Convolutional and fourier neural networks for speckle denoising of wrapped phase in digital holographic interferometry

Abstract

Owing to the unique non-Gaussian statistics and non-stationary properties, speckle denoising in digital holographic interferometry measurements is essential and challenging. Traditional Fourier-based frequency-domain filtering and deep-learning-based (DL-based) spatial-domain speckle denoising methods have realised significant achievements. However, these methods use different mechanisms and are applied separately. A deep learning-based algorithm combining the aforementioned methods is proposed, which simultaneously extracts features in the spatial and frequency domains via convolutional and Fourier neural networks (CFNN) for enhanced speckle denoising and minimising the phase unwrapping process error. Compared with the convolutional neural network (CNN), which provides spatial-domain features for the framework architecture to layer extraction operation, the Fourier neural operator (FNO) developed from traditional Fourier filtering provides the frequency-domain features. The differential gradient map of denoised wrapping is used as a loss function, further improving the smoothness of the denoised wrapped images and the subsequent phase-unwrapping performance. Compared to other algorithms, the proposed method achieves a relative improvement of 7.1% on the testing dataset and 5.0% on digital holographic deformation field experimental data. It can be extended to more fields of optical information processing, since it unifies the feature extraction and reconstruction in the spatial-domain and the frequency-domain in the same deep learning model.