Phase Retrieval Algorithm Research Articles

Dual-wavelength interferogram decoupling method for three-frame generalized dual-wavelength phase-shifting interferometry based on deep learning.

In dual-wavelength interferometry, the key issue is how to efficiently retrieve the phases at each wavelength using the minimum number of wavelength-multiplexed interferograms. To address this problem, a new dual-wavelength interferogram decoupling method with the help of deep learning is proposed in this study. This method requires only three randomly phase-shifted dual-wavelength interferograms. With a well-trained deep neural network, one can obtain three interferograms with arbitrary phase shifts at each wavelength. Using these interferograms, the wrapped phases of a single wavelength can be extracted, respectively, via an iterative phase retrieval algorithm, and then the phases at different synthetic beat wavelengths can be calculated. The feasibility and applicability of the proposed method are demonstrated by simulation experiments of the spherical cap and red blood cell, respectively. This method will provide a solution for the problem of phase retrieval in multiwavelength interferometry.

A precise three-step phase retrieval algorithm suitable for the interferograms with less than one fringes numbers

In order to improve the accuracy and expand the range of the phase-shifting algorithm application, a precise three-step phase retrieval algorithm suitable for the interferograms with less than one fringes numbers is proposed. The proposed method improves the accuracy, on the one hand because normalization and subtraction are introduced to reduce background intensity fluctuation, on the other hand because Lissajous ellipse fitting (LEF) method is introduced to reconstruct phase maps from the normalized and Gram-Schmidt (GS) orthonormalized maps. Because the approximation operations for cumulative sum aren’t used in the GS method, the proposed algorithm is suitable for not only interferograms that the fringes numbers are more than one but also interferograms that fringes numbers are less than one. Moreover, the proposed method can be applied to simple and complex patterns. Thus, the proposed algorithm has a wider range of applications. The proposed algorithm’s reliability and performance are confirmed by simulations and experiments.

Recent advances in small angle x-ray scattering for superlattice study

Small-angle x-ray scattering is used for the structure determination of superlattice for its superior resolution, nondestructive nature, and high penetration power of x rays. With the advent of high brilliance x-ray sources and innovative computing algorithms, there have been notable advances in small angle x-ray scattering analysis of superlattices. High brilliance x-ray beams have made data analyses less model-dependent. Additionally, novel data acquisition systems are faster and more competitive than ever before, enabling a more accurate mapping of the superlattices' reciprocal space. Fast and high-throughput computing systems and algorithms also make possible advanced analysis methods, including iterative phasing algorithms, non-parameterized fitting of scattering data with molecular dynamics simulations, and the use of machine learning algorithms. As a result, solving nanoscale structures with high resolutions has become an attainable task. In this review, we highlight new developments in the field and introduce their applications for the analysis of nanoscale ordered structures, including nanoparticle supercrystals, nanoscale lithography patterns, and supramolecular self-assemblies. Particularly, we highlight the reciprocal space mapping techniques and the use of iterative phase retrieval algorithms. We also cover coherent-beam-based small angle x-ray scattering techniques such as ptychography and ptycho-tomography in view of the traditional small angle x-ray scattering perspective.

Phase retrieval for sub-Gaussian measurements

Generally, the phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of linear measurements. These measurements can be, for example, the Fourier transform of the density function. Computationally the phase retrieval problem is very challenging. Many algorithms for phase retrieval are based on i.i.d. Gaussian random measurements. However, Gaussian random measurements remain one of the very few classes of measurements. In this paper, we develop an efficient phase retrieval algorithm for sub-Gaussian random frames. We provide a general condition for measurements and develop a modified spectral initialization. In the algorithm, we first obtain a good approximation of the solution through the initialization, and from there we use Wirtinger Flow to solve for the solution. We prove that the algorithm converges to the global minimizer linearly.

Single-frame coherent diffraction imaging of extended objects using triangular aperture.

We propose a method of single-frame coherent diffraction imaging using a triangular aperture, which can not only reconstruct the projection image of extended objects from a single-frame coherent diffraction pattern, but also improve the image of the wavefield of the probe. In this method, a plane-wave illuminates a triangular aperture. An object is placed immediately after the aperture or in the image plane of the aperture through a lens. A far-field coherent diffraction pattern is collected by a two-dimensional detector. The object image is reconstructed from the single-frame diffraction pattern using a phase retrieval algorithm without support constraints. We simulate feasible experimental setups in the hard X-ray regime and show that this method can be practical use for single-frame coherent diffraction imaging. The present method has the potential exploring dynamic phenomena in materials science and biology with high spatiotemporal resolution using synchrotron radiation/free-electron lasers.

Bragg coherent diffraction imaging by simultaneous reconstruction of multiple diffraction peaks

Bragg coherent diffractive imaging (BCDI) is a noninvasive microscopy technique that can visualize the morphology and internal lattice deviations of crystals with nanoscale spatial resolution and picometer deformation sensitivity. While BCDI has been successfully applied in various studies of materials, it is less successful for highly strained crystals. Specifically, it is difficult to correctly reconstruct the electron density of a highly strained object using conventional phase retrieval algorithms. Although various algorithms have been developed to overcome this challenge, most of them require a priori knowledge that is not always available in practice. Here we report a phase retrieval workflow that can invert diffraction patterns from multiple Bragg peaks simultaneously. The workflow is explored via simulated diffraction from crystals with various strain conditions. Reconstructions from the workflow consistently demonstrate more accurate electron density maps, in comparison with the conventional method. For highly strained crystals, the workflow improves the reliability and consistency of BCDI phase retrieval significantly.

Multi-image and color image encryption via multi-slice ptychographic encoding

Multi-slice ptychography is a diffractive imaging technique that can reconstruct the information of a 3-D object from its diffraction intensities. In this article, we propose a multi-slice ptychographic encoding method for the encryption of multiple and color images. Full-phase images to be encrypted together with inserted phase keys are transformed into diffraction intensities (i.e., cipher texts) via multi-slice ptychographic encoding and double random phase encoding. The multi-slice ptychographic encoding refers to the process of using ptychographic scanning and recording to encrypt a multi-slice object that is composed of secret images and inserted phase keys. During decryption, an iterative phase retrieval algorithm is modified. The feasibility, robustness and security of the proposed method are analyzed. Numerical simulation results show that the proposed method can achieve high-quality decryption, and has high security and robustness against noise, compression, and occlusion.

Spectral Method for Phase Retrieval: An Expectation Propagation Perspective

Phase retrieval refers to the problem of recovering a signal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {x}_{\star }\in \mathbb {C}^{n}$ </tex-math></inline-formula> from its phaseless measurements <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {y}_{\text {i}}=| {a}_{i}^{ \mathsf {H}} {x}_{\star }|$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\{ {a}_{\text {i}}\}_{\text {i}=1}^{ {m}}$ </tex-math></inline-formula> are the measurement vectors. Spectral method is widely used for initialization in many phase retrieval algorithms. The quality of spectral initialization can have a major impact on the overall algorithm. In this paper, we focus on the model where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {A}=[ {a}_{1},\ldots, {a}_{ {m}}]^{ \mathsf {H}}$ </tex-math></inline-formula> has orthonormal columns, and study the spectral initialization under the asymptotic setting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {m}, {n}\to \infty $ </tex-math></inline-formula> with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {m}/ {n}\to \delta \in (1,\infty)$ </tex-math></inline-formula> . We use the expectation propagation framework to characterize the performance of spectral initialization for Haar distributed matrices. Our numerical results confirm that the predictions of the EP method are accurate for not-only Haar distributed matrices, but also for realistic Fourier based models (e.g. the coded diffraction model). The main findings of this paper are the following: 1) There exists a threshold on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula> (denoted as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta _{ \mathrm {weak}}$ </tex-math></inline-formula> ) below which the spectral method cannot produce a meaningful estimate. We show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta _{ \mathrm {weak}}=2$ </tex-math></inline-formula> for the column-orthonormal model. In contrast, previous results by Mondelli and Montanari show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta _{ \mathrm {weak}}=1$ </tex-math></inline-formula> for the i.i.d. Gaussian model. 2) The optimal design for the spectral method coincides with that for the i.i.d. Gaussian model, where the latter was recently introduced by Luo, Alghamdi and Lu.

Time-Frequency Phase Retrieval for Audio—The Effect of Transform Parameters

In audio processing applications, phase retrieval (PR) is often performed from the magnitude of short-time Fourier transform (STFT) coefficients. Although PR performance has been observed to depend on the considered STFT parameters and audio data, the extent of this dependence has not been systematically evaluated yet. To address this, we studied the performance of three PR algorithms for various types of audio content and various STFT parameters such as redundancy, time-frequency ratio, and the type of window. The quality of PR was studied in terms of objective difference grade and signal-to-noise ratio of the STFT magnitude, to provide auditory- and signal-based quality assessments. Our results show that PR quality improved with increasing redundancy, with a strong relevance of the time-frequency ratio. The effect of the audio content was smaller but still observable. The effect of the window was only significant for one of the PR algorithms. Interestingly, for a good PR quality, each of the three algorithms required a different set of parameters, demonstrating the relevance of individual parameter sets for a fair comparison across PR algorithms. Based on these results, we developed guidelines for optimizing STFT parameters for a given application.

Positive Semidefinite Matrix Factorization: A Connection With Phase Retrieval and Affine Rank Minimization

Positive semidefinite matrix factorization (PSDMF) expresses each entry of a nonnegative matrix as the inner product of two positive semidefinite (psd) matrices. When all these psd matrices are constrained to be diagonal, this model is equivalent to nonnegative matrix factorization. Applications include combinatorial optimization, quantum-based statistical models, and recommender systems, among others. However, despite the increasing interest in PSDMF, only a few PSDMF algorithms were proposed in the literature. In this work, we provide a collection of tools for PSDMF, by showing that PSDMF algorithms can be designed based on phase retrieval (PR) and affine rank minimization (ARM) algorithms. This procedure allows a shortcut in designing new PSDMF algorithms, as it allows to leverage some of the useful numerical properties of existing PR and ARM methods to the PSDMF framework. Motivated by this idea, we introduce a new family of PSDMF algorithms based on iterative hard thresholding (IHT). This family subsumes previously-proposed projected gradient PSDMF methods. We show that there is high variability among PSDMF optimization problems that makes it beneficial to try a number of methods based on different principles to tackle difficult problems. In certain cases, our proposed methods are the only algorithms able to find a solution. In certain other cases, they converge faster. Our results support our claim that the PSDMF framework can inherit desired numerical properties from PR and ARM algorithms, leading to more efficient PSDMF algorithms, and motivate further study of the links between these models.

Review of partially coherent diffraction imaging

Coherent diffraction imaging (CDI), a type of lensless imaging method, relies on the use of light source with high-degree coherence to compute highly resolved complex-valued objects. The coherence of light source consists of temporal coherence and spatial coherence. In practice, it is difficult to obtain a fully coherent source. Spatial decoherence can be generated in the following three scenarios: no synchronization mechanism for the whole radiation source, a finite (non-zero) point spread function of the detector, and the sample variation within exposure time. Partial temporal coherence means that the beam is not quasi-monochromatic, behaving as the energy spread of the illumination. The consequence of reduced degree of temporal and/or spatial coherence in CDI is the decrease of visibility in the measured diffraction intensity. A fundamental assumption of CDI is the full temporal and spatial coherence, and even a relatively small deviation from full coherence can prevent the phase retrieval algorithm from converging accurately. It is necessary to break the barrier of limited coherence by improving the experimental setups directly or optimizing the phase retrieval algorithms to mitigate decoherence. Based on the Wolf’s model of coherence-mode of light and the framework of CDI using partially coherent light proposed by Nugent et al., various methods have been proposed to solve the problems induced by low coherence. Those methods generally experience a similar development process, that is, from the requirement for measuring the spatial (coherent length or complex coherent factor) or temporal (spectrum distribution) coherence properties to without the need for such priori knowledge. Here in this work, the principles of partial coherent CDI, and the major progress of CDI with partial spatial- and temporal-coherent light are reviewed.

Quantitative phase microscopy imaging based on fractional spiral phase plate

Quantitative phase imaging (QPI), which combines phase imaging with optical microscopy technology, provides a marker-free, fast, non-destructive, and high-resolution imaging method for observing transparent biological samples. It is widely used in life science, biomedicine, etc. As an emerging QPI technology, spiral phase contrast microscopy (SPCM) uses a spiral phase filter to achieve edge enhancement of amplitude or phase objects. Using the multi-step phase-shifting technology, a complex sample can be measured quantitatively, which has the advantages of high stability, high sensitivity and high precision. However, the SPCM requires at least three-step phase-shifted spiral phase filtered images to achieve the quantitative reconstruction of the amplitude and phase of a sample, and the image acquisition process and the reconstruction process are relatively complicated, which require high stability of system, and the SPCM has low temporal resolution. In order to further improve the performance of SPCM and increase the system stability, sensitivity and temporal resolution, in this paper a quantitative phase imaging method and system based on a fractional spiral phase plate is proposed. Through a sample intensity image filtered by a fractional spiral phase plate, the modified Gerchberg-Saxton iterative phase retrieval algorithm is used to quantitatively reconstruct the phase of a pure phase sample, which simplifies the experimental process and phase reconstruction steps of spiral phase contrast microsocopy. In the computer simulation experiments, the phase imaging process and the reconstruction process of spiral phase plates based on different topological charges are studied, the feasibility of which is analyzed. Finally, through imaging and phase reconstruction of the phase grating and biological cell sample, it is verified that the phase contrast microscopy method based on the fractional spiral phase plate can effectively improve the contrast of spiral phase contrast microscopy and can obtain a quantitative reconstruciton of a weak phase object. The phase information of a sample has significance in research and application for developing the spiral phase contrast microscopy.

Non-Coherent DOA Estimation via Proximal Gradient Based on a Dual-Array Structure

Although the non-coherent direction of arrival (DOA) estimation problem can be solved by sparse phase retrieval algorithms, known reference signals are required to deal with the inherent ambiguity issue of this approach. To avoid the use of reference signals, an effective array structure employing two uniform linear arrays is proposed (although other array structures are possible, such as the circular array), based on which a phase retrieval problem employing group sparsity is formulated. It is then replaced by its convex surrogate alternative by applying the majorization-minimization technique and the proximal gradient method is employed to solve the surrogate problem. The proposed algorithm is referred to as fasT grOup sparsitY Based phAse Retreival (ToyBar). Unlike the existing phase-retrieval based DOA estimation algorithm GESPAR, it does not need to know the number of incident signals in advance. Simulation results indicate that the proposed algorithm has a fast convergence speed and a better estimation performance is achieved.

Broadband scattering imaging technology based on common-mode rejection of polarization characteristic

&lt;sec&gt;Owing to the inhomogeneity of the refractive index inside the sample (e.g. biological tissue) or on the surface of the sample(e.g. ground glass), light will be strongly scattered when it propagates through the sample. Therefore, we can hardly obtain the information about the objects behind the scattering medium, except for only a complex speckle pattern. To date, many approaches to realize focusing and imaging through scattering medium have been put forward. The traditional method mainly utilizes ballistic photons for imaging through scattering medium. Since the ballistic light is attenuated exponentially with the increase of depth of propagation in the scattering medium, the reconstruction from the speckle formed by scattered light is more conducive to practicability such as deep biomedical imaging. Typically, the wavefront shaping, optical transmission matrix and speckle correlation techniques which can successfully recover hidden object from the speckle, are valuable in biomedical imaging field. However, both optical transmission matrix and wavefront shaping rely on the coherence of light waves. The physical model of speckle correlation imaging is limited by the similarity of the point spread function of the imaging system. Thus, it is restrictive to achieve imaging through random scattering medium with broadband light illumination by using the current techniques.&lt;/sec&gt;&lt;sec&gt;In this paper, we present a broadband scattering imaging method based on common-mode rejection of polarization characteristic. In order to solve the problem that current scattering imaging methods are limited by the spectral width of the light source illumination, the polarization characteristic of the speckle field is explored in depth. We qualitatively analyze the difference in polarization information between the hidden object and the background noise in the speckle field. Notably, owing to the differences among autocorrelation functions of the speckle field intensity with different rotate angles of polarization, we can obtain two images where the object information contained in the speckle field and the background noise are dominant. Specifically, two speckle patterns are selected according to the maximum value and minimum value of the peak-to-correlation energy of the different speckles’ intensity autocorrelation. Afterwards, the serious background noise caused by the broadband light illumination is significantly suppressed by using polarization speckle difference imaging, and then the hidden object is reconstructed, with basic phase retrieval algorithm combined.&lt;/sec&gt;&lt;sec&gt;Comparison with conventional speckle correlation imaging technique, the value of peak signal-to-noise ratio and structural similarity index of reconstructions through using the proposed method are improved significantly, and the fitting curves are stabilized. Emphatically, the background noise item is physically handled by developing a novel physical imaging model. Furthermore, the proposed method is highly efficient and universal to recover different types of the hidden objects with better quality under broadband light illumination. Therefore, the proposed method has more potential applications in scattering imaging and biomedical imaging.&lt;/sec&gt;

Telecentric in-line-and-off-axis hybrid digital holographic high-resolution reconstruction method

In-line digital holography usually employs a phase retrieval algorithm to decouple the phase information but fails to eliminate the unwanted DC and twin image terms when the measured sample does not agree with the sparsity. While the off-axis digital holography can efficiently remove the unwanted image terms but can not reserve the high frequencies of the sample to realize high resolution. The in-line-and-off-axis hybrid digital holography was then developed to provide a relatively high resolution digital holographic imaging without considering the effect of the unwanted terms. In other words, the in-line-and-off-axis hybrid digital holography merges all of the best virtues of the mentioned-above methods in an efficient and elegant way. However, this state-of-the-art method requires prior knowledge about the diffraction distance, which results in time-consuming and low accuracy. In other sense, telecentric technology can realize non-diffractive imaging without the knowledge about the diffraction distance or spherical aberration or defocusing aberration. Therefore, in this paper, a novel in-line-and-off-axis hybrid digital holography is proposed by introducing telecentric imaging architecture, and the corresponding reconstruction method is further proposed by utilizing constrained iterative approach. In this method, telecentric in-line-and-off-axis hybrid digital holography is first used to acquire focused off-axis and in-line holograms, respectively. The low resolution phase information is reconstructed from the off-axis hologram by using Fourier transform method with the help of the sample-free off-axis hologram, and then multiplexed with the amplitude information obtained from the in-line hologram to act as the initial complex amplitude in the iterative recovery process. As a result, constrained iterations are carried out in the spatial domain and frequency domain to realize high resolution and high speed reconstruction. After simulations, we build an experimental setup and demonstrate the operation of the method with USAF resolution target, onion cells and bee wings. Both the simulation and experimental results show that the proposed method can require no prior knowledge to suppress the phase disturbance caused by the unwanted image terms and optical aberrations, resulting in high speed and full utilization of spatial bandwidth product of the digital camera to yield high resolution reconstruction. We hope that the proposed method will have most practical applications in the case where large resolution, high speed and good quality are needed.

Phase Retrieval Using Expectation Consistent Signal Recovery Algorithm Based on Hypernetwork

Phase retrieval (PR) is an important component in modern computational imaging systems. Many algorithms have been developed over the past half-century. Recent advances in deep learning have introduced new possibilities for a robust and fast PR. An emerging technique called deep unfolding provides a systematic connection between conventional model-based iterative algorithms and modern data-based deep learning. Unfolded algorithms, which are powered by data learning, have shown remarkable performance and convergence speed improvement over original algorithms. Despite their potential, most existing unfolded algorithms are strictly confined to a fixed number of iterations when layer-dependent parameters are used. In this study, we develop a novel framework for deep unfolding to overcome existing limitations. Our development is based on an unfolded generalized expectation consistent signal recovery (GEC-SR) algorithm, wherein damping factors are left for data-driven learning. In particular, we introduce a hypernetwork to generate the damping factors for GEC-SR. Instead of learning a set of optimal damping factors directly, the hypernetwork learns how to generate the optimal damping factors according to the clinical settings, thereby ensuring its adaptivity to different scenarios. To enable the hypernetwork to adapt to varying layer numbers, we use a recurrent architecture to develop a dynamic hypernetwork that generates a damping factor that can vary online across layers. We also exploit a self-attention mechanism to enhance the robustness of the hypernetwork. Extensive experiments show that the proposed algorithm outperforms existing ones in terms of convergence speed and accuracy and still works well under very harsh settings, even under which many classical PR algorithms are unstable.

Reconstructing algorithm for frequency-resolved optical gating based on intelligent seeker optimization

Frequency-resolved optical gating (FROG) is a common technique of ultrashort pulse measurement. It reconstructs the test pulse by an iterative two-dimensional phase retrieval algorithm from a FROG trace. Now the most widely used FROG algorithm is principal component generalized projection (PCGP), yet its accuracy of pulse retrieval drops obviously under noise condition, and its iterative speed slows down significantly as the size of FROG trace increases. Actually, most of ultrashort pulses delivered from ultrafast oscillators and amplifiers as well as created in most scientific experiments are of smooth spectral phases, so that they can be determined by a few of dispersion coefficients. In this paper, we propose a FROG algorithm based on seeker optimization algorithm (SOA). After recording the spectrum of the test pulse, several main dispersion coefficients of the spectral phase of the pulse are searched directly by the SOA algorithm to fit the corresponding FROG trace. Then the shape of the test pulse can be uniquely reconstructed. Since this algorithm mainly operates in a spectral domain and its routine of iteration is much simpler than PCGP’s, faster speed and higher accuracy of pulse retrieval can be expected. In order to prove the advantages of SOA-FROG algorithm, numeral simulations are performed for test pulses with varying dispersion, in the cases without noise and with 1%, 5%, 10%, 20% noise levels, respectively. The simulation results show that the new algorithm performs much better than PCGP in accuracy and iteration speed. In the case without noise, 97% test pulses reach the condition of rigid convergence (FROG error &lt;i&gt;G&lt;/i&gt; ≤ 10&lt;sup&gt;–4&lt;/sup&gt;) after 1500 iteration circles by using the SOA, with an average FROG error &lt;i&gt;G&lt;/i&gt; &lt; 10&lt;sup&gt;–5&lt;/sup&gt;. So the accuracy of pulse reconstruction by SOA is at least three orders of magnitude higher than by PCGP. In cases with different noise levels, the accuracy of pulse reconstruction by SOA is also much higher than by PCGP. By means of background-subtraction and filtering on the FROG traces, the retrieved pulse profiles almost accord with reality. Typically for a 256 × 256 FROG trace, SOA-FROG iterates 100.8 circles per second, about 5 times faster than PCGP. After 300 iteration circles by SOA in about 3 s, most of test pulses can finish their routines of reconstruction and reach high accuracy. Besides SHG-FROG, the SOA-FROG algorithm can also be utilized in other FROG techniques based on the 3&lt;sup&gt;rd&lt;/sup&gt; order nonlinear optical effects. In summary, the SOA-FROG is expected to be suitable to the real-time pulse measurement with high accuracy in most of application cases. Yet some measures of improvement should be taken to reconstruct complex pulses with rough spectral phases or/and broken spectra.

A self‐tracking phase retrieval algorithm used in distributed disturbance sensing

AbstractThe phase‐retrieval method with delayed calibration is widely used in fiber‐optic sensing structures to extract the distributed vibration messages. Yet, the performance of this method is not satisfactory when sudden changes are introduced in sensing path, for the DC compensation is not a slow variable under this situation. To improve the adjustment of interferometric fiber‐optic structure, a self‐tracking phase retrieval method is proposed. In the novel algorithm, the static state is tracked by calibrating DC compensation value in each retrieval period. When tested in the real scene with a 20 km‐long sensing fiber, the performance of the novel retrieval algorithm has been proved. Experimental results show that, compared with the conventional delayed calibration method, self‐tracking algorithm brings a better accuracy and uniformity performance in intrusion location test and shows a better adaptability to the environment.

Non-invasive focusing and imaging in scattering media with a fluorescence-based transmission matrix

In biological microscopy, light scattering represents the main limitation to image at depth. Recently, a set of wavefront shaping techniques has been developed in order to manipulate coherent light in strongly disordered materials. The Transmission Matrix approach has shown its capability to inverse the effect of scattering and efficiently focus light. In practice, the matrix is usually measured using an invasive detector or low-resolution acoustic guide stars. Here, we introduce a non-invasive and all-optical strategy based on linear fluorescence to reconstruct the transmission matrices, to and from a fluorescent object placed inside a scattering medium. It consists in demixing the incoherent patterns emitted by the object using low-rank factorizations and phase retrieval algorithms. We experimentally demonstrate the efficiency of this method through robust and selective focusing. Additionally, from the same measurements, it is possible to exploit memory effect correlations to image and reconstruct extended objects. This approach opens up a new route towards imaging in scattering media with linear or non-linear contrast mechanisms.

Simple accurate model‐based phase diversity phase retrieval algorithm for wavefront sensing in high‐resolution optical imaging systems

Simple accurate model‐based phase diversity phase retrieval algorithm for wavefront sensing in high‐resolution optical imaging systems