An optical coherence tomography system is described which can image up to video rate. The system utilizes a high power broadband source and real time image acquisition hardware and features a high speed scanning delay line in the reference arm based on Fourier-transform pulse shaping technology. The theory of low coherence interferometry with a dispersive delay line, and the operation of the delay line are detailed and the design equations of the system are presented. Real time imaging is demonstrated in vivo in tissues relevant to early human disease diagnosis (skin, eye) and in an important model in developmental biology (Xenopus laevis).
© 1998 Optical Society of America
Optical coherence tomography (OCT) is a noninvasive imaging technique which provides microscopic tomographic sectioning of biological samples [1, 2]. OCT fills a valuable niche in imaging of tissue ultrastructure, providing subsurface imaging with high spatial resolution (~10 μm) in three dimensions and high sensitivity (>110 dB) in vivo with no contact needed between the probe and the tissue. An OCT image (B-scan) is built up as a series of adjacent axial depth scans (A-scans). Depth is gated by low coherence interferometry where the sample is placed in one arm of a Michelson interferometer (sample arm), and a scanning optical delay line is located in the other arm (reference arm). With single-mode fiber optic implementation, OCT can be adapted to minimally invasive diagnostic imaging technologies such as endoscopy and laparoscopy [3, 4]. In this application OCT may provide the physician with near-histological resolution imaging of sub-surface tissue morphology, potentially aiding in biopsy site selection or even approaching the goal of “optical biopsy.” In order to be appealing for in situ diagnostics, however, OCT must provide the clinician with near real-time imaging.
Several technical challenges must be overcome in order to image at high speed with OCT. First, a high power optical source is required to provide adequate illumination in a short amount of time. Second, a high speed scanning delay line is required in the reference arm of the interferometer in order to produce image data quickly. Finally, image data must be acquired, processed, and displayed in real time.
In OCT as in any optical heterodyne detector, the detected signal to noise ratio (SNR) in the shot noise limit is proportional to the optical power illuminating the sample and inversely proportional to the detection bandwidth :
where Ps is the power incident on the sample, Rs is the power reflectivity of the sample, e is the electronic charge, B is the detection bandwidth, and ρ is the detector responsivity given by ρ = ηλ0 e/hc. Here η is the detector quantum efficiency, λ0 is the optical source center wavelength, h is Planck’s constant, and c is the free space speed of light. In OCT, the detected signal bandwidth Δf is proportional to the image acquisition rate . Therefore, an increase in image acquisition rate will increase the signal bandwidth. In order to maintain SNR while detecting the entire signal bandwidth, any increase in image acquisition rate must be accompanied by a proportional increase in source optical power.
A high speed scanning optical delay line in the reference arm of the OCT system is needed in order to acquire images rapidly. A-scans must be collected at a rate equal to the frame rate (images per second) times the number of A-scans per frame. For example, in order to acquire 4 images per second with 250 lines (A-scans) per image, the delay line must scan at 1000 scans per second. In order to image at video rate (30 frames per second) with 100 lines per frame, 3000 scans per second is required. The scan must be long enough to provide a useful imaging depth in biological tissue. A 3mm (free space) scan, typically used in OCT systems utilizing 1300 nm center wavelength illumination, corresponds to a delay of approximately 10 psec. The most common implementation of the reference arm delay line in current OCT systems is a galvanometer-based translating retroreflector system [2, 5]. This type of delay line can scan at a maximum of approximately 100 scans per second. Clearly, a faster method is required. Faster delay lines have recently been implemented in OCT. A rotating cube [7, 8] has achieved up to 384 scans per second, but the duty cycle was very low (wasting source power) and the scan was nonlinear with time. Any nonlinearity in the scan results in a varying signal center frequency and bandwidth and also warping of the image unless processing is done to compensate for this effect. Piezoelectric-actuated fiber stretchers [9, 10] have been demonstrated which can scan up to 600 Hz, but this technique suffers from static and dynamic birefringence effects that require extra components to compensate, and is not temperature stable. A delay line based on a high speed resonant scanning mirror  has achieved 3 mm scan lengths at 1200 Hz, and may be capable of higher repetition rates. Other rapid scanning delay lines have been developed for application in autocorrelation measurements of ultrashort laser pulses. These include rotating mirrors , rotating roof prisms [13, 14], and loudspeakers . These techniques, relying on translating or rotating masses, have not achieved the scan rates necessary for real time OCT, and some suffer from low duty cycle. Some techniques scan the delay in discrete steps [16, 17]. In order to take advantage of optical heterodyne detection in an OCT system with such a delay line, however, additional Doppler shifting or phase modulating components would be required. The delay line we have implemented was developed for femtosecond pulse measurement [18, 19], and has recently been applied to OCT [3, 20]. This delay line achieves scans of several millimeters at repetition rates of several kilohertz, and also allows separation of group and phase delay which provides an additional degree of control over the center frequency and bandwidth of the OCT signal.
2.1 Low-Coherence Interferometry with a Dispersive Delay Line
The basic measurement performed in OCT imaging is an interferometric cross-correlation, R̃is (Δl), of light returning from the reference and sample arms as a function of the optical pathlength difference Δl between the arms [2, 21]. The interferometric part of the photodetector current, ĩd(Δl), is proportional to the interferometric cross-correlation as:
The interferometric cross-correlation can be expressed as the product of the cross-correlation function Ris, which is defined as the complex envelope of the interferometric cross-correlation, and a complex exponential carrier:
Here Δlg and Δl ϕ are the group and phase delays, respectively, expressed as pathlength differences, and k 0 is the center wavenumber of the optical source. Note that the cross-correlation function, Ris(Δlg), is a function of group delay, while the carrier is a function of phase delay . If dispersion in the sample and reference arms are not matched, then it is necessary to distinguish between group and phase pathlength difference. This is the case, for example, if the group delay and the phase delay effected by the delay line are not equal. The cross-correlation function can be expressed as the convolution of the autocorrelation function of the optical source, Rii (Δlg) and the amplitude backscatter profile of the sample, rs(Δlg), which can be thought of as a train of impulses with various amplitudes representing discrete reflection or scattering locations in the sample :
An OCT system with a perfect mirror in the sample arm measures the interferometric autocorrelation of the source, R̃ii, which can be expressed similarly to equation (3):
When the pathlength difference is scanned by a scanning delay line in the reference arm, the photodetector response is a time domain signal related to the interferometric autocorrelation by the scan velocity of the delay. The carrier of the detector response signal is related to the carrier of the autocorrelation by the phase delay scan speed, and hence the center frequency f 0 can be written in terms of the center of the optical source spectrum:
Here, V ϕ is the scan speed of the phase delay, defined as the time derivative of the phase delay: V ϕ = dΔl ϕ(t)/dt, and ν 0 and λ0 are the center frequency and the center wavelength, respectively of the optical source. The carrier frequency corresponds to the Doppler shift frequency of the center wavelength component of the reference arm light, and equivalently to the beat frequency of the optical heterodyne detector response. The frequency components of the detector response signal, expressed as offset from the carrier frequency f′ = (f-f 0), are related to the complex envelope of the autocorrelation by the scan speed of the group delay. They can thus be written in terms of the offset frequency ν′ = (ν-ν 0), or wavelength components of the optical source:
Differentiating equation (7) gives the expressions for the bandwidth of the detector response in terms of the optical source frequency bandwidth Δν, or wavelength bandwidth Δλ:
The group delay scan speed is defined as the time derivative of the group delay: Vg = dΔlg (t)/dt. In the case of a simple scanning retroreflecting mirror, V ϕ = Vg = 2s, where s is the velocity of the mirror. When V ϕ = Vg, the familiar expression Δf/f = Δλ/λ holds true. Note also that if the scan is linear, then V ϕ and Vg will be constants, while in the case of a nonlinear scanning delay line, V ϕ and Vg are time-varying functions.
The autocorrelation function corresponds to the point spread function of the OCT system in the axial direction (assuming low numerical aperture optics in the sample arm) . In designing a practical OCT system, therefore, the full information bandwidth of the signal must be detected in order to maximize spatial resolution. It is desirable, however, to reject frequencies outside of the information bandwidth in order to maximize system SNR. Assuming a Gaussian optical source spectrum (and therefore a Gaussian autocorrelation function), the ideal detector bandwidth corresponds to approximately two times the signal bandwidth . From equations (1) and (8), the signal to noise ratio of OCT in the shot noise limit, using the ideal detection bandwidth becomes:
Thus, it can be seen that if the bandwidth of the interferometric signal is increased by rapidly scanning the group delay, the source power must be proportionately increased in order to maintain SNR. Table 1 illustrates the tradeoff between the OCT image frame rate and the theoretical SNR in the shot noise limit.
2.2 Fourier-domain Rapid Scanning Optical Delay Line
The high speed scanning delay line consists of a grating-lens pair in a folded, double-passed Fourier-domain pulse shaping configuration (Fig. 1). A flat mirror serves as a spatial phase filter which imposes a linear phase ramp in the frequency domain. The delay line is based on the well known property of the Fourier transform that a phase ramp in the frequency domain corresponds to a group delay in the time domain:
The angle of the incident light on the grating was selected such that the center wavelength λ0 of the diffracted beam was normal to the grating and the entire grating was in the focal plane of the lens. This was done in order to prevent introduction of group velocity dispersion (GVD) which varies through the course of the scan. If the grating is at an angle not normal to the optical axis of the lens, then as light is laterally displaced on the grating by the scanning mirror, it is also displaced from the focal plane of the lens, introducing GVD [20, 23].
The mirror pivot can be offset from the center wavelength by an arbitrary distance x by a simple translation of the scanning mirror. The phase shift ϕ(λ) as a function of wavelength λ for a given mirror tilt angle σ may be written as (see Figure 1):
where lf is the focal length of the lens and p is the pitch of the grating. This function was derived using the grating equation and assuming that the small-angle approximation sinθ≅θ holds for diffraction angles between different wavelengths off of the grating and for small deflection angles effected by the scanning mirror . The distance Δy that a wavelength component λ traverses as a function of scanning mirror tilt angle σ is calculated (taking into account the fact that the beam traverses the path Δy four times) and multiplied by 2π/λ to convert from displacement to phase shift. This phase shift can also be written as a function of angular optical frequency ω:
where ω0 is the center angular optical frequency. From Eq. (12) and the definition of phase delay, t ϕ = ϕ(ω0)/ω0, the phase delay is given by:
This corresponds to the free space phase pathlength difference Δl ϕ, (referenced from a zero scan angle):
From the definition of group delay, tg = ∂ϕ(ω)/∂ω∣ω=ω0 the group delay is given by:
which corresponds to the free space group pathlength difference Δlg:
This expression for group pathlength difference can alternatively be derived by evaluating the change in path length experienced by the center wavelength as a result of an arbitrary mirror tilt angle. It can be seen that the group pathlength difference is equal to the phase pathlength difference plus an additional term which is a function of the properties of the lens, grating, and light source. Both the phase pathlength difference and the group pathlength difference are proportional to the tilt angle of the scanning mirror, so an angular scan of the mirror effects a scan of both phase and group pathlength difference. The second term in the expression for group pathlength difference is dominant in our configuration, thus the group pathlength difference is much larger than the phase pathlength difference for a given angle σ. This feature is key to the value of this delay line. The mirror need only be moved a very small amount to generate a large scan of the group pathlength difference. It is also possible to adjust the offset x for a desired center frequency without significantly affecting the scan length of the group pathlength difference.
The design equations for the high speed OCT system using this delay line are equations (16), (17), and (18). Equation (16) is used to specify the grating pitch, the lens focal length, and the maximum angular excursion of the scanning mirror for a given source center wavelength and desired group delay scan. Equations (17) and (18) are used to calculate the center frequency and bandwidth, respectively, of the OCT signal for a given mirror offset x, and mirror scan rate ∂σ(t)/∂t (note that for a linear scan, the scan rate is constant).
A block diagram of the experimental system is shown in Figure 2. The system utilized a high-power broadband source (AFC Technologies, BBS 1310 B-TS) centered around 1310 nm with 49 nm FWHM spectral width which provided 13 mW of optical power. The delay line was implemented with a low-cost resonant scanner with a 4 kHz resonant frequency. The maximum angular excursion of the resonant scanning mirror was set to effect a usable group delay scan of approximately 3 mm. This corresponds to a group delay scan rate of approximately 40 m/s. Frame rate was varied by dividing the 4000 A-scans per second into different sized images, i.e. 250 A-scans per frame at 16 frames per second, and 125 A-scans per frame at 32 frames per second (video rate). The grating was 2.5×2.5 cm with 600 lines/mm (p=1.67 μm) and the lens was an achromat with lf=50 mm.
The reference delay line was double-passed, as shown in Figure 1, in order to double the effective delay and in order to recouple the returning light into the fiber without any delay-dependent loss. This is important because as the delay line is scanned, the exit beam is displaced laterally from the incident beam. A 0.5 O.D. neutral density filter was placed in the path of the reference arm in order to reduce excess source intensity noise in the detected signal [24, 25].
The resonant scanning mirror tilts as a sinusoidal function of time, σ(t) = b sin(2πfm t), where b is the maximum excursion of the tilt angle, and fm is the resonant frequency of the scanning mirror thus, from Eq.(17) the center frequency becomes:
From Eq. (18) the interferogram bandwidth becomes:
This sinusoidal variation of center frequency and bandwidth with time is the major disadvantage of using a resonant scanner in the delay line. The advantage is that resonant scanners can operate at much higher frequencies than galvanometer-mounted scanners. In this experiment, the interferometric signal was recorded only during the middle two thirds of the forward scan , therefore the overall duty cycle was 33%. Recording both the forward and reverse scans would increase the duty cycle to 67%. A linear scanner can achieve a duty cycle of nearly 100% (at the expense of scan speed). Use of a resonant scanner required the detection bandwidth to be increased by a factor of approximately 2.7 compared to an equivalent linear scanner in order to accommodate the varying center frequency. This corresponds to a degradation in SNR of 4.3 dB. This comparison is only hypothetical, however, because to our knowledge there are currently no equivalent linear scanners available which can operate at 4000 scans per second. A polygonal scanning mirror may effect linear angular scans at a very high rate, but it will also cause a nonlinear pathlength variation, and the scan length can not be varied. Delay lines may be built with acousto-optic or electro-optic scanning devices to achieve linear delay scans at very high repetition rates. The signal was detected using a high speed photodiode detector module, bandpass filtered, and demodulated with an envelope detecting logarithmic amplifier. Digitization and display was accomplished in real time with a variable scan monochrome frame grabber with an 8 bit A/D converter, and computer. The logarithmic amplifier compresses the dynamic range of the signal such that 8 bits of A/D conversion resolution is adequate to maintain image quality. Lateral scanning was accomplished with an X-Y galvanometric scanning unit, providing for arbitrary sample sectioning and volume scanning. The images were recorded directly to SVHS video tape.
Figures 3, 4, and 5 demonstrate real time OCT imaging of living samples with the experimental high speed system. At a scan rate of about 40 m/s, the system achieved a signal to noise ratio of approximately 90 dB with a detection bandwidth of 2.6 MHz, estimated using calibrated neutral-density filters. Figure 3 is a recording of the beating heart of a Xenopus laevis embryo , recorded consecutively at 8, 16, and 32 frames per second (fps), demonstrating the trade off between image acquisition rate and transverse resolution (number of A-scans per image) for a fixed A-scan rate. Xenopus is an important developmental biology model which has previously been studied using lower speed OCT [27–29]. Notice that although the sample was moving rapidly, no motion artifacts are evident in the images. Figure 4 is a recording of in vivo human thick skin (fingertip) recorded at 16 fps. Sweat ducts are visible in the stratum corneum at different depths as the image plane moves in the sample. Such structures, only partly located in a single image plane, may be overlooked or misinterpreted in single, still images, but can be easily visualized in real-time dynamic imaging. Figure 5 is a recording (16 fps) of the anterior segment of a murine eye . The animal was live, unanesthetized, and held by hand. The imaging is free of motion artifact and allowed clear visualization and measurement of the anatomy.
In conclusion, we have implemented an OCT system capable of imaging at up to video rate. This system features a high-speed Fourier-domain variable-phase optical delay line and utilizes a commercially available optical power source and image acquisition hardware. We have briefly described the essential theory of low-coherence cross-correlation interferometry with a dispersive delay line, and of the Fourier-domain rapid scanning optical delay line. We have demonstrated in vivo imaging at various frame rates up to video rate. Real time imaging has allowed visualization of dynamic events without motion artifacts as well as visualization of features and structures in physiological samples which may be overlooked or misinterpreted in still images.
The authors would like to acknowledge the contributions of T. G. van Leeuwen and S. Chakravarti. This work was partially supported by the National Science Foundation (BES-9624617). M. D. Kulkarni received support from the Whitaker Foundation, S. Yazdanfar received support from a National Institutes of Health Training Grant, and R. Ung-arunyawee received support from the Government of Thailand.
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