The error diffusion filter in this paper is optimized with respect to the ideal blue noise pattern corresponding to a single tone level. The filter coefficients are optimized by the minimization of the squared error norm between the Fourier power spectra of the resulting halftone and the blue noise pattern. During the process of optimization, the binary pattern power spectrum matching algorithm is applied with the aid of a new blue noise model. The number of the optimum filters is equal to that of different tones. The visual fidelity of the bilevel halftones generated by the error diffusion filters is evaluated in terms of a weighted signal-to-noise ratio, Fourier power spectra, and others. Experimental results have demonstrated that the proposed filter set generates satisfactory bilevel halftones of grayscale images.