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This study presents a comprehensive optical analysis of titanium-doped sapphire (Ti:Sa) crystals, introducing two innovative measurement techniques to enhance the characterization of this material. The first method enables highly precise transmission measurements, facilitating the visualization of optical doping patterns across samples and providing accurate Figure of Merit (FoM) evaluations. This technique covers an area of 25 x 100 mm, allowing for the creation of detailed optical property maps. The second method is specifically designed to identify stress and refractive index inhomogeneities using circular polarization, leveraging the birefringent properties of Ti:Sa material. Experimental validation was performed on three Ti:Sa samples with distinct defects, analyzing and comparing their optical and structural properties. A novel central optical pattern, previously unreported, was observed in all samples. This pattern is hypothesized to originate from core formation during crystal growth. These findings provide new insights into the material's internal structure and hold significant implications for its optimization in optical applications.

Optical coating, an integral part of many optical systems, is prone to damage from environmental exposure and laser irradiation. This underscores the need for reliable and sensitive coating diagnostics. We introduce second harmonic generation (SHG) as a method for the sensitive detection of defects and inhomogeneities within optical thin films. We demonstrate the use of SHG on Si3N4 layers tested for their laser-induced damage threshold. The SHG mapping was compared with commonly used diagnostic techniques, including Nomarski microscopy, white light interferometry, and electron microscopy. Owing to its sensitivity to variations in local symmetry, SHG is able to discern minute alterations in material composition, mechanical stress, and interface structures. Therefore, SHG identified modifications in the tested layers, highly extending the damage recognized by standard methods. Furthermore, we demonstrate SHG's ability to enhance specific features by modulation of incidence angles and polarization modes. Based on these findings, we propose SHG as an ideal diagnostic tool for the early identification of laser-induced modifications in centrosymmetric thin films.

Durotaxis motion is a spectacular phenomenon manifesting itself by the autonomous motion of a nano-object between parts of a substrate with different stiffness. This motion usually takes place along a stiffness gradient from softer to stiffer parts of the substrate. Here, we propose a new design of a polymer brush substrate that demonstrates antidurotaxis droplet motion, that is, droplet motion from stiffer to softer parts of the substrate. By carrying out extensive molecular dynamics simulation of a coarse-grained model, we find that antidurotaxis is solely controlled by the gradient in the grafting density of the brush and is favorable for fluids with a strong attraction to the substrate (low surface energy). The driving force of the antidurotaxial motion is the minimization of the droplet-substrate interfacial energy, which is attributed to the penetration of the droplet into the brush. Thus, we anticipate that the proposed substrate design offers a new understanding and possibilities in the area of autonomous motion of droplets for applications in microfluidics, energy conservation, and biology., Comment: 12 pages, 9 figures

The preferential siting of the locations of monitors of hazardous environmental fields can lead to the serious underestimation of the impacts of those fields. In particular, human health effects can be severely underestimated when standard statistical are applied without appropriate adjustment. This report describes an extensive analysis of the siting of monitors for a network that measures air pollution PM10 in California's South Coast Air Basin SOCAB. That analysis uses EPA data collected during the 1986 to 2019 period. Background descriptions, including those published by the US EPA are provided. The analysis uses a very general and fast Monte Carlo test for preferential sampling developed by Dr Joe Watson, which confirms that the sites were preferentially sited, as would be expected, given the intended purpose of the network to detect noncompliance with air quality standards. Our findings demonstrate both the value of that algorithm for application where where such background knowledge is not available, and hence to situations in which standard statistical tools require modification., Comment: 65 pages and 26 figures

This work is motivated by the ECMWF CAMS reanalysis data, a valuable resource for researchers in environmental-related areas, as they contain the most updated atmospheric composition information on a global scale. Unlike observational data obtained from monitoring equipment, such reanalysis data are produced by computers via a 4D-Var data assimilation mechanism, thus their stochastic property remains largely unclear. Such lack of knowledge in turn limits their utility scope and hinders them from wider and more flexible statistical usages, especially spatio-temporal modelling except for uncertainty quantification and data fusion. Therefore, this paper studies the stochastic property of these reanalysis outputs data. We used measure theory and proved the tangible existence of spatial and temporal stochasticity associated with these reanalysis data and revealed that they are essentially realisations from digitised versions of real-world hidden spatial and/or temporal stochastic processes. This means we can treat the reanalysis outputs data the same as observational data in practice and thus ensures more flexible spatio-temporal stochastic methodologies apply to them. We also objectively analysed different types of errors in the reanalysis data and deciphered their mutual dependence/independence, which together give clear and definite guidance on the modelling of error terms. The results of this study also serve as a solid stepping stone for spatio-temporal modellers and environmental AI researchers to embark on their research directly with these reanalysis outputs data using stochastic models.

Using extensive molecular dynamics simulation of a coarse-grained model, we demonstrate the possibility of sustained unidirectional motion (durotaxis) of droplets without external energy supply when placed on a polymer brush substrate with stiffness gradient in a certain direction. The governing key parameters for the specific substrate design studied, which determine the durotaxis efficiency, are found to be the grafting density of the brush and the droplet adhesion to the brush surface, whereas the strength of the stiffness gradient, the viscosity of the droplet, or the length of the polymer chains of the brush have only a minor effect on the process. It is shown that this durotaxial motion is driven by the steady increase of the interfacial energy between droplet and brush as the droplet moves from softer to stiffer parts of the substrate whereby the mean driving force gradually declines with decreasing roughness of the brush surface. We anticipate that our findings indicate further possibilities in the area of nanoscale motion without external energy supply.

The figure of merit (FoM) of Ti:Sapphire (Ti:Sa) crystals is a generally used means to evaluate the quality of the crystals. Despite the importance of Ti:Sa, the question of FoM measurement precision stayed out of focus, while the commercially available spectrometers provide unsatisfactory 3-sigma precision reaching 60 %. In this paper, we present a setup for a single-pass high-precision transmission measurement for three different wavelengths (532 nm, 780 nm, and 1560 nm) based on Nd:YAG and Er:YAG lasers. A synchronous detection via a double integrated sphere enabled us to achieve the transmission uncertainty of 0,01-0,03%. With the presented setup, we show that it is possible to determine the FoM values with 3-sigma precision of 7,5 %. Owing to the high FoM precision, we were able to trace spatial inhomogeneities of an unannealed Ti:Sa crystal produced by a commercial manufacturer Crytur. Our measurements demonstrate that the FoM values can be significantly affected by the crystal inhomogeneities and angular mismatch between the c-axis of the Ti:Sa and polarization orientation.

Strong second harmonic generation (SHG) in silicon nitride has been extensively studied-among others, in terms of laser-induced SHG enhancement in Si3N4 waveguides. This enhancement has been ascribed to the all-optical poling induced by the coherent photogalvanic effect. Yet, an analogous process for Si3N4 thin films has not been reported. Our article reports on the observation of laser-induced 3-fold SHG enhancement in Si3N4 thin films. The observed enhancement has many features similar to all-optical poling, such as highly nonlinear power dependence, cumulative effect, or connection to the Si3N4-Si interface. However, identical experiments for low-oxygen silicon oxynitride thin films lead to complex behavior, including laser-induced SHG reduction. By a thorough experimental study, the observed results were ascribed to heat-induced SHG variation caused by multiphoton absorption. Such behavior indicates that the origin of optically-induced SHG enhancement in SiOxNy-Si structures can be a complex interplay of various phenomena., Comment: 13 pages, 3 figures

RAndom Temporal Signals (RATS) method has proven to be a useful and versatile method for measuring photoluminescence (PL) dynamics and fluorescence lifetime imaging (FLIM). Here, we present two fundamental development steps in the method. First, we demonstrate that by using random digital laser modulation in RATS, it is possible to implement the measurement of PL dynamics with temporal resolution in units of nanoseconds. Secondly, we propose an alternative approach to evaluating the FLIM measurements based on a single-pixel camera experiment. In contrast to the standard evaluation, which requires a lengthy iterative reconstruction of PL maps for each timepoint, here we use a limited set of predetermined PL lifetimes and calculate the amplitude maps corresponding to each lifetime. The alternative approach significantly saves post-processing time and, in addition, in a system with noise present, it shows better stability in terms of the accuracy of the FLIM spectrogram. Besides simulations that confirmed the functionality of the extension, we implemented the new advancements into a microscope optical setup for mapping PL dynamics on the micrometer scale. The presented principles were also verified experimentally by mapping a LuAG:Ce crystal surface.

Coded aperture snapshot spectral imaging (CASSI) makes it possible to recover 3D hyperspectral data from a single 2D image. However, the reconstruction problem is severely underdetermined and efforts to improve the compression ratio typically make the imaging system more complex and cause a significant loss of incoming light intensity. In this paper, we propose a novel approach to CASSI which enables capturing both spectrally sheared and integrated image of a scene with a single camera. We performed hyperspectral imaging of three different testing scenes in the spectral range of 500-900 nm. We demonstrate the prominent effect of using the non-diffracted image on the reconstruction of data from our camera. The use of the spectrally integrated image improves the reconstruction quality and we observed an approx. fivefold reduction in reconstruction time.

We propose a novel concept of differential coded aperture snapshot spectral imaging (D-CASSI) technique exploiting the benefits of using {-1,+1} random mask, which is demonstrated by a broadband single-snapshot hyperspectral camera using compressed sensing. To double the information, we encode the image by two complementary random masks, which proved to be superior to two independent patterns. We utilize dispersed and non-dispersed encoded images captured in parallel onto a single detector. We explored several different approaches to processing the measured data, which demonstrates significant improvement in retrieving complex hyperspectral scenes. The experiments were completed by simulations in order to quantify the reconstruction fidelity. The concept of differential CASSI could be easily implemented also by multi-snapshot CASSI without any need for optical system modification.

Advances in ultrafast spectroscopy can provide access to dynamics involving nontrivial quantum correlations and their evolutions. In coherent 2D spectroscopy, the oscillatory time dependence of a signal is a signature of such quantum dynamics. Here we study such beating signals in electronic coherent 2D spectroscopy of CdSe quantum dots (CdSe QDs) at 77 K. The beating signals are analyzed in terms of their positive and negative Fourier components. We conclude that the beatings originate from coherent LO-phonons of CdSe QDs. No evidence for the quantum dot size dependence of the LO-phonon frequency was identified., Comment: 18 pages

When assessing the strength of sawn lumber for use in engineering applications, the sizes and locations of knots are an important consideration. Knots are the most common visual characteristics of lumber, that result from the growth of tree branches. Large individual knots, as well as clusters of distinct knots, are known to have strength-reducing effects. However, industry grading rules that govern knots are informed by subjective judgment to some extent, particularly the spatial interaction of knots and their relationship with lumber strength. This case study reports the results of an experiment that investigated and modelled the strength-reducing effects of knots on a sample of Douglas Fir lumber. Experimental data were obtained by taking scans of lumber surfaces and applying tensile strength testing. The modelling approach presented incorporates all relevant knot information in a Bayesian framework, thereby contributing a more refined way of managing the quality of manufactured lumber., Comment: 20 pages, 4 figures

This paper presents a continuous optimization approach to DCOC and its application to spacecraft high-precision attitude control. The approach computes a control input sequence that maximizes the time-before-exit by solving a nonlinear programming problem with an exponentially weighted cost function and purely continuous variables. Based on results from sensitivity analysis and exact penalty method, we prove the optimality guarantee of our approach. The practical application of our approach is demonstrated through a spacecraft high-precision attitude control example. A nominal case with three functional reaction wheels (RWs) and an underactuated case with only two functional RWs were considered. Simulation results illustrate the effectiveness of our approach as a contingency method for extending spacecraft's effective mission time in the case of RW failures., Comment: Submitted to the AIAA Journal of Guidance, Control, and Dynamics as an Engineering Note

Using a random temporal signal for sample excitation (RATS method) is a new, efficient approach to measuring photoluminescence (PL) dynamics. The method can be used in single-point measurement (0D), but also it can be converted to PL decay imaging (2D) using a single-pixel camera configuration. In both cases, the reconstruction of the PL decay and PL snapshot is affected by ubiquitous noise. This article provides a detailed analysis of the noise effect on the RATS method and possible strategies for its elimination. We carried out an extensive set of simulations focusing on the effect of noise introduced through the random excitation signal and the corresponding PL waveform. We show that the PL signal noise level is critical for the method. Furthermore, we analyze the role of acquisition time, where we demonstrate the need for a non-periodic excitation signal. We show that it is beneficial to increase the acquisition time while increasing the number of measurements in the single-pixel camera configuration has a minimal effect above a certain threshold. Finally, we study the effect of a regularization parameter used in the deconvolution step, and we observe that there is an optimum value set by the noise present in the PL dataset. Our results provide a guideline for optimization of the RATS measurement, but also study effects generally occurring in PL decay measurements methods relying on the deconvolution step.

Layers with gradient refractive-index profile are an attractive alternative to conventional homogeneous stack coatings. However, the optical characterization and monitoring of the graded refractive-index profile is a complex issue, which has been typically solved by using a simplified model of mixed materials. Although this approach provides a solution to the problem, the precision, which can be expected from optical characterization of the refractive index gradient, remains unclear. In this work, we study optical characterization of SiO_xN_y layers deposited via reactive dual ion beam sputtering. To characterize the deposited layers, we use several methods including reflectance, and transmittance spectra at a broad range of incident angles, together with spectral ellipsometry. All the data were simultaneously fitted with a general profile of refractive index. The expected profile used in our fit was based on characterization of SiO_xN_y layers with a varying stoichiometry. By altering of the profile, we discussed sensitivity of such alternation on fit quality and we studied ambiguity of merit-function minimization. We demonstrate that while the scanning of particular parameters of the profile can be seemingly very precise, we obtain a very good agreement between the experimental data and model for a broad range of gradient shapes, where the refractive-index value on major part of the profile can differ as much as 0.02 from the mean value.

Photoluminesce (PL) spectroscopy offers excellent methods for mapping the PL decay on the nanosecond time scale. However, capturing maps of emission dynamics on the microsecond time scale can be highly time-consuming. We present a new approach to fluorescence lifetime imaging FLIM, which combines the concept of random temporal speckles excitation (RATS) with the concept of a single-pixel camera based on spatial speckles. The spatio-temporal speckle pattern makes it possible to map PL dynamics with unmatched simplicity. Moreover, the method can acquire all data necessary to map PL decays in the microsecond timescale within minutes. We present proof of principle measurements for two samples and compare the reconstructed decays to the non-imaging measurements. Finally, we discuss the effect of the preprocessing routine and other factors on the reconstruction noise level. The presented method is suitable for lifetime imaging processes in several samples, including charge carrier dynamics in perovskites or monitoring solid-state luminophores with a long lifetime of PL.

While general object detection has seen tremendous progress, localization of elliptical objects has received little attention in the literature. Our motivating application is the detection of knots in sawn timber images, which is an important problem since the number and types of knots are visual characteristics that adversely affect the quality of sawn timber. We demonstrate how models can be tailored to the elliptical shape and thereby improve on general purpose detectors; more generally, elliptical defects are common in industrial production, such as enclosed air bubbles when casting glass or plastic. In this paper, we adapt the Faster R-CNN with its Region Proposal Network (RPN) to model elliptical objects with a Gaussian function, and extend the existing Gaussian Proposal Network (GPN) architecture by adding the region-of-interest pooling and regression branches, as well as using the Wasserstein distance as the loss function to predict the precise locations of elliptical objects. Our proposed method has promising results on the lumber knot dataset: knots are detected with an average intersection over union of 73.05%, compared to 63.63% for general purpose detectors. Specific to the lumber application, we also propose an algorithm to correct any misalignment in the raw timber images during scanning, and contribute the first open-source lumber knot dataset by labeling the elliptical knots in the preprocessed images., Comment: Accepted at WACV 2021

Consider a population consisting of clusters of sampling units, evolving temporally, spatially, or according to other dynamics. We wish to monitor the evolution of its means, medians, or other parameters. For administrative convenience and informativeness, clustered data are often collected via a rotating plan. Under rotating plans, the observations in the same clusters are correlated, and observations on the same unit collected on different occasions are also correlated. Ignoring this correlation structure may lead to invalid inference procedures. Accommodating cluster structure in parametric models is difficult or will have a high level of misspecification risk. In this paper, we explore exchangeability in clustered data collected via a rotating sampling plan to develop a permutation scheme for testing various hypotheses of interest. We also introduce a semiparametric density ratio model to facilitate the multiple population structure in rotating sampling plans. The combination ensures the validity of the inference methods while extracting maximum information from the sampling plan. A simulation study indicates that the proposed tests firmly control the type I error whether or not the data are clustered. The use of the density ratio model improves the power of the tests., Comment: 26 pages

Building on recent work in statistical science, the paper presents a theory for modelling natural phenomena that unifies physical and statistical paradigms based on the underlying principle that a model must be nondimensionalizable. After all, such phenomena cannot depend on how the experimenter chooses to assess them. Yet the model itself must be comprised of quantities that can be determined theoretically or empirically. Hence, the underlying principle requires that the model represents these natural processes correctly no matter what scales and units of measurement are selected. This goal was realized for physical modelling through the celebrated theories of Buckingham and Bridgman and for statistical modellers through the invariance principle of Hunt and Stein. Building on recent research in statistical science, the paper shows how the latter can embrace and extend the former. The invariance principle is extended to encompass the Bayesian paradigm, thereby enabling an assessment of model uncertainty. The paper covers topics not ordinarily seen in statistical science regarding dimensions, scales, and units of quantities in statistical modelling. It shows the special difficulties that can arise when models involve transcendental functions, such as the logarithm which is used e.g. in likelihood analysis and is a singularity in the family of Box-Cox family of transformations. Further, it demonstrates the importance of the scale of measurement, in particular how differently modellers must handle ratio- and interval-scales, Comment: 41 pages. No figures. A trimmed version of the manuscript has been submitted to Statistical Science

The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics is the design of the locations of the monitoring stations for those environmental processes of interest. One particular design criterion for monitoring networks that tries to reduce the uncertainty about predictions of unseen processes is called the maximum-entropy design. However, this design criterion involves a hard optimization problem that is computationally intractable for large data sets. Previous work of Wang et al. (2017) examined a probabilistic model that can be implemented efficiently to approximate the underlying optimization problem. In this paper, we attempt to establish statistically sound tools for assessing the quality of the approximations., Comment: Accepted in Spatial Statistics, Special Issues in Spatial Data Science

Digital micromirror device (DMD) serves in a significant part of computational optical setups as a means of encoding an image by the desired pattern. The most prominent is its usage in the so-called single-pixel camera experiment. This experiment often requires an efficient and homogenous collection of light from a relatively large chip on a small area of an optical fiber or spectrometer slit. Moreover, this effort is complicated by the fact that the DMD acts as a diffractive element, which causes severe spectral inhomogeneities in the light collection. We studied the effect of light diffraction via a whiskbroom hyperspectral camera in a broad spectral range. Based on the knowledge, we designed a variety of different approaches to light collection. We mapped the efficiency and spectral homogeneity of each of the configuration - namely its ability to couple the light into commercially available fiber spectrometers working in the visible and IR range (up to 2500 nm). We found the integrating spheres to provide homogeneous light collection, which, however, suffers from very low efficiency. The best compromise between the performance parameters was provided by a combination of an engineered diffuser with an off-axis parabolic mirror. We used this configuration to create a computational microscope able to carry out hyperspectral imaging of a sample in a broad spectral range (400-2500 nm). We see such a setup as an ideal tool to carry out spectrally-resolved transmission microscopy in a broad spectral range.

Time-resolved photoluminescence (PL) is commonly used to track dynamics in a broad range of materials. Thus, the search for simplification of the acquisition of PL kinetics attracts continuous attention. This paper presents a new robust and straightforward approach to the measurement of PL decay, which is based on randomly fluctuating excitation intensity. The random excitation waveform is attained by using laser speckles generated on a rotating diffuser. Owing to this, the presented technique is able to utilize any coherent excitation source without the necessity to generate short pulses or to controllably modulate the light. PL decay can be computationally reconstructed from the Fourier image of the PL trace. The paper demonstrates the performance of the method, which is able to acquire sub-microsecond dynamics as the impulse response function reaches 300 ns. The reconstructed PL decays were compared to streak camera measurements to verify the method. Finally, potential limitations and applications of the technique are discussed.

Air pollution constitutes the highest environmental risk factor in relation to heath. In order to provide the evidence required for health impact analyses, to inform policy and to develop potential mitigation strategies comprehensive information is required on the state of air pollution. Information on air pollution traditionally comes from ground monitoring (GM) networks but these may not be able to provide sufficient coverage and may need to be supplemented with information from other sources (e.g. chemical transport models; CTMs). However, these may only be available on grids and may not capture micro-scale features that may be important in assessing air quality in areas of high population. We develop a model that allows calibration between multiple data sources available at different levels of support by allowing the coefficients of calibration equations to vary over space and time, enabling downscaling where the data is sufficient to support it. The model is used to produce high-resolution (1km $\times$ 1km) estimates of NO$_2$ and PM$_{2.5}$ across Western Europe for 2010-2016. Concentrations of both pollutants are decreasing during this period, however there remain large populations exposed to levels exceeding the WHO Air Quality Guidelines and thus air pollution remains a serious threat to health.

The ability to transfer skills across tasks has the potential to scale up reinforcement learning (RL) agents to environments currently out of reach. Recently, a framework based on two ideas, successor features (SFs) and generalised policy improvement (GPI), has been introduced as a principled way of transferring skills. In this paper we extend the SFs & GPI framework in two ways. One of the basic assumptions underlying the original formulation of SFs & GPI is that rewards for all tasks of interest can be computed as linear combinations of a fixed set of features. We relax this constraint and show that the theoretical guarantees supporting the framework can be extended to any set of tasks that only differ in the reward function. Our second contribution is to show that one can use the reward functions themselves as features for future tasks, without any loss of expressiveness, thus removing the need to specify a set of features beforehand. This makes it possible to combine SFs & GPI with deep learning in a more stable way. We empirically verify this claim on a complex 3D environment where observations are images from a first-person perspective. We show that the transfer promoted by SFs & GPI leads to very good policies on unseen tasks almost instantaneously. We also describe how to learn policies specialised to the new tasks in a way that allows them to be added to the agent's set of skills, and thus be reused in the future., Comment: Published at ICML 2018

Femtosecond spectroscopy is an important tool for tracking rapid photoinduced processes in a variety of materials. To spatially map the processes in a sample would substantially expand the capabilities of the method. This is, however, difficult to achieve due to the necessity to use low-noise detection and to maintain feasible data acquisition time. Here we demonstrate realization of an imaging pump-probe setup, featuring sub-100 fs temporal resolution, by a straightforward modification of a standard pump-probe technique, using a randomly structured probe beam. The structured beam, made by a diffuser, enabled us to computationally reconstruct the maps of transient absorption dynamics based on the concept of compressed sensing. We demonstrate the functionality of the setup in two proof-of-principle experiments, were we achieve spatial resolution of 20 \mu m. The presented concept provides a feasible route to imaging, using the pump-probe technique and ultrafast spectroscopy in general., Comment: 13 pages, 6 figures