## Performance of fourier domain vs. time domain optical coherence tomography

Optics Express, Vol. 11, Issue 8, pp. 889-894 (2003)

http://dx.doi.org/10.1364/OE.11.000889

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### Abstract

In this article we present a detailed discussion of noise sources in Fourier Domain Optical Coherence Tomography (FDOCT) setups. The performance of FDOCT with charge coupled device (CCD) cameras is compared to current standard time domain OCT systems. We describe how to measure sensitivity in the case of FDOCT and confirm the theoretically obtained values. It is shown that FDOCT systems have a large sensitivity advantage and allow for sensitivities well above 80dB, even in situations with low light levels and high speed detection.

© 2003 Optical Society of America

*et al.*in 19951

1. 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]

2. G. Häusler and M.W. Lindner, “Coherence radar and spectral radar - new tools for dermatological diagnosis,” J. Biomed. Opt . **3**, 21–31(1998). [CrossRef]

3. 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]

4. M. Wojtkowski, T. Bajraszewski, P. Targowski, and A. Kowalczyk, “Real-time in-vivo ophthalmic imaging by ultrafast spectral interferometry,” Proc. SPIE 4956, 4956-11 (2003). [CrossRef]

*R*

_{s}and

*R*

_{r}in the sample and reference arm of a Michelson interferometer. Let the part of the input power that will exit the interferometer from each arm be γ

_{r}and γ

_{s}respectively, assuming

*R*

_{s}=

*R*

_{r}=1. We have a fixed photon charge distribution

*K(n)*over the detector pixel array of the spectrometer. For each read out cycle with exposure time τ it is given by

*P*(ν

_{n}) is the spectral optical power at the interferometer entrance, and

*N*determines the number of pixels. The spectrometer efficiency ρ comprises the diffraction grating efficiency and losses due to optical components and spectrometer geometry. The optical path length difference between the two interferometer arms is Δ

*z*, and ϕ denotes an arbitrary phase shift. We assume a Gaussian spectral density of the light source

*n*

^{th}detector pixel covers a spectral range of ν

_{n}± δν/2, where δν is the spectrometer resolution. Assuming, that the full width half maximum (FWHM) of the source spectrum is imaged onto

*N/m*detector pixels, the resolution is given by δν=Δν

_{FWHM}

*m/N*. In taking the integral over Eq. (2) one calculates the output power of the light source to be

*P*(ν

_{0}) and the signal peak height at the corresponding modulation frequency after DFT

*S*

_{Peak}, and between the corresponding FWHM values read10

*N /m*. Hence, the FDOCT signal amplitude is obtained by combining Eqs. (1) and (3):

*1/N*, which seems to favour TD systems. The situation dramatically changes if we take into account the Fourier transformation process. The noise rms of each pixel contributes to the noise level at one DFT bin. This effect would increase the noise level at the DFT bin by factor of √

*N*as compared to the pixel noise rms. However, we have an additional normalization factor of 1/N due to the DFT10. We finally end up with the relation σ˜

^{2}=σ

^{2}/

*N*for white noise variances in the respective DFT spaces. Assuming that all noise contributions have a white noise characteristic, the total noise in FDOCT systems after the DFT is given by

*SNR*=〈

*S*

_{OCT}is given in Eq. (4). Since in Fourier domain setups the detector will always record the high DC background as well, the achievable dynamic range is limited by the photoelectron capacity (FWC) of the CCD. The sensitivity Σ of OCT devices is defined as the minimal sample arm reflectivity

*R*

_{s,min}, at which the SNR equals one, i.e., Σ =

*1/R*

_{s,min}. In most applications the reference arm reflectivity is much larger than that of the sample arm, i.e.,

*R*

_{s}≪

*R*

_{r}. Using this approximation the sensitivity may be written as

*B*. Following Rollins et al.11

11. A. M. Rollins, S. Yazdanfar, M. D. Kulkarni, R. Ung-Arunyawee, and J. A. Izatt, “In vivo video rate optical coherence tomography,” Opt. Express **3**, 219–229 (1998),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-6-219. [CrossRef] [PubMed]

*N/2*DFT bins, we obtain:

*v*

_{g}.

*z*

_{max}corresponding to DFT bin N/2 is limited by the spectrometer resolution δλ and is given by

*z*

_{max}= λ

^{2}/(4δλ). Any signal that exceeds this Nyquist limit will appear as aliased signal at DFT bin

*N - n*(Fig. 1). Also, the total noise power in the spectral domain is spread over all DFT bins in the time domain weighted by the sinc function. Noise frequencies outside the Nyquist border will however still be present within the signal range as aliased frequencies. This is why we assume a white noise characteristic, which, in case of photon noise, is associated with an average DC level of

*P*

_{ref}

*/N*. The SNR will drop by ~ 4 dB as the signal peak approaches the Nyquist limit of

*N/2*.

_{0}= 811nm,

*FWHM*=17nm,

*P*

_{0}=175µW, 60µW at the sample), the array detector was an ANDOR CCD camera with 1024 horizontal pixels. The spectrometer imaged the FWHM onto 470 CCD pixels. We used an exposure time of τ=1ms, which corresponds to an A-scan rate of 1000 scans per second. In order to obtain the frequency depending interference signal from the recorded wavelength depending pattern, we applied a software scaling algorithm before DFT. In addition we performed a subtraction of the reference arm signal, which was recorded initially by blocking the sample arm.

*D*=40dB to this value. Fig. 3b shows a typical A-scan obtained with this configuration. The scan confirms nicely the assumed white noise characteristic for our noise model. The receiver noise for the CCD at room temperature was measured to 250 electrons per read out cycle and pixel.

4. M. Wojtkowski, T. Bajraszewski, P. Targowski, and A. Kowalczyk, “Real-time in-vivo ophthalmic imaging by ultrafast spectral interferometry,” Proc. SPIE 4956, 4956-11 (2003). [CrossRef]

12. R. Leitgeb, L. Schmetterer, C. K. Hitzenberger, M. Sticker, M. Wojtkowski, and A. F. Fercher, “Flow Measurements by Frequency Domain Optical Coherence Tomography,” Proc. SPIE **4619**, 16–21 (2002). [CrossRef]

## Acknowledgments

## References and links

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

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

3. | 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. |

4. | M. Wojtkowski, T. Bajraszewski, P. Targowski, and A. Kowalczyk, “Real-time in-vivo ophthalmic imaging by ultrafast spectral interferometry,” Proc. SPIE 4956, 4956-11 (2003). [CrossRef] |

5. | J. W. Goodman, |

6. | R. V. Sorin and D. M. Baney, “A simple intensity noise reduction technique for optical low coherence reflectometry,” IEEE Photonics Techn. Lett. |

7. | A. M. Rollins and J. A. Izatt, “Optimal interferometer designs for optical coherence tomography,” Opt. Lett. |

8. | A. G. Podoleanou, “Unbalanced versus balanced operation in an optical coherence tomography system,” Appl. Opt. |

9. | H. Saint-Jalmes, M. Lebec, E. Beaurepierre, A. Dubois, and A. C. Boccara, in |

10. | R. Bracewell, |

11. | A. M. Rollins, S. Yazdanfar, M. D. Kulkarni, R. Ung-Arunyawee, and J. A. Izatt, “In vivo video rate optical coherence tomography,” Opt. Express |

12. | R. Leitgeb, L. Schmetterer, C. K. Hitzenberger, M. Sticker, M. Wojtkowski, and A. F. Fercher, “Flow Measurements by Frequency Domain Optical Coherence Tomography,” Proc. SPIE |

**OCIS Codes**

(110.4500) Imaging systems : Optical coherence tomography

(120.3890) Instrumentation, measurement, and metrology : Medical optics instrumentation

**ToC Category:**

Research Papers

**History**

Original Manuscript: March 17, 2003

Revised Manuscript: April 9, 2003

Published: April 21, 2003

**Citation**

R. Leitgeb, C. Hitzenberger, and Adolf Fercher, "Performance of fourier domain vs. time domain optical coherence tomography," Opt. Express **11**, 889-894 (2003)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-8-889

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### References

- A. F. Fercher, C. K. Hitzenberger, G. Kamp, S.Y. El-Zaiat, �??Measurement of intraocular distances by backscattering spectral interferometry,�?? Opt.Commun. 117, 43-48,(1995). [CrossRef]
- G. Häusler, M.W. Lindner, �??Coherence radar and spectral radar �?? new tools for dermatological diagnosis,�?? J. Biomed. Opt. 3, 21-31(1998). [CrossRef]
- M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, A. F. Fercher, �??In vivo human retinal imaging by fourier domain optical coherence tomography,�?? J. Biomed. Opt. 7, 457-463 (2002). [CrossRef] [PubMed]
- M. Wojtkowski, T. Bajraszewski, P. Targowski, A. Kowalczyk, �??Real-time in-vivo ophthalmic imaging by ultrafast spectral interferometry,�?? Proc. SPIE 4956, 4956-11 (2003). [CrossRef]
- J. W. Goodman, Statistical Optics (John Wiley & Sons, 1985).
- R. V. Sorin, D. M. Baney, �??A simple intensity noise reduction technique for optical low coherence reflectometry,�?? IEEE Photonics Technol. Lett. 4, 1404 �?? 1406, (1992). [CrossRef]
- A. M. Rollins, J. A. Izatt, �??Optimal interferometer designs for optical coherence tomography,�?? Opt. Lett. 24, 1484-1486 (1999). [CrossRef]
- A. G. Podoleanou, �??Unbalanced versus balanced operation in an optical coherence tomography system,�?? Appl. Opt. 39, 173-182 (2000). [CrossRef]
- H. Saint-Jalmes, M. Lebec, E. Beaurepierre, A. Dubois, A. C. Boccara, in Handbook of Optical Coherence Tomography , B. Bouma, E. Tearney, eds., (Marcel Dekker, Inc. 2002) Chap. 11
- R. Bracewell, The Fourier Transform and Its Applications, (McGraw-Hill 1965).
- A. M. Rollins, S. Yazdanfar, M. D. Kulkarni, R. Ung-Arunyawee, J. A. Izatt, "In vivo video rate optical coherence tomography,�?? Opt. Express 3, 219-229 (1998), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-6-219">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-6-219</a>. [CrossRef] [PubMed]
- R. Leitgeb, L. Schmetterer, C. K. Hitzenberger, M. Sticker, M. Wojtkowski, and A. F. Fercher, "Flow Measurements by Frequency Domain Optical Coherence Tomography,�?? Proc. SPIE 4619, 16-21 (2002). [CrossRef]

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