The Doppler effect was discovered by the Austrian physicist Christian Johann Doppler in the mid 1800s [1
]. For many years, various Doppler imaging techniques have been developed in the field of ultrasound imaging [3
]. Analogous to ultrasonography, optical coherence tomography (OCT) is a non-invasive imaging technology that is capable of depth sectioning of biological tissue, yet at the micrometer scale resolution [4
]. Traditionally, OCT imaging contrast relies on the variation of the strength of back-reflected light from a sample that arises from refractive index fluctuation inside a biological sample. In addition to structural mapping, many functional OCT systems have been actively developed in order to gain additional information that will lead to a better understanding of sample properties. Among the many functional OCT systems, Doppler OCT (DOCT) is one of the most useful. It is capable of in vivo
monitoring of flow activity in biological samples such as blood flow in the human retina [5
], and the cardiovascular system of animal embryos [7
]. DOCT provides information about flow location, velocity, direction, and profile that cannot be obtained by intensity mapping alone.
Recent development in DOCT is mostly based on phase sensitive detection so-called phase-resolved DOCT [9
]. The early development of phase-resolved DOCT was based on phase sensitive time domain OCT (TD-OCT) that required mechanical scanning of the reference arm and hence limited the maximum acquisition speed to a few kHz regime [10
]. Later, the phase-resolved Doppler technique was also extended to frequency domain OCT (FD-OCT), which not only has speed and sensitivity advantages over TD-OCT but also allows direct access to the phase information immediately following the Fourier transform [11
]. A spectrometer based frequency domain Doppler OCT (FD-DOCT) utilizing a continuous readout CCD camera and achieving an acquisition speed of 29.3 kHz line rate was reported [12
]. Moreover the further increase of imaging speed and the maximum detectable velocity in spectrometer based FD-DOCT, using a high-speed CMOS camera as a detector, was also investigated [5
]. However, the increase in maximum detectable velocity accommodated from high-speed acquisition comes with the cost of an increase in the minimum detectable velocity since both of them depend on the acquisition rate. With a camera line rate of 200 kHz, the minimum detectable axial velocities as measured with and without lateral scanning were 800 μm/s and 8.2 mm/s, respectively. Nevertheless, the high speed imaging capability of FD-DOCT is attractive for real time in vivo
monitoring of flow activity in biological samples as well as for flow segmentation in 3D that provides accurate information of flow angle [7
One of the main challenges in conventional FD-OCT is the obscured object structure known as a mirror image or ghost image that arises from the Fourier transformation of a real function. Since the demand of high axial-resolution requires the employment of an extremely broadband light source, achieving high axial-resolution at high acquisition speed requires sacrificing spectral resolution that eventually leads to a reduction in the imaging depth range [13
]. Therefore, the removal of the mirror image in high resolution FD-OCT is desirable to double the imaging depth range. In addition, it is evident that the performances of phase-resolved DOCT, such as Doppler phase stability and accuracy, highly rely on the signal-to-noise ratio (SNR) of the system [5
]. Therefore, the ability to employ a maximum SNR out of a given phase-resolved DOCT system is desirable. Unlike conventional FD-OCT, full-range FD-OCT allows the use of the region around the zero-delay position, which is the most sensitive region in FD-OCT. Therefore, the combination of Doppler detection and full-range OCT has the promise of improving both structural and Doppler images.
Most full-range FD-OCT techniques reported to date share the basic principle of reconstructing a complex spectral interference signal from measurable real signals. The complex spectral interference can be expressed as
, where k
= 2π/λ is the wave number, and A
) and Ψ(k
) are real functions representing the magnitude and phase of the complex spectral interference
, respectively. The early attempts of full-range FD-OCT were based on sequential phase shifting methods, where multiple spectra with a certain phase relation were sequentially acquired and used to reconstruct the complex signal directly, such as the five-step [15
], three-step [16
], and two-step [17
] phase shifting methods. The first two techniques directly determined the phase term Ψ(k
) of the spectral interference signal from a set of 3 to 5 acquired spectral interference signals. On the other hand, the third method measured the real and imaginary components of the complex spectral interference, (i.e.
). In all cases, the sequential acquisition of multiple spectra for each axial line lead to a reduction in the frame acquisition speed. Furthermore, the approach is vulnerable to sample movement that occurs during the acquisition of those axial scans used to construct the complex signal. To overcome this limitation, several simultaneous detection schemes, such as the 3x3 coupler [19
], polarization-based demodulation [21
], and dual-detection [22
] techniques were proposed. A different approach for retrieving the complex interference signal was based on Hilbert-transform methods such as the carrier frequency modulation [23
] and BM-scan [24
] methods. The Hilbert-transform based methods require no extra acquisition to reconstruct each frame of the full-range image and hence maintain the full acquisition speed of the FD-OCT. Moreover, the acquisition of BM-scan method was further improved by simply offsetting the sampling beam spot away from the pivot point of the scanning mirror to introduce the modulation frequency without additional hardware modification [26
]. The proposed modulation technique simplifies the acquisition of BM-scan method. Nevertheless in order to obtain depth profiles, the methods require extra processing steps such as forward and backward Fourier transformations as well as band-pass filtering to reconstruct complex spectral interference signals prior to normal Fourier transformation [24
The combination of full-range FD-OCT and phase-resolved Doppler imaging is challenging because in most cases, both full-range and Doppler capabilities rely on the phase relation between consecutive axial lines. A Hilbert-transform based full-range DOCT using the BM-scan method was demonstrated for imaging of the deep posterior of a human eye [29
]. The technique introduced phase modulation during lateral scanning to produce a frequency shift after Fourier transform and then applied band-pass filtering to remove negative frequency components. However, certain amounts of axial movement cause additional frequency shifts in the transformed domain and could lead to unintentional signal loss after band-pass filtering. Therefore, the presence of high axial motion of the sample could affect mirror suppression performance and lead to a reduction in the detectable velocity range of Doppler imaging as compared to what can be achieved by the same system operated in conventional FD-OCT. Recently, a modified BM-scan method based on a parabolic phase modulation technique was proposed to minimize the effect of sample motion and improve the velocity dynamic range [30
]. However, an increase in Doppler phase noise was observed.
A different approach to full-range DOCT was based on a time-frequency analysis technique built on a spectrometer-based FD-OCT system called joint spectral and time domain OCT [31
]. Contrary to phase sensitive detection, the Doppler phase shift information was determined from the amplitudes of Fourier transformations. The Doppler image determined by the proposed technique was demonstrated to be less sensitive with respect to SNR and more accurate at close to maximum detectable velocity limit than that determined by phase-resolved techniques. Nevertheless, the full range signal was achieved by introducing change in the optical path length in the reference arm at a constant speed that caused a reduction in the detectable velocity dynamic range of the Doppler signal by half when operating in the full-range mode [32
]. Moreover, the method employed a large number of axial scans, for example 16-40 A-scans, and involved 2D Fourier transformation to determine a single line of velocity map that lead to an increase in both acquisition and processing time compare to phase resolved FD-DOCT.
Simultaneous phase shifting is promising for Doppler imaging, nevertheless no experimental confirmation has been reported to date. We recently reported a technique of mirror image removal called Dual-Detection FD-OCT, in which the quadrature components of a complex spectral interference were simultaneously detected [22
]. Therefore, the full range signal was obtained without a loss in acquisition speed compared with the conventional FD-OCT. In addition, since the complex interference signal was constructed from two interference signals with a stable π/2 phase difference simultaneously detected by two independent detectors, any changes in optical path difference during acquisition equally affected the phase change in both detected signals without affecting the π/2 phase relation between them. Therefore, the mirror suppression performance of DD-FD-OCT was insensitive to sample motion, including large sample movements. One of the advantages of DD-FD-OCT to Doppler imaging is that the full-range signal is achieved without manipulation of the phase relation between consecutive axial lines. Therefore, the phase information of the full-range signal is almost identical to that acquired by the conventional FD-OCT method. Hence the full-range DD-FD-OCT is fully applicable to phase-resolved Doppler detection without reduction in detectable velocity dynamic range. In addition, phase-resolved DOCT can utilize the maximum SNR provided by the full-range capability (i.e. the 10 dB sensitivity fall-off range is doubled, and the most sensitive region around the zero path delay can be used).
In this paper, we report on an investigation of the implementation of DD-FD-OCT for phase-resolved Doppler imaging. Since the performance of phase-resolved DOCT highly depends on the SNR of the system, we have also developed an alternative scheme of DD-FD-OCT built on a combination of a fiber-based and free-space setup in a Mach-Zehnder interferometer configuration. The fiber part also adds flexibility to the system enabling integration with handheld [33
] or endoscopic devices [35
] while the free-space part provides a stable π/2 phase relation between the two detected spectral interference signals. To verify the preservation of the velocity dynamic range of phase-resolved DOCT when operating in the full-range DD-FD-OCT setup, the Doppler phase stability and the accuracy of the measured velocities up to the maximum velocity limit were quantified. The accuracy of the velocity measurement was validated through the measurement of the Doppler phase shift of a flow phantom with known flow velocity. The Doppler performance was compared to that achieved by the conventional FD-DOCT processed from the same set of acquired spectra. Finally, in vivo
Doppler imaging of an African frog tadpole is demonstrated using the full-range DD-FD-OCT.