## The effect of water dispersion and absorption on axial resolution in ultrahigh-resolution optical coherence tomography

Optics Express, Vol. 13, Issue 6, pp. 1860-1874 (2005)

http://dx.doi.org/10.1364/OPEX.13.001860

Acrobat PDF (1614 KB)

### Abstract

We examine the effects of dispersion and absorption in ultrahigh-resolution optical coherence tomography (OCT), particularly the necessity to compensate for high dispersion orders in order to narrow the axial point-spread function envelope. We present a numerical expansion in which the impact of the various dispersion orders is quantified; absorption effects are evaluated numerically. Assuming a Gaussian source spectrum (in the optical frequency domain), we focus on imaging through water as a first approximation to biological materials. Both dispersion and absorption are found to be most significant for wavelengths above ~1*µ*m, so that optimizing the system effective resolution (ER) requires choosing an operating wavelength below this limit. As an example, for 1-*µ*m source resolution (FWHM), and propagation through a 1-mm water cell, if up to third-order dispersion compensation is applied, then the optimal center wavelength is 0.8*µ*m, which generates an ER of 1.5*µ*m (in air). The incorporation of additional bandwidth yields no ER improvement, due to uncompensated high-order dispersion and long-wavelength absorption.

© 2005 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]

*in-vivo*imaging technique, capable of producing cross-sectional images of living tissue to depths of up to 2mm. Conventional OCT has been limited to axial resolutions of ~10

*µ*m. However, the recent application of broadband pulsed Ti:Al

_{2}O

_{3}lasers and other sources [2

2. W. Drexler, U. Morgner, F. X. Kärtner, 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]

*µ*m, thereby ushering in a new generation of ultrahigh-resolution OCT devices [3

3. W. Drexler, “Ultrahigh resolution optical coherence tomography,” J. Biomed. Opt. **9**, 47–74 (2004). [CrossRef] [PubMed]

5. C.K. Hitzenberger, A. Baumgartner, and A. F. Fercher, “Dispersion induced multiple signal peak splitting in partial coherence interferometry,” Opt. Commun. **154**, 179–185 (1998). [CrossRef]

6. C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. **4**, 144–150 (1999). [CrossRef]

7. 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 **12**, 2404–2422 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2404. [CrossRef] [PubMed]

*µ*m.

8. E. D. J. Smith, A. V. Zvyagin, and D. D. Sampson, “Real-time dispersion compensation in scanning interferometry,” Opt. Lett. **27**, 1998–2000 (2002). [CrossRef]

9. A. V. Zvyagin, E. D. J. Smith, and D. D. Sampson, “Delay and dispersion characteristics of a frequency-domain optical delay line for scanning interferometry,” J. Opt. Soc. Am. A **20**, 333–341 (2003). [CrossRef]

10. W. K. Niblack, J. O. Schenk, B. Liu, and M. E. Brezinski, “Dispersion in a grating-based optical delay line for optical coherence tomography,” Appl. Opt. **42**, 4115–4118 (2003). [CrossRef] [PubMed]

11. Y. Chen and X. Li, “Dispersion management up to the third order for real-time optical coherence tomography involving a phase or frequency modulator,” Opt. Express **12**, 5968–5978 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5968. [CrossRef] [PubMed]

12. J. F. de Boer, C. E. Saxer, and J. S. Nelson “Stable carrier generation and phase-resolved digital data processing in optical coherence tomography,” Appl. Opt. **40**, 5787–5790 (2001). [CrossRef]

13. A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Numerical dispersion compensation for partial coherence interferometry and optical coherence tomography,” Opt. Express **9**, 610–615 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-12-610. [CrossRef] [PubMed]

14. D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, “Digital algorithm for dispersion correction in optical coherence tomography for homogeneous and stratified media,” Appl. Opt. **42**, 204–216 (2003). [CrossRef] [PubMed]

7. 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 **12**, 2404–2422 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-11-2404. [CrossRef] [PubMed]

*a priori*knowledge of the sample. These approaches have been demonstrated to provide compensation against both second-and third-order dispersion (but no higher).

15. B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, “Group velocity dispersion effects with water and lipid in 1.3 *µ*m optical coherence tomography system,” Phys. Med. Biol. **49**, 923–930 (2004). [CrossRef] [PubMed]

## 2. Theory

*H*

_{R}(

*v*)=|

*H*

_{R}(v)|exp[

*jf*

_{R}(

*v*)] and

*H*

_{S}(

*v*)=|

*H*

_{S}(

*v*)|exp[

*jf*

_{S}(

*v*)], respectively, where

*j*=p-1, and f

_{R}and f

_{S}represent the phase responses of their respective transfer functions. These functions take into account relative delays due to scanning, and frequency-dependent dispersion and signal attenuation. (The interfering waves are assumed to have the same polarization state, so that scalar wave optics may be used to describe the scenario.) The interferometric component of the detected response can be represented in terms of the zero

*th*moment of the cross-spectral density of the returning optical signals [16, Eq. (21)],

*G*

_{0}(

*v*) represents the power spectral density of the source, ℜ denotes the “real part” operator, and the asterisk (*) denotes complex conjugation. Assuming that the only contributions to the magnitude and phase of the product

*H*

_{S}(

*v*)

*H**

_{R}(

*v*) are due to the effects of propagation through the sample medium, then:

*G*

_{0}(

*v*)=exp{-4ln2[(

*ν*-

*v*

*ν̄*)/Δ

*v*]

^{2}}, where

*v*ν is the center frequency and ν

*v*the full-width-at-half-maximum (FWHM) spectral bandwidth of the source. The effect of spectral deviations from this mathematically convenient approximation will be discussed later. Additionally, we assume at this stage that

*α*may be ignored. (This allows us to quantify the dispersion effects; absorption will be simulated in the next section.) Then the product 2

*βz*can be Taylor-series expanded:

*u*=

*ν*-

*ν̄*,

*g*(

*u*)=exp[-

*Ku*

^{2}+

*j*

*β*

_{k}

*u*

^{k}], and

*K*=4ln2/(Δ

*ν*)

^{2}. The Fourier transform operation

*𝓕*, acting between the

*u*and τ

_{g}domains, may be defined:

_{g}domain is possible since group delay τ

_{g}is proportional to sample optical pathlength

*ℓ̃*. We can measure the width of the interferogram as a function of

*ℓ̃*, and hence also of τ

_{g}.

*β*

_{k}=0 for all

*k*≥3 (there is no third-or greater-order dispersion), the interferometric signal retains a Gaussian envelope

*E*(τ

_{g})=|

*Ĩ*

_{C}(τ

_{g})|=|

*G*(τ

_{g})|. (At this point, and hereafter, we ignore the factor of 2 in Eq. (1).) We define its root-mean-square (RMS) width to be:

*β*

_{k}≠0 for some

*k*≥3, then we cannot derive a simple closed-form expression for the Fourier transform of

*g*. Instead, we resort to determining the width of the interferogram envelope

*E*(τ

_{g}) using the moments of the Fourier transform of some function of

*g*(

*u*). The determination of an expression for

*E*as the Fourier transform of a function of

*g*(

*u*) would be sufficient to determine its RMS width. Such an expression is not easily attained, but the

*square*of

*E can*be expressed as the Fourier transform of a function of

*g*(

*u*), using the autocorrelation theorem:

*u*.

*N*(

*u*); some calculation yields the result:

^{∑}∞

_{t=2}

*C*

_{s,t}

*β*

_{s}

*β*

_{t})

^{1/2}to be the envelope broadening factor (EBF), in which the coefficients

*C*

_{s,t}are given by:

*δ*

_{s,t}represents the Kronecker delta function. Note that the coefficients

*C*

_{s,t}are entirely dependent on the source spectrum, whereas the parameters

*β*

_{k}are also dependent on the properties of the medium.

*β*

_{k}=0 for all

*k*≥3, then the expressions under the radical signs in both Eqs. (8) and (11) are equal. This is due to the fact that if only second-order dispersion impacts upon the signal, then the envelope retains its Gaussian functional form. Furthermore, for any two curves which have the same functional form (but where one is possibly dilated with respect to the other), the ratio between their widths will be independent of the precise manner in which the functional “width” is defined. Consequently, the envelope RMS ratio and the

*squared*envelope RMS ratio are identical. However, it is known that third-and higher-order dispersion terms distort the interferogram envelope [19], and so, in general, the precise definition of envelope width will have some bearing on the EBF. A comparison between the broadening factors associated with various different definitions of envelope width is provided in the next section.

20. D. Marcuse, “Pulse distortion in single-mode fibers,” Appl. Opt. **19**, 1653–1660 (1980). [CrossRef] [PubMed]

5. C.K. Hitzenberger, A. Baumgartner, and A. F. Fercher, “Dispersion induced multiple signal peak splitting in partial coherence interferometry,” Opt. Commun. **154**, 179–185 (1998). [CrossRef]

## 3. Results and discussion

### 3.1. Absorption and refractive index data

*et al.*[13

13. A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Numerical dispersion compensation for partial coherence interferometry and optical coherence tomography,” Opt. Express **9**, 610–615 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-12-610. [CrossRef] [PubMed]

*et al.*[18

18. Y. Wang, J. S. Nelson, Z. Chen, B. J. Reiser, R. S. Chuck, and R. S. Windeler, “Optimal wavelength for ultrahigh-resolution optical coherence tomography,” Opt. Express **11**, 1411–1417 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-12-1411. [CrossRef] [PubMed]

21. D. J. Segelstein, “The complex refractive index of water,” (University of Missouri-Kansas City, 1981), as reported at http://atol.ucsd.edu/%7Epflatau/refrtab/water/Segelstein.H2Orefind.

22. A. G. Van Engen, S. A. Diddams, and T. S. Clement, “Dispersion measurements of water with white-light interferometry,” Appl. Opt. **37**, 5679–5686 (1998). [CrossRef]

*et al.*[23

23. A. H. Harvey, J. S. Gallagher, and J. M. H. Levelt Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data27, 761–774 (1998). The formulation is available as IAPWS 5C: “Release on refractive index of ordinary water substance as a function of wavelength, temperature and pressure,” (International Association for the Properties of Water and Steam (IAPWS), 1997), http://www.iapws.org/relguide/rindex.pdf. [CrossRef]

*µ*m in determining the dispersion properties in its wavelength neighborhood (from ~1

*µ*m to ~5

*µ*m).

## 3.2. Effect of dispersion compensation on the envelope broadening factor

*c*/

*ν̄*, and subsequently referred to as center wavelength) for two distinct cases: when absorption is taken into account, and when it is ignored. The plots were generated at three distinct SRs, under four different conditions: no dispersion compensation; second-order dispersion compensation; both second-and third-order dispersion compensation; and full dispersion compensation. The intermediate conditions were realized by subtracting, respectively, a quadratic and cubic polynomial (as a function of ν) from the expression for

*β*, choosing the coefficients (via a numerical fitting algorithm) so that the EBF was minimized. This method showed good immunity to the discrete noise and experimental error associated with the specific

*β*vs.

*ν*data set used. The plots were obtained by performing the integration of Eq. (2) numerically, substituting in the absorption and refractive index data from the previous subsection. A Gaussian source spectrum, as described in Section 2, was assumed. This spectrum was truncated at 2.5×10

^{10}Hz, so that lower frequencies were excluded. (This choice had no bearing on the results in this paper, since the effect of very low source frequencies is entirely suppressed by water absorption, and in plots where water absorption was ignored, the simulated Gaussian sources had negligible power in this extreme region.) In each case, the single-pass propagation distance

*z*=1mm.

*K*, then coefficient

*C*

_{s,t}is inversely proportional to

*s*≠

*t*.) This expansion demonstrates that high-order dispersion terms, which are suppressed at high values of SR, contribute significantly to the EBF as the bandwidth is increased. If both second-and third-order dispersion are eliminated, then the most significant term corresponds to (

*s*,

*t*)=(4,4), which is (in general) entirely negligible at 10-

*µ*m SR, but rapidly increases in significance at lower values of SR. The expansion of Eq. (11) does not, of course, strictly apply when the effects of absorption are significant. Nonetheless, it remains useful in determining the relative magnitude of the various dispersion-order effects.

*µ*m or 10-

*µ*m SR cases, if the center wavelength is greater than ~1

*µ*m. This demonstrates the dominance of high-order dispersion terms in this region. The fact that effective low-order dispersion compensation

*is*possible at 1-

*µ*m SR is seemingly in conflict with the claim in the previous paragraph that these orders should have minimal relative impact on the EBF as SR is improved. However, large-scale structure in the

*β*vs.

*v*function does significantly impact upon the EBF at broad bandwidths, and when it can be approximated by a low-order polynomial, it is possible to see significant EBF reduction by introducing low-order dispersion correction. (The ripples that are clearly visible in the 10-

*µ*m SR curves are, in general, described by low-order dispersion terms, and demonstrate the ability to resolve small-scale variations in

*β*when narrow bandwidths are used.) In Eq. (11), this effect may be explained in terms of the “coupling” between all the even-order terms, and between all the odd-order terms. For example, merely compensating for second-order dispersion (by effectively setting

*β*

_{2}to zero and leaving all other parameters unchanged) will eliminate an infinite number of terms in the EBF expansion (those corresponding to

*t*=2). However, for maximum EBF reduction,

*β*

_{2}should not be set to zero, but instead chosen so that the net sum of these particular terms is negative: that is, full compensation of

*β*

_{2}might be traded off in favor of greater partial compensation of higher even-order dispersion. This is equivalent to approximating large-scale

*β*(

*v*) structure with a quadratic polynomial.

*µ*m and 3-

*µ*m SR, whether or not absorption is included, the minimum value of the EBF occurs in the vicinity of the 1-

*µ*m wavelength. This point has been identified as the group velocity dispersion zero of water [18

18. Y. Wang, J. S. Nelson, Z. Chen, B. J. Reiser, R. S. Chuck, and R. S. Windeler, “Optimal wavelength for ultrahigh-resolution optical coherence tomography,” Opt. Express **11**, 1411–1417 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-12-1411. [CrossRef] [PubMed]

*µ*m SR, indicating that this attribution is based upon large-scale structure in the

*̂*vs.

*v*curve, as described above.) Accordingly, it is in this vicinity that second-order dispersion compensation alone has little or no effect upon the EBF. In the absence of any dispersion compensation, the EBF at this point (for 1-

*µ*m SR, when absorption is taken into account) is ~6, a figure which is large enough to demonstrate that some form of dispersion compensation is warranted even at the dispersion minimum.

*µ*m SR, as evidenced by the difference between the black and the red curves. For 3-

*µ*m SR, the difference is marginal, and for 10-

*µ*m SR, it is entirely negligible. This is consistent with the observation that second-order dispersion effects dominate over third-order effects at high values of SR (even granting dispersion-order coupling arguments).

*µ*m. The near-center wavelengths of the source are attenuated in such a way that the effective bandwidth increases. Although interferogram side lobes are produced, these are accounted for in the RMS definition of EBF. The resolution gain (of ~2%) is negligible, and comes at the expense of a significant reduction in signal power.

## 3.3. Comparison between broadening-factor definitions

6. C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. **4**, 144–150 (1999). [CrossRef]

*µ*m and 3-

*µ*m SR, in the presence of absorption. (The blue curves in Fig. 4 are identical to the respective blue curves in the top row of Fig. 3, for the same SRs.)

*µ*m), for which much of the interferogram power is concentrated into a long tail, and at higher center wavelengths, for which the distorted spectrum (following absorption) remains centered at around 1.1

*µ*m. At 1-

*µ*m SR, the presence of the tail tends to magnify both RMS-width EBFs but has less bearing on the other two EBFs. (This effect may be exploited; Hsu

*et al.*[24

24. 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]

## 3.4. Plots of interferograms

## 3.5. Dependence of envelope broadening factor on propagation distance

*z*, when the SR and center wavelength are held fixed. The plots are given in Fig. 6, and the same dispersion compensation criteria have been applied as in Subsections 3.2 and 3.4. The simulated center wavelengths were 0.8,1 and 1.3

*µ*m, and the SRs were 1, 3, and 10

*µ*m. The effects of absorption were included in all plots.

*C*

_{s,t}does not depend on

*z*, and

*β*

_{s},

*β*

_{t}are both proportional to

*z*, then EBF=(1+

*Tz*

^{2})

^{1/2}for some constant

*T*. Therefore, when the EBF is much greater than 1, it is approximately proportional to

*z*. This characteristic is clearly observed in the first (and to a lesser extent, the second) column of Fig. 6, which correspond to center wavelengths for which water absorption is modest. In the third column, corresponding to a center wavelength of 1.3

*µ*m, the impact of water absorption is observed even at very short propagation distances. For 1 and 3-

*µ*m SRs, the EBF increases very rapidly with

*z*, when

*z*is small. In a sample, this corresponds to considerable resolution degradation at shallow penetration depths. As evidenced by the other plots in the top two rows of Fig. 6, when sample absorption is not significant, at low values of SR, the EBF is approximately linearly dependent on

*z*.

## 3.6. Conditions for attaining maximum effective resolution

_{FWHM}curves in Fig. 4 are identical.) The ER is defined with respect to optical distance, like SR, and therefore represents effective physical resolution in air. We seek to determine conditions under which it is minimized.

*µ*m ER is attainable with a 1-

*µ*m SR only at center wavelengths below ~ 0.9

*µ*m, and even increasing the bandwidth will not improve upon the ER at higher wavelengths. If merely second-order dispersion compensation is utilized, then the maximum attainable ER, for

*any*SR, is 1.8

*µ*m, at a center wavelength of 0.55

*µ*m. (The required SR is 1

*µ*m). If an SR greater than 1

*µ*m is used (1.5

*µ*m or 2

*µ*m), then an ER of less than 2.5

*µ*m is attainable up to center wavelengths of ~0.85

*µ*m, but ultrahigh SRs of 1

*µ*m or less give poor results at these center wavelengths. This situation is significantly improved if third-order dispersion compensation is incorporated into the system. Under this condition, an SR of 1

*µ*m gives consistent results below 0.9-

*µ*m center wavelength, attaining a minimum ER of 1.5

*µ*m at center wavelength 0.8

*µ*m. If no dispersion compensation is applied at all, the ER is minimized at around 1–1.1

*µ*m for all SRs (the GVD “zero” of water, identified earlier). The minimum ER (3.6

*µ*m) occurs at a center wavelength of 1.0

*µ*m, for a 2-

*µ*m SR. At all center wavelengths, an SR of 2

*µ*m or greater is required to attain the minimum ER at that wavelength, due to the additional uncompensated dispersion introduced with broader-bandwidth sources.

## 3.7. Limitations of the Gaussian spectral density assumption

## 4. Conclusion

*µ*m has the effect of eliminating neighboring optical frequency components which are propagated through water. The resulting amelioration of the source bandwidth results in envelope broadening, even when dispersion has been fully compensated, as is evidenced in the upper-left panel of Fig. 7. As an example, consider the maximum signal propagation distance

*z*for which the ER remains less than 1.5

*µ*m (an effective physical resolution of ~1

*µ*m in tissue) at a common OCT operating center wavelength of 1.3

*µ*m (and an SR of 1

*µ*m). If up to third-order dispersion compensation is applied,

*z*cannot exceed ~10

*µ*m, and even for full dispersion compensation, the upper limit for

*z*is ~70

*µ*m. These observations suggest that in order to achieve ultrahigh-resolution OCT images over substantial depth ranges, it is necessary to choose a center wavelength of less than ~1

*µ*m. For up to third-order compensation, the best ER is obtained using a 1-

*µ*m SR at a center wavelength of 0.8

*µ*m (dependent, but not strongly, on propagation distance). Increasing the source bandwidth is no substitute for dispersion compensation, since the compounded dispersive effects due to the additional wavelengths present yield little or no net resolution improvement. The SR should be no less than 1

*µ*m unless high-order dispersion compensation can be applied, and then only if the center wavelength is less than ~0.9

*µ*m.

26. B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, “Optical coherence tomographic imaging of human tissue at 1.55*µ*m and 1.81*µ*m using Er-and Tm-doped fiber sources,” J. Biomed. Opt. **3**, 76–79 (1998). [CrossRef]

27. B. Považay, K. Bizheva, B. Hermann, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, C. Schubert, P. K. Ahnelt, M. Mei, R. Holzwarth, W. J. Wadsworth, J. C. Knight, and P. St. J. Russel, “Enhanced visualization of choroidal vessels using ultrahigh resolution ophthalmic OCT at 1050 nm,” Opt. Express **11**, 1980–1986 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-17-1980. [CrossRef] [PubMed]

*µ*m were noted to be local minima in the water absorption curve, in order to maximize penetration depth. The achievable OCT resolution may also be limited by sensor sensitivity [16, p. 517].

*et al.*[15

15. B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, “Group velocity dispersion effects with water and lipid in 1.3 *µ*m optical coherence tomography system,” Phys. Med. Biol. **49**, 923–930 (2004). [CrossRef] [PubMed]

*µ*m) source, for which only second-order dispersion was significant. The additional structure inherent in the axial point-spread function due to multiple dispersion orders at ultrahigh resolutions may provide even more discriminatory capacity for identifying tissue types, but this is not yet clear.

*µ*m is to be attained in OCT imaging, then it is necessary to compensate for multiple dispersion orders, no matter how great the source bandwidth. Moreover, the source center wavelength should not be located in the vicinity of a sample absorption peak, so that the entirety of the spectrum is utilized in generating the signal.

## 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. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “ |

3. | W. Drexler, “Ultrahigh resolution optical coherence tomography,” J. Biomed. Opt. |

4. | D. D. Sampson, “Trends and prospects for optical coherence tomography,” in |

5. | C.K. Hitzenberger, A. Baumgartner, and A. F. Fercher, “Dispersion induced multiple signal peak splitting in partial coherence interferometry,” Opt. Commun. |

6. | C. K. Hitzenberger, A. Baumgartner, W. Drexler, and A. F. Fercher, “Dispersion effects in partial coherence interferometry: implications for intraocular ranging,” J. Biomed. Opt. |

7. | 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 |

8. | E. D. J. Smith, A. V. Zvyagin, and D. D. Sampson, “Real-time dispersion compensation in scanning interferometry,” Opt. Lett. |

9. | A. V. Zvyagin, E. D. J. Smith, and D. D. Sampson, “Delay and dispersion characteristics of a frequency-domain optical delay line for scanning interferometry,” J. Opt. Soc. Am. A |

10. | W. K. Niblack, J. O. Schenk, B. Liu, and M. E. Brezinski, “Dispersion in a grating-based optical delay line for optical coherence tomography,” Appl. Opt. |

11. | Y. Chen and X. Li, “Dispersion management up to the third order for real-time optical coherence tomography involving a phase or frequency modulator,” Opt. Express |

12. | J. F. de Boer, C. E. Saxer, and J. S. Nelson “Stable carrier generation and phase-resolved digital data processing in optical coherence tomography,” Appl. Opt. |

13. | A. F. Fercher, C. K. Hitzenberger, M. Sticker, R. Zawadzki, B. Karamata, and T. Lasser, “Numerical dispersion compensation for partial coherence interferometry and optical coherence tomography,” Opt. Express |

14. | D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, “Digital algorithm for dispersion correction in optical coherence tomography for homogeneous and stratified media,” Appl. Opt. |

15. | B. Liu, E. A. Macdonald, D. L. Stamper, and M. E. Brezinski, “Group velocity dispersion effects with water and lipid in 1.3 |

16. | D. D. Sampson and T. R. Hillman, “Optical coherence tomography,” in |

17. | B. E. A. Saleh and M. C. Teich, |

18. | Y. Wang, J. S. Nelson, Z. Chen, B. J. Reiser, R. S. Chuck, and R. S. Windeler, “Optimal wavelength for ultrahigh-resolution optical coherence tomography,” Opt. Express |

19. | A. F. Fercher and C. K. Hitzenberger, “Optical coherence tomography,” in |

20. | D. Marcuse, “Pulse distortion in single-mode fibers,” Appl. Opt. |

21. | D. J. Segelstein, “The complex refractive index of water,” (University of Missouri-Kansas City, 1981), as reported at http://atol.ucsd.edu/%7Epflatau/refrtab/water/Segelstein.H2Orefind. |

22. | A. G. Van Engen, S. A. Diddams, and T. S. Clement, “Dispersion measurements of water with white-light interferometry,” Appl. Opt. |

23. | A. H. Harvey, J. S. Gallagher, and J. M. H. Levelt Sengers, “Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density,” J. Phys. Chem. Ref. Data27, 761–774 (1998). The formulation is available as IAPWS 5C: “Release on refractive index of ordinary water substance as a function of wavelength, temperature and pressure,” (International Association for the Properties of Water and Steam (IAPWS), 1997), http://www.iapws.org/relguide/rindex.pdf. [CrossRef] |

24. | 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. |

25. | J. G. Fujimoto, “Optical coherence tomography: Introduction,” in |

26. | B. E. Bouma, L. E. Nelson, G. J. Tearney, D. J. Jones, M. E. Brezinski, and J. G. Fujimoto, “Optical coherence tomographic imaging of human tissue at 1.55 |

27. | B. Považay, K. Bizheva, B. Hermann, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, C. Schubert, P. K. Ahnelt, M. Mei, R. Holzwarth, W. J. Wadsworth, J. C. Knight, and P. St. J. Russel, “Enhanced visualization of choroidal vessels using ultrahigh resolution ophthalmic OCT at 1050 nm,” Opt. Express |

**OCIS Codes**

(110.4500) Imaging systems : Optical coherence tomography

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(170.4500) Medical optics and biotechnology : Optical coherence tomography

(260.2030) Physical optics : Dispersion

(300.1030) Spectroscopy : Absorption

**ToC Category:**

Research Papers

**History**

Original Manuscript: December 24, 2004

Revised Manuscript: February 23, 2005

Published: March 21, 2005

**Citation**

Timothy Hillman and David Sampson, "The effect of water dispersion and absorption on axial resolution in ultrahigh-resolution optical coherence tomography," Opt. Express **13**, 1860-1874 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-1860

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