The noise perception model proposed by Dooley and Shaw1 includes an experimental function decreasing monotonically with average density. The sample patches they used did not include any periodic structure such as a halftone screen. To establish a similar model for digital images having periodic structures, we first tried to obtain the visual sensitivity function for graininess detection using a noise-free halftone test-chart distributed by the Society of Electrophotography of Japan (SEPJ). The chart consists of halftone tints with 65 to 200 lpi rulings and area coverage ranging from 5% to 95%. Among each patch group of constant area coverage, three observers were asked to choose the threshold patch at which the halftone structure or, in other words, graininess, can be detected. The result shows that human vision has a sensitivity peak at area coverage of about 20%. Because this result must be closely associated with the density dependence of noise detectivity of human vision, we will assume that the threshold patches represent equivalent graininess. Next, similar to the treatment adopted by Dooley and Shaw, the graininess index without the density dependence function was calculated for every patch in the test chart. Our approach is different from theirs in that we use fluctuations of lightness to calculate the Wiener spectrum instead of reflection density. Finally, we calculated our graininess index using a new sensitivity function based on a model describing our observations. To confirm our approach, we made subjective assessments for the patches including selected patches from the test chart, and obtained good relationship between our graininess indexes and subjectively evaluated levels. urthermore, we applied our model to hardcopies of gray scales made by some digital copiers on the market. The hardcopies have their own specific screens depending on the model of copier. Our results reflected the subjective judgments reasonably well.