Abstract: This invention discloses an improved method and apparatus for generating a screened reproduction of an image. The apparatus comprises a matrix defining an arrangement of a plurality of areas within a printing dot, each having an assigned reference value. The screening logic apparatus receives input density information with respect to an image and includes apparatus for assigning to each input density a corresponding plurality of reference values. The apparatus also includes a method for combining with each of the plurality of reference values a random additional reference value, thereby defining a randomized plurality of reference values. The apparatus also causes the exposure of those areas in the matrix having reference values which correspond to the randomized plurality of reference values.