Analysis of ordered dither for arbitrary sampling lattices and screen periodicities

Ordered dither is considered a simple and effective method of image binarization. For rectangular lattices, it has been shown that this method of spatially periodic quantization causes aliasing in the frequency domain, resulting in a degradation of halftone image quality. This result is extended by deriving an expression for the spectrum of the halftoned image, generalized for any sampling lattice and any screen periodicity. This expression will show the explicit relationship between screen function and halftone image quality. Using this expression, the nonlinearities associated with four optimized screens are analyzed to determine which screens are best suited to halftone rectangularly and hexagonally sampled images