Phase Recovery Method Research Articles

Simplified phase-recovery method in temporal speckle pattern interferometry.

A simplified method for object phase recovering is implemented in temporal speckle pattern interferometry when the employed interferometer admits the introduction of a temporal carrier, and the well-known two-beam interferometry equation is verified. The spatiotemporal evolution of the object phase is isolated by modulating the acquired interferometric intensity signals with a known temporal carrier in order to carry out its analysis by using a bivariate empirical mode decomposition framework that avoids the application of the Hilbert transform, which is not suitable for intensity signals with abrupt fluctuations. The advantages and limitations of this technique are analyzed and discussed by comparing computation time and phase recovery capability with well-known phase-retrieval methods by means of numerical simulations and experimental data.

Improved eighth-order statistics blind phase recovery algorithm for coherent receivers with 16-QAM modulation format

An improved eighth-order statistics (EOS) blind phase recovery method is proposed for high-order coherent modulation formats. The method uses a multistage feed-forward carrier phase recovery algorithm by combining an EOS blind phase estimate with a maximum-likelihood carrier phase estimate. Experimental results show that the proposed new algorithm can reduce the required computational effort by more than a factor of 3 for a 16-QAM system.

Improving the Phase Noise Tolerance of Subbanded DFT-Spread OFDM by Nonredundant Interleaving

DFT-Spread (DFT-S) OFDM is a variant of OFDM with multiple advantages, however, one disadvantage is its degraded phase noise tolerance, due to sampling rate slow-down in each DFT-S subband. Here, we propose a phase recovery method for 16-QAM coherent transmission, based on the combination of nonredundant (de)interleaving, differential precoding, and multisymbol delay detection (MSDD), applicable to either conventional DFT-S OFDM receivers or to filter-bank subbanded DFT-S OFDM receivers. Laser and nonlinear phase noise tolerances are significantly improved, as simulated for a filter-bank-based subbanded DFT-S OFDM receiver for 16-QAM over 1000 km SMF.

Non-Linear Phase Tomography Based on Fréchet Derivative

Phase imaging coupled to micro-tomography acquisition has emerged as a powerful tool to investigate specimens in a non-destructive manner. While the intensity data can be acquired and recorded, the phase information of the signal has to be “retrieved” from the data modulus only. Phase retrieval is an ill-posed non-linear problem and regularization techniques including a priori knowledge are necessary to obtain stable solutions. Several linear phase recovery methods have been proposed and it is expected that some limitations resulting from the linearization of the direct problem will be overcome by taking into account the non-linearity of the phase problem. To achieve this goal, we propose and evaluate a non-linear algorithm for in-line phase micro-tomography based on an iterative Landweber method with an analytic calculation of the Fréchet derivative of the phase-intensity relationship and of its adjoint. The algorithm was applied in the projection space using as initialization the linear mixed solution. The efficacy of the regularization scheme was evaluated on simulated objects with a slowly and a strongly varying phase. Experimental data were also acquired at ESRF using a propagation-based X-ray imaging technique for the given pixel size 0.68 μm. Two regularization scheme were considered: first the initialization was obtained without any prior on the ratio of the real and imaginary parts of the complex refractive index and secondly a constant a priori value was assumed on . The tomographic central slices of the refractive index decrement were compared and numerical evaluation was performed. The non-linear method globally decreases the reconstruction errors compared to the linear algorithm and is achieving better reconstruction results if no prior is introduced in the initialization solution. For in-line phase micro-tomography, this non-linear approach is a new and interesting method in biomedical studies where the exact value of the a priori ratio is not known.

Efficient Joint Carrier Frequency Offset and Phase Noise Compensation Scheme for High-Speed Coherent Optical OFDM Systems

The vulnerable sensitivity to laser linewidth induced inter-carrier interference (ICI) has long been recognized as a major problem to coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems. Among the existing phase noise compensation algorithms, the RF-pilot aided phase recovery (RAPR) method shows a better compensation capability to laser linewidth. However, RAPR may fail to extract the pre-inserted RF-pilot at the receiver due to the influence of carrier frequency offset (CFO). An effective frequency offset estimation (FOE) is thus required to implement before performing RAPR. In consideration of the fact that the conventional FOE algorithm not only has high computational complexity, but more importantly cannot work in coordination with RAPR, a new RF-pilot aided frequency offset estimation (RAFOE) algorithm is proposed, in which CFO can be easily estimated by searching the peak of spectral samples. Furthermore, in order to obtain the optimum compensation performance with lower computing cost at combining RAFOE and RAPR, a joint frequency offset and phase noise compensation scheme is also proposed, and its performance is numerically verified in a 475 Gbit/s polarization multiplexed 16-ary quadrature amplitude modulation coherent optical orthogonal frequency-division multiplexing (PM-16QAM- CO-OFDM) system.

Phase recovery of the coherent carrier frequency using digital phase filter

This paper considers a phase recovery method for the coherent carrier frequency of the signal Revised by a digital receiver using a unit of digital recovery of the coherent carrier phase. The use of digital phase filter makes it possible to do without the application of traditional phase-locked loop frequency control. The paper also presents a technique for deriving a transfer function of the specified digital filter and considers the issue of its robustness in relation to self-excitation. In addition, the paper presents a functional diagram of this filter.

Single-shot phase recovery using two laterally separated defocused images

We present a single-shot method for phase recovery based on the transport of irradiance equation (TIE). The system utilizes a beamsplitter and mirrors to achieve two simultaneous (laterally separated) images with different defocusing degrees, which are acquired with a digital camera. The proposed method provides a simple achromatic system for one-shot phase imaging with potential application for phase recovery of dynamic samples. Validation experiments are presented.

Lens-free computational imaging of capillary morphogenesis within three-dimensional substrates

Endothelial cells cultured in three-dimensional (3-D) extracellular matrices spontaneously form microvessels in response to soluble and matrix-bound factors. Such cultures are common for the study of angiogenesis and may find widespread use in drug discovery. Vascular networks are imaged over weeks to measure the distribution of vessel morphogenic parameters. Measurements require micron-scale spatial resolution, which for light microscopy comes at the cost of limited field-of-view (FOV) and shallow depth-of-focus (DOF). Small FOVs and DOFs necessitate lateral and axial mechanical scanning, thus limiting imaging throughput. We present a lens-free holographic on-chip microscopy technique to rapidly image microvessels within a Petri dish over a large volume without any mechanical scanning. This on-chip method uses partially coherent illumination and a CMOS sensor to record in-line holographic images of the sample. For digital reconstruction of the measured holograms, we implement a multiheight phase recovery method to obtain phase images of capillary morphogenesis over a large FOV (24 mm2) with ≈ 1.5 μm spatial resolution. On average, measured capillary length in our method was within approximately 2% of lengths measured using a 10 × microscope objective. These results suggest lens-free on-chip imaging is a useful toolset for high-throughput monitoring and quantitative analysis of microvascular 3-D networks.

Experimental results from a preclinical X-ray phase-contrast CT scanner

To explore the future clinical potential of improved soft-tissue visibility with grating-based X-ray phase contrast (PC), we have developed a first preclinical computed tomography (CT) scanner featuring a rotating gantry. The main challenge in the transition from previous bench-top systems to a preclinical scanner are phase artifacts that are caused by minimal changes in the grating alignment during gantry rotation. In this paper, we present the first experimental results from the system together with an adaptive phase recovery method that corrects for these phase artifacts. Using this method, we show that the scanner can recover quantitatively accurate Hounsfield units in attenuation and phase. Moreover, we present a first tomography scan of biological tissue with complementary information in attenuation and phase contrast. The present study hence demonstrates the feasibility of grating-based phase contrast with a rotating gantry for the first time and paves the way for future in vivo studies on small animal disease models (in the mid-term future) and human diagnostics applications (in the long-term future).

Improved Pilot-Aided Optical Carrier Phase Recovery for Coherent $M$-QAM

We propose an improved pilot-aided (PA) optical carrier phase recovery (CPR) method, using average operation for noise suppression in PA coherent systems. Performance of this method is investigated and compared with other CPR methods through simulations for 28 Gbaud QPSK, 16-, and 64-QAM systems. Results show that PA-CPR with averaging greatly outperforms PA-CPR without averaging, and achieves better or similar performance compared with other PAor non-PA-CPR methods. In addition, we propose a method using maximum likelihood (ML) phase estimation following PA-CPR with averaging to further improve the laser phase noise tolerance. Specifically, after optimizing the bandwidth of the pilot extraction filter, the maximum linewidth symbol duration products (Δf·T) for 1-dB optical signal to noise ratio penalty at BER of 1 × 10-3 are improved from 1 × 10-4, 3.5 × 10-5, and 1 × 10-5 (by PA-CPR without averaging) to 6.6 × 10-4, 2 × 10-4, and 3.8 × 10-5 (by PA-CPR with averaging), for 28 Gbaud QPSK, 16-and 64-QAM systems, respectively. When ML is following PA-CPR with averaging, Δf·T values for 1-dB OSNR penalty are further improved to 9 × 10-4, 4.8 × 10-4, and 6.5 × 10-5 for QPSK, 16-and 64-QAM systems, respectively.

Improved pilot-aided optical carrier phase recovery using average processing for pilot phase estimation

We propose and numerically investigate an improved pilot-aided (PA) optical carrier phase recovery (CPR) method using average processing for pilot phase estimation in order to suppress the amplified spontaneous emission (ASE) noise in PA coherent transmission systems. Extensive simulations for 28Gbuad QPSK systems are implemented. The performance of proposed PA-CPR with averaging is comprehensively investigated and compared with PA-CPR without averaging and Viterbi & Viterbi phase estimation (VVPE). Results show that, PA-CPR with averaging can significantly improve the performance of PA-CPR without averaging, and the best averaging length in the average operation is determined by trading off between ASE noise and laser phase noise (PN). By comparing the optical-signal-to-noise-ratio (OSNR) penalties at bit error rate (BER) of 1×10−3using PA-CPR without averaging, PA-CPR with averaging and VVPE, the advantage of PA-CPR with averaging is further confirmed. Quantitatively, the tolerable linewidth-symbol-duration products (Δf·T) at 1-dB OSNR penalty by using PA-CPR without averaging, VVPE, and PA-CPR with averaging are 6×10−5, 1.2×10−4, and 5×10−4, respectively.

Sperm elution: An improved two phase recovery method for sexual assault samples

This report describes the validation of a two phase cell recovery technique for the elution of two common cell types, epithelia and spermatozoa, from frequently examined items submitted as part of sexual assault casework. Furthermore, separation of cell types prior to microscopic examination of cell pellets improves the scientist's confidence in observing and scoring spermatozoa that may be present. During the validation, Orchid Cellmark's Sperm Elution© method consistently recovered a greater number of spermatozoa from simulated sexual assault items and swabs taken following consensual sexual intercourse compared to a water extraction technique. On average the Sperm Elution method recovered over twice the number of spermatozoa compared to the water method. The ability to separate the cell types present allows a rapid microscope slide search for spermatozoa and faster DNA extraction protocol in comparison to Cellmark's previous preferential method.

Carrier phase estimation for optically coherent QPSK based on Wiener-optimal and adaptive Multi-Symbol Delay Detection (MSDD)

The MSDD carrier phase estimation technique is derived here for optically coherent QPSK transmission, introducing the principle of operation while providing intuitive insight in terms of a multi-symbol extension of naïve delay-detection. We derive here for the first time Wiener-optimized and LMS-adapted versions of MSDD, introduce simplified hardware realizations, and evaluate complexity and numerical performance tradeoffs of this highly robust and low-complexity carrier phase recovery method. A multiplier-free carrier phase recovery version of the MSDD provides nearly optimal performance for linewidths up to ~0.5 MHz, whereas for wider linewidths, the Wiener or LMS versions provide optimal performance at about 9 taps, using 1 or 2 complex multipliers per tap.

欠采样包裹相位图的恢复方法

欠采样包裹相位图的恢复方法

欠采样包裹相位图的恢复方法

欠采样包裹相位图的恢复方法

欠采样包裹相位图的恢复方法

欠采样包裹相位图的恢复方法

相干光正交频分复用传输系统中的无导频相位纠偏方法

Aiming at the shortcoming that the M-th power based traditional phase recovery method cannot be used for high-order QAM signal constellations,a carrier phase recovery method for 16-QAM constellations is presented.The proposed method is able to applied in CO-OFDM system to implement blind phase recovery with low computational cost.In the verification experiment,the method is used in 112 Gb/s 1 040 km CO-OFDM transmission,and its performance is compared to those using the fourth-power estimator.Experimental results indicate that the proposed method significantly outperform the fourth-power estimator.

An Improved Feed-Forward Carrier Recovery Algorithm for Coherent Receivers With $M$-QAM Modulation Format

An improved feed-forward carrier phase recovery method is proposed for coherent receivers using M-ary quadrature amplitude modulation-based modulation formats. It is shown that by introducing multiple cascaded feed-forward carrier recovery stages, the required compute power can be significantly reduced compared to the prior art using the single-stage-based blind phase search method.

Microstructure reconstructions from 2-point statistics using phase-recovery algorithms

Two-point statistics describe the first-order spatial correlations between the constituent distinct local states in the internal structure of the material. These are usually recovered by randomly throwing vectors of all sizes and orientations into the material microstructure. Building on very recent advances in this emerging field, it is demonstrated in this paper that the complete set of 2-point correlations carry all of the information needed to uniquely reconstruct an eigen microstructure to within an translation and/or an inversion. For this purpose, novel algorithms based on phase-recovery methods used in signal processing have been developed and successfully implemented. The computational speed and the versatility of these new mathematical procedures are demonstrated through reconstruction of several two- and three-dimensional microstructures from their 2-point statistics.

Phase and amplitude recovery and diffraction image generation method: structure of Sb/Au(110)–√3 × √3R54.7° from surface X-ray diffraction

The discovery that the phase problem of diffraction from non-periodic objects may be solved by oversampling the diffraction intensities in reciprocal space with respect to a Nyquist criterion has opened up new vistas for structure determination by diffraction methods. A similar principle may be applied to the problem of surface X-ray diffraction (SXRD), where, owing to the breaking of a crystal periodicity normal to its surface, diffraction data consist of a set of superstructure rods (SRs) due to scattering from the parts of the surface whose structure is different from that of the truncated bulk and of crystal truncation rods (CTRs), formed by interfering contributions from the surface and the bulk. A phase and amplitude recovery and diffraction image generation method (PARADIGM) is described that provides a prescription for finding the unmeasured amplitudes and phases of the surface contributions to the CTRs in addition to the phases of the SRs, directly from the diffraction data. The resulting `diffraction image' is the basis of a determination of the previously unknown multidomain structure of Sb/Au(110)–√3 × √3R54.7°.