Analytical Modeling of Geometrical Dot Gain Relationship Between AM and FM Halftone Screening Technologies

Geometrical dot gain represents a fundamental physical phenomenon influencing tonal reproduction in halftone printing, particularly in offset and flexographic processes. However, a formally defined analytical framework capable of determining the tonal conditions of equal geometrical dot gain, particularly for hybrid screening design and tonal consistency optimization, has not yet been clearly established. In this study, a geometrical analytical model is formulated to determine the transition points of equal geometrical dot gain between AM and FM screening. Two analytical approaches were applied. The first compares the total contour length of halftone elements in both screening technologies, while the second relates the AM dot diameter to predefined FM microdot sizes. Calculations were performed for eight AM screen rulings (120–340 lpi) and six FM microdot diameters (20–50 μm) under predefined geometrical conditions (2540 dpi output resolution and circular dot shape). The results indicate that transition points predominantly occur within the highlight tonal region and systematically shift toward higher tonal percentages with increasing screen ruling. Both analytical procedures, although conceptually different, yield identical results, confirming the internal consistency of the model. The analytically determined transition points provide a geometrically justified basis for defining switching zones in hybrid and XM screening systems, enabling improved tonal stability and more consistent screening transitions.