## Phase-sensitive swept-source interferometry for absolute ranging with application to measurements of group refractive index and thickness |

Optics Express, Vol. 19, Issue 9, pp. 8117-8126 (2011)

http://dx.doi.org/10.1364/OE.19.008117

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### Abstract

Interferometric range measurements using a wavelength-tunable source form the basis of several measurement techniques, including optical frequency domain reflectometry (OFDR), swept-source optical coherence tomography (SS-OCT), and frequency-modulated continuous wave (FMCW) lidar. We present a phase-sensitive and self-referenced approach to swept-source interferometry that yields absolute range measurements with axial precision three orders of magnitude better than the transform-limited axial resolution of the system. As an example application, we implement the proposed method for a simultaneous measurement of group refractive index and thickness of an optical glass sample.

© 2011 OSA

## 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. J. G. Fujimoto, “Optical coherence tomography for ultrahigh resolution *in vivo* imaging,” Nat. Biotechnol. **21**, 1361–1367 (2003). [CrossRef] [PubMed]

3. R. C. Youngquist, S. Carr, and D. E. N. Davies, “Optical coherence-domain reflectometry: a new optical evaluation technique,” Opt. Lett. **12**, 158–160 (1987). [CrossRef] [PubMed]

4. S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. **22**, 340–342 (1997). [CrossRef] [PubMed]

5. 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). [CrossRef] [PubMed]

*A*-scans) within the sample under test. By laterally scanning either the probe beam or the sample under test, depth-resolved 2- and 3-dimensional images can be produced. The high axial resolution offered by these measurements provide a unique ability to image subsurface biological structures based on the level of scattering returned by underlying tissues. For both low-coherence and swept-source (SS-) OCT, the axial resolution is inversely proportional to the frequency bandwidth of the optical source [6]. Axial resolutions on the order of 1

*μ*m have been achieved with low-coherence approaches using extremely broadband supercontinuum sources [7

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

*μ*m due to the more limited spectral breadth available from swept-wavelength sources.

8. M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, “Spectral-domain phase microscopy,” Opt. Lett. **30**(10), 1162–1164 (2005). [CrossRef] [PubMed]

13. B. J. Vakoc, S. H. Yun, J. F. de Boer, G. J. Tearney, and B. E. Bouma, “Phase-resolved optical frequency domain imaging,” Opt. Express **13**(14), 5483–5493 (2005). [CrossRef] [PubMed]

*A*-scan data by applying a Fourier transform to the acquired fringe patterns. Small displacements of discrete reflectors can be detected by noting changes in the phase of the complex-valued

*A*-scan data at the location in the data array corresponding to the reflector. These phase measurements provide a relative displacement measurement from scan to scan, and have been applied to surface profiling [9

9. M. V. Sarunic, S. Weinberg, and J. A. Izatt, “Full-field swept-source phase microscopy,” Opt. Lett. **31**(10), 1462–1464 (2006). [CrossRef] [PubMed]

11. C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. **30**(16), 2131–2133 (2005). [CrossRef] [PubMed]

12. M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, “Doppler flow imaging of cytoplasmic streaming using spectral domain phase microscopy,” J. Biomed. Opt. **11**(2), 024014 (2006). [CrossRef] [PubMed]

13. B. J. Vakoc, S. H. Yun, J. F. de Boer, G. J. Tearney, and B. E. Bouma, “Phase-resolved optical frequency domain imaging,” Opt. Express **13**(14), 5483–5493 (2005). [CrossRef] [PubMed]

*A*-scan. In this paper, we present a novel implementation of phase-sensitive SS-OCT where phase information is used to perform measurements of lengths and thicknesses spanning multiple resolution-limited depth bins to nanometer precision. Additionally, we present a means for accurate calibration of the time (or, equivalently, spatial) domain sampling grid, leading to highly accurate optical path length measurements.

## 2. Principles

*A*-scan performs an axial reflectivity measurement using optical frequency domain reflectometry (OFDR) [4

4. S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. **22**, 340–342 (1997). [CrossRef] [PubMed]

*ν*about a central frequency

*ν*

_{0}, a fringe pattern is observed at the interferometer output. The frequency of the fringe pattern indicates the differential group delay between the reference path and the sample path. For a sample with

*M*distinct reflectors distributed axially, the oscillating portion of the photodetector voltage at the interferometer output is where

*ν*is the instantaneous frequency of the laser source,

*τ*is the group delay difference between the

_{i}*i*

^{th}reflection in the sample path and the reference path, and

*ξ*is a constant phase offset. The factor

_{i}*r*is the effective reflection coefficient of the

_{i}*i*

^{th}reflection [17

17. U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Technol. **11**, 1377–1384 (1993). [CrossRef]

18. T.-J. Ahn, J. Y. Lee, and D. Y. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation,” Appl. Opt. **44**, 7630–7634 (2005). [CrossRef] [PubMed]

19. E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express **16**, 13139–13149 (2008). [CrossRef] [PubMed]

*Ũ*(

_{i}*τ*) due to the

*i*

^{th}reflector is where

*ψ*=

_{i}*ξ*+ 2π

_{i}*ν*

_{0}

*τ*and sinc(

_{i}*x*) = sin(

*πx*)/(

*πx*). Here the sinc function arises due to the assumption of a constant amplitude over the spectral range Δ

*ν*. Other spectral shapes (or the application of a windowing function prior to the Fourier transform) will change the shape of the time domain response. The width Δ

*τ*of this response function determines the axial resolution of an

_{w}*A*-scan, and this width will generally be Δ

*τ*≈ 1/Δ

_{w}*ν*for most spectra. Note also that

*δτ*= 1/Δ

*ν*will be the sample spacing of the time domain data, so that in the best case the axial resolution will be equivalent to one temporal bin. If there are two reflectors spaced by

*δτ*or less, they will not be resolvable. For an isolated reflector, however, the location of the reflector, described by

*τ*, can be determined to within a small fraction of

_{i}*δτ*by analyzing the phase of the reflector’s contribution to the time domain reflectogram.

### 2.1. Phase slope measurements for improved range precision

*τ*is accomplished by noting the location

_{i}*τ*

_{i}_{,}

*of the*

_{q}*i*

^{th}peak in the time domain data array. An example of such time domain data for a single

*A*-scan is plotted in Fig. 1(a) for a single isolated reflector. The precision of this coarse determination of the reflector position is

*δτ*, or one temporal bin. The true value of

*τ*is likely to lie between sampled points. This offset between the location of the peak value in the time domain data array and the true value of

_{i}*τ*can be found by applying the shift theorem of Fourier transforms [20] to a subset of time domain data surrounding the

_{i}*i*

^{th}peak. The shift theorem states that a translation in the time domain is accompanied by a corresponding linear phase factor in the frequency domain. Thus, determination of the offset between the value of

*τ*and the

_{i}*i*

^{th}peak location can be accomplished through a linear phase measurement in the frequency domain. For an isolated reflection peak, the corresponding phase contribution in the frequency domain can be found by windowing out the single peak using a digital filter and then performing an inverse FFT on the windowed data subset. Figure 1(b) is a plot of the amplitude of the windowed reflection peak selected by applying a digital filter to the positive delay peak in Fig. 1(a). The phase of the resulting frequency domain data set will wrap rapidly between 0 and 2

*π*unless the time domain subset is rotated such that the amplitude maximum occupies the first (DC) index location in the data array. Performing this rotation prior to the inverse FFT results in a slowly-varying frequency domain phase that can be straightforwardly unwrapped. Fitting a line to the unwrapped phase

*φ*(

*ν*), as shown in Fig. 1(c), gives a slope that represents a fine adjustment to the coarse measurement

*τ*

_{i}_{,}

*, illustrated in Fig. 1(d).*

_{q}### 2.2. Sampling grid calibration for accurate absolute ranging

*τ*

_{i}_{,}

*. Because of the discrete Fourier transform relationship between the acquired frequency domain fringe pattern and the time domain*

_{q}*A*-scan, the range of the

*A*-scan is given by the reciprocal of the frequency domain step size,

*δν*. For an

*N*-point

*A*-scan, the time domain step size is therefore

*δτ*= (

*Nδν*)

^{−1}. As mentioned above, the fringe pattern must be sampled on a grid of equal frequency increments, either through the use of a frequency clock to trigger data acquisition or by monitoring the instantaneous frequency of source throughout a sweep and resampling the fringe data in postprocessing. Thus the uncertainty in the time domain step size depends on the accuracy with which the instantaneous optical frequency can be determined during a wavelength sweep.

*τ*between the auxiliary interferometer paths and the mean laser sweep rate

*γ*= d

*ν*/d

*t*are chosen such that Δ

*τ*

_{2}

*γ*≪ 1, then the output fringe pattern will be a periodic function of optical frequency with a period of 1/Δ

*τ*[19

19. E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express **16**, 13139–13149 (2008). [CrossRef] [PubMed]

*δν*is equal to 1/Δ

*τ*, then Δ

*τ*will be the full range of the dual-sided time domain data set, and the Nyquist-limited measurable group delay will be Δ

*τ*/2. The accuracy of the time and frequency domain sampling grids then depend on the accuracy with which Δ

*τ*(or its reciprocal) can be measured. Once Δ

*τ*has been determined, a range measurement with a measured delay

*τ*

_{i}_{,}

*performed by locating a peak at a fractional index*

_{q}*k*in the time domain data array will have an uncertainty given by where

*u*(

*x*) is used to denote the uncertainty in the quantity

*x*. Thus, the relative error in the range measurement will equal the relative error in the calibration of the auxiliary interferometer.

*ν*. For a given auxiliary interferometer with a differential group delay Δ

_{c}*τ*, the number of periods over the range Δ

*ν*will be

_{c}*m*= Δ

*ν*Δ

_{c}*τ*. Using this relationship to determine Δ

*τ*, there will be contributions to the uncertainty due to the quality of the wavelength reference

*u*(Δ

*ν*), as well an uncertainty in the determination of

_{c}*m*to a fraction of a fringe. Therefore, the total uncertainty in Δ

*τ*is When this interferometer is used to trigger data acquisition during a frequency sweep over a range Δ

*ν*, the number of samples

*N*will be

*N*= Δ

*ν*Δ

*τ*, and the uncertainty in the time domain step size will be

*u*(

*δτ*) =

*u*(Δ

*τ*)/

*N*. Figure 2 is a plot of

*u*(

*δτ*) for some representative values over a range of interferometer path imbalances from 100

*μ*m to 100 m. This range covers typical SS-OCT systems on the short end, and typical OFDR systems designed for fiber sensing and telecommunications system testing on the upper end. The frequency sweep range is Δ

*ν*= 3.49 THz, corresponding to the spectral separation between the R20 and P20 absorption lines of H

_{c}^{13}CN at 100 Torr, a common wavelength reference material for the range between 1528 and 1562 nm. The R20 and P20 lines are located at 1530.3061 nm and 1558.0329 nm, respectively, and the uncertainty in their location is ±0.3 pm. The three curves represent the uncertainty in the time domain step size for three values of the uncertainty in the number of fringes between the absorption lines. The asymptotic value of 4.4 as is reached when the uncertainty of the wavelength reference dominates. Interestingly, this plot shows that an extremely high degree of temporal accuracy can be achieved over a range of interferometer length imbalances spanning several orders of magnitude. For short interferometers, such as those typically used for SS-OCT, more care must be taken to accurately determine the number of periods between the absorption lines to a fraction of a fringe. This is typically accomplished by fitting a Lorentzian curve to the sampled absorption line data. For longer interferometers, high temporal accuracy can be achieved without the need for fractional fringe counting.

## 3. Experimental results and discussion

^{13}CN gas cell (dBm Optics model WA-1528-1562). The absorption spectrum of the gas cell was acquired using the auxiliary interferometer to trigger data acquisition. The number of samples between the R20 and P20 absorption lines was determined to a fraction of a sample by curve fitting the absorption lines to precisely locate their minima. In this process, the uncertainty of the absorption line wavelengths (known to ±0.3 pm) dominate the interferometer calibration error. The resulting measurement yielded a group delay difference between the two paths of the auxiliary interferometer of Δ

*τ*= 63.9413 ± 0.0012 ns. The AC-coupled output of this interferometer was used as an analog clock to trigger data acquisition on the polarization-diverse outputs of the measurement interferometer using a National Instruments PCI-6115 data acquisition card. The tunable laser was an Agilent 81680A with a maximum sweep rate of 40 nm/s. Measurements were performed by sweeping the laser from 1500 to 1564.17 nm. This sweep range coupled with the frequency domain step size of 1/Δ

*τ*= 15.6395 MHz yields

*A*-scans comprising 524,288 data points.

*A*-scans with the SUT present and absent are plotted in Fig. 4. The physical thickness

*T*of the plate is determined from relative group delay measurements according to where

*c*is the speed of light in vacuum and

*n*is the group index of the SUT, which is found using [15

_{g}15. H.-C. Cheng and Y.-C. Liu, “Simultaneous measurement of group refractive index and thickness of optical samples using optical coherence tomography,” Appl. Opt. **49**, 790–797 (2010). [CrossRef] [PubMed]

*τ*

_{21}and

*τ*

_{43}. We employed the model described by Ciddor and Hill [22

22. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. **35**(9), 1566–1573 (1996). [CrossRef] [PubMed]

23. P. E. Ciddor and R. J. Hill, “Refractive index of air. 2. Group index,” Appl. Opt. **38**(9), 1663–1667 (1999). [CrossRef]

^{6}(

*n*

_{g}_{,air}– 1) = 2184 ±1 at the center sweep wavelength for the atmospheric conditions present during the experiment. The value of

*τ*

_{21}is found directly in a single scan, so noise due to environmental fluctuations and scan-to-scan variations in the laser sweep cancel. Determination of

*τ*

_{43}requires two

*A*-scans, one with the SUT present and one without. By referencing the mirror range measurement to the reflection from the fiber end facet (

*τ*

_{0}in Fig. 4), scan-to-scan variations largely cancel, and the measurement noise of

*τ*

_{43}approaches that of

*τ*

_{21}. To illustrate the level of measurement noise in each group delay measurement, plots of 50 repeated measurements of referenced and unreferenced group delays defined in Fig. 4 are shown in Fig. 5. The standard deviation of unreferenced group delay measurements was 4.4 fs, whereas the standard deviations of self-referenced group delay measurements were as small as 5.2 as for

*τ*

_{21}, where the relative measurement involved two facets of a single glass plate. This value corresponds to a distance of 780 pm in air.

*τ*

_{21}shown in Fig. 5, as well as an increased uncertainty in

*τ*

_{43}due to drift in the position of the reference mirror during the process of inserting or removing the fused silica test plate. We estimated this uncertainty to be a factor of 2 greater than the standard deviation based on the repeated measurements of

*τ*

_{40}and

*τ*

_{30}shown in Fig. 5. Because the group index measurement is a relative measurement (apparent from Eq. (7)), the value of the time domain step size falls out of the measurement and does not affect the final uncertainty. The small uncertainty value for this measurement is a direct result of the use of phase slope measurement and self-referencing in the determination of the group delays

*τ*

_{21}and

*τ*

_{43}.

24. D. B. Leviton and B. J. Frey, “Temperature-dependent absolute refractive index measurements of synthetic fused silica,” Proc. SPIE **6273**, 62732K (2006). [CrossRef]

*u*(

*δτ*) = 2.3 as. Because

*τ*

_{21}is determined by the sum of an integer number of time domain samples and an adjustment of a fraction of a sample determined by the phase slope, the total uncertainty in the absolute determination of

*τ*

_{21}is given by where the function int() denotes rounding to the nearest integer. For macroscopic thicknesses, the uncertainty in the time domain step size dominates, and the total uncertainty can be approximated as If

*u*(Δ

*τ*) is independent of the magnitude of Δ

*τ*(as it is for the auxiliary interferometer calibration routine presented in the previous section), Eq. 9 reveals that the accuracy of relative distance measurements can be improved by increasing the total time domain range of the system beyond simply that which is necessary to measure the distances of interest. The overall limitation on Δ

*τ*is generally imposed by either the coherence length of the laser or the speed capability of the data acquisition system.

*τ*

_{21}suggests. This is because the uncertainty in the time domain step size is constant for any given set of measurements. This can be exploited for highly precise relative measurements, such as thickness variations in a single sample. In this case

*u*(

*δτ*) can be ignored, and the uncertainty in the relative thickness measurement now becomes dominated by the determination of the group index. To illustrate this case, taking

*u*(

*δτ*) = 0 for the experimental thickness measurement of the fused silica plate, the uncertainty is reduced to ±4.5 nm. Furthermore, for relative measurements on the same sample where the group index doesn’t change, or if the group index were known exactly (for example, in a measurement of the variation in thickness of a region of vacuum between reflectors), the uncertainty is further diminished. Neglecting the group index uncertainty for the fused silica test sample results in a thickness uncertainty of ±530 pm. For monocrystalline silicon, the refractive index of 3.481 at 1550 nm would yield a thickness uncertainty of 224 pm, less than half of the crystal lattice spacing of 543 pm and comparable to the Si-Si bond length of 235 pm. Our results therefore open the door to thickness profiling of macroscopic samples with single atomic monolayer resolution.

## 4. Conclusions

^{−6}, and for the thickness measurement the uncertainty was ± 61 nm.

## 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. | J. G. Fujimoto, “Optical coherence tomography for ultrahigh resolution |

3. | R. C. Youngquist, S. Carr, and D. E. N. Davies, “Optical coherence-domain reflectometry: a new optical evaluation technique,” Opt. Lett. |

4. | S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. |

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

6. | M. E. Brezinkski, |

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

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

9. | M. V. Sarunic, S. Weinberg, and J. A. Izatt, “Full-field swept-source phase microscopy,” Opt. Lett. |

10. | D. C. Adler, R. Huber, and J. G. Fujimoto, “Phase-sensitive optical coherence tomography at up to 370,000 lines per second using buffered Fourier domain mode-locked lasers,” Opt. Lett. |

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

12. | M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, “Doppler flow imaging of cytoplasmic streaming using spectral domain phase microscopy,” J. Biomed. Opt. |

13. | B. J. Vakoc, S. H. Yun, J. F. de Boer, G. J. Tearney, and B. E. Bouma, “Phase-resolved optical frequency domain imaging,” Opt. Express |

14. | W. V. Sorin and D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. |

15. | H.-C. Cheng and Y.-C. Liu, “Simultaneous measurement of group refractive index and thickness of optical samples using optical coherence tomography,” Appl. Opt. |

16. | J. Na, H. Y. Choi, E. S. Choi, C. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. |

17. | U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Technol. |

18. | T.-J. Ahn, J. Y. Lee, and D. Y. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation,” Appl. Opt. |

19. | E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express |

20. | J. W. Goodman, |

21. | W. C. Swann and S. L. Gilbert, “Accuracy limits for simple molecular absorption based wavelength references,” in |

22. | P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. |

23. | P. E. Ciddor and R. J. Hill, “Refractive index of air. 2. Group index,” Appl. Opt. |

24. | D. B. Leviton and B. J. Frey, “Temperature-dependent absolute refractive index measurements of synthetic fused silica,” Proc. SPIE |

**OCIS Codes**

(110.4500) Imaging systems : Optical coherence tomography

(120.1840) Instrumentation, measurement, and metrology : Densitometers, reflectometers

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(280.3400) Remote sensing and sensors : Laser range finder

(290.3030) Scattering : Index measurements

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: January 20, 2011

Revised Manuscript: March 25, 2011

Manuscript Accepted: March 29, 2011

Published: April 13, 2011

**Virtual Issues**

Vol. 6, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Eric D. Moore and Robert R. McLeod, "Phase-sensitive swept-source interferometry for absolute ranging with application to measurements of group refractive index and thickness," Opt. Express **19**, 8117-8126 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8117

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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]
- J. G. Fujimoto, “Optical coherence tomography for ultrahigh resolution in vivo imaging,” Nat. Biotechnol. 21, 1361–1367 (2003). [CrossRef] [PubMed]
- R. C. Youngquist, S. Carr, and D. E. N. Davies, “Optical coherence-domain reflectometry: a new optical evaluation technique,” Opt. Lett. 12, 158–160 (1987). [CrossRef] [PubMed]
- S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. 22, 340–342 (1997). [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). [CrossRef] [PubMed]
- M. E. Brezinkski, Optical Coherence Tomography: Principles and Applications (Elsevier, 2006).
- B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight, P. S. J. Russel, M. Vetterlein, and E. Scherzer, “Submicrometer axial resolution optical coherence tomography,” Opt. Lett. 27, 1800–1802 (2002). [CrossRef]
- M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, “Spectral-domain phase microscopy,” Opt. Lett. 30(10), 1162–1164 (2005). [CrossRef] [PubMed]
- M. V. Sarunic, S. Weinberg, and J. A. Izatt, “Full-field swept-source phase microscopy,” Opt. Lett. 31(10), 1462–1464 (2006). [CrossRef] [PubMed]
- D. C. Adler, R. Huber, and J. G. Fujimoto, “Phase-sensitive optical coherence tomography at up to 370,000 lines per second using buffered Fourier domain mode-locked lasers,” Opt. Lett. 32(6), 626–628 (2007). [CrossRef] [PubMed]
- C. Joo, T. Akkin, B. Cense, B. H. Park, and J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. 30(16), 2131–2133 (2005). [CrossRef] [PubMed]
- M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, “Doppler flow imaging of cytoplasmic streaming using spectral domain phase microscopy,” J. Biomed. Opt. 11(2), 024014 (2006). [CrossRef] [PubMed]
- B. J. Vakoc, S. H. Yun, J. F. de Boer, G. J. Tearney, and B. E. Bouma, “Phase-resolved optical frequency domain imaging,” Opt. Express 13(14), 5483–5493 (2005). [CrossRef] [PubMed]
- W. V. Sorin and D. F. Gray, “Simultaneous thickness and group index measurement using optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4(1), 105–107 (1992). [CrossRef]
- H.-C. Cheng and Y.-C. Liu, “Simultaneous measurement of group refractive index and thickness of optical samples using optical coherence tomography,” Appl. Opt. 49, 790–797 (2010). [CrossRef] [PubMed]
- J. Na, H. Y. Choi, E. S. Choi, C. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 48(13), 2461–2467 (2009). [CrossRef] [PubMed]
- U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Technol. 11, 1377–1384 (1993). [CrossRef]
- T.-J. Ahn, J. Y. Lee, and D. Y. Kim, “Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation,” Appl. Opt. 44, 7630–7634 (2005). [CrossRef] [PubMed]
- E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express 16, 13139–13149 (2008). [CrossRef] [PubMed]
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