Abstract

We have developed a differential form of singularimetry, which utilizes phase vortices or intensity gradient singularities as topological fiducial markers in a structured illumination context. This approach analytically measures phase gradients imparted by refracting specimens, yielding quantitative information that is both local and deterministic. We have quantified our phase gradient experiments to demonstrate that lattices of wave field singularities can be used to detect subtle phase gradients imparted by a spherical specimen and fiber optic cylinders.

© 2016 Optical Society of America

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References

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  47. T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, “TEM-based phase retrieval of p-n junction wafers using the transport of intensity equation,” Philos. Mag. 87(24), 3565–3578 (2007).
    [Crossref]
  48. A. Parvizi, J. Müller, S. A. Funken, and C. T. Koch, “A practical way to resolve ambiguities in wavefront reconstructions by the transport of intensity equation,” Ultramicroscopy 154, 1–6 (2015).
    [Crossref] [PubMed]
  49. J. C. Petruccelli, L. Tian, and G. Barbastathis, “The transport of intensity equation for optical path length recovery using partially coherent illumination,” Opt. Express 21(12), 14430–14441 (2013).
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2015 (2)

C. Dwyer, C. B. Boothroyd, S. L. Y. Chang, and R. E. Dunin-Borkowski, “Three-wave electron vortex lattices for measuring nanofields,” Ultramicroscopy 148, 25–30 (2015).
[Crossref] [PubMed]

A. Parvizi, J. Müller, S. A. Funken, and C. T. Koch, “A practical way to resolve ambiguities in wavefront reconstructions by the transport of intensity equation,” Ultramicroscopy 154, 1–6 (2015).
[Crossref] [PubMed]

2014 (1)

T. Niermann, J. Verbeeck, and M. Lehmann, “Creating arrays of electron vortices,” Ultramicroscopy 136, 165–170 (2014).
[Crossref] [PubMed]

2013 (5)

T. C. Petersen, M. Weyland, D. M. Paganin, T. P. Simula, S. A. Eastwood, and M. J. Morgan, “Electron vortex production and control using aberration induced diffraction catastrophes,” Phys. Rev. Lett. 110(3), 033901 (2013).
[Crossref] [PubMed]

H. C. Huang, B. J. Chang, L. J. Chou, and S. Y. Chiang, “Three-beam interference with circular polarization for structured illumination microscopy,” Opt. Express 21(20), 23963–23977 (2013).
[Crossref] [PubMed]

M. R. Dennis and J. B. Götte, “Beam shifts for pairs of plane waves,” J. Opt. 15(1), 014015 (2013).
[Crossref]

A. Popiołek-Masajada, M. Borwińska, T. Przerwa-Tetmajer, and P. Kurzynowski, “Application of the Fourier analysis methods to the three beam interferometry,” Opt. Laser Technol. 48, 503–508 (2013).
[Crossref]

J. C. Petruccelli, L. Tian, and G. Barbastathis, “The transport of intensity equation for optical path length recovery using partially coherent illumination,” Opt. Express 21(12), 14430–14441 (2013).
[Crossref] [PubMed]

2012 (3)

D. R. G. Mitchell and T. C. Petersen, “RDFTools: A software tool for quantifying short-range ordering in amorphous materials,” Microsc. Res. Tech. 75(2), 153–163 (2012).
[Crossref] [PubMed]

S. A. Eastwood, A. I. Bishop, T. C. Petersen, D. M. Paganin, and M. J. Morgan, “Phase measurement using an optical vortex lattice produced with a three-beam interferometer,” Opt. Express 20(13), 13947–13957 (2012).
[Crossref] [PubMed]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100(12), 124102 (2012).
[Crossref]

2011 (3)

2010 (3)

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[Crossref]

G. Gbur and T. D. Visser, “The structure of partially coherent fields,” Prog. Opt. 55, 285–341 (2010).
[Crossref]

T. Brunet, J. L. Thomas, and R. Marchiano, “Transverse shift of helical beams and subdiffraction imaging,” Phys. Rev. Lett. 105(3), 034301 (2010).
[Crossref] [PubMed]

2009 (3)

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

M. V. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11(9), 094001 (2009).
[Crossref]

M. V. Berry and M. R. Dennis, “Natural superoscillations in monochromatic waves in D dimensions,” J. Phys. A Math. Theor. 42(2), 022003 (2009).
[Crossref]

2008 (1)

2007 (2)

A. Popiołek-Masajada, M. Borwińska, and B. Dubik, “Reconstruction of a plane wave’s tilt and orientation using an optical vortex interferometer,” Opt. Eng. 46(7), 073604 (2007).
[Crossref]

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, “TEM-based phase retrieval of p-n junction wafers using the transport of intensity equation,” Philos. Mag. 87(24), 3565–3578 (2007).
[Crossref]

2006 (1)

2005 (3)

2004 (2)

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[Crossref] [PubMed]

J. Masajada, “Small-angle rotations measurement using optical vortex interferometer,” Opt. Commun. 239(4-6), 373–381 (2004).
[Crossref]

2003 (1)

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mater. 15(18), 1526–1528 (2003).
[Crossref]

2001 (4)

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198(1-3), 21–27 (2001).
[Crossref]

J. H. Massig, “Deformation measurement on specular surfaces by simple means,” Opt. Eng. 40(10), 2315–2318 (2001).
[Crossref]

J. H. Massig and J. Heppner, “Fringe-pattern analysis with high accuracy by use of the fourier-transform method: theory and experimental tests,” Appl. Opt. 40(13), 2081–2088 (2001).
[Crossref] [PubMed]

2000 (1)

C. D. Perciante, J. A. Ferrari, and A. Dubra, “Visualization of phase objects using incoherent illumination,” Opt. Commun. 183(1-4), 15–18 (2000).
[Crossref]

1999 (1)

1997 (2)

D. Rozas, C. T. Law, and G. A. Swartzlander., “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14(11), 3054–3065 (1997).
[Crossref]

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8(6), 601–605 (1997).
[Crossref]

1995 (1)

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

1994 (1)

T. Lindeberg, “Scale-space theory: A basic tool for analysing structures at different scales,” J. Appl. Stat. 21(1), 224–270 (1994).
[Crossref]

1987 (1)

K. W. Nicholls and J. F. Nye, “3-beam model for studying dislocations in wave pulses,” J. Phys. Math. Gen. 20(14), 4673–4696 (1987).
[Crossref]

1983 (1)

1982 (1)

1971 (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

1968 (1)

1967 (1)

1965 (1)

Altmeyer, S.

Ampem-Lassen, E.

Barbastathis, G.

Barty, A.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[Crossref] [PubMed]

Baxter, G. W.

Bernet, S.

Berry, M. V.

M. V. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11(9), 094001 (2009).
[Crossref]

M. V. Berry and M. R. Dennis, “Natural superoscillations in monochromatic waves in D dimensions,” J. Phys. A Math. Theor. 42(2), 022003 (2009).
[Crossref]

Bishop, A. I.

Boothroyd, C. B.

C. Dwyer, C. B. Boothroyd, S. L. Y. Chang, and R. E. Dunin-Borkowski, “Three-wave electron vortex lattices for measuring nanofields,” Ultramicroscopy 148, 25–30 (2015).
[Crossref] [PubMed]

Borwinska, M.

A. Popiołek-Masajada, M. Borwińska, T. Przerwa-Tetmajer, and P. Kurzynowski, “Application of the Fourier analysis methods to the three beam interferometry,” Opt. Laser Technol. 48, 503–508 (2013).
[Crossref]

A. Popiołek-Masajada, M. Borwińska, and B. Dubik, “Reconstruction of a plane wave’s tilt and orientation using an optical vortex interferometer,” Opt. Eng. 46(7), 073604 (2007).
[Crossref]

Brunet, T.

T. Brunet, J. L. Thomas, and R. Marchiano, “Transverse shift of helical beams and subdiffraction imaging,” Phys. Rev. Lett. 105(3), 034301 (2010).
[Crossref] [PubMed]

Chan, C. T.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mater. 15(18), 1526–1528 (2003).
[Crossref]

Chang, B. J.

Chang, S. L. Y.

C. Dwyer, C. B. Boothroyd, S. L. Y. Chang, and R. E. Dunin-Borkowski, “Three-wave electron vortex lattices for measuring nanofields,” Ultramicroscopy 148, 25–30 (2015).
[Crossref] [PubMed]

Chiang, S. Y.

Chou, L. J.

Collins, S.

Dennis, M. R.

M. R. Dennis and J. B. Götte, “Beam shifts for pairs of plane waves,” J. Opt. 15(1), 014015 (2013).
[Crossref]

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

M. V. Berry and M. R. Dennis, “Natural superoscillations in monochromatic waves in D dimensions,” J. Phys. A Math. Theor. 42(2), 022003 (2009).
[Crossref]

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express 14(7), 3039–3044 (2006).
[Crossref] [PubMed]

Dragomir, N. M.

Dubik, B.

A. Popiołek-Masajada, M. Borwińska, and B. Dubik, “Reconstruction of a plane wave’s tilt and orientation using an optical vortex interferometer,” Opt. Eng. 46(7), 073604 (2007).
[Crossref]

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198(1-3), 21–27 (2001).
[Crossref]

Dubra, A.

C. D. Perciante, J. A. Ferrari, and A. Dubra, “Visualization of phase objects using incoherent illumination,” Opt. Commun. 183(1-4), 15–18 (2000).
[Crossref]

Dunin-Borkowski, R. E.

C. Dwyer, C. B. Boothroyd, S. L. Y. Chang, and R. E. Dunin-Borkowski, “Three-wave electron vortex lattices for measuring nanofields,” Ultramicroscopy 148, 25–30 (2015).
[Crossref] [PubMed]

Duvall, S.

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, “TEM-based phase retrieval of p-n junction wafers using the transport of intensity equation,” Philos. Mag. 87(24), 3565–3578 (2007).
[Crossref]

Dwyer, C.

C. Dwyer, C. B. Boothroyd, S. L. Y. Chang, and R. E. Dunin-Borkowski, “Three-wave electron vortex lattices for measuring nanofields,” Ultramicroscopy 148, 25–30 (2015).
[Crossref] [PubMed]

Eastwood, S. A.

T. C. Petersen, M. Weyland, D. M. Paganin, T. P. Simula, S. A. Eastwood, and M. J. Morgan, “Electron vortex production and control using aberration induced diffraction catastrophes,” Phys. Rev. Lett. 110(3), 033901 (2013).
[Crossref] [PubMed]

S. A. Eastwood, A. I. Bishop, T. C. Petersen, D. M. Paganin, and M. J. Morgan, “Phase measurement using an optical vortex lattice produced with a three-beam interferometer,” Opt. Express 20(13), 13947–13957 (2012).
[Crossref] [PubMed]

Ferrari, J. A.

C. D. Perciante, J. A. Ferrari, and A. Dubra, “Visualization of phase objects using incoherent illumination,” Opt. Commun. 183(1-4), 15–18 (2000).
[Crossref]

Fraczek, W.

A. Popiołek-Masajada and W. Frączek, “Evaluation of a phase shifting method for vortex localization in optical vortex interferometry,” Opt. Laser Technol. 43(7), 1219–1224 (2011).
[Crossref]

Frank, J.

Friese, M. E.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

Funken, S. A.

A. Parvizi, J. Müller, S. A. Funken, and C. T. Koch, “A practical way to resolve ambiguities in wavefront reconstructions by the transport of intensity equation,” Ultramicroscopy 154, 1–6 (2015).
[Crossref] [PubMed]

Fürhapter, S.

Gbur, G.

G. Gbur and T. D. Visser, “The structure of partially coherent fields,” Prog. Opt. 55, 285–341 (2010).
[Crossref]

Götte, J. B.

M. R. Dennis and J. B. Götte, “Beam shifts for pairs of plane waves,” J. Opt. 15(1), 014015 (2013).
[Crossref]

He, H.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

Heckenberg, N. R.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

Heppner, J.

Horstmann, J.

Huang, H. C.

Huntington, S. T.

Ina, H.

Jack, B.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[Crossref]

Jesacher, A.

Johnson, K.

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, “TEM-based phase retrieval of p-n junction wafers using the transport of intensity equation,” Philos. Mag. 87(24), 3565–3578 (2007).
[Crossref]

Keast, V. J.

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, “TEM-based phase retrieval of p-n junction wafers using the transport of intensity equation,” Philos. Mag. 87(24), 3565–3578 (2007).
[Crossref]

King, R. P.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[Crossref]

Kitcher, D. J.

Kobayashi, S.

Koch, C. T.

A. Parvizi, J. Müller, S. A. Funken, and C. T. Koch, “A practical way to resolve ambiguities in wavefront reconstructions by the transport of intensity equation,” Ultramicroscopy 154, 1–6 (2015).
[Crossref] [PubMed]

Köser, J.

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8(6), 601–605 (1997).
[Crossref]

Kouskousis, B.

Kurzynowski, P.

A. Popiołek-Masajada, M. Borwińska, T. Przerwa-Tetmajer, and P. Kurzynowski, “Application of the Fourier analysis methods to the three beam interferometry,” Opt. Laser Technol. 48, 503–508 (2013).
[Crossref]

Law, C. T.

Lehmann, M.

T. Niermann, J. Verbeeck, and M. Lehmann, “Creating arrays of electron vortices,” Ultramicroscopy 136, 165–170 (2014).
[Crossref] [PubMed]

Lindeberg, T.

T. Lindeberg, “Scale-space theory: A basic tool for analysing structures at different scales,” J. Appl. Stat. 21(1), 224–270 (1994).
[Crossref]

Malitson, I. H.

Marchiano, R.

T. Brunet, J. L. Thomas, and R. Marchiano, “Transverse shift of helical beams and subdiffraction imaging,” Phys. Rev. Lett. 105(3), 034301 (2010).
[Crossref] [PubMed]

Masajada, J.

J. Masajada, “Small-angle rotations measurement using optical vortex interferometer,” Opt. Commun. 239(4-6), 373–381 (2004).
[Crossref]

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198(1-3), 21–27 (2001).
[Crossref]

Massig, J. H.

Matrisch, J.

McMahon, P. J.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[Crossref] [PubMed]

Mitchell, D. R. G.

D. R. G. Mitchell and T. C. Petersen, “RDFTools: A software tool for quantifying short-range ordering in amorphous materials,” Microsc. Res. Tech. 75(2), 153–163 (2012).
[Crossref] [PubMed]

D. R. G. Mitchell and B. Schaffer, “Scripting-customized microscopy tools for Digital Micrograph,” Ultramicroscopy 103(4), 319–332 (2005).
[Crossref] [PubMed]

Montgomery, W. D.

Morgan, K. S.

Morgan, M. J.

T. C. Petersen, M. Weyland, D. M. Paganin, T. P. Simula, S. A. Eastwood, and M. J. Morgan, “Electron vortex production and control using aberration induced diffraction catastrophes,” Phys. Rev. Lett. 110(3), 033901 (2013).
[Crossref] [PubMed]

S. A. Eastwood, A. I. Bishop, T. C. Petersen, D. M. Paganin, and M. J. Morgan, “Phase measurement using an optical vortex lattice produced with a three-beam interferometer,” Opt. Express 20(13), 13947–13957 (2012).
[Crossref] [PubMed]

Müller, J.

A. Parvizi, J. Müller, S. A. Funken, and C. T. Koch, “A practical way to resolve ambiguities in wavefront reconstructions by the transport of intensity equation,” Ultramicroscopy 154, 1–6 (2015).
[Crossref] [PubMed]

Ng, C. Y.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mater. 15(18), 1526–1528 (2003).
[Crossref]

Nicholls, K. W.

K. W. Nicholls and J. F. Nye, “3-beam model for studying dislocations in wave pulses,” J. Phys. Math. Gen. 20(14), 4673–4696 (1987).
[Crossref]

Niermann, T.

T. Niermann, J. Verbeeck, and M. Lehmann, “Creating arrays of electron vortices,” Ultramicroscopy 136, 165–170 (2014).
[Crossref] [PubMed]

Nugent, K. A.

E. Ampem-Lassen, S. T. Huntington, N. M. Dragomir, K. A. Nugent, and A. Roberts, “Refractive index profiling of axially symmetric optical fibers: a new technique,” Opt. Express 13(9), 3277–3282 (2005).
[Crossref] [PubMed]

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[Crossref] [PubMed]

Nye, J. F.

K. W. Nicholls and J. F. Nye, “3-beam model for studying dislocations in wave pulses,” J. Phys. Math. Gen. 20(14), 4673–4696 (1987).
[Crossref]

O’Holleran, K.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express 14(7), 3039–3044 (2006).
[Crossref] [PubMed]

Padgett, M. J.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express 14(7), 3039–3044 (2006).
[Crossref] [PubMed]

Paganin, D.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[Crossref] [PubMed]

Paganin, D. M.

T. C. Petersen, M. Weyland, D. M. Paganin, T. P. Simula, S. A. Eastwood, and M. J. Morgan, “Electron vortex production and control using aberration induced diffraction catastrophes,” Phys. Rev. Lett. 110(3), 033901 (2013).
[Crossref] [PubMed]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100(12), 124102 (2012).
[Crossref]

S. A. Eastwood, A. I. Bishop, T. C. Petersen, D. M. Paganin, and M. J. Morgan, “Phase measurement using an optical vortex lattice produced with a three-beam interferometer,” Opt. Express 20(13), 13947–13957 (2012).
[Crossref] [PubMed]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “Quantitative single-exposure x-ray phase contrast imaging using a single attenuation grid,” Opt. Express 19(20), 19781–19789 (2011).
[Crossref] [PubMed]

Parvizi, A.

A. Parvizi, J. Müller, S. A. Funken, and C. T. Koch, “A practical way to resolve ambiguities in wavefront reconstructions by the transport of intensity equation,” Ultramicroscopy 154, 1–6 (2015).
[Crossref] [PubMed]

Perciante, C. D.

C. D. Perciante, J. A. Ferrari, and A. Dubra, “Visualization of phase objects using incoherent illumination,” Opt. Commun. 183(1-4), 15–18 (2000).
[Crossref]

Petersen, T. C.

T. C. Petersen, M. Weyland, D. M. Paganin, T. P. Simula, S. A. Eastwood, and M. J. Morgan, “Electron vortex production and control using aberration induced diffraction catastrophes,” Phys. Rev. Lett. 110(3), 033901 (2013).
[Crossref] [PubMed]

D. R. G. Mitchell and T. C. Petersen, “RDFTools: A software tool for quantifying short-range ordering in amorphous materials,” Microsc. Res. Tech. 75(2), 153–163 (2012).
[Crossref] [PubMed]

S. A. Eastwood, A. I. Bishop, T. C. Petersen, D. M. Paganin, and M. J. Morgan, “Phase measurement using an optical vortex lattice produced with a three-beam interferometer,” Opt. Express 20(13), 13947–13957 (2012).
[Crossref] [PubMed]

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, “TEM-based phase retrieval of p-n junction wafers using the transport of intensity equation,” Philos. Mag. 87(24), 3565–3578 (2007).
[Crossref]

Petruccelli, J. C.

Platt, B. C.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Popiolek-Masajada, A.

A. Popiołek-Masajada, M. Borwińska, T. Przerwa-Tetmajer, and P. Kurzynowski, “Application of the Fourier analysis methods to the three beam interferometry,” Opt. Laser Technol. 48, 503–508 (2013).
[Crossref]

A. Popiołek-Masajada and W. Frączek, “Evaluation of a phase shifting method for vortex localization in optical vortex interferometry,” Opt. Laser Technol. 43(7), 1219–1224 (2011).
[Crossref]

A. Popiołek-Masajada, M. Borwińska, and B. Dubik, “Reconstruction of a plane wave’s tilt and orientation using an optical vortex interferometer,” Opt. Eng. 46(7), 073604 (2007).
[Crossref]

Przerwa-Tetmajer, T.

A. Popiołek-Masajada, M. Borwińska, T. Przerwa-Tetmajer, and P. Kurzynowski, “Application of the Fourier analysis methods to the three beam interferometry,” Opt. Laser Technol. 48, 503–508 (2013).
[Crossref]

Rheims, J.

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8(6), 601–605 (1997).
[Crossref]

Ritsch-Marte, M.

Roberts, A.

Rozas, D.

Rubinsztein-Dunlop, H.

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

Schaffer, B.

D. R. G. Mitchell and B. Schaffer, “Scripting-customized microscopy tools for Digital Micrograph,” Ultramicroscopy 103(4), 319–332 (2005).
[Crossref] [PubMed]

Shack, R. V.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Sheng, P.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mater. 15(18), 1526–1528 (2003).
[Crossref]

Simula, T. P.

T. C. Petersen, M. Weyland, D. M. Paganin, T. P. Simula, S. A. Eastwood, and M. J. Morgan, “Electron vortex production and control using aberration induced diffraction catastrophes,” Phys. Rev. Lett. 110(3), 033901 (2013).
[Crossref] [PubMed]

Siu, K. K. W.

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

Swartzlander, G. A.

Takeda, M.

Tam, W. Y.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mater. 15(18), 1526–1528 (2003).
[Crossref]

Teague, M. R.

Thomas, J. L.

T. Brunet, J. L. Thomas, and R. Marchiano, “Transverse shift of helical beams and subdiffraction imaging,” Phys. Rev. Lett. 105(3), 034301 (2010).
[Crossref] [PubMed]

Tian, L.

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

Verbeeck, J.

T. Niermann, J. Verbeeck, and M. Lehmann, “Creating arrays of electron vortices,” Ultramicroscopy 136, 165–170 (2014).
[Crossref] [PubMed]

Visser, T. D.

G. Gbur and T. D. Visser, “The structure of partially coherent fields,” Prog. Opt. 55, 285–341 (2010).
[Crossref]

Wang, X.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mater. 15(18), 1526–1528 (2003).
[Crossref]

Wernicke, G.

Weyland, M.

T. C. Petersen, M. Weyland, D. M. Paganin, T. P. Simula, S. A. Eastwood, and M. J. Morgan, “Electron vortex production and control using aberration induced diffraction catastrophes,” Phys. Rev. Lett. 110(3), 033901 (2013).
[Crossref] [PubMed]

Wriedt, T.

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8(6), 601–605 (1997).
[Crossref]

Adv. Mater. (1)

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mater. 15(18), 1526–1528 (2003).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100(12), 124102 (2012).
[Crossref]

J. Appl. Stat. (1)

T. Lindeberg, “Scale-space theory: A basic tool for analysing structures at different scales,” J. Appl. Stat. 21(1), 224–270 (1994).
[Crossref]

J. Microsc. (1)

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214(1), 51–61 (2004).
[Crossref] [PubMed]

J. Opt. (1)

M. R. Dennis and J. B. Götte, “Beam shifts for pairs of plane waves,” J. Opt. 15(1), 014015 (2013).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

M. V. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11(9), 094001 (2009).
[Crossref]

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. B (1)

J. Phys. A Math. Theor. (1)

M. V. Berry and M. R. Dennis, “Natural superoscillations in monochromatic waves in D dimensions,” J. Phys. A Math. Theor. 42(2), 022003 (2009).
[Crossref]

J. Phys. Math. Gen. (1)

K. W. Nicholls and J. F. Nye, “3-beam model for studying dislocations in wave pulses,” J. Phys. Math. Gen. 20(14), 4673–4696 (1987).
[Crossref]

Meas. Sci. Technol. (1)

J. Rheims, J. Köser, and T. Wriedt, “Refractive-index measurements in the near-IR using an Abbe refractometer,” Meas. Sci. Technol. 8(6), 601–605 (1997).
[Crossref]

Microsc. Res. Tech. (1)

D. R. G. Mitchell and T. C. Petersen, “RDFTools: A software tool for quantifying short-range ordering in amorphous materials,” Microsc. Res. Tech. 75(2), 153–163 (2012).
[Crossref] [PubMed]

Nat. Phys. (1)

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, and M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6(2), 118–121 (2010).
[Crossref]

Opt. Commun. (3)

C. D. Perciante, J. A. Ferrari, and A. Dubra, “Visualization of phase objects using incoherent illumination,” Opt. Commun. 183(1-4), 15–18 (2000).
[Crossref]

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198(1-3), 21–27 (2001).
[Crossref]

J. Masajada, “Small-angle rotations measurement using optical vortex interferometer,” Opt. Commun. 239(4-6), 373–381 (2004).
[Crossref]

Opt. Eng. (2)

A. Popiołek-Masajada, M. Borwińska, and B. Dubik, “Reconstruction of a plane wave’s tilt and orientation using an optical vortex interferometer,” Opt. Eng. 46(7), 073604 (2007).
[Crossref]

J. H. Massig, “Deformation measurement on specular surfaces by simple means,” Opt. Eng. 40(10), 2315–2318 (2001).
[Crossref]

Opt. Express (7)

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13(3), 689–694 (2005).
[Crossref] [PubMed]

E. Ampem-Lassen, S. T. Huntington, N. M. Dragomir, K. A. Nugent, and A. Roberts, “Refractive index profiling of axially symmetric optical fibers: a new technique,” Opt. Express 13(9), 3277–3282 (2005).
[Crossref] [PubMed]

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express 14(7), 3039–3044 (2006).
[Crossref] [PubMed]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “Quantitative single-exposure x-ray phase contrast imaging using a single attenuation grid,” Opt. Express 19(20), 19781–19789 (2011).
[Crossref] [PubMed]

S. A. Eastwood, A. I. Bishop, T. C. Petersen, D. M. Paganin, and M. J. Morgan, “Phase measurement using an optical vortex lattice produced with a three-beam interferometer,” Opt. Express 20(13), 13947–13957 (2012).
[Crossref] [PubMed]

J. C. Petruccelli, L. Tian, and G. Barbastathis, “The transport of intensity equation for optical path length recovery using partially coherent illumination,” Opt. Express 21(12), 14430–14441 (2013).
[Crossref] [PubMed]

H. C. Huang, B. J. Chang, L. J. Chou, and S. Y. Chiang, “Three-beam interference with circular polarization for structured illumination microscopy,” Opt. Express 21(20), 23963–23977 (2013).
[Crossref] [PubMed]

Opt. Laser Technol. (2)

A. Popiołek-Masajada and W. Frączek, “Evaluation of a phase shifting method for vortex localization in optical vortex interferometry,” Opt. Laser Technol. 43(7), 1219–1224 (2011).
[Crossref]

A. Popiołek-Masajada, M. Borwińska, T. Przerwa-Tetmajer, and P. Kurzynowski, “Application of the Fourier analysis methods to the three beam interferometry,” Opt. Laser Technol. 48, 503–508 (2013).
[Crossref]

Philos. Mag. (1)

T. C. Petersen, V. J. Keast, K. Johnson, and S. Duvall, “TEM-based phase retrieval of p-n junction wafers using the transport of intensity equation,” Philos. Mag. 87(24), 3565–3578 (2007).
[Crossref]

Phys. Rev. Lett. (3)

T. C. Petersen, M. Weyland, D. M. Paganin, T. P. Simula, S. A. Eastwood, and M. J. Morgan, “Electron vortex production and control using aberration induced diffraction catastrophes,” Phys. Rev. Lett. 110(3), 033901 (2013).
[Crossref] [PubMed]

H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995).
[Crossref] [PubMed]

T. Brunet, J. L. Thomas, and R. Marchiano, “Transverse shift of helical beams and subdiffraction imaging,” Phys. Rev. Lett. 105(3), 034301 (2010).
[Crossref] [PubMed]

Prog. Opt. (3)

G. Gbur and T. D. Visser, “The structure of partially coherent fields,” Prog. Opt. 55, 285–341 (2010).
[Crossref]

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[Crossref]

Ultramicroscopy (4)

T. Niermann, J. Verbeeck, and M. Lehmann, “Creating arrays of electron vortices,” Ultramicroscopy 136, 165–170 (2014).
[Crossref] [PubMed]

C. Dwyer, C. B. Boothroyd, S. L. Y. Chang, and R. E. Dunin-Borkowski, “Three-wave electron vortex lattices for measuring nanofields,” Ultramicroscopy 148, 25–30 (2015).
[Crossref] [PubMed]

D. R. G. Mitchell and B. Schaffer, “Scripting-customized microscopy tools for Digital Micrograph,” Ultramicroscopy 103(4), 319–332 (2005).
[Crossref] [PubMed]

A. Parvizi, J. Müller, S. A. Funken, and C. T. Koch, “A practical way to resolve ambiguities in wavefront reconstructions by the transport of intensity equation,” Ultramicroscopy 154, 1–6 (2015).
[Crossref] [PubMed]

Other (2)

W. H. Press, B. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, the Art of Scientific Computing, 2nd ed. (Cambridge University, 1992).

D. M. Paganin, Coherent X-ray Optics (Oxford University, 2006).

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Figures (4)

Fig. 1
Fig. 1 Experimental configuration. Imaging system (1) was used for the benchmark specimen. The fiber optic experiments used system (2) with a condensing pair of lenses, to shrink the probing vortex lattice, in conjunction with a higher numerical aperture microscope objective lens. Similarly, the initial polarizing beam splitter was reproducibly interchanged with a mirror to flip between 3-beam laser measurements and LED imaging, for which two of the three beams were blocked. The vortex lattice is an unprocessed 3-beam laser image from the experiment, in the absence of the specimen, showing a 142 μm field of view.
Fig. 2
Fig. 2 a) Experimentally measured phase gradient due to the lens specimen (left), compared to the analytical calculation in b) (right). Colors indicate the magnitude of the phase gradient.
Fig. 3
Fig. 3 Horizontally averaged vertical phase gradient for the single-mode fiber measured with vortex lattice singularimetry and deterministic in-line holography. Both measurements are compared to an analytical estimate based upon the projection approximation, which assumes a perfect cylinder containing a cylindrical step-index core.
Fig. 4
Fig. 4 Measured phase gradients for the multi-mode graded-index fiber, which was immersed in glycerol. The field of view is 142 μm in each direction and contains the horizontal fiber of width 140 μm. The singularimetry measurements are shown in a) and the TIE based in-line holography phase gradients have been sampled at the same points in b).

Tables (2)

Tables Icon

Table 1 Experimental details.

Tables Icon

Table 2 Results for benchmark lens specimen.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

ψ non ( r, k A ) + + δ( k A k' )g( k' ) e 2πik'r dk' = 0 2π g( θ ) e 2πikr dθ ,
ψ+Δz z ψ = e iη( r ) 0 2π g( k ) e 2πikr { 1+i Δz 2k [ 4πkη( r )+i 2 η( r ) ε 2 α 2 ] }dθ = e iη( r )i Δz 2k [ ε 2 + α 2 i 2 η( r ) ] 0 2π g( k ) e 2πikr e i Δz k [ 2πkη( r ) ] d θ = e iη( r )i Δz 2k [ ε 2 + α 2 i 2 η( r ) ] ψ non ( r Δz k η( r ) ),
I( r,z+Δz )= I obj e Δz k 2 ϕ( r ) I non ( r Δz k η( r ) ),
Ψ f ( r,Z )=ik Z 1 e ikZ S + + g( R ) e 2πiRr / ( λZ )+iη( r ) dR ,
Ψ F ( r,Z+Δz )=ik Z 1 e ikZ + + g( R ) e 2πiRr / ( λZ )+iη( r ) { 1+i Δz 2k f( r,R ) }dR ,
f( r,R )=i 2 η' | η' 2πR / ( λZ ) | 2 =i 2 η' | η' | 2 ( 2π ) 2 N( R ) / ( λZ ) 4π / ( λZ ) η'R
Ψ F ( r,Z+Δz )=ik Z 1 e ikZ+i η i Δz 2k ( | η | 2 i 2 η ) + + g( R ) e 2πiR{ r η } / ( λz ) dR = e i η i Δz 2k ( | η | 2 i 2 η ) Ψ F ( r Δz k η ,Z ),

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