This paper considers the capacity of two-dimensional optical intensity channels in which transmit images are constrained to be binary-level. Examples of such links exist in holographic storage, page-oriented memories, optical interconnects, two-dimensional barcodes, as well as MIMO wireless optical links. Data are transmitted by sending a series of time-varying binary-level optical intensity images from transmitter to receiver. Strict spatial alignment between transmitter and receiver is not required nor is independence among the spatial channels assumed. Our approach combines spatial discrete multitone modulation developed for spatially frequency selective channels with halftoning to produce a binary-level output image. Data is modulated in spatial frequency domain as dictated by a water pouring spectrum over the optical transfer function as well as channel and quantization noise. A binary-level output image is produced by exploiting the excess spatial bandwidth available at the transmitter to shape quantization noise out of band. We present a general mathematical framework in which such systems can be analyzed and designed. In a pixelated wireless optical channel application, halftoning achieves 99.8% of the capacity of an equivalent unconstrained continuous amplitude channel using 1 megapixel arrays.
Spatial degrees of freedom in optical wireless channels can be exploited to multiplex data or to improve reliability. A short-range MIMO optical wireless system is presented which combines spatial discrete multitone modulation with digital halftoning to produce binary-level transmit images. An experimental prototype pixelated wireless optical channel is constructed and a rate of 450 Mbps is predicted for a 1 m link with 0.5 megapixel arrays at a frame rate of 7 kiloframes/sec. In long-range turbulent links, a novel receiver based on digital micro-mirror devices (DMD) is presented to provide spatial diversity by estimating the focal-plane signal distribution due to atmospheric turbulence. The performance of the DMD receiver is analyzed on a time-varying channel model rather than the "frozen atmosphere" model conventionally used. Symbol-error rates are simulated for a photon counting channel and show an improvement of about 3 dBo over a single-detector receiver.
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