High Phase Accuracy Research Articles

Carrier fringe pattern analysis: Links between methods

Introducing a carrier into a fringe pattern makes the phase retrieval problem well-posed, and has become one of the pillar techniques in optical metrology. The carrier fringe pattern analysis for high-accuracy phase retrieval is hence important, for which, many well-known methods have been developed, such as the Fourier transform method, the windowed Fourier transform based methods (the windowed Fourier filtering and the windowed Fourier ridges), the spatial carrier phase-shifting method, and the sampling moiré method. These methods were developed independently and seemingly different. The purpose of this paper is to reveal the close relationships between them, and to connect these methods into a tight-knit methodology family.

Self-correction of air refractive index in distance measurement using two-color sinusoidal phase modulating interferometry

A two-color sinusoidal phase modulating (SPM) interferometer based on electro-optic modulator (EOM) is devised for self-correction of air refractive index in distance measurement. Two laser sources with high frequency stability and close wavelengths (633 nm and 782 nm) are used in this scheme. High-accuracy phase demodulation was realized using phase generated carrier (PGC) demodulation techniques with an FPGA-based signal processing board. Experimental results of nanometer displacement measurements show that the resolution and accuracy of PGC demodulation is better than 1°, and the nonlinear error is less than 0.2°. Performance tests of two-color SPM interferometer compared with one-color interferometers under dynamic environment were implemented with an arm length difference of 4 m. The results show that, the measured distance of one-color interferometer drifts 4.8 μm in 600 s, which is caused by the deviation between the measured value of air refractive index and the actual value along the laser propagation path, and this drift reduces to ±1.5 μm using two-color interferometer without environmental sensing.

Gamma Precorrection and Phase Error Compensation Methods Based on Three-Frequency with Three-Phase Shift

Digital fringe projection measurement technology has been widely used in computer vision and optical three-dimensional (3D) measurement. Considering the phase error caused by the gamma distortion and nonlinear error, the active gamma precorrection and phase error compensation methods based on the three-frequency with three-phase shifts are designed to reversely solve the initial phase and accurately compensate phase error. On the one hand, the gamma coefficient of the measurement system depends on precoding two groups of fringe sequences with different gamma coefficients to calculate the corresponded proportional coefficient of harmonic component. On the other hand, the phase error compensation method is designed to compensate the phase error and improve the accuracy and speed of phase calculation after gamma correction. Experiments show that the proposed precalibration gamma coefficient method can effectively reduce the sinusoidal error in nearly 80 percent which only needs fewer fringe patterns. Compared with the traditional three-frequency with four-phase shift method, the proposed method not only has higher phase accuracy and better noise resistance but also has good robustness and flexibility, which is not limited to the gamma distortion model.

Two-dimensional complex wavelet with directional selectivity used in fringe projection profilometry.

The continuous wavelet transform (CWT) has been used in fringe projection profilometry (FPP) to recover a three-dimensional surface from a single-frame fringe. This Letter constructs a two-dimensional (2D) continuous complex wavelet employing a 2D real Mexican hat wavelet function, combined with the single-orthant analytical 2D Hilbert transform. The 2D complex wavelet has an asymmetric frequency envelope in the radial direction and the ability of direction selectivity, which results in better matching between the local fringe and daughter wavelets. We provide a complex wavelet construction model, present a theoretical analysis, and conduct experimental validation. The experiments demonstrate that the proposed method provides high phase accuracy in the single-frame FPP method.

Distributed Fiber Deformation Measurement by High-Accuracy Phase Detection in OFDR Scheme

Fiber deformation measurement is crucial in the structure health monitor, which reflects the stress, strain or deformation of the structure where the fiber is laid. The principle of the fiber deformation measurement by the optical phase tracking in OFDR scheme is described and the data processing algorithm is demonstrated in details to receive accurate results. The differential phase is acquired by making a difference between the phase spectrum of the reference and measurement states. A robust phase unwrapping method based on the density distribution is proposed to get the whole unwrapped low-noise phase of the fiber. Additionally, the phase decoherence caused by the scatter unit misalignment induced by the fiber deformation is analyzed and the phase correction method is proposed to improve the phase coherence. The fiber deformation can be tracked along the fiber with a resolution of tens of microns, depending on the set parameters of the OFDR system. Moreover, the strain distribution is also derived from the differential phase. In the experiments, the measurements of the standard single-mode fiber with uniform and non-uniform deformation have been accomplished in a spatial resolution of 40 μm. The noise is about 0.1 μm in a stretching range of about 40 μm. Simultaneously, hundreds of microstrain are obtained and show a high accuracy with a resolution of the level of millimeter.

Development of terahertz two-dimensional phase gratings for multiple beam generation based on a high-accuracy phase retrieval algorithm.

High efficiency and accuracy phase gratings are of crucial importance for large format heterodyne array receivers at terahertz frequencies. Here, by developing a design approach that can create gratings with arbitrary two-dimensional diffraction distributions, we have realized a reflective metallic phase grating that generates 2×2 diffraction beams at 0.85 THz. The measured total power efficiency of the diffraction beam pattern is 81.9%, which demonstrates at least 17% improvement in efficiency compared with the standard pseudo-2D Fourier phase grating. In addition, we report the realization of up to 10×10 diffraction beam two-dimensional phase grating designs at terahertz wavelengths, using an adaptation of the Gerchberg-Saxton (GS) scheme known as the Mixed-Region-Amplitude-Freedom algorithm. Rigorous full wave simulation proves the efficiency and accuracy of the design, which overcomes the inaccurate intensity of the beam distribution drawbacks originated from the standard GS algorithm. The results pave the way for the development of large-pixel terahertz multi-beam heterodyne receivers.

Non-interferometric accurate phase imaging via linear-convergence iterative optimization

This paper reported a general non-interferometric high-accuracy quantitative phase imaging (QPI) method for arbitrary complex-valued objects. Given by a typical 4-f optical configuration as the imaging system, three frames of small-window phase modulation are applied on the object's Fourier spectrum so that redistributed intensity patterns are produced on the image plane, in which the object phase emerges at different degree. Then, an algebraic relationship that connects the object phase with the output intensity is established to provide us with an approximate closed-form phase recovery. Further, an efficient iterative optimization strategy is developed to turn that approximate solution into an accurate one. Due to the linear convergence property of the iteration, a high-accuracy phase recovery is achieved without requiring heavy iterations. The feasibility and accuracy of the proposed method are verified by both numerical simulations and experiments on diverse phase objects including biomedical tissues.

Real time high accuracy phase contrast imaging with parallel acquisition speckle tracking* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11675253 and 11505278).

X-ray speckle tracking based methods can provide results with best reported angular accuracy up to 2 nrad. However, duo to the multi-frame requirement for phase retrieval and the possible instability of the x-ray beam, mechanical and background vibration, the actual accuracy will inevitably be degraded by these time-dependent fluctuations. Therefore, not only spatial position, but also temporal features of the speckle patterns need to be considered in order to maintain the superiority of the speckle-based methods. In this paper, we propose a parallel acquisition method with advantages of real time and high accuracy, which has potential applicability to dynamic samples imaging as well as on-line beam monitoring. Through simulations, we demonstrate that the proposed method can reduce the phase error caused by the fluctuations to 1% at most compared with current speckle tracking methods. Meanwhile, it can keep the accuracy deterioration within 0.03 nrad, making the high theoretical accuracy a reality. Also, we find that waveforms of the incident beam have a little impact on the phase retrieved and will not influence the actual accuracy, which relaxes the requirements for speckle-based experiments.

The Research Activities of the Main Astronomical Observatory of the National Academy of Sciences of Ukraine on the Use of GNSS Technology

The current state of the research activities of the Main Astronomical Observatory of the National Academy of Sciences of Ukraine (MAO NASU) on the use of GNSS technology is presented. Today, MAO operates a permanent GNSS network consisting of five stations (two stations are temporarily inactive). All stations are included in EPN and the EPOS network, GLSV, KHAR, and UZHL stations are also integrated to the IGS network. MAO Operational Centre also provides automatic data transfer from 12 stations installed by other Ukrainian organizations included in the international networks. Data from approximately 300 Ukrainian permanent GNSS stations are stored in the MAO Local Data Centre. The MAO Local Analysis Centre uses Bernese GNSS Software for different types of data processing of GNSS observations. Rapid processing is performed on a daily basis for monitoring the stability of the permanent stations from some Ukrainian RTK networks. All available observations data from the Ukrainian stations for the period from December 7, 1997, to January 28, 2017, were processed according EPN standards during the MAO’s second reprocessing campaign and regular processing. As a result, the coordinates in the IGb08 reference frame and tropospheric zenith delays for 233 permanent stations (202 of them are the Ukrainian stations), as well as the velocities for the 128 stations that have observation period more than 3 years, were estimated. The creation and development of local GNSS networks, as well as the long-term filling of databases with high-precision coordinate solutions and estimates of the displacement velocities of GNSS stations, made possible to conduct geodynamic studies at the local level. The strain ellipses and rotation were found based on estimated coordinates and velocities of the GNSS stations. In 2016–2019, Kharkiv National University of Radio Electronics, in cooperation with MAO NASU, performed a number of studies on high-precision GNSS positioning and navigation. New implementations of modern methods and algorithms for the PPP positioning were created and experimentally tested. The errors of the daily floating PPP solutions were 5…8 mm (with a probability of P ≈ 95%) for static mode and 5…8 cm (P ≈ 68%) for kinematic mode. The decimeter/centimeter error of determining the coordinates of current satellites with low Earth orbits (LEO) in the implementation of kinematic floating and fixed PPP solutions was proven. The development of a high-accuracy multiposition phase system of trajectory measurements for field tests of high dynamic aircrafts (HDA) were proposed. The estimated values of the root-mean-square error (RMSE) in determining the HDA motion variables were in the range from 0.05 to 0.40 m for coordinates and from 0.5 to 1.6 cm/s for the velocity vector components.

Implementation of a high-accuracy phase unwrapping algorithm using parallel-hybrid programming approach for displacement sensing using self-mixing interferometry

Phase unwrapping is an integral part of multiple algorithms with diverse applications. Detailed phase unwrapping is also necessary for achieving high-accuracy metric sensing using laser feedback-based self-mixing interferometry (SMI). Among SMI specific phase unwrapping approaches, a technique called Improved Phase Unwrapping Method (IPUM) provides the highest accuracy. However, due to its complex, sequential, and compute-intensive nature, this method requires a high-performance computing architecture, capable of scalable parallel processing so that such a high-accuracy algorithm can be used for high-bandwidth sensing applications. In this work, the existing sequential IPUM C program is parallelized by using hybrid OpenMP/MPI (Open Multi-Processing/Message Passing Interface) parallel programming models and tested on Barcelona Supercomputing Center Nord-III Supercomputer. The computational performance of the proposed parallel-hybrid IPUM algorithm is compared with existing IPUM sequential code by executing multi-core and uni-core processor architecture, respectively. While comparing the performance of sequential IPUM with the parallel-hybrid IPUM algorithm on 16 nodes of Nord-III supercomputer, the results show that the parallel-hybrid algorithm gets 345.9x times performance improvement as compared to IPUM’s standard, sequential implementation on a single node system. The results show that the parallel-hybrid version of IPUM gives a scalable performance for different target velocities and a different number of processing cores.

High-accuracy phase demodulation method compatible to closed fringes in a single-frame interferogram based on deep learning.

Interferogram demodulation is a fundamental problem in optical interferometry. It is still challenging to obtain high-accuracy phases from a single-frame interferogram that contains closed fringes. In this paper, we propose a neural network architecture for single-frame interferogram demodulation. Furthermore, instead of using real experimental data, an interferogram generation model is constructed to generate the dataset for the network's training. A four-stage training strategy adopting appropriate optimizers and loss functions is developed to guarantee the high-accuracy training of the network. The experimental results indicate that the proposed method can achieve a phase demodulation accuracy of 0.01 λ (root mean square error) for actual interferograms containing closed fringes.

Analog Front-End Circuits With Input Current Attenuation and Heterodyne Techniques for Low-Cost Phase-Shift LADAR Receiver

Analog front-end (AFE) circuits with wide dynamic range and low walk error for cost-effective phase-shift LADAR receiver are presented in this work. The inverter-based trans-impedance amplifier (TIA) utilized in the proposed AFE has been modified with two additional transistors in its input node, which can attenuate the input current automatically and adjust the bandwidth dynamically. The improved TIA significantly increases the dynamic range of AFE without any complicated gain-control circuits, while keeping the walk error in a low level. Heterodyne techniques are then adopted to modulate the received signals to low-frequency carriers, as well as the driving signal of laser diode, which is modulated with a mirrored voltage-input channel. Thus, systematic errors caused by the uncertainty of the initial phase in transmitted signal can be reduced. As a result, high-accuracy phase detections and range measurements can be realized conveniently by just sampling two low-frequency (~100 kHz in this design) output signals. The AFE circuits have been fabricated in a standard 65-nm CMOS technology with a total chip area of $0.59\times0.68$ mm2 including the IO PADs. The measured power consumption is 24.3 mW with a 2.5-V supply. With a modulated frequency of 30 MHz and a local oscillator frequency of 30.1 MHz, the measured input-referred noise of the proposed AFE is 8.4 nA $_{RMS}$ and the walk error is less than ±1.8% for a wide dynamic range of 500 nA ~ 10 mA. The measurement results show that the proposed AFE can achieve wide dynamic range and low walk error, while the system complexity and cost of the phase-shift LADAR receiver can also be reduced.

Joint Coding Strategy of the Phase Domain and Intensity Domain for Absolute Phase Retrieval

Codewords used to determine fringe orders are significant for absolute phase retrieval based on the phase-coding method. However, because of inevitable interference from image blurring, image noise, and system nonlinearity, it is challenging to significantly increase the number of codewords for high-accuracy phase retrieval. To address this challenge, this article proposes a joint coding strategy to perform the coding of high-density stripes. More specifically, codewords are simultaneously embedded into the phase domain and the intensity domain of composite fringe patterns, which greatly extends the encoding range of valid codewords. Moreover, to improve the anti-interference capability of the proposed coding strategy, a regional correction technique (RCT) is presented to remove jump phase errors induced by the inevitable interference. The results of experiments indicate that the proposed method is effective and accurate for both complex objects and a standard sphere.

High-accuracy 3D surface measurement using hybrid multi-frequency composite-pattern temporal phase unwrapping.

Multi-frequency temporal phase unwrapping (TPU) has been extensively used in phase-shifting profilometry (PSP) for the high-accuracy measurement of objects with surface discontinuities and isolated objects. However, a large number of fringe patterns are commonly required. To reduce the number of required patterns, a new hybrid multi-frequency composite-pattern TPU method was developed using fewer patterns than conventional TPU. The new method combines a unit-frequency ramp pattern with three low-frequency phase-shifted fringe patterns to form three composite patterns. These composite patterns are used together with three high-frequency phase-shifted fringe patterns to generate a high-accuracy phase map. The optimal high frequency to achieve high measurement accuracy and reliable phase unwrapping is determined by analyzing the effect of temporal intensity noise on phase error. Experimental results demonstrated that new grayscale hybrid and color hybrid multi-frequency composite-pattern TPU methods can achieve a high-accuracy measurement using only six and three images, respectively.

Scanning ion beam etching: A method for the fabrication of computer-generated hologram with nanometric accuracy for aspherical testing

The phase type computer generated hologram (CGH) plays an important role in aspherical surface optical testing, especially for low reflectivity material mirror surfaces, owing to its high diffractive efficiency. With the increasing demand for high precision CGHs, traditional methods such as reactive ion etching and focusing ion beam, have difficulty realizing the fabrication of a large aperture and high accuracy phase type CGH. In this study, fabrication of a high precision CGH has been demonstrated via a new method called scanning ion beam etching (SIBE), which is suitable for most common optical materials and the fabrication of high performance CGH. On the basis of the movable radio frequency ion source, we determine an etching depth calculation method to realize high accuracy etching regardless of whether the removal function is a perfect Gaussian distribution. Experiments are conducted to verify the etching depth accuracy. Moreover, the linewidth, sidewall angle, roughness, and etching uniformity results of the CGH are superior to the fabrication of CGH via the conventional method. As a proof of concept, a phase type CGH with an aperture of 80 mm is fabricated, and the wavefront accuracy is 6.2 nm, which can meet the processing requirements of a high precision aspheric mirror. Thus, a SIBE method is developed for high performance CGH, which may aid in the development of high accuracy diffractive optics.

A high-accuracy phase shifting retrieval approach based on phase shifts search

To achieve high measurement accuracy without the restriction of fringe number, a high-accuracy phase shifting retrieval approach based on phase shifts search (PSS) is proposed. Firstly, by setting the search conditions related to the phase shifts and using the PSS method to obtain the phase shifts between the phase shifting interferograms, subsequently, the phase distribution of the sample can be accurately obtained by using the obtained phase shifts. To our knowledge, the proposed method has the highest accuracy among the multi-step arbitrary phase shifting algorithms, and it is not limited to the number of fringes and the distribution of phase shifts between the interferograms. In the case of sparse fringes, the phase can still be retrieved with high accuracy, which proves that the proposed method is a high accuracy method with fewer constraints and wider applications. The feasibility and superiority of this method are proved by the simulation analysis and experiment.

A DLL-Based Quadrature Clock Generator With a 3-Stage Quad Delay Unit Using the Sub-Range Phase Interpolator for Low-Jitter and High-Phase Accuracy DRAM Applications

In an effort to keep pace with bandwidth growth, DRAM employes the quad data rate (QDR) to transfer four data in one clock cycle. In recent graphic memories, QDR is being implemented by a phase-locked loop (PLL). However, it is hard to apply a PLL to main and mobile memories for its high power dissipation and hardware cost. Therefore, we propose a new delay-locked loop-based quadrature clock generator (DLL-QCG) to replace a PLL. A sub-range technique is adopted for a phase interpolator (PI) to achieve a very fine resolution with low power and small area. A tiny resolution mitigates the jitter accumulation effect of the conventional all-digital DLL-QCG and reduces a phase error. With the introduction of the sub-range PI, the delay line structure is changed from two-stage (coarse-fine) to three-stage (coarse-fine-finer). To control this, we also develop a new controller, which ensures clock quality through seamless boundary switching at the fine-to-finer. The circuit is fabricated using a 28 nm CMOS FDSOI technology with a 1 V supply voltage and an area of 0.0072 mm2. It operates from 1.8 to 2.5 GHz and achieves a phase error of 3.35° to 6.35° without a quadrature-phase collector. In addition, the measured RMS and peak-to-peak jitters at operating bandwidth are 1.05 to 1.71 ps and 8.4 to 12 ps, respectively.

Automatic Phase Picking From Microseismic Recordings Using Feature Extraction and Neural Network

High-accuracy microseismic phase picking is fundamental to microseismic signal processing. Phase picking methods based on deep learning show great potential dealing with low signal to noise ratio (SNR) data but need enormous training data. However, it's not easy to obtain a big size of field datasets and label them manually to train the neural network. In this paper, a novel method is proposed by applying feature extraction (Gammatone Feature) and neural networks to pick phases automatically. The feature extraction scheme aims to train the neural network using a relatively small size of training datasets. To test the performances of the proposed method, synthetic datasets were obtained by numerical simulation and used to train the neural network. Both synthetic datasets and field datasets were used to test the neural network for picking P- and S-phases of microseismic events. The results of phase picking illustrate that: (1) feature extraction scheme in the training stage can help reduce the size of training datasets; (2) The neural network can be trained well just by synthetic data and phase picking results are accurate and satisfying when the method was tested by both synthetic and field datasets.

Single-shot isotropic quantitative phase microscopy based on color-multiplexed differential phase contrast

We present a single-shot isotropic quantitative phase imaging method based on color-multiplexed differential phase contrast. In our method, the illumination source is modulated by an LCD into an annular color-multiplexed pattern matching the numerical aperture of the objective precisely to maximize the frequency response for both low and high frequencies (from 0 to 2NAobjλ). In addition, we propose an alternating illumination scheme to provide a perfectly circularly symmetrical phase transfer function, achieving isotropic imaging resolution and signal-to-noise ratio. A color camera records the light transmitted through the specimen, and three monochromatic intensity images at each color channel are then separated and utilized to recover the phase of the specimen. We display the derivation, implementation, simulation and experimental results, which demonstrate that our method accomplishes high resolution, noise-robustness and reconstruction accuracy phase reconstruction at camera-limited frame rates.

A 76-GHz to 81-GHz, 0.6° RMS Phase Error Multichannel Transmitter With a Novel Phase Detector and Compensation Technique

A multichannel transceiver operating in 76–81 GHz with precisely phase-controlled transmitter for the automotive radar application is presented. To achieve high phase accuracy of transmit signal, a novel phase detector using third-order distortion is proposed to compensate the phase control error. To avoid the insensitivity region on specific phase condition, the frequency-shifted method applying the propagation delay difference between transmit and reference signal path is also presented. The multichannel transmitter using proposed detector achieves less than 0.6° root-mean-square (RMS) phase error in 76-GHz to 81-GHz frequency range, over −40 °C–125 °C ambient temperature condition. Since the proposed phase detector does not use the other TX as reference, it is suitable for extending the number of channels. This transceiver, including the proposed phase detector is implemented in 65-nm CMOS technology. The phase detector consumes 1.8 mW per channel and occupies 0.15 mm2 per channel.