Long-range gap detection with interferometric sensitivity using spatial phase of interference patterns

An apparatus for measuring a gap between first and second plates, comprising:

• a first plate;
• a second plate;
• said first plate having a gapping mark on a first surface of said first plate;
• said gapping mark including,
• a first grating on said first surface of said first plate, said first grating having a first uniform period in a first direction,
• a second grating on said first surface of said first plate, said second grating being adjacent to said first grating in said first direction, said second grating having a second uniform period in said first direction,
• a third grating on said first surface of said first plate, said third grating being adjacent to said first grating in a second direction, said second direction being substantially orthogonal to said first direction, said third grating having said second uniform period in said first direction, and
• a fourth grating on said first surface of said first plate, said fourth grating being adjacent to said third grating in said first direction, said fourth grating having said first uniform period in said first direction;
• a light source for illuminating a second surface of said second plate through said gapping mark on said first plate to produce an interference pattern;
• and
• a detector to measure spatial phases of said interference pattern, the spatial phases of said interference pattern corresponding to a gap between the first and second surfaces of said first and second plates.

A lithographic mask, comprising:

• a gapping mark on a first surface of the lithographic mask;
• said gapping mark including,
• a first grating on the first surface of the lithographic mask, said first grating having a first uniform period in a first direction,
• a second grating on the first surface of the lithographic mask, said second grating being adjacent to said first grating in said first direction, said second grating having a second uniform period in said first direction,
• a third grating on the first surface of the lithographic mask, said third grating being adjacent to said first grating in a second direction, said second direction being substantially orthogonal to said first direction, said third grating having said second uniform period in said first direction, and
• a fourth grating on the first surface of the lithographic mask, said fourth grating being adjacent to said third grating in said first direction, said fourth grating having said first uniform period in said first direction.

A method of measuring the gap between first and second plates, comprising:

• (a) providing a gapping mark on a first surface of the first plate, the gapping mark including a first grating on the first surface of the first plate, the first grating having a first uniform period in a first direction, a second grating on the first surface of the first plate, the second grating being adjacent to the first grating in the first direction, the second grating having a second uniform period in the first direction, a third grating on the first surface of the first plate, the third grating being adjacent to the first grating in a second direction, the second direction being substantially orthogonal to the first direction, the third grating having the second uniform period in the first direction, and a fourth grating on the first surface of the first plate, the fourth grating being adjacent to the third grating in the first direction;
• (b) illuminating a second surface of the second plate through the gapping mark on the first plate to produce an interference pattern;
• (c) measuring a phase of the interference pattern;
• and
• (d) determining a gap between the first and second surfaces from the measured phase of the interference pattern.