Thin optical security element and method of designing it

A method of designing a reflective light-redirecting surface, or a refractive transparent or partially transparent light-redirecting surface, having a relief pattern of depth δf, of an optical security element adapted to redirect incident light received from a point-light source and form a projected image containing a caustic pattern on a projection surface, said caustic pattern reproducing a reference pattern and being visually recognizable, comprising:

• a) calculating a relief pattern profile having discontinuities;
• and
• b) machining a surface of an optical material piece according to the relief pattern profile having discontinuities calculated at a), thereby having a machined profile of the relief pattern with abrupt variations corresponding to the discontinuities of the relief pattern profile calculated at a),
• wherein, at a), calculating the relief pattern profile having discontinuities further comprises:
• slicing an initial relief pattern profile of a model light-redirecting surface into smaller contiguous profile portions, said initial relief pattern profile having a depth δi greater than δf and being operable to reproduce by optical path simulation said caustic pattern on the projection surface under illumination by the point-light source, the slicing generating a boundary surface between any two contiguous profile portions which extends parallel to an optical axis of said model light-redirecting surface;
• and
• collapsing along the optical axis each profile portion comprised between two consecutive boundary surfaces, thereby forming the calculated relief profile having a discontinuity along each boundary surface,
• at a), collapsing a profile portion of the initial relief pattern profile, of which height is measured with respect to the optical axis of said model light-redirecting surface and which extends above a base plane perpendicular to said optical axis, is performed by translating, parallel to the optical axis and toward the base plane, the profile portion by a distance value corresponding to a minimal height at which its boundary surfaces intersect said profile portion, thereby obtaining the calculated relief profile having a relief pattern of reduced depth less than δi;
• and
• at b), the surface of the optical material piece is machined according to the calculated relief pattern profile of reduced depth less than δi,
• thereby obtaining the machined reflective light-redirecting surface, or a refractive transparent or partially transparent light-redirecting surface, of the optical security element with the relief pattern of reduced depth δf less than δi.