In many cases including Dr. W. F. Schreiber's writing, the Adobe Accurate Screens etc., designing to construct the rational tangent screens is performed in the image domain. This paper reports a newly developed construction method of digital screen sets. In the proposed method, the design of rational tangent screens having screen angles of ±15-degree and 45-degree is performed in the spatial frequency domain. At first, frequency components generated by superimposing the +15-degree halftone screen on the -15-degree halftone screen are investigated. Next, the most appropriate combination of ±15-degree screens and 45-degree screen are studied in the spatial frequency domain to determine conditions of moire-free and appearance of conventional rosette shapes. In the process of studies, the “rosette” in frequency domaine is defined and rosette shapes corresponding to various rational tangent values are depicted. A method named “Multi- unit Area Method” has been proposed in this report to convert the spatial frequency component array having rational tangent values to the halftone dot array in image domain. Examples of the method for ±15-degree and 45-degree halftone screen sets which have conditions to provide the conventional rosettes are described in Chapter 4. Because the minimum area of threshold matrix pattern to be stored (MTP) of realized halftone screen contains lots of unit areas, an automatic mapping method of MTP which is left for the next report has been developed for the application. A thermal printer image halftoned by using the Multi-unit Area Method is shown in Figure 9 on which the conventional rosette shapes may be observed clearly. In conclusion, this report provides a theoretical basis of the digital screening process.
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