S. Ma, H. Gao, and L. Wu, “Modified Fourier-Hankel method based on analysis of errors in Abel inversion using Fourier transform techniques,” Appl. Opt. 47, 1350–1357 (2008).

[CrossRef]
[PubMed]

S. Ma, H. Gao, L. Wu, and G. Zhang, “Abel inversion using Legendre polynomials approximations,” J. Quant. Spectrosc. Radiat. Transfer 109, 1745–1757 (2008).

[CrossRef]

S. Ma, H. Gao, G. Zhang, and L. Wu, “A versatile analytical expression for the inverse Abel transform applied to experimental data with noise,” Appl. Spectrosc. 62, 701–707(2008).

[CrossRef]
[PubMed]

F. Magnus and J. T. Gudmundsson, “Digital smoothing of the Langmuir probe I-V characteristic,” Rev. Sci. Instrum. 79, 073503 (2008).

[CrossRef]
[PubMed]

G. C.-Y. Chan and G. M. Hieftje, “Estimation of confidence intervals for radial emissivity and optimization of data treatment techniques in Abel inversion,” Spectrochim. Acta B 61, 31–41 (2006).

[CrossRef]

G. A. Garcia, L. Nahon, and I. Powis, “Two-dimensional charged particle image inversion using a polar basis function expansion,” Rev. Sci. Instrum. 75, 4989–4996 (2004).

[CrossRef]

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of Abel-transformable images: the Gaussian basis-set expansion Abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).

[CrossRef]

R. Álvarez, A. Rodero, and M. C. Quintero, “An Abel inversion method for radially resolved measurements in the axial injection torch,” Spectrochim. Acta B 57, 1665–1680(2002).

[CrossRef]

M. J. Buie, J. T. P. Pender, J. P. Holloway, T. Vincent, P. L. G. Ventzek, and M. L. Brake, “Abel’s inversion applied to experimental spectroscopic data with off axis peaks,” J. Quant. Spectrosc. Radiat. Transfer 55, 231–243 (1996).

[CrossRef]

J. I. Fernández Palop, J. Ballesteros, V. Colomer, and M. A. Hernández, “A new smoothing method for obtaining the electron energy distribution function in plasmas by the numerical differentiation of the I-V probe characteristic,” Rev. Sci. Instrum. 66, 4625–4636 (1995).

[CrossRef]

L. M. Smith, “Nonstationary noise effects in the Abel inversion,” IEEE Trans. Inf. Theory 34, 158–161 (1988).

[CrossRef]

M. Kalal and K. A. Nugent, “Abel inversion using fast Fourier transforms,” Appl. Opt. 27, 1956–1959 (1988).

[CrossRef]
[PubMed]

L. M. Smith, D. R. Keefer, and S. I. Sudharsanan, “Abel inversion using transform techniques,” J. Quant. Spectrosc. Radiat. Transfer 39, 367–373 (1988).

[CrossRef]

G. N. Minerbo and M. E. Levy, “Inversion of Abel’s integral equation by means of orthogonal polynomials,” SIAM J. Numer. Anal. 6, 598–616 (1969).

[CrossRef]

O. H. Nestor and H. N. Olsen, “Numerical methods for reducing line and surface probe data,” SIAM Rev. 2, 200–207(1960).

[CrossRef]

R. Álvarez, A. Rodero, and M. C. Quintero, “An Abel inversion method for radially resolved measurements in the axial injection torch,” Spectrochim. Acta B 57, 1665–1680(2002).

[CrossRef]

G. E. Andrews, R. Askey, and R. Roy, Special Functions(Cambridge University Press, 1999).

G. E. Andrews, R. Askey, and R. Roy, Special Functions(Cambridge University Press, 1999).

J. I. Fernández Palop, J. Ballesteros, V. Colomer, and M. A. Hernández, “A new smoothing method for obtaining the electron energy distribution function in plasmas by the numerical differentiation of the I-V probe characteristic,” Rev. Sci. Instrum. 66, 4625–4636 (1995).

[CrossRef]

M. J. Buie, J. T. P. Pender, J. P. Holloway, T. Vincent, P. L. G. Ventzek, and M. L. Brake, “Abel’s inversion applied to experimental spectroscopic data with off axis peaks,” J. Quant. Spectrosc. Radiat. Transfer 55, 231–243 (1996).

[CrossRef]

M. J. Buie, J. T. P. Pender, J. P. Holloway, T. Vincent, P. L. G. Ventzek, and M. L. Brake, “Abel’s inversion applied to experimental spectroscopic data with off axis peaks,” J. Quant. Spectrosc. Radiat. Transfer 55, 231–243 (1996).

[CrossRef]

G. C.-Y. Chan and G. M. Hieftje, “Estimation of confidence intervals for radial emissivity and optimization of data treatment techniques in Abel inversion,” Spectrochim. Acta B 61, 31–41 (2006).

[CrossRef]

J. I. Fernández Palop, J. Ballesteros, V. Colomer, and M. A. Hernández, “A new smoothing method for obtaining the electron energy distribution function in plasmas by the numerical differentiation of the I-V probe characteristic,” Rev. Sci. Instrum. 66, 4625–4636 (1995).

[CrossRef]

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of Abel-transformable images: the Gaussian basis-set expansion Abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).

[CrossRef]

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, Vol. 3 of Combustion Science and Technology Book Series, 2nd ed. (Gordon & Breach, 1996).

S. Ma, H. Gao, L. Wu, and G. Zhang, “Abel inversion using Legendre polynomials approximations,” J. Quant. Spectrosc. Radiat. Transfer 109, 1745–1757 (2008).

[CrossRef]

S. Ma, H. Gao, G. Zhang, and L. Wu, “A versatile analytical expression for the inverse Abel transform applied to experimental data with noise,” Appl. Spectrosc. 62, 701–707(2008).

[CrossRef]
[PubMed]

S. Ma, H. Gao, and L. Wu, “Modified Fourier-Hankel method based on analysis of errors in Abel inversion using Fourier transform techniques,” Appl. Opt. 47, 1350–1357 (2008).

[CrossRef]
[PubMed]

G. A. Garcia, L. Nahon, and I. Powis, “Two-dimensional charged particle image inversion using a polar basis function expansion,” Rev. Sci. Instrum. 75, 4989–4996 (2004).

[CrossRef]

H. R. Griem, Principles of Plasma Spectroscopy (Cambridge University Press, 1997).

[CrossRef]

F. Magnus and J. T. Gudmundsson, “Digital smoothing of the Langmuir probe I-V characteristic,” Rev. Sci. Instrum. 79, 073503 (2008).

[CrossRef]
[PubMed]

J. I. Fernández Palop, J. Ballesteros, V. Colomer, and M. A. Hernández, “A new smoothing method for obtaining the electron energy distribution function in plasmas by the numerical differentiation of the I-V probe characteristic,” Rev. Sci. Instrum. 66, 4625–4636 (1995).

[CrossRef]

G. C.-Y. Chan and G. M. Hieftje, “Estimation of confidence intervals for radial emissivity and optimization of data treatment techniques in Abel inversion,” Spectrochim. Acta B 61, 31–41 (2006).

[CrossRef]

M. J. Buie, J. T. P. Pender, J. P. Holloway, T. Vincent, P. L. G. Ventzek, and M. L. Brake, “Abel’s inversion applied to experimental spectroscopic data with off axis peaks,” J. Quant. Spectrosc. Radiat. Transfer 55, 231–243 (1996).

[CrossRef]

L. M. Smith, D. R. Keefer, and S. I. Sudharsanan, “Abel inversion using transform techniques,” J. Quant. Spectrosc. Radiat. Transfer 39, 367–373 (1988).

[CrossRef]

G. N. Minerbo and M. E. Levy, “Inversion of Abel’s integral equation by means of orthogonal polynomials,” SIAM J. Numer. Anal. 6, 598–616 (1969).

[CrossRef]

S. Ma, H. Gao, L. Wu, and G. Zhang, “Abel inversion using Legendre polynomials approximations,” J. Quant. Spectrosc. Radiat. Transfer 109, 1745–1757 (2008).

[CrossRef]

S. Ma, H. Gao, G. Zhang, and L. Wu, “A versatile analytical expression for the inverse Abel transform applied to experimental data with noise,” Appl. Spectrosc. 62, 701–707(2008).

[CrossRef]
[PubMed]

S. Ma, H. Gao, and L. Wu, “Modified Fourier-Hankel method based on analysis of errors in Abel inversion using Fourier transform techniques,” Appl. Opt. 47, 1350–1357 (2008).

[CrossRef]
[PubMed]

F. Magnus and J. T. Gudmundsson, “Digital smoothing of the Langmuir probe I-V characteristic,” Rev. Sci. Instrum. 79, 073503 (2008).

[CrossRef]
[PubMed]

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of Abel-transformable images: the Gaussian basis-set expansion Abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).

[CrossRef]

G. N. Minerbo and M. E. Levy, “Inversion of Abel’s integral equation by means of orthogonal polynomials,” SIAM J. Numer. Anal. 6, 598–616 (1969).

[CrossRef]

G. A. Garcia, L. Nahon, and I. Powis, “Two-dimensional charged particle image inversion using a polar basis function expansion,” Rev. Sci. Instrum. 75, 4989–4996 (2004).

[CrossRef]

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice-Hall, 1996).

O. H. Nestor and H. N. Olsen, “Numerical methods for reducing line and surface probe data,” SIAM Rev. 2, 200–207(1960).

[CrossRef]

O. H. Nestor and H. N. Olsen, “Numerical methods for reducing line and surface probe data,” SIAM Rev. 2, 200–207(1960).

[CrossRef]

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice-Hall, 1996).

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of Abel-transformable images: the Gaussian basis-set expansion Abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).

[CrossRef]

J. I. Fernández Palop, J. Ballesteros, V. Colomer, and M. A. Hernández, “A new smoothing method for obtaining the electron energy distribution function in plasmas by the numerical differentiation of the I-V probe characteristic,” Rev. Sci. Instrum. 66, 4625–4636 (1995).

[CrossRef]

M. J. Buie, J. T. P. Pender, J. P. Holloway, T. Vincent, P. L. G. Ventzek, and M. L. Brake, “Abel’s inversion applied to experimental spectroscopic data with off axis peaks,” J. Quant. Spectrosc. Radiat. Transfer 55, 231–243 (1996).

[CrossRef]

R. Piche, “Noise-filtering properties of numerical methods for the inverse Abel transform,” IEEE Trans. Instrum. Meas. 41, 517–522 (1992).

[CrossRef]

G. A. Garcia, L. Nahon, and I. Powis, “Two-dimensional charged particle image inversion using a polar basis function expansion,” Rev. Sci. Instrum. 75, 4989–4996 (2004).

[CrossRef]

R. Álvarez, A. Rodero, and M. C. Quintero, “An Abel inversion method for radially resolved measurements in the axial injection torch,” Spectrochim. Acta B 57, 1665–1680(2002).

[CrossRef]

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of Abel-transformable images: the Gaussian basis-set expansion Abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).

[CrossRef]

R. Álvarez, A. Rodero, and M. C. Quintero, “An Abel inversion method for radially resolved measurements in the axial injection torch,” Spectrochim. Acta B 57, 1665–1680(2002).

[CrossRef]

G. E. Andrews, R. Askey, and R. Roy, Special Functions(Cambridge University Press, 1999).

L. M. Smith, “Nonstationary noise effects in the Abel inversion,” IEEE Trans. Inf. Theory 34, 158–161 (1988).

[CrossRef]

L. M. Smith, D. R. Keefer, and S. I. Sudharsanan, “Abel inversion using transform techniques,” J. Quant. Spectrosc. Radiat. Transfer 39, 367–373 (1988).

[CrossRef]

L. M. Smith, D. R. Keefer, and S. I. Sudharsanan, “Abel inversion using transform techniques,” J. Quant. Spectrosc. Radiat. Transfer 39, 367–373 (1988).

[CrossRef]

M. J. Buie, J. T. P. Pender, J. P. Holloway, T. Vincent, P. L. G. Ventzek, and M. L. Brake, “Abel’s inversion applied to experimental spectroscopic data with off axis peaks,” J. Quant. Spectrosc. Radiat. Transfer 55, 231–243 (1996).

[CrossRef]

M. J. Buie, J. T. P. Pender, J. P. Holloway, T. Vincent, P. L. G. Ventzek, and M. L. Brake, “Abel’s inversion applied to experimental spectroscopic data with off axis peaks,” J. Quant. Spectrosc. Radiat. Transfer 55, 231–243 (1996).

[CrossRef]

G. N. Watson, Theory of Bessel Functions (Cambridge University Press, 1966).

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice-Hall, 1996).

S. Ma, H. Gao, G. Zhang, and L. Wu, “A versatile analytical expression for the inverse Abel transform applied to experimental data with noise,” Appl. Spectrosc. 62, 701–707(2008).

[CrossRef]
[PubMed]

S. Ma, H. Gao, and L. Wu, “Modified Fourier-Hankel method based on analysis of errors in Abel inversion using Fourier transform techniques,” Appl. Opt. 47, 1350–1357 (2008).

[CrossRef]
[PubMed]

S. Ma, H. Gao, L. Wu, and G. Zhang, “Abel inversion using Legendre polynomials approximations,” J. Quant. Spectrosc. Radiat. Transfer 109, 1745–1757 (2008).

[CrossRef]

S. Ma, H. Gao, L. Wu, and G. Zhang, “Abel inversion using Legendre polynomials approximations,” J. Quant. Spectrosc. Radiat. Transfer 109, 1745–1757 (2008).

[CrossRef]

S. Ma, H. Gao, G. Zhang, and L. Wu, “A versatile analytical expression for the inverse Abel transform applied to experimental data with noise,” Appl. Spectrosc. 62, 701–707(2008).

[CrossRef]
[PubMed]

C. J. Cremers and R. C. Birkebak, “Application of the Abel integral equation to spectrographic data,” Appl. Opt. 5, 1057–1064 (1966).

[CrossRef]
[PubMed]

M. Kalal and K. A. Nugent, “Abel inversion using fast Fourier transforms,” Appl. Opt. 27, 1956–1959 (1988).

[CrossRef]
[PubMed]

S. Ma, H. Gao, and L. Wu, “Modified Fourier-Hankel method based on analysis of errors in Abel inversion using Fourier transform techniques,” Appl. Opt. 47, 1350–1357 (2008).

[CrossRef]
[PubMed]

C. J. Dasch, “One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered backprojection methods,” Appl. Opt. 31, 1146–1152 (1992).

[CrossRef]
[PubMed]

P. S. Kolhe and A. K. Agrawal, “Abel inversion of deflectometric data: comparison of accuracy and noise propagation of existing techniques,” Appl. Opt. 48, 3894–3902(2009).

[CrossRef]
[PubMed]

L. M. Smith, “Nonstationary noise effects in the Abel inversion,” IEEE Trans. Inf. Theory 34, 158–161 (1988).

[CrossRef]

R. Piche, “Noise-filtering properties of numerical methods for the inverse Abel transform,” IEEE Trans. Instrum. Meas. 41, 517–522 (1992).

[CrossRef]

S. Ma, H. Gao, L. Wu, and G. Zhang, “Abel inversion using Legendre polynomials approximations,” J. Quant. Spectrosc. Radiat. Transfer 109, 1745–1757 (2008).

[CrossRef]

L. M. Smith, D. R. Keefer, and S. I. Sudharsanan, “Abel inversion using transform techniques,” J. Quant. Spectrosc. Radiat. Transfer 39, 367–373 (1988).

[CrossRef]

M. J. Buie, J. T. P. Pender, J. P. Holloway, T. Vincent, P. L. G. Ventzek, and M. L. Brake, “Abel’s inversion applied to experimental spectroscopic data with off axis peaks,” J. Quant. Spectrosc. Radiat. Transfer 55, 231–243 (1996).

[CrossRef]

F. Magnus and J. T. Gudmundsson, “Digital smoothing of the Langmuir probe I-V characteristic,” Rev. Sci. Instrum. 79, 073503 (2008).

[CrossRef]
[PubMed]

J. I. Fernández Palop, J. Ballesteros, V. Colomer, and M. A. Hernández, “A new smoothing method for obtaining the electron energy distribution function in plasmas by the numerical differentiation of the I-V probe characteristic,” Rev. Sci. Instrum. 66, 4625–4636 (1995).

[CrossRef]

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, “Reconstruction of Abel-transformable images: the Gaussian basis-set expansion Abel transform method,” Rev. Sci. Instrum. 73, 2634–2642 (2002).

[CrossRef]

G. A. Garcia, L. Nahon, and I. Powis, “Two-dimensional charged particle image inversion using a polar basis function expansion,” Rev. Sci. Instrum. 75, 4989–4996 (2004).

[CrossRef]

G. N. Minerbo and M. E. Levy, “Inversion of Abel’s integral equation by means of orthogonal polynomials,” SIAM J. Numer. Anal. 6, 598–616 (1969).

[CrossRef]

O. H. Nestor and H. N. Olsen, “Numerical methods for reducing line and surface probe data,” SIAM Rev. 2, 200–207(1960).

[CrossRef]

R. Álvarez, A. Rodero, and M. C. Quintero, “An Abel inversion method for radially resolved measurements in the axial injection torch,” Spectrochim. Acta B 57, 1665–1680(2002).

[CrossRef]

G. C.-Y. Chan and G. M. Hieftje, “Estimation of confidence intervals for radial emissivity and optimization of data treatment techniques in Abel inversion,” Spectrochim. Acta B 61, 31–41 (2006).

[CrossRef]

G. E. Andrews, R. Askey, and R. Roy, Special Functions(Cambridge University Press, 1999).

G. N. Watson, Theory of Bessel Functions (Cambridge University Press, 1966).

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice-Hall, 1996).

H. R. Griem, Principles of Plasma Spectroscopy (Cambridge University Press, 1997).

[CrossRef]

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, Vol. 3 of Combustion Science and Technology Book Series, 2nd ed. (Gordon & Breach, 1996).