US 12,214,612 B2
Method of designing a light-redirecting surface of a caustic layer, an optical security element comprising the designed light-redirecting surface of the caustic layer, a marked object, use and method of authenticating the object
Andrea Callegari, Chavannes-près-Renens (CH); Mathieu Gillieron, Cossonay-Ville (CH); and Oscar De Feo, Lausanne (CH)
Assigned to SICPA HOLDING SA, Prilly (CH)
Appl. No. 17/282,983
Filed by SICPA HOLDING SA, Prilly (CH)
PCT Filed Oct. 4, 2019, PCT No. PCT/EP2019/076949
§ 371(c)(1), (2) Date Apr. 5, 2021,
PCT Pub. No. WO2020/070304, PCT Pub. Date Apr. 9, 2020.
Claims priority of application No. 18198938 (EP), filed on Oct. 5, 2018.
Prior Publication US 2021/0339553 A1, Nov. 4, 2021
Int. Cl. B42D 25/324 (2014.01); B42D 25/36 (2014.01); G02B 27/00 (2006.01); G02B 27/09 (2006.01)
CPC B42D 25/324 (2014.10) [B42D 25/36 (2014.10); G02B 27/0012 (2013.01); G02B 27/0927 (2013.01)] 8 Claims
OG exemplary drawing
 
1. A method of forming a caustic layer having a relief pattern formed on a lens element and adapted to redirect incident light received from a light source and to form a projected image containing a caustic pattern, the method comprising computer implemented steps of:
providing a discrete representation of an input target image comprising a set P of N image pixels pi of coordinates {(xi,yi)} in an image plane with associated nonzero target light intensities {Ii}, i=1, . . . , N, distributed within a given area of the input target image and corresponding to a target caustic pattern of the input target image;
computing a piecewise representation of a light-redirecting surface z=F(x,y) of the caustic layer, with height z above an (x,y) coordinates plane, based on a representation of the light-redirecting surface by intersecting pieces of surfaces z=fi(x,y), i=1, . . . , N, respectively obtained from stationarity of an optical path length of rays refracted, or reflected, by the caustic layer and focused on points P(i) of the image plane of coordinates (xi,yi), i=1, . . . , N, wherein each piece of surface z=fi(x,y) is a surface of revolution around an axis passing through a point P(i) and having a vertex at point (xi,yi,zi), with height zi=fi(xi,yi), i=1, . . . , N, the piecewise representation of the light-redirecting surface associated with respective values of the heights of the N vertices being formed by an envelope of intersections of the corresponding N pieces of surfaces z=fi(x,y), i=1, . . . , N;
for a given set of respective values of heights z1, . . . , zN of the vertices of the N pieces of surfaces, calculating a corresponding set of values of light intensities I(1), . . . , I(N) which are respectively focused on points P(1), . . . , P(N) by the caustic layer redirecting incident light via the associated piecewise light-redirecting surface; and
calculating the respective values of the N heights z1, . . . , zN of the N vertices of the corresponding N pieces of surfaces that causes the differences between the values of calculated light intensities I(1), . . . , I(N) focused on the points P(1), . . . , P(N) via the associated light-redirecting surface and the respective corresponding values of the target light intensities I1, . . . , IN to be minimized to a least value as a result of calculating the respective values of the N heights z1, . . . , zN; and
forming the caustic layer having the light-redirecting surface with the calculated values of the N heights z1, . . . , zN of the N vertices of the corresponding N pieces of surfaces on an optical material substrate.