Modal decomposition of fiber modes based on direct far-field measurements at two different distances with a multi-variable optimization algorithm

General error analysis of matrix-operation-mode decomposition technique in few-mode fiber laser

The mode decomposition based on matrix operation (MDMO) is one of the fastest mode decomposition (MD) techniques, which is important to the few-mode fiber laser characterization and its applications. In this paper, the general error of the MDMO technique was analyzed, where different influencing factors, such as position deviation of the optical imaging system, coordinate deviation of the image acquisition system, aberrations, and mode distortion were considered. It is found that the MDMO technique based on far-field intensity distribution is less affected by optical imaging system position deviation, coordinate deviation of the image acquisition system, and mode distortion than those based on direct near-field decomposition. But far-field decomposition is more affected by aberration than those based on near-field decomposition. In particular, the numerical results show that the deviation of the coordinate axis direction is an important factor limiting the accuracy of MD. In addition, replacing the ideal eigenmode basis with a distorted eigenmode basis can effectively suppress the decrease in mode decomposition accuracy caused by fiber bending. Moreover, based on detailed numerical analysis results, fitting formulas for estimating the accuracy of the MDMO technique with imperfections are also provided, which provides a comprehensive method for evaluating the accuracy of the MDMO technique in practical engineering operations.

Noise robust Zernike phase retrieval via learning based algorithm only with 2-step phase shift measurements

We present a noise robust deep learning based aberration analysis method using 2-step phase shift measurement data. We first propose a realistic aberration pattern generation method to synthesize a sufficient amount of real-world-like aberration patterns for training a deep neural network by exploiting the asymptotic statistical distribution parameters of the real-world Zernike coefficients extracted from a finite number of experimentally measured real-world aberration patterns. As a result, we generate a real-world-like synthetic dataset of 200,000 different aberrations from 15 sets of real-world aberration patterns obtained by a Michelson interferometer under a variety of measurement conditions using the 4-step derivative fitting method together with the exploitation of the Gaussian density estimation. We then train the deep neural network with the real-world-like synthetic dataset, using two types of network architectures, GoogLeNet and ResNet101. By applying the proposed learning based 2-step aberration analysis method to the analysis of numerically generated aberrations formed under 100 different conditions, we verify that the proposed 2-step method can clearly outperform the existing 4-step iterative methods based on 4-step measurements, including the derivative fitting, transport of intensity equation (TIE), and robust TIE methods, in terms of noise robustness, root mean square error (RMSE), and inference time. By applying the proposed 2-step method to the analysis of the real-world aberrations experimentally obtained under a variety of measurement conditions, we also verify that the proposed 2-step method achieves compatible performance in terms of the RMSE between the reconstructed and measured aberration patterns, and also exhibits qualitative superiority in terms of reconstructing more realistic fringe patterns and phase distributions compared to the existing 4-step iterative methods. Since the proposed 2-step method can be extended to an even more general analysis of aberrations of any higher order, we expect that it will be able to provide a practical way for comprehensive aberration analysis and that further studies will extend its usefulness and improve its operational performance in terms of algorithm compactness, noise robustness, and computational speed.

On similarity metrics evaluating the performance of mode decomposition in few-mode optical fibers

Mode decomposition refers to a set of techniques aimed to recover modal content in multimode optical fibers. In this Letter, we examine the appropriateness of the similarity metrics commonly used in experiments on mode decomposition in few-mode fibers. We show that the conventional Pearson correlation coefficient is often misleading and should not be used as the sole criterion for justifying decomposition performance in the experiment. We consider several alternatives to the correlation and propose another metric that most accurately reflects the discrepancy between complex mode coefficients, given received and recovered beam speckles. In addition, we show that such a metric enables transfer learning of deep neural networks on experimental data and tangibly ameliorates their performance.

Analysis of an image noise sensitivity mechanism for matrix-operation-mode-decomposition and a strong anti-noise method

Mode decomposition (MD) based on the matrix operation (MDMO) is one of the fastest mode decomposition methods in fiber laser which has great potential for optical communications, nonlinear optics and spatial characterization applications. However, we found that the image noise sensitivity is the main limit to the accuracy of the original MDMO method, but improving the decomposition accuracy by using conventional image filtering methods is almost ineffective. By using the norm theory of matrices, the analysis result shows that both the image noise and the coefficient matrix condition number determine the total upper-bound error of the original MDMO method. Besides, the greater the condition number, the more sensitive of MDMO method is to noise. In addition, it is found that the local error of each mode information solution in the original MDMO method is different, which depends on the L2-norm of each row vector of the inverse coefficient matrix. Moreover, a more noise-insensitive MD method is achieved by screening out the information corresponding to large L2-norm. In particular, selecting the higher accuracy among the original MDMO method and such noise-insensitive method as the result in a single MD process, a strong anti-noise MD method was proposed in this paper, which displays high MD accuracy in strong noise for both near-filed and far-filed MD cases.

2D least-squares mode decomposition for mode division multiplexing

We investigate a fast and accurate technique for mode decomposition in multimode optical fibers. Initial decomposition task of near-field beam patterns is reformulated in terms of a system of linear equations, requires neither machine learning nor iterative routines. We apply the method to step and graded-index fibers and compare the decomposition performance. We determine corresponding application boundaries, propose an efficient algorithm for phase retrieval and carry out a specific preselective procedure that increases the number of decomposable modes and makes it possible to handle up to fifteen modes in presence of realistic noise levels.