## Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography

Optics Express, Vol. 14, Issue 3, pp. 1006-1020 (2006)

http://dx.doi.org/10.1364/OE.14.001006

Acrobat PDF (410 KB)

### Abstract

A numerical deconvolution method to cancel lateral defocus in Fourier domain optical coherence tomography (FD-OCT) is presented. This method uses a depth-dependent lateral point spread function and some approximations to design a deconvolution filter for the cancellation of lateral defocus. Improved lateral resolutions are theoretically estimated;
consequently, the effect of lateral superresolution in this method is derived. The superresolution is experimentally confirmed by a razor blade test, and an intuitive physical interpretation of this effect is presented. The razor blade test also confirms that this method enhances the signal-to-noise ratio of OCT. This method is applied to OCT images of medical samples, *in vivo* human anterior eye segments, and exhibits its potential to cancel the defocusing of practical OCT images. The validity and restrictions involved in each approximation employed to design the deconvolution filter are discussed. A chromatic and a two-dimensional extensions of this method are also described.

© 2006 Optical Society of America

## 1. Introduction

1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science **254**, 1178–1181 (1991). [CrossRef] [PubMed]

2. W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “*In vivo* ultrahigh-resolution optical coherence tomography,” Opt. Lett. **24**, 1221–1223 (1999). [CrossRef]

3. B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W.J. Wadsworth, J. C. Knight, P. St. J. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer axial resolution
optical coherence tomography,” Opt. Lett. **27**, 1800–1802 (2002). [CrossRef]

4. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. **117**, 43–48 (1995). [CrossRef]

5. Gerd Háusler and Michael Walter Lindner, “‘Coherence radar’ and ‘spectral radar’ -New tools for dermatological diagnosis,” J. Biomed. Opt. **3**, 21–31 (1998). [CrossRef]

6. P. Andretzky, M.W. Lindner, J. M. Herrmann, A. Schultz, M. Konzog, F. Kiesewetter, and G. H ausler , “Optical coherence tomography by spectral radar: dynamic range estimation and in-vivo measurements of skin,” Proc. SPIE **3567**, 78–87 (1999). [CrossRef]

12. N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, “*In vivo* high-resolution video-rate spectral-domain optical coherence tomography of the human retina and
optic nerve,” Opt. Express **12**, 367–376 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367. [CrossRef] [PubMed]

13. R. Huber, M. Wojtkowski, K. Taira, J. G. Fujimoto, and K. Hsu, “Amplified, frequency swept lasers for frequency
domain reflectometry and OCT imaging: design and scaling principles,” Opt. Express **13**3513–3528 (2005),
http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-9-3513. [CrossRef] [PubMed]

14. M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “*In vivo* human retinal imaging
by Fourier domain optical coherence tomography,” J. Biomed. Opt. **7**, 457–463 (2002). [CrossRef] [PubMed]

21. Z. P. Chen, T. E. Milner, S. Srinivas, X. Wang, A. Malekafzali, M. J. C. van Gemert, and J. S. Nelson, “Noninvasive imagingof in vivo blood flow velocity usingoptical Doppler tomography,” Opt. Lett. **22**, 1119–1121
(1997). [CrossRef] [PubMed]

22. Y. Zhao, Z. Chen, C. Saxer, S. Xiang, J. de Boer, and J. Nelson, “Phase-resolved optical coherence tomography
and optical Doppler tomography for imaging blood f low in human skin with fast scanning speed and high velocity sensitivity,” Opt. Lett. **25**, 114–116 (2000). [CrossRef]

23. Y. Yasuno, S. Makita, Y. Sutoh, M. Itoh, and T. Yatagai, “Birefringence imaging of human skin by polarization-sensitive spectral interferometric optical coherence tomography,” Opt. Lett. **27**, 1803–1805 (2002). [CrossRef]

26. B. Park, M. Pierce, B. Cense, S. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based
multi-functional spectral-domain optical coherence tomography at 1.3 μm,” Opt. Express **13**, 3931–3944 (2005),
http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-3931. [CrossRef] [PubMed]

32. M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, “Spectral-domain phase microscopy,” Opt. Lett. **30**, 1162–1164 (2005). [CrossRef] [PubMed]

33. C. Joo, T. Akkin, B. Cense, B. Park, and J. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. **30**, 2131–2133 (2005). [CrossRef] [PubMed]

33. C. Joo, T. Akkin, B. Cense, B. Park, and J. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. **30**, 2131–2133 (2005). [CrossRef] [PubMed]

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

41. R. Tripathi, N. Nassif, J. Nelson, B. Park, and J. de Boer, “Spectral shaping for non-Gaussian source spectra in
optical coherence tomography,” Opt. Lett. **27**, 406–408 (2002). [CrossRef]

42. M. Szkulmowski, M. Wojtkowski, T. Bajraszewski, I. Gorczyńska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence
tomography with supercontinuum source,” Opt. Commun. **246**, 569–578 (2004). [CrossRef]

*in vivo*measurement are shown. A few limitations of this method that takes into account the approximations employed in the designing process of the deconvolution filter, and some possible extensions of this method are discussed.

## 2. Methods

### 2.1. Lateral point spread function of OCT

*f*the focal length of an objective, and

*d*the 1/

*e*

^{2}-diameter of a probe beam. It is evident that the lateral resolution improves as

*d*/

*f*(~2NA) becomes large. On the other hand, the depth measurement range, namely DOF, decreases with the second power of

*d*/

*f*as

*x*and

*ξ*respectively denote the lateral position and its Fourier conjugate, i.e., the spatial frequency, exp (-

*παx*

^{2}) represents the field distribution on the front-focal-plane and

*α*≡ 4/

*πd*

^{2}is a constant defined by the 1/

*e*

^{2}-diameter of the Gaussian probe beam;

*d*.

*z*=

*z*

_{0}) is calculated as the Fresnel diffraction of Eq. (3) with a propagation length of -

*z*

_{0};

*p*(

*x*,

*z*

_{0})

*f*(

*x*,

*z*

_{0}) where

*f*(

*x*,

*z*

_{0}) represents the back scattering distribution, or optical structure of the sample on the sample plane.

44. D. J Smithies, T. Lindmo, Z. P. Chen, J. S. Nelson, and T. E. Milner, “Signal attenuation and localization in
optical coherence tomography studied by Monte Carlo simulation,” Phys. Med. Biol. **43**, 3025–3044 (1998). [CrossRef] [PubMed]

*x*= 0 is expressed as

*x*) scan, this equation can be rewritten as

*p*(

*x*,

*z*

_{0}) and

*q*(

*x*,

*z*

_{0}) are even functions and ∗ denotes the convolution operator over

*x*. From this equation, it is evident that the PSF of this OCT detection is

### 2.2. Design of deconvolution filter

*a*=

*αλ*

^{2}

*f*

^{2}/(

*α*

^{2}

*λ*

^{4}

*f*

^{4}+

*λ*

^{2}

*z*

^{2}

_{0}) and

*b*= 2

*λ*

*z*

_{0}/(

*α*

^{2}

*λ*

^{4}

*f*

^{4}+

*λ*

^{2}

*z*

^{2}

_{0}). However, it is evident that the amplitude of this deconvolution filter tends to infinity and enhances the noise energy as the spatial frequency ξ increases. To avoid this problem, we introduced the first approximation; we set the amplitude of this deconvolution filter to a constant, 1. Since only the relative profile of this function is important, the conservation of the signal energy was reasonably ignored to simplify the equation.

*z*

_{0}→0 (see appendix B). To deal with this problem, the second approximation

*λ*/

*π*)(

*f*/

*d*)

^{2}, as determined in Eq. (2), hence, this approximation is at least valid in the OOF range. The validity in the DOF range will be demonstrated in the following sections.

### 2.3. Deconvolution of the OCT image

*N*denotes the number of A-scans for a B-scan and

*M*denotes the number of wavelength bins in a digitized spectral interferogram. To apply this deconvolution method to an OCT image, a conventional two-dimensional complex FD-OCT image is first calculated from a two-dimensional spectral interferogram [4

4. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. **117**, 43–48 (1995). [CrossRef]

12. N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, “*In vivo* high-resolution video-rate spectral-domain optical coherence tomography of the human retina and
optic nerve,” Opt. Express **12**, 367–376 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367. [CrossRef] [PubMed]

14. M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “*In vivo* human retinal imaging
by Fourier domain optical coherence tomography,” J. Biomed. Opt. **7**, 457–463 (2002). [CrossRef] [PubMed]

12. N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, “*In vivo* high-resolution video-rate spectral-domain optical coherence tomography of the human retina and
optic nerve,” Opt. Express **12**, 367–376 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367. [CrossRef] [PubMed]

### 2.4. Improved lateral resolution

*γ*= (

*α*

^{2}

*λ*

^{2}

*f*

^{4}+

*z*

^{2}

_{0})/(

*α*

^{2}

*λ*

^{2}

*f*

^{4}+4

*z*

^{2}

_{0}). Now, the lateral resolution is no longer a constant but a function of

*z*

_{0}. When

*z*

_{0}= 0, this improved lateral resolution is identical to the in-focus resolution. Figure 4 shows a viewgraph of this equation. According to this viewgraph, we can conclude that the above-mentioned second approximation is acceptable not only in the OOF range but also in the DOF range. Additionally, this equation suggests an interesting property of this deconvolution method. As shown in Eq. (13) and Fig. 4, the lateral resolution approaches Δ

*x*/2, i.e., one half of the original in-focus resolution as

*z*

_{0}approaches ±∞. This property predicts the lateral superresolution of this deconvolution method and is experimentally validated in the following section.

## 3. Experimental validations

### 3.1. FD-OCT setup

*μ*m in air. This light is introduced into a fiber Michelson interferometer, and 20% of the beam illuminates the sample via an objective with a focal length of 60 mm while the rest is used as a reference beam. The reference beam and 80% of the back scattered light from the sample is corrected and introduced into a spectrometer comprising of a volume holographic grating (Wasatch Photonics, UT, USA) with a groove density of 1200 lp/mm, an achromatic doublet lens (Thorlabs, Inc.) with a focal length of 200 mm, and a high-speed line CCD camera (L103k-2k, Basler Vision Technologies, Germany) with 2048 pixels and a line rate of 18.7 KHz. The digital output from the CCD camera, i.e., a spectral interferogram, is transferred to a computer via CameraLink frame grabber (mvTITAN-CL, MATRIX VISION GmbH, Germany). The spectral interferogram is rescaled from the

*λ*-domain to

*k*-domain by zero-filling interpolation [12

*In vivo* high-resolution video-rate spectral-domain optical coherence tomography of the human retina and
optic nerve,” Opt. Express **12**, 367–376 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367. [CrossRef] [PubMed]

45. C. Dorrer, N. Belabas, J. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B **17**, 1795–1802 (2000). [CrossRef]

*μ*W probe power, while the shot noise limited sensitivity is 107 dB. A CCD quantum efficiency of 50% and a grating diffraction efficiency of 80% are used to calculate the shot noise limited sensitivity.

### 3.2. Razor blade test

*η*and

*ε*are fitting coefficients that correspond to the steepness and the center position of the sigmoidal curve respectively. Consequently, the full width of 20% and 80% maximum (20–80 width) of the curve is determined from

*η*and is used as a measure of lateral resolution. Figure 6 plots the 20–80 widths over defocus

*z*

_{0}. The red curve corresponds to the 20–80 width of the raw OCT images and the blue curve corresponds to that of the deconvolved OCT images. Here, it is evident that the 20–80 width of the OOF range is twice as better as that of the in-focus. This plot experimentally proves superresolution in the OOF range.

*μ*m with our optical parameters of

*d*= 1.5 mm and

*f*= 60 mm, and it is agreed with the experiment. In the OOF range, the relationship between the 20–80 width and the 1/

*e*

^{2}-width is too elaborate to obtain analytically. However, the razor blade test is one of the standard tests for lateral resolution of in-focus imaging. Since the improved 1/

*e*

^{2}-resolution can not be measured directly, the 20–80 width of the razor blade test may be a reasonable measure of the lateral resolution.

### 3.3. Physical interpretation of superresolution

### 3.4. SNR enhancement

### 3.5. Measurement of biological sample

*in vivo*OCT measurement of human anterior eye segments. The investigation of anterior eye segments is one of the applications of OCT that requires a large depth-measurement range where a short DOF range is problematic. Figure 7(a) shows an example of an in-focus OCT of a human anterior eye segment. Here, the surface of the crystalline lens and iris stroma are evident. Figure 7(b) shows an OCT image of the same sample with 4-mm defocusing, and Fig. 7(c) shows the same image after deconvolution. This effect is also evident in Figs. 7(d) and 7(e), in which the defocus length is 8 mm. The faint structures on the surface of the iris in Figs. 7(d) are clearly improved and easily recognized in Fig. 7(e). Here, it should be noted that the drop in SNR in Figs. 7(c) and 7(e) is caused by the confocality of the fiber interferometer. The confocal parameter of this setup is 1.9 mm, and is relatively smaller than the defocus length.

## 4. Discussions

### 4.1. Limitation of the NA of an objective

*d*and focal length of the objective

*f*should satisfy the criterion of Fresnel diffraction [46]

*l*denotes the propagation length, and

_{z}*W*and

_{x}*W*´

_{x}denote the lateral extensions of electric fields on the source and destination planes of the diffraction, respectively.

*l*corresponds to the focal length of the objective

_{z}*f*, the probe beam diameter

*d*can be regarded as

*W*, and the condition becomes

_{x}*W*´

_{x}is much smaller than the beam diameter

*d*.

*d*= 1.5 mm and

*λ*= 838 nm, the above condition becomes

*f*> 6.7 mm; our setup satisfies this condition. This condition can also be written in other forms, e.g., an effective NA < 0.11 or

*d*/

*f*< 0.22; this condition is satisfactory for most OCT systems. Another description of this condition is that the virtually doubled NA (described in section 3.3) can not exceed 0.22 with the above-mentioned experimental parameters.

### 4.2. Limitation of the superresolution range

*p*(

*x*,

*z*

_{0}) (Eq. (4)) was derived from the field distribution of the back-focal-plane (Eq. (3)) by Fresnel diffraction. This Fresnel diffraction imposes the following condition on the propagation length

*z*

_{0}by Eq. (16);

*W*=

_{x}*W*´

_{x}= Δ

*x*. The experimental parameters of

*λ*= 838 nm,

*f*= 60 mm, and

*d*= 1.5 mm yield the condition ∣

*z*

_{0}∣ > 67 μm.

*z*

_{0}∣ ≫ 780

*μ*m. Since this condition is stricter than Eq. (18), Eq. (11) determines the minimum defocus length for the approximations.

### 4.3. Monochromatic versus chromatic algorithms

*λ*was regarded as a constant and we typically used the center wavelength of the broadband light source as

*λ*(monochromatic approximation).

*M*+

*N*)

*N*one-dimensional DFTs, while a monochromatic algorithm requires performing (

*M*+

*N*) DFTs. Hence, chromatic algorithm requires a calculation time that is

*N*times longer than that required for a monochromatic algorithm; for example

*N*= 2048 for our setup. Furthermore, for a typical semiconductor light source employed in OCT, i.e. with a bandwidth of a few tens of nanometers, we could not observe any significant differences in the qualities of the OCT images of monochromatic and chromatic algorithms. Hence, it is more reasonable to use the monochromatic algorithm than the chromatic algorithm.

### 4.4. One-dimensional and two-dimensional deconvolution

*x*, whereas, in reality, both of them are lateral two-dimensional functions. Consequently, the designed deconvolution filter is also a one-dimensional function of

*x*.

*In vivo* high-resolution video-rate spectral-domain optical coherence tomography of the human retina and
optic nerve,” Opt. Express **12**, 367–376 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367. [CrossRef] [PubMed]

18. B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S. H. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,”
Opt. Express **12**, 2435–2447 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2435. [CrossRef] [PubMed]

## 5. Conclusions

*in vivo*human anterior eye segments, and it cancels the defocusing in these images.

## Appendix

## A. Fourier transform of lateral point spread function

*a*≡

*αλ*

^{2}

*f*

^{2}/(

*α*

^{2}

*λ*

^{4}

*f*

^{4}+

*λ*

^{2}

*z*

^{2}

_{0}) and

*b*≡ 2

*λ*

*z*

_{0}/(

*α*

^{2}

*λ*

^{4}

*f*

^{4}+

*λ*

^{2}

*z*

^{2}

_{0}), Eq. (8) is rewritten as

*σ*=

*π*(

*a*-

*ib*), and

*h*(

*x*,

*z*

_{0}) is denoted as

*h*(

*x*) for simplicity.

*h*(

*x*) is

*ρ*=

*i*2

*πξ*/

*σ*.

*H*(

*ξ*) becomes

**B. Phase property of***H*^{-1}(*ξ*)

*ξ*,

*a*and

*b*in Eq. (9) should fulfill the following conditions;

*a*≪ 1 and

*a*≪

*b*.

*z*

_{0}→ 0.

## Acknowledgements

## References and links

1. | D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science |

2. | W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “ |

3. | B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W.J. Wadsworth, J. C. Knight, P. St. J. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer axial resolution
optical coherence tomography,” Opt. Lett. |

4. | A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. |

5. | Gerd Háusler and Michael Walter Lindner, “‘Coherence radar’ and ‘spectral radar’ -New tools for dermatological diagnosis,” J. Biomed. Opt. |

6. | P. Andretzky, M.W. Lindner, J. M. Herrmann, A. Schultz, M. Konzog, F. Kiesewetter, and G. H ausler , “Optical coherence tomography by spectral radar: dynamic range estimation and in-vivo measurements of skin,” Proc. SPIE |

7. | T. Mitsui, “Dynamic range of optical reflectometry with spectral interferometry,” Jpn. J. Appl. Phys. |

8. | R. A. Leitgeb, C. K. Hitzenberger, and A. F. Fercher,”Performance of fourier domain
vs. time domain optical coherence tomography,” Opt. Express |

9. | J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma,”“Improved signal-to-noise
ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. |

10. | M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, “Sensitivity advantage of swept source
and Fourier domain optical coherence tomography,” Opt. Express |

11. | S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,”
Opt. Express |

12. | N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, “ |

13. | R. Huber, M. Wojtkowski, K. Taira, J. G. Fujimoto, and K. Hsu, “Amplified, frequency swept lasers for frequency
domain reflectometry and OCT imaging: design and scaling principles,” Opt. Express |

14. | M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “ |

15. | N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, “ |

16. | R. A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. F. Fercher,
“Ultrahigh resolution Fourier domain optical coherence tomography,” Opt. Express |

17. | M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express |

18. | B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S. H. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,”
Opt. Express |

19. | S. Jiao, R. Knighton, X. Huang, G. Gregori, and C. A. Puliafito, “Simultaneous acquisition of sectional and
fundus ophthalmic images with spectral-domain optical coherence tomography,” Opt. Express |

20. | M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional
retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology |

21. | Z. P. Chen, T. E. Milner, S. Srinivas, X. Wang, A. Malekafzali, M. J. C. van Gemert, and J. S. Nelson, “Noninvasive imagingof in vivo blood flow velocity usingoptical Doppler tomography,” Opt. Lett. |

22. | Y. Zhao, Z. Chen, C. Saxer, S. Xiang, J. de Boer, and J. Nelson, “Phase-resolved optical coherence tomography
and optical Doppler tomography for imaging blood f low in human skin with fast scanning speed and high velocity sensitivity,” Opt. Lett. |

23. | Y. Yasuno, S. Makita, Y. Sutoh, M. Itoh, and T. Yatagai, “Birefringence imaging of human skin by polarization-sensitive spectral interferometric optical coherence tomography,” Opt. Lett. |

24. | Y. Yasuno, S. Makita, T. Endo, M. Itoh, T. Yatagai, M. Takahashi, C. Katada, and M. Mutoh, “Polarization-sensitive
complex Fourier domain optical coherence tomography for Jones matrix imaging of biological samples,” Appl. Phys. Lett. |

25. | J. Zhang, W. Jung, J. S. Nelson, and Z. P. Chen, “Full range polarization-sensitive
Fourier domain optical coherence tomography,” Opt. Express |

26. | B. Park, M. Pierce, B. Cense, S. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based
multi-functional spectral-domain optical coherence tomography at 1.3 μm,” Opt. Express |

27. | R. A. Leitgeb, L. Schmetterer, W. Drexler, A. F. Fercher, R. J. Zawadzki, and T. Bajraszewski, “Real-time assessment
of retinal blood flow with ultrafast acquisition by color Doppler Fourier domain optical coherence tomography,”
Opt. Express |

28. | B. R. White, M. C. Pierce, N. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, “ |

29. | R. A. Leitgeb, L. Schmetterer, C. K. Hitzenberger, A. F. Fercher, F. Berisha, M. Wojtkowski, and T. Bajraszewski,
“Real-time measurement of in vitro flow by Fourier-domain color Doppler optical coherence tomography,” Opt.
Lett. |

30. | L. Wang, Y. Wang, S. Guo, J. Zhang, M. Bachman, G.P. Li, and Z. P. Chen, “Frequency domain phase-resolved
optical Doppler and Deppler variance tomography,” Opt. Commun. |

31. | J. Zhang and Z. Chen, “ |

32. | M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, “Spectral-domain phase microscopy,” Opt. Lett. |

33. | C. Joo, T. Akkin, B. Cense, B. Park, and J. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. |

34. | Y. Zhang, J. Rha, R. Jonnal, and D. Miller, “Adaptive optics parallel spectral domain optical
coherence tomography for imaging the living retina,” Opt. Express |

35. | R. Zawadzki, S. Jones, S. Olivier, M. Zhao, B. Bower, J. Izatt, S. Choi, S. Laut, and J. Werner, “Adaptive-optics
optical coherence tomography for high-resolution and high-speed 3D retinal in vivo imaging,” Opt. Express |

36. | M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. |

37. | J. M. Schmitt, “Restoration of optical coherence images of living tissue using the clean algorithm,” J. Biomed.
Opt. |

38. | D. Piao, Q. Zhu, N. Dutta, S. Yan, and L. Otis, “Cancellation of coherent artifacts in optical coherence tomography imaging,” Appl. Opt. |

39. | I. J. Hsu, C.W. Sun, C.W. Lu, C. C. Yang, C. P. Chiang, and C.W. Lin, “Resolution improvement with dispersion
manipulation and a retrieval algorithm in optical coherence tomography,” Appl. Opt. |

40. | M. Bashkansky, M.D. Duncan, J. Reintjes, and P.R. Battle, “Signal processing for improving field cross-correlation function in optical coherence tomography,” Appl. Opt. |

41. | R. Tripathi, N. Nassif, J. Nelson, B. Park, and J. de Boer, “Spectral shaping for non-Gaussian source spectra in
optical coherence tomography,” Opt. Lett. |

42. | M. Szkulmowski, M. Wojtkowski, T. Bajraszewski, I. Gorczyńska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence
tomography with supercontinuum source,” Opt. Commun. |

43. | E.g., James G. Fujimoto, “Handbook of optical coherence tomography,” Chapter 1, Edited by G.R. Bouma, G.J. Tearney, Marcel Dekker, Inc. (2002). |

44. | D. J Smithies, T. Lindmo, Z. P. Chen, J. S. Nelson, and T. E. Milner, “Signal attenuation and localization in
optical coherence tomography studied by Monte Carlo simulation,” Phys. Med. Biol. |

45. | C. Dorrer, N. Belabas, J. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B |

46. | E.g.,J. W. Goodman, “Introduction to Fourier optics,” 2nd ed., The McGraw-Hill Companies, Inc. (1996). |

**OCIS Codes**

(100.1830) Image processing : Deconvolution

(100.6640) Image processing : Superresolution

(110.2990) Imaging systems : Image formation theory

(110.4500) Imaging systems : Optical coherence tomography

(170.4500) Medical optics and biotechnology : Optical coherence tomography

**ToC Category:**

Image Processing

**History**

Original Manuscript: December 15, 2005

Revised Manuscript: January 20, 2006

Manuscript Accepted: January 23, 2006

Published: February 6, 2006

**Virtual Issues**

Vol. 1, Iss. 3 *Virtual Journal for Biomedical Optics*

**Citation**

Yoshiaki Yasuno, Jun-ichiro Sugisaka, Yusuke Sando, Yoshifumi Nakamura, Shuichi Makita, Masahide Itoh, and Toyohiko Yatagai, "Non-iterative numerical method for laterally superresolving Fourier domain optical coherence tomography," Opt. Express **14**, 1006-1020 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-3-1006

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### References

- D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991). [CrossRef] [PubMed]
- W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24, 1221–1223 (1999). [CrossRef]
- B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight, P. St. J. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer axial resolution optical coherence tomography,” Opt. Lett. 27, 1800–1802 (2002). [CrossRef]
- A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995). [CrossRef]
- Gerd Häusler and Michael Walter Lindner, “ ‘Coherence radar’ and ‘spectral radar’ —New tools for dermatological diagnosis,” J. Biomed. Opt. 3, 21–31 (1998). [CrossRef]
- P. Andretzky, M.W. Lindner, J. M. Herrmann, A. Schultz, M. Konzog, F. Kiesewetter, and G. H ausler , “Optical coherence tomography by spectral radar: dynamic range estimation and in-vivo measurements of skin,” Proc. SPIE 3567, 78–87 (1999). [CrossRef]
- T. Mitsui, “Dynamic range of optical reflectometry with spectral interferometry,” Jpn. J. Appl. Phys. 38, 6133– 6137 (1999). [CrossRef]
- R. A. Leitgeb, C. K. Hitzenberger, and A. F. Fercher,” Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11, 889–894 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-889">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-889</a>. [CrossRef] [PubMed]
- J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma,” “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28, 2067–2069 (2003). [CrossRef] [PubMed]
- M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11, 2183–2189 (2003), <a href="http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183">http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-18-2183</a>. [CrossRef] [PubMed]
- S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, “High-speed optical frequency-domain imaging,” Opt. Express 11, 2953–2963 (2003), <a href="http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-22-2953">http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-22-2953</a>. [CrossRef] [PubMed]
- N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, “In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve,” Opt. Express 12, 367–376 (2004), <a href="http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367">http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-367</a>. [CrossRef] [PubMed]
- R. Huber,M.Wojtkowski, K. Taira, J. G. Fujimoto, and K. Hsu, “Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles,” Opt. Express 13 3513–3528 (2005), <a href="http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-9-3513">http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-9-3513</a>. [CrossRef] [PubMed]
- M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. 7, 457–463 (2002). [CrossRef] [PubMed]
- N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, “In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve,” Opt. Express 12, 367–376 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-367">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-367</a>. [CrossRef] [PubMed]
- R. A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl, and A. F. Fercher, “Ultrahigh resolution Fourier domain optical coherence tomography,” Opt. Express 12, 2156–2165 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2156">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2156</a>. [CrossRef] [PubMed]
- M. Wojtkowski, V. J. Srinivasan, T. H. Ko, and J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express 12, 2404–2422 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2404">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2404</a>. [CrossRef] [PubMed]
- B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S. H. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express 12, 2435–2447 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2435">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2435</a>. [CrossRef] [PubMed]
- S. Jiao, R. Knighton, X. Huang, G. Gregori, and C. A. Puliafito, “Simultaneous acquisition of sectional and fundus ophthalmic images with spectral-domain optical coherence tomography,” Opt. Express 12, 444–452 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-444">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-444</a>. [CrossRef]
- M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112, 1734–1746 (2005). [CrossRef] [PubMed]
- Z. P. Chen, T. E. Milner, S. Srinivas, X. Wang, A. Malekafzali, M. J. C. van Gemert, and J. S. Nelson, “Noninvasive imagingof in vivo blood flow velocity usingoptical Doppler tomography,” Opt. Lett. 22, 1119–1121 (1997). [CrossRef] [PubMed]
- Y. Zhao, Z. Chen, C. Saxer, S. Xiang, J. de Boer, and J. Nelson, “Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood f low in human skin with fast scanning speed and high velocity sensitivity,” Opt. Lett. 25, 114–116 (2000). [CrossRef]
- Y. Yasuno, S. Makita, Y. Sutoh, M. Itoh, and T. Yatagai, “Birefringence imaging of human skin by polarization-sensitive spectral interferometric optical coherence tomography,” Opt. Lett. 27, 1803–1805 (2002). [CrossRef]
- Y. Yasuno, S. Makita, T. Endo, M. Itoh, T. Yatagai, M. Takahashi, C. Katada, and M. Mutoh, “Polarization-sensitive complex Fourier domain optical coherence tomography for Jones matrix imaging of biological samples,” Appl. Phys. Lett. 85, 3023–3025 (2004). [CrossRef]
- J. Zhang, W. Jung, J. S. Nelson, and Z. P. Chen, “Full range polarization-sensitive Fourier domain optical coherence tomography,” Opt. Express 12, 6033–6039 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-6033">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-6033</a>. [CrossRef] [PubMed]
- B. Park, M. Pierce, B. Cense, S. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 ∫m,” Opt. Express 13, 3931–3944 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-3931">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-3931</a>. [CrossRef] [PubMed]
- R. A. Leitgeb, L. Schmetterer, W. Drexler, A. F. Fercher, R. J. Zawadzki, and T. Bajraszewski, “Real-time assessment of retinal blood flow with ultrafast acquisition by color Doppler Fourier domain optical coherence tomography,” Opt. Express 11, 3116–3121 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-3116">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-3116</a>. [CrossRef] [PubMed]
- B. R. White, M. C. Pierce, N. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, “In vivo dynamic human retinal blood flow imaging using ultra- high-speed spectral domain optical coherence tomography,” Opt. Express 11, 3490-3497 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-25-3490">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-25-3490</a>. [CrossRef] [PubMed]
- R. A. Leitgeb, L. Schmetterer, C. K. Hitzenberger, A. F. Fercher, F. Berisha, M.Wojtkowski, and T. Bajraszewski, “Real-time measurement of in vitro flow by Fourier-domain color Doppler optical coherence tomography,” Opt. Lett. 29, 171–173 (2004). [CrossRef] [PubMed]
- L. Wang, Y. Wang, S. Guo, J. Zhang, M. Bachman, G.P. Li, and Z. P. Chen, “Frequency domain phase-resolved optical Doppler and Deppler variance tomography,” Opt. Commun. 242, 345–350 (2005). [CrossRef]
- J. Zhang, and Z. Chen, “In vivo blood flow imaging by a swept laser source based Fourier domain optical Doppler tomography,” Opt. Express 13, 7449–7457 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-19-7449">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-19-7449</a>. [CrossRef] [PubMed]
- M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, “Spectral-domain phase microscopy,” Opt. Lett. 30, 1162–1164 (2005). [CrossRef] [PubMed]
- C. Joo, T. Akkin, B. Cense, B. Park, and J. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. 30, 2131–2133 (2005). [CrossRef] [PubMed]
- Y. Zhang, J. Rha, R. Jonnal, and D. Miller, “Adaptive optics parallel spectral domain optical coherence tomography for imaging the living retina,” Opt. Express 13, 4792–4811 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4792">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4792</a>. [CrossRef] [PubMed]
- R. Zawadzki, S. Jones, S. Olivier, M. Zhao, B. Bower, J. Izatt, S. Choi, S. Laut, and J. Werner, “Adaptive-optics optical coherence tomography for high-resolution and high-speed 3D retinal in vivo imaging,” Opt. Express 13, 8532–8546 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-21-8532">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-21-8532</a>. [CrossRef] [PubMed]
- M. D. Kulkarni,C. W. Thomas, and J. A. Izatt, “Image enhancement in optical coherence tomography using deconvolution,” Electron. Lett. 33 1365–1367 (1997). [CrossRef]
- J. M. Schmitt, “Restoration of optical coherence images of living tissue using the clean algorithm,” J. Biomed. Opt. 3, 66–75 (1998). [CrossRef]
- D. Piao, Q. Zhu, N. Dutta, S. Yan, and L. Otis, “Cancellation of coherent artifacts in optical coherence tomography imaging,” Appl. Opt. 40, 5124–5131 (2001). [CrossRef]
- I. J. Hsu, C.W. Sun, C.W. Lu, C. C. Yang, C. P. Chiang, and C.W. Lin, “Resolution improvement with dispersion manipulation and a retrieval algorithm in optical coherence tomography,” Appl. Opt. 42, 227–234 (2003). [CrossRef] [PubMed]
- M. Bashkansky, M.D. Duncan, J. Reintjes, and P.R. Battle, “Signal processing for improving field cross-correlation function in optical coherence tomography,” Appl. Opt. 37, 8137–8138 (1998).
- R. Tripathi, N. Nassif, J. Nelson, B. Park, and J. de Boer, “Spectral shaping for non-Gaussian source spectra in optical coherence tomography,” Opt. Lett. 27, 406–408 (2002). [CrossRef]
- M. Szkulmowski, M. Wojtkowski, T. Bajraszewski, I. Gorczy´nska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246, 569–578 (2004). [CrossRef]
- E.g., James G. Fujimoto, “Handbook of optical coherence tomography,” Chapter 1, Edited by G.R. Bouma, G.J. Tearney, Marcel Dekker, Inc. (2002).
- D. J Smithies, T. Lindmo, Z. P. Chen, J. S. Nelson, and T. E. Milner, “Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation,” Phys. Med. Biol. 43, 3025–3044 (1998). [CrossRef] [PubMed]
- C. Dorrer, N. Belabas, J. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1795–1802 (2000). [CrossRef]
- E.g., J. W. Goodman, “Introduction to Fourier optics,” 2nd ed., The McGraw-Hill Companies, Inc. (1996).

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