A theory of binary images (two density levels) is presented. By considering the spatial frequency response function of the viewer, it is shown that binary images can provide a good representation of band-limited, continuous-tone images. The analytical formulation given permits a quantitative evaluation of effective image errors for a large class of binary images. As the spacing between binary elements decreases, the image improves until the spacing is about one-third the period of the highest spatial frequency in the continuous image. The analysis is applied to the design of transparency masks for spatial modulation of light beams. These shaped beams are used for input and output image scanning as part of digital image-processing operations. A binary gaussian function has been generated which effectively approximates a continuous gaussian to within ±0.5%.
T. W. Barnard, "Binary Imagery and Its Application to Beam Shaping," Appl. Opt. 10, 2274-2278 (1971)