Digital holography (DH) has emerged as one of the most effective coherent imaging technologies. The technological developments of digital sensors and optical elements have made DH the primary approach in several research fields, from quantitative phase imaging to optical metrology and 3D display technologies, to name a few. Like many other digital imaging techniques, DH must cope with the issue of speckle artifacts, due to the coherent nature of the required light sources. Despite the complexity of the recently proposed de-speckling methods, many have not yet attained the required level of effectiveness. That is, a universal denoising strategy for completely suppressing holographic noise has not yet been established. Thus the removal of speckle noise from holographic images represents a bottleneck for the entire optics and photonics scientific community. This review article provides a broad discussion about the noise issue in DH, with the aim of covering the best-performing noise reduction approaches that have been proposed so far. Quantitative comparisons among these approaches will be presented.

This paper discusses on a quantitative comparison of the performances of different advanced algorithms for phase data de-noising. In order to quantify the performances, several criteria are proposed: the gain in the signal-to-noise ratio, the Q index, the standard deviation of the phase error, and the signal to distortion ratio. The proposed methodology to investigate de-noising algorithms is based on the use of a realistic simulation of noise-corrupted phase data. A database including 25 fringe patterns divided into 5 patterns and 5 different signal-to-noise ratios was generated to evaluate the selected de-noising algorithms. A total of 34 algorithms divided into different families were evaluated. Quantitative appraisal leads to ranking within the considered criteria. A fairly good correlation between the signal-to-noise ratio gain and the quality index has been observed. There exists an anti-correlation between the phase error and the quality index which indicates that the phase errors are mainly structural distortions in the fringe pattern. Experimental results are thoroughly discussed in the paper.

This paper presents a deep-learning-based algorithm dedicated to the processing of speckle noise in phase measurements in digital holographic interferometry. The deep learning architecture is trained with phase fringe patterns including faithful speckle noise, having non-Gaussian statistics and non-stationary property, and exhibiting spatial correlation length. The performances of the speckle de-noiser are estimated with metrics, and the proposed approach exhibits state-of-the-art results. In order to train the network to de-noise phase fringe patterns, a database is constituted with a set of noise-free and speckled phase data. The algorithm is applied to de-noising experimental data from wide-field digital holographic vibrometry. Comparison with the state-of-the-art algorithm confirms the achieved performance.

Robust phase unwrapping in the presence of high noise remains an open issue. Especially, when both noise and fringe densities are high, pre-filtering may lead to phase dislocations and smoothing that complicate even more unwrapping. In this paper an approach to deal with high noise and to unwrap successfully phase data is proposed. Taking into account influence of noise in wrapped data, a calibration method of the 1st order spatial phase derivative is proposed and an iterative approach is presented. We demonstrate that the proposed method is able to process holographic phase data corrupted by non-Gaussian speckle decorrelation noise. The algorithm is validated by realistic numerical simulations in which the fringe density and noise standard deviation is progressively increased. Comparison with other established algorithms shows that the proposed algorithm exhibits better accuracy and shorter computation time, whereas others may fail to unwrap. The proposed algorithm is applied to phase data from digital holographic metrology and the unwrapped results demonstrate its practical effectiveness. The realistic simulations and experiments demonstrate that the proposed unwrapping algorithm is robust and fast in the presence of strong speckle decorrelation noise.