Quantitative appraisal for noise reduction in digital holographic phase imaging

Unsupervised speckle denoising in digital holographic interferometry based on 4-f optical simulation integrated cycle-consistent generative adversarial network

The speckle noise generated during digital holographic interferometry (DHI) is unavoidable and difficult to eliminate, thus reducing its accuracy. We propose a self-supervised deep-learning speckle denoising method using a cycle-consistent generative adversarial network to mitigate the effect of speckle noise. The proposed method integrates a 4-f optical speckle noise simulation module with a parameter generator. In addition, it uses an unpaired dataset for training to overcome the difficulty in obtaining noise-free images and paired data from experiments. The proposed method was tested on both simulated and experimental data, with results showing a 6.9% performance improvement compared with a conventional method and a 2.6% performance improvement compared with unsupervised deep learning in terms of the peak signal-to-noise ratio. Thus, the proposed method exhibits superior denoising performance and potential for DHI, being particularly suitable for processing large datasets.

Phase unwrapping for phase imaging using the plug-and-play proximal algorithm

Phase unwrapping (PU) is essential for various scientific optical applications. This process aims to estimate continuous phase values from acquired wrapped values, which are limited to the interval (-π,π]. However, the PU process can be challenging due to factors such as insufficient sampling, measurement errors, and inadequate equipment calibration, which can introduce excessive noise and unexpected phase discontinuities. This paper presents a robust iterative method based on the plug-and-play (PnP) proximal algorithm to unwrap two-dimensional phase values while simultaneously removing noise at each iteration. Using a least-squares formulation based on local phase differences and reformulating it as a partially differentiable equation, it is possible to employ the fast cosine transform to obtain a closed-form solution for one of the subproblems within the PnP framework. As a result, reliable phase reconstruction can be achieved even in scenarios with extremely high noise levels.

Noise reduction in digital holography phase maps by phase-preserving discrete Fourier resampling

Several methods have been proposed to reduce the detrimental effects of coherent noise in holographic imaging. Among them, the use of spatial-frequency masking or resampling has been widely applied because of its low implementation complexity and well-studied trade-off between denoising effectiveness and spatial resolution. While the digital application of this method has been successfully demonstrated for intensity images, its application to phase maps fails. This work shows that the phase applicability of these methods depends on the use of resampling masks that strictly keep the zero-order spatial frequencies. Alternative masks are proposed that demonstrate effective single-shot noise reduction in experimental phase maps from digital holographic microscopy. The resulting method is potentially extendable to any other complex-valued-field retrieval technique.

Deep sound-field denoiser: optically-measured sound-field denoising using deep neural network

This paper proposes a deep sound-field denoiser, a deep neural network (DNN) based denoising of optically measured sound-field images. Sound-field imaging using optical methods has gained considerable attention due to its ability to achieve high-spatial-resolution imaging of acoustic phenomena that conventional acoustic sensors cannot accomplish. However, the optically measured sound-field images are often heavily contaminated by noise because of the low sensitivity of optical interferometric measurements to airborne sound. Here, we propose a DNN-based sound-field denoising method. Time-varying sound-field image sequences are decomposed into harmonic complex-amplitude images by using a time-directional Fourier transform. The complex images are converted into two-channel images consisting of real and imaginary parts and denoised by a nonlinear-activation-free network. The network is trained on a sound-field dataset obtained from numerical acoustic simulations with randomized parameters. We compared the method with conventional ones, such as image filters, a spatiotemporal filter, and other DNN architectures, on numerical and experimental data. The experimental data were measured by parallel phase-shifting interferometry and holographic speckle interferometry. The proposed deep sound-field denoiser significantly outperformed the conventional methods on both the numerical and experimental data. Code is available on GitHub (https://github.com/nttcslab/deep-sound-field-denoiser).

Two-dimensional phase unwrapping based on U2-Net in complex noise environment

This paper proposes applying the nested U2-Net to a two-dimensional phase unwrapping (PU). PU has been a classic well-posed problem since conventional PU methods are always limited by the Itoh condition. Numerous studies conducted in recent years have discovered that data-driven deep learning techniques can overcome the Itoh constraint and significantly enhance PU performance. However, most deep learning methods have been tested only on Gaussian white noise in a single environment, ignoring the more widespread scattered noise in real phases. The difference in the unwrapping performance of deep network models with different strategies under the interference of different kinds of noise or drastic phase changes is still unknown. This study compares and tests the unwrapping performance of U-Net, DLPU-Net, VUR-Net, PU-GAN, U2-Net, and U2-Netp under the interference of additive Gaussian white noise and multiplicative speckle noise by simulating the complex noise environment in the real samples. It is discovered that the U2-Net composed of U-like residual blocks performs stronger anti-noise performance and structural stability. Meanwhile, the wrapped phase of different heights in a high-level noise environment was trained and tested, and the network model was qualitatively evaluated from three perspectives: the number of model parameters, the amount of floating-point operations, and the speed of PU. Finally, 421 real-phase images were also tested for comparison, including dynamic candle flames, different arrangements of pits, different shapes of grooves, and different shapes of tables. The PU results of all models are quantitatively evaluated by three evaluation metrics (MSE, PSNR, and SSIM). The experimental results demonstrate that U2-Net and the lightweight U2-Netp proposed in this work have higher accuracy, stronger anti-noise performance, and better generalization ability.

Decorrelation and anti-correlation from defocus in digital holographic interferometry

This paper presents a theoretical modeling of the speckle noise decorrelation in digital Fresnel holographic interferometry in out-of-focus reconstructed images. The complex coherence factor is derived by taking into account the focus mismatch, which depends on both the sensor-to-object distance and the reconstruction distance. The theory is confirmed by both simulated data and experimental results. The very good agreement between data demonstrates the high relevance of the proposed modeling. The particular phenomenon of anti-correlation in phase data from holographic interferometry is highlighted and discussed.

Deep Learning Network for Speckle De-Noising in Severe Conditions

Digital holography is well adapted to measure any modifications related to any objects. The method refers to digital holographic interferometry where the phase change between two states of the object is of interest. However, the phase images are corrupted by the speckle decorrelation noise. In this paper, we address the question of de-noising in holographic interferometry when phase data are polluted with speckle noise. We present a new database of phase fringe images for the evaluation of de-noising algorithms in digital holography. In this database, the simulated phase maps present characteristics such as the size of the speckle grains and the noise level of the fringes, which can be controlled by the generation process. Deep neural network architectures are trained with sets of phase maps having differentiated parameters according to the features. The performances of the new models are evaluated with a set of test fringe patterns whose characteristics are representative of severe conditions in terms of input SNR and speckle grain size. For this, four metrics are considered, which are the PSNR, the phase error, the perceived quality index and the peak-to-valley ratio. Results demonstrate that the models trained with phase maps with a diversity of noise characteristics lead to improving their efficiency, their robustness and their generality on phase maps with severe noise.

Speckle denoising based on deep learning via a conditional generative adversarial network in digital holographic interferometry

Speckle denoising can improve digital holographic interferometry phase measurements but may affect experimental accuracy. A deep-learning-based speckle denoising algorithm is developed using a conditional generative adversarial network. Two subnetworks, namely discriminator and generator networks, which refer to the U-Net and DenseNet layer structures are used to supervise network learning quality and denoising. Datasets obtained from speckle simulations are shown to provide improved noise feature extraction. The loss function is designed by considering the peak signal-to-noise ratio parameters to improve efficiency and accuracy. The proposed method thus shows better performance than other denoising algorithms for processing experimental strain data from digital holography.

High-speed measurement of mechanical micro-deformations with an extended phase range using dual-wavelength digital holographic interferometry

The implementation of a digital holographic interferometry setup for high-speed micro-deformation measurement is presented. This proposal uses a dual-wavelength recording strategy to reconstruct micro-deformations up to 4.85 µm with no phase wrapping. The numerical processing required to recover the phase maps containing the information of micro-deformations is carried out in a general-purpose computing on graphics processing unit environment to boost its performance. The method completely processes recorded holograms of 1024×1024pixels in 48 ms, i.e., 21 frames per second (FPS) for a single-wavelength acquisition and 96 ms or 11 FPS for dual-wavelength recordings. The method is experimentally evaluated measuring deformations ranging from 0.033 µm to 4.85 µm with no need for phase unwrapping algorithms for an 8 cm diameter aluminum plate in a 110cm² field of view.

Deep learning speckle de-noising algorithms for coherent metrology: a review and a phase-shifted iterative scheme [Invited]

We present a review of deep learning algorithms dedicated to the processing of speckle noise in coherent imaging. We focus on methods that specifically process de-noising of input images. Four main classes of applications are described in this review: optical coherence tomography, synthetic aperture radar imaging, digital holography amplitude imaging, and fringe pattern analysis. We then present deep learning approaches recently developed in our group that rely on the retraining of residual convolutional neural network structures to process decorrelation phase noise. The paper ends with the presentation of a new approach that uses an iterative scheme controlled by an input SNR estimator associated with a phase-shifting procedure.

Tri-wavelength simultaneous ESPI for 3D micro-deformation field measurement

Electronic speckle pattern interferometry (ESPI), a well-established technique for micro-deformation measurement, can be used to determine both in-plane and out-of-plane displacement components. Although many works in ESPI have been reported for three-dimensional (3D) displacement measurement, few works have focused on the simultaneous measurement of 3D deformation fields. Here we present an ESPI system that consists of three sub-interferometers for simultaneous measurement of all three displacement components and in-plane strain fields. A 3CCD color camera, a specially designed shifting stage, and three lasers with optimal wavelengths are used in this system. The lasers and 3CCD camera provide independent interferograms with different color signals, while the shifting stage allows the sub-interferometers to achieve simultaneous phase shifting. The results of color separation and experimental measurement demonstrate the utility of the system.

Modeling of speckle decorrelation in digital Fresnel holographic interferometry

This paper presents analytical modeling of the speckle decorrelation noise in digital Fresnel holographic interferometry. The theoretical analysis is carried out by considering the complex coherence factor between two speckled images from two digitally reconstructed holograms at two different instants. The expression giving the modulus of the coherence factor is established and depends on the local surface deformation and parameters from the holographic setup. The analysis is supported by realistic simulations and experiments. Both simulations and experimental results exhibit a very good agreement with the theoretical prediction.

Towards Reduced CNNs for De-Noising Phase Images Corrupted with Speckle Noise

Digital holography is a very efficient technique for 3D imaging and the characterization of changes at the surfaces of objects. However, during the process of holographic interferometry, the reconstructed phase images suffer from speckle noise. In this paper, de-noising is addressed with phase images corrupted with speckle noise. To do so, DnCNN residual networks with different depths were built and trained with various holographic noisy phase data. The possibility of using a network pre-trained on natural images with Gaussian noise is also investigated. All models are evaluated in terms of phase error with HOLODEEP benchmark data and with three unseen images corresponding to different experimental conditions. The best results are obtained using a network with only four convolutional blocks and trained with a wide range of noisy phase patterns.

Theoretical analysis of surface-shape-induced decorrelation noise in multi-wavelength digital holography

This paper presents analytical modelling for describing the speckle noise decorrelation in phase data from two- or multiple-wavelength digital holography. A novel expression for the modulus of the coherence factor is proposed for the case of two-wavelength speckle decorrelation from imaging roughness and surface shape through an optical system. The expression permits us to estimate the speckle decorrelation phase noise in surface shape measurements. The theoretical analysis is supported by realistic simulations including both the surface roughness and shape. The results demonstrate the very good agreement between the modulus of the coherence factor estimated with the simulation and the one calculated with theory.

Improving the intensity-contrast image of a noisy digital hologram by convolution of Chebyshev type 2 and elliptic filters

In this paper, a new, to the best of our knowledge, technique convolves the windowed Fourier filtering (WFF) of the Fresnel transform with the transfer functions of both Chebyshev type 2 and elliptic filters to enhance the intensity-contrast image of a noisy digital hologram. The recorded digital hologram is reconstructed by the Fresnel approach, the reconstructed intensity-contrast image is transformed by WFF, and the obtained spectrum is convolved in frequency domain with the transfer functions of Chebyshev type 2 and elliptic filters. The result of convolution is transformed by inverse WFF to produce a speckle-free image with a sharp roll-off and no ripples in both pass- and stop-bands. The experimental results with a die in the presence and absence of a rotating ground glass diffuser are shown and demonstrate that the resolution can be effectively enhanced with simple setup and procedure. The proposed technique can improve the capabilities of digital holography in three-dimensional (3D) microscopy.

Influence of noise-reduction techniques in sparse-data sample rotation tomographic imaging

Data acquisition and processing is a critical issue for high-speed applications, especially in three-dimensional live cell imaging and analysis. This paper focuses on sparse-data sample rotation tomographic reconstruction and analysis with several noise-reduction techniques. For the sample rotation experiments, a live Candida rugosa sample is used and controlled by holographic optical tweezers, and the transmitted complex wavefronts of the sample are recorded with digital holographic microscopy. Three different cases of sample rotation tomography were reconstructed for dense angle with a step rotation at every 2°, and for sparse angles with step rotation at every 5° and 10°. The three cases of tomographic reconstruction performance are analyzed with consideration for data processing using four noise-reduction techniques. The experimental results demonstrate potential capability in retaining the tomographic image quality, even at the sparse angle reconstructions, with the help of noise-reduction techniques.

Lock-in vibration retrieval based on high-speed full-field coherent imaging

The use of high-speed cameras permits to visualize, analyze or study physical phenomena at both their time and spatial scales. Mixing high-speed imaging with coherent imaging allows recording and retrieving the optical path difference and this opens the way for investigating a broad variety of scientific challenges in biology, medicine, material science, physics and mechanics. At high frame rate, simultaneously obtaining suitable performance and level of accuracy is not straightforward. In the field of mechanics, this prevents high-speed imaging to be applied to full-field vibrometry. In this paper, we demonstrate a coherent imaging approach that can yield full-field structural vibration measurements with state-of-the-art performances in case of high spatial and temporal density measurements points of holographic measurement. The method is based on high-speed on-line digital holography and recording a short time sequence. Validation of the proposed approach is carried out by comparison with a scanning laser Doppler vibrometer and by realistic simulations. Several error criteria demonstrate measurement capability of yielding amplitude and phase of structural deformations.

Behavior of CAD/CAM ceramic veneers under stress: A 3D holographic study

OBJECTIVES

Ceramic veneers restorations may undergo damages, such as cracks, fractures, or debonding. Full-field measurements must be carried out in order to visualize and analyze the strain fields. This paper demonstrates that digital holography permits to investigate the mechanical behavior under stress of a natural incisor and a natural incisor reconstructed with CAD/CAM ceramic veneer.

METHODS

The facial surface of a maxillary central incisor is prepared to receive a monolithic ceramic reconstruction manufactured using a chairside computer-aided design and computer aided manufacturing (CAD/CAM) system (Cerec AC® system, Sirona Dental System®, Bensheim, Germany). One incisor is kept intact for comparison. The samples are sectioned longitudinally to obtain a planar observation of the region of interest. A mechanical indentation head and digital holographic set-ups permit a full-field, contact-less and single-shot measurement of the three-dimensional displacement fields at the surface of the tooth sample when subjected to load. Stain fields are then estimated and comparison of the results between two samples can be carried out.

RESULTS

3D displacement, fields and strain fields are measured and highlight the behavior of the region of interest in three directions of space for the ceramic veneer and the natural incisor. The strain maps reveal the local behavior, especially the concentration or the sudden change in strain. The transition zones are clearly observed, particularly for the veneered sample.

CONCLUSION

Digital holography highlights the localization of stress concentration zones in regions of interest and yields comparative analysis between samples with different tooth preparations.

SIGNIFICANCE

holography permits to visualize and compare the mechanical response of the ceramic veneer and natural tooth. This helps choosing the mechanical properties of the bonding interface.

Speckle reduction in digital holography with low-dimensional reconstruction

Speckle reduction is a crucial technique since the presence of speckle disturbs the quality of the reconstruction in digital holography. In this paper, we present an easy, fast, and efficient single-shot method to reduce speckle noise in digital holography. The method reconstructs subholograms from a single hologram. Then, sub-reconstruction images are randomly shuffled and divided into several groups and low-dimensional noise-reduced images can be achieved by averaging sub-reconstruction image groups by groups. Next, these low-dimensional noise-reduced images are combined to obtain a noise-reduced image. Finally, the noise-reduced image is processed by a mean filter to obtain a final image, which has substantially less speckle noise while preserving the dimensions of the original image. The experimental results demonstrate the effectiveness of the proposed method and indicate its potential in real-time digital holography.

Physical pupil manipulation for speckle reduction in digital holographic microscopy

The reduction of speckle noise by physically changing the pupil of the imaging system, as first envisioned in optical holography, is experimentally applied to a digital holographic microscope (DHM). The imaging pupil of a DHM, operating in image plane telecentric-afocal architecture, is changed in a controlled way between successive recordings, allowing the shooting of multiple partially-decorrelated holograms. Averaging the numerically reconstructed holograms yields amplitude and/or phase images with reduced speckle noise. Experimental results of biological specimens and a phase-only resolution test show the feasibility to recover micron-sized features in images with reduced speckle noise.

Polychromatic digital holographic microscopy: a quasicoherent-noise-free imaging technique to explore the connectivity of living neuronal networks

Significance: Over the past decade, laser-based digital holographic microscopy (DHM), an important approach in the field of quantitative-phase imaging techniques, has become a significant label-free modality for live-cell imaging and used particularly in cellular neuroscience. However, coherent noise remains a major drawback for DHM, significantly limiting the possibility to visualize neuronal processes and precluding important studies on neuronal connectivity. Aim: The goal is to develop a DHM technique able to sharply visualize thin neuronal processes. Approach: By combining a wavelength-tunable light source with the advantages of hologram numerical reconstruction of DHM, an approach called polychromatic DHM (P-DHM), providing OPD images with drastically decreased coherent noise, was developed. Results: When applied to cultured neuronal networks with an air microscope objective ( 20 × , 0.8 NA), P-DHM shows a coherent noise level typically corresponding to 1 nm at the single-pixel scale, in agreement with the 1 / N -law, allowing to readily visualize the 1 - μ m -wide thin neuronal processes with a signal-to-noise ratio of ∼ 5 . Conclusions: Therefore, P-DHM represents a very promising label-free technique to study neuronal connectivity and its development, including neurite outgrowth, elongation, and branching.

Deep Learning-Based Wrapped Phase Denoising Method for Application in Digital Holographic Speckle Pattern Interferometry

This paper presents a new processing method for denoising interferograms obtained by digital holographic speckle pattern interferometry (DHSPI) to serve in the structural diagnosis of artworks. DHSPI is a non-destructive and non-contact imaging method that has been successfully applied to the structural diagnosis of artworks by detecting hidden subsurface defects and quantifying the deformation directly from the surface illuminated by coherent light. The spatial information of structural defects is mostly delivered as local distortions interrupting the smooth distribution of intensity during the phase-shifted formation of fringe patterns. Distortions in fringe patterns are recorded and observed from the estimated wrapped phase map, but the inevitable electronic speckle noise directly affects the quality of the image and consequently the assessment of defects. An effective method for denoising DHSPI wrapped phase based on deep learning is presented in this paper. Although a related method applied to interferometry for reducing Gaussian noise has been introduced, it is not suitable for application in DHSPI to reduce speckle noise. Thus, the paper proposes a new method to remove speckle noise in the wrapped phase. Simulated data and experimental captured data from samples prove that the proposed method can effectively reduce the speckle noise of the DHSPI wrapped phase to extract the desired information. The proposed method is helpful for accurately detecting defects in complex defect topography maps and may help to accelerate defect detection and characterization procedures.

Single-shot speckle reduction by elimination of redundant speckle patterns in digital holography

Speckle reduction is a crucial technique, since the presence of speckle disturbs the quality of the reconstruction in digital holography. In this paper, we present a redundant speckle elimination method to suppress the speckle noise. For the same position in each of the reconstructed sub-images, we consider pixels with the same gray value as information with the same speckle distribution. Therefore, a speckle-suppressed gray value can be obtained by extracting pixels with different gray values and then averaging. Through theoretical analysis and experiments, we demonstrate that speckle contrast can be decreased significantly by using the proposed method. Moreover, we show that the despeckle strength of the proposed method highly depends on the number of binary masks. These results indicate the potential of the proposed method for various applications.

Robust and fast filtering method for enhancement of two-dimensional quality-guided path unwrapping algorithms

This paper presents a new filtering algorithm for reducing phase noise based on the bicubic interpolation method (BIM). The unwrapped phase map accuracy is enhanced by the combination of BIM with a conventional unwrapping algorithm. The bicubic interpolation filtering (BIF) and bicubic interpolation smoothed filtering (BISF) methods are two powerful low-pass filters. The simulation shows that the BIF and BISF convert the initial noise distribution to Gaussian distribution. The Mirau interferometer is used to improve the performance of the proposed filtering algorithms. The root mean square error between two quality-guided path unwrapping algorithms and BISF method is estimated at approximately 31 nm.

SPUD: simultaneous phase unwrapping and denoising algorithm for phase imaging

Recent methods for phase unwrapping in the presence of noise include denoising algorithms to filter out noise as a preprocessing stage. However, including a denoising stage increases the overall computational complexity resulting in long execution times. In this paper, we present a noniterative simultaneous phase unwrapping and denoising algorithm for phase imaging, referred to as SPUD. The proposed method relies on the least squares discrete cosine transform (DCT) solution for phase unwrapping with an additional sparsity constraint on the DCT coefficients of the unwrapped solution. Simulation results with different levels of noise and wrapped phase fringe density reveal the suitability of the proposed method for accurate phase unwrapping and restoration. When compared to the 2D windowed Fourier transform filter, SPUD performs better in terms of phase error and execution times. The processing of experimental data from synthetic aperture radar showed the capability for processing real images, including removing phase dislocations. An implementation of the proposed algorithm can be accessed and executed through a Code Ocean compute capsule.

Noise suppression for ballistic-photons based on compressive in-line holographic imaging through an inhomogeneous medium

Noise suppression is one of the most important tasks in imaging through inhomogeneous mediums. Here, we proposed a denoising approach based on compressive in-line holography for imaging through an inhomogeneous medium. A reference-beam-free system with a low-cost continuous-wave laser is presented. The suppression against the noise, which is brought by the scattering photons, is presented in simulations using the proposed algorithm. The noise immunity is demonstrated in lensless imaging behind a random phase mask with an optical depth of 1.42 by single exposure, as well as behind a ground glass with an optical depth of 6.38 by multiple exposures.

Optimal processing scheme for restoration of phase data corrupted by strong decorrelation noise and dislocations

The presence of speckle noise and dislocations makes phase restoration potentially difficult in quantitative phase imaging and metrology. Unfortunately, there is no appropriate approach to deal with phase data corrupted by high speckle noise and phase dislocations. Usually, processing schemes may deal with low-pass phase filtering, phase unwrapping, or phase inpainting. This paper discusses the efficient processing to deal with noisy phase maps corrupted with phase dislocations. Six processing schemes, combining four operations, are evaluated. The investigation is carried out by realistic numerical simulations in which strong decorrelation phase noise and phase dislocations are generated. As a result, most robust and faster processing is established. The applicability of the optimal scheme is demonstrated through deformation measurement in dental materials.

Assessment of speckle denoising filters for digital holography using subjective and objective evaluation models

Digital holography is an emerging imaging technique for displaying and sensing three-dimensional objects. The perceived image quality of a hologram is frequently corrupted by speckle noise due to coherent illumination. Although several speckle noise reduction methods have been developed so far, there are scarce quality assessment studies to address their performance, and they typically focus solely on objective metrics. However, these metrics do not reflect the visual quality perceived by a human observer. In this work, the performances of four speckle reduction algorithms, namely, the nonlocal means-the Lee, the Frost, and the block-matching 3D filters, with varying parameterizations-were subjectively evaluated. The results were ranked with respect to the perceived image quality to obtain the mean opinion scores using pairwise comparison. The correlation between the subjective results and 20 different no-reference objective quality metrics was evaluated. The experiment indicates that block-matching 3D and Lee are the preferred filters, depending on hologram characteristics. The best-performing objective metrics were identified for each filter.

Hybrid method for speckle noise reduction in digital holography

In digital holography, the inherited speckle noise degrades imaging quality due to the coherent laser source. To overcome this problem, a hybrid method for speckle noise reduction is presented by combining a novel angular diversity approach with the block-matching and 3D filtering (BM3D) algorithm. A serial of holograms is first captured by the proposed recording approach, and then the image with high signal-to-noise ratio is obtained by averaging multiple reconstructed intensity images. Finally, the residual noise in the averaged image is further eliminated by the BM3D filtering algorithm. The speckle noise is significantly suppressed, and a nearly speckle-free image can be obtained. Experimental results demonstrate the effectiveness of the proposed method.

Denoising for variable density ESPI fringes in nondestructive testing by an adaptive multiscale morphological filter based on local mean

Analysis of speckle images with variable density fringes is a challenging task when electronic speckle pattern interferometry (ESPI) is used for nondestructive testing of defects. In this paper, an adaptive multiscale morphological filter based on local mean is proposed. First, the image is segmented, and the regions are divided into different density levels using local mean. Then, the structural elements that adapt to different density levels are designed, and the proper size of the structural elements is determined by an iterative procedure. Finally, the morphological open-closing filtering is conducted, and the block edges are smoothed by averaging. The proposed method was applied to computer-simulation fringes and fringes experimentally obtained from a prefabricated defect specimen under thermal loading and then compared with the commonly used methods, i.e., discrete cosine filter, wavelet filter, Lee filter, and nonlocal mean filter. The experimental results showed that the proposed method had the best performance in terms of noise reduction and edge preservation. With the capability of noise reduction for ESPI images of variable density fringes, the proposed method will be helpful to build a quantitative relationship between fringes and defects in the cases of nonuniform deformation of speckle interferometry, such as nondestructive defect detecting, thermal structural analysis, and heterogeneous materials mechanical analysis.

Speckle denoising by variant nonlocal means methods

This study aims to demonstrate the performances of nonlocal means (NLM) and their variant denoising methods, mainly focusing on NLM-shaped adaptive patches and several NLM-reprojection schemes for speckle noise reduction in amplitude and phase images of the digital coherent imaging systems. In the digital coherent imaging systems such as digital speckle pattern interferometry, digital holographic interferometry, etc., the image quality is severely degraded by additive uncorrelated speckle noise, due to the coherent nature of the light source, and therefore limits the development of several applications of these imaging systems in many fields. NLM and its variant denoising methods are employed to denoise the intensity/phase images obtained from these imaging systems, and their effectiveness is evaluated by considering various parameters. The performance comparison of these methods with other existing speckle denoising methods is also presented. The performance of these methods for speckle noise reduction is quantified on the basis of two criteria matrices, namely, the peak-to-signal noise ratio and the image quality index. Based on these criteria matrices, it is observed that these denoising methods have the ability to improve the intensity and phase images favorably in comparison to other speckle denoising techniques, and these methods are more effective and feasible in speckle-noise reduction.

Contrast transfer function of de-noising algorithms

This paper presents a comprehensive study on the contrast transfer function of de-noising algorithms. In order to cover a broad variety of methods, 45 de-noising algorithms are chosen considering their recognized efficiency in the different application domains of image processing. Advanced methods are targeted: wavelet transform-based algorithms with Daubechies, symlets, curvelets, contourlets, patch-based methods such as BM3D, NL-means algorithms and deep learning approaches; in addition, classical spatial filtering methods are considered, such as Wiener, median, Gauss filtering, and adaptive filtering approaches such as anisotropic diffusion and synthetic aperture radar filtering. The contrast transfer function is provided for each algorithm. Ranking of the set of de-noising algorithms is established according to proposed metrics. The paper provides practical methodology and novel results dedicated to the evaluation of the contrast transfer function of de-noising approaches from literature.

Automatized fringe pattern preprocessing using unsupervised variational image decomposition

Successful single-frame fringe pattern preprocessing comprising high-frequency noise minimization and low-frequency background removal represents often the crucial step of the fringe pattern based full-field optical metrology (i.e., interferometry, moiré, structured light). It directly determines the measurement accuracy. Data-driven decomposition by means of the 2D empirical mode decomposition (EMD) serves the filtering purpose in adaptive and detail-preserving manner. The mode-mixing phenomenon resulting in troublesome automatic grouping of modes into three main fringe pattern components (background, information part and noise) is significantly limiting this process, however. In this paper we are introducing the unsupervised variational image decomposition (uVID) model especially tailored to overcome this preprocessing problem and assure successful sparse three-component fringe pattern decomposition. Comprehensive analysis and detailed studies of accomplished significant advancements ensuring automation, versatility and robustness of the proposed approach are provided. Main advancements include: (1) tailoring the VID calculation scheme to fringe pattern preprocessing purpose by focusing onto accurate fringe extraction with tolerance parameter and custom-made decomposition parameter values; (2) fringe pattern tailored BM3D denoising algorithm with fixed parameter values. Numerical and experimental investigations corroborate that the demonstrated uVID method compares favorably with the reference 2D EMD algorithm and classical VID model. Remarkable range of acceptable local variations of the fringe pattern orientation, period, noise, contrast and background terms is to be highlighted.

Comparative study of multi-look processing for phase map de-noising in digital Fresnel holographic interferometry

This paper presents a comparative study of multi-look approaches for de-noising phase maps from digital holographic interferometry. A database of 160 simulated phase fringe patterns with eight different phase fringe patterns with fringe diversity was computed. For each fringe pattern, 20 realistic noise realizations are generated in order to simulate a multi-look process with 20 inputs. A set of 22 de-noising algorithms was selected and processed for each simulation. Three approaches for multi-look processing are evaluated. Quantitative appraisal is obtained using two metrics. The results show good agreement for algorithm rankings obtained with both metrics. One singular and highly practical result of the study is that a multi-look approach with average looks before noise processing performs better than averaging computed with all de-noised looks. The results also demonstrate that the two-dimensional windowed Fourier transform filtering exhibits the best performance in all cases and that the block-matching 3D (BM3D) algorithm is second in the ranking.

Speckle noise reduction in digital speckle pattern interferometric fringes by nonlocal means and its related adaptive kernel-based methods

Digital speckle pattern interferometry (DSPI) is widely used in many scientific and industrial applications. Besides its several advantages, one of the basic problems encountered in DSPI is the undesired speckle noise existing in the fringe pattern. In this paper, we demonstrate the performance of nonlocal means (NLM) and its related adaptive kernel-based filtering methods for speckle noise reduction in DSPI fringes. The NLM filter and its related kernel-based filters such as NLM-average, NLM-local polynomial regression, and NLM-shape adaptive patches are implemented first on simulated DSPI fringes, and their performances are quantified on the basis of peak signal-to-noise ratio (PSNR), mean square error (MSE), and quality index (Q). Further, their effectiveness and abilities in reducing speckle noise are compared with other speckle denoising methods. These filtering methods are then employed on experimental DSPI fringes. The obtained results reveal that these filtering methods have the ability to improve the PSNR and Q of the DSPI fringes and provide better visual and quantitative results. It is also observed that the proposed filtering methods preserve the edge information of the DSPI fringes, which is evaluated on the basis of the edge preservation index of the resultant filtered images.

Strategies for reducing speckle noise in digital holography

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.

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter

A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.

Digital hologram transformations for RGB color holographic display with independent image magnification and translation in 3D

A new framework for in-plane transformations of digital holograms (DHs) is proposed, which provides improved control over basic geometrical features of holographic images reconstructed optically in full color. The method is based on a Fourier hologram equivalent of the adaptive affine transformation technique [Opt. Express18, 8806 (2010)OPEXFF1094-408710.1364/OE.18.008806]. The solution includes four elementary geometrical transformations that can be performed independently on a full-color 3D image reconstructed from an RGB hologram: (i) transverse magnification; (ii) axial translation with minimized distortion; (iii) transverse translation; and (iv) viewing angle rotation. The independent character of transformations (i) and (ii) constitutes the main result of the work and plays a double role: (1) it simplifies synchronization of color components of the RGB image in the presence of mismatch between capture and display parameters; (2) provides improved control over position and size of the projected image, particularly the axial position, which opens new possibilities for efficient animation of holographic content. The approximate character of the operations (i) and (ii) is examined both analytically and experimentally using an RGB circular holographic display system. Additionally, a complex animation built from a single wide-aperture RGB Fourier hologram is presented to demonstrate full capabilities of the developed toolset.

Reference-free metric for quantitative noise appraisal in holographic phase measurements

This paper presents a reference-free metric for quantitative appraisal of de-noising algorithms for phase measurements in digital holography. In the literature, quality metrics are not self-contained because they require a noise-free reference phase fringe pattern in order to be computed. In practical situations, no exact phase is available to evaluate the quality of processing. In order to bypass such limitations, one needs a metric directly capable of providing information on how efficient the filtering is, without any help from any reference measurements and by only considering the measured available phase data. This paper presents a novel reference-free metric, called estimated phase error for quantitative appraisal of de-noising algorithms for noisy phase data processing. This metric is based on the computation of an estimator of the standard deviation of the phase error between data processed with an external algorithm and that from the evaluated algorithm. A benchmark, including 37 different de-noising algorithms, demonstrates that the proposed metric is capable of producing the same rankings as those obtained with classical metrics, requiring a reference phase. Application to phase data from mechanical testing demonstrates that the ranking obtained from experimental phase data is similar to that obtained during the benchmarking with simulated data.

Coherent noise reduction in digital holographic microscopy by averaging multiple holograms recorded with a multimode laser

In digital holographic microscopy (DHM), it is undesirable to observe coherent noise in the reconstructed images. The sources of the noise are mainly the parasitic interference fringes caused by multiple reflections and the speckle pattern caused by the optical scattering on the object surface. Here we propose a noise reduction approach in DHM by averaging multiple holograms recorded with a multimode laser. Based on the periodicity of the temporal coherence of a multimode semiconductor laser, we acquire a series of holograms by changing the optical path length difference between the reference beam and object beam. Because of the use of low coherence light, we can remove the parasitic interference fringes caused by multiple reflections in the holograms. In addition, the coherent noise patterns change in this process due to the different optical paths. Therefore, the coherent noise can be reduced by averaging the multiple reconstructions with uncorrelated noise patterns. Several experiments have been carried out to validate the effectiveness of the proposed approach for coherent noise reduction in DHM. It is shown a remarkable improvement both in amplitude imaging quality and phase measurement accuracy.

Quantitative study on a resampling mask method for speckle reduction with amplitude superposition

One-shot digital holographic imaging has the advantages of high stability and low temporal cost. However, its reconstruction is degraded severely by the laser speckle. A rectangle, ellipse, and diamond resampling mask method in spatial domain for speckle reduction is proposed. The effectiveness of the method for speckle reduction is explained successfully. In the method, one hologram recorded in a certain size is divided into N=S×T sub-holograms. Angular spectrum transform is applied to the holographic reconstruction of a diffuse object. N reconstructed amplitude images are calculated from the corresponding sub-holograms. Benefitting from speckle's random distribution, superimposing these N uncorrelated amplitude images would lead to a final reconstructed image with reduced speckle. Normalized relative standard deviation values of the reconstructed image are in good agreement with the asymptotical law. The maximum relative errors between the experiment data and the theoretical values are below 7.2%. The effect of the method on the spatial resolution of the reconstructed image is also quantitatively evaluated. Experimental and simulation results prove the feasibility and effectiveness of the proposed method.

Robust processing of phase dislocations based on combined unwrapping and inpainting approaches

This Letter proposes a robust processing of phase dislocations to recover continuous phase maps. The approach is based on combined unwrapping and inpainting methods. Phase dislocations are determined using an estimator based on the second order phase gradient. The algorithm is validated using a realistic simulation of phase dislocations, and the phase restoration exhibits only weak errors. A comparison with other inpainting algorithms is also provided, demonstrating the suitability of the approach. The approach is applied to experimental data from off-axis digital holographic interferometry. The phase dislocation from phase data from a wake flow at Mach 0.73 are identified and processed. Excellent phase restoration can be appreciated.

Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise

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.

On-speckle suppression in IR digital holography

Long-IR wavelength is the best option for capturing digital holograms of large-size, real-world objects. However, the coherent noise level in a long-IR hologram is by far larger than that of a visible wavelength recording, thus resulting in a poor quality of both numerical and optical reconstructions. In this Letter, we show how such coherent noise can be efficiently suppressed by employing an optical scanning multi-look approach, in combination with 3D block matching numerical filtering. Results demonstrate the possibility to obtain near noise-free numerical reconstructions of IR digital holograms of large-size objects, while preserving resolution. We applied this method to the holograms of a rotating statuette. It will be shown that a remarkable contrast enhancement is achievable along with the recovery of object details that otherwise would be lost because of large speckle grains intrinsically due to the source coherence.