Dot-Matrix Hologram Rendering Algorithm and its Validation through Direct Laser Interference Patterning

The fight against forgery of valuable items demands efficient and reasonably priced solutions. A security tag featuring holographic elements for anti-counterfeiting is one of them. However, the content and colours of a diffraction image that would be seen by an observer are often counterintuitive in the design stage. Here, we propose an original algorithm based on the conical diffraction formalism, which can be used to describe the variations of a diffraction image with respect to all aspects of observation. We validate the output of the algorithm by comparing it to test holograms, which we have produced by employing direct laser interference patterning (DLIP) in electrochemically grown nickel foil. We have employed a motorized femtosecond laser system to micro-machine arrays of 65 µm × 65 µm sized diffraction gratings with a defined orientation and pitch on the order of 1 µm. Based on completed diffraction efficiency measurements, we determined optimal ablation parameters, i.e. 57.4 mJ/cm² fluence per pulse and 1100 pulses/pixel. Furthermore, we show how accurate the proposed algorithm is through measured diffraction spectra as well as captured diffraction images of test holograms produced using the obtained parameters. Finally, we showcase anti-counterfeiting tag prototypes with complex holographic effects, i.e. colour reconstruction, animation effects, and image multiplexing. The proposed algorithm can severely shorten the time between design and production of a holographic tag, especially when realizing it via a competitive origination technology-DLIP.