Spatial frequency analysis

Measuring Toner Particle Size Distributions Using Spatial Frequency Analysis... 

W. Lawrence, Spatial frequency analysis of line edge roughness in nine chemically related photo resists, Proc. SPIE 5039, 713 724 (2003) R. Brainard, P. Trefonas, J.H. Lammers, C.A. Cutler, J.F. Mackevich, A. Trefonas, and S.A. Robertson, Shot noise, LER and quantum efficiency of EUV photoresists, Proc. SPIE 5374, 74 85 (2004). 

Thorwirth, G., Optical Spatial Frequency Analysis Principle and Results, Jena Review, 1990, 2, 95-97. 

The classical treatment of diffuse SAXS (analysis and elimination) is restricted to isotropic scattering. Separation of its components is frequently impossible or resting on additional assumptions. Anyway, curves have to be manipulated one-by-one in a cumbersome procedure. Discussion of diffuse background can sometimes be avoided if investigations are resorting to time-resolved measurements and subsequent discussion of observed variations of SAXS pattern features. A background elimination procedure that does not require user intervention is based on spatial frequency filtering (cf. p. 140). 

Fourier analysis is used to find the velocity and attenuation of surface waves. Let the range in z over which data is available be (. If there were no attenuation, then by the convolution theorem the Fourier transform F ( ) would be a sine function centred at a spatial frequency... 

An example of quasi CW THz detection [86] uses a THz wave parametric oscillator (TPO) consisting of a Q-switched Nd YAG laser and parametric oscillator [87,88], In this technique, MgO LiNb3 is employed as a non-linear material to generate CW THz. Silicon prisms couple the THz radiation from the non-linear crystal where it is detected using a pyroelectric detector. THz images are collected at discrete THz frequencies and then spectroscopically analyzed using a component spatial pattern analysis method to determine sample composition. 

It is emphasized that by means of the statistical frequency analysis it is possible to separate dataset in populations, even if can be difficult to select one or two general threshold to utilize as reference to identify background values. In addition, the value distributions are not sufficient to divide the dataset into different populations, because they show an overlap, and give no idea of the spatial distribution and geometry of the geochemical anomalies. This is true both at local and regional scale. 

Lima A. describes statistical methods to evaluate background values, namely, statistical frequency analysis and spatial analysis. The author illustrates the application of GeoDAS software to perform multifractal inverse distance weighted (MIDW) interpolation and a fractal filtering technique, named spatial and spectral analysis (S-A) method, to evaluate geochemical background at regional and local scale. 

Martinez A, Di Russo F, Anllo-Vento L, Hillyard SA. 2001. Electrophysiological analysis of cortical mechanisms of selective attention to high and low spatial frequencies. Clin Neurophysiol 112 1980-1998. 

Optical media that can record elementary gratings, such as photorefractive polymers, are in high demand. In many fields, the decomposition of a signal into a superposition of harmonic functions (Fourier analysis) is a powerful tool. In optics, Fourier analysis often provides an efficient way to implement complex operations and is at the basis of many optical systems. For instance, any arbitrary image can be decomposed into a sum of harmonic functions with different spatial frequencies and complex amplitudes. Each of these periodic functions can be considered... 

Here, the mean height (/z)=0, Eq. (6.1) is calculated on an image with scan length L, f is the spatial frequency (i.e. the inverse distance), and /max is the Nyquist frequency. The analysis for the relevant scaling properties (viz. correlation length, roughness exponent, etc.) can be carried out either on the roughness (6-7)... 

The Multichannel ("Stroboscopic") Optical Spectrum Analyser (MOSA) allows us to carry out spatial Fourier analysis of the images of a ruffled water surface. One can show (see, Appendix) that the frequency spectrum s(co) = < i cof > (<...> denotes statistical averaging) of the MOSA signal i t) can be written in the form... 

Roth et al. [1988] recast the expression for the effective longitudinal conductivity in terms of spatial frequency, k (rad/m). This approach has two advantages. First, the temporal and spatial behaviors are both described using frequency analysis. Second, a parameter describing the size of a specific piece of tissue is not necessary the spatial frequency dependence becomes a property of the tissue, not the measurement. The expression for the DC effective longitudinal conductivity is... 

Spatial autocorrelation analysis of allozyme frequencies led to similar results (Barbujani and Sbordoni, unpublished). With the exception of the previously discussed Pgm locus, a substantial lack of spatial autocorrelation was revealed, suggesting the absence of either constant gene flow, even very low, or selection pressures producing a geographic structure. 

Surface-Enhanced Raman spectroscopy (SERS) [10] is also one of the analytical tools for a sample s surface. When laser beams with frequency vq irradiated to the sample, some of the beams are scattered. Almost all of the frequency of the scattered beams is the same as that of incident beam (vq), but the fi equency of some scattered beams (vo Vi) is slightly different fi om that of the incident beam. This is called Raman scattering spectroscopy (RSS). The frequency of lattice vibration of the samples is Vj so that RSS gives us knowledge concerning molecular stmcmre, crystal structure and residual stress. The combination of RSS with an optical microscope as well as an atomic force microscope (AFM) is also effective for spatial distribution analysis. 

Chan Pang 2000) described the Fourier transform approach to detect the structural defect of fabrics. Since the three-dimensional frequency spectrum is very difficult to analyze and many defects occur along the horizontal and vertical axes, two significant spectral diagrams (called the central spatial frequency spectra) are introduced to increase the efficiency of the analysis process. Seven significant characteristic parameters were extracted from the central spatial frequency spectra to describe the defect type. 

In addition, the analysis of roughness components inducing light scattering (in the visible spectrum) of optical surfaces is focused on the mid-spatial frequency range / = (5 x 10 , ..2) jm ... 

The hazard frequency assessment includes two part temporal frequency and spatial frequency. Temporal frequency is a hkehhood characteristic of rockfall occurrence per unit of time period i.e. one year. It indicates the rock instabiUty or failure in the source area. Temporal frequency can be inferred from historical catalogue or using relative rock failure rating system (Jaboyedoff et al., 2005). Distribution laws have been proposed for rockfaUs based on statistical analysis of historical data sets to derive their recurrent probability (Dussauge et al., 2002,2003). 

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