Current Optics and Photonics

Optical Society of Korea (한국광학회)
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Retrieving Phase from Single Interferogram with Spatial Carrier Frequency by Using Morlet Wavelet

  • Hongxin Zhang (Robotics & ITs Engineering Research Center, School of Mechanical and Electronic Engineering, Harbin University of Science and Technology) ;
  • Mengyuan Cui (Robotics & ITs Engineering Research Center, School of Mechanical and Electronic Engineering, Harbin University of Science and Technology)
  • Received : 2023.05.09
  • Accepted : 2023.07.17
  • Published : 2023.10.25
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Abstract

The Morlet wavelet transform method is proposed to analyze a single interferogram with spatial carrier frequency that is captured by an optical interferometer. The method can retain low frequency components that contain the phase information of a measured optical surface, and remove high frequency disturbances by wavelet decomposition and reconstruction. The key to retrieving the phases from the low-frequency wavelet components is to extract wavelet ridges by calculating the maximum value of the wavelet transform amplitude. Afterwards, the wrapped phases can be accurately solved by multiple iterative calculations on wavelet ridges. Finally, we can reconstruct the wave-front of the measured optical element by applying two-dimensional discrete cosine transform to those wrapped phases. Morlet wavelet transform does not need to remove the spatial carrier frequency components manually in the processing of interferogram analysis, but the step is necessary in the Fourier transform algorithm. So, the Morlet wavelet simplifies the process of the analysis of interference fringe patterns compared to Fourier transform. Consequently, wavelet transform is more suitable for automated programming analysis of interference fringes and avoiding the introduction of additional errors compared with Fourier transform.

Keywords

Acknowledgement

This research is supported by the Natural Science Foundation of Heilongjiang Province of China (No. LH2021E080).

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