We have experimentally implemented a time-resolved diffusive optical tomography system via a novel spread spectrum approach. A low power (~5 mW) laser diode modulated with pseudo-random bit sequences replaces the short pulse laser used in conventional time-resolved optical systems, while the time-resolved transmittance is retrieved by correlating the detected signal with the stimulation sequence. Temporal point spread functions of diffusive light propagating through a turbid medium have been measured with remarkably low noise levels and a temporal resolution of 2.24 nanosecond. We also present results of 2-dimensional scanning imaging experiments as evidences of the great potential of this new imaging technique.
©2003 Optical Society of America
Diffusive optical tomography (DOT) is a rapidly developing imaging technology for medical diagnoses and biomedical research. Breast cancer detection [1–5], brain function study [6, 7], infant  and fetus  monitoring, arthritis diagnosis , and small animal imaging  are among the numerous applications of DOT. Diffusive light can penetrate into turbid media such as human soft tissues for several centimeters, in contrast to the millimeter penetration depth of coherent light. Another advantage of DOT is its inherent functional imaging capability. By using dual-wavelength or multi-wavelength excitation, tumor angiogenesis can be mapped . Presently, one of the major obstacles that prevent DOT from being clinically acceptable is the low spatial resolution. A few millimeter resolution is possible in ideal situations, but the image quality can be seriously deteriorated by many practical issues such as irregular boundary conditions, heterogeneity of tissues, and the imperfect contact between the optical probe and the human body. To achieve higher spatial resolution and image quality, it is critical to retrieve as much information as possible from diffusive photons. Time-resolved method [13–17], which measures the temporal point spread function (TPSF) of diffusive light, is regarded as a solution to at least part of problems related to DOT. In a turbid medium, photons propagate in a random way and have a wide range of time delays (or optical path lengths) from the light source to the photodetector, in contrast to the direct path that connects a source and detector pair in X-ray computerized tomography. Early arriving photons, which suffer less scattering than those arriving later, are the key component towards high resolution optical tomography [18, 19]. A variety of time-resolved optical measurements techniques have been reported [20–22]. However, many of them are appropriate only for the detection of ballistic photons, but not diffusive and near diffusive lights. Currently, the most commonly used technique that has been applied to DOT is the time correlated single photon counting (TCSPC) method [23, 24]. In this report, we present a novel design and implementation of time-resolved DOT system. It has significant advantages over existing technologies, including high data acquisition speed, superior signal to noise ratio, and low costs.
In all conventional time-resolved optical measurement systems, a pulsed light source is necessary. For diffusive optical imaging, a picosecond or femtosecond laser is used to illuminate a sample while various detection schemes may be employed. The cost of such a system is always prohibitory due to the use of an ultra-short pulse (picosecond or femtosecond) laser and ultra-fast detection channels. It can be even more costly if multiple wavelengths are needed for functional imaging. Usually, a TPSPC system offers the best dynamic range and temporal linearity at the expense of very long data acquisition time. We have been exploring an entirely new approach, which is called spread spectrum time-resolved method. In such a spread spectrum time-resolved system, a low power (<100 mW) laser diode modulated with a pseudo-random bit sequence (PRBS) replaces the pulsed laser as the light source. When the coded excitation sequence propagates through a turbid medium, it is split into a group of components that have different path lengths going into the detector. The correlation of the detected signals with the excitation sequence can pick up each component with a specific delay. We have previously predicted the feasibility of such a time-resolve DOT system with computer simulation . However, this is the first time that we report its experimental implementation with a nanosecond temporal resolution. In addition, the potential of our method toward high spatial resolution is demonstrated with results from two-dimensional scanning imaging experiments.
2. System architecture
The schematic of our system is shown in Fig. 1. Pseudo-random bit sequences are generated continuously at a 622 Mb/s rate by a network analyzer transmitter (ME3620A, Anritsu). The sequence is repeated every 215-1 bits, leading to a sequence length of approximately 52.68 µs. A digital trigger signal, whose status is flipped for every 32 repetitions of the sequence, is also available from the network analyzer transmitter. A radio frequency power splitter (ZFSC-2-4, Mini-Circuits) distributes the pseudo random signal evenly to two branches. One is used to modulate a laser diode, while another acts as a reference signal. We use a 5 mW laser diode at 808 nm as the light source. Its modulated output is directed to a piece of sample under investigation. The transmitted (as shown in Fig. 1) and/or reflected (not shown in Fig. 1) light is detected by a Silicon Avalanche Photodiode (APD) from Hamamatsu (S3884). The APD has a cutoff frequency at around 400 MHz, and an active area 1.5 mm in diameter. The opto-electrical signal is pre-amplified by a low noise TIA (transimpedance amplifier, TZA3023-3, Philips Semiconductors), and then the amplified signal goes to the RF port of a frequency mixer (SBL-1, Mini-Circuits). The local oscillation (LO) port of the mixer is connected to the reference signal via a variable delay line. Currently we do not have a digitally controlled delay line, so we manually switch coaxial cables of different lengths. The velocity factor of these cables is 0.66. The estimated group delay of electrical signal propagating through a 19.8 cm coaxial cable is about 1 ns. The frequency mixer acts as an analog multiplier, which is the key component for the correlation detection scheme. The next stage low frequency amplifier has a gain of 50 dB and a low cut off high frequency around 40 kHz. The resulting low frequency signal represents the detected light intensity at a specific time delay defined by the variable delay line. However, the mixer is by no means a perfect multiplier. The nonlinear interaction of the reference signal with itself results in an additive dc offset. To get rid of the dc offsets from the mixer and subsequent operational amplifiers, the laser diode is switched on and off by the trigger signal (296.6 Hz) from the network analyzer transmitter. As a result, the output of the low frequency amplifier becomes a square wave. A personal computer acquires the waveforms from the detection channel with a data acquisition board and the waveform amplitudes are translated into time-resolved intensities.
The system was calibrated with neutral density filters inserted between the laser diode and the detector. The total attenuation factor was about 10-5. The black curve in Fig. 2 is the measured TPSF (temporal point spread function), or the impulse response, of the system. If all the components used in this system had wide enough bandwidths, the TPSF should be similar to a triangle near the origin and the FWHM (full width at half magnitude) would be 1.61 ns . Nonetheless, the measured TPSF was slightly wider than the theoretical predication for ideal situations. This was due to the limited bandwidths of some components in this prototype instrument. For example, the APD had a high cutoff frequency around 400 MHz. The transimpedance amplifier should have a flat frequency response from dc to 600 MHz in ideal situations. However, the terminal capacitance of the APD was about 10 pF, which might deteriorate the high frequency performance of the TIA. Consequently, the temporal resolution, or the FWHM of the TPSF, was measured about 2.24 ns. While it is necessary to move further into the sub-nanosecond regime for high resolution optical imaging, a nanosecond temporal resolution could also prove useful for certain applications. In addition, our approach provides an outstanding signal to noise ratio and short data acquisition time. Experimental results are provided in the following section to demonstrate the capability and potential of this new technique.
3. Experimental setup
Phantom experiments were performed to demonstrate our prototype spread spectrum time-resolved system. Shown in Figure 3 is the geometry of our experimental setup. A rectangular transparent container was filled with 0.5% Intralipid solution, which had similar optical properties to human soft tissues. The dimension of Intralipid solution was 21cm by 5.5 cm in the X and Z directions, and 10 cm in height. The origin of the coordinate system was located at the up-left corner of a 6 cm by 4 cm imaging area (enclosed by the purple rectangle). The output beam of the light source pointed perpendicularly to one side of the phantom, while the detector was placed on the opposite side. The source and the detector were so aligned that the ballistic path was parallel to the Z-axis. A 3-dimensional translation stage was used to scan the source detector pair at a 2 mm step in both X and Y directions.
Three targets of different type were embedded in the Intralipid solution for image acquisition (Fig. 4). The first was a black cylinder 5.5 mm in diameter and 15 mm long. It was nearly a pure absorber. The second was a sphere 18 mm in diameter, with µa≈0.07cm -1 and µ′s≈9cm -1. Its absorption and reduced scattering coefficients were slightly higher than the background values. The third was a small clear glass bottle sealed with glue, which made a void region in the turbid background. The outer diameter of the bottle was 14 mm, while the total length was 31 mm. In each image acquisition, one target was placed around the center of the imaging area, equal distant to the interfaces to both the light source and the detector.
No target was embedded inside the Intralipid solution when the background TPSF of the transmitted diffusive light wave was acquired. The time delay was scanned at a 0.6 ns interval from -2.4 ns to 9.6 ns. The data acquisition time for each point was about 0.1 second. The corresponding measurement errors are represented by the error bars superimposed on the curve (Fig. 5). The measured TPSF should be perceived as a convolution of the real TPSF with the system response (Fig. 2). As a consequence of the 2.24 ns temporal resolution, the measured TPSF stretches out into the negative time delay region and the rising edge became less steep due to mixed contributions from diffusive photons. The oscillation between 6 to 9.6 ns was mainly caused by the low cutoff frequency of the mixer (around 0.5 MHz).
Three specific time delay points were selected for 2-dimensional scanning imaging, i. e., - 0.6 ns, 0 ns, and 1.2 ns. The first two involve near diffusive photons, while the last one corresponds to the peak value the background TPSF. For each target, images were acquired with these three time delays. Images associated with various target and time delays are compared in Fig. 6 through Fig. 8. In Fig. 6 and 7, the absorbing targets caused decrease in transmittance in the target regions. The images are scaled between zero and the maximum background values. For Fig. 8, the void target resulted in increased transmittance and the images are scaled between zero and the maximum transmittance in the target regions.
It is obvious that the images get sharper with shorter time delay. As one can see in Fig. 6, each image can be roughly separated into three different regions: the yellow target region, the red transition region, and the dark red background region. In Fig. 6(a), the target region is only slightly bigger than the real target dimensions and the transition region is relatively small compared with the background region. With longer time delays (Figs. 6(b) and (c)), the background regions are pushed to the boundaries while the target regions and the transition regions swell much bigger. Similar trends can be found in Fig. 7.
In the void target case, image qualities for time delays -0.6 ns (Fig. 8(a)) and 0 ns (Fig. 8(b)) are close. However, Fig. 8(a) is slightly better that one can even identify the outline of the bottleneck. Fig. 8(c) appears much more blurred with a lower contrast. Plotted in Fig. 9 are line profiles extracted from images in Fig. 8 at Y=24 mm. The maximal perturbation decreases from 52.1% for -0. 6 ns and 50.6% for 0 ns to 26.5% for 1.2 ns. However, for absorbing targets, the differences in the maximal perturbation among different time delays are not significant.
To quantify the effect of time delay on spatial resolution, two parameters are employed. One is the FWHM of the representative profile along a horizontal scanning line across the target centers. Another is the maximal absolute edge slope normalized with respect to the maximal perturbation, denoted as Knorm. The bigger Knorm, the smaller edge spread and the higher spatial resolution. Summarized in Table 1 are these parameters for three targets at different time delays. According to this table, improvement in the spatial resolution due to reduced time delay is more evident for absorbing targets than for the void target.
Images shown in Fig. 6 through 8 are simply 2-dimensional projections without any image processing, and thus should not be directly compared with those tomographic images reconstructed with dedicated inversion algorithms. If we define the spatial resolution as the reciprocal of Knorm, then its value for the black cylinder increases from about 5.5 mm to 8.1 mm with increasing time delay. Interestingly, the improvement in spatial resolution depends on the type of targets embedded, as suggested by our study. However, rigorous assessment of the achievable spatial resolution via the time-resolved approach needs more extensive investigations. Incorporation of reconstruction algorithms to the time-resolved measurement system is definitely necessary, while optimization of the scan geometry might be equally important. These issues are beyond the scope of this paper, but will be investigated in our future studies.
The signal to noise ratio also plays a critical role for higher image quality. For our spread spectrum time-resolved system, the noise level is consistent through the time domain. Consequently, the signal to noise ratio becomes lower for early arriving photons as the signal strength decreases. Compromises should be made to balance the spatial resolution, the noise level, and the data acquisition time for a specific application. As a prototype system, our time-resolved instrument has manifested a superior signal to noise ratio. The relative measurement error is about 0.81% for the peak value of the TPSF, or 0.49% for the integrated signal (the total transmittance). This is already better than the shot noise alone (about 1%) for a TCSPC system that works in an ideal condition with a 105 count/s photon-counting rate and the same data acquisition time of 0.1 second. The signal to noise ratio has not been explicitly specified in most literatures on time-resolved DOT systems based on TCSPC. It is argued that the noise levels of such systems are dominated by the shot noise after subtraction of background counts caused by environmental lights. However, the noise and stability of ultrafast lasers are usually worse than 1% and will definitely degrade the system performance. Another problem with TCSPC is that the ultimate signal to noise ratio is limited by the detector, or more specifically, the counting rate. The light source has to be maintained at a rather low output level in order to fulfill the requirement of single photon counting and not to damage the detector. On the other hand, the noise level of our system can be further reduced by about 20 dB by simply increasing the source power by a factor of 10. Actually the noise level of our system is dominated by the electronic circuitry noises (including the preamplifier noise) and has much room to improve before reaching the shot noise floor.
To compare the performance of our prototype system with frequency domain systems, a virtual 200 MHz system is picked  because of the similar imaging geometry. The amplitude noise is about 0.32% for a 10 Hz bandwidth if only the shot noise is considered, and it should become around 0.5% if taking into account the excess noise factor of PMT. In a practical situation, the noises from the detector itself, the preamplifier, and the light source will also contribute to the total noise of the system. For example, the 50 MHz frequency domain system developed at the University of Pennsylvania has an estimated amplitude noise of 1% and phase noise of 0.3 degree . In addition, the PMT used in those systems generally have an internal gain (typically 105–107) several orders higher than that of the APD in our system, which is around 100. Using high-speed PMT is another option to increase the sensitivity and the signal to noise ratio for our system.
Higher temporal resolution is definitely desirable for retrieval of the time-resolved transmittance or reflectance more accurately. Fortunately, components for 2.5 Gb/s and even 10 Gb/s data rates are readily available from the telecommunication industry. By using a higher bit rate pattern generator together with wider bandwidth laser diodes and detectors (APD or photomultiplier tube), it would be highly feasible to reach a 100-ps temporal resolution. It should be noted that the method presented in the report could be well adopted in a wide range of other applications, such as time-resolved fluorescence spectroscopy and imaging.
We have developed a prototype spread spectrum time-resolved diffusive optical imaging system, which has a temporal resolution of 2.24 ns. Phantom experiments with such a system have demonstrated the great potential of this new technique to improve diffusive optical tomography in terms of the spatial resolution and the signal to noise ratio.
We would like to thank the following for their funding support: DOD ARMY Breast Cancer Program (DAMD17-00-1-0217, DAMD17-01-1-0216), and NIH (8R01EB002136-02). Dr. Bing Wang of the ECE department at University of Connecticut is gratefully acknowledged for proofreading the manuscript.
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