A novel hybrid trust region minimax fitting algorithm for accurate dimensional metrology of aspherical shapes

摘要

Ultra-high precision measuring machines enable to measure aspheric shapes with an uncertainty of few tens of nanometres. The resulting clouds of points are then associated to theoretical model at the same level of accuracy so as to obtain parameters that indicate about form error. Minimum zone (MZ), defined as the least value of peak to valley (PV), is widely used to assess form error. Least squares method (L-2) is often used to determine MZ but the resulting value is usually overestimated. For this reason, L-2 is replaced by L-infinity norm because it gives a more accurate value of MZ since it directly minimizes PV. Using L-infinity norm results in a non-smooth optimization problem and consequently its resolution becomes more challenging compared to L-2.