Abstract

We developed a versatile method for three-dimensional shape measurement where a specific particle can be selected on the substrate and its cross-sectional shape and size can be measured. A non-contact fast measurement is possible for the particle in the resonance domain. We applied rigorous coupled-wave analysis to the particle and calculated the diffraction patterns, comparing the patterns with the experimental results to obtain the size and shape. The shape and position of the focusing spot on the scattering particle was controlled precisely. With this method, the category of the analyzable object is extended to more shapes, such as rectangles and triangles, in addition to a conventional ellipsoid.

© 2017 Optical Society of America

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References

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2016 (2)

T. Hoshino and M. Itoh, “Cross-sectional shape evaluation of a particle by scatterometry,” Opt. Commun. 359, 240–244 (2016).

Y. Wu, X. Wu, L. Yao, M. Brunel, S. Coëtmellec, D. Lebrun, G. Gréhan, and K. Cen, “3d boundary line measurement of irregular particle with digital holography,” Powder Technol. 295, 96–103 (2016).

2014 (2)

A. Kuriyama and Y. Ozaki, “Assessment of active pharmaceutical ingredient particle size in tablets by Raman chemical imaging validated using polystyrene microsphere size standards,” AAPS PharmSciTech 15(2), 375–387 (2014).
[PubMed]

H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomo-geneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14, 143–157 (2014).

2013 (1)

T. Hoshino, M. Itoh, and T. Yatagai, “Scatterometry of Slant Incidence to Isolated Scatterers for High-Density Memory,” Jpn. J. Appl. Phys. 52, 09LA05 (2013).

2012 (1)

2011 (3)

A. Abdelmonem, M. Schnaiter, P. Amsler, E. Hesse, J. Meyer, and T. Leisner, “First correlated measurements of the shape and light scattering properties of cloud particles using the new particle habit imaging and polar scattering (PHIPS) probe,” Atmos. Meas. Tech. 4, 2125–2142 (2011).

T. Nousiainen, M. Kahnert, and H. Lindqvist, “Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?” J. Quant. Spectrosc. Radiat. Transf. 112, 2213–2225 (2011).

H. E. Exner, “Stereology and 3D microscopy: useful alternatives or competitors in the quantitative analysis of microstructures?” Image Anal. Stereol. 23, 73–82 (2011).

2010 (3)

2009 (2)

T. Hoshino, S. Banerjee, M. Itoh, and T. Yatagai, “Diffraction pattern of triangular grating in the resonance domain,” J. Opt. Soc. Am. A 26(3), 715–722 (2009).
[PubMed]

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).

2008 (1)

V. Myroshnychenko, E. Carbo-Argibay, I. Pastoriza-Santos, J. Perez-Juste, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008).

2007 (4)

2004 (2)

M. Sperazza, J. N. Moore, and M. S. Hendrix, “High-resolution particle size analysis of naturally occurring very fine-grained sediment through laser diffractometry,” J. Sediment. Res. 74, 736–743 (2004).

A. Taguchi, T. Miyoshi, Y. Takaya, and S. Takahashi, “Optical 3D profilometer for in-process measurement of microsurface based on phase retrieval technique,” Precis. Eng. 28, 152–163 (2004).

2003 (1)

2001 (1)

1999 (2)

K. S. Al-Rubaie, H. N. Yoshimura, and J. D. B. de Mello, “Two-body abrasive wear of Al–SiC composites,” Wear 233, 444–454 (1999).

A. Jones, “Light scattering for particle characterization,” Prog. Energ. Combust. 25, 1–53 (1999).

1998 (1)

T. Smith, M. Irwanto, D. Haines, K. Ghiggino, and D. Millar, “Time-resolved fluorescence anisotropy measurements of the adsorption of rhodamine-b and a labelled polyelectrolyte onto colloidal silica,” Colloid Polym. Sci. 276, 1032–1037 (1998).

1994 (1)

1992 (1)

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” Applied optics and optical engineering 11, 28–39 (1992).

1991 (1)

1984 (1)

1983 (1)

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of grating diffraction E-mode polarization and losses,” J. Opt. Soc. Am. A 73, 451–455 (1983).

1981 (1)

1979 (1)

1975 (1)

Abdelmonem, A.

A. Abdelmonem, M. Schnaiter, P. Amsler, E. Hesse, J. Meyer, and T. Leisner, “First correlated measurements of the shape and light scattering properties of cloud particles using the new particle habit imaging and polar scattering (PHIPS) probe,” Atmos. Meas. Tech. 4, 2125–2142 (2011).

Al-Rubaie, K. S.

K. S. Al-Rubaie, H. N. Yoshimura, and J. D. B. de Mello, “Two-body abrasive wear of Al–SiC composites,” Wear 233, 444–454 (1999).

Amsler, P.

A. Abdelmonem, M. Schnaiter, P. Amsler, E. Hesse, J. Meyer, and T. Leisner, “First correlated measurements of the shape and light scattering properties of cloud particles using the new particle habit imaging and polar scattering (PHIPS) probe,” Atmos. Meas. Tech. 4, 2125–2142 (2011).

Banerjee, S.

Barber, P.

Berg, M. J.

Brunel, M.

Y. Wu, X. Wu, L. Yao, M. Brunel, S. Coëtmellec, D. Lebrun, G. Gréhan, and K. Cen, “3d boundary line measurement of irregular particle with digital holography,” Powder Technol. 295, 96–103 (2016).

Carbo-Argibay, E.

V. Myroshnychenko, E. Carbo-Argibay, I. Pastoriza-Santos, J. Perez-Juste, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008).

Cen, K.

Y. Wu, X. Wu, L. Yao, M. Brunel, S. Coëtmellec, D. Lebrun, G. Gréhan, and K. Cen, “3d boundary line measurement of irregular particle with digital holography,” Powder Technol. 295, 96–103 (2016).

Chakrabarti, K.

Coëtmellec, S.

Y. Wu, X. Wu, L. Yao, M. Brunel, S. Coëtmellec, D. Lebrun, G. Gréhan, and K. Cen, “3d boundary line measurement of irregular particle with digital holography,” Powder Technol. 295, 96–103 (2016).

Cole, J. B.

Creath, K.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” Applied optics and optical engineering 11, 28–39 (1992).

de Mello, J. D. B.

K. S. Al-Rubaie, H. N. Yoshimura, and J. D. B. de Mello, “Two-body abrasive wear of Al–SiC composites,” Wear 233, 444–454 (1999).

Exner, H. E.

H. E. Exner, “Stereology and 3D microscopy: useful alternatives or competitors in the quantitative analysis of microstructures?” Image Anal. Stereol. 23, 73–82 (2011).

Fowler, B. W.

Friesem, A. A.

Garcia de Abajo, F. J.

V. Myroshnychenko, E. Carbo-Argibay, I. Pastoriza-Santos, J. Perez-Juste, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008).

Gaylord, T. K.

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of grating diffraction E-mode polarization and losses,” J. Opt. Soc. Am. A 73, 451–455 (1983).

Ghiggino, K.

T. Smith, M. Irwanto, D. Haines, K. Ghiggino, and D. Millar, “Time-resolved fluorescence anisotropy measurements of the adsorption of rhodamine-b and a labelled polyelectrolyte onto colloidal silica,” Colloid Polym. Sci. 276, 1032–1037 (1998).

Golub, M. A.

Grann, E. B.

Greenberg, J. M.

Gréhan, G.

Y. Wu, X. Wu, L. Yao, M. Brunel, S. Coëtmellec, D. Lebrun, G. Gréhan, and K. Cen, “3d boundary line measurement of irregular particle with digital holography,” Powder Technol. 295, 96–103 (2016).

Grimminck, M.

A. G. Hoekstra, M. Grimminck, and P. M. Sloot, “Simulating light scattering from micron-sized particles,” in “International Conference on High-Performance Computing and Networking,” (Springer, 1996), pp. 269–275.

Gustafson, B. A. S.

Hage, J. I.

Haines, D.

T. Smith, M. Irwanto, D. Haines, K. Ghiggino, and D. Millar, “Time-resolved fluorescence anisotropy measurements of the adsorption of rhodamine-b and a labelled polyelectrolyte onto colloidal silica,” Colloid Polym. Sci. 276, 1032–1037 (1998).

Hendrix, M. S.

M. Sperazza, J. N. Moore, and M. S. Hendrix, “High-resolution particle size analysis of naturally occurring very fine-grained sediment through laser diffractometry,” J. Sediment. Res. 74, 736–743 (2004).

Hennelly, B. M.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).

Hesse, E.

A. Abdelmonem, M. Schnaiter, P. Amsler, E. Hesse, J. Meyer, and T. Leisner, “First correlated measurements of the shape and light scattering properties of cloud particles using the new particle habit imaging and polar scattering (PHIPS) probe,” Atmos. Meas. Tech. 4, 2125–2142 (2011).

Hill, S. C.

Hoekstra, A. G.

A. G. Hoekstra, M. Grimminck, and P. M. Sloot, “Simulating light scattering from micron-sized particles,” in “International Conference on High-Performance Computing and Networking,” (Springer, 1996), pp. 269–275.

Hoshino, T.

Irwanto, M.

T. Smith, M. Irwanto, D. Haines, K. Ghiggino, and D. Millar, “Time-resolved fluorescence anisotropy measurements of the adsorption of rhodamine-b and a labelled polyelectrolyte onto colloidal silica,” Colloid Polym. Sci. 276, 1032–1037 (1998).

Itoh, M.

Iwasaki, S.

Jericho, M. H.

Jokinen, O.

H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomo-geneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14, 143–157 (2014).

Jones, A.

A. Jones, “Light scattering for particle characterization,” Prog. Energ. Combust. 25, 1–53 (1999).

Kahnert, M.

T. Nousiainen, M. Kahnert, and H. Lindqvist, “Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?” J. Quant. Spectrosc. Radiat. Transf. 112, 2213–2225 (2011).

Kandler, K.

H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomo-geneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14, 143–157 (2014).

Kelly, D. P.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).

Kreuzer, H. J.

Kuriyama, A.

A. Kuriyama and Y. Ozaki, “Assessment of active pharmaceutical ingredient particle size in tablets by Raman chemical imaging validated using polystyrene microsphere size standards,” AAPS PharmSciTech 15(2), 375–387 (2014).
[PubMed]

Lebrun, D.

Y. Wu, X. Wu, L. Yao, M. Brunel, S. Coëtmellec, D. Lebrun, G. Gréhan, and K. Cen, “3d boundary line measurement of irregular particle with digital holography,” Powder Technol. 295, 96–103 (2016).

Leisner, T.

A. Abdelmonem, M. Schnaiter, P. Amsler, E. Hesse, J. Meyer, and T. Leisner, “First correlated measurements of the shape and light scattering properties of cloud particles using the new particle habit imaging and polar scattering (PHIPS) probe,” Atmos. Meas. Tech. 4, 2125–2142 (2011).

Lindqvist, H.

H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomo-geneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14, 143–157 (2014).

T. Nousiainen, M. Kahnert, and H. Lindqvist, “Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?” J. Quant. Spectrosc. Radiat. Transf. 112, 2213–2225 (2011).

Liz-Marzan, L. M.

V. Myroshnychenko, E. Carbo-Argibay, I. Pastoriza-Santos, J. Perez-Juste, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008).

Meinertzhagen, I. A.

Meyer, J.

A. Abdelmonem, M. Schnaiter, P. Amsler, E. Hesse, J. Meyer, and T. Leisner, “First correlated measurements of the shape and light scattering properties of cloud particles using the new particle habit imaging and polar scattering (PHIPS) probe,” Atmos. Meas. Tech. 4, 2125–2142 (2011).

Millar, D.

T. Smith, M. Irwanto, D. Haines, K. Ghiggino, and D. Millar, “Time-resolved fluorescence anisotropy measurements of the adsorption of rhodamine-b and a labelled polyelectrolyte onto colloidal silica,” Colloid Polym. Sci. 276, 1032–1037 (1998).

Miyoshi, T.

A. Taguchi, T. Miyoshi, Y. Takaya, and S. Takahashi, “Optical 3D profilometer for in-process measurement of microsurface based on phase retrieval technique,” Precis. Eng. 28, 152–163 (2004).

Mizusawa, M.

K. Sakurai and M. Mizusawa, “X-ray diffraction imaging of anatase and rutile,” Anal. Chem. 82(9), 3519–3522 (2010).
[PubMed]

Moharam, M. G.

D. A. Pommet, M. G. Moharam, and E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11, 1827–1834 (1994).

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of grating diffraction E-mode polarization and losses,” J. Opt. Soc. Am. A 73, 451–455 (1983).

Moore, J. N.

M. Sperazza, J. N. Moore, and M. S. Hendrix, “High-resolution particle size analysis of naturally occurring very fine-grained sediment through laser diffractometry,” J. Sediment. Res. 74, 736–743 (2004).

Myroshnychenko, V.

V. Myroshnychenko, E. Carbo-Argibay, I. Pastoriza-Santos, J. Perez-Juste, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008).

Naughton, T. J.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).

Nousiainen, T.

H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomo-geneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14, 143–157 (2014).

T. Nousiainen, M. Kahnert, and H. Lindqvist, “Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?” J. Quant. Spectrosc. Radiat. Transf. 112, 2213–2225 (2011).

T. Nousiainen, “Impact of particle shape on refractive-index dependence of scattering in resonance domain,” J. Quant. Spectrosc. Radiat. Transf. 108, 464–473 (2007).

Okamoto, H.

Ozaki, Y.

A. Kuriyama and Y. Ozaki, “Assessment of active pharmaceutical ingredient particle size in tablets by Raman chemical imaging validated using polystyrene microsphere size standards,” AAPS PharmSciTech 15(2), 375–387 (2014).
[PubMed]

Pan, Y.-L.

Pandey, N.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).

Pastoriza-Santos, I.

V. Myroshnychenko, E. Carbo-Argibay, I. Pastoriza-Santos, J. Perez-Juste, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008).

Perez-Juste, J.

V. Myroshnychenko, E. Carbo-Argibay, I. Pastoriza-Santos, J. Perez-Juste, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008).

Pommet, D. A.

Rhodes, W. T.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).

Sakurai, K.

K. Sakurai and M. Mizusawa, “X-ray diffraction imaging of anatase and rutile,” Anal. Chem. 82(9), 3519–3522 (2010).
[PubMed]

Schaefer, R. W.

Scheuvens, D.

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A. Abdelmonem, M. Schnaiter, P. Amsler, E. Hesse, J. Meyer, and T. Leisner, “First correlated measurements of the shape and light scattering properties of cloud particles using the new particle habit imaging and polar scattering (PHIPS) probe,” Atmos. Meas. Tech. 4, 2125–2142 (2011).

Schuerman, D. W.

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A. G. Hoekstra, M. Grimminck, and P. M. Sloot, “Simulating light scattering from micron-sized particles,” in “International Conference on High-Performance Computing and Networking,” (Springer, 1996), pp. 269–275.

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T. Smith, M. Irwanto, D. Haines, K. Ghiggino, and D. Millar, “Time-resolved fluorescence anisotropy measurements of the adsorption of rhodamine-b and a labelled polyelectrolyte onto colloidal silica,” Colloid Polym. Sci. 276, 1032–1037 (1998).

Sperazza, M.

M. Sperazza, J. N. Moore, and M. S. Hendrix, “High-resolution particle size analysis of naturally occurring very fine-grained sediment through laser diffractometry,” J. Sediment. Res. 74, 736–743 (2004).

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A. Taguchi, T. Miyoshi, Y. Takaya, and S. Takahashi, “Optical 3D profilometer for in-process measurement of microsurface based on phase retrieval technique,” Precis. Eng. 28, 152–163 (2004).

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Y. Wu, X. Wu, L. Yao, M. Brunel, S. Coëtmellec, D. Lebrun, G. Gréhan, and K. Cen, “3d boundary line measurement of irregular particle with digital holography,” Powder Technol. 295, 96–103 (2016).

Wu, Y.

Y. Wu, X. Wu, L. Yao, M. Brunel, S. Coëtmellec, D. Lebrun, G. Gréhan, and K. Cen, “3d boundary line measurement of irregular particle with digital holography,” Powder Technol. 295, 96–103 (2016).

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Yao, L.

Y. Wu, X. Wu, L. Yao, M. Brunel, S. Coëtmellec, D. Lebrun, G. Gréhan, and K. Cen, “3d boundary line measurement of irregular particle with digital holography,” Powder Technol. 295, 96–103 (2016).

Yatagai, T.

Yeh, C.

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K. S. Al-Rubaie, H. N. Yoshimura, and J. D. B. de Mello, “Two-body abrasive wear of Al–SiC composites,” Wear 233, 444–454 (1999).

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A. Kuriyama and Y. Ozaki, “Assessment of active pharmaceutical ingredient particle size in tablets by Raman chemical imaging validated using polystyrene microsphere size standards,” AAPS PharmSciTech 15(2), 375–387 (2014).
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V. Myroshnychenko, E. Carbo-Argibay, I. Pastoriza-Santos, J. Perez-Juste, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Modeling the optical response of highly faceted metal nanoparticles with a fully 3D boundary element method,” Adv. Mater. 20, 4288–4293 (2008).

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Applied optics and optical engineering (1)

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H. Lindqvist, O. Jokinen, K. Kandler, D. Scheuvens, and T. Nousiainen, “Single scattering by realistic, inhomo-geneous mineral dust particles with stereogrammetric shapes,” Atmos. Chem. Phys. 14, 143–157 (2014).

Atmos. Meas. Tech. (1)

A. Abdelmonem, M. Schnaiter, P. Amsler, E. Hesse, J. Meyer, and T. Leisner, “First correlated measurements of the shape and light scattering properties of cloud particles using the new particle habit imaging and polar scattering (PHIPS) probe,” Atmos. Meas. Tech. 4, 2125–2142 (2011).

Colloid Polym. Sci. (1)

T. Smith, M. Irwanto, D. Haines, K. Ghiggino, and D. Millar, “Time-resolved fluorescence anisotropy measurements of the adsorption of rhodamine-b and a labelled polyelectrolyte onto colloidal silica,” Colloid Polym. Sci. 276, 1032–1037 (1998).

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H. E. Exner, “Stereology and 3D microscopy: useful alternatives or competitors in the quantitative analysis of microstructures?” Image Anal. Stereol. 23, 73–82 (2011).

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T. Nousiainen, M. Kahnert, and H. Lindqvist, “Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?” J. Quant. Spectrosc. Radiat. Transf. 112, 2213–2225 (2011).

T. Nousiainen, “Impact of particle shape on refractive-index dependence of scattering in resonance domain,” J. Quant. Spectrosc. Radiat. Transf. 108, 464–473 (2007).

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M. Sperazza, J. N. Moore, and M. S. Hendrix, “High-resolution particle size analysis of naturally occurring very fine-grained sediment through laser diffractometry,” J. Sediment. Res. 74, 736–743 (2004).

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T. Hoshino, M. Itoh, and T. Yatagai, “Scatterometry of Slant Incidence to Isolated Scatterers for High-Density Memory,” Jpn. J. Appl. Phys. 52, 09LA05 (2013).

Opt. Commun. (1)

T. Hoshino and M. Itoh, “Cross-sectional shape evaluation of a particle by scatterometry,” Opt. Commun. 359, 240–244 (2016).

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D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).

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Y. Wu, X. Wu, L. Yao, M. Brunel, S. Coëtmellec, D. Lebrun, G. Gréhan, and K. Cen, “3d boundary line measurement of irregular particle with digital holography,” Powder Technol. 295, 96–103 (2016).

Precis. Eng. (1)

A. Taguchi, T. Miyoshi, Y. Takaya, and S. Takahashi, “Optical 3D profilometer for in-process measurement of microsurface based on phase retrieval technique,” Precis. Eng. 28, 152–163 (2004).

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A. Jones, “Light scattering for particle characterization,” Prog. Energ. Combust. 25, 1–53 (1999).

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K. S. Al-Rubaie, H. N. Yoshimura, and J. D. B. de Mello, “Two-body abrasive wear of Al–SiC composites,” Wear 233, 444–454 (1999).

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Figures (19)

Fig. 1
Fig. 1 Lens-particle distances fp1, fp2 and the diffraction patterns on the screen.
Fig. 2
Fig. 2 Scattering measurement by using an Ar laser (488 nm): fp is the distance between the lens and particle.
Fig. 3
Fig. 3 Scattering patterns of the particles: (a) Particles P2, P3, P4, and P5. (b) Zoomed up P2. (c) Iris diaphragm applied to P2. (d) Slit and iris diaphragm applied to P2.
Fig. 4
Fig. 4 Scattering patterns of particle P2, to which the slit and iris diaphragm are applied. The focusing lens was moved from P2. The analyzed part for angular distribution is indicated by dotted line. The bright area at the right hand of each picture is the strayed beam of light source.
Fig. 5
Fig. 5 Scheme of the optical system for simulation. Diffraction angle is θd.
Fig. 6
Fig. 6 Scattering pattern and its analysis simulated using RCWA for a square. [ fz = fp] (a) Scattering pattern with width w = 6λ and distance fz = 45λ, and (b) its contrast analysis by Imax/Imin for different fz.
Fig. 7
Fig. 7 Horizontal projection profile of the diffraction pattern of particle P1. θi = 0°, 15°, 30°, and 45°.
Fig. 8
Fig. 8 Optical system of simulation for three types of particles. Particles and a substrate have same refractive index of 1.5.
Fig. 9
Fig. 9 Diffraction pattern of the particles with different incident angles. The widths and aspect ratio of the particles are changed. (a) The ellipsoidal particle has a width of 3λ and aspect ratio of 0.4. (b) The rectangular particle has a width of 3λ and aspect ratio of 0.2. (c) The triangular particle has a width of 5λ and aspect ratio of 0.2.
Fig. 10
Fig. 10 Horizontal projection profiles of the diffraction patterns of particles P2–P5; θi = 0°.
Fig. 11
Fig. 11 Structures of the particles. The order of the images is—cross section, projected image, and microscopic image—from left to right. Cross sectional shape is added to the projected left images. The widths for four directions are indicated by bidirectional arrows in the middle images.
Fig. 12
Fig. 12 The electric field of lens focusing in xz plane for TE mode. A lens and a square particle are indicated by dotted gray line.
Fig. 13
Fig. 13 Contrast derived from scattering pattern simulated using RCWA for a triangle. w = 2λ, 6λ and 10λ.
Fig. 14
Fig. 14 Contrast derived from scattering pattern simulated using RCWA for a circle. w = 2λ, 6λ and 10λ.
Fig. 15
Fig. 15 The diffraction pattern of a circular particle. The unit is λ. (a)(b)(c)(d) Polarization, h and w are varied.
Fig. 16
Fig. 16 The diffraction pattern of a triangular particle with different aspect ratio. Polarization is TM. (a) rasp = 0.2. (b) rasp = 0.6. (c) rasp = 1.0.
Fig. 17
Fig. 17 The diffraction pattern of a rectangular particle with different aspect ratio. Polarization is TM. (a) rasp = 0.2. (b) rasp = 0.6. (c) rasp = 1.0.
Fig. 18
Fig. 18 The diffraction pattern of an ellipsoidal particle with different aspect ratio. Polarization is TM. (a) rasp = 0.2. (b) rasp = 0.6. (c) rasp = 1.0.
Fig. 19
Fig. 19 The diffraction pattern of a rectangular particle with different aspect ratio. Polarization is TM. (a) w = 10λ. (b) w = 20λ.

Tables (2)

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Table 1 Criterion to judge the shape and aspect ratio from the diffraction pattern

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Table 2 Number of peaks. −50° < θd - θi < 0°. The width of particle is 20λ.

Equations (1)

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w = mλ÷[ n 0 sin ( θ ) ]

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