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.