Simultaneous reconstruction of surface shapes and inhomogeneity of optics using sampling iteration error analysis

Consisting of the front and rear surfaces of the measured optics and two reference surfaces, the four-surface interferometry system can obtain parameters of the measured surface profiles and refractive index inhomogeneity by acquiring and decoding the fringe patterns of the measured plate and the rear reference plate respectively. However, the difficulty of such measurement comes from the complex superposition of at least six interference sub-signals, and the setting of the phase-shift interval determines whether the harmonics can be reconstructed or not. To improve the measurement accuracy, two kinds of convolutional fitting window functions are redesigned based on the Hanning window to enhance the function performance. Then, by analyzing the reconstruction errors of each wavefront under different combinations of sampling intervals and cavity lengths during four-surface measurements, an error quantization matrix obtained by triple iteration is constructed. By setting a threshold condition, the optimal phase-shifts under different cavity lengths can be matched adaptively. The multi-surface measurement accuracy and reliability of adaptive phase-shift matching are verified in the simulation. The interferogram acquisition and phase demodulation of two transparent flats were performed using a Fizeau wavelength-tuning interferometer, and the reconstruction errors of the surfaces in the repetitive measurements further verified the reliability of the proposed method.