Optical Phase Measurement Research Articles

Multi task deep learning phase unwrapping method based on semantic segmentation

Abstract Phase unwrapping is a key step to obtain continuous phase distribution in optical phase measurement. When the wrapped phase obtained from the interference pattern is unclear and noisy, estimating the unwrapped phase becomes more challenging. As deep learning advances in optical image processing, it will enhance processing efficiency and accuracy, bringing broader possibilities for various applications. This paper introduces an innovative phase unwrapping method based on multi-task learning, aiming to simultaneously enhancing denoised images and predicting wrap count. The proposed network, named ICER-Net, comprises an encoder and two decoders, transforming the input low-luminance, noisy wrapped phase into two intermediate outputs: enhanced wrapped phase and wrap count. Finally, these two intermediate results are fused to obtain the unwrapped phase. Experimental results demonstrate that ICER-Net not only enhances the accuracy of phase unwrapping, particularly when facing challenges of various noise levels and luminance sizes but also exhibits outstanding performance in actual collected speckle phase images. This indicates that ICER-Net holds significant superiority in addressing complex issues in optical image processing.

High-Performance NOON State from a Quantum Dot Single Photon for Supersensitive Optical Phase Measurement

We investigate the utilization of advanced single photons produced by quantum dots (QDs) in a microcavity for quantum metrology. Through the integration of lateral excitation and the Purcell effect in an Fabry–Perot microcavity, we realized single-photon emission with an extraction efficiency of 46.39%, high purity of 96.91%, and high indistinguishability of 98.32%. Our QD-generated single photons enabled the creation of high-quality NOON states (N = 2) for phase measurement, yielding an interference contrast of 79.79% and surpassing the standard quantum limit (SQL) with phase super-sensitivity. Our results underscore the immense potential of QD-derived single photons for propelling quantum metrology forward, facilitating enhanced precision measurements across diverse applications.

Optical phase and amplitude measurements of underwater turbulence via self-heterodyne detection

The creation of underwater optical turbulence is driven by density variations that lead to small changes in the water’s refractive index, which induce optical path length differences that affect light propagation. Measuring a laser beam’s optical phase after traversing these turbulent variations can provide insight into how the water’s turbulence behaves. The sensing technique to measure turbulent fluctuations is a self-heterodyne beatnote enhanced by light’s orbital angular momentum (OAM) to obtain simultaneous optical phase and amplitude information. Experimental results of this method are obtained in a water tank that creates a thermally driven flow called Rayleigh–Bénard (RB) convection. The results show time-varying statistics of the beatnote that depend on the incident OAM mode order and the strength of the temperature gradient. Beatnote amplitude and phase power spectral densities are compared to analytic theory to obtain estimates of the turbulent length scales using the Taylor hypothesis that include mean flow speed, turbulent strength, and length scales, and flow dynamics due to intermittency in the RB process.

Error Analysis of the plate beamsplitter in near optical coaxial phase measurement deflectometry

Phase-measuring deflectometry (PMD) is a key measurement technology for specular surfaces form measurement. Compared with the phase measuring deflectometry techniques based on the conventional configuration, the near optical coaxial phase measuring deflectometry (NCPMD) can achieve compact configuration, light weight and insignificant measurement error caused by structure shadows by utilizing a plate beamsplitter. However, the introduction of the plate beamsplitter will make some influence of the measurement accuracy of the NCPMD system. In the one hand, the introduction of the plate beamsplitter can reduce the measurement accuracy of the NCPMD system due to the refractive of the ray between the two surfaces of the beamsplitter. In the other hand, due to the processing and manufacturing problems of the beamsplitter, there are inevitably certain unevenness errors on the upper and lower surfaces. In this paper, a virtual simulation system of NCPMD is established, and an error model of the NCPMD system by considering both the refraction influence and reflection influence of the plate beamsplitter is presented to analyse the shape reconstruction error caused by the plate beamsplitter.

Scalable low-latency optical phase sensor array

Optical phase measurement is critical for many applications, and traditional approaches often suffer from mechanical instability, temporal latency, and computational complexity. In this paper, we describe compact phase sensor arrays based on integrated photonics, which enable accurate and scalable reference-free phase sensing in a few measurement steps. This is achieved by connecting multiple two-port phase sensors into a graph to measure relative phases between neighboring and distant spatial locations. We propose an efficient post-processing algorithm, as well as circuit design rules to reduce random and biased error accumulations. We demonstrate the effectiveness of our system in both simulations and experiments with photonics integrated circuits. The proposed system measures the optical phase directly without the need for external references or spatial light modulators, thus providing significant benefits for applications including microscope imaging and optical phased arrays.

Synchronous optical intensity and phase measurements to characterize Rayleigh-Bénard convection.

Propagation of a laser beam through the Rayleigh-Bénard (RB) convection is experimentally investigated using synchronous optical wavefront and intensity measurements. Experimental results characterize the turbulence strength and length scales, which are used to inform numerical wave optic simulations employing phase screens. Experimentally found parameters are the refractive index structure constant, mean flow rate, kinetic and thermal dissipation rates, Kolmogorov microscale, outer scale, and shape of the refractive index power spectrum using known models. Synchronization of the wavefront and intensity measurements provide statistics of each metric at the same instance in time, allowing for two methods of comparison with numerical simulations. Numerical simulations prove to be within agreement of experimental and published results. Synchronized measurements provided more insight to develop reliable propagation models. It is determined that the RB test bed is applicable for simulating realistic undersea environments.

Multiscale optical phase fluctuations link disorder strength and fractal dimension of cell structure

Optical methods for examining cellular structure based on endogenous contrast rely on analysis of refractive index changes to discriminate cell phenotype. These changes can be visualized using techniques such as phase contrast microscopy, detected by light scattering, or analyzed numerically using quantitative phase imaging. The statistical variations of refractive index at the nanoscale can be quantified using disorder strength, a metric seen to increase with neoplastic change. In contrast, the spatial organization of these variations is typically characterized using a fractal dimension, which is also seen to increase with cancer progression. Here, we seek to link these two measurements using multiscale measurements of optical phase to calculate disorder strength and in turn to determine the fractal dimension of the structures. First, quantitative phase images are analyzed to show that the disorder strength metric changes with resolution. The trend of disorder strength with length scales is analyzed to determine the fractal dimension of the cellular structures. Comparison of these metrics is presented for different cell lines with varying phenotypes including MCF10A, MCF7, BT474, HT-29, A431, and A549 cell lines, in addition to three cell populations with modified phenotypes. Our results show that disorder strength and fractal dimension can both be obtained with quantitative phase imaging and that these metrics can independently distinguish between different cell lines. Furthermore, their combined use presents a new approach for better understanding cellular restructuring during different pathways.

Bosonic Pair Production and Squeezing for Optical Phase Measurements in Long-Lived Dipoles Coupled to a Cavity.

We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the electronic states, and we propose to exploit this for quantum-enhanced sensing of an optical phase (common and differential between two ensembles). We discuss a specific implementation based on Sr atoms and show that our sensing protocol is robust to sources of decoherence intrinsic to cavity platforms. Our proposal can open unique opportunities for next-generation optical atomic clocks.

High-Precision Optical Carrier Phase Measurement Technology Based on Two-Satellite Formation

High-Precision Optical Carrier Phase Measurement Technology Based on Two-Satellite Formation

VDE-Net: a two-stage deep learning method for phase unwrapping.

Phase unwrapping is a critical step to obtaining a continuous phase distribution in optical phase measurements and coherent imaging techniques. Traditional phase-unwrapping methods are generally low performance due to significant noise or undersampling. This paper proposes a deep convolutional neural network (DCNN) with a weighted jump-edge attention mechanism, namely, VDE-Net, to realize effective and robust phase unwrapping. Experimental results revealed that the weighted jump-edge attention mechanism, which is first proposed and simple to calculate, is useful for phase unwrapping. The proposed algorithm outperformed other networks or common attention mechanisms. In addition, an unseen wrapped phase image of a living red blood cell (RBC) was successfully unwrapped by the trained VDE-Net, thereby demonstrating its strong generalization capability.

Relative phase distribution and the precision of optical phase sensing in quantum metrology

One of the quantum metrology goals is to improve the precision in the measurement of a small optical phase introduced in one optical mode in an interferometer, i.e., phase sensing. In this paper, we obtain the relative phase distribution introduced by Luis and Sánchez-Soto (LSS) (Luis and Sánchez-Soto, 1996) for several two-mode pure quantum light states useful in quantum metrology. We show that, within the numerical precision of our calculations, the Fisher information obtained from the LSS relative phase distribution is equal to the quantum Fisher information for the considered states (the average difference for the tested states is smaller than 0.1%). Our results indicate that the LSS relative phase distribution can be used to predict the minimum uncertainty possible in the process of phase sensing in quantum metrology, since this uncertainty depends on the quantum Fisher information, at least for pure states.

Three-dimensional density field of a screeching under-expanded jet in helical mode using multi-view digital holographic interferometry

A synchronised multi-axis digital holographic interferometry set-up is presented for the study of 3-D flow fields with large density gradients. This optical configuration provides instantaneous interferograms with fine spatial resolution in six directions of projection. A regularised tomographic approach taking into account the presence of possible shock waves is furthermore considered to reconstruct 3-D density fields. Applied to a screeching under-expanded supersonic jet with helical dynamics, this set-up is used to provide dense optical phase measurements in the initial region of the jet. The jet mean density field is shown to be satisfactorily estimated with sharply resolved density gradients. In addition, an approach based on azimuthal Fourier transform and snapshot proper orthogonal decomposition (POD) applied to the instantaneous flow observations is proposed to study the main coherent dynamics of the jet. Relying on a cluster analysis of the azimuthal POD mode coefficients, a reduced dynamical model in the POD mode phase space is used as an approximation of the two observed limit cycles. A clear 3-D representation of the density field of a helical instability associated with screech mode C is then evidenced, with two equally probable directions of rotation. Switching between the two directions is reported, highlighting intermittency in the feedback loop. This helical structure is particularly seen to extend to the jet core, driving its internal dynamics and inducing out-of-phase density fluctuations between the outer and inner shear layers. These out-of-phase motions are related to the non-uniform radial distribution of fluctuation phase associated with the outer-layer Kelvin–Helmholtz instability wave.

Ultra-low noise phase measurement of fiber optic sensors via weak value amplification.

The noise floor is a vital specification that determines the minimum detectable signal in the phase measurement. However, the noise floor in optical phase measurement conducted via conventional optical interferometry tends to approach the intrinsic limit. In this study, a low noise phase measurement of a fiber optic sensor conducted via weak value amplification is experimentally demonstrated. The system has a flat, wideband frequency response from 0.1 Hz to 10 kHz, as well as adequate linearity. The operating band is wider than the present sensor using the same mechanism. In particular, the system noise floor is measured to be -98 dB at 1 Hz and -155 dB at 1 kHz. The results indicate that the minimum detectable signal can reach as low as 5.6 × 10-6 rad at 1 Hz and 8 × 10-9 rad at 1 kHz. In addition, it is demonstrated that the noise result of the proposed system is two-order of magnitude lower than that of the typical interferometric fiber optic sensors through the comparison experiment. With the characteristic of low-noise, the system is promising in the field of weak signal detection such as underwater acoustic signal detection, seismic wave detection, and mineral resource exploration.

Robust phase unwrapping algorithm based on Zernike polynomial fitting and Swin-Transformer network

Phase unwrapping plays an important role in optical phase measurements. In particular, phase unwrapping under heavy noise conditions remains an open issue. In this paper, a deep learning-based method is proposed to conduct the phase unwrapping task by combining Zernike polynomial fitting and a Swin-Transformer network. In this proposed method, phase unwrapping is regarded as a regression problem, and the Swin-Transformer network is used to map the relationship between the wrapped phase data and the Zernike polynomial coefficients. Because of the self-attention mechanism of the transformer network, the fitting coefficients can be estimated accurately even under extremely harsh noise conditions. Simulation and experimental results are presented to demonstrate the outperformance of the proposed method over the other two polynomial fitting-based methods. This is a promising phase unwrapping method in optical metrology, especially in electronic speckle pattern interferometry.

Impact of the rolling shutter effect in optical phase measurements using spatial carrier

The impact of the rolling shutter effect in interferometry using the spatial carrier method is presented. A spatial carrier method is of interest as it avoids moveable devices inside the interferometer, thus allowing the design of low-cost and portable optical systems. An out-of-plane digital holographic interferometer is used to analyze the retrieved optical phase acquired by a camera sensor which can be hardware switched between rolling and global shutter mode. Under well-controlled and repeatable deformations, a series of image holograms were recorded. Optical phase comparison is performed for both shutter modes to analyze the presence or absence of the rolling shutter effect (RSE) in the spatial carrier. The optical phase study involves the Fourier spectrum, where this spatial carrier could be explored in a bi-dimensional form. Results show a significant distortion of the spatial carrier at the Fourier space, close to the edges of the optical aperture image, indicating a phase error that can be reduced using a reduced section of the aperture.

Towards supersensitive optical phase measurement using a deterministic source of entangled multiphoton states

Precision measurements of optical phases have many applications in science and technology. Entangled multi-photon states have been suggested for performing such measurements with precision that significantly surpasses the shot-noise limit. Until recently, such states have been generated mainly using spontaneous parametric down-conversion -- a process which is intrinsically probabilistic, counteracting the advantages that the entangled photon states might have. Here, we use a semiconductor quantum dot to generate entangled multi-photon states in a deterministic manner, using periodic timed excitation of a confined spin. This way we entangle photons one-by-one at a rate which exceeds 300 MHz. We use the resulting multi-photon state to demonstrate super-resolved optical phase measurement. Our results open up a scalable way for realizing genuine quantum enhanced super-sensitive measurements in the near future.

Three-dimensional entanglement on a silicon chip

Entanglement is a counterintuitive feature of quantum physics that is at the heart of quantum technology. High-dimensional quantum states offer unique advantages in various quantum information tasks. Integrated photonic chips have recently emerged as a leading platform for the generation, manipulation and detection of entangled photons. Here, we report a silicon photonic chip that uses interferometric resonance-enhanced photon-pair sources, spectral demultiplexers and high-dimensional reconfigurable circuitries to generate, manipulate and analyse path-entangled three-dimensional qutrit states. By minimizing on-chip electrical and thermal cross-talk, we obtain high-quality quantum interference with visibilities above 96.5% and a maximally entangled-qutrit state with a fidelity of 95.5%. We further explore the fundamental properties of entangled qutrits to test quantum nonlocality and contextuality, and to implement quantum simulations of graphs and high-precision optical phase measurements. Our work paves the path for the development of multiphoton high-dimensional quantum technologies.

Comparative study of phase unwrapping algorithms based on solving the Poisson equation

Phase unwrapping is a crucial process to obtain the absolute phase profile in many optical phase measurement techniques such as interferometry, holography, profilometry, etc. In this paper, we have studied several phase unwrapping algorithms based on solving the discrete Poisson equation. The differences among those algorithms lie in two aspects: one is the calculation of the input for the Poisson equation using the wrapped phase data and the other is the way to compute the output (unwrapped phase data) using the corresponding input. Firstly, the method to compute the input for the Poisson equation was investigated using the finite difference and fast Fourier transform (FFT) methods. Then different methods, based on FFT or discrete cosine transform, were employed to calculate the unwrapped phase, and their performances were compared in terms of accuracy and efficiency. To enhance the precision of those algorithms, an iteration strategy was introduced and its performance was investigated under different noise conditions. Finally, several pieces of real phase data was tested by using the direct and iterative methods. The detailed software package can be found online (www.mathworks.com/matlabcentral/fileexchange/71810-phase-unwrapping-algorithms-by-solving-the-poisson-equation).

Mechanical test study in composites using digital holographic interferometry and optical coherence tomography simultaneously.

A dual optical configuration to inspect the internal and external mechanical response of a composite specimen is presented. The inspection simultaneously uses two equally aligned optical techniques, digital holographic interferometry and Fourier domain optical coherence tomography, to retrieve surface and internal data, respectively. The sample under study is a composite specimen of poly-methyl-methacrylate reinforced with metallic particles. Two different sets of samples are analyzed to compare their mechanical behavior. A homemade, fully controlled testing machine is used to apply a controlled compression load while each technique registers an image. In this form, the surface and internal optical phase measurements are correlated to the same compression value for comparison purposes. Results for each technique are directly presented as simultaneous displacement maps, and a discussion and conclusion of this proposed dual method of inspection are presented.

8-port homodyne detection of optical fields using IQ demodulation

A phase-sensitive detection scheme for optical fields is described, which allows for the simultaneous measurement of orthogonal field quadratures. The recent achievement of -radian cross-phase shifts between a single photon and a second light field has opened the door to quantum computing protocols which utilize photonic quantum bits. Optical phase measurements play an integral role in these schemes. The detection scheme presented here was designed to measure such transient phase shifts of a laser field as it interacts with another light field through a cloud of laser-cooled Rb atoms. In place of conventional spatial interferometry, which is very sensitive to mechanical instabilities, the scheme utilizes beat-note interferometry to improve on the robustness of the measurement. Beat-note interferometry serves to map a signal from a THz-frequency carrier onto a radio-frequency carrier. A variant of 8-port optical homodyne detection, the scheme then uses IQ demodulation, a well-established technique in communications engineering, to extract amplitude information for both the in-phase (I) and quadrature-phase (Q) components of the radio-frequency signal. This IQ data can then be used to extract any amplitude variation and/or phase shifts of the original THz-frequency optical field. The technique is illustrated here by simultaneously measuring the absorption and dispersion experienced by an optical beam as it passes through a cloud of laser-cooled atoms, which have been prepared in a state of electromagnetically-induced transparency. A thorough characterization of the measurement is presented, which identifies the dominant noise sources and illustrates the utility of IQ demodulation in eliminating noise. This scheme has been used to measure rad phase shifts on nanosecond time scales.