Resolution Enhancement for Spectra of Chemical and Physical Interest

Allen, Leland C.; Gladney, H. M.; Glarum, S. H.

doi:10.1063/1.1724976

Cited by 73 publications

(26 citation statements)

References 3 publications

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“…Rather than attempting to accurately perform the full deconvolution, it is more sensible to "sharpen" the spectrum so that a better identifiability of the locations and number of peaks is achieved compared with that available from a visual inspection of the available data u δ [2,9]. As explained in the Introduction, this corresponds to finding the solution z of the sharpening equatioñ B β * z = u for the data u δ where the regularity of z is determined by the source condition…”

Section: Application-deconvolution By Sharpeningmentioning

confidence: 99%

Dilational interpolatory inequalities

Hegland

Anderssen

2011

Math. Comp.

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Abstract. Operationally, index functions of variable Hilbert scales can be viewed as generators for families of spaces and norms and, thereby, associated scales of interpolatory inequalities. Using one-parameter families of index functions based on the dilations of given index functions, new classes of interpolatory inequalities, dilational interpolatory inequalities (DII), are constructed. They have ordinary Hilbert scales (OHS) interpolatory inequalities as special cases. They represent a precise and concise subset of variable Hilbert scales interpolatory inequalities appropriate for deriving error estimates for peak sharpening deconvolution. Only for Gaussian and Lorentzian deconvolution do the DIIs take the standard form of OHS interpolatory inequalities. For other types of deconvolution, such as a Voigt, which is the convolution of a Gaussian with a Lorentzian, the DIIs yield a new class of interpolatory inequality. An analysis of deconvolution peak sharpening is used to illustrate the role of DIIs in deriving appropriate error estimates.

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Section: Application-deconvolution By Sharpeningmentioning

confidence: 99%

Dilational interpolatory inequalities

Hegland

Anderssen

2011

Math. Comp.

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“…Basic principles behind this method are quite clear -differentiation amplifies higher frequency components of the profile more than lower frequency components. This idea was firstly proposed by Tikhonov, 11 and almost at the same time by Allen, Gladney and Glarum, 12 using as the basis the fact that in the Fourier space differentiation corresponds to multiplication with independent variable. Allen et al 12 stated that if the maximum is symmetric and has a smooth Fourier transform one can subtract the second (and higher) derivatives from the original maximum in order to enhance its intensity.…”

Section: Methodsmentioning

confidence: 99%

New Algorithm for Microstructural Information Determination from the Overlapping X-ray Diffraction Profiles

Dekanić¹,

Skoko²,

Lončarić

2016

ACSi

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Knowledge about the microstructure is crucial in targeted synthesis of novel nanomaterials. The microstructural parameters, crystallite size and crystallite strain play a major role in physical and chemical properties of the material. X-ray diffraction (XRD) is a very suitable method for this task, since it is non-destructive and it enables a very quick and precise determination of these parameters. The main problem lies in the case where the two neighboring diffraction profiles overlap each other. Here we present a new method for the separation of the overlapping profiles based on the differentiation of the profiles. Further, this method is appropriate for non-crystallographers working in the field of material science since it does not require any crystallographic experience and the full knowledge about the structure of the sample investigated. The microstructural results obtained by the proposed method are very accurate.

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“…resolution enhancement (Martin , 1959 ;Allen et al , 1964). The den yative theorm of the Fourier transforms (Bracewell ,196 5) st ates t h a t if the imaginary part of the Fourier transformation of a function is multiplied by a linear ramp starting at the origin the result is the real part of the Fourier transformation of the derivative of the original function .…”

Section: Differentiationmentioning

confidence: 99%