We present raster image processing algorithms for rehalftoning error diffused halftones and producing interpolated error diffused halftones. Rehalftoning converts a halftone created by one method into one created by another method. In interpolated halftoning, interpolation increases the image size before halftoning, e.g. for printing. Both rehalftoning and interpolated halftoning introduce blur and noise in the output image. To compensate for the blur, we use modified error diffusion, which has a variable gain parameter to control the sharpness. We derive optimal formulas for the sharpness control parameter to make the overall frequency response flat. The high-frequency noise is masked by error diffusion. The proposed algorithms yield halftones of high fidelity at a low computational cost.