Patent ID: 8462353

Claim:
An apparatus for measuring a shape of a surface to be measured, the apparatus comprising: a measurement head that measures a direction of a normal from the surface to a reference point by detecting test light, which is generated by emitting light that passes through the reference point from the measurement head, reflected from the surface and returning to the measurement head through the reference point; a scanning mechanism that scans the measurement head to move the reference point; and a processor that calculates the shape of the surface based on the direction of the normal measured using the measurement head and a position of the reference point, wherein, letting (s, t, u) be coordinates of the reference point, (x, y, z) be coordinates of a point on the surface, (α, β, γ) be a unit normal vector from the point (x, y, z) on the surface to the reference point, which is obtained through the measurement by the measurement head as the direction of the normal, and q 0 be a constant, the processor calculates: q using the measured (α, β, γ) based on: q=q 0 +∫(αds+βdt+γdu); and the shape of the surface using the calculated q and the measured (α, β, γ) based on (x, y, z)=(s, t, u)−q(α, β, γ).