Flatness error resistant photomask measurement techniques

An apparatus, comprising:

• a support configured to maintain a substrate at one or more orientations using one or more support members;
• an interferometer configured to:
• measure a first flatness measurement of the substrate at a first orientation relative to a vertical direction;
• measure a second flatness measurement of the substrate at a second orientation relative to the vertical direction;
• measure a third flatness measurement of the substrate at a third orientation relative to a vertical direction;
• and
• measure a fourth flatness measurement of the substrate at a fourth orientation relative to a vertical direction, each of the first orientation, the second orientation, the third orientation, and the fourth orientation being at a different orientation relative to the vertical direction;
• and
• a controller configured to:
• generate a first set of differences between one of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement and another of the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement;
• fit the first set of differences to respective orthogonal polynomials and generating a fifth flatness measurement;
• select a flatness measurement from the first flatness measurement, the second flatness measurement, the third flatness measurement, and the fourth flatness measurement;
• replace orthogonal polynomial components associated with the selected flatness measurement with orthogonal polynomial components associated with the fifth flatness measurement;
• and
• generate a true flatness of the substrate.