Tilt-effect of holograms and images displayed on a spatial light modulator.

We show that a liquid crystal spatial light modulator (LCOS-SLM) can be used to display amplitude images, or phase holograms, which change in a pre-determined way when the display is tilted, i.e. observed under different angles. This is similar to the tilt-effect (also called "latent image effect") known from various security elements ("kinegrams") on credit cards or bank notes. The effect is achieved without any specialized optical components, simply by using the large phase shifting capability of a "thick" SLM, which extends over several multiples of 2π, in combination with the angular dependence of the phase shift. For hologram projection one can use the fact that the phase of a monochromatic wave is only defined modulo 2π. Thus one can design a phase pattern extending over several multiples of 2π, which transforms at different readout angles into different 2π-wrapped phase structures, due to the angular dependence of the modulo 2π operation. These different beams then project different holograms at the respective readout angles. In amplitude modulation mode (with inserted polarizer) the intensity of each SLM pixel oscillates over several periods when tuning its control voltage. Since the oscillation period depends on the readout angle, it is possible to find a certain control voltage which produces two (or more) selectable gray levels at a corresponding number of pre-determined readout angles. This is done with all SLM pixels individually, thus constructing different images for the selected angles. We experimentally demonstrate the reconstruction of multiple (Fourier- and Fresnel-) holograms, and of different amplitude images, by readout of static diffractive patterns in a variable angular range between 0° and 60°.