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1. (WO2019063779) OPTICAL SECURITY ELEMENT
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CLAIMS

1. Optical security element comprising a reflective light-redirecting surface, or a refractive transparent or partially transparent light-redirecting surface of refractive index n, having a relief pattern of depth δ adapted to redirect incident light received from a point-like source, at a distance ds from the light -redirecting surface, and form a projected image containing a caustic pattern on a projection surface disposed at a distance di from the light-redirecting surface, said caustic pattern reproducing a reference pattern, characterized in that:

upon illumination by the light source of an area of value A of the relief pattern and delivering an illuminance value EA by the optical security element to the projection surface, an average illuminance value Εαι over a circular area of value oil selected within an area of the projected image on the projection surface fulfills the following projection criterion Εαι ≤ EA (1/2 + a0 i + V(l/4 + a0/«i) ) , with scaling area parameter 0 = 4n di δ for the reflective light-redirecting surface, or a0 = 2n (n-1) di δ for the refractive light-redirecting surface, and <¾ is smaller than the area value A.

2. The optical security element according to claim 1, wherein a value of d± is less than or equal to 30 cm and a value of the ratio ds/di is greater than or equal to at least 5.

3. The optical security element according to any one of claims 1 and 2, wherein a value of depth δ of the relief pattern is less than or equal to 30 μνα.

4. The optical security element according to any one of claims 1 and 2, wherein a value of depth δ of the relief pattern is less than or equal to 250 μχα.

5. The optical security element according to any one of claims 1 to 3 , wherein the relief pattern is disposed over a flat base, an overall thickness of the optical security element being less than or equal to 100 μιη.

6. Method for designing a relief pattern of depth less than or equal to a value δ of a reflective light-redirecting surface, or a transparent or partially transparent light -redirecting surface of refractive index n, adapted to redirect incident light received from a point-like source, at a distance ds from the light-redirecting surface, and form a projected image containing a caustic pattern on a flat projection surface disposed at a distance di from the light-redirecting surface, so that upon illumination by the light source of an area of value A of the relief pattern and delivering of an illuminance value EA by the optical security element to the projection surface, an average illuminance value Ed over a circular area of value x selected within an area of the projected image on the projection surface fulfills the following projection criterion Εαι ≤ EA (1/2 + Οίο/θίι + V(l/4 + οίο/οίι) ) , with scaling area parameter a0 = 4n di δ for the reflective light-redirecting surface, or a0 = 2n (n-1) di δ for the refractive light -redirecting surface, and oil is smaller than the area value A, said method being characterized by comprising the steps of:

a) selecting a digital image of a reference pattern to be reproduced by the caustic pattern on the projection surface, the digital image comprising a total number of pixels NA and a sum of all pixel values over the digital image being IA, by checking that for each circular area of N pixels within the digital image, with N integer and 1 ≤ N ≤ NA, a value I (N) of a sum of each pixel value of the N pixels in the circular area is less than a value Imax(N) = N (IA/NA) (1/2 + N0/N + V(l/4 + N0/N) ) , wherein N0 is a number of pixels given by NA(a0/A) within the digital image;

b) calculating a relief pattern of depth less than or equal to δ corresponding to the reference pattern on the digital image selected at step a) ; and

c) machining a surface of an optical material substrate to form a light-redirecting surface reproducing the relief pattern calculated at step b) , thereby obtaining an optical security element comprising said machined light-redirecting surface .

7. Method according to claim 6, wherein the step a) of selecting a digital image of a reference pattern comprises a further step of modifying a candidate digital image of the reference pattern of which a part does not fulfill the selection criterion that I (N) is less than Imax (N) , by adapting the pixel values within said part of the candidate digital image, by making said part of the candidate digital image with adapted pixel values to comply with the selection criterion for any N, with l < N NA, thereby providing a modified candidate digital image to be selected.

8. Method according to claim 7, wherein the pixel values of the candidate digital image are adapted by filtering with a filter the candidate image to reduce image contrast.

9. Method according to any one of claims 6 to 8 , wherein the machining of the surface of the optical material substrate comprises any one of ultra-precision machining, laser ablation, and lithography.

10. Method according to any one of claims 6 to 9, further comprising that the machined light-redirecting surface is a master light-redirecting surface to be used to build a replica.

11. Method according to claim 10, further comprising replicating the machined light-redirecting surface on a substrate .

12. Method according to any one of claims 10 and 11, wherein replication comprises one of UV casting and embossing.

13. Method of visually authenticating an object, marked with an optical security element according to claim 1, by a user, comprising the steps of:

illuminating the light-redirecting surface of the optical security element with a point-like light source at the distance ds from the light-redirecting surface;

visually observing on the caustic pattern as projected on the projection surface at distance di form the optical security element; and

deciding that the object is genuine upon evaluation by the user that the projected caustic pattern is visually similar to the reference pattern.