Single Fringe Research Articles

Optical trapping in air on a single interference fringe

Stable and reproducible trapping in air of 1μm and 500 nm dielectric particles has been realized using a dual beam optical fiber tweezers with cleaved commercial single mode fibers. The influence of the interference fringes of the two coherent and counter-propagating trapping beam is investigated by controlling the fringe visibility. Optical trapping on a series of up to 10 fringes or trapping on only one to two fringes has been observed in distinct experiments. High axial trapping efficiencies of up to 1 nN μm−1W−1 is observed. The experimental results are supported by numerical simulations.

Untrained deep learning-based phase retrieval for fringe projection profilometry

Fringe projection profilometry (FPP) based on deep learning shows potential for challenging 3-D sensing tasks, e.g., bio-medicine, reverse engineering, and face recognition, etc. Supervised deep learning has been introduced to retrieve the desired phase for the 3-D reconstruction, which relies on lots of advanced training to construct the fringe-to-phase transformation. The traditional deep learning-based method becomes unreliable for scenes that are different from the training ones, which restricts it to be applied for actual applications. In this paper, an untrained deep learning-based phase retrieval method is proposed. By adding a camera to the traditional FPP system, scene-independent physical constraints such as phase, structure and 3-D consistency are constructed to optimize the fringe-to-phase transformation. The proposed deep learning-based method can retrieve the desired phase from a single fringe pattern without advance training. Both theoretical analyses and experimental results demonstrate its accurateness and robustness. The proposed method also shows potential for single-shot 3-D sensing applications such as high-speed 3-D measurement.

Deep learning-enabled anti-ambient light approach for fringe projection profilometry.

Achieving high-quality surface profiles under strong ambient light is challenging in fringe projection profilometry (FPP) since ambient light inhibits functional illumination from exhibiting sinusoidal stripes with high quantization levels. Conventionally, large-step phase shifting approaches are presented to enhance the anti-interference capability of FPP, but the image acquisition process in these approaches is highly time-consuming. Inspired by the promising performance of deep learning in optical metrology, we propose a deep learning-enabled anti-ambient light (DLAL) approach that can help FPP extract phase distributions from a single fringe image exposed to unbalanced lighting. In this work, the interference imposed by ambient light on FPP is creatively modeled as ambient light-induced phase error (ALPE). Guided by the ALPE model, we generate the dataset by precisely adjusting the stripe contrast before performing active projection, overcoming the challenge of collecting a large sample of fringe images with various illumination conditions. Driven by the novel dataset, the generated deep learning model can effectively suppress outliers among surface profiles in the presence of strong ambient light, thereby implementing high-quality 3D surface imaging. Experimentally, we verify the effectiveness and adaptability of the proposed DLAL approach in both indoor and outdoor scenarios with strong irradiation.

Different structured-light patterns in single-shot 2D-to-3D image conversion using deep learning.

Single-shot 3D shape reconstruction integrating structured light and deep learning has drawn considerable attention and achieved significant progress in recent years due to its wide-ranging applications in various fields. The prevailing deep-learning-based 3D reconstruction using structured light generally transforms a single fringe pattern to its corresponding depth map by an end-to-end artificial neural network. At present, it remains unclear which kind of structured-light patterns should be employed to obtain the best accuracy performance. To answer this fundamental and much-asked question, we conduct an experimental investigation of six representative structured-light patterns adopted for single-shot 2D-to-3D image conversion. The assessment results provide a valuable guideline for structured-light pattern selection in practice.

Wavelet based deep learning for depth estimation from single fringe pattern of fringe projection profilometry

Wavelet based deep learning for depth estimation from single fringe pattern of fringe projection profilometry

Hilbert transformation deep learning network for single-shot moiré profilometry

Phase demodulation from a single moiré fringe pattern is an ill-posed inverse problem that limits the applications of moiré profilometry in dynamic three-dimensional (3D) measurement. In this paper, a deep-learning-based high-precision technique is used to solve this problem arising from highly under sampled inputs. Our novel approach termed two-dimensional (2D) Hilbert transformation network uses two Res U-Net networks paired with a dichotomous network to generate the desired quadrature fringe pattern by referring to the input. This process can be viewed as 2D Hilbert transformation of a fringe pattern. By using the proposed network, the wrapped phase can be extracted easily if the sampled fringe pattern is filtered and normalized in advance. Experimental results obtained using the proposed Hilbert transformation network trained on simulated data indicate that it is a simple, albeit robust solution for phase extraction from a single fringe pattern with a phase error of less than 0.02 rad. Thus, the proposed network represents a novel approach to reliable and practical learning-based single-shot Moiré profilometry.

Single frame color fringe projection profilometry based on empirical mode decomposition imbalance correction algorithm for fast three-dimensional reconstruction

Phase-shifting profilometry (PSP) is considered to be the most accurate technique for phase retrieval with fringe projection profilometry (FPP) systems. However, PSP requires that multiple phase-shifted fringe patterns be acquired, usually sequentially, which limits PSP to static or quasistatic imaging. We introduce color FPP (CFPP), which provides three-dimensional (3D) imaging using a single acquisition, for the application of real-time profiling. A single frame acquisition provides all three phase-shifted fringe patterns needed for the PSP phase retrieval algorithm. However, some problems must be overcome in CFPP, namely, color coupling and imbalance. Following up on the study, we propose a fixed coefficient decoupling method based on point-to-point correction and then introduce the empirical mode decomposition algorithm to decompose a color fringe pattern into three high-frequency components and three low-frequency components for imbalance correction, which improves measurement accuracy and realizes a single frame measurement for complex and discontinuous objects. After correction by the proposed method, the shape of the tested object can be recovered by one a single frame color fringe pattern, which meets the need for dynamic measurement, and the accuracy is not limited by the movement speed of object. The simulations and experimental results show that the proposed method can significantly reduce the influence of color coupling and imbalance in CFPP, and thus realize dynamic and high-precision 3D reconstruction.

Experimental realization of two-dimensional single-layer ultracold gases of 87Rb in an accordion lattice

We experimentally realize two-dimensional (2D) single-layer ultracold gases of 87Rb by dynamically tuning the periodicity of a standing wave, known as accordion lattice. In order to load 87Rb Bose–Einstein condensate into single dark fringe node of the blue detuning optical lattice, we reduce the lattice periodicity from 26.7 μm to 3.5 μm with the help of an acousto-optic deflector (AOD) to compress the three-dimensional BEC adiabatically into a flat and uniform quasi-2D single-layer. We describe the experimental procedure of the atoms loading into the accordion lattice in detail and present the characteristics of the quasi-2D ultracold gases. This setup provides an important platform for studying in- and out-of equilibrium physics, phase transition and 2D topological matter.

Phase retrieval for objects in rain based on a combination of variational image decomposition and variational mode decomposition in FPP.

As far as we know, there is no paper reported to retrieve the phase of an object in rain by the fringe projection profilometry (FPP) method. The fringe projection pattern taken in rain contains much rain noise, which makes it difficult to accurately retrieve the phase of the object. In this paper, we focus on the phase retrieval of the object in rain by the FPP method. We first decompose the original fringe projection pattern into a series of band-limited intrinsic mode functions by the two-dimensional variational mode decomposition (2D-VMD) method. Then we screen out fringe-associated modes adaptively based on mutual information and reconstruct the fringe projection pattern. Next, we decompose the reconstructed fringe projection pattern by the TGV-Hilbert-BM3D variational model to obtain the de-rained fringe component. Finally, we use the Fourier transform method, phase unwrapping method, and carrier-removal method to obtain the unwrapped phase. We test the proposed method on three fringe projection patterns taken in simulated rain weather, and we compare our proposed method with the phase-shifting method, windowed Fourier method, morphological operation-based bidimensional empirical mode decomposition method, 2D-VMD method, and the TGV-Hilbert-BM3D method. The experimental results demonstrate that, for the first time to our knowledge, our method can effectively retrieve the phase of an object in rain from a single fringe projection pattern.

Sign-singularity solution in single-frame speckle interferometry with vortex-phase modulation

We propose a sign-singularity solution in single-shot digital speckle interferometry based on vortex-phase modulation. The vortex phase is introduced through the reference beam as variation information by a reflective liquid crystal spatial light modulator. The sign singularity is eliminated with the help of a single spiral speckle fringe pattern. To effectively obtain the deformation phase, the measurement process is specially designed on the consideration of the modulation principle of the vortex phase, which is discussed in terms of theoretical analysis and simulation results. Experiments on out-of-plane deformation measurement reveal the feasibility of the proposed method and suggest the potential in actual dynamic measurement applications.

Variational image decomposition model TGV-Hilbert-BM3D for phase retrieval in FPP and its application for an on-site wall surface bulge.

Mass loss from wall surface bulge deformation can be used to estimate the strength loss of reinforcement, bond reduction, and ductility degradation, so it is very important to accurately measure the three-dimensional (3D) shape of on-site wall surface bulge. In this paper, we try to solve the problem by use of fringe projection profilometry. In the fringe projection patterns of wall surface bulge, the contrast of the fringes is very weak, and there are sometimes cracks in patterns. We first present a preprocessing method to inpaint fringes if there are damaged fringes caused by cracks. Then we propose a new, to the best of our knowledge, image decomposition model, total generalized variation (TGV)-Hilbert-block-matching (BM)3D, to effectively extract the fringe component. Finally, we use Fourier transform, phase unwrapping, and carrier-removal methods to obtain the unwrapped phase. We test the proposed method on a simulated fringe projection pattern and two real fringe projection patterns of wall surface bulge. We compare our method with the advanced total variation space-generalized functions space-BM3D, TV-Hilbert-L2, and Beppo-Levi-space-Hilbert-BM3D methods. In addition, we perform ablation experiments to prove that our preprocessing method is necessary. The experimental results demonstrate that our method can effectively measure the 3D shape of wall surface bulge from a single fringe projection pattern for the first time, to our knowledge.

Lateral chromatic aberration: a tool for retrieving the fringes phase.

In this work, the possibility of using the inherent lateral chromatic aberration (LCA) of the lenses to calculate the phase of fringe patterns is reported. It is shown that a single fringe pattern can be decomposed into three phase shifted images and that the phase can be retrieved successfully from those images. Experiments are carried out to retrieve the phase of some fringes, and the results are compared with those obtained using standard temporal and spatial phase shifting algorithms.

Composite fringe projection deep learning profilometry for single-shot absolute 3D shape measurement.

Single-shot fringe projection profilometry (FPP) is essential for retrieving the absolute depth information of the objects in high-speed dynamic scenes. High-precision 3D reconstruction using only one single pattern has become the ultimate goal in FPP. The frequency-multiplexing (FM) method is a promising strategy for realizing single-shot absolute 3D measurement by compounding multi-frequency fringe information for phase unwrapping. In order to solve the problem of serious spectrum aliasing caused by multiplexing schemes that cannot be removed by traditional spectrum analysis algorithms, we apply deep learning to frequency multiplexing composite fringe projection and propose a composite fringe projection deep learning profilometry (CDLP). By combining physical model and data-driven approaches, we demonstrate that the model generated by training an improved deep convolutional neural network can directly perform high-precision and unambiguous phase retrieval on a single-shot spatial frequency multiplexing composite fringe image. Experiments on both static and dynamic scenes demonstrate that our method can retrieve robust and unambiguous phases information while avoiding spectrum aliasing and reconstruct high-quality absolute 3D surfaces of objects only by projecting a single composite fringe image.

Deep-learning-enabled dual-frequency composite fringe projection profilometry for single-shot absolute 3D shape measurement

Single-shot high-speed 3D imaging is important for reconstructions of dynamic objects. For fringe projection profilometry (FPP), however, it is still challenging to recover accurate 3D shapes of isolated objects by a single fringe image. In this paper, we demonstrate that the deep neural networks can be trained to directly recover the absolute phase from a unique fringe image that involves spatially multiplexed fringe patterns of different frequencies. The extracted phase is free from spectrum-aliasing problem which is hard to avoid for traditional spatial-multiplexing methods. Experiments on both static and dynamic scenes show that the proposed approach is robust to object motion and can obtain high-quality 3D reconstructions of isolated objects within a single fringe image.

Noise reduction in speckle interferometry fringe pattern using adaptive Kalman filter

Fringe pattern denoising is of prime importance in phase demodulation, especially for a single fringe pattern in speckle interferometry. A fringe speckle noise removal algorithm using the Kalman filter is proposed. The conventional linear Kalman filter is implemented with a fixed value of the process and measurement noise covariances; the adaptive Kalman filter is implemented with the process, and measurement noise covariances are estimated in an adaptive manner. The fringe denoising is performed sequentially in a rowwise and columnwise manner. The simulated and experimental results demonstrate the practical applicability of the proposed method, and its performance is appraised using metrics such as the quality index, peak signal-to-noise-ratio, and speckle index.

Deep-learning-based fringe-pattern analysis with uncertainty estimation

Deep learning has gained increasing attention in the field of optical metrology and demonstrated great potential in solving a variety of optical metrology tasks, such as fringe analysis and phase unwrapping. However, deep neural networks cannot always produce a provably correct solution, and the prediction error cannot be easily detected and evaluated unless the ground-truth is available. This issue is critical for optical metrology, as the reliability and repeatability of the measurement are of major importance for high-stakes scenarios. In this paper, for the first time to our knowledge, we demonstrate that a Bayesian convolutional neural network (BNN) can be trained to not only retrieve the phase from a single fringe pattern but also produce uncertainty maps depicting the pixel-wise confidence measure of the estimated phase. Experimental results show that the proposed BNN can quantify the reliability of phase predictions under conditions of various training dataset sizes and never-before-experienced inputs. Our work allows for making better decisions in deep learning solutions, paving a new way to reliable and practical learning-based optical metrology.

Method with high accuracy for phase retrieval in Fourier FPP based on the modified FCM and variational image decomposition

Phase retrieval with high accuracy remains one of the most challenging problems in Fourier fringe projection profilometry (FPP). The variational image decomposition TV-Hilbert- L 2 model has been proved to be a powerful tool for phase retrieval. In this paper, we first propose a modified fuzzy c-means (FCM) clustering algorithm to remove background from fringe projection patterns. In order to further improve the accuracy, we combine the modified FCM and the variational image decomposition TV-Hilbert- L 2 model and propose a new method to get the fringe part from the single frame fringe projection pattern. We evaluate the performance of this method via application to two simulated and one experimental fringe projection patterns and comparison with the Fourier transform, morphological operation-based bi-dimensional empirical mode decomposition, and variational image decomposition TV-Hilbert- L 2 model. The experiment results show that our method improves the accuracy of phase retrieval for TV-Hilbert- L 2 model and can achieve similar accuracy to the phase-shifting method.

Batch fringe extraction from the single FPP fringe pattern based on a triple serial and parallel convolution neural network

Batch fringe extraction from the single FPP fringe pattern based on a triple serial and parallel convolution neural network

The terminal segment of the human phrenic nerve as a novel implantation site for diaphragm pacing electrodes: Anatomical and clinical description

BackgroundDiaphragm pacing allows certain ventilator-dependent patients to achieve weaning from mechanical ventilation. The reference method consists in implanting intrathoracic contact electrodes around the phrenic nerve during video-assisted thoracic surgery, which involves time-consuming phrenic nerve dissection with a risk of nerve damage. Identifying a phrenic segment suitable for dissection-free implantation of electrodes would constitute progress. Study designThis study characterizes a free terminal phrenic segment never fully described before. We conducted a cadaver study (n = 14) and a clinical observational study during thoracic procedures (n = 54). ResultsA free terminal phrenic segment was observed on both sides in 100% of cases, "jumping" from the pericardium to the diaphragm and measuring 60 mm [95% confidence interval; 48–63] and 72.5 mm [65–82] (right left, respectively; p = 0.0038; cadaver study). This segment rolled up on itself at end-expiration and became unravelled and elongated with diaphragm descent (clinical study). Three categories of fat pads were defined (type 1: pericardiophrenic bundle free of surrounding fat; type 2: single fatty fringe leaving the phrenic nerve visible until diaphragmatic entry; type 3: multiple fatty fringes masking the site of penetration of the phrenic nerve) that depended on body mass index (p = 0.001, clinical study). Hematoxylin-eosin and toluidine blue staining (cadaver study) showed that all of the phrenic fibers in the distal, pre-branching part of the terminal segment were contained within a single epineurium containing a variable number of fascicles (right: 1 [95%CI 0.65–4.01]; left 5 [3.37–7.63]; p = 0.03). ConclusionDiaphragm pacing through periphrenic electrodes positioned on the terminal phrenic segment should be tested.

Single-shot circular fringe projection for the profiling of objects having surface discontinuities.

Fringe projection profilometry (FPP) is a widely used non-contact optical method for 3D profiling of objects. The commonly used linear fringe pattern in FPP has periodic intensity variations along the lateral direction. As a result, the linear fringe pattern used in FPP cannot uniquely represent the lateral shift induced by the objects having surface discontinuities. Thus, unambiguous surface profiling of objects, especially with surface discontinuities, using a single linear fringe image having a single fringe frequency, is unfeasible. This paper proposes using a radially symmetric circular fringe pattern as the structured light pattern for accurate unambiguous surface profiling of sudden height-discontinuous objects. To the best of our knowledge, this is the only method that can reconstruct discontinuous height profiles with the help of a single fringe image having a single frequency. The performance of the proposed algorithm is evaluated on several synthetic and real objects having smooth variations and discontinuities. Compared to the well-known fringe projection methods, the results depict that for a tolerable range of error, the proposed method can be applied for the reconstruction of objects with 4 times higher dynamic range and even at much lower fringe frequencies.