A security device for security documents provides an angle-dependent Moiré effect. A security device for a security document and method for making the security device are provided. At least two interlaced laser engraved images form an angle dependent parallax effect. First and second images are laser engraved at a substrate of the security document. To render the security device more difficult to copy, a colour changing effect or a nonreciprocal transmission effect may be achieved by adding a coloured (absorptive or emissive) layer between or within non-laser engravable layers situated between the laser engravable layers, and/or by adding a patterned phase diffraction grating situated between the laser engravable layers.