Abstract
A new method is proposed for computing the microrelief of phase diffractive optical elements (DOEs) forming 2D images with kinematic effects of motion. The DOE is subdivided into elementary areas with a size of approximately 50 microns. The synthesis of optical security elements includes the computation of the beam pattern in each elementary area. The beam pattern in each elementary area uniquely defines the phase function of the optical element. The computation of the phase function involves solving a nonlinear operator equation. Efficient methods are developed for computing the microrelief of DOEs forming 2D images with kinematic effects of motion. Sample optical elements are made using electron-beam technology. The microrelief is shaped with a precision of ∼10 nm, and the resolution is equal to ∼0.1 micron. The synthesis method developed is universal in nature. Given different sets of frames, one can achieve different behaviours of the motion of image fragments. The new optical elements can be used to protect banknotes, passports, IDs, and brands against counterfeiting.
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