The invention relates to a thin optical security element comprising a reflective or refractive light-redirecting surface having a relief pattern operable to redirect incident light from a light source and form a projected image on a projection surface, the optical parameters of this optical security element fulfilling a specific projection criterion such that the projected image comprises a caustic pattern reproducing a reference pattern that is easily visually recognizable by a person. The invention also relates to a method for designing a relief pattern of an optical security element.