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

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

Steady‐State Absorption Rate Models for Use in Relaxation Rate Studies with Continuous LaserExcited Photothermal Lens Spectrometry

This paper examines the solutions of kinetic rate equations for prediction of the photothermal lens signals under irradiance conditions that can lead to optical saturation or bleaching. The relaxation kinetics resulting from forcing excited state populations in multiple levels by high excitation irradiance continuous lasers is examined and irradiance-dependent photothermal lens signals are predicted. The analyses described in this paper are based on simple kinetic models for optical excitation and subsequent excited state relaxation. Dark-state relaxation is assumed to be extremely fast compared to limiting kinetics resulting in simplified excited state models. Kinetic models are derived for two, four and five active level molecular systems. Gaussian laser beam profiles are assumed and time dependent photothermal lens signals are calculated. Models account for excitation laser profile, thermal relaxation of the spatially and temporally distorted heating rate distribution resulting from nonlinear absorption, and metastable state relaxation. This heating rate is used to calculate the temperature change distribution and subsequently the optical elements needed to model the experimental photothermal signals

Binary Code Decimal to Binary Program Modification of a Popular Digital Delay Module

A simple modification is described for converting the digital program code format of an Evans Associates model 4145 programmable time delay module from binary‐coded decimal to binary. The modification results in a delay module which is more easily interfaced to a computer, has a greater programmable delay range with equivalent temporal resolution, and requires less power. Similar modifications are expected to have the same results on the models 4145‐1 and 4146 modules

Optimal Estimation of Impulse‐Response Signals Through Digital Innovations and Matched FilterSmoothing

A real‐time digital filter is described which may be most useful for optimal determination of the magnitude of impulse‐response functions found in pulsed, repetitive experiments of low duty cycle. This filter is based on a matched filter but employs an interference orthogonalization step. This results in a signal magnitude estimate which is independent of coherent interference. The filter updates the signal magnitude estimate upon each repetition of the experimental cycle. Comparisons to signal estimation using gated sampling devices are given

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