Time-multiplexed optical Hadamard image transforms with ferroelectric-liquid-crystal-over-silicon spatial light modulators

The Hadamard transform is an example of a matrix transform that allows images to be represented in terms of orthogonal basis functions with binary-valued matrix elements. Such basis functions can be displayed on binary amplitude modulating ferroelectric-liquid-crystal-over-silicon spatial light modulators, permitting novel, real-time, and high-speed implementation of the transform on incoherently illuminated input scenes. An example of an optical Hadamard transform performed in real time by using a spatial light modulator is described. To show the validity of this optical decomposition, we electronically reconstruct the transformation data for comparison with the original input scene.