Power Spectral Density Fitting Research Articles

农田地面与沥青路面不平度特征的测试、分析与比较

Measuring and analysing the roughness of agricultural field and road have great significance for studying the characteristics of tractor dynamic response. This study was designed to analyse and compare the roughness characteristics of agricultural field and asphalt road profiles. A profiling apparatus was developed to measure field and road surface profiles of parallel tracks. The profile measurements were conducted in a grass field, a corn stubble field, a harvested potato field and on an asphalt road. The root mean square value and two spectrum parameters of surface profiles were calculated and analysed to investigate the roughness characteristics of fields and asphalt road. The results of the study indicate that for the values of the agricultural field and asphalt road surface roughness, waviness and roughness index are both positive associated with the root mean square value. Most of the waviness values of all measured field profiles were less than 2 with the average of 1.8, while the waviness values of all measured asphalt road profiles were greater than 2 with the average of 2.08. The roughness of both field and asphalt road profiles can be distinguished by the power spectral density fitting method. However, it has better performance in characterizing asphalt road profiles than characterizing field profiles with the power spectral density fitting method.

Spectral analysis of sidewall roughness during resist-core self-aligned double patterning integration

Double patterning technology has now proved its efficiency to go beyond the standard lithographic printing limits and address the resolution requirements of the sub-20 nm technological node. However, some data are still lacking regarding the characterization of line edge/width roughness (LER/LWR) in such integration. In this work, a detailed spectral analysis of the sidewall roughness evolution during a resist-core self-aligned double patterning (SADP) integration is presented. A 20 nm half-pitch SADP process using photoresist as the core material, and SiO2 deposited by plasma enhanced atomic layer deposition as the spacer material is developed. The LER and LWR have been characterized at each technological step involved in the SADP process flow, using a power spectral density fitting method, which provides a full description of the sidewalls roughness with the estimation of noise-free roughness amplitude (σ), correlation length (ξ), and roughness exponent (α). Results show that the SADP process allows to decrease drastically the LWR and LER amplitudes down to 2.0 nm corresponding to a reduction of about 70% and 50%, respectively, compared to the initial resist patterns. Although the SADP concept generates two asymmetric populations of lines, the final features present similar LWR, LERleft, and LERright parameters. The study also highlights the effectiveness of the SADP concept to decrease critical dimension variation and low-frequency LWR components to values inferior to 1 nm, which is an outstanding improvement compared to other single or double patterning techniques. However, this work brings out that the deposition process is the key step to ensure successful resist-core SADP integration. It must not only be as conformal as possible but also preserve the square shape of the core material. It is shown that the resist lateral erosion occurring during the deposition step introduces some random resist sidewalls angles that contribute to the formation of short range roughness during the spacer etching transfer, resulting in residual LWR mainly composed of high-and medium-frequency components. Contrary to LWR, the beneficial impact of the conformal spacer deposition on low-frequency roughness components has rather no effect on LER. The LER parameters after spacer etching mainly depend on the core ones prior to deposition. LER low-frequency components remain a key issue to address for an optimized integration.

Daniell method for power spectral density estimation in atomic force microscopy.

An alternative method for power spectral density (PSD) estimation--the Daniell method--is revisited and compared to the most prevalent method used in the field of atomic force microscopy for quantifying cantilever thermal motion--the Bartlett method. Both methods are shown to underestimate the Q factor of a simple harmonic oscillator (SHO) by a predictable, and therefore correctable, amount in the absence of spurious deterministic noise sources. However, the Bartlett method is much more prone to spectral leakage which can obscure the thermal spectrum in the presence of deterministic noise. By the significant reduction in spectral leakage, the Daniell method leads to a more accurate representation of the true PSD and enables clear identification and rejection of deterministic noise peaks. This benefit is especially valuable for the development of automated PSD fitting algorithms for robust and accurate estimation of SHO parameters from a thermal spectrum.

Sparse Frequency Waveform Design for Radar-Embedded Communication

According to the Tag application with function of covert communication, a method for sparse frequency waveform design based on radar-embedded communication is proposed. Firstly, sparse frequency waveforms are designed based on power spectral density fitting and quasi-Newton method. Secondly, the eigenvalue decomposition of the sparse frequency waveform sequence is used to get the dominant space. Finally the communication waveforms are designed through the projection of orthogonal pseudorandom vectors in the vertical subspace. Compared with the linear frequency modulation waveform, the sparse frequency waveform can further improve the bandwidth occupation of communication signals, thus achieving higher communication rate. A certain correlation exists between the reciprocally orthogonal communication signals samples and the sparse frequency waveform, which guarantees the low SER (signal error rate) and LPI (low probability of intercept). The simulation results verify the effectiveness of this method.

Designing sequence sets with good correlation properties based on PSD fitting

Sequence sets with good correlation properties lie at the core of many communication and radar applications. A new approach to the design of sequence sets is proposed. The ideal correlation matrix is defined, and the design problem is formulated as a power spectral density (PSD) fitting problem. In this manner, a simpler minimisation problem is obtained, and an iterative method is applied to solve it. Simulation results demonstrate that the performance of the proposed approach is superior to that of the previous state-of-the-art algorithm.

Designing sequence with low sidelobe levels at specified intervals based on PSD fitting

A new approach for designing a sequence that has very low autocorrelation sidelobe levels at specified intervals is proposed. The synthesised autocorrelation function is defined for denoting the autocorrelation properties, and the design problem is formulated as a power spectral density (PSD) fitting problem. In this way, a simple optimisation objective function is obtained and an iterative optimisation technique is applied. The proposed approach is computationally efficient and can generate a sequence with autocorrelation sidelobes that are practically zero at the required lag intervals.

PSD of ballastless track irregularities of high-speed railway

The calculation method, fitting function and fitting spectrum of power spectral density (PSD) of track irregularity were proposed in the paper. To improve the calculation accuracy of PSD of track irregularity, a linear interpolation method and a wavelet analysis method are given and used to eliminate the outliers and trends in the track irregularities. The paper describes the window function, window length and PSD estimation method to calculate track irregularity PSD. For comparison the track irregularity power spectral densities (PSDs) calculated with different window functions, window lengths and PSD estimation methods. Combing the above mentioned results and the data from the high speed comprehensive inspection train, the paper determines the track irregularity PSD fitting equation and introduces the frequency multiplication energy table to reflect the impact of track periodical structure of High Speed Railway. PSD of ballastless track irregularities of high-speed railway includes fitting spectrum and frequency multiplication energy table, which provides basis for maintenance and optimization design for High Speed Railway.

A waveform design method for suppressing range sidelobes in desired intervals

We propose an approach for designing unimodular waveforms with low correlation sidelobes in one or more lag intervals. The approach includes an iterative spectral approximation algorithm (ISAA) and derivative-based non-linear optimization algorithms. ISAA is based on power spectral density fitting, phase retrieval, and alternating projection. Phase-only versions of the derivative-based optimization algorithms are also derived. These algorithms eliminate the unimodular constraint by expanding the objective function with respect to the phase vector and by replacing the normal line search with the phase-only line search. The effectiveness of the approach is demonstrated by numerical simulations.

Benefits of plasma treatments on critical dimension control and line width roughness transfer during gate patterning

The present work focuses on the line width roughness (LWR) transfer and the critical dimension control during a typical gate stack patterning and shows the benefits of introducing 193 nm photoresist treatments before pattern transfer into the gate stack to improve process performance. The two investigated treatments (HBr plasma and vacuum ultra violet (VUV) plasma radiation) have been tested on both blanket photoresist films and resist patterns to highlight the etching and roughening mechanisms of cured resists. Both treatments reinforce the etch resistance of the photoresist exposed to fluorocarbon plasma etching process used to open the Si-ARC (silicon antireflective coating) layer. The etch resistance improvement of cured resists is attributed to both the decrease in oxygen content within the resist and the crosslinking phenomena caused by VUV radiation during the treatment. As the magnitude of the surface roughness is directly correlated to the etched thickness, cured resists, which are etched less rapidly, will develop a lower surface roughness for the same processing time compared to reference resists. The LWR evolution along the pattern sidewalls has been studied by critical dimension atomic force microscopy during the Si-ARC plasma etching step. The study shows that the LWR is degraded at the top of the resist pattern and propagates along the pattern sidewalls. However, as long as the degradation does not reach the interface between resist and Si-ARC, the LWR decreases during the Si-ARC etching step. As resist pretreatments reinforce the resist etch resistance during Si-ARC etching, the LWR degradation along the sidewalls is limited leading to minimized LWR transfer. The LWR decrease observed after plasma etching has been explained thanks to a spectral analysis of the LWR performed by critical dimension scanning electron microscopy combined with the power spectral density fitting method. The study shows that the high and medium frequency components of the roughness (periodicity below 200 nm) are not totally transferred during the gate patterning allowing a LWR decrease at each plasma step.

Power Spectrum of Smoothed Line-Edge and Line-Width Roughness

Line-edge and line-width roughness (LER and LWR) is a challenge for device variability control, especially in future devices. Actual device patterns have LER/LWR that is smoothed from the original photoresist patterns used as etching masks. In this study, the LER/LWR of these actual patterns was assumed to have a modified exponential autocorrelation function, which was smoothed by another exponential function. An analytical formula of the discrete power spectral density (PSD) of this LER/LWR was derived on the basis of the previous formula for non-smoothed LER/LWR, for use in a PSD fitting method. The PSDs calculated using this formula excellently fit the experimental PSDs of both types of polycrystalline-silicon lines without and with sidewall spacers. Through these fittings, it was found that the actual LER/LWR is accurately characterized using the variance and correlation length of the original non-smoothed LER/LWR simply by introducing a third parameter that characterizes the smoothing effect.

Statistical-noise effect on power spectrum of long-range-correlated line-edge and line-width roughness

We formerly developed the for analyzing the line-edge and line-width roughness (LER/LWR) that has a long-range correlation beyond the conventional analysis limit, as reported in a previous work. In that method, we repeatedly assembled virtual long lines by gathering line segments, which were arbitrarily disposed on actual long lines and by randomly changing their combination and order, permitting the assembled lines to share the same line segments. Then, we obtained the power spectral density (PSD) of the LER/LWR of the assembled lines considering the lines as seamless. We also derived an analytic formula of the assembled-line PSDs for use in the PSD fitting method. This formula agreed very well with experimental PSDs. In this report, we propose guidelines for suppressing the statistical-noise effect on the assembly method for the purpose of accurately analyzing the long-range-correlated LER/LWR. The guidelines will greatly help shed light on the long-range correlation, which causes the variability even in large devices but has long been veiled due to the lack of metrology.

Ocean Wavenumber Estimation From Wave-Resolving Time Series Imagery

We review several approaches that have been used to estimate ocean surface gravity wavenumbers from wave-resolving remotely sensed image sequences. Two fundamentally different approaches that utilize these data exist. A power spectral density approach identifies wavenumbers where image intensity variance is maximized. Alternatively, a cross-spectral correlation approach identifies wavenumbers where intensity coherence is maximized. We develop a solution to the latter approach based on a tomographic analysis that utilizes a nonlinear inverse method. The solution is tolerant to noise and other forms of sampling deficiency and can be applied to arbitrary sampling patterns, as well as to full-frame imagery. The solution includes error predictions that can be used for data retrieval quality control and for evaluating sample designs. A quantitative analysis of the intrinsic resolution of the method indicates that the cross-spectral correlation fitting improves resolution by a factor of about ten times as compared to the power spectral density fitting approach. The resolution analysis also provides a rule of thumb for nearshore bathymetry retrievals-short-scale cross-shore patterns may be resolved if they are about ten times longer than the average water depth over the pattern. This guidance can be applied to sample design to constrain both the sensor array (image resolution) and the analysis array (tomographic resolution).