Abstract

In optical tomography, isotropic edge-enhancement of phase-object slices under the refractionless limit approximation can be reconstructed using spatial filtering techniques. The optical Hilbert-transform of the transmittance function leaving the object at projection angles ϕ(00,3600), is one of these techniques with some advantages. The corresponding irradiance of the so modified transmittance is considered as projection data, and is proved that they share two properties with the Radon transform: its symmetry property and its zeroth-moment conservation. Accordingly, a modified sinogram able to reconstruct edge-enhanced phase slices is obtained. In this paper, the theoretical model is amply discussed and illustrated both with numerical and experimental results.

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References

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  1. S. R. Deans, “The Radon Transform and Some of its Applications,” (Wiley, New York. 1983).
  2. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
    [CrossRef]
  3. G. P. Montgomery and D. L. Reuss, “Effects of refraction on axisymmetric flame temperatures measured by holographic interferometry,” Appl. Opt. 21(8), 1373–1380 (1982).
    [CrossRef] [PubMed]
  4. J. M. Mehta and W. Z. Black, “Errors associated with interferometric measurement of convective heat transfer coefficients,” Appl. Opt. 16(6), 1720–1726 (1977).
    [CrossRef] [PubMed]
  5. J. M. Mehta and W. M. Worek, “Analysis of refraction errors for interferometric measurements in multicomponent systems,” Appl. Opt. 23(6), 928–933 (1984).
    [CrossRef] [PubMed]
  6. S. Cha and C. M. Vest, “Tomographic reconstruction of strongly refracting fields and its application to interferometric measurement of boundary layers,” Appl. Opt. 20(16), 2787–2794 (1981).
    [CrossRef] [PubMed]
  7. C. Meneses-Fabian, G. Rodriguez-Zurita, and V. Arrizón, “Optical tomography of transparent objects with phase-shifting interferometry and stepwise-shifted Ronchi ruling,” J. Opt. Soc. Am. A 23(2), 298–305 (2006).
    [CrossRef]
  8. C. Meneses-Fabian, G. Rodriguez-Zurita, R. Rodriguez-Vera, and F. Jose, “Optical tomography with parallel projection differences and Electronic Speckle Pattern Interferometry,” Opt. Commun. 228(4-6), 201–210 (2003).
    [CrossRef]
  9. G. Rodríguez-Zurita, C. Meneses-Fabián, J.-S. Pérez-Huerta, and J.-F. Vázquez-Castillo, ““Tomographic directional derivative of phase objects slices using 1-D derivative spatial filtering of fractional order ½,” ICO20,” Proc. SPIE 6027, 410–416 (2006).
  10. J. A. Davis, D. E. McNamara, and D. M. Cottrell, “Analysis of the fractional hilbert transform,” Appl. Opt. 37(29), 6911–6913 (1998).
    [CrossRef]
  11. J. A. Davis, D. E. McNamara, D. M. Cottrell, and J. Campos, “Image processing with the radial Hilbert transform: theory and experiments,” Opt. Lett. 25(2), 99–101 (2000).
    [CrossRef]
  12. J. A. Davis and M. D. Nowak, “Selective edge enhancement of images with an acousto-optic light modulator,” Appl. Opt. 41(23), 4835–4839 (2002).
    [CrossRef] [PubMed]
  13. J. Hsieh, “Computed Tomography: principles, design, artifacts, and recent advances,” (SPIE PRESS, Bellingham, Washington USA, 2003).

2006 (2)

G. Rodríguez-Zurita, C. Meneses-Fabián, J.-S. Pérez-Huerta, and J.-F. Vázquez-Castillo, ““Tomographic directional derivative of phase objects slices using 1-D derivative spatial filtering of fractional order ½,” ICO20,” Proc. SPIE 6027, 410–416 (2006).

C. Meneses-Fabian, G. Rodriguez-Zurita, and V. Arrizón, “Optical tomography of transparent objects with phase-shifting interferometry and stepwise-shifted Ronchi ruling,” J. Opt. Soc. Am. A 23(2), 298–305 (2006).
[CrossRef]

2003 (2)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

C. Meneses-Fabian, G. Rodriguez-Zurita, R. Rodriguez-Vera, and F. Jose, “Optical tomography with parallel projection differences and Electronic Speckle Pattern Interferometry,” Opt. Commun. 228(4-6), 201–210 (2003).
[CrossRef]

2002 (1)

2000 (1)

1998 (1)

1984 (1)

1982 (1)

1981 (1)

1977 (1)

Arrizón, V.

Black, W. Z.

Campos, J.

Cha, S.

Cottrell, D. M.

Davis, J. A.

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

Jose, F.

C. Meneses-Fabian, G. Rodriguez-Zurita, R. Rodriguez-Vera, and F. Jose, “Optical tomography with parallel projection differences and Electronic Speckle Pattern Interferometry,” Opt. Commun. 228(4-6), 201–210 (2003).
[CrossRef]

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

McNamara, D. E.

Mehta, J. M.

Meneses-Fabian, C.

C. Meneses-Fabian, G. Rodriguez-Zurita, and V. Arrizón, “Optical tomography of transparent objects with phase-shifting interferometry and stepwise-shifted Ronchi ruling,” J. Opt. Soc. Am. A 23(2), 298–305 (2006).
[CrossRef]

C. Meneses-Fabian, G. Rodriguez-Zurita, R. Rodriguez-Vera, and F. Jose, “Optical tomography with parallel projection differences and Electronic Speckle Pattern Interferometry,” Opt. Commun. 228(4-6), 201–210 (2003).
[CrossRef]

Meneses-Fabián, C.

G. Rodríguez-Zurita, C. Meneses-Fabián, J.-S. Pérez-Huerta, and J.-F. Vázquez-Castillo, ““Tomographic directional derivative of phase objects slices using 1-D derivative spatial filtering of fractional order ½,” ICO20,” Proc. SPIE 6027, 410–416 (2006).

Montgomery, G. P.

Nowak, M. D.

Pérez-Huerta, J.-S.

G. Rodríguez-Zurita, C. Meneses-Fabián, J.-S. Pérez-Huerta, and J.-F. Vázquez-Castillo, ““Tomographic directional derivative of phase objects slices using 1-D derivative spatial filtering of fractional order ½,” ICO20,” Proc. SPIE 6027, 410–416 (2006).

Reuss, D. L.

Rodriguez-Vera, R.

C. Meneses-Fabian, G. Rodriguez-Zurita, R. Rodriguez-Vera, and F. Jose, “Optical tomography with parallel projection differences and Electronic Speckle Pattern Interferometry,” Opt. Commun. 228(4-6), 201–210 (2003).
[CrossRef]

Rodriguez-Zurita, G.

C. Meneses-Fabian, G. Rodriguez-Zurita, and V. Arrizón, “Optical tomography of transparent objects with phase-shifting interferometry and stepwise-shifted Ronchi ruling,” J. Opt. Soc. Am. A 23(2), 298–305 (2006).
[CrossRef]

C. Meneses-Fabian, G. Rodriguez-Zurita, R. Rodriguez-Vera, and F. Jose, “Optical tomography with parallel projection differences and Electronic Speckle Pattern Interferometry,” Opt. Commun. 228(4-6), 201–210 (2003).
[CrossRef]

Rodríguez-Zurita, G.

G. Rodríguez-Zurita, C. Meneses-Fabián, J.-S. Pérez-Huerta, and J.-F. Vázquez-Castillo, ““Tomographic directional derivative of phase objects slices using 1-D derivative spatial filtering of fractional order ½,” ICO20,” Proc. SPIE 6027, 410–416 (2006).

Vázquez-Castillo, J.-F.

G. Rodríguez-Zurita, C. Meneses-Fabián, J.-S. Pérez-Huerta, and J.-F. Vázquez-Castillo, ““Tomographic directional derivative of phase objects slices using 1-D derivative spatial filtering of fractional order ½,” ICO20,” Proc. SPIE 6027, 410–416 (2006).

Vest, C. M.

Worek, W. M.

Appl. Opt. (6)

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

Opt. Commun. (1)

C. Meneses-Fabian, G. Rodriguez-Zurita, R. Rodriguez-Vera, and F. Jose, “Optical tomography with parallel projection differences and Electronic Speckle Pattern Interferometry,” Opt. Commun. 228(4-6), 201–210 (2003).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

G. Rodríguez-Zurita, C. Meneses-Fabián, J.-S. Pérez-Huerta, and J.-F. Vázquez-Castillo, ““Tomographic directional derivative of phase objects slices using 1-D derivative spatial filtering of fractional order ½,” ICO20,” Proc. SPIE 6027, 410–416 (2006).

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

Other (2)

S. R. Deans, “The Radon Transform and Some of its Applications,” (Wiley, New York. 1983).

J. Hsieh, “Computed Tomography: principles, design, artifacts, and recent advances,” (SPIE PRESS, Bellingham, Washington USA, 2003).

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Figures (5)

Fig. 1
Fig. 1

(color online) A beam of parallel rays crosses a phase object at z constant, z = z 0 . (a) 3-D view showing a rotated reference system (x, y) about z with respect to the ( p , p ) system. (b) 2-D view of plane z = z 0 with p axis translated.

Fig. 2
Fig. 2

(color online) 4f L optical imaging system with a sign filter at the Fourier plane to obtain the HT of the projection data leaving the phase object.

Fig. 3
Fig. 3

(color online) Numerical simulation. (a) object slice (1) and sinogram (2), (b) the field leaving the phase object slice: real (1) and imaginary (2) parts (c) HT of the field leaving the phase object slice, (d) IH-sinogram (1) and the zero-moment of the RT (2), and (e) Edge-enhancement reconstruction: gray levels (1) and 3-D plot (2).

Fig. 4
Fig. 4

(color online) Numerical simulations. (a) Two test slices: uniform ring and non-symmetric object, (b) IH-Sinograms, (c) Zero-moment of RT, d-e) reconstructions showing isotropic edge-enhancement.

Fig. 5
Fig. 5

(color online) Experimental results, (a) rectangular slide glass block, (b) pipette.

Equations (10)

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A ϕ ( p , z ) = A exp [ i 2 π λ f ϕ ( p , z ) ] ,
{ f ( x , y , z ) } = f ϕ ( p , z ) = d ξ d η f ( ξ , η , z ) δ ( p ξ cos ϕ η sin ϕ ) ,
A ϕ ( p , z ) = 1 { i sgn ( w ) A ~ ϕ ( w , ζ ) } ,
A ϕ ( p , z ) = δ ( z ) π p A ϕ ( p , z ) ,
I ϕ ( p , z ) = A ϕ ( p , z ) A ϕ * ( p , z ) = | A ϕ ( p , z ) | 2 = | δ ( z ) π p A ϕ ( p , z ) | 2 ,
I ϕ + π ( p , z ) = | δ ( z ) π p A ϕ + π ( p , z ) | 2 = | δ ( z ) π ( p ) A ϕ ( p , z ) | 2 = I ϕ ( p , z ) ,
d p I ϕ ( p , z ) = I ~ ϕ ( w , z ) | w = 0 = { i sgn ( w ) A ~ ϕ ( w , z ) i sgn ( w ) A ϕ * ~ ( w , z ) } | w = 0 ,
d p I ϕ ( p , z ) = d u sgn 2 ( u ) A ~ ϕ ( u , z ) A ϕ * ~ ( u , z ) ,
d p I ϕ ( p , z ) = d p A ϕ ( p , z ) A ϕ * ( p , z ) ,
d p I ϕ ( p , z ) = Γ / 2 Γ / 2 d p A 2 = A 2 Γ ,

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