lement.c 15 The sheet of base material is removed, leaving an exposed array of relatively free $l~ g cube corner el~ formed on the substrate.
A suitable b~L ;. ~g layer may be made of any transparent or opaque m~teri~l, inrl~ ing colored or non-colored material, which can be sealingly çng~ge~i with the ,~llole[lective Pl~ c Suitable backing materials include ~ mim~m cheeting, 20 galvanized steel, polymeric materials such as polymethyl meth~r,rylates, polyesters, polyamides, polyvinyl fluorides, poly.,~l,onates, polyvinyl chlorides, and a wide variety of l~ t.. c made from these and other materials.
The b~r~ing layer or sheet may be sealed to the reflecting cube corner el~ C, in a grid pattern or in any other suitable configuration. Sealing may be 2s ~cted by used of a number of methods, inclu-ling ultrasonic welding, adhesives, or by heat sealing at discrete locations on the array of reflecting ~lPmentS (see, for . Ie, U.S. Pat. No. 3,924,928). Sealing is desirable to prevent entry of co~ such as soil or moisture and to preserve the air spaces around the cube corner r~flectinp surfaces. Edge sealing may be beneficial in applic~tionc such as 30 tluck cûn-cpicl~ity which require relatively long narrow strips of rel-o~t:nective ;,h~

W O 96/42024 PCT~US9~092?,2 If added ~ h or tou~hn~cc is required in the composite, backing sheets of polycarbonate, polybutyrate or fiber-reil~u~-;ed plastic may be used. Depending upon the degree of fl~.Yihility ofthe resulting l~;L,olGnective material, the material may be rolled or cut into strips or other suitable designs. The rt;L,olellective m~tçri~l may S also be backed wil:h an adhesive and release sheet to render it useful for appliç~ti~ n to any substrate wilhu~ll the added step of applying an adhesive or using other t~
means.
While not speçifi~lly dicc~osed in conne.;l;on with each embodiments ~iccllcced above, various mo-lific~tionc or CollL;ll~lionsillcGl~ol~l;ng existing 10 rcalur~.s of the cube corner l elr~,renective arts are contemplated by the present invention. For e ~&lllple, it would be obvious to one of ordinary skill in the art to provide a separatiûn surface in the grooves which separate cube corner P~le"~ s iti~n~ny~ it would be obvious to coat a portion of the structured surface with aspecllls~ly reflective ~ -ce such as, for PY~mplç, by vapor coating a layer of ~1.. ;~.. " or silver on the surface. Further, one of oldi~ y skill will recognize that the dihedral angles between ~ cPnt cube co ner Pl~ .lc may be varied as ~1icclosed in U.S. Pat. No. 4,775,219 to Appeldorn. Products incoll,o~ lg such obvious mo-lifi-~tions or cc,l,ll~;llalions are considered to be within the scope of the present invention.
EXAMPLE I
This .. . '~ illu~ les the angular range of cube corner Pl~mP!nt canting which results in a desired amount of angular deviation bt;lween a plane in which the optical axes of the cube corner Pl~ s are canted and a plane of broadest entrance angularity. Figs. 16A to 16J are isobrightnPcc curves which illustrate the predicted 25 .~,L,or~e~,liv~ pt;lrollllallce of a cube corner element m~tçhçd pair as depicted in Figs. 1-2. Generally, Figs. 16A to 16E dçmonctrate the inw~as;llg angular pl~ce~~~P!nt of the broadest planes of entrance angularity from the plane in which the cube corner Plr-..~-.lc are canted as the elemPnts are canted through increasing cant angles up to a cant angle which results in â 65-65-50 base triangle. Thereafter, ~ 30 i~ ,as;llg the cant angle of opposing cube corner çlemçnts results in decreasing angular displ~cçmf nt between the broad planes of entrance angularity and the plane in which the cube comer elf m~ntc are canted.
Fig. 16A is an isobrightnçse profile for a single cube corner f.'iF~ having an equilateral base triangle and a refractive index of 1.59. It exhibits the we11-known six-lobe isob~ .f ~c pattetn, resulting from the three axes of symmetry of the equil~tP-~a1 base triangle cube corner F~ mf nt Figs. 16B to 16J illustrate the dislc,- lion of the isobri~htnçcc pattern of a cube corner çl~mf~nt m~tçhed pair as the oppos:ng cube corner Pl~ .".~ c are canted through increasing cant angles. The opposing cube corner fl- ~"~,lY are canted in a plane which extends holi~onlally0 though the isobri~htn~cc graph. Fig.16B rel)res~.lLs a 1.60 degree cant, to yield an isosceles base triangle having inl~luded angles which measure applvx ...~ y 61 degrees, 61 degrees, and 58 degrees. Fig. 16C l~plesellls a 3.14 degree cant, to yieid an isosceles base triangle having inc1uded angles which measure appro,.;...~lFly 62 degrees, 62 degrees, and 56 degrees. Fig. 16D repre~e~ a 4.63 degree cant, to yieid lS an iCQsceles base triangle having included angles which measure appro,~;,~lf-ly 63 degrees, 63 degrees, and 54 degrees. Fig. 16E lt;plese.lls a 7.47 degree cant, to yield an iCoscF~les base triangle having in~ rled angles which measure applvx;~lA~ely 65 degrees, 65 degrees, and 50 degrees. Fig. 16F lt;plf se.lls a 10.15 degree cant, to yield an isosccles base triangle having inrlu~ed angles which measure applox;.n~lf~ly 20 67 degrees, 67 degrees, and 46 degrees An f ~ lion ofthis sequence of isobri~htness graphs illu~ es the incr~s;ll~ angular ~icpl~cFmpnt of the broadest planes of entrance angularity from the plA~e in which the opposing cube corner e~emPntc are canted.
The r~....A~ isobli~ ..çss graphs illustrate the decreasing angular 2s divergence bt;lwf;ell the broadest plane of e ll~ ce angularity and the plane in which OppGS;I-g cube corner e1e-..F,..l~ are canted.. Fig. 16G lt;presenls a 12.69 degree cant, to yield an icoscçles base triangle having in~lllded angles which measure applv~;~n~lçly 69 degrees, 69 degrees, and 42 degrees. Fig.16H l~leselll~ a 15.12 degree cant, to yield an icoscF~Ies base triangle having inr~ led angles which measure a~plu~;.n~çly 71 degrees, 71 degrees, and 38 degrees. Fig.16I rel~lese,ll~ a 17.46 degree cant, to yield an isosceles base triangle having int~luded angles which measure W 096/42024 PCTAUS~6J~3232 app,vx;~Ately 73 degrees, 73 degrees, and 34 degrees. Fig. 16J .ep,esc~,ls a 19.72 degree cant, to yield an isosceles base triangle having in~ ded angles which measure approx;...A~Iy 75 degrees, 75 degrees, and 30 degrees.
This series of isob. ;~ .e ~s graphs de"~ons~ es that as opposing cube corner s el~ are canted through increasing cant angles up to about 12 degrees, the e..l.~ce angularity ofthe article cQntimles to broaden in two subst~nti~ny p~.r,nr1 ~ r planes which are oriented at approx;...~ ~ly 45 degrees relative to the plane in wbich the cube corner e~ are canted. Further canting increases the e.,L.~Ice angularity in these planes and de~,-cases the e,~ ce angularity in a plane 0 which is sub~L~--lially coinri~lPt)t with the plane of cant. While the opli---ul-. amount of canting appears to be app.u,~ lçly 7.47 degrees, co.-t;sponding to a 65-65-50 base tri~le it will be apprecialed that a range of cant angles ~oyten~ing from app~u~ ely S degrees to ap~-v~ ely 12 degrees appear feasible to produce a -v.~nective article having two broad planes of entrance angularity oriented 5 ap~)~V~ y pel~ç~ c~ r to one another.

Claims (12)

What is claimed is:

1. A cube corner article, comprising:
a substrate having a base surface disposed in a base plane; and a structured surface (100, 120) displaced from the base surface and including an array of cube corner element matched pairs formed by three intersecting sets of substantially parallel grooves (102, 104, 106; 122, 124, 126);
characterized in that (a) only two groove sets (104, 106; 124, 126), intersect at an angle less than 60 degrees; and (b) a plurality of cube corner elements in the array comprise a base triangle bounded by one groove from each of the three intersecting groove sets (102, 104, 106; 122, 124, 126); the base triangle being scalene.

2. A cube corner article according to claim 1, wherein:
adjacent grooves in a groove set are separated by a distance that measures less than 600 microns.

3. The cube corner article of claim 1, wherein:
at least one groove in at least one groove set includes a section surface.

4. The cube corner article of claim 1, wherein:
the article comprises a master article.

5. The cube corner article of claim 1, wherein:
the article comprises a mold suitable for forming retroreflective sheeting.

6. The cube corner article of claim 1, wherein:
the article comprises retroreflective sheeting.

7. The cube corner article of claim 6, wherein:
a portion of the article is coated with a specularly reflective substance.

8. A thin, flexible retroreflective sheeting formed from a substantially optically transparent material, comprising:
a substrate having a base surface disposed in a base plane;
a structured surface (100, 120) displaced from the base surface and including an array of canted cube corner element matched pairs formed by three mutually intersecting sets of substantially parallel grooves (102, 104, 106; 122, 124, 126), each matched pair including a first cube corner element and an optically opposing second cube corner element, characterized in that (a) a plurality of cube corner elements in the array have their symmetry axes canted in a first plane;
(b) a plurality of cube corner elements in the array comprise a base triangle bounded by one groove from each of the three intersecting groove sets, the base triangle being scalene; and (c) the sheeting exhibits its broadest range of entrance angularity in a second plane, angularly displaced from the first plane.

9. The retroreflective sheeting of claim 8, wherein:
the cube comer elements are oriented such that the second plane intersects an edge of the article at an angle less than 15°.

10. The retroreflective sheeting of claim 8, wherein:
the cube corner elements are oriented such that the second plane intersects an edge of the article at an angle less than 5°.

11. The retroreflective sheeting of claim 8, wherein:
the sheeting exhibits a substantially similarly broad range of entrance angularity in a third plane; and the third plane intersects the second plane at an angle between 75° and 90°.

12. The retroreflective sheeting of claim 8, wherein:
the sheeting exhibits a substantially similarly broad range of entrance angularity in a third plane; and the third plane intersects the second plane at a 90° angle.