## K-space linear Fourier domain mode locked laser and applications for optical coherence tomography

Optics Express, Vol. 16, Issue 12, pp. 8916-8937 (2008)

http://dx.doi.org/10.1364/OE.16.008916

Acrobat PDF (3567 KB)

### Abstract

We report on a Fourier Domain Mode Locked (FDML) wavelength swept laser source with a highly linear time-frequency sweep characteristic and demonstrate OCT imaging without k-space resampling prior to Fourier transformation. A detailed theoretical framework is provided and different strategies how to determine the optimum drive waveform of the piezo-electrically actuated optical bandpass-filter in the FDML laser are discussed. An FDML laser with a relative optical frequency deviation Δν/ν smaller than 8·10^{-5} over a 100 nm spectral bandwidth at 1300 nm is presented, enabling high resolution OCT over long ranging depths. Without numerical time-to-frequency resampling and without spectral apodization a sensitivity roll off of 4 dB over 2 mm, 12.5 dB over 4 mm and 26.5 dB over 1 cm at 3.5 µs sweep duration and 106.6 dB maximum sensitivity at 9.2 mW average power is achieved. The axial resolution in air degrades from 14 to 21 µm over 4 mm imaging depth. The compensation of unbalanced dispersion in the OCT sample arm by an adapted tuning characteristic of the source is demonstrated. Good stability of the system without feedback-control loops is observed over hours.

© 2008 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. R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express **11**, 889–894 (2003). [CrossRef] [PubMed]

5. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, “Measurement of Intraocular Distances by Backscattering Spectral Interferometry,” Opt. Commun. **117**, 43–48 (1995). [CrossRef]

12. R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express **14**, 3225–3237 (2006). [CrossRef] [PubMed]

13. R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett. **31**, 2975–2977 (2006). [CrossRef] [PubMed]

14. 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**, 626–628 (2007). [CrossRef] [PubMed]

12. R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express **14**, 3225–3237 (2006). [CrossRef] [PubMed]

15. S. W. Huang, A. D. Aguirre, R. A. Huber, D. C. Adler, and J. G. Fujimoto, “Swept source optical coherence microscopy using a Fourier domain mode-locked laser,” Opt. Express **15**, 6210–6217 (2007). [CrossRef] [PubMed]

14. 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**, 626–628 (2007). [CrossRef] [PubMed]

16. R. Huber, D. C. Adler, V. J. Srinivasan, and J. G. Fujimoto, “Fourier domain mode locking at 1050 nm for ultra-high-speed optical coherence tomography of the human retina at 236,000 axial scans per second,” Opt. Lett. **32**, 2049–2051 (2007). [CrossRef] [PubMed]

17. L. A. Kranendonk, R. Huber, J. G. Fujimoto, and S. T. Sanders, “Wavelength-agile H2O absorption spectrometer for thermometry of general combustion gases,” Proceedings of the Combustion Institute **31**, 783–790 (2007). [CrossRef]

18. L. A. Kranendonk, X. An, A. W. Caswell, R. E. Herold, S. T. Sanders, R. Huber, J. G. Fujimoto, Y. Okura, and Y. Urata, “High speed engine gas thermometry by Fourier-domain mode-locked laser absorption spectroscopy,” Opt. Express **15**, 15115–15128 (2007). [CrossRef] [PubMed]

19. D. C. Adler, J. Stenger, I. Gorczynska, H. Lie, T. Hensick, R. Spronk, S. Wolohojian, N. Khandekar, J. Y. Jiang, S. Barry, A. E. Cable, R. Huber, and J. G. Fujimoto, “Comparison of three-dimensional optical coherence tomography and high resolution photography for art conservation studies,” Opt. Express **15**, 15972–15986 (2007). [CrossRef] [PubMed]

20. S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, “High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter,” Opt. Lett. **28**, 1981–1983 (2003). [CrossRef] [PubMed]

21. R. Huber, M. Wojtkowski, J. G. Fujimoto, J. Y. Jiang, and A. E. Cable, “Three-dimensional and C-mode OCT imaging with a compact, frequency swept laser source at 1300 nm,” Opt. Express **13**, 10523–10538 (2005). [CrossRef] [PubMed]

12. R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express **14**, 3225–3237 (2006). [CrossRef] [PubMed]

22. M. Y. Jeon, J. Zhang, Q. Wang, and Z. Chen, “High-speed and wide bandwidth Fourier domain mode-locked wavelength swept laser with multiple SOAs,” Opt. Express **16**, 2547–2554 (2008). [CrossRef] [PubMed]

23. S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. **12**, 1429–1433 (2006). [CrossRef] [PubMed]

24. D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics **1**, 709–716 (2007). [CrossRef]

24. D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics **1**, 709–716 (2007). [CrossRef]

25. B. Hofer, B. Povazay, B. Hermann, A. Unterhuber, G. Matz, F. Hlawatsch, and W. Drexler, “Signal post processing in frequency domain OCT and OCM using a filter bank approach - art. no. 64430O,” Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing Xiv **6443**, O4430–O4430 (2007).

10. 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). [CrossRef] [PubMed]

### 1.2 Quality parameter and error tolerance

_{Lin}(t) is the deviation from the perfect linear time-frequency characteristic ν

_{Lin}(t) that can be calculated by a linear fit to ν(t) in the given time interval of interest Δt. Summations are done over all sample points N within Δt.

26. Z. Hu and A. M. Rollins, “Fourier domain optical coherence tomography with a linear-in-wavenumber spectrometer,” Opt. Lett. **32**, 3525–3527 (2007). [CrossRef] [PubMed]

20. S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, “High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter,” Opt. Lett. **28**, 1981–1983 (2003). [CrossRef] [PubMed]

21. R. Huber, M. Wojtkowski, J. G. Fujimoto, J. Y. Jiang, and A. E. Cable, “Three-dimensional and C-mode OCT imaging with a compact, frequency swept laser source at 1300 nm,” Opt. Express **13**, 10523–10538 (2005). [CrossRef] [PubMed]

10. 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). [CrossRef] [PubMed]

**14**, 3225–3237 (2006). [CrossRef] [PubMed]

22. M. Y. Jeon, J. Zhang, Q. Wang, and Z. Chen, “High-speed and wide bandwidth Fourier domain mode-locked wavelength swept laser with multiple SOAs,” Opt. Express **16**, 2547–2554 (2008). [CrossRef] [PubMed]

*wavelenth-linear*laser source in contrast to the source that is

*sinusoidal in wavelength*. Only for the latter one, a smaller duty cycle can yield better linearity. The lasing range is centered at 1308 nm, the sweep range of the filter is centered at 1318 nm. The chosen 10 nm offset minimizes the non-linearity in case of the sinusoidal sweep, because the slightly non-linear part of the sine can be used to partially cancel the 1/λ dependence. The sweep duration of the sinusoidal drive waveform equals 3.4 µs. Figure 1 (center) displays the relative frequency error Δν/ν for these three sources relative to a perfectly linear evolution over the time range where the laser source is active (1260 nm to 1360 nm - see hatched area). All three curves from Fig. 1 (left) were fitted linearly in the 100 nm lasing range (blue area) and the relative frequency error was plotted. Because the effective sweep speed of the sinusoidal source is higher, the sweep duration is shorter. Naturally, for the perfectly linear evolution (black line) the relative frequency error is zero. Remarkably, for this specific example, the sinusoidally driven source (green) already exhibits a deviation comparable to the wavelength-linear source, as a direct result of the large drive amplitude of the filter (175 nm) compared to the lasing range. The integrated relative frequency error for the sinusoidal driven source (green line) is χ

_{sine}=3.9·10

^{-4}, for the wavelength-linear source (red line) χ

_{lin_lambda}=4.3·10

^{-4}respectively.

^{-4}is required and an extremely high accuracy and repeatability of the filter is needed.

## 2. Experimental setup

### 2.1 Laser and interferometer setup

### 2.2 Filter response

## 3. Semi-analytical/non-iterative approach

### 3.1 General considerations

### 3.2 Semi-analytical/non-iterative approaches

_{0}is the wavelength offset, i.e. the center wavelength of the sweep, c is the speed of light in vacuum, A

_{i}represent the amplitudes of the respective components in wavelength; φ

_{i}are the different phases of the three harmonics respectively and ω=2π·56.902 kHz is the drive frequency of the filter.

### 3.3 Simple Fourier expansions

_{lin}(t) with a wavelength offset λ

_{0}and a sweep range A. All Fourier-components up to third order will be considered, higher orders are neglected, yielding the A

_{i}s and φ

_{i}s. A

_{1}is chosen such that ν(t) exhibits a sweep range of 175 nm.

## 4. Numerical methods A: constant sweep duration

13. R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett. **31**, 2975–2977 (2006). [CrossRef] [PubMed]

_{1}, A

_{2}, A

_{3}, the phases of the first three orders φ

_{1}, φ

_{2}, φ

_{3}and the wavelength offset λ

_{0}. Since sweep duration and frequency interval are given, two boundary points in the time-frequency domain can be defined. We can assume a linear sweep from high to low frequency. Hence, the integrated relative frequency error χ can be calculated as described in section 1. χ has to be minimized finding the ideal parameter combination by a non-linear numeric fit procedure.

_{drive}≈57 kHz, which would yield a 228 kHz repetition rate for a 4× buffering scheme [13

13. R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett. **31**, 2975–2977 (2006). [CrossRef] [PubMed]

_{2}=13.2%·A

_{1}and A

_{3}=0.6%·A

_{1}(Fig. 5, black cross) with the corresponding phases φ

_{1}=0.024 π, φ

_{2}=0.980 π and φ

_{3}=1.324 π. The minimum of χ corresponds to a wavelength offset λ

_{0}=1315 nm, indicating that the nonlinearity induced by the ν=c/λ relation is reduced by choosing an offset slightly above the center wavelength of laser activity of 1308 nm (see section 3).

^{-3}to the minimum of 3.346·10

^{-5}, which is approximately one order of magnitude improvement over wavelength linear sources (see section 1). It should be noted that the result obtained for the chosen parameter set leads to a minimum of χ located in an area of rather high amplitudes of second harmonic, resulting in relatively high drive voltages due to the weak response of the filter. Solutions with smaller amplitudes of the higher harmonics would be preferred.

_{1}(from 82.5 nm to 102.5 nm) result in similar error plots. However, higher values of A

_{1}yield smaller minimum values for χ, so a compromise between electro-mechanical load and required minimum error has to be made.

## 5. Numerical methods B: arbitrary sweep duration

_{1}as well as for increasing A

_{2}and A

_{3}, the problem diverges towards higher amplitudes. So A

_{1}, A

_{2}, A

_{3}and the wavelength offset λ

_{0}are kept invariant during optimization and are changed in a reasonable raster to plot an error map. φ

_{2}and φ

_{3}are optimized with a nonlinear optimization algorithm (Matlab V7.4.0 function “fminsearch”) for each parameter configuration. Since the time interval of laser activity is found by the search algorithm, the absolute phase is not essential and one can arbitrarily chose the phase of the first harmonic φ

_{1}to 0.

_{2}and A

_{3}in order to avoid very high driving voltages for the higher harmonics, preventing excessive electro-mechanical stress on the piezo of the FFP-TF. Hence, the operation point will be set in the lower branch in the region near zero 2nd order amplitude (A

_{2}=2.4 % and A

_{3}=5 %; indicated as point 4 in Fig. 6(A)). This solution is a good compromise between having small amplitudes and sufficient linearity. The expected value of χ is 2.307·10

^{-5}, this is 20× smaller than the equivalent χ, achieved with a sinusoidal or linear time-wavelength sweep characteristic (see section 1).

_{2}and φ

_{3}(raster of 2°) for the parameter combinations representing three characteristic points in the error map (Fig. 6(A), points number 4,8,9). The absolute minimum of each plot is indicated with crosses. Figure 7(A) depicts the chosen operation point (point 4) with relative small values for A

_{2}=2.4 %, A

_{3}=5 % and an ideal λ

_{0}=1315 nm. Figure 7(B) is illustrating a case with high A

_{2}=14.4 %, small A

_{3}=0.5 % and ideal λ

_{0}=1310 nm (point 8). Finally Fig. 7(C) demonstrates a case with high A

_{2}=14.4 %, high A

_{3}=9 % and ideal λ

_{0}=1320 nm (point 9). In all three cases the domain of high linearity in the plots is an S-shaped blue curve but the orientations differ. Considering point 4, the range of φ

_{3}yielding small χ is much smaller than the corresponding range of φ

_{2}whereas the situation is inverse at point 8.

## 6. Experimental results and comparison to theory

### 6.1 Measurements confirming numerical simulation

_{1}equals 87.5 nm. The wavelength offset λ

_{0}is set to the appropriate value by tuning the applied DC-voltage of the piezo of the FFP-TF. Both, first order harmonic amplitude A

_{1}and wavelength offset λ

_{0}, can directly be monitored with the OSA. In order to derive the relative frequency error Δν/ν and calculate the integrated frequency error χ, a 100 times averaged interference signal is recorded with the oscilloscope and a Hilbert transformation is performed at the part of the signal where the envelope drop is smaller than 10 dB (≈ 1260 nm to 1360 nm). The accumulative phase evolution of the interference fringes can be extracted and fitted linearly. So Δν/ν and χ result from the phase deviation Δφ (phase of the electronic beat signal from the MZI), assuming a wavelength range of the analyzed data from 1260 nm to 1360 nm and setting all ν

_{i}s in Eq. (1) to a center frequency ν

_{M}=c/1310 nm.

_{2}of 2.4 %·A

_{1}and the respective values of A

_{3}have to be applied, accounting for the amplitude response of the filter (see paragraph 2).

_{3}(blue). Here, the dominant error is caused by the inaccuracy in the determination of the wavelength range. The red points indicate the values of χ expected from simulation. Figure 8 (right) presents the expected optimum phases of the second and third order harmonic AC-voltage according to the simulation (red points: third order harmonic phases; pink points: second order harmonic phases). The phases are corrected for the phase shift due to the filter response. The optimum phases for second and third order harmonic found in experiment are plotted as blue line (third order harmonic phase) and as dark blue line (second order harmonic points). The error bars indicate the error for the second order harmonic phase, the third order harmonic error is too small to be drawn.

### 6.2 Discrepancy between theory and experiment – non-linear coupling

*total errors*, discrepancies in theoretically and experimentally optimized

*phase*can be identified in Fig. 8 (right), especially for the last four amplitude points. To understand this observation, one has to recall the phase maps of Fig. 7, demonstrating that for the parameter set of a given point on the error map, there are several phase combinations (S-shaped curve) yielding almost identical error values χ.

_{0}is slightly increased, the linearity can be improved, yielding smaller values of χ. This particularly applies for the last three points. Here, the predicted decrease of optimum offset from 1310 nm to 1285 nm could only be observed to a minor degree. Furthermore, the two polynomial fits (third order) in Fig. 8 (left) indicate that the minimum of the experimental error curve is shifted to higher amplitudes (absolute deviation of approximately 1 %). This result is also underlined by the following comparison.

_{3}=6 % instead A

_{3}=5 %. The optimum offset is about 1320 nm instead of 1310 nm. The optimum phase of the second order harmonic is 1.138 π, the corresponding phase of the third order harmonic is 1.351 π respectively. As can be seen in Fig. 9 (left) the two solutions are in very good agreement, yielding nearly the same characteristic and sweep duration (3.5 µs instead of 3.6 µs expected from simulation). The resulting integrated frequency error of the experimental data is 2.11·10

^{-5}and therefore in very good agreement with the optimal χ of 2.31·10

^{-5}predicted by simulation.

### 6.3 Required accuracy and procedure to set k-space linear FDML

_{i}are calculated with a numerical fit procedure. (3) A good operation point within the experimental constraints is chosen on the error map, with an error as small as necessary and drive amplitudes as small as possible. (4) The system is set to amplitude and phase values predicted by the simulation and a fine adjustment of the offset center wavelength and the phases is used for final optimization, using online feedback from an oscilloscope. Possible small discrepancies between theory and experiment due to effects like for example non-linear coupling can be corrected. Usually the width of the PSF generated by the built in FFT-function of an oscilloscope is sufficient. With this method, an integrated frequency error of χ=2.11·10

^{-5}for a sweep duration of 3.5 µs was achieved which is about a factor of 20x improvement compared to a wavelength-linear or sinusoidal sweep characteristic (chapter 1). For the online analysis on the oscilloscope a simple, inexpensive fixed MZI, built of two fusion spliced 50/50 couplers, could be applied.

### 6.4 OCT performance

28. V. J. Srinivasan, R. Huber, I. Gorczynska, J. G. Fujimoto, J. Y. Jiang, P. Reisen, and A. E. Cable, “High-speed, high-resolution optical coherence tomography retinal imaging with a frequency-swept laser at 850 nm,” Opt. Lett. **32**, 361–363 (2007). [CrossRef] [PubMed]

4. M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express **11**, 2183–2189 (2003). [CrossRef] [PubMed]

**31**, 2975–2977 (2006). [CrossRef] [PubMed]

29. Y. L. Chen, D. M. de Bruin, C. Kerbage, and J. F. de Boer, “Spectrally balanced detection for optical frequency domain imaging,” Opt. Express **15**, 16390–16399 (2007). [CrossRef] [PubMed]

30. S. Moon and D. Y. Kim, “Normalization detection scheme for high-speed optical frequency-domain imaging and reflectometry,” Opt. Express **15**, 15129–15146 (2007). [CrossRef] [PubMed]

**31**, 2975–2977 (2006). [CrossRef] [PubMed]

### 6.5 Imaging with k-space linear FDML without resampling and apodizing

10. 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). [CrossRef] [PubMed]

*in vivo*, are presented for each of three different situations: In Fig. 12(A) and Fig. 12(B) the filter was driven sinusoidally (175 nm scan range) with no recalibration step prior to FFT. For the images in Fig. 12(C) and Fig. 12(D) the same filter drive waveform was used but here a recalibration step was performed. Therefore, an interference signal (single depth) was recorded with the interferometer once and the phase characteristic is extracted and used for recalibration of all lines of the image. Finally, Fig. 12(E) and Fig. 12(F) are demonstrating the case where the k-space linear FDML described in the previous chapters is applied and no recalibration step was used. The presented data sets consist of 4000 lines×1664 samples (1536 samples for Figs. 12(A), 12(C), and 12(E)), each image was acquired in 0.070s. The transversal scan range is 4.3 mm the axial scan range is 6 mm. The animation in Fig. 12(G) is a rendered 3D representation of the human finger, recorded with the k-space linear FDML and no recalibration step. The movie was created from a 3D data set of 512 frames×512 lines×1536 samples, acquired in 4.6 s. The scan range equals 4.3 mm in length, 3.0 mm in width and 6 mm in depth. The images are cropped (3.3 mm×1.7 mm×1.9 mm) for better visibility. The three images Fig. 12(A), Fig. 12(C) and Fig. 12(E) as well as Fig. 12(B), Fig. 12(D) and Fig. 12(E) are acquired at the same sample position.

^{-4}is not sufficient to perform OCT without resampling.

**31**, 2975–2977 (2006). [CrossRef] [PubMed]

### 6.6 K-space adaptive FDML – Dispersion compensation

31. 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). [CrossRef] [PubMed]

*et al.*[31

31. 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). [CrossRef] [PubMed]

15. S. W. Huang, A. D. Aguirre, R. A. Huber, D. C. Adler, and J. G. Fujimoto, “Swept source optical coherence microscopy using a Fourier domain mode-locked laser,” Opt. Express **15**, 6210–6217 (2007). [CrossRef] [PubMed]

32. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, “Optical Coherence Microscopy in Scattering Media,” Opt. Lett. **19**, 590–592 (1994). [CrossRef] [PubMed]

## 7. Conclusion and outlook

^{-5}. The high degree of the linearity enables swept source OCT imaging without the step of resampling or of spectral reshaping prior to FFT. A comparison of image quality shows no difference of k-space linear FDML without recalibration or resampling and standard FDML. Good stability and reproducibility of the system is observed over hours. With the resampling step being obsolete, hardware FFT solutions become feasible, paving the way for future ultrafast real time OCT systems for clinical environments. Furthermore, additional noise generated by the resampling step is avoided. The tuning rate restrictions imposed by the requirement to drive with three harmonics can be solved. In order to improve the speed performance and multiply the effective sweep rate, the technique of buffered FDML [13

**31**, 2975–2977 (2006). [CrossRef] [PubMed]

## Acknowledgment

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

3. | 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. |

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

5. | A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, “Measurement of Intraocular Distances by Backscattering Spectral Interferometry,” Opt. Commun. |

6. | F. Lexer, C. K. Hitzenberger, A. F. Fercher, and M. Kulhavy, “Wavelength-tuning interferometry of intraocular distances,” Appl. Opt. |

7. | G. Häusler and M. W. Lindner, ““Coherence radar” and “spectral radar”-new tools for dermatological diagnosis,” J. Biomed. Opt. |

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

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

10. | 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 |

11. | Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K. P. Chan, M. Itoh, and T. Yatagai, “Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments,” Opt. Express |

12. | R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express |

13. | R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s,” Opt. Lett. |

14. | 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. |

15. | S. W. Huang, A. D. Aguirre, R. A. Huber, D. C. Adler, and J. G. Fujimoto, “Swept source optical coherence microscopy using a Fourier domain mode-locked laser,” Opt. Express |

16. | R. Huber, D. C. Adler, V. J. Srinivasan, and J. G. Fujimoto, “Fourier domain mode locking at 1050 nm for ultra-high-speed optical coherence tomography of the human retina at 236,000 axial scans per second,” Opt. Lett. |

17. | L. A. Kranendonk, R. Huber, J. G. Fujimoto, and S. T. Sanders, “Wavelength-agile H2O absorption spectrometer for thermometry of general combustion gases,” Proceedings of the Combustion Institute |

18. | L. A. Kranendonk, X. An, A. W. Caswell, R. E. Herold, S. T. Sanders, R. Huber, J. G. Fujimoto, Y. Okura, and Y. Urata, “High speed engine gas thermometry by Fourier-domain mode-locked laser absorption spectroscopy,” Opt. Express |

19. | D. C. Adler, J. Stenger, I. Gorczynska, H. Lie, T. Hensick, R. Spronk, S. Wolohojian, N. Khandekar, J. Y. Jiang, S. Barry, A. E. Cable, R. Huber, and J. G. Fujimoto, “Comparison of three-dimensional optical coherence tomography and high resolution photography for art conservation studies,” Opt. Express |

20. | S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, “High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter,” Opt. Lett. |

21. | R. Huber, M. Wojtkowski, J. G. Fujimoto, J. Y. Jiang, and A. E. Cable, “Three-dimensional and C-mode OCT imaging with a compact, frequency swept laser source at 1300 nm,” Opt. Express |

22. | M. Y. Jeon, J. Zhang, Q. Wang, and Z. Chen, “High-speed and wide bandwidth Fourier domain mode-locked wavelength swept laser with multiple SOAs,” Opt. Express |

23. | S. H. Yun, G. J. Tearney, B. J. Vakoc, M. Shishkov, W. Y. Oh, A. E. Desjardins, M. J. Suter, R. C. Chan, J. A. Evans, I. K. Jang, N. S. Nishioka, J. F. de Boer, and B. E. Bouma, “Comprehensive volumetric optical microscopy in vivo,” Nat. Med. |

24. | D. C. Adler, Y. Chen, R. Huber, J. Schmitt, J. Connolly, and J. G. Fujimoto, “Three-dimensional endomicroscopy using optical coherence tomography,” Nat. Photonics |

25. | B. Hofer, B. Povazay, B. Hermann, A. Unterhuber, G. Matz, F. Hlawatsch, and W. Drexler, “Signal post processing in frequency domain OCT and OCM using a filter bank approach - art. no. 64430O,” Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing Xiv |

26. | Z. Hu and A. M. Rollins, “Fourier domain optical coherence tomography with a linear-in-wavenumber spectrometer,” Opt. Lett. |

27. | C. Chong, A. Morosawa, and T. Sakai, “High speed wavelength-swept laser source with simple configuration for optical coherence tomography - art. no. 662705,” Proc. SPIE |

28. | V. J. Srinivasan, R. Huber, I. Gorczynska, J. G. Fujimoto, J. Y. Jiang, P. Reisen, and A. E. Cable, “High-speed, high-resolution optical coherence tomography retinal imaging with a frequency-swept laser at 850 nm,” Opt. Lett. |

29. | Y. L. Chen, D. M. de Bruin, C. Kerbage, and J. F. de Boer, “Spectrally balanced detection for optical frequency domain imaging,” Opt. Express |

30. | S. Moon and D. Y. Kim, “Normalization detection scheme for high-speed optical frequency-domain imaging and reflectometry,” Opt. Express |

31. | 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 |

32. | J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, “Optical Coherence Microscopy in Scattering Media,” Opt. Lett. |

**OCIS Codes**

(110.4500) Imaging systems : Optical coherence tomography

(110.6880) Imaging systems : Three-dimensional image acquisition

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(140.3600) Lasers and laser optics : Lasers, tunable

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

(170.4500) Medical optics and biotechnology : Optical coherence tomography

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: March 4, 2008

Revised Manuscript: April 19, 2008

Manuscript Accepted: April 24, 2008

Published: June 3, 2008

**Virtual Issues**

Vol. 3, Iss. 7 *Virtual Journal for Biomedical Optics*

**Citation**

Christoph M. Eigenwillig, Benjamin R. Biedermann, Gesa Palte, and Robert Huber, "K-space linear Fourier domain mode locked laser and applications for optical coherence tomography," Opt. Express **16**, 8916-8937 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8916

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