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Simultaneous intensity, birefringence, and flow measurements with high-speed fiber-based optical coherence tomography Mark C. Pierce, B. Hyle Park, Barry Cense, and Johannes F. de Boer Wellman Laboratories of Photomedicine, Harvard Medical School, Massachusetts General Hospital, Boston, Massachusetts 02114 Received February 25, 2002 We demonstrate that tissue structure, birefringence, and blood f low can be imaged simultaneously by use of techniques of polarization-sensitive optical coherence tomography and phase-resolved optical Doppler tomography. An efficient data-acquisition procedure is implemented that optimizes the concurrent processing and display of all three image types. Images of in vivo human skin acquired with a high-speed fiber-based system are presented. © 2002 Optical Society of America OCIS codes: 170.0170, 170.4500, 170.1870, 110.7050, 260.1440, 280.2490.
Optical coherence tomography (OCT) has become established as a noninvasive technique that is capable of imaging tissue microstructure.1,2 Based on lowcoherence interferometry, OCT produces cross-sectional images of tissue by determining the amplitude of interference fringes formed on ref lection of light from sample and reference arms of a two-beam interferometer. Combining OCT with polarization-sensitive OCT (PS-OCT) and optical Doppler tomography enhances structural and functional imaging in tissue, providing additional information that is not revealed by conventional OCT ref lectivity images alone. PS-OCT probes the sample with polarized incident light and employs polarization-sensitive detection of interference fringes, enabling tissue birefringence and optic axis orientation to be determined by use of the Stokes parameter3 or Mueller matrix4 formalisms. Early free-space PS-OCT systems were based on bulk components,5 but more recently fiber-based systems were developed6,7 that offer ease of handling and alignment for clinical applications. Optical Doppler tomography permits localized imaging of f luid f low in biological systems.8 – 12 In a recently developed technique, regions of f low are identified by calculation of the change in phase at each pixel between successive A lines.10 With this phase-resolved technique, high-velocity sensitivity can be maintained without compromising spatial resolution. We describe here a f iber-based OCT system that, for the f irst time to our knowledge, provides simultaneous imaging of tissue structure, birefringence, and f low. Instead of using four polarization states of light as described by Saxer et al.,6 we use only two states, one for forward and one for reverse depth scans. This arrangement permits comparison of the phase between points in successive forward (or reverse) axial scans with incident light in the same polarization state for f low imaging. Birefringence and optic axis orientation are determined by use of data from successive axial scans, in this case A lines with incident light in different polarization states.6,13 The fiber-based system is shown in Fig. 1. A low-coherence source (AFC BBS1310) with a center wavelength of 1310 nm, a FWHM bandwidth of 70 nm, and total output power of 9 mW was linearly polarized such that equal-magnitude wave components were 0146-9592/02/171534-03$15.00/0
aligned parallel and perpendicular to the optic axis of an electro-optic polarization modulator. Light was coupled through standard single-mode fiber to a polarization-independent optical circulator14,15 and then divided by a fiber optic splitter in a 90:10 ratio into sample and reference arms. 2.5 mW of source light was incident onto the sample surface in a focused spot of 30-mm diameter. A grating-based rapid scanning optical delay line (RSOD) was used with the source spectrum offset on the scanning mirror to provide both group and phase delay scanning,16 generating a carrier frequency at 800 kHz. The two-step voltage function used to drive the polarization modulator was synchronized with the 1-kHz triangular scanning waveform of the RSOD, such that the polarization states that are incident upon the sample during inward and outward A-line scans were orthogonal in the Poincaré sphere representation.6 A polarizing cube was inserted into the reference arm to ensure that light in the RSOD was always in the same linear state, regardless of the polarization state at the sample. Static polarization controllers in the detection and reference arms were aligned for equal distribution of reference arm light over both horizontal and vertical detection channels for both input polarization states. Electronic signals from each detector were amplif ied, f iltered, and digitized with a 12-bit 5-Msample兾s analog-to-digital board (National Instruments NI 6110). We obtained sine and cosine components of the interference fringe signals at each detector over sections Dz in each A line by multiplying the measured signal f 共z兲 by a
Fig. 1. Schematic diagram of the fiber-based OCT system: Pol, polarizer; PCs, passive polarization controllers; P. Mod, electro-optic polarization modulator; OC, optical circulator; FPB, all-f iber polarizing beam splitter; HP, scanning handpiece; PD, fiber-pigtailed photodiodes. © 2002 Optical Society of America
September 1, 2002 / Vol. 27, No. 17 / OPTICS LETTERS
sine and a cosine term at carrier frequency v0 and averaging over a few cycles of the oscillation that correspond to the coherence length of the source. One can conveniently extract both cosine and sine terms by determining the real and imaginary parts of the single function f 共z兲exp共2iv0 z兲 and averaging them over Dz. Using the convolution theorem, we can express our function of interest in the following manner: ∑Z ∏ √ f 共z兲exp共2iv0 z兲 苷 F f 共v 2 q兲d共q 2 v0 兲dq √
苷 F 关 f 共v 2 v0 兲兴 ,
(1)
√ where we have also used f 共z兲g共z兲 苷 F 兵F 关 f 共z兲g共z兲其 苷 √ F 关 f 共v兲 ≠ g共v兲兴, where F 关exp共2iv0 z兲兴 苷 d共q 2 v0 兲 and √ F and F represent forward and reverse Fourier transformations, respectively. Equation (1) demonstrates that one can obtain the sine and cosine components of interest by taking the inverse Fourier transform of the shifted Fourier spectrum f 共v 2 v0 兲 of the original intereference fringe signal, f 共z兲. We implement this formulation here by first performing a fast Fourier transform on interference fringe data f 共z兲 in each A line (2048 points), generating the (complex) components of the power spectrum, f 共v兲. This Fourier spectrum was then frequency shifted such that the center frequency was brought to the start of the complex data set. Those components at frequencies outside the bandwidth of interest were removed, which resulted in an averaging of the signal over Dz after the reverse transform. This procedure reduces the size of the original data set by a factor of 4 to only those 256 complex Fourier components within the signal band, at the same time enabling spectral f iltering and dispersion compensation to be implemented in the Fourier domain.17,18 When a reverse fast Fourier transform is performed on this frequency-shifted and reduced data set the cosine and sine components of each A line are then given as described, by the real and imaginary parts of the reverse transform. The Stokes parameters, I , Q, U , and V , are then determined as described previously,3,6 from the calculated sine and cosine components. Structural OCT images are formed by display of values of the Stokes parameter I 共z兲 mapped onto a logarithmic gray-scale range for all A lines in an image. Birefringent regions in tissue are imaged by mapping of the accumulated phase retardation from the sample surface. Stokes parameters are calculated for light in each of the two input polarization states; vectors of length I are def ined with components Q, U , and V at all points in each A line. The tissue optic axis and accumulated phase retardation are found as described earlier.6,13 Phase-resolved imaging of blood f low is achieved by comparison of the phase at each point in A line i with the phase at the same point in A line i 1 2, which therefore compares consecutive A lines with incident light in the same polarization state. f共z兲 describes the phase in an A line at position z and is calculated not by the Hilbert transform but by use of the same sine and cosine components of the intereference fringe signals obtained previously:
fH , V 共z兲 苷 arctan
∑
∏ sinH , V 共z兲 . cosH , V 共z兲
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(2)
Subscripts H and V indicate horizontal and vertical polarization channels, respectively. The phase difference between points in successive A lines, Df共z兲, is used for calculating the Doppler frequency shift v that is due to scattering of light from moving particles and is given by v 苷 Df共z兲兾T , where T is the time interval between consecutive A line scans with light in the same polarization state (1 ms). To improve the signal-to-noise ratio we averaged values of Df共z兲 over eight consecutive A lines. Knowledge of the imaging geometry then enabled the bidirectional f low velocity to be determined. We calculated a value of 24 mm兾s for the minimum detectable f low velocity, based on T 苷 1 ms and on an intensity-weighted average phase standard deviation in the absence of f low of 0.24 rad, after the phase-noise reduction algorithm described here. The spatial resolution of f low data was 10 mm in depth by 30 mm lateral diameter. This velocity sensitivity is equivalent to the value of 10 mm兾s at 400 Hz reported in Ref. 10, indicating no increase in the phase-noise f loor in this system where polarization information is additionally obtained. We also used DfH , V 共z兲 to calculate the phase variance Var共z兲, def ined as Var共z兲 苷 DfH 2 共z兲 1 DfV 2 共z兲. Displaying these values in a variance map provides a semiquantitative measure of f low in a sample, with higher contrast than that provided by mapping of only the Doppler shift.11 Imaging regions of f low with this phase-resolved technique relies on consistently sampling data at the same points within each A line to ensure that measured phase shifts are due purely to the presence of f low. To reduce system complexity, cost, and insertion loss associated with use of a phase modulator, we achieved carrier generation by offsetting the source spectrum on the scanning mirror in a RSOD, which resulted in greater phase instability than operation with the spectrum centered on the RSOD18; however, we successfully countered this reduction in phase stability by using a correction algorithm in our software. The corrected phase difference between A lines i and i 1 2 is given by Dfi 0 共z兲 苷 Dfi 共z兲 1 a 1 bz, where parameters a and b are determined for each A-line pair by an intensity-weighted linear least-squares fit to the originally calculated phase difference, Dfi 共z兲. It should be noted that contributions from a dominate those from b and that the method relies on a minimization of the phase difference between A lines and may underestimate the magnitude of f low in particularly large vessels. Phase-variance images taken at the inside surface of a human finger, with and without these corrections, are presented in Fig. 2. Values of phase variance ranging from 0 to 2.5 rad2 are mapped onto the gray-scale range. In the left (uncorrected) image, a blood vessel is identif ied as the large structure at a depth of approximately 1 mm, but, with the phase differences between A lines appearing as vertical white lines, it is difficult to resolve finer detail. The intensity-weighted average phase variance over the
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Fig. 2. Phase-resolved f low image from the inside surface of a human finger, demonstrating the effect of correction in data processing for phase instability. The image is 1.2 mm 3 1.2 mm, uncorrected on the left, corrected on the right. For details of these corrections, see text.
mapping of two small vessels circled at the left side of the image. In conclusion, we have demonstrated that, by efficient extraction of fringe amplitude and phase, the individual features of OCT, PS-OCT, and optical Doppler tomography images can be combined to provide simultaneous imaging of structure, birefringence, and f low in skin. Each image is generated without penalty to the signal-to-noise ratio and without degradation in the accompanying image types. Our demonstration of near-real-time simultaneous imaging with a fiber-based system renders the technique suitable for clinical use. Applications for which all three image types are of interest include determination of burn depth13; the techniques described here may also be applied to OCT systems for imaging tissues other than skin. Research grants from the Whitaker Foundation (26083), the National Eye Institute (1R24 EY12877), and Department of Defense (F4 962001-1-0014) are gratefully acknowledged. The firstand last-named authors’ e-mail addresses are
[email protected] and
[email protected]. harvard.edu.
Fig. 3. Single frame from a movie sequence demonstrating simultaneous in vivo imaging of structure, birefringence, and f low at the inner surface of a human lip. Upper left, structural image; upper right, phase map; lower left, phase variance; lower right, Doppler shift. Each image is 2.5 mm 3 1.2 mm, with all data acquired in 1 s.
image is 0.64 rad2 . In the right (corrected) image the same large vessel is again apparent, but now two smaller capillaries can also be identified at lesser depths. Removing contributions to phase variance that are caused by scanning instability reduces the intensity-weighted average phase variance over the image, in this case to a value of 0.058 rad2 , representing a lowering of the noise f loor to less than 3% of the image dynamic range. Figure 3 presents images taken at the inner surface of the lip of a human volunteer, with the tissue surface visible at the top of each frame in light contact with the window of our handpiece. The uppermost layer in the structural image is the squamus epithelium, ranging from 200 to 400 mm in thickness. The lamina propria appears below as a darker and more uneven layer, 100 200 mm thick, with submucosal tissue extending to the lower boundary of the image. The transition from black to white in the phase map indicates the presence of birefringent tissue, approximately following the epithelium– lamina propria boundary. Blood vessels ranging in diameter from 25 to 100 mm are evident in the Doppler shift and phase-variance maps, located in the lower two structural layers at depths of 400 600 mm. Blood f low is imaged with high contrast in the phase-variance map; the Doppler map indicates the directionality of f low as positive Doppler shifts are mapped toward white and negative shifts toward black, as illustrated by the opposite gray-scale
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