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ZHANG Kang-yang, NI Zi-hao, DONG Bo, BAI Yu-lei. Phase gradient estimation using Bayesian neural network[J]. Chinese Optics. doi: 10.37188/CO.2023-0168
Citation: ZHANG Kang-yang, NI Zi-hao, DONG Bo, BAI Yu-lei. Phase gradient estimation using Bayesian neural network[J]. Chinese Optics. doi: 10.37188/CO.2023-0168

Phase gradient estimation using Bayesian neural network

doi: 10.37188/CO.2023-0168
Funds:  Supported by National Natural Science Foundation of China (No. 61705047;No. 62171140) and Natural Science Foundation of Guangdong Province (No. 2021A1515011945;No. 2021A1515012598;No. 2021A1515011343).
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  • Objective 

    Strain reconstruction is a vital component in the characterization of mechanical properties using phase-contrast optical coherence tomography (PC-OCT). It requires an accurate calculation for gradient distributions on the wrapped phase map. In order to address the challenge of low signal-to-noise ratio (SNR) in phase gradient calculation under severe noise interference, a Bayesian-neural-network-based phase gradient calculation is presented.

    Method 

    Initially, wrapped phase maps with varying levels of speckle noise and their corresponding ideal phase gradient distributions are generated through a computer simulation. These wrapped phase maps and phase gradient distributions serve as the training datasets. Subsequently, the network learns the “end-to-end” relationship between the wrapped phase maps and phase gradient distributions in a noisy environment by utilizing a Bayesian inference theory. Finally, the Bayesian neural network (BNN), after being trained, accurately predicts the high-quality distribution of phase gradients by inputting the measured wrapped phase-difference maps into the network. Additionally, the statistical process introduced by BNN allows for the utilization of model uncertainty in the quantitative assessment of the network predictions’ reliability.

    Result 

    Computer simulation and three-point bending mechanical loading experiment compare the performance of the BNN and the popular vector method. The results indicate that the BNN can enhance the SNR of estimated phase gradients by 8% in the presence of low noise levels. Importantly, the BNN successfully recovers the phase gradients that the vector method is unable to calculate due to the unresolved phase fringes in the presence of strong noise. Moreover, the BNN model uncertainty can be used to quantitatively analyze the prediction errors.

    Conclusion 

    It is expected that the contribution of this work can offer effective strain estimation for PC-OCT, enabling the internal mechanical property characterization to become high-quality and high-reliability.

     

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