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Spatial frequency domain imaging (SFDI) has witnessed very rapid growth over the last decade, owing to its unique capabilities for imaging optical properties and chromophores over a large field-of-view and in a rapid manner. We provide a comprehensive review of the principles of this imaging method as of 2019, review the modeling of light propagation in this domain, describe acquisition methods, provide an understanding of the various implementations and their practical limitations, and finally review applications that have been published in the literature. Importantly, we also introduce a group effort by several key actors in the field for the dissemination of SFDI, including publications, advice in hardware and implementations, and processing code, all freely available online.

We present a Monte Carlo (MC) method to determine depth-dependent probability distributions of photon visitation and detection for optical reflectance measurements performed in the spatial frequency domain (SFD). These distributions are formed using an MC simulation for radiative transport that utilizes a photon packet weighting procedure consistent with the two-dimensional spatial Fourier transform of the radiative transport equation. This method enables the development of quantitative metrics for SFD optical sampling depth in layered tissue and its dependence on both tissue optical properties and spatial frequency. We validate the computed depth-dependent probability distributions using SFD measurements in a layered phantom system with a highly scattering top layer of variable thickness supported by a highly absorbing base layer. We utilize our method to establish the spatial frequency-dependent optical sampling depth for a number of tissue types and also provide a general tool to determine such depths for tissues of arbitrary optical properties.

Diffuse optical imaging probes deep living tissue enabling structural, functional, metabolic, and molecular imaging. Recently, due to the availability of spatial light modulators, wide-field quantitative diffuse optical techniques have been implemented, which benefit greatly from structured light methodologies. Such implementations facilitate the quantification and characterization of depth-resolved optical and physiological properties of thick and deep tissue at fast acquisition speeds. We summarize the current state of work and applications in the three main techniques leveraging structured light: spatial frequency-domain imaging, optical tomography, and single-pixel imaging. The theory, measurement, and analysis of spatial frequency-domain imaging are described. Then, advanced theories, processing, and imaging systems are summarized. Preclinical and clinical applications on physiological measurements for guidance and diagnosis are summarized. General theory and method development of tomographic approaches as well as applications including fluorescence molecular tomography are introduced. Lastly, recent developments of single-pixel imaging methodologies and applications are reviewed.

Fast estimation of optical properties from reflectance measurements at two spatial frequencies could pave way for real-time, wide-field and quantitative mapping of vital signs of tissues. We present a machine learning-based approach for estimating optical properties in the spatial frequency domain, where a random forest regression algorithm is trained over data obtained from Monte-Carlo photon transport simulations. The algorithm learns the nonlinear mapping between diffuse reflectance at two spatial frequencies, and the absorption and reduced scattering coefficient of the tissue under consideration. Using this method, absorption and reduced scattering properties could be obtained over a 1 megapixel image in 450 ms with errors as low as 0.556% in absorption and 0.126% in reduced scattering.

Structural damages occur in modern structures during operations due to environmental and human factors. The damages accumulating with time may lead to a significant decrease in structure performance or even destruction; natural symmetry is broken, resulting in an unexpected life and economic loss. Therefore, it is necessary to monitor the structural response to detect the damage in an early stage, evaluate the health condition of structures, and ensure the operation safety of structures. In fact, the structure and the evaluation can be considered as a special symmetry. Among several SHM methods, vibration-based SHM techniques have been widely adopted recently. Hence, this paper reviews the vibration-based SHM methods in terms of the vibrational parameters used. In addition, the technical codes on vibration based SHM system have also been reviewed, since they are more important in engineering applications. Several related ISO standards and national codes have been developed and implemented, while more specific technical codes are still required to provide more detailed guidelines in practice to maintain structure safety and natural symmetry.

Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new stationarity test for functional time series based on frequency domain methods. The proposed test statistics is based on joint dimension reduction via functional principal components analysis across the spectral density operators at all Fourier frequencies, explicitly allowing for frequency-dependent levels of truncation to adapt to the dynamics of the underlying functional time series. The properties of the test are derived both under the null hypothesis of stationary functional time series and under the smooth alternative of locally stationary functional time series. The methodology is theoretically justified through asymptotic results. Evidence from simulation studies and an application to annual temperature curves suggests that the test works well in finite samples.

ABSTRACT Computationally efficient frequency‐domain models can play a very important role in facilitating conceptual design optimization of floating wind turbines (FWTs). However, achieving sufficient accuracy in such models is challenging due to the nonlinear variation of the aerodynamic loads, particularly the interaction between the floating platform motions and the controller. Building on previously proposed approaches from the literature, this work implements and improves upon three methods to evaluate the influence of rotor dynamics on FWTs dynamics in the frequency domain. The investigated methods rely on coupled fixed‐nacelle simulations in turbulent wind, decay tests in steady wind, and linearized analytical expressions of the steady‐state aerodynamic loads. The main objective is to assess the suitability of these methods for future optimization of the floating platform and the mooring system. The various techniques are compared through a case study of three semi‐submersible FWTs with increasing rotor size. While all approaches have good accuracy below rated wind speed, only the decay test approach provides good estimates of the wind‐induced global responses across all tested conditions.

The study of wave-structure interactions involving nonlinear forces would often make use of the popular hybrid frequency–time domain method. In the hybrid method, the frequency-domain analysis could firstly provide the reliable and accurate dynamic parameters and responses; then these parameters and responses are transformed to the parameters to establishing the basic time-domain equation. Additionally, with the addition of the required linear and nonlinear forces, the time-domain analysis can be used to solve for the practical problems. However, the transformation from the frequency domain to the time domain is not straightforward, and the implementation of the time-domain equation could become increasingly complicated when different modes of motion are coupled. This research presents a systematic introduction on how to implement the time-domain analysis for floating structures, including the parameter transformations from the frequency domain to the time domain, and the methods for calculating and approximating the impulse functions and the fluid-memory effects, with special attention being paid to the coupling terms among the different motion modes, and the correctness of the time-domain-equation implementation. The main purpose of this article is to provide relevant information for those who wish to build their own time-domain analyses with the open-source hydrodynamic analysis packages, although commercial packages are available for time-domain analyses.

The Bitcoin has emerged as a fascinating phenomenon in the Financial markets. Without any central authority issuing the currency, the Bitcoin has been associated with controversy ever since its popularity, accompanied by increased public interest, reached high levels. Here, we contribute to the discussion by examining the potential drivers of Bitcoin prices, ranging from fundamental sources to speculative and technical ones, and we further study the potential influence of the Chinese market. The evolution of relationships is examined in both time and frequency domains utilizing the continuous wavelets framework, so that we not only comment on the development of the interconnections in time but also distinguish between short-term and long-term connections. We find that the Bitcoin forms a unique asset possessing properties of both a standard financial asset and a speculative one.

Imaging Cherenkov emission during radiotherapy permits real-time visualization of external beam delivery on superficial tissue. This signal is linear with absorbed dose in homogeneous media, indicating potential for quantitative dosimetry. In humans, the inherent heterogeneity of tissue optical properties (primarily from blood and skin pigment) distorts the linearity between detected Cherenkov signal and absorbed dose. We examine the potential to correct for superficial vasculature using spatial frequency domain imaging (SFDI) to map tissue optical properties for large fields of view. In phantoms, applying intensity corrections to simulate blood vessels improves Cherenkov image (CI) negative contrast by 24% for a vessel 1.9-mm-in diameter. In human trials, SFDI and CI are acquired for women undergoing whole breast radiotherapy. Applied corrections reduce heterogeneity due to vasculature within the sampling limits of the SFDI from a 22% difference as compared to the treatment plan, down to 6% in one region and from 14% down to 4% in another region. The optimal use for this combined imaging system approach is to correct for small heterogeneities such as superficial blood vessels or for interpatient variations in blood/melanin content such that the corrected CI more closely represents the surface dose delivered.