Influence of Edge Effects on Laser-Induced Surface Displacement of Opaque Materials by Photothermal Interferometry

We demonstrate the influence of edge effects on the photothermal-induced phase shift measured by a homodyne quadrature laser interferometer and compare the experiments with rigorous theoretical descriptions of thermoelastic surface displacement of metals. The finite geometry of the samples is crucial in determining how the temperature is distributed across the material and how this affects the interferometer phase shift measurements. The optical path change due to the surface thermoelastic deformation and thermal lens in the surrounding air is decoded from the interferometric signal using analytical and numerical tools. The boundary/edge effects are found to be relevant to properly describe the interferometric signals. The tools developed in this study provide a framework for the study of finite size effects in heat transport in opaque materials and are applicable to describe not only the phase shift sensed by the interferometer but also to contribute to the photothermal-based technologies employing similar detection mechanisms

EMSL Pore Scale Modeling Challenge/Workshop

Report covers the background for the workshop, objectives, important research directions, necessary capabilities and overall recommendations

Progress Toward a Better Understanding of Signal Generation Processes in the Laser‐ExcitedPhotothermal Spectroscopy of Homogeneous Samples

This article examines some recent experiments and theories that have advanced our understanding of the physical effects following thermal relaxation of the excited state. Experiments which show that the temperature-dependent refractive index is composed of density and pure-thermal terms are discussed. The importance of the purely thermal term is that it allows ultra-fast pulsed excitation sources to be used in photothermal refraction spectroscopy. This opens up new areas of applications in ultra-fast measurement. The effect of and progress towards the elucidation of specific volume changes are reviewed. Finally, recent progress in understanding nonlinear optical absorption and its effect on the photothermal signal are summarized

Optimized Spectroscopic Signal Estimates Using Integration and Matched Filters

This paper examines theories of signal processing as applied to peak magnitude estimation in absorption and emission spectroscopy. Signals obtained from Fourier transform, fixed wavelength, and scanning dispersive instruments are modeled in terms of the time required to obtain a spectrum. The differences between these techniques and the signal processing procedures that should be used for each technique are characterized for a Lorentzian spectral feature. Including the time required to scan over a range of optical frequencies results in optimal signal processing procedures that are different from those previously supposed. In particular, it is found that the optimal matched filter is less efficient than repetitive measurements at a single frequency. The theory developed for the Lorentzian line model is extended to include an arbitrary shaped peak

Data Analysis in the Shot Noise Limit Part I: Single Parameter Estimation with Poisson and NormalProbability Density Functions

This paper describes some of the basic statistics required to analyze data that has random variables dlstributed according to shot, or more appropriately quantum noise statistics. This type of noise Is described by the Poisson and normal dlstrlbution with parameters related to the parent binomlal distrlbutlon. Both the Poisson and the normal dtotrlbutlon functions are analyzed In terms of the estlmation results for analysis of replicate data from a sIngle process. Analytical solutions for the parameter that best descrlbes data Obtained by replicate measurements are determined from jolnt dlstrlbutlon functions by the maximum Ilkellhood method. Parameter estimation results are different for these two dstributions. Maximum ilkelhood parameter estimation uslng the Poisson dlstrlbutlon yields results that are equivalent to the measurement mean obtalned based on a normal dlstrlbutlon with constant variance. The normal dlstributlon results in a quadratic equatbn for the single parameter that describes both the variance and the average. The maxlmun likelhood method with the joint Poisson distribution Is also used to determine the parameter that best descrlbes the mean of a random variable distributed accordlng to an Independent parameter

Expectation‐Maximization Algorithm for Regression, Deconvolution, and Smoothing of Shot‐Noise‐Limit Data

A simple algorithm for deconvolution and regression of shot-noise-limited data is illustrated in this paper. The algorithm is easily adapted to almost any model and converges to the global optimum. Multiple-component spectrum regression, spectrum deconvolution and smoothing examples are used to illustrate the algorithm. The algorithm and a method for determining uncertainties in the parameters based on the Fisher information matrix are given and illustrated with three examples. An experimental example of spectrograph grating order compensation of a diode array solar spectroradiometer is given to illustrate the use of this technique in environmental analysis. The major advantages of the EM algorithm are found to be its stability, simplicity, conservation of data magnitude and guaranteed convergence

Simple Scheme for Variable High Power Laser Beam Attenuation

A venetian style infrared attenuator placed prior to a pinhole spatial filter results in variable high‐power laser attenuation. This attenuation scheme has a wide dynamic range, results in high‐quality Gaussian beams, does not introduce beam walk‐off error, and is independent of polarization