Ординатура / Офтальмология / Английские материалы / Handbook of Optical Coherence Tomography_Bouma, Tearney_2002

Figure 29 Spectrum and autocorrelation function for the self-phase-modulated Cr4þ : forsterite laser.

through self-phase modulation [14]. The mode-locked output of the Cr4þ : forsterite laser at 100 mW of average power was coupled into a singlemode Corning SMF/DS dispersion-shifted fiber (zero group velocity at 1:55 m) as shown in Fig. 29. Figure 29 also displays the demodulated autocorrelation function corresponding to the spectrum. The FWHM coherence length produced from this source measures 5:7 m. Side lobes in the autocorrelation function due to the rectangular shape of the spectrum are almost 20 dB lower than the maximum peak intensity.

A cross-sectional tomographic image of human adipose tissue generated in vitro with the Cr4þ : forsterite self-phase-modulated source is shown in Fig. 30. Again, the transverse resolution, determined by the spot size on the sample, was chosen to approximately match the axial resolution of the self-phase-modulated laser source, 6 m. The power incident on the sample was 2 mW, corresponding to a measured signal-to-noise ratio of 115 dB. The image dimensions were 5.0 mm transverse (600 pixels) by 5 mm axial (200 pixels). The entire image was acquired in 30 s. The high resolution of this system permits the visualization of tissue microstructure including cell membranes and intercellular spaces.

Figure 30 Optical coherence tomographic image of in vitro human adipose tissue acquired using the self-phase-modulated Cr4þ : forsterite source. Bar represents 100 m.

Figure 31 Images of human cadaver trachea at various wavelengths using an optical parametric oscillator.

most likely due to prominent water absorption bands. At other wavelengths, very little change is noticed in either contrast or depth of penetration.

In the images of Fig. 31, it is apparent that the axial point spread function of the OPO used in this study varied significantly both in width and in roll-off. The prominence of this artifact at wavelengths of 1350, 1450, 1850, and 1900 nm suggests that water vapor absorption in the OPO resonator may be responsible. If more efficient purging of the resonator can be used to significantly reduce this effect, the femtosecond OPO may become a more useful tool for OCT imaging. One application for a stable, tunable source of low coherence light would be the investigation of the wavelength dependence of optical properties in biological tissues [24].

3.5SELF-PHASE MODULATION

Self-phase modulation is based on a third-order nonlinear effect known as the optical Kerr effect. The nonlinear polarization component at frequency ! produces a change in the susceptibility of the medium, , such that

94 Bouma and Tearney

is the intensity of the incident optical wave and PNL is the nonlinear polarization.

the Kerr nonlinearity gives rise to an intensity-dependent change in the refractive index:

Because of the optical Kerr effect, a pulse of light confined in an optical fiber is modulated in phase such that

For most glasses and laser host crystals, the magnitude of n2 requires focused femtosecond pulses to generate appreciable frequency shifts. When these conditions are met, however, the rising edge of the pulse gives rise to a red-shifted spectrum while the falling edge creates a blue shift.

In typical media, the diffraction that results from tight focusing and normal dispersion acts to limit the integrated nonlinear frequency shift that can be achieved. In the work described Section 2.4.2 on Cr4þ : Mg2SiO4, femtosecond pulses at a wavelength of 1:3 m were focused into SMF-DS fiber for which dispersion is weak. This allowed the femtosecond pulses to travel a longer distance before dispersion reduced their intensity below the threshold for self-phase modulation by temporally broadening the pulses.

The generation of significant frequency broadening through self-phase modulation at a wavelength of 800 nm where standard optical fibers have large normal dispersion is not possible with unamplified laser pulses. A very exciting advancement in this area has recently come from Lucent Technologies, where a new type of optical fiber has been developed [25]. Lucent’s fiber uses a microstructured cladding to induce a large difference between the index of refraction of the fiber core and the surrounding cladding (Fig. 32). This results in both stronger guiding and significant waveguide dispersion. Stronger guiding is advantageous for self-phase modulation, because as the cross-sectional area of the guide is reduced the power density of the light is increased. The anomalous waveguide dispersion of Lucent’s fiber has been designed to balance the normal dispersion of bulk silica so that the net dispersion experienced by propagating pulses is zero near 800 nm. The combined result of strong confinement and dispersion-free propagation can lead to significant integrated nonlinearity and pronounced spectral broadening.

Using a 75 cm section of the microstructured fiber and 800 pJ, 100 fs pulses with a center wavelength of 790 nm, the Lucent researchers were able to generate a broadband continuum extending from 400 nm to 1600 nm (Fig. 33) [25]. Although it remains to be demonstrated as a source for OCT imaging, this spectrum could potentially provide submicrometer axial resolution. Perhaps more interesting, however, would be the use of this source for combined OCT imaging and spectroscopy.

Figure 32 Air–silica microstructured fiber from Lucent Technologies.

3.6SUMMARY

Solid-state lasers provide high power, broad-spectrum, low coherence light that enables both high speed and high resolution OCT. In their current state of development, they are valuable tools for performing preliminary OCT studies in vitro. However, the cost and size of these devices make their use impractical outside of a research setting. Development performed to miniaturize KLM solid-state lasers would greatly increase the likelihood that these sources could be integrated into a clinical setting. A second possibility for the use of femtosecond lasers in OCT would be as pulse sources for continuum generation in microstructured fiber. The exceptional bandwidth and potential for high power of this hybrid source will undoubtedly make it the focus of intense investigation in the next few years.

Figure 33 Spectrum generated through self-phase modulation of Ti : sapphire laser pulses in air–silica microstructured fiber.

The REDF ASE sources also require improvement. Both the filtered Nd : silica and the Yb : silica REDFs suffer from side lobes due to a rectangularly shaped emission spectrum. Distortions in the OCT images caused by autocorrelation side lobes should be improved in second generation ASE devices that not only diminish gain narrowing but also provide spectral shaping to avoid side lobes. Praseodymium : silica and Tm : silica REDF sources have broad enough gain bandwidths to be used without filtering, and their spectra are much closer to Gaussian. However, no 590 nm semiconductor diode is currently available to pump the Pr : silica ASE source. Although 785 nm diodes are available to pump the Tm : silica source, cladding-pumped geometries are impractical because the emission of 1800 for Tm : silica is not four-level. Although the shape of the Tm : silica REDF ASE spectrum and the optical properties of tissue at 1800 nm make the Tm : silica ASE source the most desirable of all of the REDFs, the cost of a single-mode pump may prohibit its widespread use. Most likely, the next generation clinically viable REDF source will be either a spectrally shaped Nd : silica or Yb : silica REDF with shaping that not only accounts for the spectral narrowing but also makes the spectrum more Gaussian.

Of all the sources investigated for OCT to date, semiconductors remain the only viable option for clinical implementation. Although potential advances in semiconductor source power and bandwidth are possible, they will require significant investment that may require a driving force in a much larger commercial sector such as the telecommunications industry.

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delivered to and collected from the ODL by separate optics. If a transmissive ODL is desired, many of the configurations to be presented here are adaptable to a transmissive mode, and the theoretical and design principles will still be applicable. The ODLs reviewed here will also be continuously scanning. Delay lines have been developed that scan pathlength in discrete steps, but these are seldom selected for OCT because in order to take advantage of heterodyne detection an additional phase modulation element would be required. If a continuously scanning ODL is used, the reference light is Doppler shifted, directly providing the needed phase modulation.

The appropriate ODL for a given OCT system depends on many factors, including imaging requirements, interferometer configuration, and available skills and resources. Some parameters and characteristics of ODLs that are important for OCT are

1.Working pathlength scan range

2.Pathlength scan velocity

3.Scan repetition rate

4.Pathlength scan duty cycle

5.Linearity of pathlength scan

6.Optical power loss

7.Polarization effects

8.Dispersion effects

The importance of these parameters will be discussed, and the ODLs discussed here will be characterized and compared according to these criteria.

4.1.1Cross-Correlation and Autocorrelation

The essential theory will now be presented that relates the properties of the ODL to the OCT signal [1]. The basic measurement performed in OCT imaging is an interferometric cross-correlation, R~isð lÞ, of light returning from the reference and sample arms of the interferometer as a function of the optical pathlength differencel between the arms [2,3]. This cross-correlation measurement can be intuitively understood as a pathlength-resolved ‘‘gate’’ for the signal returning from the sample, set by a reference signal split off from the optical source. In other words, OCT probes a sample with light and uses an interferometer to localize backscatter sites in the sample. The straightforward way to obtain a measurement of the cross-corre- lation is to scan the optical pathlength difference by using a scanning optical delay line in the reference arm. The interferometric part of the photodetector current, i~d ð lÞ, recorded as the ODL is scanned, is proportional to the interferometric cross-correlation:

where is the responsivity of the photodetector (in amperes per watt). The interferometric cross-correlation can be expressed as the product of the complex envelope of the interferometric cross-correlation, Ris, and a complex exponential carrier:

R~is lg; l ¼ Risð lgÞe jk0 l ð2Þ

Here lg and l are the group and phase delays, respectively, expressed as pathlength differences, and k0 is the center wavenumber of the optical source. Note that