Method of spectral subtraction of gas-phase Fourier transform infrared (FT-IR) spectra by minimizing the spectrum length

A new method of spectral subtraction for gas-phase Fourier transform infrared (FT-IR) spectra was developed for long-path gas measurements. The method is based on minimization of the length of the spectrum that results from subtracting the spectrum of an individual component of a gas mixture (water, CO(2), etc.) from the experimental spectrum of the mixture. For this purpose a subtraction coefficient (k(min)) is found for which the length of the resulting spectrum is minimized. A mathematical simulation with two Lorentzian absorption bands was conducted and the limits of application for the proposed method were determined. Two experimental examples demonstrate that a successful result could be achieved in the case when the subtrahend spectrum contains a number of narrow absorption bands (such as the spectrum of water vapor).     

Effect of signal-to-noise ratio and number of data points upon precision in measurement of peak amplitude,position and width in fourier transform spectrometry

Chen, L., Cottrell, C.E. and Marshall, A.G., 1986. Effect of signal-to-noise ratio and number of data points upon precision in measurement of peak amplitude, position and width in Fourier transform spectrometry. Chemometrics and Intelligent Laboratory Systems, 1: 51–58.The theoretical precision in determining experimental spectral peak parameters (height, width, and position) should depend in a calculable way upon the peak shape, signal-to-noise ratio, and number of data points per line width. Expressions for precision in peak position and width for absorption-mode Lorentzian and Gaussian line shapes have been derived previously. We have extended the theory to include absorption-mode sinc as well as magnitude-mode Lorentzian and sinc line shapes, and have computed the predicted precision in peak amplitude as well as in position and width. Experimental (Fourier transform ion cyclotron resonance mass spectrometry and Fourier transform nuclear magnetic resonance spectrometry) precision for each of these parameters is found to be significantly poorer (e.g., factor of 5) than the theoretical predictions. The present results provide a direct test of the nature of noise (e.g., vertical vs. horizontal) in Fourier transform spectra, and suggest that experimental measurements of Fourier transform spectral line shape parameters may be much less precise than previously suspected.     

Investigation of spermatozoa and seminal plasma by fourier transform infrared spectroscopy

Fourier transform infrared (FT-IR) spectra of human spermatozoa and seminal plasma were recorded and analyzed. The procedure that was established for sample preparation enabled acquisition of reproducible spectra. The parameter I(1087)/I(966) for controlling spectra reproducibility was defined. The assignment of bands was carried out using an empirical approach and the origin of the "sperm specific doublet", the bands at 968 cm(-1) and 981 cm(-1), was determined. The principal component regression (PCR) algorithm was used to define the specific spectral regions correlating to characteristics of spermatozoa, such as concentration, straight-line velocity (VSL), and beat cross frequency (BCF). Then, simple spectral parameters, such as band intensities and band ratios, were tested to determine which one best correlates to characteristics of spermatozoa. The region of the amide I band, between 1700 cm(-1) and 1590 cm(-1), was defined as a specific spectral region that correlates to the concentration of spermatozoa. The parameter that gave the linear dependence to the concentration of spermatozoa was the intensity of the amide I band. For VSL, the bands between 1119 cm(-1) and 943 cm(-1) were defined as the specific spectral region. The relative amount of nucleic acids with respect to proteins showed linear dependence on the straight-line velocity of spermatozoa. BCF showed the best correlation to the bands between 3678 cm(-1) and 2749 cm(-1), which largely represent lipids and proteins. These results suggest that FT-IR spectroscopy can serve as an adjunct to conventional histopathology studies.     

Analysis of overlapping bands by an analytic geometric approach: the potential of band-stripping and the complementary matching method in extraction of band components from overlapping bands

As a novel method for extracting individual band components from heavily overlapping bands, we propose a band stripping/complementary matching method that is based on first-derivative-second-derivative (D1-D2) plots of an experimental spectrum, coupled with a new concept called a complementary band. By using the concept of complement of a set, the ith band can be indirectly expressed by using a complementary band created by subtracting all the bands, exclusive of the ith estimated band, from an experimental spectrum. The degree of coincidence of both shapes between an estimated band and its complementary band provides a very suitable measure for the quality of fit for each individual band. The analysis method consists of two stages. The first stage is concerned with the geometric approach, which estimates a set of values for the parameters of a component band in the overlapping bands, and repeats band decomposition of the remaining bands in the same manner after removing the estimated band from the overlapping bands. The second stage is to minimize the difference between the profiles of the estimated band and its complementary band by a least-squares optimization and then determine the optimum values of the band parameters with the best-fit band shape. The algorithm and procedures of this method are illustrated by use of a synthetic spectrum consisting of a number of component bands, a background component, and random noise. The quality of fit is so satisfactory in terms of the coincidence between the individual estimated band and the corresponding complementary one that visual observation permits us to determine the optimum estimates of the band parameters and avoid potential problems of curve fitting.     

Multiscale complex moments of the local power spectrum

Complex moments of the local power spectrum (CMP) are investigated in a multiscale context. The multiscale CMPs are shown to approximate well the 1D angular Fourier transform of the band in question. This observation is used to derive further properties of the power spectrum in terms of texture orientations or n-folded symmetry patterns. A method is presented to approximate the power spectrum using only separable filtering in the spatial domain. Interesting implications to the Gabor decomposition are shown. The number of orientations in the filter bank is related to the order of n-folded symmetry detectable. Furthermore, the multiscale CMPs can be estimated incrementally in the spatial domain, which is both fast and reliable. Experiments on power spectrum estimation, orientation estimation, and texture segmentation are presented.     

Orientation-insensitive spectra for Raman microspectroscopy

Separating effects due to molecular conformation from those due to orientation in the spectra of oriented samples obtained by Raman microspectroscopy is a complex issue. To solve this problem, we propose a procedure to calculate an orientation-insensitive spectrum (so-called isotropic spectrum) from polarized spectra obtained by Raman microspectroscopy that is valid for systems that exhibit a uniaxial symmetry. The method has first been tested on highly oriented samples of high-density polyethylene (HDPE). Polarized and isotropic spectra of a highly oriented HDPE cylindrical rod and an isotropic HDPE sample have been compared. The differences in the relative intensities, which occur in the polarized spectra and are due to orientation of the polyethylene chains, are nearly cancelled in the isotropic spectra, showing that the orientation-insensitive spectrum adequately represents the molecular conformation without contributions of orientation. Second, spectra of silk fibroins have been compared in the amide I region for Bombyx mori cocoon silk fibers and methanol-treated regenerated fibroin films. The similarity of the shape of the amide I band of the isotropic spectra indicates that the secondary structure of the fibroins is very close in both samples. These experimental results support the conclusion that the molecular conformation can be efficiently characterized from the intensity and the shape of Raman bands in the orientation-insensitive spectrum.     

Hydrogen-deuterium exchange in bovine serum albumin protein monitored by fourier transform infrared spectroscopy, part I: structural studies

The structure of the amide I band of bovine serum albumin (BSA) was determined using an H/D exchange experiment. The difference between the dry and hydrated exchange spectrum revealed the fine structure of the amide I band. The band at 1717 +/- 2 cm(-1) is due to the vibration of the COOH moieties from the protein side chains. Band components at 1682 +/- 2 cm(-1), 1655 +/- 2 cm(-1), and 1637 +/- 2 cm(-1) are assigned to the vibrations of the backbone C=O. These three bands belong to vibrations of three different populations of amide groups differing in the number of established H-bonds. The connectivity between the frequencies of various amide vibrations was determined by two-dimensional generalized correlation spectroscopy and spectral decomposition. About 7% of the whole exchangeable hydrogen atom population (NH, NH2, and OH groups from backbone and side chains) remains unexchanged, and these hydrogen atoms belong mainly to the NH groups, which are H-bonded to specific C=O groups. Moreover, this study concerns the approximately 10% of hydrogen atoms belonging to a particular HN...O=C population with a characteristic amide A frequency at 3290 cm(-1) and an amide I band at 1655 +/- 2 cm(-1), usually attributed to the alpha-helical structure that remains unexchanged. At higher temperature the exchange is more efficient. Upon heating, a further 4% of these NH groups are deuterated. The comparison of the exchange spectrum at higher temperature with the structural changes of the protein at the same temperature implies that the change in overall dynamics of the protein improve the level of exchange.     

Ab initio calculations of proline vibrations with and without water: consequences on the infrared spectra of proline-rich proteins

The infrared spectra of proline-rich proteins display a strong band in the 1450 cm(-1) region. In the literature, this band has been assigned either to the deformation modes of the CH(2) and CH(3) groups or to the CN stretching mode of proline residues. In order to establish the correct assignment of this band, the impact of proline vibrations in a polypeptide chain is studied and ab initio calculations are performed for a model molecule (I) containing a repeat unit of polyproline. A strong band is effectively calculated in the 1450 cm(-1) region and mostly assigned to CN stretching, whereas, due to the absence of the N-H bond, there is no amide II band. These results are in good agreement with the spectral features observed in the Fourier transform infrared (FT-IR) spectra of gliadins. Moreover, the spectral shifts calculated when a water molecule is complexed with (I) are consistent with the hydration effect observed in the experimental data.     

Deconvolution of Lorentzian broadened spectra part I: Direct deconvolution

A method is discussed of deconvolution of Lorentzian broadened experimental spectra directly in the “time” domain, that is, in the domain of the independent spectroscopic variable. The method consist in a numerical convolution of the spectrum with a deconvoluting function which is calculated in conformity with an theoretical analysis of the sampled form of the input and output spectra and their Fourier transforms. An almost complete elimination of the distortions and complete deconvolution degree are achieved. The restrictions imposed by the noise enhancement are estimated.     

Single-pass attenuated total reflection Fourier transform infrared spectroscopy for the prediction of protein secondary structure

Principal component regression (PCR) was applied to a spectral library of proteins in H2O solution acquired by single-pass attenuated total reflectance (ATR) Fourier transform infrared (FT-IR) spectroscopy. PCR was used to predict the secondary structure content, principally alpha-helical and the beta-sheet content, of proteins within a spectral library. Quantitation of protein secondary structure content was performed as a proof of principle that use of single-pass ATR-FT-IR is an appropriate method for protein secondary structure analysis. The ATR-FT-IR method permits acquisition of the entire spectral range from 700 to 3900 cm(-1) without significant interference from water bands. An "inside model space" bootstrap and a genetic algorithm (GA) were used to improve prediction results. Specifically, the bootstrap was utilized to increase the number of replicates for adequate training and validation of the PCR model. The GA was used to optimize PCR parameters, particularly wavenumber selection. The use of the bootstrap allowed for adequate representation of variability in the amide A, amide B, and C-H stretching regions due to differing levels of sample hydration. Implementation of the bootstrap improved the robustness of the PCR models significantly; however, the use of a GA only slightly improved prediction results. Two spectral libraries are presented where one was better suited for beta-sheet content prediction and the other for alpha-helix content prediction. The GA-optimized PCR method for alpha-helix content prediction utilized 120 wavenumbers within the amide I, II, A, B, and IV and the C-H stretching regions and 18 factors. For beta-sheet content predictions, 580 wavenumbers within the amide I, II, A, and B and the C-H stretching regions and 18 factors were used. The validation results using these two methods yielded an average absolute error of 1.7% for alpha-helix content prediction and an average absolute error of 2.3% for beta-sheet content prediction. After the PCR models were developed and validated, they were used to predict the alpha-helix and beta-sheet content of two unknowns, casein and immunoglobulin G.     

Maximum entropy deconvolution of infrared spectra: use of a novel entropy expression without sign restriction

Absorbance and difference infrared spectra are often acquired aiming to characterize protein structure and structural changes of proteins upon ligand binding, as well as for many other chemical and biochemical studies. Their analysis requires as a first step the identification of the component bands (number, position, and area) and as a second step their assignment. The first step of the analysis is challenged by the habitually strong band overlap in infrared spectra. Therefore, it is useful to make use of a mathematical method able to narrow the component bands to the extent to eliminate, or at least reduce, the band overlap. Additionally, to be of general applicability this method should permit negative values for the solution. We present a maximum entropy deconvolution approach for the band-narrowing of absorbance and difference spectra showing the required characteristics, which uses the generalized negative Burg-entropy (Itakura-Saito discrepancy) generalized for difference spectra. We present results on synthetic noisy absorbance and difference spectra, as well as on experimental infrared spectra from the membrane protein bacteriorhodopsin.     

Maximum-likelihood estimation of a laser system pointing parameters by use of return photon counts

A maximum-likelihood estimator used to determine boresight and jitter performance of a laser pointing system has been derived. The estimator is based on a Gaussian jitter model and uses a Gaussian far-field irradiance profile. The estimates are obtained using a set of return shots from the intended target. An experimental setup with a He-Ne laser and steering mirrors is used to study the performance of the proposed method. Both Monte Carlo simulations and experimental results demonstrate excellent performance of the estimator. Our study shows that boresight estimation is more challenging than jitter estimation when both quantities are estimated. Furthermore, their estimation performance improves with an increase in the number of shots. The experimental results are found to agree well with the simulation results.     

Spectroscopic probing of dynamic changes during stimulation and cell remodeling in the single cardiac myocyte

Optical microscopy, involving both fluorescence imaging and confocal Raman microspectroscopy, was used to visualize single, isolated, electrically active heart muscle cells. For example, short-term, dynamic changes in Raman bands during the contraction cycle, as well as persistent band changes during structural remodeling (microscopic rearrangements of cellular structures) in culture over longer periods of time, were obtained from the cellular content (sarcoplasm) of the heart cells. The results of the short-term studies, collected during electrical stimulation, showed dynamic changes in the Raman amide I band intensity, which occurred in phase with changes in cell length during cardiomyocyte contraction. The longer term studies of quiescent cardiomyocytes in culture over 3 days revealed a progressive and sustained increase in the intensity of the amide I band. Over the same period of culture, a decrease in the number of t-tubules (invaginations of the cell membrane, sarcolemma, which ensure the spreading of the action potential into the bulk of the sarcoplasm) was observed using confocal z-sections of the fluorescently labeled sarcolemma. The ability to measure both short-term dynamic changes associated with stimulated contraction and longer term persistent remodeling in the structure of intracellular macromolecules is valuable for assessing the physiological state of the cell, in real time.     

Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics

We report the experimental observation of the fractional Fourier transform (FRT) for a partially coherent optical beam with Gaussian statistics [i.e., partially coherent Gaussian Schell-model (GSM) beam]. The intensity distribution (or beam width) and the modulus of the square of the spectral degree of coherence (or coherence width) of a partially coherent GSM beam in the FRT plane are measured, and the experimental results are analyzed and agree well with the theoretical results. The FRT optical system provides a convenient way to control the properties, e.g., the intensity distribution, beam width, spectral degree of coherence, and coherence width, of a partially coherent beam.     

Evidence of a structural defect in Ice VII and the side-chain-dependent response of small model peptides to increased pressure

The effect of high pressure on the OH stretch of dilute HOD in D(2)O was examined using high-pressure Fourier transform infrared (FT-IR) spectroscopy. It was found that at pressures directly above the ice VI to ice VII transition, ice VII displays a splitting in the OH absorption indicative of differing hydrogen bonding environments. This result is contrary to published structures of ice VII in which each OH oscillator should experience an identical electronic environment. The anomalous band was found to decrease in absorbance and finally disappear at ～43.0 kbar. In addition, the pressure response of the amide I' and II' bands of three small model peptides was examined. Analysis of these bands' response to increased pressure indicates significant side-chain dependence of their structural rearrangement, which may play a role in the composition of full length proteins of barophilic organisms.     

Revealing covariance structures in fourier transform infrared and Raman microspectroscopy spectra: a study on pork muscle fiber tissue subjected to different processing parameters

The aim of this study was to investigate the correlation patterns between Fourier transform infrared (FT-IR) and Raman microspectroscopic data obtained from pork muscle tissue, which helped to improve the interpretation and band assignment of the observed spectral features. The pork muscle tissue was subjected to different processing factors, including aging, salting, and heat treatment, in order to induce the necessary degree of variation of the spectra. For comparing the information gained from the two spectroscopic techniques with respect to the experimental design, multiblock principal component analysis (MPCA) was utilized for data analysis. The results showed that both FT-IR and Raman spectra were mostly affected by heat treatment, followed by the variation in salt content. Furthermore, it could be observed that IR amide I, II, and III band components appear to be effected to a different degree by brine-salting and heating. FT-IR bands assigned to specific protein secondary structures could be related to different Raman C-C stretching bands. The Raman C-C skeletal stretching bands at 1,031, 1,061, and 1,081 cm(-1) are related to the IR bands indicative of aggregated beta-structures, while the Raman bands at 901 cm(-1) and 934 cm(-1) showed a strong correlation with IR bands assigned to a alpha-helical structures. At the same time, the IR band at 1,610 cm(-1), which formerly was assigned to tyrosine in spectra originating from pork muscle, did not show a correlation to the strong tyrosine doublet at 827 and 852 cm(-1) found in Raman spectra, leading to the conclusion that the IR band at 1,610 cm(-1) found in pork muscle tissue is not originating from tyrosine.     

Improved modelling of the loading spectra using a mixture model approach

In order to perform a fatigue-life analysis of structures the parameters of the structure loading spectra must be assessed. If the load time series are counted using a two-parametric rainflow counting method, the structure loading spectrum provides a probability for the occurrence of a load-cycle with certain amplitude and mean values. It is beneficial for the prediction of the fatigue life to describe the loading spectrum by a continuous function. We have previously discovered that mixtures of Gaussian probability density functions can be used to model the loading spectra. The main problems of this approach that have not been satisfactorily resolved before are related to the estimation of the number of components in the applied mixture models, and to the modelling of the load-cycle distributions with relatively fat tails. In this article, we describe a method for estimating the parameters of mixture models, which allows automatic determination of the number of components in a mixture model. The presented method is applied for modelling simulated and measured loading spectra using mixtures of the multivariate Gaussian or t probability density functions. In the article we also show that the mixture of t probability density functions sometimes better describes the loading spectra than the mixture of Gaussian probability density functions.     

Transmittance analysis of three-dimensional photonic crystals by the effective medium theory

A simple method for calculating the transmittance of three-dimensional photonic crystals is proposed. The crystals are divided into multilayer thin films, and each film is divided into rectangles with a minute width to calculate the effective permittivity of the film by the effective medium theory. Transmittance of the multilayer thin films is calculated with the matrix method. As the number of atomic layers increases, remarkable stop bands appear. When the refractive index of photonic atoms increases, the stop band shifts to a lower frequency, the band widens, and the number of bands increases. Polarization and incident angle dependences are also analyzed. The limit of application for this calculation method is also discussed.     

Analysis of Reflectance Properties in 1D Photonic Crystal Containing Metamaterial and High-Temperature Superconductor

In the present work, reflectance properties of one-dimensional photonic crystal (1D PC) containing a metamaterial and high-temperature superconductor have been investigated theoretically and analyzed. The reflectance/transmittance spectrum of the proposed structure is obtained by using the characteristic or transfer-matrix method (TMM). The results show that by increasing the thickness of the metamaterial layer, the width of the second reflection band decreases while the width of the first reflection band remains almost the same though it shifts towards the higher frequency side. In addition to this, a new band gap arises in the lower side of frequency. But, when the thickness of the superconductor layer is increased, the width of both the bands increases and no additional band arises in this case. Moreover, the reflection band is also affected by varying the operating temperature of the superconducting layer and the results show that bands get narrower by increasing the operating temperature. Finally, the effect of incident angle on the reflection band has been discussed for both transverse electric (TE) and transverse magnetic (TM) polarizations.     

Vapor-detection sensitivity as a function of spectral resolution for a single Lorentzian band

The objective of this effort is to provide guidance for the determination of spectral resolution for the passive remote detection of organic vapors. Target bands were modeled as Lorentzian bands. Several sensor models were used, including a detector-limited sensor model and a background-limited model.

An expression for the signal-to-noise ratio (SNR) was derived, and the SNR was computed for an SF(6) target band. The results show that substantial gains in sensitivity are possible if the conventional laboratory spectral resolution of 2 cm(-1) is reduced to 8 or even 16 cm(-1).