Random two-frame phase-shifting interferometry via minimization of coefficient of variation

Random two-frame phase-shifting interferometry (PSI) is an advanced technique to retrieve the phase information from as few as two interferograms with unknown phase steps. Because of the advantages of no requirement for accurate phase shifters and much less time for data acquisition and processing, random two-frame PSI is attracting more and more interest in fast and high-precision optical metrology. However, reconstructing the phase from only two interferograms is challenging because it is an ill-posed problem in essence, especially when the phase step is unknown. Although some solutions have been proposed for this problem to date, most of them require complicated preprocessing or special usage preconditions for interferograms to be demodulated. In this letter, we developed an elegant phase reconstruction method for random two-frame PSI, which is much different from frameworks of existing methods. In the proposed approach, the phase of random two-frame PSI can be accurately reconstructed using the phase step value which minimizes the coefficient of variation (CV) of the modulation term of interferograms. Sufficient numerical simulations and experimental data demonstrate the high accuracy and high efficiency of this CV minimization (CVM) method. Moreover, its performance is not limited by the number of fringes in interferograms, in contrast to existing state-of-the-art approaches. We anticipate extensive applications of the CVM method in random two-frame PSI in the future

Random two-frame phase-shifting interferometry via minimization of coefficient of variation

Random two-frame phase-shifting interferometry (PSI) is an advanced technique to retrieve the phase information from as few as two interferograms with unknown phase steps. Because of the advantages of no requirement for accurate phase shifters and much less time for data acquisition and processing, random two-frame PSI is attracting more and more interest in fast and high-precision optical metrology. However, reconstructing the phase from only two interferograms is challenging because it is an ill-posed problem in essence, especially when the phase step is unknown. Although some solutions have been proposed for this problem to date, most of them require complicated preprocessing or special usage preconditions for interferograms to be demodulated. In this letter, we developed an elegant phase reconstruction method for random two-frame PSI, which is much different from frameworks of existing methods. In the proposed approach, the phase of random two-frame PSI can be accurately reconstructed using the phase step value which minimizes the coefficient of variation (CV) of the modulation term of interferograms. Sufficient numerical simulations and experimental data demonstrate the high accuracy and high efficiency of this CV minimization (CVM) method. Moreover, its performance is not limited by the number of fringes in interferograms, in contrast to existing state-of-the-art approaches. We anticipate extensive applications of the CVM method in random two-frame PSI in the future

Fighting against fast speckle decorrelation for light focusing inside live tissue by photon frequency shifting

Light focusing inside live tissue by digital optical phase conjugation (DOPC) has drawn increasing interest due to its potential biomedical applications in optogenetics, microsurgery, phototherapy, and deep-tissue imaging. However, fast physiological motions in a live animal, including blood flow and respiratory motions, produce undesired photon perturbation and thus inevitably deteriorate the performance of light focusing. Here, we develop a photon-frequency-shifting DOPC method to fight against fast physiological motions by switching the states of a guide star at a distinctive frequency. Therefore, the photons tagged by the guide star are well detected at the specific frequency, separating them from the photons perturbed by fast motions. Light focusing was demonstrated in both phantoms in vitro and mice in vivo with substantially improved focusing contrast. This work puts a new perspective on light focusing inside live tissue and promises wide biomedical applications

Single-Shot Time-Reversed Optical Focusing into and through Scattering Media

Optical time reversal can focus light through or into scattering media, which raises a new possibility for conquering optical diffusion. Because optical time reversal must be completed within the correlation time of speckles, enhancing the speed of time-reversed optical focusing is important for practical applications. Although employing faster digital devices for time-reversal helps, more efficient methodologies are also desired. Here, we report a single-shot time-reversed optical focusing method to minimize the wavefront measurement time. In our approach, all information requisite for optical time reversal is extracted from a single-shot on-axis hologram, and hence, no other preconditions or measurements are required. In particular, we demonstrate the first realization of single-shot time-reversed ultrasonically encoded (TRUE) optical focusing into scattering media. By using the minimum amount of measurement, this work breaks the fundamental speed limit of digitally based time reversal for focusing into and through scattering media and constitutes an important step toward high-speed wavefront shaping applications

Single-Shot Time-Reversed Optical Focusing into and through Scattering Media

Optical time reversal can focus light through or into scattering media, which raises a new possibility for conquering optical diffusion. Because optical time reversal must be completed within the correlation time of speckles, enhancing the speed of time-reversed optical focusing is important for practical applications. Although employing faster digital devices for time-reversal helps, more efficient methodologies are also desired. Here, we report a single-shot time-reversed optical focusing method to minimize the wavefront measurement time. In our approach, all information requisite for optical time reversal is extracted from a single-shot on-axis hologram, and hence, no other preconditions or measurements are required. In particular, we demonstrate the first realization of single-shot time-reversed ultrasonically encoded (TRUE) optical focusing into scattering media. By using the minimum amount of measurement, this work breaks the fundamental speed limit of digitally based time reversal for focusing into and through scattering media and constitutes an important step toward high-speed wavefront shaping applications

Dual-polarization analog optical phase conjugation for focusing light through scattering media

Focusing light through or inside scattering media by the analog optical phase conjugation (AOPC) technique based on photorefractive crystals (PRCs) has been intensively investigated due to its high controlled degrees of freedom and short response time. However, the existing AOPC systems only phase-conjugate the scattered light in one polarization direction, while the polarization state of light scattered through a thick scattering medium is spatially random in general, which means that half of the scattering information is lost. Here, we propose dual-polarization AOPC for focusing light through scattering media to improve the efficiency and fidelity in the phase conjugation. The motivations of the dual-polarization AOPC are illustrated by theoretical analysis and numerical simulation, and then an experimental system is established to realize the dual-polarization AOPC. By separating and rotating the two orthogonal polarization components of the randomly polarized scattered light, light in all polarization states is recorded and phase-conjugated using the same PRC. Experimental results for focusing through a thick biological tissue show that the intensity of the time-reversed focus from the dual-polarization AOPC can be enhanced by a factor of approximate four compared with the existing single-polarization AOPC

Towards Probabilistic Tensor Canonical Polyadic Decomposition 2.0: Automatic Tensor Rank Learning Using Generalized Hyperbolic Prior

Tensor rank learning for canonical polyadic decomposition (CPD) has long been deemed as an essential but challenging problem. In particular, since the tensor rank controls the complexity of the CPD model, its inaccurate learning would cause overfitting to noise or underfitting to the signal sources, and even destroy the interpretability of model parameters. However, the optimal determination of a tensor rank is known to be a non-deterministic polynomial-time hard (NP-hard) task. Rather than exhaustively searching for the best tensor rank via trial-and-error experiments, Bayesian inference under the Gaussian-gamma prior was introduced in the context of probabilistic CPD modeling and it was shown to be an effective strategy for automatic tensor rank determination. This triggered flourishing research on other structured tensor CPDs with automatic tensor rank learning. As the other side of the coin, these research works also reveal that the Gaussian-gamma model does not perform well for high-rank tensors or/and low signal-to-noise ratios (SNRs). To overcome these drawbacks, in this paper, we introduce a more advanced generalized hyperbolic (GH) prior to the probabilistic CPD model, which not only includes the Gaussian-gamma model as a special case, but also provides more flexibilities to adapt to different levels of sparsity. Based on this novel probabilistic model, an algorithm is developed under the framework of variational inference, where each update is obtained in a closed-form. Extensive numerical results, using synthetic data and real-world datasets, demonstrate the excellent performance of the proposed method in learning both low as well as high tensor ranks even for low SNR cases

Fighting against fast speckle decorrelation for light focusing inside live tissue by photon frequency shifting

Light focusing inside live tissue by digital optical phase conjugation (DOPC) has drawn increasing interest due to its potential biomedical applications in optogenetics, microsurgery, phototherapy, and deep-tissue imaging. However, fast physiological motions in a live animal, including blood flow and respiratory motions, produce undesired photon perturbation and thus inevitably deteriorate the performance of light focusing. Here, we develop a photon-frequency-shifting DOPC method to fight against fast physiological motions by switching the states of a guide star at a distinctive frequency. Therefore, the photons tagged by the guide star are well detected at the specific frequency, separating them from the photons perturbed by fast motions. Light focusing was demonstrated in both phantoms in vitro and mice in vivo with substantially improved focusing contrast. This work puts a new perspective on light focusing inside live tissue and promises wide biomedical applications

Structural basis for suppression of hypernegative DNA supercoiling by E. coli topoisomerase I

Escherichia coli topoisomerase I has an essential function in preventing hypernegative supercoiling of DNA. A full length structure of E. coli topoisomerase I reported here shows how the C-terminal domains bind single-stranded DNA (ssDNA) to recognize the accumulation of negative supercoils in duplex DNA. These C-terminal domains of E. coli topoisomerase I are known to interact with RNA polymerase, and two flexible linkers within the C-terminal domains may assist in the movement of the ssDNA for the rapid removal of transcription driven negative supercoils. The structure has also unveiled for the first time how the 4-Cys zinc ribbon domain and zinc ribbon-like domain bind ssDNA with primarily π-stacking interactions. This novel structure, in combination with new biochemical data, provides important insights into the mechanism of genome regulation by type IA topoisomerases that is essential for life, as well as the structures of homologous type IA TOP3α and TOP3β from higher eukaryotes that also have multiple 4-Cys zinc ribbon domains required for their physiological functions