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

Abstract : 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 (L2) is often used to determine MZ but the resulting value is usually overestimated. For this reason, L2 is replaced by L∞ norm because it gives a more accurate value of MZ since it directly minimizes PV. Using L∞ norm results in a non-smooth optimization problem and consequently its resolution becomes more challenging compared to L2. In this paper, a novel minimax fitting method for accurate metrology of aspheres and freeform based on a hybrid trust region algorithm (HTR) is proposed. To assess performance of the introduced method, it was compared to an available minimax fitting algorithm based on a smoothing technique: exponential penalty function (EPF). The choice of EPF is justified by superior performances in comparison to existing techniques. Comparison was conducted on reference data, data available in literature and data gathered form measurements of a real optical high quality asphere. Results show superiority of HTR over EPF in both returned PV values and execution time.
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Submitted on : Tuesday, November 23, 2021 - 2:05:49 PM
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Yassir Arezki, Hichem Nouira, Nabil Anwer, Charyar Mehdi-Souzani. A novel hybrid trust region minimax fitting algorithm for accurate dimensional metrology of aspherical shapes. Measurement - Journal of the International Measurement Confederation (IMEKO), Elsevier, 2018, 127, pp.134 - 140. ⟨10.1016/j.measurement.2018.05.071⟩. ⟨hal-01822156⟩



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