Single-angle-of-incidence ellipsometry

We introduce single angle-of-incidence (SAI) ellipsometry [U.S. patent application 20070024850 (14 July 2006)] as a technique to completely identify, i.e., totally characterize, film-substrate systems. We show that only one measurement of the ellipsometric function rho at one angle of incidence and one wavelength is totally sufficient to determine the optical constant of the film N1, its thickness d, and the substrate's optical constant N2. Obviously, it is also sufficient for characterizing only the film, determining N1 and d, and for characterizing only the substrate, determining N2 and d, as well as for characterizing only bare substrates. An inverse genetic algorithm (IGA) for complete identification is presented that is based on a physical condition of the transparent-film-absorbing-substrate system . This IGA is used to identify the film-substrate system in four separate cases. We show that removing the film thickness from the fitness function of the genetic algorithm and using the defined optimum population size to characterize the film reduces the computational effort from 20,000 to 69 fitness-function calculations; the number of calculations to characterize an absorbing layer is reduced from 80,000 to 180. This is a very significant reduction and is very welcome in real-time applications. An error analysis is presented that shows that the IGA is resilient to, not affected by, random experimental errors and that it gives very good results in the presence of both random and systematic errors of the ellipsometer system. Experimental results are given that also prove the robustness, stability, and high accuracy of the method. We present data only for the SiO2-Si film-substrate system, but the IGA works for any film-substrate system, physical or not.     

Channel capacity of dual-branch diversity systems over correlated Nakagami-m fading with channel inversion and fixed rate transmission scheme

Closed-form expressions are derived for the channel capacity of dual-branch maximal ratio combining, equal gain combining, selection combining, and switch and stay combining (SSC) diversity systems over correlated Nakagami-m fading for the channel inversion with fixed rate transmission scheme. Since some of the final capacity expressions contain infinite series, the series are truncated and upper bounds on the truncation errors are presented. An expression is also derived that can be used to numerically determine the optimum adaptive switching threshold for the capacity of a dual-branch SSC system over correlated Nakagami-m fading channels. A closed-form expression for the optimum adaptive switching threshold is derived, however, for the case of independent branches. The corresponding expressions for Rayleigh fading are obtained as a special case of Nakagami-m fading. Finally, numerical results are presented, which are then compared to the capacity results that the authors previously obtained for the rate adaptation with constant power transmission scheme.     

15-term self-calibration methods for the error-correction ofon-wafer measurements

An improved method of network analyzer calibration is described using the 15-term full model which includes all leakage errors between on-wafer probe tips. This model is well suited to eliminate measurement errors of network analyzer measurements on the wafer. All procedures presented are so-called self-calibration methods, allowing for standards that are not completely known. This allows one to create calibration standards in an easy way and to monitor the calibration process. Simple and robust closed-form equations are presented for all procedures. All procedures can be derived from the general method MURN (match, unknown, reflect, network). The MORN (match, open, reflect, network) is presented, which is particular interesting for on-wafer-measurements. Furthermore, the TMRN (through, match, reflect, network) procedure presented is especially designed for coaxial measurement problems. Experimental results of the TMRN method attest to the very good accuracy and viability of the 15-term self-calibration procedures and can be compared with other 15-term procedures     

基于差异进化算法的椭偏测量数据反演

为解决椭偏法测量薄膜厚度和折射率实验数据处理较为复杂的问题,采用一种新的基于群体智能的优化算法—差异进化算法处理实验数据;以单层吸收薄膜的测量为例,利用该算法进行数据处理,实验结果表明,三个薄膜参数(折射率n,消光系数k和薄膜厚度d)是可以同时获得的,而且在未知参数确切范围情况下,较大范围内进行搜索仍然能保证快速收敛到最优解。文中算法和粒子群算法、遗传算法以及利用椭偏仪数据处理软件得出的结果相比较,表明该算法在椭偏测量数据反演中是一种可行的智能优化算法。     

Average BER performance of FSO SIM-QAM systems in the presence of atmospheric turbulence and pointing errors

This paper presents the exact average bit error rate (BER) analysis of the free-space optical system employing subcarrier intensity modulation (SIM) with Gray-coded quadrature amplitude modulation (QAM). The intensity fluctuations of the received optical signal are caused by the path loss, atmospheric turbulence and pointing errors. The exact closed-form analytical expressions for the average BER are derived assuming the SIM-QAM with arbitrary constellation size in the presence of the Gamma–Gamma scintillation. The simple approximate average BER expressions are also provided, considering only the dominant term in the finite summations of obtained expressions. Derived expressions are reduced to the special case when optical signal transmission is affected only by the atmospheric turbulence. Numerical results are presented in order to illustrate usefulness of the derived expressions and also to give insights into the effects of different modulation, channel and receiver parameters on the average BER performance. The results show that the misalignment between the transmitter laser and receiver detector has the strong effect on the average BER value, especially in the range of the high values of the average electrical signal-to-noise ratio.     

Correction of static optical errors in a segmented adaptive optical system

Adaptive optical systems are designed to compensate for wave-front errors caused by atmospheric turbulence. In addition, they may also correct for wave-front errors associated with fixed optical aberrations in the host telescope. In general, however, adaptive optical systems cannot sense wave-front errors caused by imperfections in their own internal optical components. Consequently, these fixed internal errors will remain uncorrected. The problem of fixed internal aberrations has been noted in a segmented adaptive optics system designed for solar astronomy. This problem has been eliminated by measurement of the fixed errors, off line, through the use of a simple adaptation of a Hartmann test. Results from a recent experiment demonstrating the correction of the errors are presented.     

Removal of Probe Liftoff Effects on Crack Detection and Sizing in Metals by the AC Field Measurement Technique

In the alternative current field measurement (ACFM) technique, the nonzero value of liftoff distance for the magnetic sensor acts as a low-pass filter on surface crack signals, causing errors in crack detection and sizing. We present a blind deconvolution algorithm for liftoff evaluation and surface crack signal restoration. The algorithm employs the available closed-form expressions for the distribution of electromagnetic fields at the metal surface in the vicinity of a crack. To examine the accuracy of the algorithm, we use the original and the restored signals for crack sizing by a wavelet network inversion method. We present simulated and experimental results to demonstrate the role of the proposed algorithm in improving the inversion process.      

Calibration method of the specific characteristic of an electronic system of a rotating-analyzer ellipsometer

In photometric ellipsometry the optical signal is transformed into an electrical signal by a photodetector, and it passes an electronic system to reduce the noise and to amplify the signal. But inherently it will induce a phase shift and an amplitude attenuation of the output signal. Such a specific characteristic of an electronic system depends on the angular frequency of the signal and gives systematic errors to the results of the measurement of rotating-analyzer ellipsometry. We propose a modified method of measurement that enables us to calibrate the electronic system in the ellipsometric measurement configuration.     

A discussion of two ways of treating measurements of optical fiberloss

The loss measurement errors that arise from cutting optical fibers in fiber links and in pigtailed optical devices are analyzed in detail. Two methods of treating loss measurement data are compared: averaging P_i/P_o measurement and using just the maximum P_i/P_o measurement. Based on a large number of cutting experiments, a block diagram of cutting power distribution was constructed, and the measurement errors for both techniques were calculated. The results show that the measurement error of the maximum value taken at the input and output ends is less than the measurement error of the average value     

Error analysis for Mueller matrix measurement

The linear errors of Mueller matrix measurements are formulated for misalignment, depolarization, and incorrect retardation of the polarimetric components. The measured errors of a Mueller matrix depend not only on the imperfections of the measuring system but also on the Mueller matrix itself. The error matrices for different polarimetric systems are derived and also evaluated for the straight-through case. The error matrix for a polarizer-sample-analyzer system is much simpler than those for more complicated systems. The general error matrix is applied to null ellipsometry, and the obtained errors in ellipsometric parameters psi and delta are identical to the errors specifically derived for null ellipsometry with depolarization.     

New figures of merit for comprehensive functional genomics data: the metabolomics case

In the field of metabolomics, hundreds of metabolites are measured simultaneously by analytical platforms such as gas chromatography/mass spectrometry (GC/MS), liquid chromatography/mass spectrometry (LC/MS) and NMR to obtain their concentration levels in a reliable way. Analytical repeatability (intrabatch precision) is a common figure of merit for the measurement error of metabolites repeatedly measured in one batch on one platform. This measurement error, however, is not constant as its value may depend on the concentration level of the metabolite. Moreover, measurement errors may be correlated between metabolites. In this work, we introduce new figures of merit for comprehensive measurements that can detect these nonconstant correlated errors. Furthermore, for the metabolomics case we identified that these nonconstant correlated errors can result from sample instability between repeated analyses, instrumental noise generated by the analytical platform, or bias that results from data pretreatment.     

Real-time monitoring and growth control of Si-gradient-index structures by multiwavelength ellipsometry

Real-time monitoring and control of the growth of plasma-deposited gradient-index structures by multiwavelength phase-modulated ellipsometry are presented. An efficient method for estimating the optical parameters based on a least-squares fitting on the most recent recorded measurements is described. This method is used for real-time monitoring of the outerlayer refractive index and rate of deposition during deposition of inhomogeneous transparent films. An accurate integral expansion of the reflection coefficient, giving a continuous optical model describing inhomogeneous films, is used in the real-time modeling of the deposited structure. A variety of increasing complexities of the optical model is studied within inversion algorithms. Furthermore several ways of defining the optical parameters to be estimated are discussed. Inversion of simulated growth trajectories by using the described algorithms show what kind of information is available from the various approximations and in what conditions they are useful. Since real-time measurements during growth involves statistical noise and systematic errors, it becomes necessary to stabilize the fit. Various stabilizing functionals are discussed and implemented to solve this problem. Several plasma-deposited silicon oxynitride gradient-index structures where both rate of deposition and the refractive index are varied continuously are inverted in real time. As an example of application, a successful real-time control of the growth of a linear gradient index is demonstrated by using inversion algorithms. Inversion algorithms are extremely fast, with calculation times from less than a second (for the lowest-order approximation) to ~3 s.     

Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films

The determination of optical parameters of thin films from experimental data is a typical task in the field of optical-coating technology. The optical characterization of a single layer deposited on a substrate with known optical parameters is widely used for this purpose. Results of optical characterization are dependent on not only the choice of the thin-film model but also on the quality of experimental data. The theoretical results presented highlight the effect of systematic errors in measurement data on the determination of thin-film parameters. Application of these theoretical results is illustrated by the analysis of experimental data for magnesium fluoride thin films.     

Simultaneous measurement of refractive index and thickness of birefringent wave plates

A nondestructive measurement system based on a position sensing detector (PSD) and a laser interferometer for determining the thickness and refractive indices of birefringent optical wave plates has been developed. Unlike previous methods presented in the literature, the proposed metrology system allows the refractive index and thickness properties of the optical plate to be measured simultaneously. The experimental results obtained for the e-light and o-light refractive indices of a commercially available birefringent optical wave plate with refractive indices of n(o)=1.542972 and n(e)=1.552033 are found to be accurate to within 0.004132 and 0.000229, respectively. Furthermore, the experimentally derived value of the wave plate thickness deviates by no more than 0.9 microm from the analytically derived value of 453.95 microm. Overall, the experimental results confirm that the proposed metrology system provides a simple yet highly accurate means of obtaining simultaneous measurements of the refractive indices and thickness of birefringent optical wave plates.     

Accurate first-order leaky-wave analysis of antiresonant reflecting optical waveguides

We present a closed-form approximation for estimating both the field distribution and complex propagating constant of the antiresonant reflecting optical waveguide (ARROW) based on a first-order leaky-mode analysis. The formula was obtained from a novel coupled-electric-coupled-magnetic matrix method and provides six significant figures of the real part of the propagation constant beta of a SiO2/TiO2/SiO2/Si ARROW with an 8-microm core. The accuracy for the quantity of the imaginary part of beta is greater than 98.4% for the TE0 mode and 99.3% for TM0. The approximate values for field components are 96.1% accurate. In addition, a slight absorption by the substrate will result in modification of the initial improper leaky-mode behavior, which grows exponentially in the substrate, yielding a proper solution.     

Influence of incoherent superposition of light on ellipsometric coefficients

Reflections from the back surface of a transparent substrate influence the evaluation of optical constants of thin films from ellipsometric measurements. If the thickness of the substrate is large compared with the coherence length of the light, the relative phase between the p and s mode, which commonly is measured by ellipsometry, cannot be defined properly. We show how the reflections from the back surface of the substrate are taken into account in ellipsometric measurements by calculating the intensities of reflections for arbitrary angles of polarization. Applications of the new method, such as transmittance ellipsometry, ellipsometry at the back surface of the substrate, and the determination of the optical constants at the substrate-layer interface, are compared with measurements.     

Dependence of the Brillouin gain spectrum on linear strain distribution for optical time-domain reflectometer-type strain sensors

We theoretically derive the shape of the Brillouin gain spectrum, that is, the Briilouin backscattered-light power spectrum produced in an optical fiber under conditions of a strain distribution that changes linearly with a constant slope. The modeled measurement system is an optical time-domain reflectometer-type strain sensor system. The linear strain distribution is one of the fundamental distributions and is produced in, for example, a beam to which a concentrated load is applied. By analyzing a function that expresses the shape of the derived Brillouin gain spectrum, we show that the strain calculated from the frequency at which the spectrum has a peek value coincide. with that at the center of the effective pulsed light. In addition, the peak value and the full width at half maximum of the Brillouin gain spectrum are both influenced by the strain difference between the two ends of the effective pulse. We investigate this influence in detail and obtain the relationship between strain difference and strain measurement error.     

Determination of film thickness and refractive index in one measurement of phase-modulated ellipsometry

Ellipsometry is often used to determine the refractive index and/or the thickness of a polymer layer on a substrate. However, simultaneous determination of these parameters from a single-wavelength single-angle measurement is not always possible. The present study determines the sensitivity of the method to errors of measurement for the case of phase modulated ellipsometry and identifies conditions for decoupling film thickness and refractive index. For a specific range of film thickness, both the thickness and the refractive index can be determined from a single measurement with high precision. This optimal range of the film thickness is determined for organic thin films, and the analysis is tested on hydrogel-like polymer films in air and in water.     

Genetic algorithm for ellipsometric data inversion of absorbing layers

A new data reduction method is presented for single-wavelength ellipsometry. A genetic algorithm is applied to ellipsometric data to find the best fit. The sample consists of a single absorbing layer on a semi-infinite substrate. The genetic algorithm has good convergence and is applicable to many different problems, including those with different independent measurements and situations with more than two angles of incidence. Results are similar to those obtained by other inversion techniques.     

Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: theory

A method is proposed that permits one to retrieve physical parameters of tropospheric particle size distributions, e.g., effective radius, volume, surface-area, and number concentrations, as well as the mean complex refractive index on a routine basis from backscatter and extinction coefficients at multiple wavelengths. The optical data in terms of vertical profiles are derived from multiple-wavelength lidar measurements at 355, 400, 532, 710, 800, and 1064 nm for backscatter data and 355 and 532 nm for extinction data. The algorithm is based on the concept of inversion with regularization. Regularization is performed by generalized cross-validation. This method does not require knowledge of the shape of the particle size distribution and can handle measurement errors of the order of 20%. It is shown that at least two extinction data are necessary to retrieve the particle parameters to an acceptable accuracy. Simulations with monomodal and bimodal logarithmic-normal size distributions show that it is possible to derive effective radius, volume, and surface-area concentrations to an accuracy of +/-50%, the real part of the complex refractive index to +/-0.05, and the imaginary part to +/-50%. Number concentrations may have errors larger than +/-50%.