Reconstruction of surfaces from phase-shifting speckle interferometry: Bayesian approach

A method is proposed for checking the reliability of a quantitative estimate of longitudinal displacements in metallic beam samples when they are investigated by electronic speckle interferometry and phase-shifting speckle interferometry. Theoretical and experimental results are presented for the investigation of longitudinal surface displacements of samples by electronic difference speckle interferometry and phase-shifting speckle interferometry. © 2004 Optical Society of America

Optimization of wavefield intensities in phase-shifting speckle interferometry

A theoretical and numerical investigation of the systematic phase errors in phase-shifting speckle interferometry is presented. The theoretical investigation analyzes the behavior of some systematic error induced by intensity variations in two cases of data-computing techniques. The first case deals with the technique in which the phase change is computed, unwrapped, and then linearly filtered; the second case deals with the technique in which the data are linearly filtered before the arctangent calculation and then unwrapped. With the first filtering technique it is shown that it is preferable when the phase change is of relatively low spatial frequency, leading to a particularly accurate method. With the second case it is demonstrated that an important parameter of speckle interferometry is the modulation factor of the interference frame that induces phase errors when the data are filtered before the arctangent calculation. We show that this technique is better than the first when the phase change is composed of high-spatial-frequency variations. The theoretical investigation of the two techniques is compared with numerical simulations, considering the frequency characteristics of the phase change, and this shows a good match between theory and simulations.

The interference between a uniform reference wave and a speckle object wave results in variable fringe contrast and background level. Taking these variations into account, we optimize system parameters of phase-shifting speckle interferometry. The results show that the optimal reference intensity should always be equal to one fourth of the detector’s saturation level. The optimal reference to the object-intensity ratio shows an increase from one up to, in most practical cases, six as a chosen interference dynamic range increases from its minimum value. The dependence of a maximal fraction of acceptable measurements on the dynamic range is calculated. Numerical examples indicate that we may hope for a readout accuracy in the range of 1/50th to 1/100th of a fringe period and still cover more than half of the image area with acceptable data. These data are taken without spatial averaging and have maximum resolution.

Phase-field modeling of fracture has gained popularity within the last decade due to the flexibility of the related computational framework in simulating three-dimensional arbitrarily complicated fracture processes. However, the numerical predictions are greatly affected by the presence of uncertainties in the mechanical properties of the material originating from unresolved heterogeneities and the use of noisy experimental data. The objective of this work is to apply the Bayesian approach to estimate bulk and shear moduli, tensile strength and fracture toughness of the phase-field model, thus improving accuracy of the simulations with the help of experimental data. Conventional approaches for estimating the Bayesian posterior probability density function adopt sampling schemes, which often require a large amount of model estimations to achieve the desired convergence, thus resulting in a high computational cost. In order to alleviate this problem, we employ a more efficient approach called sampling-free linear Bayesian update, which relies on the evaluation of the conditional expectation of parameters given experimental data. We identify the mechanical properties of cement mortar by conditioning on the experimental data of the three-point bending test (observations) in an online and offline manner. In the online approach the parameter values are sequentially updated on the fly as the new experimental information comes in. In contrast, the offline approach is used only when the whole history of experimental data is provided once the experiment is performed. Both versions of estimation are discussed and compared by validating the phase-field fracture model on an unused set of experimental data.

The mean, the variance, and the correlation function of the intensity pattern resulting from an incoherent source that has propagated through a complex ABCD optical system are derived. The number of speckle correlation cells (or modes, N) within an effective measurement area is presented and discussed. Optical field decorrelation effects with respect to secondary fringe formation in phase-shifting speckle interferometry are discussed. In particular, the correlation coefficient resulting from load-induced object tilt, in-plane translations, and displacements parallel to the optic axis as a function of the number of modes propagating through the optical system is derived and discussed. In contrast to previous research, in which the calculation of speckle interferometric decorrelation effects was restricted to direct imaging systems and the special case where N → ∞, the correlation coefficients that we derive are valid for arbitrary complex ABCD systems (i.e., nonimaging configurations) and for all finite values of N ≥ 1.

The present paper describes a fitting procedure capable of providing a smooth approximation of experimental data distributed on a bidimensional domain, e.g. the typical output of an interferometric technique. The procedure is based on the optimization of an analytical model defined on the whole domain by the B-spline formulation. In the paper rectangular, circular and polygonal convex domains are considered in details, but, according to the need of the operating conditions, the procedure can be extended to domains of different shapes. The proposed procedure was initially calibrated by an analytical case study: a thin square plate simply supported along the edges and loaded by a uniform pressure. Subsequently, by the operative parameters defined by the analyses carried out on the analytic data, the fitting procedure was applied on experimental data obtained by phase shifting speckle interferometry.

We investigated the estimation of the ensemble channelized Hotelling observer (CHO) signal-to-noise ratio (SNR) for ordered-subset (OS) image reconstruction using noisy projection data. Previously, we computed the ensemble CHO SNR using a method for approximating the channelized covariance of OS reconstruction, which requires knowledge of the noise-free projection data. Here, we use a “plug-in” approach, in which noisy data is used in place of the noise-free data in the aforementioned channelized covariance approximation. Additionally, we evaluated the use of smoothing of the noisy projections before use in the covariance approximation. Additionally, we evaluated the use of smoothing of the noisy projections before use in the covariance calculation. The task was detection of a 10% contrast Gaussian signal within a slice of the MCAT phantom. Simulated projections of the MCAT phantom were scaled and Poisson noise was added to create 100 noisy signal-absent data sets. Simulated projections of the scaled signal were then added to the noisy background projections to create 100 noisy signal-present data set. These noisy data sets were then used to generate 100 estimates of the ensemble CHO SNR for reconstructions at various iterates. For comparison purposes, the same calculation was repeated with the noise-free data. The results, reported as plots of the average CHO SNR generated in this fashion, along with 95% confidence intervals, demonstrate that this approach works very well, and would allow optimization of imaging systems and reconstruction methods using a more accurate object model (i.e., real patient data).

We present a novel, physically-motivated method for surface reconstruction that can recover smooth surfaces from noisy and sparse data sets, without using orientation information. A new volumetric technique based on regularized-membrane potentials for aggregating the input sample points is introduced, which manages improved noise tolerability and outlier removal, without sacrificing much with respect to detail (feature) recovery. In this method, sample points are first aggregated on a volumetric grid. A labeling algorithm that relies on intrinsic properties of the smooth scalar field emerging after aggregation is used to classify grid points as exterior or interior to the surface. We also introduce a mesh-smoothing paradigm based on a mass-spring system, enhanced with a bending-energy minimizing term to ensure that the final triangulated surface is smoother than piecewise linear. The method compares favorably with respect to previous approaches in terms of speed and flexibility.

Methods of 3D reconstruction of medical images mainly included surface and volume reconstruction at present. In the experiment of 3D ultrasound reconstruction for spine of people, the result using volume reconstruction was unsatisfactory because of the ultrasound images' characteristic. So, we brought forward a method which was based on contour line to reconstruct 3D surface of spine. In this paper, we collected spinal ultrasound images using 3D freehand ultrasound firstly; next, tracing spinal contour line of each ultrasound images manually; finally, we used these contour lines to reconstruct spinal surface. The result showed that spinal surface reconstruction based on 2D contour line was close to real spinal surface, it could give physicians a better help in diagnosis of the spine.

The atmosphere of the earth restricts the resolution of conventional astrophotography to about 1". We will discuss various high-resolution speckle methods which can overcome image degradation caused by the atmosphere and telescope aberrations. All methods yield diffraction-limited resolution, for example 0.03" for a 3.6m telescope. We will show various astronomical applications of speckle interferometry, observations of asteroids, Pluto/Charon, double stars and the gravitational-lens triple quasar. Speckle interferometry can yield a true diffraction-limited image if there is a point source (reference star) in the isoplanatic neighbourhood of the object (holographic speckle interferometry). We show an application of holographic speckle interferometry to the central object R136a of the 30 Doradus nebula in the Large Magellanic Cloud. A true diffraction-limited image of R136a has been reconstructed. The image shows that R136a consists of 8 stars. Speckle masking is a triple correlation method which yields diffraction-limited images of general astronomical objects. A point source near the object is not required. We will describe an application of speckle masking to the central object in the giant H II region NGC 3603. The reconstructed image shows that this central object is a star cluster of 4 stars with magnitudes 11m, 12m, 13m and 13m. The signal-to-noise ratio of the speckle masking image is about the same as the signal-to-noise ratio of the speckle interferometry autocorrelation. Speckle spectroscopy is a speckle method which yields diffraction-limited objective prism spectra. It is also possible to apply speckle masking to multiple-mirror interferometers or long-baseline interferometers on the ground or in space. True images of very high angular resolution can be obtained by these techniques. We will show computer simulations which illustrate the dependence of the signal-to-noise ratio on photon noise.

A Bayesian iterative method can be the basis for a wide range of technologies in the field of pattern recognition and image reconstruction. It involves finding the most probable solutions for images or patterns, if functionals describing the likelihood function and a priori information, respectively, are already known. The article describes the basic principles and recent advances in the development of BIM and its applications in various fields, mainly in tomography and restoration of functions from incomplete and noisy data.

Ultrafast X-ray tomographic imaging of multiphase flow in bubble columns - Part 1: Image processing and reconstruction comparison

Statistical and probability inferences are basically dependent on two major methods of reasoning, conventional (frequentist) and Bayesian probability. Frequentists’ methods are mainly based on numerous events, where Bayesian probability applies prior knowledge and subjective belief. Frequentist models of probability do not permit the introduction of prior knowledge into the calculations. This is traditionally to maintain the rigour of a scientific method and as way to prevent the introduction of extraneous data that might skew the experimental results. However, there are times when the use of prior knowledge would be a useful contribution to evaluation a situation. The Bayesian approach was proposed to help us reason in situation where prior knowledge is need, and especially under highly uncertain circumstances. This Chapter provides an overview of the main principles underlying the Bayesian method and Bayesian belief networks. The ultimate goal is to provide the reader with the basic knowledge necessary for understanding the Bayesian Belief Network approach to building computational model. The Chapter does not go into more technical details of probability theory and Bayesian statistics. But to make it more accessible to a wide range of readers, some technical details are simplified.

For more than three decades, Deborah Mayo has defended severe testing, a framework for evaluating the strength of scientific evidence that provides philosophical foundations for (variants of) classical statistical methods. In her newest book, Statistical Inference as Severe Testing, Mayo (1) extends and refines her views on severe testing, (2) takes aim at researchers who claim that the reproducibility crisis is a result of the use of classical statistics, and (3) exposes some contemporary Bayesian methods as lacking philosophical foundations. The book is engaging, sometimes funny, and often insightful. After reviewing the basics of severe testing, I summarize three lessons from Mayo's book that are valuable for philosophers and scientists alike. I then discuss one way in which I think Mayo's arguments could be tightened.Mayo argues that one has evidence for a hypothesis to the extent the hypothesis has passed a severe test. More precisely, she argues that “for data to warrant a hypothesis H requires not just that (S-1) H agrees with the data (H passes the test), but also (S-2) with high probability, H would not have passed the test so well, were H false” (92). Mayo's two criteria are inspired by the Neyman-Pearsonian maxim that good statistical tests minimize Type 1 and Type 2 errors, but they are novel in at least two ways. First, Mayo's criteria are applicable outside of statistical contexts. For example, let H be the hypothesis that the Cleveland Browns played an excellent team last weekend, and suppose our data is that the Cleveland Browns lost their game. If the Cleveland Browns lose to all opponents regardless of ability, then our data fails to satisfy S-2 and so does not severely test H. Since S-1 and S-2 are applicable in both statistical and nonquantitative contexts, Mayo's criteria unify the logic of statistical testing with qualitative logics of evidence.Second, severity is a function of data, unlike size and power, the two core quantities of orthodox Neyman-Pearsonian methodology. For this reason, Mayo's two criteria closely resemble Nozick's adherence and sensitivity conditions when those conditions are relativized to “methods” (Nozick 1981).1Mayo draws several important lessons from this seemingly simple, two-pronged framework. Here, I discuss three that recur throughout the newest book. First, Mayo carefully distinguishes between statistical hypotheses (e.g., about the frequency of a trait in a population) and “substantive” scientific hypotheses about, for example, causation or the existence of a theoretical entity (84, 93). Conflating the two can lead one to mistakenly infer that a substantive scientific hypothesis has been severely tested, when in fact the evidence against the hypothesis is stronger than that for it.As a vivid example, Mayo discusses a series of psychological experiments used to defend the hypothesis H that heterosexual “men's implicit self-esteem is lower when a [female] partner succeeds than when a [female] partner fails” (101). Mayo carefully distinguishes four statistical hypotheses that are plausibly consequences of ¬ H and then argues that the data were sufficient to reject only one of the four; call it ¬ H 1. Mayo concludes that the experimental data failed to fit H, as researchers could not reject three statistical hypotheses that were compatible with ¬ H. Further, Mayo argues that the statistical evidence against ¬ H 1 (i.e., the purported evidence for ¬¬ H = H ) was perfectly compatible with the falsity of the substantive hypothesis H. So the data also failed to satisfy S-2.Second, Mayo argues that, whereas the severe tester has a unified account of testing both statistical hypotheses and modeling assumptions, likelihoodists and Bayesians lack a cogent story about when to reject a bad statistical model (298–320). Some likelihoodists, for example, argue that measures of evidential strength must be comparative and that the likelihood ratio P (E|H 0)/P (E|H 1) quantifies the degree to which evidence E fits a hypothesis H 0 better than H 1 (Edwards 1984; Royall 1997). It is easy to construct cases in which such a likelihood ratio is enormous, because the data fit H 0 much better than H 1, and yet the data fit neither statistical hypothesis well. If H 0 and H 1 are the only statistical hypotheses under investigation, one might erroneously conclude that one has good evidence for H 0. The right conclusion, according to the severe tester, is to recognize that the two hypotheses do not exhaust logical space and to reject that underlying modeling assumption instead.Naive Bayesian reasoning falls victim to the same criticism. According to some Bayesians, experimenters ought to assign prior probabilities to a fixed set of hypotheses H and then update their degrees of belief by conditionalization. Again, suppose the data fit all hypotheses in H poorly but fit one H ∈ H much better than its rivals. Then a naive Bayesian's posterior degree of belief in H might be nearly one. Again, the right conclusion, according to the severe tester, is to consider more hypotheses. But orthodox Bayesianism is silent about when to do that.Finally, Mayo argues that several novel Bayesian approaches to statistical inference lack foundations (400–415). These parts of the book will be of special interest to philosophers who are unfamiliar with the substantial differences between Bayesianism in theory and in practice. According to textbook philosophical presentations, prior and posterior probabilities represent an experimenter's beliefs. However, some contemporary Bayesians have given up on the myth that the infinitely precise densities that appear in journal articles are appropriate idealizations of any person's beliefs. Those Bayesians, however, disagree about what justifies the choice of prior (e.g., transparent communication vs. frequentist coverage properties) and the use of further Bayesian mathematical machinery.Mayo levels several different criticisms against these contemporary Bayesian approaches, but I think all share the same underlying philosophical problem. Rationality, so says standard decision theory, requires one to maximize expected utility relative to one own's degrees of belief. So some contemporary “Bayesian” methods require a new theory of rationality to justify the behavior of an experimenter whose decisions employ posterior probabilities that do not even approximately represent her (or perhaps anyone's) beliefs.There are other important lessons scattered through Mayo's engaging and fairly accessible book. That leads me to my main criticism: accessibility sometimes comes at the cost of precision. I focus on one example that is directly relevant to Mayo's analysis of the causes of the replicability crisis, a central topic of the book.Mayo repeatedly suggests that a hypothesis is not severely tested if it is the result of “data-dredging.” Data-dredging is one of several pejorative terms (including p-hacking) that some statistical reformers use, and it refers to a loosely defined set of purportedly objectionable practices for finding associations in data. Often, “data-dredging” describes the practice of subjecting a single data set to many (sometimes hundreds or thousands of) statistical tests in an attempt to find a statistically significant result that is publishable.Critics of data-dredging allege that, because there is always a chance of finding a spurious association between two variables, one should be wary of “dredged” hypotheses. For severe testers, that default skepticism is justifiable: if an experiment is not designed to test a hypothesis, it is unlikely to be a severe test by chance. However, intuitions about data-dredging depend upon how the practice is described. Searching through data for patterns sounds exactly like what scientists should do!Mayo illustrates the dangers of data-dredging via several thought experiments. For example, she imagines a pharmaceutical company that hires scientists to find the benefits of a recently developed drug (267–68). When the hired researchers find no evidence that the drug is salutary in any of ways the manufacturer had hoped, they mine their data to find some salutary effect. Sure enough, they find the drug has an “impressive benefit on factor B” and begin marketing the drug with that promise. Mayo concludes that the hired scientists fail to subject the hypothesis to a severe test because they would have found an effect no matter what.Unfortunately, Mayo never explicitly applies her two criteria for severity to this example. Which hypothesis exactly is being tested? Here are two candidates. Let H 1 be the hypothesis “The drug has some salutary effect” and let H 2 be the hypothesis “The drug has the specific salutary effect found on B.” Even if the drug manufacturer is guaranteed to find some effect (i.e., H 1 is not severely tested), it does not follow that the manufacturer lacks evidence that the drug has the specific effect found by mining the data (i.e., it does not follow that H 2 is not severely tested). When I grade student logic exams, I am guaranteed to find that some student scored highest, but I do not thereby lack evidence that Roshan scored best when I tally her score and see it is highest. Similarly, cigarette manufacturers cannot avoid liability for causing lung cancer by (1) collecting enormous amounts of data, (2) investigating the relationship between cigarette smoking and hundreds of health problems, and then (3) claiming they were destined to find some statistically significant effect or another.2Some accusations of data-dredging, I claim, are instances of a fallacy that Mayo typically distinguishes for her readers with great care: the conflation of the pre-experimental reliability of a test with the postexperimental evidence provided by a particular data set.3 The history of science is replete with examples of unlikely, happy discoveries, where the data unequivocally support a hypothesis that scientists did not intend to test. In accessible, vivid prose, Mayo illustrates why one should typically be wary of data-dredging, but readers will be disappointed if they wish to learn how Mayo's two criteria can be used to distinguish between (a) hypotheses that are illicitly “dredged” and (b) hypotheses that are supported by one's data, despite being formulated postexperiment.Quibbles aside, Mayo's newest book is a yet another deep and engaging contribution to the philosophy of statistics and philosophy of science. Most importantly, it shows how foundational philosophical debates matter to pressing issues in science policy.