Phase retrieval of two random phase-shifting interferograms using Zernike coefficient extraction network.

This paper proposes a deep learning method for phase retrieval from two interferograms. The proposed method converts phase retrieval into the Zernike coefficient extraction problem, which can achieve Zernike coefficient extraction from two interferograms with random phase shifts. After knowing Zernike coefficients, the phase distribution can be retrieved using Zernike polynomials. The pre-filtering and phase unwrapping process are not required using the proposed method. The simulated data are analyzed, and the root mean square (RMS) of phase error reaches 0.01 λ. The effectiveness of the method is verified by the measured data.

Virtual temporal phase-shifting phase extraction using generative adversarial networks.

In this paper, a virtual temporal phase-shifting method based on generative adversarial networks (GANs) is proposed to realize dynamic measurement, which is referred to as PSNet. The proposed PSNet can produce the virtual phase-shifting fringe patterns from the single-frame fringe pattern, and the standard n-step phase-shifting method is employed to obtain the wrapped phase from the virtual fringe patterns. The wrapped phase can further be unwrapped by the unwrapping algorithm. Simulation analysis shows that the PSNet can produce the virtual phase-shifting fringe patterns without noise, and thus, the denoising process is eliminated. The performance of the method is verified from the captured fringe in the interferometer, which demonstrates the practicability of the proposed method.

Measurement of acylindrical surface with transport of intensity equation.

High-precision aspherical cylindrical (acylindrical) lenses are difficult to directly measure because of the phase deviation in the off-axis region. To achieve rapid and non-contact measurement of the acylindrical lens surface, a novel optical structure phase measurement, to the best of our knowledge, is presented in this work. Both common finite-difference and noise-reduction finite-difference methods were used for solving the transport of intensity equation (TIE) for reconstruction of high-resolution surface measurement. The results suggest that both common finite-difference and noise-reduction finite-difference methods can obtain good measurement results. The proposed method allows for the direct measurement of surface information without interference stitching. The accuracy of the TIE measurement has been verified through direct contact measurement.

Temporal phase unwrapping using deep learning.

The multi-frequency temporal phase unwrapping (MF-TPU) method, as a classical phase unwrapping algorithm for fringe projection techniques, has the ability to eliminate the phase ambiguities even while measuring spatially isolated scenes or the objects with discontinuous surfaces. For the simplest and most efficient case in MF-TPU, two groups of phase-shifting fringe patterns with different frequencies are used: the high-frequency one is applied for 3D reconstruction of the tested object and the unit-frequency one is used to assist phase unwrapping for the wrapped phase with high frequency. The final measurement precision or sensitivity is determined by the number of fringes used within the high-frequency pattern, under the precondition that its absolute phase can be successfully recovered without any fringe order errors. However, due to the non-negligible noises and other error sources in actual measurement, the frequency of the high-frequency fringes is generally restricted to about 16, resulting in limited measurement accuracy. On the other hand, using additional intermediate sets of fringe patterns can unwrap the phase with higher frequency, but at the expense of a prolonged pattern sequence. With recent developments and advancements of machine learning for computer vision and computational imaging, it can be demonstrated in this work that deep learning techniques can automatically realize TPU through supervised learning, as called deep learning-based temporal phase unwrapping (DL-TPU), which can substantially improve the unwrapping reliability compared with MF-TPU even under different types of error sources, e.g., intensity noise, low fringe modulation, projector nonlinearity, and motion artifacts. Furthermore, as far as we know, our method was demonstrated experimentally that the high-frequency phase with 64 periods can be directly and reliably unwrapped from one unit-frequency phase using DL-TPU. These results highlight that challenging issues in optical metrology can be potentially overcome through machine learning, opening new avenues to design powerful and extremely accurate high-speed 3D imaging systems ubiquitous in nowadays science, industry, and multimedia.

Research on a Novel Fabry⁻Perot Interferometer Model Based on the Ultra-Small Gradient-Index Fiber Probe.

A novel Fabry⁻Perot (F⁻P) interferometer model based on the ultra-small gradient-index (GRIN) fiber probe is investigated. The signal arm of the F⁻P interferometer is organically combined with the ultra-small GRIN fiber probe to establish the theoretical model of the novel F⁻P interferometer. An interferometer experimental system for vibration measurements was built to measure the performance of the novel F⁻P interferometer system. The experimental results show that under the given conditions, the output voltage of the novel interferometer is 3.9 V at the working distance of 0.506 mm, which is significantly higher than the output voltage 0.48 V of the single-mode fiber (SMF) F⁻P interferometer at this position. In the range of 0.1⁻2 mm cavity length, the novel interferometer has a higher output voltage than an SMF F⁻P interferometer. Therefore, the novel F⁻P interferometer is available for further study of the precise measurement of micro vibrations and displacements in narrow spaces.

Optical image hiding under framework of computational ghost imaging based on an expansion strategy.

A novel optical image hiding scheme based on an expansion strategy is presented under the framework of computational ghost imaging. The image to be hidden is concealed into an expanded interim with the same size as the host image. This is implemented by rearranging the measured intensities of the original object after the process of ghost imaging. An initial Hadamard matrix is used to generate additional matrices by shifting it circularly along the column direction, so that enough 2D patterns are engendered to retrieve phase-only profiles for imaging. Next, the frequency coefficients of the host image are modified with that of the expanded interim by controlling a small weighting factor. After an inverse transform, the host image carrying the hidden information can be obtained with high imperceptibility. Security is assured by considering optical parameters, such as wavelength and axial distance, as secret keys due to their high sensitivity to tiny change. Importantly, differing from other computational ghost imaging based schemes, many phase-only profiles are used to collect the measured intensities to enhance the resistance against noise and occlusion attacks. The simulated experiments illustrate the feasibility and effectiveness of the proposed scheme.

Measurement of thermal effects of diode-pumped solid-state laser by using digital holography.

Thermal lensing is one of the most important factors that can affect the performance of high-power solid-state lasers, such as limiting the power scaling capability and deteriorating output beam quality. In this paper, a novel and accurate measurement of digital holography is proposed to determine the thermal lensing of diode-pumped solid-state lasers with high resolution. The digitally recorded hologram can reveal the phase change when light travels through the laser gain medium. From the phase map, we can obtain the index variations induced by temperature differences inside the laser crystal when it is pumped by laser diodes, as well as determine the focal length of the integrated thermal lensing focus length. There was much work on measuring the static laser medium thermal lens because there is no laser output from the cavity in the setup. Our experiment setup was able to achieve online measurement with laser output at the same time. The measuring result can provide an accurate guide for compensating the thermal lensing in laser design to achieve high-power output and good beam quality. Moreover, detailed index variations in the direction of the laser crystal cross-section can be numerically reconstructed, by which the thermal effects, pump uniformity, crystal uniformity, etc., can be revealed from the holography result.

Chitosan nanoparticles' functionality as redox active drugs through cytotoxicity, radical scavenging and cellular behaviour.

Targeting the oxidative stress response has recently emerged as a promising strategy for the development of therapeutic drugs for a broad spectrum of diseases. Supporting this strategy, we have reported that chitosan nanoparticles synthesized with a controlled size had selective cytotoxicity in leukemia cells through the mechanism related to reactive oxygen species (ROS) generation. Herein, we found that the cellular uptake of chitosan nanoparticles was enhanced in a time dependent manner and inhibited the cellular proliferation of leukemia cells in a dose dependent manner with elevation of the reactive oxygen species (ROS) showing a stronger effect on apoptosis, associated with the upregulation of caspase activity and the depletion of reduced glutathione. Propidium iodide and calcein staining demonstrated the central role of the chitosan nanoparticles in triggering elevated ROS, inducing cell death and intracellular oxidative activity. The enhanced free radical scavenging activity of the chitosan nanoparticles further iterates its antioxidant activity. In vitro quantitative phase imaging studies at the single cell level further demonstrated the inhibition of cellular proliferation with significant changes in cellular behavior and this supported our hypothesis. Hemocompatibility tests demonstrated that chitosan nanoparticles could be used safely for in vivo applications. Our findings suggest that chitosan nanoparticles may be a promising redox active candidate for therapeutic applications.

Simultaneous measurement and reconstruction tailoring for quantitative phase imaging.

We propose simultaneous measurement and reconstruction tailoring (SMaRT) for quantitative phase imaging; it is a joint optimization approach to inverse problems wherein minimizing the expected end-to-end error yields optimal design parameters for both the measurement and reconstruction processes. Using simulated and experimentally-collected data for a specific scenario, we demonstrate that optimizing the design of the two processes together reduces phase reconstruction error over past techniques that consider these two design problems separately. Our results suggest at times surprising design principles, and our approach can potentially inspire improved solution methods for other inverse problems in optics as well as the natural sciences.

Full-color holographic 3D display using slice-based fractional Fourier transform combined with free-space Fresnel diffraction.

The fractional Fourier transform (FRT) has been used for computing holograms in holographic displays due to its continuity of describing wave diffraction in the near field and far field. In this study, we propose a method to realize a full-color holographic 3D display with combined use of the FRT and the free-space Fresnel diffraction. A slice-based optical configuration and the calculation algorithm of the FRT are proposed for generating phase-only holograms of full-color 3D objects. Sequential phase-only holograms are generated for reducing the speckle noise of reconstructed images by the time-averaging effect. Free-space Fresnel diffraction is used for 3D image reconstruction from the generated holograms. The relationship between the fractional orders of different color channels and the free-space Fresnel diffraction distance is analyzed. Chromatic aberrations caused by different wavelengths of RGB lasers are also compensated. A full-color holographic display system using a reflective phase-only spatial light modulator (SLM) is established. Both the numerical and optical reconstruction results demonstrate the feasibility of the proposed method.

Full-color holographic 3D display using slice-based fractional Fourier transform combined with free-space Fresnel diffraction: erratum.

We have addressed some errors in our recent work [Appl. Opt.56, 5668 (2017)APOPAI0003-693510.1364/AO.56.005668]. Especially, we note that the formulae for reconstruction of phase-only holograms are different from the formulae for amplitude holograms. So Eqs. (9) and (12) must be modified.

High-resolution transport-of-intensity quantitative phase microscopy with annular illumination.

For quantitative phase imaging (QPI) based on transport-of-intensity equation (TIE), partially coherent illumination provides speckle-free imaging, compatibility with brightfield microscopy, and transverse resolution beyond coherent diffraction limit. Unfortunately, in a conventional microscope with circular illumination aperture, partial coherence tends to diminish the phase contrast, exacerbating the inherent noise-to-resolution tradeoff in TIE imaging, resulting in strong low-frequency artifacts and compromised imaging resolution. Here, we demonstrate how these issues can be effectively addressed by replacing the conventional circular illumination aperture with an annular one. The matched annular illumination not only strongly boosts the phase contrast for low spatial frequencies, but significantly improves the practical imaging resolution to near the incoherent diffraction limit. By incorporating high-numerical aperture (NA) illumination as well as high-NA objective, it is shown, for the first time, that TIE phase imaging can achieve a transverse resolution up to 208 nm, corresponding to an effective NA of 2.66. Time-lapse imaging of in vitro Hela cells revealing cellular morphology and subcellular dynamics during cells mitosis and apoptosis is exemplified. Given its capability for high-resolution QPI as well as the compatibility with widely available brightfield microscopy hardware, the proposed approach is expected to be adopted by the wider biology and medicine community.

Full-color holographic display with increased-viewing-angle [Invited].

Among the important features of holographic displays are the wide viewing angles and the full color of the reconstructed images. The present work focuses on achievement of both features. We propose an increased-viewing-angle full-color holographic display using two tiled phase-only spatial light modulators (SLMs), a 4f concave mirrors system, and a temporal-spatial multiplexing method. The 4f optical system consists of two concave mirrors and serves to increase the viewing angle. A temporal-spatial multiplexing synchronization control (TSMSC) method is developed to achieve a full-color image and to remove the color crosstalk of the image. We calculate RGB phase-only holograms of a computer-generated color pyramid by using a slice-based Fresnel diffraction algorithm. The experimental results indicate that the proposed display system is feasible to reconstruct a full-color holographic 3D image with a viewing angle of 12.8°, which is about 3.8 times wider than the viewing angle formed by a single SLM.

Linear programming phase unwrapping for dual-wavelength digital holography.

A linear programming phase unwrapping method in dual-wavelength digital holography is proposed and verified experimentally. The proposed method uses the square of height difference as a convergence standard and theoretically gives the boundary condition in a searching process. A simulation was performed by unwrapping step structures at different levels of Gaussian noise. As a result, our method is capable of recovering the discontinuities accurately. It is robust and straightforward. In the experiment, a microelectromechanical systems sample and a cylindrical lens were measured separately. The testing results were in good agreement with true values. Moreover, the proposed method is applicable not only in digital holography but also in other dual-wavelength interferometric techniques.

Motion-oriented high speed 3-D measurements by binocular fringe projection using binary aperiodic patterns.

Fringe projection is an extensively used technique for high speed three-dimensional (3-D) measurements of dynamic objects. To precisely retrieve a moving object at pixel level, researchers prefer to project a sequence of fringe images onto its surface. However, the motion often leads to artifacts in reconstructions due to the sequential recording of the set of patterns. In order to reduce the adverse impact of the movement, we present a novel high speed 3-D scanning technique combining the fringe projection and stereo. Firstly, promising measuring speed is achieved by modifying the traditional aperiodic sinusoidal patterns so that the fringe images can be cast at kilohertz with the widely used defocusing strategy. Next, a temporal intensity tracing algorithm is developed to further alleviate the influence of motion by accurately tracing the ideal intensity for stereo matching. Then, a combined cost measure is suggested to robustly estimate the cost for each pixel and lastly a three-step framework of refinement follows not only to eliminate outliers caused by the motion but also to obtain sub-pixel disparity results for 3-D reconstructions. In comparison with the traditional method where the effect of motion is not considered, experimental results show that the reconstruction accuracy for dynamic objects can be improved by an order of magnitude with the proposed method.

Close-range photogrammetry with light field camera: from disparity map to absolute distance.

A new approach to measure the 3D profile of a texture object is proposed utilizing light field imaging, in which three key steps are required: a disparity map is first obtained by detecting the slopes in the epipolar plane image with the multilabel technique; the intrinsic parameters of the light field camera are then extracted by camera calibration; at last, the relationship between disparity values and real distances is built up by depth calibration. In the last step, a linear calibration method is proposed to achieve accurate results. Furthermore, the depth error is also investigated and compensated for by reusing the checkerboard pattern. The experimental results are in good agreement with the 3D models, and also indicate that the light field imaging is a promising 3D measurement technique.

Geometric analysis of influence of fringe directions on phase sensitivities in fringe projection profilometry.

In fringe projection profilometry, phase sensitivity is one of the important factors affecting measurement accuracy. A typical fringe projection system consists of one camera and one projector. To gain insight into its phase sensitivity, we perform in this paper a strict analysis in theory about the dependence of phase sensitivities on fringe directions. We use epipolar geometry as a tool to derive the relationship between fringe distortions and depth variations of the measured surface, and further formularize phase sensitivity as a function of the angle between fringe direction and the epipolar line. The results reveal that using the fringes perpendicular to the epipolar lines enables us to achieve the maximum phase sensitivities, whereas if the fringes have directions along the epipolar lines, the phase sensitivities decline to zero. Based on these results, we suggest the optimal fringes being circular-arc-shaped and centered at the epipole, which enables us to give the best phase sensitivities over the whole fringe pattern, and the quasi-optimal fringes, being straight and perpendicular to the connecting line between the fringe pattern center and the epipole, can achieve satisfyingly high phase sensitivities over whole fringe patterns in the situation that the epipole locates far away from the fringe pattern center. The experimental results demonstrate that our analyses are practical and correct, and that our optimized fringes are effective in improving the phase sensitivities and, further, the measurement accuracies.

Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization.

A micro-electro-mechanical-system (MEMS) is a widely used component in many industries, including energy, biotechnology, medical, communications, and automotive. However, effective inspection and characterization metrology systems are needed to ensure the functional reliability of MEMS. This study presents a system based on digital holography as a tool for MEMS metrology. Digital holography has gained increasing attention in the past 20 years. With the fast development and decreasing cost of sensor arrays, resolution of such systems has increased broadening potential applications. Thus, it has attracted attention from both research and industry sides as a potential reliable tool for industrial metrology. Indeed, by recording the interference pattern between an object beam (which contains sample height information) and a reference beam on a CCD camera, one can retrieve the quantitative phase information of an object. However, most of digital holographic systems are bulky and thus not easy to implement on industry production lines. The novelty of the system presented is that it is lens-less and thus very compact. In this study, it is shown that the Compact Digital Holographic Microscope (CDHM) can be used to evaluate several characteristics typically consider as criteria in MEMS inspections. The surface profiles of MEMS in both static and dynamic conditions are presented. Comparison with AFM is investigated to validate the accuracy of the CDHM.

Focal length calibration of an electrically tunable lens by digital holography.

The electrically tunable lens (ETL) is a novel current-controlled adaptive optical component which can continuously tune its focus in a specific range via changing its surface curvature. To quantitatively characterize its tuning power, here we assume the ETL to be a pure phase object and present a novel calibration method to dynamically measure its wavefront by use of digital holographic microscopy (DHM). The least squares method is then used to fit the radius of curvature of the wavefront. The focal length is obtained by substituting the radius into the Zemax model of the ETL. The behavior curve between the focal length of the ETL and its driven current is drawn, and a quadratic mathematic model is set up to characterize it. To verify our model, an ETL and offset lens combination is proposed and applied to ETL-based transport of intensity equation (TIE) phase retrieval microscopy. The experimental result demonstrates the calibration works well in TIE phase retrieval in comparison with the phase measured by DHM.

Phase retrieval with the transport-of-intensity equation in an arbitrarily shaped aperture by iterative discrete cosine transforms.

A transport-of-intensity equation (TIE)-based phase retrieval method is proposed with putting an arbitrarily shaped aperture into the optical wavefield. In this arbitrarily shaped aperture, the TIE can be solved under nonuniform illuminations and even nonhomogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and nonuniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phase distribution under nonuniform illumination and nonhomogeneous boundary conditions within an arbitrarily shaped aperture, which enables the technique of TIE with hard aperture to become a more flexible phase retrieval tool in practical measurements.