Mask having an arbitrary complex transmission function

A mask having a complex transmission function, comprising:

• a transparent layer having three types of phase-shifting elements arranged such that points common to borders of all three types form a regularly spaced grid;
• and
• a non-transparent layer having holes coinciding with the points on the grid,
• wherein each type of phase-shifting element imparts a different phase shift relative to the others, and wherein centers of the holes in the transparent layer have different offsets from the points on the grid.

A mask having a complex transmission function, comprising:

• a transparent layer having three types of phase-shifting elements, each imparting a different phase shift relative to the others;
• and
• a non-transparent layer having holes arranged in an approximately equally spaced grid pattern,
• wherein the holes are approximately identical in size and overlap the three types of phase-shifting elements in different combinations.

A mask blank comprising:

• a transparent layer having three types of phase-shifting elements arranged such that points common to borders of all three types form a regularly spaced grid;
• and
• a non-transparent layer,
• wherein each type of phase-shifting element imparts a different phase shift relative to the others.