Performance Of Phase Retrieval Research Articles

Impact of resampling interpolation FIR filter in the practical Kramers-Kronig receiver.

The practical Kramers-Kronig (KK) receiver has been a competitive receiving technique in the data-center, medium reach, and even long-haul metropolitan networks. Nevertheless, an extra digital resampling operation is required at both ends of the KK field reconstruction algorithm due to the spectrum broadening caused by adopting the nonlinear function. Generally, the digital resampling function can be implemented by using linear interpolation (LI-ITP), the Lagrange cubic interpolation (LC-ITP), the spline cubic interpolation (SC-ITP), time-domain anti-aliasing finite impulse response (FIR) filter method (TD-FRM) scheme, and fast Fourier transform (FFT)-based scheme. However, the performance and the computational complexity analysis of different resampling interpolation schemes in the KK receiver have not been thoroughly investigated yet. Different from the interpolation schemes of conventional coherent detection, the interpolation function of the KK system is followed by the nonlinear operation, which will broaden the spectrum significantly. Due to the frequency-domain transfer function of different interpolation schemes, the broadened spectrum will have a potential spectrum aliasing, which will cause serious inter-symbol interference (ISI) and further impair the KK phase retrieval performance. We experimentally investigate the performance of different interpolation schemes under different digital up-sampling rates (i.e. the computational complexity) as well as the cut-off frequency, the tap number of the anti-aliasing filter, and the shape factor of the TD-FRM scheme in a 112-Gbit/s SSB DD 16-QAM system over 1920-km Raman amplification (RFA)-based standard single-mode fiber (SSMF). The experimental results involve that the TD-FRM scheme outperforms other interpolation schemes and the complexity is reduced by at least 49.6%. In fiber transmission results, take 20% soft decision-forward error correction (SD-FEC) of 2×10-2 as the threshold, the LI-ITP and LC-ITP schemes only reach 720-km while others can reach up to 1440-km.

Direct wavefront sensing with a plenoptic sensor based on deep learning.

Traditional plenoptic wavefront sensors (PWS) suffer from the obvious step change of the slope response which leads to the poor performance of phase retrieval. In this paper, a neural network model combining the transformer architecture with the U-Net model is utilized to restore wavefront directly from the plenoptic image of PWS. The simulation results show that the averaged root mean square error (RMSE) of residual wavefront is less than 1/14λ (Marechal criterion), proving the proposed method successfully breaks through the non-linear problem existed in PWS wavefront sensing. In addition, our model performs better than the recently developed deep learning models and traditional modal approach. Furthermore, the robustness of our model to turbulence strength and signal level is also tested, proving the good generalizability of our model. To the best of our knowledge, it is the first time to perform direct wavefront detection with a deep-learning-based method in PWS-based applications and achieve the state-of-the-art performance.

Adaptive optics compensation of orbital angular momentum beams using a hybrid input-output algorithm with complementary binary masks.

For orbital angular momentum (OAM) beams, we show that the twin-image problem in the single-intensity-measurement hybrid input-output algorithm (HIOA) severely impairs the phase retrieval performance and propose a very simple method to overcome this problem. First, we introduce the principle of the single-intensity-measurement HIOA together with the underlying reason for the twin-image problem and propose a new scheme of the HIOA using a pair of complementary binary masks (CBMs) to overcome the twin-image problem. To verify the usefulness of the proposed CBM-HIOA in the OAM free-space optical system, a wave-optics simulation is used to produce relatively realistic atmospheric turbulence, and the turbulence-induced distorted phase of the probe Gaussian beam is retrieved to compensate for the phase distortion of OAM beams. The suppression of the bidirectional and stagnant convergence caused by the twin-image problem, the compensation of the turbulence-induced distorted phase of the OAM beams, and the influence of different CBM shapes are studied in detail by numerical simulations. The corresponding numerical results show the feasibility and efficacy of the CBM-HIOA used for the adaptive optics compensation of OAM beams.

Phase Retrieval of Complex OFDM Signal by Solving Temporal Transport-of-Intensity Equation

We simulate the complex signal reconstruction by solving the temporal transport-of-intensity equation (TIE) in a direct detection orthogonal frequency division multiplexing (OFDM) system. At the receiver, by measuring two intensities before and after a dispersive element, we construct a TIE and retrieve the phase information of the complex OFDM signal by solving it. We investigate the influence of the carrier-signal power ratio (CSPR), the value of the dispersion, signal baud rate, sampling rate, laser linewidth, and frequency offset on the performance of phase retrieval (PR). In a 20 Gbaud 16 quadrature-amplitude-modulation (16QAM) OFDM system, the TIE-based direct-detection requires a 12 dB CSPR, which is comparable to Kramers–Kronig (KK)-based receiver and the single carrier TIE scheme. A proof-of-concept adaptive modulation scheme has also been applied to the TIE-based OFDM system.

Deep learning-based single-shot phase retrieval algorithm for surface plasmon resonance microscope based refractive index sensing application

A deep learning algorithm for single-shot phase retrieval under a conventional microscope is proposed and investigated. The algorithm has been developed using the context aggregation network architecture; it requires a single input grayscale image to predict an output phase profile through deep learning-based pattern recognition. Surface plasmon resonance imaging has been employed as an example to demonstrate the capability of the deep learning-based method. The phase profiles of the surface plasmon resonance phenomena have been very well established and cover ranges of phase transitions from 0 to 2π rad. We demonstrate that deep learning can be developed and trained using simulated data. Experimental validation and a theoretical framework to characterize and quantify the performance of the deep learning-based phase retrieval method are reported. The proposed deep learning-based phase retrieval performance was verified through the shot noise model and Monte Carlo simulations. Refractive index sensing performance comparing the proposed deep learning algorithm and conventional surface plasmon resonance measurements are also discussed. Although the proposed phase retrieval-based algorithm cannot achieve a typical detection limit of 10–7 to 10–8 RIU for phase measurement in surface plasmon interferometer, the proposed artificial-intelligence-based approach can provide at least three times lower detection limit of 4.67 × 10–6 RIU compared to conventional intensity measurement methods of 1.73 × 10–5 RIU for the optical energy of 2500 pJ with no need for sophisticated optical interferometer instrumentation.

Performance of Phase Retrieval via Phaselift and Quadratic Inversion in Circular Scanning Case

The reconstruction of the field radiated by a source from square amplitude-only data falls into the realm of phase retrieval . In this paper, we tackle the phase retrieval with two different approaches. The first one is based on a convex optimization problem called PhaseLift . The latter exploits the lifting technique to recast phase retrieval as a linear problem with an increased number of unknowns and then, because the linear problem is highly undetermined, it adds further constraints (based on the mathematical properties of the solution) to estimate it. The second approach formulates phase retrieval as a least squares problem and, therefore, it requires to tackle the minimization of a quartic functional which will be carried out by applying a gradient descent method. In the second part of this paper, in order to corroborate the effectiveness of both approaches, we present the numerical results. Afterward, we provide a comparison between the two methods and finally, we emphasize how the ratio between the number of independent data and the number of unknowns impacts on the performance in both approaches.

Investigation on the Dependency of Phase Retrieval Accuracy Versus Edge Enhancement to the Noise Ratio of X-ray Propagation-Based Phase-Contrast Imaging.

Phase retrieval is necessary for propagation-based phase-contrast imaging (PB-PCI). Arhatari established a model for predicting the impact of the sample-to-detector distance and the system noise on the phase retrieval performance. We have extended Arhatari's model to account for the parameters of excessive source size, finite detector resolution, and geometrical magnification for more practical cases. However, there exist interaction effects among these parameters resulting in difficulty of predicting the phase retrieval performance. In this study, we found that optimizing the trade-off among these parameters for phase retrieval is consistent with the improvement of edge enhancement to noise ratio (EE/N) in the "forward problem" of the PB-PCI. Hence, we engaged in establishing a relationship between EE/N and phase retrieval performance in terms of the "forward problem" and "inverse problem" of the PB-PCI, respectively. Our results showed that, at fixed detector resolution, phase retrieval from the phase-contrast projections at the same EE/N level resulted in the consistent phase retrieval performance. Therefore, the performance of phase retrieval can be predicted based on the EE/N level and be quantitatively optimized by increasing EE/N.

Reducing radiation dose in grating based x-ray phase contrast CT with twin-peaks in its phase stepping curves.

Differential phase contrast CT has been recognized as an x-ray imaging method with the potential to greatly improve the differentiation of soft tissues. Talbot interferometry has been one of the promising solutions allowing implementation with commercially available x-ray tubes with a polychromatic spectrum. Mainly due to imperfections in grating fabrication and the polychromatic spectrum of x-ray beam, a twin-peaks phenomenon may exist in phase stepping curves (PSCs) and degrade the performance of phase retrieval. The authors have previously proposed a Fourier analysis based method for phase retrieval in the scenario wherein the twin-peaks phenomenon occurs in PSCs. In this work, the authors propose a 5-step algebraic method for phase retrieval and investigate the potential of reducing radiation dose while both the Fourier and algebraic methods are being utilized for phase retrieval. The algebraic method to deal with the twin-peaks phenomenon, in which a set of linear equations with five unknown variables is needed for phase retrieval, is an extension of the so-called 3-step method that has been used in the scenario wherein only single-peak exists in the PSCs. In addition to a numerical phantom, two sets of experimental data (a phantom made of organic materials and a small animal) acquired by a prototype differential phase contrast CT system are employed to evaluate the performance of the Fourier and algebraic phase retrieval methods and their potential in radiation dose reduction. The evaluation by both numerical phantom and experimental data shows that the algebraic method works as well as the Fourier method in phase retrieval if the twin-peaks phenomenon in the PSCs is appropriately dealt with. In addition, while the radiation dose associated with data acquisition is being reduced via fewer phase shifting steps, the algebraic method can maintain a better performance compared to the Fourier method. Along with the Fourier method, the proposed 5-step algebraic method can cope with the twin-peaks phenomenon in phase retrieval. With decreased phase shifting steps and thus radiation dose, the proposed algebraic method performs better than the Fourier method, providing a practical solution for implementation of grating based differential phase contrast CT.

Phase retrieval in X-ray phase-contrast imaging suitable for tomography

In-line phase-contrast X-ray imaging provides images where both absorption and refraction contribute. For quantitative analysis of these images, the phase needs to be retrieved numerically. There are many phase-retrieval methods available. Those suitable for phase-contrast tomography, i.e., non-iterative phase-retrieval methods that use only one image at each projection angle, all follow the same pattern though derived in different ways. We outline this pattern and use it to compare the methods to each other, considering only phase-retrieval performance and not the additional effects of tomographic reconstruction. We also outline derivations, approximations and assumptions, and show which methods are similar or identical and how they relate to each other. A simple scheme for choosing reconstruction method is presented, and numerical phase-retrieval performed for all methods.

Theoretical performance of phase retrieval on a subdivided aperture

Phase retrieval is a nonlinear technique used to recover the phase in the Fourier domain using intensity measurements at the image plane and additional constraints. We describe a method to solve the phase retrieval problem using linear iterations near the solution, which provides both analytical insight into phase retrieval and numerical results. The algorithm finds the maximum a posteriori estimate of the phase using prior information about the statistics of the noise and the phase, and it was found to converge well in practice. When phase retrieval is performed on data from subdivided apertures, there is a loss of information regarding the relative piston terms of the subapertures. This error is quantified. We find that there is a smaller wavefront error when estimating the phase from a full aperture rather than from a subdivided aperture. Using a combination of intensity measurements from full and subdivided apertures results in a small improvement at very high photon levels only.