Abstract

We analyzed the point spread function (PSF) of the typical 4f optical image processing system by use of a spatially variable half-wave plate as the spatial filter and found that the PSF is an elementary vector beam. Theoretical analysis and real experiments show that the optical system can be used for a radially symmetric Hilbert transform that permits two-dimensional edge enhancement as the spiral phase plate. This kind of radial Hilbert transform is useful for image processing because it can enhance the edges of an input image selectively by exerting a polarization analyzer before the output plane. The optical system also can be used for generation of vector beams with arbitrary array and shape in real time conveniently.

© 2013 Optical Society of America

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2012 (1)

2011 (1)

2009 (1)

2007 (1)

2006 (2)

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, Opt. Commun. 259, 449 (2006).
[CrossRef]

C.-S. Guo, Y.-J. Han, J.-B. Xu, and J. Ding, Opt. Lett. 31, 1394 (2006).
[CrossRef]

2005 (4)

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
[CrossRef]

G. Foo, D. M. Palacios, and G. A. Swartzlander, Opt. Lett. 30, 3308 (2005).
[CrossRef]

S. Quabis, R. Dorn, and G. Leuchs, Appl. Phys. B 81, 597 (2005).
[CrossRef]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

2000 (1)

1992 (1)

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Bernet, S.

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
[CrossRef]

Bouchal, P.

Bouchal, Z.

Campos, J.

Cottrell, D. M.

Davis, J. A.

Ding, J.

Ding, J.-P.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, Opt. Commun. 259, 449 (2006).
[CrossRef]

Dorn, R.

S. Quabis, R. Dorn, and G. Leuchs, Appl. Phys. B 81, 597 (2005).
[CrossRef]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Foo, G.

Fürhapter, S.

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

Guo, C.-S.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, Opt. Commun. 259, 449 (2006).
[CrossRef]

C.-S. Guo, Y.-J. Han, J.-B. Xu, and J. Ding, Opt. Lett. 31, 1394 (2006).
[CrossRef]

Han, Y.-J.

C.-S. Guo, Y.-J. Han, J.-B. Xu, and J. Ding, Opt. Lett. 31, 1394 (2006).
[CrossRef]

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, Opt. Commun. 259, 449 (2006).
[CrossRef]

Jackel, S.

Jesacher, A.

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

Joseph, J.

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Leuchs, G.

S. Quabis, R. Dorn, and G. Leuchs, Appl. Phys. B 81, 597 (2005).
[CrossRef]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Lumer, Y.

Machavariani, G.

McNamara, D. E.

Meir, A.

Moshe, I.

Osten, W.

Palacios, D. M.

Pedrini, G.

Quabis, S.

S. Quabis, R. Dorn, and G. Leuchs, Appl. Phys. B 81, 597 (2005).
[CrossRef]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Ritsch-Marte, M.

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Lett. 30, 1953 (2005).
[CrossRef]

Senthilkumaran, P.

Sharma, M. K.

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Situ, G.

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Swartzlander, G. A.

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Wang, H.-T.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, Opt. Commun. 259, 449 (2006).
[CrossRef]

Xu, J.-B.

Zhang, Y.

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, Opt. Commun. 259, 449 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

S. Quabis, R. Dorn, and G. Leuchs, Appl. Phys. B 81, 597 (2005).
[CrossRef]

J. Mod. Opt. (1)

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

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

Opt. Commun. (1)

C.-S. Guo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, Opt. Commun. 259, 449 (2006).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. Lett. (2)

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the experimental setup.

Fig. 2.
Fig. 2.

Visualized picture of the convolution process between a kernel vector beam and an input light spot.

Fig. 3.
Fig. 3.

Photo of the segmented HWP.

Fig. 4.
Fig. 4.

Experimental results of input pattern with definite circular array: (a) the photo of the input pattern with 6×6 circular spots array; (b) the total intensity distribution of the output field with the segmented HWP as the spatial filter; (c)–(f) the intensity distributions of the output field passes through the polarization analyzer with different axes.

Fig. 5.
Fig. 5.

Experimental results of input pattern with arbitrary shape: (a) the photo of input pattern with arbitrary shapes; (b) the total intensity distribution of the output field with the segmented HWP as the spatial filter; (c)–(f) the intensity distributions of the output field passes through the polarization analyzer with different axes.

Equations (6)

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

TH(r,θ)=[cosαsinαsinαcosα],
TS(ρ,φ)=circ(ρR)[cosφsinφsinφcosφ],
HT(ρ,φ)=circ(ρR)[cos(φα)sin(φα)sin(φα)cos(φα)].
h(r,θ)=Cλf0RJ1(2πλfrρ)ρdρ[cos(θα)sin(θα)],
h(r,θ)=Cjλf0RJ1(2πλfrρ)ρdρexp(jθ).
gout(r,θ)=gin(r,θ)*h(r,θ),

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