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

Fourier components. Nevertheless, again only relatively abrupt changes in the scattering potential, occurring within a few wavelengths, can be seen by backscattering tomography.

In the optical regime, diffraction tomography presents considerable difficulties. Only a few experimental works concerning three-dimensional or even twodimensional computational reconstruction from measured ODT data can be found in the literature [3]. No lasting biomedical application has been reported so far, though an interesting aspect of ODT is the possibility of quantitative imaging [10].

A straightforward application of ODT is also hindered by the large amount of (three-dimensional) data that would have to be collected in order to provide high resolution (two-dimensional) tomograms. Because the scattered field data belong to the three-dimensional Fourier spectrum, an N2 pixel (two-dimensional) tomogram would roughly require N3 three-dimensional Fourier data, which means that a photodetector array with N3 detector elements would have to be used. Hence, modifications of ODT have been sought [11].

One class of successful modifications are the spectral interferometric techniques. Only one direction of scattering is detected with these techniques, usually the backscattering direction. A spectrometer is used to disperse different wavelengths on a linear photodetector array. Hence, a two-dimensional version of the Fourier slice theorem [2], following straightforwardly from the Fourier integral, is useful:

where F^oð0; 0; KzÞ F^oðKÞ are the wavelength-dependent backscattered field data. This theorem relates the Fourier transform of the object along a line in Fourier space ½F^ð0; 0; KzÞ& to the Fourier transform of a two-dimensional projection (in the xy plane) of the object. Hence, to maintain transverse resolution the object must be illuminated by a slim light beam (narrow in the xy plane) as is usual in OCT.

Depth resolution is defined by the Fourier uncertainty relation. Using the full width at half-maximum (FWHM) z as a measure of the minimal extension of a scattering potential in direct space that can be resolved using a light source with FWHM bandwidth Kz in Fourier space, and assuming a Gaussian shape of the scattering potential and of the source spectrum, we obtain a space–bandwidth product

This defines OCT depth resolution. It equals the so-called round-trip coherence length of the light, which has been used as a definition of coherence length [12,13]. It should be noted, however, that light in backscattering travels along the same path twice—there and back—through the object. Hence, the corresponding FWHM coherence length lC is twice as large [14]:

scattered field explicitly. It serves to introduce a carrier frequency in the spectrum in order to separate the various correlation terms in the reconstruction. Hence, these techniques are generalizations of the old channeled spectra interferometric technique [21]. An important advantage of the spectral techniques is that the reference mirror need not be mechanically moved. A disadvantage is the limited wavelength coverage of available photodetector arrays. A further disadvantage is the usually large dc component on the photodetector array, which limits the dynamic range of the detector because a straightforward ac coupling, as with single photodetectors, is not possible with CCD arrays.

13.2.3 Wavelength Tuning (Chirp) OCT

Wavelength tuning OCT (WT-OCT) is related to spectral interferometry. (This technique is sometimes called chirp OCT, a term derived from the corresponding frequency-modulated electronic radar technique.) In this case, however, the wave- length-dependent intensity data are not recorded simultaneously by use of a broadband light source and a spectrometer; instead, they are recorded subsequently by illuminating the interferometer with a tunable narrowband laser and recording the intensity at the interferometer exit by a single photodetector.

Similar to spectral OCT, this technique has been used so far only with backscattered light, i.e., to obtain depth information on the object. Lateral information is obtained by performing several WT interferometric (WTI) scans at adjacent positions.

We explain the measurement of a path difference 2L in an interferometer with reference to Fig. 4. If the wavelength of the tunable laser diode is kept at a fixed value, the intensity at the photodetector can be calculated as

Figure 4 Schematic diagram of the principle of wavelength tuning interferometry. (Adapted from Ref. 28.)

where I1 and I2 are the light intensities reflected at mirrors 1 and 2, respectively, andis the phase difference of the two beams. This phase difference is given by

where k is the wavenumber corresponding to . If the wavenumber is changed, the phase difference changes accordingly. This causes the intensity at the photodetector to oscillate with a frequency f :

Hence, the frequency is directly proportional to the tuning rate of the wavenumber dk=dt and to the path difference L. If dk=dt is constant, L can be obtained by a Fourier transform of the time-dependent intensity signal recorded by the photodetector during tuning. If the object contains several reflecting or backscattering surfaces located at different depth positions, each individual path length difference 2Li gives rise to a corresponding frequency fi. A Fourier transform retains all of the corresponding distances and reflectivities, i.e., the backscattering potential distribution along the z axis. Hence, the Fourier transform of the time domain signal recorded during wavelength tuning retains the same information as an optical A- scan recorded by PCI.

The advantage of this technique compared to standard OCT techniques is again that a fixed reference arm length is used and no moving parts are needed. The use of a single photodetector has the advantage of simple elimination of the unwanted dc intensity terms by high-pass filtering of the photodetector signal. This enhances the usable dynamic range of the detection system considerably.

The drawback of WTI and WT-OCT, which restricted its use to only a few demonstrations [22–28], are the constraints of the available laser sources. The wavelength of the laser must be continuously tunable, without mode hops. The tuning range determines the depth resolution according to Eq. (15). The wider the tuning range, the better the resolution. Two different types of compact tunable laser diodes have been used up to now: external cavity laser diodes [22,24–26] and distributed Bragg reflector (DBR) laser diodes [23,27,28]. External cavity laser diodes have a wide tuning range of 10 nm and more. However, their slow tuning speed restricted the use of this large bandwidth to in vitro objects. DBR laser diodes can be tuned within milliseconds, but their tuning range is low and hence the resolution obtained is poor (on the order of 100 m). Moreover, their tuning rate is not constant, and they are not mode-hop-free. This situation can be improved, however, by using advanced solid-state laser technology. Recently, the first experiments with a Cr4þ:forsterite laser demonstrated scan repetition rates of 2 kHz, yielding WTI with a resolution of 15 m [29].

A first application of the use of a three-section DBR laser diode for measuring intraocular distances in vivo by WTI has recently been reported [28]. The problems of the nonlinear tuning rate and the mode hops were solved by using an auxiliary Michelson interferometer that provided a reference signal for numerically correcting the nonlinearities of dk=dt and for eliminating the signal distortion caused by the mode hops. Figure 5 shows a schematic diagram of the instrument. With a tuning range of 2 nm, a depth resolution of 150 m was obtained. Figure 6 shows the

Figure 7 WT-OCT image of a stack of microscopy cover glasses. The figure contains a sketch of the object as an insert. (Courtesy of J. G. Fujimoto, MIT. Reprinted from Ref. 24 by permission of the Optical Society of America.)

38 m was obtained. The first WT-OCT images of a scattering phantom were reported by Haberland et al. [27]. These authors used a DBR laser diode. They also claim that information on flow velocities can be obtained with this technique.

13.3DUAL-BEAM OCT

In dual-beam OCT the object is illuminated by both beams exiting from a Michelson interferometer (or another two-beam interferometer) [30]. In the optical scheme of Fig. 8 a superluminescent diode illuminates a Michelson interferometer. The interferometer splits the beam into two subcomponents, generates a path difference, and recombines the two subcomponents. The recombined beams leave the interferometer as a coaxial ‘‘dual beam.’’ A beamsplitter at the interferometer exit reflects the dual beam toward the object. A lateral scanning mirror directs the beam to transversely adjacent positions at the object (here the eye’s fundus). The reflected beams pass through the interferometer exit beamsplitter and are detected by the photodetector.

The basic principle of the dual-beam technique is to match the path difference generated by the interferometer to path differences between the light-remitting sites in the object. This makes the dual-beam technique insensitive to distance variations between object and interferometer. The optical scheme is explained in more detail with the help of Fig. 9.

The two subcomponents E 0 and E of the dual beam that leave the interferometer toward the object have a path difference corresponding to twice the interferometer arm length difference, 2z. A PCI depth scan is performed by shifting one of the interferometer mirrors, subsequently called the ‘‘measurement mirror’’ (MM). This mirror is moved, for example, by a stepper motor with a constant speed v, which

causes a Doppler shift fD ¼ 2v= of the light frequency of the corresponding beam. Each subcomponent is reflected at the object interfaces separating regions of different refractive indices. For example, the components EF0 and EF in Fig. 9 have been reflected at the fundus (F) of the eye, whereas the components EC0 and EC have been reflected at the anterior corneal surface (C). If z ¼ d, the components EF and EC0 overlap and generate a photodetector signal alternating at a frequency fD. The photodetector signal is then amplified and filtered by a bandpass filter that transmits only signals with fD. The envelope of the rectified signal (S in Fig. 9) is the final PCI signal and is recorded as a function of the interferometer’s arm-length difference z with a personal computer.

The dual-beam technique is somehow ambiguous. The same signal will appear at the photodetector at an interferometer path difference z ¼ d (indicated in Fig. 9). In fact, the autocorrelation of the object structure is obtained. This, however, does not create a severe problem. Either one of the object interfaces (in the case of the eye, for example, this is provided by the anterior corneal interface) generates a strong wave, leading to dominating autocorrelation terms, or a corresponding interface may be attached to the object.

The PCI scans or optical A-scans recorded in this way contain signal peaks characteristic of the object interfaces. From the positions of these peaks on the z axis the respective optical distances of the object structure can be determined (typically, as usual in OCT, within the so-called round-trip coherence length, lC=2 [12]). The geometrical distances are obtained by dividing the optical distances by the group index of the respective medium. The dual-beam PCI technique has found important medical applications itself, in particular in the ophthalmological field of intraocular distance measurement [31–35]. Its exceptional stability in an axial direction is rather helpful, in particular if the depth scans go over some millimeters. For example, it has recently been shown that the refractive outcome of cataract surgery can be improved substantially if PCI biometric data are used [36].

In dual-beam OCT, as usual, the image is synthesized from a series of laterally adjacent PCI depth scans [37]. These positions can be addressed by the lateral scanning mirror. The unique depth measurement stability of the dualbeam PCI technique may be used here too and lead to high precision OCT depth and thickness measurement techniques. Investigation of dual-beam OCT has only recently been started [38]. In a first step a simple lateral scanning unit was added to a PCI interferometer. As an example, Fig. 10 shows a horizontal foveal cross-sectional dual-beam tomogram of a patient with macular edema. The low transverse resolution is due to a detection aperture of less than 0.1 and caused by the laboratory-type instrument permitting reproducible transverse steps only on the order of 0:5 .

One drawback of the dual-beam OCT technique in ophthalmological fundus imaging is the poor signal-to-noise ratio due to the wave front mismatch of the two interfering beams reflected at the anterior corneal surface and the retina. If the probing beam is collimated, the light reflected at the retina will be collimated by the optical elements of the eye whereas the beam reflected at the cornea will be divergent. If the probing beam is focused at the cornea, the light reflected at the retina will be divergent. In either case, a concentric ring-shaped interference fringe system is formed. The diameter of the pinhole in front of the photodetector has to be small enough that only a single fringe is transmitted onto the detector

Figure 10 Horizontal foveal cross-sectional dual-beam tomogram of a diabetic retinopathy patient with macular edema [38]. Thickness values are optical; the geometrical values are obtained by dividing the optical distances by the group index ( 1:4). SLD with¼ 855 nm; ¼ 24:6 nm.

surface. This leads to a pinhole diameter in the 50 m range, resulting in a rather low light power at the detector surface and a correspondingly poor signal-to-noise ratio.

To overcome this drawback, a diffractive optical element (DOE) can be used [39]. A Fresnel zone lens can be implemented in front of the eye to focus part of the incident light beam on the vertex of the cornea and transmit part of the beam uninfluenced. The latter part is focused by the optics of the eye onto the retina. The beams reflected by the anterior corneal surface and the retina will thereby both be converted to parallel beams on their way back to the detection unit. A corresponding DOE has been designed to focus 40% of the intensity of the incident light beam on the vertex of the cornea and to let 60% pass through as a collimated beam. This led to an increase of about 20–25 dB in the signal-to-noise ratio for in vivo measurements [40].

We used the dual-beam OCT technique to demonstrate the depth resolution obtainable in retinal tomograms of a human eye in vivo. The closest distance of two layers that can be resolved is usually lC=2, which is inversely proportional to the source bandwidth . Therefore an increased bandwidth improves the resolu-

trally displaced SLDs (at 830 and 855 nm) was used. The two combined light sources had an effective spectral width of ¼ 50 nm; the corresponding coherence length is lC 15 m in air.

However, if measurements are performed through dispersive media, caution has to be taken. Because the measurement beam travels, for example, through the dispersive eye media whereas the reference beam travels through air, the coherence envelope of the optical A-scans broadens and resolution decreases. If the length of a dispersive medium in one of the interferometer arms is L and the group dispersion of