Abstract

We analyze the point spread function (PSF) of the image processing system for radial Hilbert transform and propose a novel spiral phase filter, called the Laguerre–Gaussian spatial filter (LGSF). Theoretical analysis and real experiments show that the LGSF possesses some advantages in comparison with the conventional spiral phase plate (SPP). For example, the PSF of the imaging system with a LGSF presents smaller suboscillations than that with the conventional SPP, which allows us to realize a radial Hilbert transform for achieving a high contrast edge enhancement with high resolution.

© 2006 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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2006 (1)

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

2005 (4)

2004 (1)

2001 (1)

Bernet, S.

S. Fuerhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Express 13, 689 (2005).
[CrossRef]

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

Cottrell, D. M.

Davis, J. A.

Ding, J. P.

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

Foo, G.

Fuerhapter, S.

S. Fuerhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Express 13, 689 (2005).
[CrossRef]

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

Grier, D. G.

Gruzberg, I.

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, X. Liu, J. L. He, and H. T. Wang, Opt. Express 12, 4625 (2004).
[CrossRef] [PubMed]

Han, Y. J.

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

He, J. L.

Jesacher, A.

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

S. Fuerhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Express 13, 689 (2005).
[CrossRef]

Liu, X.

McNamara, D. E.

Palacios, D. M.

Ritsch-Marte, M.

S. Fuerhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Express 13, 689 (2005).
[CrossRef]

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

Sundbeck, S.

Swartzlander, G. A.

Wang, H. T.

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

C. S. Guo, X. Liu, J. L. He, and H. T. Wang, Opt. Express 12, 4625 (2004).
[CrossRef] [PubMed]

Zhang, Y.

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

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Figures (5)

Fig. 1
Fig. 1

A typical experimental result of the radial Hilbert transform using a SPP as the spatial filter, where (a) is the photo of the input object, and (b) is the intensity distribution of the output image after the radial Hilbert transform.

Fig. 2
Fig. 2

Amplitude profile in one radial section of the PSF for the radial Hilbert transform using (a) SPP, (b) LGSF with w = 0.74 R , and (c) LGSF with w = 0.64 R .

Fig. 3
Fig. 3

Examples of the CGHs we designed for the radial Hilbert transform, where (a) and (b) are based on the SPP of Eq. (1) and the LGSF of Eq. (2), respectively.

Fig. 4
Fig. 4

Experimental result of the radial Hilbert transform using a LGSF with the parameters of R = 256   pixels and w = 148   pixels .

Fig. 5
Fig. 5

Intensity profiles of the output circular image in its radial direction when (a) SPP and (b) LGSF are adopted in experiments, respectively.

Equations (4)

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H ( ρ , φ ) = circ ( ρ R ) exp ( j φ ) ,
h ( r , θ ) = π R j 2 r [ H 0 ( x ) J 1 ( x ) H 1 ( x ) J 0 ( x ) ] exp ( j θ ) .
H ( ρ , φ ) = ρ w exp [ ( ρ w ) 2 ] circ ( ρ R ) exp ( j φ ) ,
h ( r , θ ) = 1 λ f FT [ ( ρ w ) exp ( ρ 2 w 2 ) exp ( j φ ) ] = w 2 j λ f x exp ( x 2 4 ) exp ( j θ ) ,

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