Patent ID: 8514407

Claim:
An apparatus for measuring a shape of a surface to be measured, the apparatus comprising: a measurement head which measures a distance between a reference point and a point of the surface by detecting interference between test light and reference light, wherein the test light emits through the reference point from the measurement head, reflects off the surface, and returns to the reference point; a scanning mechanism which scans the measurement head; and a processor which calculates the shape of the surface based on the distance measured using the measurement head and coordinates of the reference point, wherein, letting (s, t, u) be the coordinates of the reference point, (x, y, z) be coordinates of the point on the surface, q be the distance from the reference point to the point on the surface, and (α β γ) be a unit normal vector at the point on the surface, the processor calculates: (α β γ) using the measured q based on: (α β γ)=(∂q/∂s ∂q/∂t ∂q/∂u); and the shape of the surface using the calculated (α β γ) and the measured q based on: ( xyz )=( stu )−q(αβγ), and wherein the scanning mechanism scans the measurement head so that that the reference point is positioned at a plurality of positions, wherein the measurement head measures the distance q for each of the plurality of positions, and wherein the processor calculates the unit normal vectors (α β γ) based on the coordinates of the plurality of positions and the distances q respectively corresponding to the plurality of positions.