Full-complex amplitude modulation with binary spatial light modulators

Imperfections and nonrobust behavior of practical multilevel spatial light modulators (SLMs) degrade the performance of many proposed full-complex amplitude modulation schemes. We consider the use of more robust binary SLMs for this purpose. We propose a generic method, by which, out of K binary (or 1 bit) SLMs of size M×N, we effectively create a new 2(K)-level (or K bit) SLM of size M×N. The method is a generalization of the well-known concepts of bit plane representation and decomposition for ordinary gray scale digital images and relies on forming a properly weighted superposition of binary SLMs. When K is sufficiently large, the effective SLM can be regarded as a full-complex one. Our method is as efficient as possible from an information theoretical perspective. A 4f system is discussed as a possible optical implementation. This 4f system also provides a means for eliminating the undesirable higher diffraction orders. The components of the 4f system can easily be customized for different production technologies.