Abstract

This paper describes a digital method that is capable of automatically focusing optical coherence tomography (OCT) en face images without prior knowledge of the point spread function of the imaging system. The method utilizes a scalar diffraction model to simulate wave propagation from out-of-focus scatter to the focal plane, from which the propagation distance between the out-of-focus plane and the focal plane is determined automatically via an image-definition-evaluation criterion based on information entropy theory. By use of the proposed approach, we demonstrate that the lateral resolution close to that at the focal plane can be recovered from the imaging planes outside the depth of field region with minimal loss of resolution. Fresh onion tissues and mouse fat tissues are used in the experiments to show the performance of the proposed method.

©2012 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2011 (1)

2010 (1)

2009 (2)

Y. Liu, Y. Liang, G. Mu, and X. Zhu, “Deconvolution methods for image deblurring in optical coherence tomography,” J. Opt. Soc. Am. A 26(1), 72–77 (2009).
[Crossref] [PubMed]

J. Holmes and S. Hattersley, “Image blending and speckle noise reduction in multi-beam OCT,” Proc. SPIE 7168, 71681N, 71681N-8 (2009).
[Crossref]

2007 (4)

2006 (5)

2005 (5)

M. J. Cobb, X. Liu, and X. Li, “Continuous focus tracking for real-time optical coherence tomography,” Opt. Lett. 30(13), 1680–1682 (2005).
[Crossref] [PubMed]

L. Yu and M. K. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett. 30(16), 2092–2094 (2005).
[Crossref] [PubMed]

P. H. Tomlins and R. K. Wang, “Theory, developments and applications of optical coherence tomography,” J. Phys. D Appl. Phys. 38(15), 2519–2535 (2005).
[Crossref]

A. Divetia, T. H. Hsieh, J. Zhang, Z. Chen, M. Bachman, and G. P. Li, “Dynamically focused optical coherence tomography for endoscopic applications,” Appl. Phys. Lett. 86(10), 103902 (2005).
[Crossref]

T. S. Ralston, D. L. Marks, F. Kamalabadi, and S. A. Boppart, “Deconvolution methods for mitigation of transverse blurring in optical coherence tomography,” IEEE Trans. Image Process. 14(9), 1254–1264 (2005).
[Crossref] [PubMed]

2004 (1)

B. Qi, A. P. Himmer, L. M. Gordon, X. D. V. Yang, L. D. Dickensheets, and I. A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a micro-electromechanical mirror,” Opt. Commun. 232(1-6), 123–128 (2004).
[Crossref]

2003 (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]

2002 (1)

1999 (1)

R. K. Wang, “Resolution improved optical coherence-gating tomography for imaging biological tissue,” J. Mod. Opt. 46, 1905–1913 (1999).

1997 (1)

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33(16), 1365–1367 (1997).
[Crossref]

Bachman, M.

A. Divetia, T. H. Hsieh, J. Zhang, Z. Chen, M. Bachman, and G. P. Li, “Dynamically focused optical coherence tomography for endoscopic applications,” Appl. Phys. Lett. 86(10), 103902 (2005).
[Crossref]

Boppart, S. A.

B. J. Davis, S. C. Schlachter, D. L. Marks, T. S. Ralston, S. A. Boppart, and P. S. Carney, “Nonparaxial vector-field modeling of optical coherence tomography and interferometric synthetic aperture microscopy,” J. Opt. Soc. Am. A 24(9), 2527–2542 (2007).
[Crossref] [PubMed]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3(2), 129–134 (2007).
[Crossref]

T. S. Ralston, D. L. Marks, F. Kamalabadi, and S. A. Boppart, “Deconvolution methods for mitigation of transverse blurring in optical coherence tomography,” IEEE Trans. Image Process. 14(9), 1254–1264 (2005).
[Crossref] [PubMed]

Bradu, A.

Brenner, M.

Carney, P. S.

Chen, Z.

Chen, Z. P.

Cobb, M. J.

Dainty, Ch.

Davis, B. J.

Dickensheets, L. D.

B. Qi, A. P. Himmer, L. M. Gordon, X. D. V. Yang, L. D. Dickensheets, and I. A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a micro-electromechanical mirror,” Opt. Commun. 232(1-6), 123–128 (2004).
[Crossref]

Ding, Z. H.

Divetia, A.

A. Divetia, T. H. Hsieh, J. Zhang, Z. Chen, M. Bachman, and G. P. Li, “Dynamically focused optical coherence tomography for endoscopic applications,” Appl. Phys. Lett. 86(10), 103902 (2005).
[Crossref]

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]

Gordon, L. M.

B. Qi, A. P. Himmer, L. M. Gordon, X. D. V. Yang, L. D. Dickensheets, and I. A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a micro-electromechanical mirror,” Opt. Commun. 232(1-6), 123–128 (2004).
[Crossref]

Gruber, A.

Guo, S.

Hanson, S. R.

Hattersley, S.

J. Holmes and S. Hattersley, “Image blending and speckle noise reduction in multi-beam OCT,” Proc. SPIE 7168, 71681N, 71681N-8 (2009).
[Crossref]

Himmer, A. P.

B. Qi, A. P. Himmer, L. M. Gordon, X. D. V. Yang, L. D. Dickensheets, and I. A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a micro-electromechanical mirror,” Opt. Commun. 232(1-6), 123–128 (2004).
[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]

Holmes, J.

J. Holmes and S. Hattersley, “Image blending and speckle noise reduction in multi-beam OCT,” Proc. SPIE 7168, 71681N, 71681N-8 (2009).
[Crossref]

Hsieh, T. H.

A. Divetia, T. H. Hsieh, J. Zhang, Z. Chen, M. Bachman, and G. P. Li, “Dynamically focused optical coherence tomography for endoscopic applications,” Appl. Phys. Lett. 86(10), 103902 (2005).
[Crossref]

Hurst, S.

Itoh, M.

Izatt, J. A.

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33(16), 1365–1367 (1997).
[Crossref]

Jacques, S. L.

Kamalabadi, F.

T. S. Ralston, D. L. Marks, F. Kamalabadi, and S. A. Boppart, “Deconvolution methods for mitigation of transverse blurring in optical coherence tomography,” IEEE Trans. Image Process. 14(9), 1254–1264 (2005).
[Crossref] [PubMed]

Kim, M. K.

Kulkarni, M. D.

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33(16), 1365–1367 (1997).
[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]

Lee, K. S.

Li, G. P.

A. Divetia, T. H. Hsieh, J. Zhang, Z. Chen, M. Bachman, and G. P. Li, “Dynamically focused optical coherence tomography for endoscopic applications,” Appl. Phys. Lett. 86(10), 103902 (2005).
[Crossref]

Li, X.

Liang, Y.

Liu, G.

Liu, X.

Liu, Y.

Ma, Z.

Makita, S.

Marks, D. L.

B. J. Davis, S. C. Schlachter, D. L. Marks, T. S. Ralston, S. A. Boppart, and P. S. Carney, “Nonparaxial vector-field modeling of optical coherence tomography and interferometric synthetic aperture microscopy,” J. Opt. Soc. Am. A 24(9), 2527–2542 (2007).
[Crossref] [PubMed]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3(2), 129–134 (2007).
[Crossref]

T. S. Ralston, D. L. Marks, F. Kamalabadi, and S. A. Boppart, “Deconvolution methods for mitigation of transverse blurring in optical coherence tomography,” IEEE Trans. Image Process. 14(9), 1254–1264 (2005).
[Crossref] [PubMed]

Meemon, P.

Merino, D.

Mu, G.

Mukai, D.

Murali, S.

Nakamura, Y.

Nelson, J. S.

Podoleanu, A. G.

Qi, B.

B. Qi, A. P. Himmer, L. M. Gordon, X. D. V. Yang, L. D. Dickensheets, and I. A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a micro-electromechanical mirror,” Opt. Commun. 232(1-6), 123–128 (2004).
[Crossref]

Ralston, T. S.

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3(2), 129–134 (2007).
[Crossref]

B. J. Davis, S. C. Schlachter, D. L. Marks, T. S. Ralston, S. A. Boppart, and P. S. Carney, “Nonparaxial vector-field modeling of optical coherence tomography and interferometric synthetic aperture microscopy,” J. Opt. Soc. Am. A 24(9), 2527–2542 (2007).
[Crossref] [PubMed]

T. S. Ralston, D. L. Marks, F. Kamalabadi, and S. A. Boppart, “Deconvolution methods for mitigation of transverse blurring in optical coherence tomography,” IEEE Trans. Image Process. 14(9), 1254–1264 (2005).
[Crossref] [PubMed]

Rao, B.

Ren, H. W.

Rolland, J. P.

Sando, Y.

Schlachter, S. C.

Su, J.

Sugisaka, J. I.

Thomas, C. W.

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33(16), 1365–1367 (1997).
[Crossref]

Thompson, K. P.

Tomlins, P. H.

P. H. Tomlins and R. K. Wang, “Theory, developments and applications of optical coherence tomography,” J. Phys. D Appl. Phys. 38(15), 2519–2535 (2005).
[Crossref]

Vitkin, I. A.

B. Qi, A. P. Himmer, L. M. Gordon, X. D. V. Yang, L. D. Dickensheets, and I. A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a micro-electromechanical mirror,” Opt. Commun. 232(1-6), 123–128 (2004).
[Crossref]

Wang, Q.

Wang, R. K.

Xie, T.

Yang, X. D. V.

B. Qi, A. P. Himmer, L. M. Gordon, X. D. V. Yang, L. D. Dickensheets, and I. A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a micro-electromechanical mirror,” Opt. Commun. 232(1-6), 123–128 (2004).
[Crossref]

Yasuno, Y.

Yatagai, T.

Yousefi, S.

Yu, L.

Zhang, J.

L. Yu, B. Rao, J. Zhang, J. Su, Q. Wang, S. Guo, and Z. Chen, “Improved lateral resolution in optical coherence tomography by digital focusing using two-dimensional numerical diffraction method,” Opt. Express 15(12), 7634–7641 (2007).
[Crossref] [PubMed]

A. Divetia, T. H. Hsieh, J. Zhang, Z. Chen, M. Bachman, and G. P. Li, “Dynamically focused optical coherence tomography for endoscopic applications,” Appl. Phys. Lett. 86(10), 103902 (2005).
[Crossref]

Zhao, Y. H.

Zhi, Z.

Zhu, X.

Appl. Phys. Lett. (1)

A. Divetia, T. H. Hsieh, J. Zhang, Z. Chen, M. Bachman, and G. P. Li, “Dynamically focused optical coherence tomography for endoscopic applications,” Appl. Phys. Lett. 86(10), 103902 (2005).
[Crossref]

Electron. Lett. (1)

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33(16), 1365–1367 (1997).
[Crossref]

IEEE Trans. Image Process. (1)

T. S. Ralston, D. L. Marks, F. Kamalabadi, and S. A. Boppart, “Deconvolution methods for mitigation of transverse blurring in optical coherence tomography,” IEEE Trans. Image Process. 14(9), 1254–1264 (2005).
[Crossref] [PubMed]

J. Mod. Opt. (1)

R. K. Wang, “Resolution improved optical coherence-gating tomography for imaging biological tissue,” J. Mod. Opt. 46, 1905–1913 (1999).

J. Opt. Soc. Am. A (2)

J. Phys. D Appl. Phys. (1)

P. H. Tomlins and R. K. Wang, “Theory, developments and applications of optical coherence tomography,” J. Phys. D Appl. Phys. 38(15), 2519–2535 (2005).
[Crossref]

Nat. Phys. (1)

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3(2), 129–134 (2007).
[Crossref]

Opt. Commun. (1)

B. Qi, A. P. Himmer, L. M. Gordon, X. D. V. Yang, L. D. Dickensheets, and I. A. Vitkin, “Dynamic focus control in high-speed optical coherence tomography based on a micro-electromechanical mirror,” Opt. Commun. 232(1-6), 123–128 (2004).
[Crossref]

Opt. Express (7)

Y. Yasuno, J. I. Sugisaka, Y. Sando, Y. Nakamura, S. Makita, M. Itoh, and T. Yatagai, “Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography,” Opt. Express 14(3), 1006–1020 (2006).
[Crossref] [PubMed]

T. Xie, S. Guo, Z. Chen, D. Mukai, and M. Brenner, “GRIN lens rod based probe for endoscopic spectral domain optical coherence tomography with fast dynamic focus tracking,” Opt. Express 14(8), 3238–3246 (2006).
[Crossref] [PubMed]

D. Merino, Ch. Dainty, A. Bradu, and A. G. Podoleanu, “Adaptive optics enhanced simultaneous en-face optical coherence tomography and scanning laser ophthalmoscopy,” Opt. Express 14(8), 3345–3353 (2006).
[Crossref] [PubMed]

R. K. Wang, S. L. Jacques, Z. Ma, S. Hurst, S. R. Hanson, and A. Gruber, “Three dimensional optical angiography,” Opt. Express 15(7), 4083–4097 (2007).
[Crossref] [PubMed]

L. Yu, B. Rao, J. Zhang, J. Su, Q. Wang, S. Guo, and Z. Chen, “Improved lateral resolution in optical coherence tomography by digital focusing using two-dimensional numerical diffraction method,” Opt. Express 15(12), 7634–7641 (2007).
[Crossref] [PubMed]

J. P. Rolland, P. Meemon, S. Murali, K. P. Thompson, and K. S. Lee, “Gabor-based fusion technique for optical coherence microscopy,” Opt. Express 18(4), 3632–3642 (2010).
[Crossref] [PubMed]

G. Liu, S. Yousefi, Z. Zhi, and R. K. Wang, “Automatic estimation of point-spread-function for deconvoluting out-of-focus optical coherence tomographic images using information entropy-based approach,” Opt. Express 19(19), 18135–18148 (2011).
[Crossref] [PubMed]

Opt. Lett. (5)

Proc. SPIE (1)

J. Holmes and S. Hattersley, “Image blending and speckle noise reduction in multi-beam OCT,” Proc. SPIE 7168, 71681N, 71681N-8 (2009).
[Crossref]

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 (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw Hill, Boston, 1996).

Supplementary Material (2)

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Figures (8)

Fig. 1
Fig. 1 The effect of numerical aperture on the desirable lateral resolution and the DOF in the OCT imaging, for the cases of (a) low NA, resulting in relatively long DOF but low lateral resolution; and (b) high NA, leading to relatively shorter DOF but much high lateral resolution.

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Fig. 2
Fig. 2 Geometry of diffraction. Σ0, de-focal plane; Σ, focal plane.

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Fig. 3
Fig. 3 Flow diagram of OCT 3D volume recovery.

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Fig. 4
Fig. 4 Schematic of the OCT system used in this study

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Fig. 5
Fig. 5 Change of the information entropy of recovered images A-F as a function of the diffraction distance z. Image C is the original de-focal image (z = 0) and image D is the clearest image with the lowest entropy, deemed as the recovered image at this plane.

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Fig. 6
Fig. 6 (a) Typical defocused en face image of an onion when the sample was placed outside the DOF region. (b) Recovered image from (a). (c) Typical en- face image of the onion when the sample was placed within DOF region.

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Fig. 7
Fig. 7 Plots of OCT signal strength across the line located at the marked position in Fig. 6. The x-axis indicates the pixel numbers, and the y-axis gives the grey-scale values corresponding to the OCT image.

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Fig. 8
Fig. 8 (a) Defocused en face image of the fat tissue when the sample was placed outside the DOF region. (b) Recovered image from (a). (c) Typical en- face image of the fat tissue when the sample was placed within DOF region.

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Equations (14)

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

u ( P 0 , t ) = A ( P 0 ) cos [ 2 π ν t + φ ( P 0 ) ]
U ( P 0 ) = A ( P 0 ) exp [ − j φ ( P 0 ) ]
( ∇ 2 + k 2 ) U = 0
k = 2 π n ν c = 2 π λ
U ( P ) = 1 j λ ∬ Σ 0 U ( P 0 ) exp ( j k r ) r cos ( n → , r → ) d Σ 0
U ( x , y ) = 1 j λ ∬ Σ 0 U ( x 0 , y 0 ) exp ( j k ( x − x 0 ) 2 + ( y − y 0 ) 2 + z 2 ) ( x − x 0 ) 2 + ( y − y 0 ) 2 + z 2 z ( x − x 0 ) 2 + ( y − y 0 ) 2 + z 2 d x 0 d y 0 = z j λ ∬ Σ 0 U ( x 0 , y 0 ) exp ( j k ( x − x 0 ) 2 + ( y − y 0 ) 2 + z 2 ) ( x − x 0 ) 2 + ( y − y 0 ) 2 + z 2 d x 0 d y 0
U ( x , y ) = 1 j λ z ∬ Σ 0 U ( x 0 , y 0 ) exp { j k z + j k 2 z ( x − x 0 ) 2 + ( y − y 0 ) 2 } d x 0 d y 0
U ( x , y ) = 1 j λ z exp ( j k z ) { U ( x 0 , y 0 ) ⊗ exp [ j k 2 z ( x 2 + y 2 ) ] }
U ( x , y ) = 1 2 π exp ( j k z ) F − 1 { F [ U ( x 0 , y 0 ) ] × exp [ j z 2 k ( k x 2 + k y 2 ) ] }
| U ( x , y ) | = 1 2 π | F − 1 { F [ U ( x 0 , y 0 ) ] × exp [ j z 2 k ( k x 2 + k y 2 ) ] } |
P ( X ) = P ( p i ) = ∑ i = 1 n p i log ( 1 / p i )
E ( I ) = − ∑ i = 1 n p ( I i ) ⋅ log ( p ( I i ) )
p ( I i ) = The number of pixels with intensity value equal to  I i  in the image    Total number of pixels in the image
{ F i n d M i n s . t . z E ( I z ) z min < z < z max

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