Multi-parameter reconstruction of interference harmonics by effective tuning combination selection and sampling boundary fitting

[Display omitted] •In flexible cavities, multi-surface measurement can be realized with high accuracy and lower iterative cost.•Efficient and effective combinations at different cavity lengths and sampling frequencies can be obtained.•Two harmonic selection modes are developed and more optimal phase-shifting schemes are designed.•Less iterative computational cost makes the multi-surface interferometry technique easier to be applied. To efficiently and accurately realize four-surface measurements with flexible cavity lengths and sampling frequencies, a wavelength-tuning phase-shifting matching algorithm based on harmonic selection modes is developed. The developed MPSA-AHR method utilizes pre-iterative wavefront reconstruction errors to quantitatively analyze the multi-harmonic reconstruction performance and to obtain efficient sample combinations. Combined with the densified power spectral density method, the harmonic frequencies can be obtained with high accuracy, enabling the simultaneous measurement of front/rear surfaces, thickness variation, and inhomogeneous distribution of refractive index for the tested transparent plates. The proposed method outperforms the existing methods and can realize multi-surface measurements with fewer sampling frames under the designed harmonic selecting mode, which is verified by sufficient simulations and error analysis under several measurement conditions. Repeatability measurements of a transparent plate with an average thickness of 50 mm using a Fizeau wavelength-tuning phase-shifting interferometer also verify the practical validity of our method.