Abstract

The technique of an inverted chromascope is introduced for determining the points of amplitude zeroes for the spectral components of a polychromatic radiation field. Applications of this technique for processing of experimentally obtained light distributions are demonstrated, both arising from birefringence and from speckle fields.

© 2005 Optical Society of America

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References

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  1. H. He, N.R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
    [Crossref]
  2. N.B. Simpson, J.L. Allen, and M.J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
    [Crossref]
  3. C. Rockstuhl, M. Salt, and H.P. Herzig, “Theoretical and experimental investigation of phase singularities generated by optical micro- and nano-structures,” J. Opt. A: Pure Appl.Opt. 6, 271–276 (2004).
    [Crossref]
  4. H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “The diffraction of light by narrow slits in plates of different materials” J. Opt. A: Pure Appl.Opt. 6, 277–280 (2004).
    [Crossref]
  5. H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “Phase singularities and Enhanced Transmission at a Subwavelength slit,” Opt. Photon. News 14, 23 (2003).
    [Crossref]
  6. M. Mujat and A. Dogariu, “Polarimetric and spectral changes in random electromagnetic fields,” Opt. Lett. 28, 2153–2155 (2003).
    [Crossref] [PubMed]
  7. G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
    [Crossref] [PubMed]
  8. V.K. Polyanskii, O.V. Angelsky, and P.V. Polyanskii, “Scattering-induced spectral changes as a singular optical effect,” Opt. Appl. 32, 843–848 (2003).
  9. J.W. Goodman, Statistical Optics (Wiley, New York, 1985).
  10. M.V. Berry “Coloured phase singularities,” New J. Phys.,  4, 66.1–66.14 (2002).
    [Crossref]
  11. M.V. Berry “Exploring the colours of dark light,” New J. Phys. 4, 74.1–74.14 (2002).
    [Crossref]
  12. J. Leach and M. Padgett “Observation of chromatic effects near a white-light vortex,” New J. Phys.154.1–154.7 (2003).

2004 (2)

C. Rockstuhl, M. Salt, and H.P. Herzig, “Theoretical and experimental investigation of phase singularities generated by optical micro- and nano-structures,” J. Opt. A: Pure Appl.Opt. 6, 271–276 (2004).
[Crossref]

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “The diffraction of light by narrow slits in plates of different materials” J. Opt. A: Pure Appl.Opt. 6, 277–280 (2004).
[Crossref]

2003 (3)

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “Phase singularities and Enhanced Transmission at a Subwavelength slit,” Opt. Photon. News 14, 23 (2003).
[Crossref]

M. Mujat and A. Dogariu, “Polarimetric and spectral changes in random electromagnetic fields,” Opt. Lett. 28, 2153–2155 (2003).
[Crossref] [PubMed]

V.K. Polyanskii, O.V. Angelsky, and P.V. Polyanskii, “Scattering-induced spectral changes as a singular optical effect,” Opt. Appl. 32, 843–848 (2003).

2002 (3)

M.V. Berry “Coloured phase singularities,” New J. Phys.,  4, 66.1–66.14 (2002).
[Crossref]

M.V. Berry “Exploring the colours of dark light,” New J. Phys. 4, 74.1–74.14 (2002).
[Crossref]

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
[Crossref] [PubMed]

1996 (1)

N.B. Simpson, J.L. Allen, and M.J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

1995 (1)

H. He, N.R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[Crossref]

Allen, J.L.

N.B. Simpson, J.L. Allen, and M.J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

Angelsky, O.V.

V.K. Polyanskii, O.V. Angelsky, and P.V. Polyanskii, “Scattering-induced spectral changes as a singular optical effect,” Opt. Appl. 32, 843–848 (2003).

Berry, M.V.

M.V. Berry “Coloured phase singularities,” New J. Phys.,  4, 66.1–66.14 (2002).
[Crossref]

M.V. Berry “Exploring the colours of dark light,” New J. Phys. 4, 74.1–74.14 (2002).
[Crossref]

Blok, H.

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “The diffraction of light by narrow slits in plates of different materials” J. Opt. A: Pure Appl.Opt. 6, 277–280 (2004).
[Crossref]

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “Phase singularities and Enhanced Transmission at a Subwavelength slit,” Opt. Photon. News 14, 23 (2003).
[Crossref]

Dogariu, A.

M. Mujat and A. Dogariu, “Polarimetric and spectral changes in random electromagnetic fields,” Opt. Lett. 28, 2153–2155 (2003).
[Crossref] [PubMed]

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
[Crossref] [PubMed]

Gbur, G.

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “The diffraction of light by narrow slits in plates of different materials” J. Opt. A: Pure Appl.Opt. 6, 277–280 (2004).
[Crossref]

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “Phase singularities and Enhanced Transmission at a Subwavelength slit,” Opt. Photon. News 14, 23 (2003).
[Crossref]

Goodman, J.W.

J.W. Goodman, Statistical Optics (Wiley, New York, 1985).

He, H.

H. He, N.R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[Crossref]

Heckenberg, N.R.

H. He, N.R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[Crossref]

Herzig, H.P.

C. Rockstuhl, M. Salt, and H.P. Herzig, “Theoretical and experimental investigation of phase singularities generated by optical micro- and nano-structures,” J. Opt. A: Pure Appl.Opt. 6, 271–276 (2004).
[Crossref]

Leach, J.

J. Leach and M. Padgett “Observation of chromatic effects near a white-light vortex,” New J. Phys.154.1–154.7 (2003).

Lenstra, D.

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “The diffraction of light by narrow slits in plates of different materials” J. Opt. A: Pure Appl.Opt. 6, 277–280 (2004).
[Crossref]

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “Phase singularities and Enhanced Transmission at a Subwavelength slit,” Opt. Photon. News 14, 23 (2003).
[Crossref]

Mujat, M.

Padgett, M.

J. Leach and M. Padgett “Observation of chromatic effects near a white-light vortex,” New J. Phys.154.1–154.7 (2003).

Padgett, M.J.

N.B. Simpson, J.L. Allen, and M.J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

Polyanskii, P.V.

V.K. Polyanskii, O.V. Angelsky, and P.V. Polyanskii, “Scattering-induced spectral changes as a singular optical effect,” Opt. Appl. 32, 843–848 (2003).

Polyanskii, V.K.

V.K. Polyanskii, O.V. Angelsky, and P.V. Polyanskii, “Scattering-induced spectral changes as a singular optical effect,” Opt. Appl. 32, 843–848 (2003).

Popescu, G.

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
[Crossref] [PubMed]

Rockstuhl, C.

C. Rockstuhl, M. Salt, and H.P. Herzig, “Theoretical and experimental investigation of phase singularities generated by optical micro- and nano-structures,” J. Opt. A: Pure Appl.Opt. 6, 271–276 (2004).
[Crossref]

Rubinsztein-Dunlop, H.

H. He, N.R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[Crossref]

Salt, M.

C. Rockstuhl, M. Salt, and H.P. Herzig, “Theoretical and experimental investigation of phase singularities generated by optical micro- and nano-structures,” J. Opt. A: Pure Appl.Opt. 6, 271–276 (2004).
[Crossref]

Schouten, H.F.

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “The diffraction of light by narrow slits in plates of different materials” J. Opt. A: Pure Appl.Opt. 6, 277–280 (2004).
[Crossref]

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “Phase singularities and Enhanced Transmission at a Subwavelength slit,” Opt. Photon. News 14, 23 (2003).
[Crossref]

Simpson, N.B.

N.B. Simpson, J.L. Allen, and M.J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

Visser, T.D.

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “The diffraction of light by narrow slits in plates of different materials” J. Opt. A: Pure Appl.Opt. 6, 277–280 (2004).
[Crossref]

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “Phase singularities and Enhanced Transmission at a Subwavelength slit,” Opt. Photon. News 14, 23 (2003).
[Crossref]

J. Mod. Opt. (2)

H. He, N.R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995).
[Crossref]

N.B. Simpson, J.L. Allen, and M.J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. 43, 2485–2491 (1996).
[Crossref]

J. Opt. A: Pure Appl.Opt. (2)

C. Rockstuhl, M. Salt, and H.P. Herzig, “Theoretical and experimental investigation of phase singularities generated by optical micro- and nano-structures,” J. Opt. A: Pure Appl.Opt. 6, 271–276 (2004).
[Crossref]

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “The diffraction of light by narrow slits in plates of different materials” J. Opt. A: Pure Appl.Opt. 6, 277–280 (2004).
[Crossref]

New J. Phys. (2)

M.V. Berry “Coloured phase singularities,” New J. Phys.,  4, 66.1–66.14 (2002).
[Crossref]

M.V. Berry “Exploring the colours of dark light,” New J. Phys. 4, 74.1–74.14 (2002).
[Crossref]

Opt. Appl. (1)

V.K. Polyanskii, O.V. Angelsky, and P.V. Polyanskii, “Scattering-induced spectral changes as a singular optical effect,” Opt. Appl. 32, 843–848 (2003).

Opt. Lett. (1)

Opt. Photon. News (1)

H.F. Schouten, T.D. Visser, G. Gbur, D. Lenstra, and H. Blok, “Phase singularities and Enhanced Transmission at a Subwavelength slit,” Opt. Photon. News 14, 23 (2003).
[Crossref]

Phys. Rev. Lett. (1)

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
[Crossref] [PubMed]

Other (2)

J.W. Goodman, Statistical Optics (Wiley, New York, 1985).

J. Leach and M. Padgett “Observation of chromatic effects near a white-light vortex,” New J. Phys.154.1–154.7 (2003).

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Figures (13)

Fig. 1.
Fig. 1.

Spatial intensity distribution over an isolated fragment of a speckle-field produced by three spectral components.

Fig. 2.
Fig. 2.

Spatial phase distribution of an isolated fragment of a speckle-field produced by red (a); green (b); blue (c) and for all three spectral components (d).

Fig. 3.
Fig. 3.

Color distribution resulting from processing of the isolated fragment of a speckle-field by a chromascope. Fragment (1) depicts a zone of low intensity of the distribution shown in Fig. 1.

Fig. 4.
Fig. 4.

Color distribution resulting from processing of an isolated fragment of a speckle-field by the inverted chromascope.

Fig. 5.
Fig. 5.

Spatial phase distribution of an isolated fragment of a speckle-field produced by red (a); green (c); blue (e), and spatial distribution of amplitude zeroes of the isolated fragment of a speckle-field for red (b); green (d); blue (f) spectral component.

Fig. 6.
Fig. 6.

The experimental optical arrangement: 1 - source of light; 2,4,8 - objectives; 3 - diaphragm; 5 - polarizer; 6 - film; 7 - analyzer; 9 - CCD-camera; 10 - computer.

Fig. 7.
Fig. 7.

Conoscopic patterns obtained for matched polarizer and analyzer (a), and for crossed polarizer and analyzer (b).

Fig. 8.
Fig. 8.

Patterns shown in Fig. 7 processed by a chromascope for matched polarizer and analyzer (a), and for crossed polarizer and analyzer (b).

Fig. 9.
Fig. 9.

Pattern shown in Fig. 7(a) processed by the inverted chromascope.

Fig. 10.
Fig. 10.

Patterns illustrating the positions of amplitude zeroes of the field for red (a), green (b) and blue (c) spectral components.

Fig. 11.
Fig. 11.

Fragment of polychromatic speckle-field resulting from scattering by a rough surface.

Fig. 12.
Fig. 12.

The pattern obtained by applying a chromascope (a) and inverse chromascope (b) to the experimentally found intensity distribution shown in Fig. 11.

Fig. 13.
Fig. 13.

The patterns illustrating the positions of amplitude zeroes of the speckle-field for red (a), green (b) and blue(c) spectral components.

Equations (4)

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U ( ξ , η ) = z i λ A ( x , y ) R 2 ( x , y , z , ξ , η ) exp { ik [ R ( x , y , z , ξ , η ) + ( n 1 ) h ( x , y ) ] } dxdy ,
( R G B ) CR = ( R G B ) max ( R , G , B ) .
( R G B ) INV = 1 ( R G B ) CR
( R G B ) Y = { 1 , for Y INV + δ Y 1 0 , for Y INV + δ Y < 1 and Y = 0 ,

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