Full-field Phase Research Articles

Surface profile inspection for large structures with laser scanning

Fringe projection profilometry is a powerful tool that is widely applied to shape measurement of objects in engineering. Limited by the light intensity of the projection unit, this technique is difficult to be applied to surface inspection of large structures, especially in outdoor applications. In this study, a line laser source is selected as the light projection unit. The line laser beam is controlled to scan the surface with the predefined angular speed while a stationary imaging unit captures images. An image fusion strategy has been proposed to construct grating images with a constant phase shift, which facilitates full-field phase shifting in determination of the structural profile. The accuracy of the measurement method is discussed and compared with a commercial 3D laser scanner. The proposed technique has also been applied to the surface topography of the wind turbine blades. The experimental results show that the bulging defects on the surface of the wind turbine blade model are detectable, which shows the feasibility of the proposed method in characterization of surface profile on large structures.

Modal Reconstruction Based on Arbitrary High-Order Zernike Polynomials for Deflectometry

Deflectometry is a non-destructive, full-field phase measuring method, which is usually used for inspecting optical specimens with special characteristics, such as highly reflective or specular surfaces, as well as free-form surfaces. One of the important steps in the Deflectometry method is to retrieve the surface from slope data of points on the sample map or surface reconstruction. This paper proposes a modal reconstruction method using an adjustable number of Zernike polynomials. In addition, the proposed method enables the analyses on practical surfaces that require an infinite number of Zernike terms to be represented. Experiments on simulated surfaces indicated that the algorithm is able to reveal the number of major-contributing Zernike terms, as well as reconstruct the surface with a micrometer-scale from slope data with a signal-to-noise ratio of 10.

Digital phase-shift method based on distance mapping for phase recovery of an ESPI fringe pattern.

In view of the limitation of the traditional method to recover the phase of the single fringe pattern, we propose a digital phase-shift method based on distance mapping for phase recovery of an electronic speckle pattern interferometry fringe pattern. First, the direction of each pixel point and the centerline of the dark fringe are extracted. Secondly, the normal curve of the fringe is calculated according to the fringe orientation to obtain the fringe moving direction. Thirdly, the distance between each pixel point and the next pixel point in the same phase is calculated by a distance mapping method according to the adjacent centerlines; then the moving distance of the fringes is obtained. Next, combining the moving direction and moving distance, the fringe pattern after the digital phase shift is obtained by full-field interpolation. Finally, the full-field phase corresponding to the original fringe pattern is recovered by four-step phase shifting. The method can extract the fringe phase from a single fringe pattern through digital image processing technology. The experiments show that the proposed method can effectively improve the phase recovery accuracy of a single fringe pattern.

Full-field quantitative X-ray phase nanotomography via space-domain Kramers–Kronig relations

Given the low absorption contrast of X-rays, phase shift has been playing an important role as an alternative source of contrast in X-ray nanoimaging. Numerous phase-measuring techniques have been proposed, most of which, however, are based on significant assumptions or sample translations. In this study, we propose the application of Kramers–Kronig (KK) relations in the spatial domain as a solution to allow the X-ray quantitative phase image to be directly calculated from the measured intensity image without any additional requirements. Based on this straightforward principle, we have presented KK nanotomography by introducing a spatial-frequency cutoff filter into a conventional tomographic setup. The robustness and versatility of the proposed method were experimentally verified based on various sample tomograms. We expect KK nanotomography to be widely adopted as a powerful and easy-to-adapt phase quantification solution for X-ray microscopes.

Super-resolution 4D flow MRI to quantify aortic regurgitation using computational fluid dynamics and deep learning

Changes in cardiovascular hemodynamics are closely related to the development of aortic regurgitation (AR), a type of valvular heart disease. Metrics derived from blood flows are used to indicate AR onset and evaluate its severity. These metrics can be non-invasively obtained using four-dimensional (4D) flow magnetic resonance imaging (MRI), where accuracy is primarily dependent on spatial resolution. However, insufficient resolution often results from limitations in 4D flow MRI and complex aortic regurgitation hemodynamics. To address this, computational fluid dynamics simulations were transformed into synthetic 4D flow MRI data and used to train a variety of neural networks. These networks generated super-resolution, full-field phase images with an upsample factor of 4. Results showed decreased velocity error, high structural similarity scores, and improved learning capabilities from previous work. Further validation was performed on two sets of in vivo 4D flow MRI data and demonstrated success in de-noising flow images. This approach presents an opportunity to comprehensively analyse AR hemodynamics in a non-invasive manner.

Single-Shot Multi-Frequency 3D Shape Measurement for Discontinuous Surface Object Based on Deep Learning

It is challenging to stably and rapidly achieve accurate absolute phase retrieval for isolated objects with a single-shot pattern in fringe projection profilometry (FPP). In this context, a single-shot multi-frequency absolute phase retrieval (SAPR-DL) method based on deep learning is proposed, which only needs to capture one fringe image to obtain the full-field precise absolute phase. Specifically, a low-frequency deformed fringe image is loaded into the trained one-to-two deep learning framework (DLFT) to predict unit-frequency and high-frequency deformed fringe images. Then, three fringe images with different frequencies are loaded into the trained deep learning phase retrieval framework (DLPR) to calculate the corresponding absolute phase. The experimental results prove that the proposed SAPR-DL method can obtain the three-dimensional (3D) shape measurement of multiple complex objects by collecting a single-shot fringe image, showing great prospects in advancing scientific and engineering applications.

Dynamic range expansion of spatial light modulators based on a module-nπ method.

It is known that the cumbersome 2π correction is needed in the traditional module-2π method (i.e.,the phase wrapping method) due to the 2π deviation of the phase modulation depth of spatial light modulators (SLMs). To avoid the cumbersome 2π correction in the module-2π method, this paper proposes a module-n π method, and it can directly utilize any full-field phase modulation depth. First, for a Gaussian phase with a phase depth of 30rad, wrapped by the module-3.6π, it is reconstructed with the root-mean-square (RMS) values of its phase response are 0.1006λ (for the Twyman-Green interferometer) and 0.1101λ (for the Shack-Hartmann wavefront sensor method), respectively, which proves that the monitoring accuracy is relatively consistent. Subsequently, some comparative experiments based on the traditional module-2π are performed. The experimental results show that the RMS values of its phase response are 0.8886λ (for a modulation depth of 11.3rad) and 0.2261λ (for a modulation depth of 6.28rad), respectively. All the results have proved that the SLM with a phase modulation depth exceeding 2π (e.g.,11.3rad) has more prominent advantages. More specifically, increasing the SLM's phase modulation depth can effectively reduce the fringe orders of the wrapped patterns generated by the module-n π method. With the further reduction of the fringe orders, the influence of the fly-back zone error on the wavefront phase modulation is reduced, that is, the modulation accuracy is improved (the RMS values are reduced from 0.2261λ to 0.1006λ). Different from the traditional module-2π method, there is no need to consider the problems of the SLMs' over modulation or the insufficient modulation in the module-n π method. Furthermore, it avoids the cumbersome 2π correction process, which will make the use of the SLM more convenient.

Label-free full-field Doppler phase microscopy based on optical computation.

The capability to image subtle mechanical motion at cellular and sub-cellular scales can be used to study how extracellular particles interact with cultured cells and, more generally, how cells interact with their environment. However, current technologies need to provide sufficient spatial resolution, temporal resolution, and motion sensitivity to image cellular and sub-cellular motion in the en face plane. To address this unmet need, we investigate a full-field Doppler phase microscopy (FF-DPM) technology based on an innovative optical computation strategy that enables depth-resolved imaging and phase quantification. In this study, we validated the motion tracking (displacements and velocities) capability of FF-DPM by imaging samples actuated by a piezo transducer (PZT). We demonstrated FF-DPM imaging of magnetic particles under different conditions with different motion characteristics. Our results show that free particles (suspended in a cell culture medium) had a significantly larger magnitude of motion than particles adhered to a cell. The key innovation of this study is the use of an optical computation strategy to perform depth-resolved phase quantification and Doppler measurement. The FF-DPM will have a significant impact, as it provides a unique capability to quantitatively measure subtle motion for models based on cultured cells.

Nonlinear error full-field compensation method for phase measuring profilometry.

Phase measuring profilometry (PMP) has the highest measuring accuracy among structured light projection-based three-dimensional (3D) sensing methods. Due to their low-cost and high-resolution features, commercial projectors are extensively used in PMP, but they are all designed with a gamma effect purpose that considers the characteristics of human vision. Affected by the gamma effect, a set of phase-shifting sinusoidal deformed patterns captured in PMP may contain high-order harmonics which lead to nonlinear phase errors. Then, a novel nonlinear error full-field compensation method is proposed. First, the unwrapped phases modulated by the reference plane are measured several times, and their average phase is taken as the measured phase modulated by the reference plane to eliminate random errors as much as possible. Second, an expected phase plane is fitted from this average phase with the least-squares method. Third, the nonlinear phase error can be detected by subtracting the fitted expected phase from this average phase. Finally, the full-field look-up table (LUT) can be established between the nonlinear phase error and the measured phase. When an object is measured, the unwrapped phase modulated by the object is taken as the measured phase of the LUT, so the corresponding nonlinear phase error can be directly searched in the LUT. In this way, the full-field nonlinear phase error can be efficiently compensated. Experimental results show the feasibility and validity of the proposed method. The mean absolute error (MAE) can be improved from 0.48mm to 0.06mm, and the root mean square error (RMSE) can be improved from 0.55mm to 0.07mm.

Full-field phase shifting and stress quantification using a polarization camera

Phase shifting technique is widely used in determination of photoelastic parameters.Efficient full-field stress quantification remains a challenge due to cumbersome rotation of optical elements in the polarizer and the complex stress separation strategy. By deriving the mathematical expressions with the Stokes parameters with the use of a polarization camera, a simple operation method achieving phase shifting for accurately determining photoelastic parameters has been proposed. A stress separation strategy for full-field stress calculation has also been developed. Experiments are presented on a circular plate subjected to diametric compression and a special-shaped sample subjected to compressive loads.Experimental results indicate that the proposed methods enable a simple and accurate full-field stress determination for photoelastic samples.

Photothermal Radar Shearography: A Novel Transient-Based Speckle Pattern Interferometry for Depth-Tomographic Inspection

As an increasingly recognized optical interferometric technique for nondestructive testing and evaluation, shearography has attracted extensive interest in various industrial applications. However, it suffers from the ignorance of the whole process of dynamic surface deformation and the difficulty in determining the depth-resolved information of inhomogeneities. In this regard, a novel speckle pattern interferometric modality named photothermal radar shearography is proposed. Unlike the differential mode of conventional shearography, the present article focuses on the dynamic surface displacement field channel technique with more comprehensive understanding of the subsurface structural information. With the utilization of frequency modulated photothermal excitation, the depth-distributed information of subsurface structures and inhomogeneities is encoded into the induced dynamic surface deformation. Using Hilbert transform and least-square method solved by discrete cosine transform, the time-domain interference signal of each pixel from the recorded speckle patterns sequence is demodulated and unwrapped to obtain the transient full-field shearographic phase distribution which indicates the dynamic surface deformation. In the meanwhile, incrementally delayed cross-correlation matched filtering allows for the localization of axial energy distribution to generate depth-selective structural display for tomography. This proposed transient-based interferometric methodology thus enables depth-tomographic profiles and three-dimensional visualization of subsurface anomalies for the first time, which significantly improves the superiority and attractiveness of shearography in providing insight into the status, performance and reliability of industry.

A novel phase-shifting profilometry to realize temporal phase unwrapping simultaneously with the least fringe patterns

A novel phase-shifting profilometry (PSP) to realize temporal phase unwrapping (TPU) simultaneously with the least fringe patterns is proposed. By combining a unit-frequency ramp pattern with the least three phase-shifting sinusoidal fringe patterns at a shifted-phase of π/2 respectively, three composite patterns are formed. While these three composite patterns are projected onto the measured object successively, three corresponding deformed patterns can be captured by a CCD camera. After demodulation, both the unit-frequency component and the high-frequency components characterized by phase-shifting deformed patterns can be extracted efficiently. So the wrapped phase caused by the measured object can be calculated from the high-frequency components of the deformed patterns with PSP and the fringe orders can be derived from the unit-frequency components to pixel-wise auxiliary phase unwrapping. It employs no other additional structure pattern to achieve full-field phase unwrapping. The accuracy of the measurement is guaranteed by using three phase-shifting fringe patterns, and the combination of the TPU can measure the discontinuous surfaces or multiple isolated objects simultaneously. PSP and TPU are integrated skillfully with least fringe patterns in the proposed method. The experimental results demonstrated the feasibility and validity of the proposed method.

Efficient sorting for an orbital angular momentum multiplexing communication link based on a digital micromirror device and a diffuser.

Efficient sorting multiple orbital angular momentum (OAM) spatial modes is a significant step in OAM multiplexing communications. Recently, wavefront shaping (WS) techniques have been implemented to manipulate light scattering through a diffuser. We reported a novel scheme for sorting multiplexed OAM modes faster and more accurately, using the complex amplitude WS based on a digital micromirror device (DMD) through a diffuser to shape the full field (phase and amplitude) of the OAM modes. In this study, we simulate this complex sorter for demultiplexing multiple modes and make a performance comparison with the previous sorter using the phase-only WS. Our results showed that for arbitrary two multiplexed modes, the sorter could achieve a high detection probability of more than 0.99. As the number of the multiplexed modes increases, the detection probability decreases to ∼0.82 when sorting seven modes, which contrasts the ∼0.71 of the phase-only sorters. We also experimentally verified the feasibility, that for arbitrary two modes, the sorter could reach a high detection probability of more than 0.99, and the complex sorter is capable of higher detection probability than the phase-only sorter under the same conditions. Hence, we anticipate that this sorter may potentially be demultiplexing multiple OAM spatial modes efficiently and quickly.

Lensless Fourier-Transform Terahertz Digital Holography for Full-Field Reflective Imaging

Continuous-wave terahertz digital holography (TDH) is a full-field lensless phase imaging approach usually with the coherent THz laser. It has the potential to be applied to nondestructive testing. In order to simplify the reconstruction and utilize the THz radiation with higher efficiency, a full-field reflective lensless Fourier-transform TDH (RLF-TDH) configuration is proposed with oblique illumination mode based on 2.52 THz radiation. A spherical reference beam is generated by a reflective concave mirror in order to reduce the loss of THz radiation, which is different from other configurations of the same kind. In the reconstruction process, the complex-amplitude image can be obtained by directly applying single Fourier transform to the digital hologram; thus, it is very possible to achieve real-time imaging. A tilted plane correction method is implemented to correct the anamorphism caused by the nonparallel planes between the object and recording plane. The profile information of the object can be measured from the unwrapped, aberration-free phase image. Two reflective gold-coated samples are adopted to demonstrate the validity of the RLF-TDH imaging system.

Collaborative Strategy Heightens Efficiency of North Sea Predrilling Campaign

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper OTC 30850, “Perfecting the ‘Perfect Well’: Lessons Learned From the Predrilling Campaign for Johan Sverdrup,” by Janne Vølstad and Stian Bærheim, Equinor, and Knut Henriksen, Baker Hughes, et al. The paper has not been peer reviewed. Copyright 2021 Offshore Technology Conference. Reproduced by permission. The predrilling campaign for the Johan Sverdrup development was a key contributor to the successful execution of the first phase of the megaproject. After a summary of the results of the campaign, the focus of the complete paper is to identify some of the key factors behind the success of the campaign and outline lessons learned relevant to future drilling campaigns. Since the completion of the predrilling campaign, the project has successfully tied back, completed, and begun production of eight predrilled oil producers and injection in 12 subsea injectors. Johan Sverdrup Field The field is approximately 150 km west of Stavanger in a water depth of 110–120 m. The top reservoir is situated approximately 1800 m below mean sea level. The reservoir features hydrostatic pressure and undersaturated oil with a low gas/oil ratio. The field has been developed in two phases. Phase 1, approved by Norwegian authorities in 2015, includes four bridge-linked platforms (Fig. 1). These platforms include a living-quarters platform (LQ) with utility system functions, a process platform (P1), a drilling platform (DP), and a riser platform (RP) with tie-in of onshore power. Phase 1 includes three injection templates tied back to the RP. All platforms have jacket substructures. Main power to the field is supplied from shore. The full field development includes 64 wells, both platform and subsea. The field came onstream in October 2019. Ramp-up of the predrilled wells went smoothly to a field production level of approximately 350,000 B/D. Phase 2 of the development was approved in 2019 and is expected to begin production in Q4 2022. Phase 2 includes development of another processing platform (P2), modifications of the RP and the field center, and five subsea production and injection templates. At peak, this field will account for approximately one-third of all oil production in Norway. Expected recoverable reserves are 2.7 billion BOE. The full field (Phase 1 and 2) expected oil production capacity is 105,000 std m3/d (660,000 B/D) at peak. Breakeven price for the full-field development is less than $20/bbl.

Lensless Fourier-transform terahertz digital holography for real-time full-field phase imaging

With the development of continuous-wave terahertz (THz) sources and array detectors, the pursuit of high-fidelity real-time imaging is receiving significant attention within the THz community. Here, we report a real-time full-field THz phase imaging approach based on lensless Fourier-transform THz digital holography. A triangular interferometric layout is proposed based on an oblique illumination of 2.52 THz radiation, which is different from other lensless holographic configurations at other frequencies. A spherical reference beam is generated by a reflective parabolic mirror with minor propagation loss. The complex-valued images are reconstructed using a single inverse Fourier transform of the hologram without complex calculation of the diffraction propagation. The experimental result for a Siemens star validates the lateral resolution of ∼ 346 μm in the diagonal direction. Sub-pixel image registration and image stitching algorithms are applied to enlarge the area of the reconstructed images. The dehydration process of an aquatic plant leaf (Hottonia inflata) is monitored for the first time, to the best of our knowledge, at the THz band. Rapid variations in water content and morphology are measured with a time interval of 0.6 s and a total time of 5 min from a series of reconstructed amplitude and phase images, respectively. The proposed method has the potential to become a powerful tool to investigate spontaneous phenomena at the THz band.

Multi-slice coded coherent diffraction imaging

Coded coherent diffraction imaging (CDI) introduces wavefront modulation to realize full-field phase retrieval, without mechanical scanning as in ptychography. The conventional coded CDI relies on the assumption of thin samples, which breaks down when handling thick objects with multiple scattering and diffraction effects. In this study, we report a multi-slice coded CDI technique that enables to reconstruct thick objects with high fidelity. The object is modeled as a group of multiple slices, and the wavefront exiting the object is calculated after slice-to-slice propagation. We develop an optimization algorithm to simultaneously reconstruct multiple complex-field slices, as well as the slice distances. This enables successful reconstruction without the prior knowledge of slice separations that is hard to calibrate. Experimental results show that reconstruction of more slices can be achieved by increasing the number of modulations. The required modulation number is 7 for 2-slice objects, 14 for 3-slice objects, and 20 for 4-slice objects. Unknown slice distance that is at most ∼±30% deviating from the groundtruth can be effectively corrected.

Full-field heterodyne phase shifting two-wavelength interferometry surface testing technologies

Full-field heterodyne phase shifting two-wavelength interferometry surface testing technologies

2D full-field displacement and vibration measurements of specularly reflecting surfaces by two-beam common-path digital holography.

A new, to the best of our knowledge, configuration of common-path off-axis digital holography is proposed for simultaneous evaluation of out-of-plane and in-plane displacements of the vibrating object. The object is illuminated from two different directions, and each illumination interferes with its corresponding reference beam generated near the object, resulting in two independent holograms that are spatially multiplexed in a single camera image. Two multiplexed holograms, at undeformed and deformed states of the object, are recorded and processed to obtain the out-of-plane and in-plane displacements simultaneously. The proposed digital holographic system has the advantage of a simple and compact optical setup, is less sensitive to environmental disturbances, and has high temporal phase stability. The two-dimensional (z,x) full-field amplitude and phase vibration analysis of a perfect specularly reflecting surface are also demonstrated by the proposed holographic system. The experimental results authenticate the feasibility of the proposed system and reveal its unique advantages. The proposed digital holographic system, owing to simple and compact geometry and providing several advantages over other two-channel holographic systems, may find a wide range of applications in investigating real-time dynamic phenomena.

Low-latency full-field temporal magnification based on spectral compression

Temporal magnification is an emerging technology for the observation of single-shot optical signals with irregular and ultrafast dynamics, which exceed the speed, precision, and record length of conventional digitizers. Conventional temporal magnification schemes suffer from transmission delay and large volume of dispersive elements. Because only the signal envelope can be magnified in the dispersion-based schemes, real-time full-field (phase and amplitude) measurement for a complex ultrafast optical signal remains an open challenge. Here, a bandwidth-compressed temporal magnification scheme for low-latency full-field measurements of ultrafast dynamics is proposed. Unlike the dispersion-based schemes, temporal magnification of a complex optical signal is achieved by bandwidth compression. The bandwidth is coherently compressed by the Vernier effect relying on the detuned free spectral range of a periodic optical filter and time lens. Experimentally, a temporal magnification factor of 224 is realized, and full-field measurements for picosecond pulses are demonstrated. The proposal eliminates the dependence on dispersive elements and shows great potential in integration, which may pave a new path toward full-field measurement for nonrepetitive and statistically rare signals.