B. Andreas, G. Mana, and C. Palmisano, “Vectorial ray-based diffraction integral,” J. Opt. Soc. Am. A 32, 1403–1424 (2015).

[Crossref]

J. E. Harvey, R. G. Irvin, and R. N. Pfisterer, “Modeling physical optics phenomena by complex ray tracing,” Opt. Eng. 54, 035105 (2015).

[Crossref]

J. Goldfeather and V. Interrante, “A novel cubic-order algorithm for approximating principal direction vectors,” ACM Trans. Graph. 23, 45–63 (2004).

[Crossref]

A. Rohani, A. Shishegar, and S. Safavi-Naeini, “A fast Gaussian beam tracing method for reflection and refraction of general vectorial astigmatic Gaussian beams from general curved surfaces,” Opt. Commun. 232, 1–10 (2004).

[Crossref]

M. J. Bastiaans, “Gabor’s signal expansion based on a nonorthogonal sampling geometry,” Proc. SPIE 4392, 46–59 (2001).

[Crossref]

M. Cywiak, M. Servín, and F. M. Santoyo, “Wave-front propagation by Gaussian superposition,” Opt. Commun. 195, 351–359 (2001).

[Crossref]

M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2093 (1986).

[Crossref]

A. W. Greynolds, “Vector formulation of the ray-equivalent method for general Gaussian beam propagation,” Proc. SPIE 679, 129–134 (1986).

[Crossref]

A. W. Greynolds, “Propagation of generally astigmatic Gaussian beams along skew ray paths,” Proc. SPIE 560, 33–52 (1986).

[Crossref]

P. Einziger, S. Raz, and M. Shapira, “Gabor representation and aperture theory,” J. Opt. Soc. Am. A 3, 508–522 (1986).

[Crossref]

J. Arnaud, “Nonorthogonal optical waveguides and resonators,” Bell Labs Tech. J. 49, 2311–2348 (1970).

[Crossref]

M. J. Bastiaans, “Gabor’s signal expansion based on a nonorthogonal sampling geometry,” Proc. SPIE 4392, 46–59 (2001).

[Crossref]

M. J. Bastiaans, “The expansion of an optical signal into a discrete set of Gaussian beams,” in Erzeugung und Analyse von Bildern und Strukturen (Springer, 1980), pp. 23–32.

B. Stone and T. Bruegge, “Practical considerations for simulating beam propagation: a comparison of three approaches,” in International Optical Design Conference (Optical Society of America, 2002), paper IWA3.

H. T. Tanaka, M. Ikeda, and H. Chiaki, “Curvature-based face surface recognition using spherical correlation. Principal directions for curved object recognition,” in 3rd IEEE International Conference on Automatic Face and Gesture Recognition (IEEE, 1998), pp. 372–377.

M. Cywiak, M. Servín, and A. Morales, “Diffractive and geometric optical systems characterization with the Fresnel Gaussian shape invariant,” Opt. Express 19, 1892–1904 (2011).

[Crossref]

M. Cywiak, A. Morales, M. Servín, and R. Gómez-Medina, “A technique for calculating the amplitude distribution of propagated fields by Gaussian sampling,” Opt. Express 18, 19141–19155 (2010).

[Crossref]

M. Cywiak, M. Servín, and F. M. Santoyo, “Wave-front propagation by Gaussian superposition,” Opt. Commun. 195, 351–359 (2001).

[Crossref]

G. E. Fasshauer, Meshfree Approximation Methods with MATLAB (World Scientific, 2007).

J. Goldfeather and V. Interrante, “A novel cubic-order algorithm for approximating principal direction vectors,” ACM Trans. Graph. 23, 45–63 (2004).

[Crossref]

A. Goshtasby and D. Schonfeld, “Signal representation based on a Gaussian decomposition,” in Proceedings of the 1991 Conference Information Sciences and System (1991), pp. 1–6.

A. W. Greynolds, “Propagation of generally astigmatic Gaussian beams along skew ray paths,” Proc. SPIE 560, 33–52 (1986).

[Crossref]

A. W. Greynolds, “Vector formulation of the ray-equivalent method for general Gaussian beam propagation,” Proc. SPIE 679, 129–134 (1986).

[Crossref]

A. W. Greynolds, “Fat rays revisited: a synthesis of physical and geometrical optics with Gaußlets,” in International Optical Design Conference (Optical Society of America, 2014), paper ITu1A.3.

J. E. Harvey, R. G. Irvin, and R. N. Pfisterer, “Modeling physical optics phenomena by complex ray tracing,” Opt. Eng. 54, 035105 (2015).

[Crossref]

H. T. Tanaka, M. Ikeda, and H. Chiaki, “Curvature-based face surface recognition using spherical correlation. Principal directions for curved object recognition,” in 3rd IEEE International Conference on Automatic Face and Gesture Recognition (IEEE, 1998), pp. 372–377.

J. Goldfeather and V. Interrante, “A novel cubic-order algorithm for approximating principal direction vectors,” ACM Trans. Graph. 23, 45–63 (2004).

[Crossref]

J. E. Harvey, R. G. Irvin, and R. N. Pfisterer, “Modeling physical optics phenomena by complex ray tracing,” Opt. Eng. 54, 035105 (2015).

[Crossref]

F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt. 58, 449–466 (2011).

[Crossref]

X. Li, Z. Li, and Z. Zeng, “Curvature analysis and geometric description of landforms using MATLAB,” in International Conference on Environmental Science and Information Application Technology (ESIAT) (IEEE, 2010), Vol. 1, pp. 712–715.

X. Li, Z. Li, and Z. Zeng, “Curvature analysis and geometric description of landforms using MATLAB,” in International Conference on Environmental Science and Information Application Technology (ESIAT) (IEEE, 2010), Vol. 1, pp. 712–715.

M. Cywiak, M. Servín, and A. Morales, “Diffractive and geometric optical systems characterization with the Fresnel Gaussian shape invariant,” Opt. Express 19, 1892–1904 (2011).

[Crossref]

M. Cywiak, A. Morales, M. Servín, and R. Gómez-Medina, “A technique for calculating the amplitude distribution of propagated fields by Gaussian sampling,” Opt. Express 18, 19141–19155 (2010).

[Crossref]

J. E. Harvey, R. G. Irvin, and R. N. Pfisterer, “Modeling physical optics phenomena by complex ray tracing,” Opt. Eng. 54, 035105 (2015).

[Crossref]

A. Rohani, A. Shishegar, and S. Safavi-Naeini, “A fast Gaussian beam tracing method for reflection and refraction of general vectorial astigmatic Gaussian beams from general curved surfaces,” Opt. Commun. 232, 1–10 (2004).

[Crossref]

A. Rohani, A. Shishegar, and S. Safavi-Naeini, “A fast Gaussian beam tracing method for reflection and refraction of general vectorial astigmatic Gaussian beams from general curved surfaces,” Opt. Commun. 232, 1–10 (2004).

[Crossref]

M. Cywiak, M. Servín, and F. M. Santoyo, “Wave-front propagation by Gaussian superposition,” Opt. Commun. 195, 351–359 (2001).

[Crossref]

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE, 2010).

A. Goshtasby and D. Schonfeld, “Signal representation based on a Gaussian decomposition,” in Proceedings of the 1991 Conference Information Sciences and System (1991), pp. 1–6.

M. Cywiak, M. Servín, and A. Morales, “Diffractive and geometric optical systems characterization with the Fresnel Gaussian shape invariant,” Opt. Express 19, 1892–1904 (2011).

[Crossref]

M. Cywiak, A. Morales, M. Servín, and R. Gómez-Medina, “A technique for calculating the amplitude distribution of propagated fields by Gaussian sampling,” Opt. Express 18, 19141–19155 (2010).

[Crossref]

M. Cywiak, M. Servín, and F. M. Santoyo, “Wave-front propagation by Gaussian superposition,” Opt. Commun. 195, 351–359 (2001).

[Crossref]

A. Rohani, A. Shishegar, and S. Safavi-Naeini, “A fast Gaussian beam tracing method for reflection and refraction of general vectorial astigmatic Gaussian beams from general curved surfaces,” Opt. Commun. 232, 1–10 (2004).

[Crossref]

B. Stone and T. Bruegge, “Practical considerations for simulating beam propagation: a comparison of three approaches,” in International Optical Design Conference (Optical Society of America, 2002), paper IWA3.

H. T. Tanaka, M. Ikeda, and H. Chiaki, “Curvature-based face surface recognition using spherical correlation. Principal directions for curved object recognition,” in 3rd IEEE International Conference on Automatic Face and Gesture Recognition (IEEE, 1998), pp. 372–377.

F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt. 58, 449–466 (2011).

[Crossref]

X. Li, Z. Li, and Z. Zeng, “Curvature analysis and geometric description of landforms using MATLAB,” in International Conference on Environmental Science and Information Application Technology (ESIAT) (IEEE, 2010), Vol. 1, pp. 712–715.

J. Goldfeather and V. Interrante, “A novel cubic-order algorithm for approximating principal direction vectors,” ACM Trans. Graph. 23, 45–63 (2004).

[Crossref]

J. Stock, A. Broemel, J. Hartung, D. Ochse, and H. Gross, “Description and reimplementation of real freeform surfaces,” Appl. Opt. 56, 391–396 (2017).

[Crossref]

J. Arnaud, “Representation of Gaussian beams by complex rays,” Appl. Opt. 24, 538–543 (1985).

[Crossref]

J. Arnaud, “Nonorthogonal optical waveguides and resonators,” Bell Labs Tech. J. 49, 2311–2348 (1970).

[Crossref]

F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt. 58, 449–466 (2011).

[Crossref]

B. Andreas, G. Mana, and C. Palmisano, “Vectorial ray-based diffraction integral,” J. Opt. Soc. Am. A 32, 1403–1424 (2015).

[Crossref]

P. Einziger, S. Raz, and M. Shapira, “Gabor representation and aperture theory,” J. Opt. Soc. Am. A 3, 508–522 (1986).

[Crossref]

E. Şahin and L. Onural, “Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition,” J. Opt. Soc. Am. A 29, 1459–1469 (2012).

[Crossref]

E. Şahin and L. Onural, “Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams,” J. Opt. Soc. Am. A 30, 527–536 (2013).

[Crossref]

M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2093 (1986).

[Crossref]

M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives: erratum Certain computational aspects of vector diffraction problems: erratum,” J. Opt. Soc. Am. A 10, 382–383 (1993).

[Crossref]

M. Cywiak, M. Servín, and F. M. Santoyo, “Wave-front propagation by Gaussian superposition,” Opt. Commun. 195, 351–359 (2001).

[Crossref]

A. Rohani, A. Shishegar, and S. Safavi-Naeini, “A fast Gaussian beam tracing method for reflection and refraction of general vectorial astigmatic Gaussian beams from general curved surfaces,” Opt. Commun. 232, 1–10 (2004).

[Crossref]

J. E. Harvey, R. G. Irvin, and R. N. Pfisterer, “Modeling physical optics phenomena by complex ray tracing,” Opt. Eng. 54, 035105 (2015).

[Crossref]

M. Cywiak, M. Servín, and A. Morales, “Diffractive and geometric optical systems characterization with the Fresnel Gaussian shape invariant,” Opt. Express 19, 1892–1904 (2011).

[Crossref]

M. Cywiak, A. Morales, M. Servín, and R. Gómez-Medina, “A technique for calculating the amplitude distribution of propagated fields by Gaussian sampling,” Opt. Express 18, 19141–19155 (2010).

[Crossref]

A. W. Greynolds, “Vector formulation of the ray-equivalent method for general Gaussian beam propagation,” Proc. SPIE 679, 129–134 (1986).

[Crossref]

M. J. Bastiaans, “Gabor’s signal expansion based on a nonorthogonal sampling geometry,” Proc. SPIE 4392, 46–59 (2001).

[Crossref]

A. W. Greynolds, “Propagation of generally astigmatic Gaussian beams along skew ray paths,” Proc. SPIE 560, 33–52 (1986).

[Crossref]

A. W. Greynolds, “Fat rays revisited: a synthesis of physical and geometrical optics with Gaußlets,” in International Optical Design Conference (Optical Society of America, 2014), paper ITu1A.3.

B. Stone and T. Bruegge, “Practical considerations for simulating beam propagation: a comparison of three approaches,” in International Optical Design Conference (Optical Society of America, 2002), paper IWA3.

G. E. Fasshauer, Meshfree Approximation Methods with MATLAB (World Scientific, 2007).

A. Goshtasby and D. Schonfeld, “Signal representation based on a Gaussian decomposition,” in Proceedings of the 1991 Conference Information Sciences and System (1991), pp. 1–6.

M. J. Bastiaans, “The expansion of an optical signal into a discrete set of Gaussian beams,” in Erzeugung und Analyse von Bildern und Strukturen (Springer, 1980), pp. 23–32.

H. T. Tanaka, M. Ikeda, and H. Chiaki, “Curvature-based face surface recognition using spherical correlation. Principal directions for curved object recognition,” in 3rd IEEE International Conference on Automatic Face and Gesture Recognition (IEEE, 1998), pp. 372–377.

X. Li, Z. Li, and Z. Zeng, “Curvature analysis and geometric description of landforms using MATLAB,” in International Conference on Environmental Science and Information Application Technology (ESIAT) (IEEE, 2010), Vol. 1, pp. 712–715.

J. D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE, 2010).