A method of designing a refractive transparent or partially transparent light-redirecting surface, or a reflective light-redirecting surface, of 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 p i of coordinates {(x i,y i)} in the image plane with associated nonzero target light intensities {I i}, i=1,..., N, distributed within a given area of the target image and corresponding to a target caustic pattern of the target image; computing a piecewise representation of the light-redirecting surface z = F(x,y) of the caustic layer, with height z above the (x,y) coordinates plane, based on a representation of the light-redirecting surface by means of intersecting pieces of surfaces z = f i (x,y), i=1,..., N, respectively obtained from the stationarity of the optical path length of rays refracted, or reflected, by the caustic layer and focused on points P(i) of the image plane of coordinates (x i,y i), i=1,..., N, characterised in that each piece of surface z = f i (x,y) is a surface of revolution around an axis passing through the point P(i) and having a vertex at point (x i, y i, z i), with height z i = f i (x i,y i), 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 the intersections of the corresponding N pieces of surfaces z = f i (x,y), i=1,..., N; for a given set of respective values of heights z 1,..., z N of the vertices of the N pieces of surfaces, calculating a corresponding set of values of light intensities I,..., I which are respectively focused on the points P,..., P by the caustic layer redirecting incident light via the associated piecewise light-redirecting surface; and calculating the respective values of the N heights z 1,..., z N of the N vertices of the corresponding N pieces of surfaces which minimize the differences between the respective values of calculated light intensities I,..., I focused on the points P,..., P via the associated light-redirecting surface and the respective corresponding values of the target light intensities I 1,..., I N, thereby obtaining the light-redirecting surface having a relief pattern adapted to redirect incident light received from the light source and form a projected image containing the target caustic pattern of the target image. providing a discrete representation of an input target image comprising a set P of N image pixels p i of coordinates {(x i,y i)} in the image plane with associated nonzero target light intensities {I i}, i=1,..., N, distributed within a given area of the target image and corresponding to a target caustic pattern of the target image; computing a piecewise representation of the light-redirecting surface z = F(x,y) of the caustic layer, with height z above the (x,y) coordinates plane, based on a representation of the light-redirecting surface by means of intersecting pieces of surfaces z = f i (x,y), i=1,..., N, respectively obtained from the stationarity of the optical path length of rays refracted, or reflected, by the caustic layer and focused on points P(i) of the image plane of coordinates (x i,y i), i=1,..., N, characterised in that each piece of surface z = f i (x,y) is a surface of revolution around an axis passing through the point P(i) and having a vertex at point (x i, y i, z i), with height z i = f i (x i,y i), 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 the intersections of the corresponding N pieces of surfaces z = f i (x,y), i=1,..., N; for a given set of respective values of heights z 1,..., z N of the vertices of the N pieces of surfaces, calculating a corresponding set of values of light intensities I,..., I which are respectively focused on the points P,..., P by the caustic layer redirecting incident light via the associated piecewise light-redirecting surface; and calculating the respective values of the N heights z 1,..., z N of the N vertices of the corresponding N pieces of surfaces which minimize the differences between the respective values of calculated light intensities I,..., I focused on the points P,..., P via the associated light-redirecting surface and the respective corresponding values of the target light intensities I 1,..., I N, thereby obtaining the light-redirecting surface having a relief pattern adapted to redirect incident light received from the light source and form a projected image containing the target caustic pattern of the target image.