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A mask is provided which has a complex transmission function and which includes a transparent layer and a non-transparent layer. The transparent layer has three types of phase-shifting elements, each imparting a different phase shift relative to the others, with the phase-shifting elements alternating in both x and y directions. The non-transparent layer has holes arranged in an approximately equally spaced grid pattern defined by common points in borders of the phase-shifting elements. Centers of at least two holes in the non-transparent layer have different offsets from their corresponding common points. Also provided is a mask blank which includes a transparent layer and a non-transparent layer. The transparent layer has three types of phase-shifting elements, each imparting a different phase shift relative to the others, with the phase-shifting elements alternating in both x and y directions.