An efficient algorithm for polynomial surface fitting

Balch, S.J.; Thompson, G. T.

doi:10.1016/0098-3004(89)90058-7

Cited by 8 publications

(3 citation statements)

References 2 publications

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“…To obtain a 3D surface, the 2D Kikuchi pattern should be transformed into a 3D Kikuchi curve by converting the value of the gray scale at (X i , Y i ) to the Z i value corresponding to a point at (X i , Y i , Z i ) in 3D. The latter can be approximated by a smooth surface with polynomials 37 , which are used for curve fitting techniques and given by the following: where N is the order in the range between 1 and 5, and is the coefficient of the polynomial function. The order N is considered larger than 3, and the fitting background includes detailed diffraction information, that is, diffraction signals.…”

Section: Resultsmentioning

confidence: 99%

Polynomial fitting method of background correction for electron backscatter diffraction patterns

Tsai

Pan

Kuo

2022

Sci Rep

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A raw electron backscatter diffraction (EBSD) signal can be empirically decomposed into a Kikuchi diffraction pattern and a smooth background. For pattern indexing, the latter is generally undesirable but can reveal topographical, compositional, or diffraction contrast. In this study, we proposed a new background correction method using polynomial fitting (PF) algorithm to obtain clear Kikuchi diffraction patterns for some applications in nonconductive materials due to coating problems, at low accelerated voltage and at rough sample surfaces and for the requirement of high pattern quality in HR-EBSD. To evaluate the quality metrics of the Kikuchi patterns, we initially used three indices, namely, pattern quality, Tenengrad variance, and spatial–spectral entropy-based quality to detect the clarity, contrast, and noise of Kikuchi patterns obtained at 5 and 15 kV. Then, we examined the performance of PF method by comparing it with pattern averaging and Fourier transform-based methods. Finally, this PF background correction is demonstrated to extract the background images from the blurred diffraction patterns of EBSD measurements at low kV accelerating voltage and with coating layer, and to provide clear Kikuchi patterns successfully.

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Section: Resultsmentioning

confidence: 99%

Polynomial fitting method of background correction for electron backscatter diffraction patterns

Tsai

Pan

Kuo

2022

Sci Rep

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“…As expressões acima são uma extensão, para funções de três variáveis, da expansão em série de Maclaurin, proposta por Balch e Thompson (1989), para o ajuste de superfícies em duas dimensões. Com o objetivo de reduzir o valor dos coeficientes, as variáveis Lat, Long e t são subtraída, em todos os monômios, de um valor constante que corresponde ao centro do intervalo de validade do modelo.…”

Section: Dados Usados No Ajuste Do Modelounclassified

“…Adotou-se o seguinte critério para estimar os pesos de cada categoria de dados. O parâmetro de ajuste FIT é usado para quantificar a qualidade de um ajuste, Balch e Thompson (1989) A i,j,k BB i,j,k C i,j,k 0 0 0 7,4520E+00 -1,9016E+01 3,1613E+04 1 0 0 1,7119E-01 1,7207E-01 -5,4918E+01 2 0 0 -8,6148E-03 -3,4256E-04 9,4536E-03 3 0 0 -3,5591E-04 -2,7294E-04 3,4257E-02 4 0 0 6,3897E-06 -2,3227E-06 4,2533E-04 5 0 0 2,0718E-07 2,4661E-07 -1,0819E-05 0 1 0 -4,3622E-01 1,8176E+00 -2,3089E+02 1 1 0 -7,3758E-03 1,5421E-04 1,4462E+00 2 1 0 6,4512E-04 4,3512E-05 -2,9463E-02 3 1 0 4,4600E-06 8,4998E-07 -7,3263E-04…”

Section: Determinação Dos Pesosunclassified