High-gain and high-speed wavefront shaping through scattering media.

Wavefront shaping (WFS) is emerging as a promising tool for controlling and focusing light in complex scattering media. The shaping system's speed, the energy gain of the corrected wavefronts, and the control degrees of freedom (DOF) are the most important metrics for WFS, especially for highly scattering and dynamic samples. Despite recent advances, current methods suffer from trade-offs that limit satisfactory performance to only one or two of these metrics. Here, we report a WFS technique that simultaneously achieves high speed, high energy gain, and high control DOF. By combining photorefractive crystal-based analog optical phase conjugation (AOPC) and stimulated emission light amplification, our technique achieves an energy gain approaching unity, more than three orders of magnitude larger than conventional AOPC. The response time of ~10 µs with about 106 control modes corresponds to an average mode time of about 0.01 ns/mode, which is more than 50 times lower than some of the fastest WFS systems to date. We anticipate that this technique will be instrumental in overcoming the optical diffusion limit in photonics and translate WFS techniques to real-world applications.

Adam SPGD algorithm in freeform surface in-process interferometry.

The adaptive interferometer has been recently proposed to realize the metrology of unknown freeform surfaces with several restructured algorithms for feedback control. The adaptive moment estimation (Adam) stochastic parallel gradient descent (SPGD) algorithm is employed in this paper for fringes release. The proposed algorithm makes considerable progress in relieving conflict of the convergence rate, speed, and parameters intervention. Simulations and experiments show its 37% time saving and 99% convergence rate, with arbitrarily configured parameter increment, compared with the SPGD algorithm. It would have great potential in in-process tests in freeform surface fabrication or large-volume testing.

Focusing light into scattering media with ultrasound-induced field perturbation.

Focusing light into scattering media, although challenging, is highly desirable in many realms. With the invention of time-reversed ultrasonically encoded (TRUE) optical focusing, acousto-optic modulation was demonstrated as a promising guidestar mechanism for achieving noninvasive and addressable optical focusing into scattering media. Here, we report a new ultrasound-assisted technique, ultrasound-induced field perturbation optical focusing, abbreviated as UFP. Unlike in conventional TRUE optical focusing, where only the weak frequency-shifted first-order diffracted photons due to acousto-optic modulation are useful, here UFP leverages the brighter zeroth-order photons diffracted by an ultrasonic guidestar as information carriers to guide optical focusing. We find that the zeroth-order diffracted photons, although not frequency-shifted, do have a field perturbation caused by the existence of the ultrasonic guidestar. By detecting and time-reversing the differential field of the frequency-unshifted photons when the ultrasound is alternately ON and OFF, we can focus light to the position where the field perturbation occurs inside the scattering medium. We demonstrate here that UFP optical focusing has superior performance to conventional TRUE optical focusing, which benefits from the more intense zeroth-order photons. We further show that UFP optical focusing can be easily and flexibly developed into double-shot realization or even single-shot realization, which is desirable for high-speed wavefront shaping. This new method upsets conventional thinking on the utility of an ultrasonic guidestar and broadens the horizon of light control in scattering media. We hope that it provides a more efficient and flexible mechanism for implementing ultrasound-guided wavefront shaping.

Intelligently optimized digital optical phase conjugation with particle swarm optimization.

Wavefront shaping (WFS) based on digital optical phase conjugation (DOPC) has gained major interest in focusing light through or inside scattering media. However, the quality of DOPC is greatly limited by imperfections of the system in a complicated and coupled way. In this Letter, we incorporate the concept of global optimization to solve this problem comprehensively for the first time, to the best of our knowledge. An automatic and intelligent optimization framework for DOPC techniques is proposed, leveraging the global optimization ability of particle swarm optimization (PSO). We demonstrate the general and powerful ability of the proposed approach in a series of DOPC-related experiments for focusing through and inside scattering media. This novel work can improve the OPC quality greatly and simplify the development of a high-performance DOPC system, which may open up a new avenue for the general scientific community to benefit from DOPC-based WFS in their potential applications.

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

Focusing light inside live tissue by digital optical phase conjugation (DOPC) has been intensively investigated due to its potential biomedical applications in deep-tissue imaging, optogenetics, microsurgery, and phototherapy. However, fast physiological motions in a live animal, such as 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 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.

Universal phase reconstruction approach of self-calibrating phase-shifting interferometry.

Self-calibrating phase-shifting interferometry (PSI) reconstructs the phase map from three-frame or more phase-shifting interferograms without the need for knowing accurate phase steps. The existing phase reconstruction methods for self-calibrating PSI still have many constraints in terms of the required number of interferograms, special usage preconditions, etc. In this Letter, a universal, accurate, and efficient phase reconstruction method for self-calibrating PSI is proposed. In this approach, we search the solution space of phase shifts to obtain the modulation amplitude of interferograms with the minimum coefficient of variation (CV). Then the phase is reconstructed through the searched phase shifts. Numerical and experimental studies demonstrate that this method can realize highly accurate phase reconstruction consistently, compared to the currently popular methods in their own usable ranges. We anticipate that this Letter may provide a universal and powerful solution for the phase reconstruction of self-calibrating PSI.

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.

Fast and accurate wavefront reconstruction in two-frame phase-shifting interferometry with unknown phase step.

A fast and accurate wavefront reconstruction method for two-frame phase-shifting interferometry is proposed. The unknown phase step between the two interferograms is estimated directly by solving a quartic polynomial equation, and then the phase map is readily reconstructed after obtaining the phase step. The whole phase reconstruction process is nearly analytical and thus very fast and easy to realize. Good performance of the proposed method is demonstrated by reconstructing the phase maps from simulated and real fringes along with comparisons to several existing well-established algorithms.

Polarization properties of receiving telescopes in atmospheric remote sensing polarization lidars.

A receiving telescope is an indispensable component in an atmospheric remote sensing polarization lidar. In order to achieve accurate atmospheric depolarization measurements, it is necessary to study the polarization properties of receiving telescopes, which are embodied by their Mueller matrices. In this paper, the Mueller matrices of receiving telescopes are obtained by ray tracing with space vectors. The relationship between the measurement errors of the atmospheric depolarization parameter and the elements of the Mueller matrix of receiving telescopes is derived. The polarization properties of receiving telescopes in terms of orientation, field of view, and F number are analyzed, respectively. By comparing two common receiving telescopes in linear and circular polarization lidars, it is found that the measurement errors caused by the Newton telescopes in circular polarization lidars are significantly greater than those in linear polarization lidars, while the performances of the Cassegrain telescopes in the two lidars are almost identical. What is more, the measurement errors caused by the Cassegrain telescopes are much less than the counterparts caused by the Newton telescopes. According to the comparison results, the optimal telescopes are respectively presented for polarization lidars working in different polarization states and laser wavelengths.

Retrieving the seawater volume scattering function at the 180° scattering angle with a high-spectral-resolution lidar.

A high-spectral-resolution lidar (HSRL) is proposed to retrieve the seawater volume scattering function at the 180° scattering angle ßπ without the assumption of the lidar extinction-to-backscatter ratio. A field-widened Michelson interferometer is employed as the ultra-narrow spectral discriminator to reject particulate scattering and molecular Rayleigh scattering but transmit molecular Mandelshtam-Brillouin scattering. The theoretical framework to retrieve ßπ is presented in detail based on a dual-channel HSRL configuration. Simulation on the retrieval and error estimation shows that, the proposed oceanographic HSRL based on the ship or aircraft can perform well to extract the profile of ßπ and has a real potential in the oceanographic remote sensing.

Design of iodine absorption cell for high-spectral-resolution lidar.

Iodine absorption cells are extensively employed by high-spectral-resolution Lidars (HSRLs) for aerosol optical properties and atmosphere state parameters profiling. To the best of our knowledge, the optimal design of the parameters of iodine cells has not been talked about systematically. In this paper, a heuristic method based on multi-objective concept is proposed for the design of iodine cells employed in HSRLs for aerosol profiling, and the method can be also applied to different types of HSRLs. The bi-objective model is established based on the retrieval error analysis of HSRL and then the Pareto optimal solutions are obtained through the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The performance of different absorption lines are compared according to the Pareto solution sets, and the stability of transmittance characteristics of different absorption lines are discussed through sensitivity analysis. The results are expected to provide guidance for the design of HSRLs based on iodine absorption filters.

Generalized high-spectral-resolution lidar technique with a multimode laser for aerosol remote sensing.

High-spectral-resolution lidar (HSRL) is a powerful tool for atmospheric aerosol remote sensing. The current HSRL technique often requires a single longitudinal mode laser as the transmitter to accomplish the spectral discrimination of the aerosol and molecular scattering conveniently. However, single-mode laser is cumbersome and has very strict requirements for ambient stability, making the HSRL instrument not so robust in many cases. In this paper, a new HSRL concept, called generalized HSRL technique with a multimode laser (MML-gHSRL), is proposed, which can work using a multimode laser. The MML-gHSRL takes advantage of the period characteristic of the spectral function of the interferometric spectral discrimination filter (ISDF) thoroughly. By matching the free spectral range of the ISDF with the mode interval of the multimode laser, fine spectral discrimination for the lidar return from each longitudinal mode can be realized. Two common ISDFs, i.e., the Fabry-Perot interferometer (FPI) and field-widened Michelson interferometer (FWMI), are introduced to develop the MML-gHSRL, and their performance is quantitatively analyzed and compared. The MML-gHSRL is a natural but significant generalization for the current HSRL technique based on the IDSF. It is potential that this technique would be a good entrance to future HSRL developments, especially in airborne and satellite-borne aerosol remote sensing applications.

Design of the interferometric spectral discrimination filters for a three-wavelength high-spectral-resolution lidar.

We address design of the interferometric spectral discrimination (ISD) filters for a specific three-wavelength high-spectral-resolution lidar (HSRL) in this paper. Taking into account the strong dependence of the transmittance of the ISD filters on the incident angle of light ray, the optical path of the receiving channel with an ISD filter in HSRL is analyzed. We derive the lidar equation with the angular distribution of backscatter signal, through which Monte Carlo (MC) simulations are then carried out to obtain the optimal parameters of the ISD filters for the HSRL at 1064 nm, 532 nm and 355 nm, respectively. Comparing the retrieval errors of the MC simulations based on different ISD filters, the configuration and parameters of the best ISD filter at each wavelength are determined. This paper can be employed as a theoretical guidance during the design of a three-wavelength HSRL with ISD filters.

Frequency locking of a field-widened Michelson interferometer based on optimal multi-harmonics heterodyning.

A general resonant frequency locking scheme for a field-widened Michelson interferometer (FWMI), which is intended as a spectral discriminator in a high-spectral-resolution lidar, is proposed based on optimal multi-harmonics heterodyning. By transferring the energy of a reference laser to multi-harmonics of different orders generated by optimal electro-optic phase modulation, the heterodyne signal of these multi-harmonics through the FWMI can reveal the resonant frequency drift of the interferometer very sensitively within a large frequency range. This approach can overcome the locking difficulty induced by the low finesse of the FWMI, thus contributing to excellent locking accuracy and lock acquisition range without any constraint on the interferometer itself. The theoretical and experimental results are presented to verify the performance of this scheme.

Field-widened Michelson interferometer for spectral discrimination in high-spectral-resolution lidar: practical development.

A field-widened Michelson interferometer (FWMI), which is intended as the spectroscopic discriminator in ground-based high-spectral-resolution lidar (HSRL) for atmospheric aerosol detection, is described in this paper. The structure, specifications and design of the developed prototype FWMI are introduced, and an experimental approach is proposed to optimize the FWMI assembly and evaluate its comprehensive characteristic simultaneously. Experimental results show that, after optimization process, the peak-to-valley (PV) value and root-mean-square (RMS) value of measured OPD variation for the FWMI are 0.04λ and 0.008λ respectively among the half divergent angle range of 1.5 degree. Through an active locking technique, the frequency of the FWMI can be locked to the laser transmitter with accuracy of 27 MHz for more than one hour. The practical spectral discrimination ratio (SDR) for the developed FWMI is evaluated to be larger than 86 if the divergent angle of incident beam is smaller than 0.5 degree. All these results demonstrate the great potential of the developed FWMI as the spectroscopic discriminator for HSRLs, as well as the feasibility of the proposed design and optimization process. This paper is expected to provide a good entrance for the lidar community in future HSRL developments using the FWMI technique.

Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique.

A phase unwrapping algorithm for interferometric fringes based on the unscented Kalman filter (UKF) technique is proposed. The algorithm can bring about accurate phase unwrapping and good noise suppression simultaneously by incorporating the true phase and its derivative in the state vector estimation through the UKF process. Simulations indicate that the proposed algorithm has better accuracy than some widely employed phase unwrapping approaches in the same noise condition. Also, the time consumption of the algorithm is reasonably acceptable. Applications of the algorithm in our different optical interferometer systems are provided to demonstrate its practicability with good performance. We hope this algorithm can be a practical approach that can help to reduce the systematic errors significantly induced by phase unwrapping process for interferometric measurements such as wavefront distortion testing, surface figure testing of optics, etc.

Field-widened Michelson interferometer for spectral discrimination in high-spectral-resolution lidar: theoretical framework.

A field-widened Michelson interferometer (FWMI) is developed to act as the spectral discriminator in high-spectral-resolution lidar (HSRL). This realization is motivated by the wide-angle Michelson interferometer (WAMI) which has been used broadly in the atmospheric wind and temperature detection. This paper describes an independent theoretical framework about the application of the FWMI in HSRL for the first time. In the framework, the operation principles and application requirements of the FWMI are discussed in comparison with that of the WAMI. Theoretical foundations for designing this type of interferometer are introduced based on these comparisons. Moreover, a general performance estimation model for the FWMI is established, which can provide common guidelines for the performance budget and evaluation of the FWMI in the both design and operation stages. Examples incorporating many practical imperfections or conditions that may degrade the performance of the FWMI are given to illustrate the implementation of the modeling. This theoretical framework presents a complete and powerful tool for solving most of theoretical or engineering problems encountered in the FWMI application, including the designing, parameter calibration, prior performance budget, posterior performance estimation, and so on. It will be a valuable contribution to the lidar community to develop a new generation of HSRLs based on the FWMI spectroscopic filter.

Effects of spectral discrimination in high-spectral-resolution lidar on the retrieval errors for atmospheric aerosol optical properties.

This paper presents detailed analysis about the effects of spectral discrimination on the retrieval errors for atmospheric aerosol optical properties in high-spectral-resolution lidar (HSRL). To the best of our knowledge, this is the first study that focuses on this topic comprehensively, and our goal is to provide some heuristic guidelines for the design of the spectral discrimination filter in HSRL. We first introduce a theoretical model for retrieval error evaluation of an HSRL instrument with a general three-channel configuration. The model only takes the error sources related to the spectral discrimination parameters into account, while other error sources not associated with these focused parameters are excluded on purpose. Monte Carlo (MC) simulations are performed to validate the correctness of the theoretical model. Results from both the model and MC simulations agree very well, and they illustrate one important, although not well realized, fact: a large molecular transmittance and a large spectral discrimination ratio (SDR, i.e., ratio of the molecular transmittance to the aerosol transmittance) are beneficial to promote the retrieval accuracy. More specifically, we find that a large SDR can reduce retrieval errors conspicuously for atmosphere at low altitudes, while its effect on the retrieval for high altitudes is very limited. A large molecular transmittance contributes to good retrieval accuracy everywhere, particularly at high altitudes, where the signal-to-noise ratio is small. Since the molecular transmittance and SDR are often trade-offs, we suggest considering a suitable SDR for higher molecular transmittance instead of using unnecessarily high SDR when designing the spectral discrimination filter. These conclusions are expected to be applicable to most of the HSRL instruments, which have similar configurations as the one discussed here.

Interferometric filters for spectral discrimination in high-spectral-resolution lidar: performance comparisons between Fabry-Perot interferometer and field-widened Michelson interferometer.

Thanks to wavelength flexibility, interferometric filters such as Fabry-Perot interferometers (FPIs) and field-widened Michelson interferometers (FWMIs) have shown great convenience for spectrally separating the molecule and aerosol scattering components in the high-spectral-resolution lidar (HSRL) return signal. In this paper, performance comparisons between the FPI and FWMI as a spectroscopic discrimination filter in HSRL are performed. We first present a theoretical method for spectral transmission analysis and quantitative evaluation on the spectral discrimination. Then the process in determining the parameters of the FPI and FWMI for the performance comparisons is described. The influences from the incident field of view (FOV), the cumulative wavefront error induced by practical imperfections, and the frequency locking error on the spectral discrimination performance of the two filters are discussed in detail. Quantitative analyses demonstrate that FPI can produce higher transmittance while the remarkable spectral discrimination is one of the most appealing advantages of FWMI. As a result of the field-widened design, the FWMI still performs well even under the illumination with large FOV while the FPI is only qualified for a small incident angle. The cumulative wavefront error attaches a great effect on the spectral discrimination performance of the interferometric filters. We suggest if a cumulative wavefront error is less than 0.05 waves RMS, it is beneficial to employ the FWMI; otherwise, FPI may be more proper. Although the FWMI shows much more sensitivity to the frequency locking error, it can outperform the FPI given a locking error less than 0.1 GHz is achieved. In summary, the FWMI is very competent in HSRL applications if these practical engineering and control problems can be solved, theoretically. Some other estimations neglected in this paper can also be carried out through the analytical method illustrated herein.