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Abstract
A diffuse optical tomography system with chaotic laser is proposed for the three-dimensional optical phantom. The high signal-to-noise ratio is beneficial to improve the spatial resolution of diffuse optical tomography. It is essential to drive the chaotic laser as the incident light into the optical phantom. The transmitted light emitted from phantom as the detection light and a part of the incident light as the reference light to carry out cross-correlation analysis. The high-density source-detector configuration in parallel plate structure is designed for detecting targets in the phantom. The propagation of chaotic laser in the phantom is studied theoretically and experimentally based on the diffusion equation. Image reconstruction is achieved by the cross-correlation analysis of chaotic laser and the Newton-Raphson nonlinear algorithm. The performance of the proposed system has been assessed by reconstruction localization accuracy and contrast-noise-ratio. The results show that the spatial resolution of the proposed system can reach 1.5 mm and the localization error is less than 1 mm.
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1. Introduction
Diffuse optical tomography (DOT) in medical diagnosis is used to analyze the deep lesions in the biological tissues [1–4], which estimates the absorption and scattering properties of the biological tissues using light in the red and near-infrared (NIR) wavelength range of 600-1100 nm [5–7]. Light is detected by passing through biological tissue and the optical properties are reconstructed spatially using mathematical models [8,9].
The absorption and scattering of biological tissues can affect the light propagation, especially the light scattering makes the light propagation randomly in the tissue. Hence, DOT has a limited spatial resolution while providing high spatial resolution in spatial reconstruction is challenging. The investigation has been developed to improve image resolution by increasing the variety of measurements. The spatial resolution of DOT can be improved by three different technologies, namely continuous wave (CW), frequency domain (FD), and time domain (TD). CW DOT provides the attenuation of light from a continuous light source, therefore only the differential changes in absorption can be recovered [10]. Shimokawa et al. introduced sensitivity-normalized regularization and sparsity into the hierarchical Bayesian method to achieve a high spatial resolution in CW DOT [11]. Bhowmik et al. proposed an optimization algorithm based on Dimensionality Reduction to improve spatial resolution [12]. Narasimhan et al. presented a fast imaging algorithm for high spatial resolution CW DOT with a line imaging and illumination system [13]. FD DOT is a radio-frequency intensity-modulated approach to light source. FD DOT provides information about the amplitude and phase of the photon propagation, and the phase information reflects the average time spent from the light source to detectors of photon travel [14]. It has been shown that FD DOT can improve image quality and spatial resolution over CW DOT due to the deeper sensitivity of measurements of phase delay [15,16]. TD DOT measures the time of photon flight of the light pulse in the tissue to establish a histogram of the detected temporal point spread function (TPSF) [17]. The TPSFs contain the information about the time and intensity in light propagation. Lyons et al. proposed a computational TD DOT for detecting hidden objects in scattering medium, and the spatial resolution can reach 1 mm [18]. Zhao et al. utilized confocal TD DOT and reached a spatial resolution of 0.5 mm [19]. Zhang et al. demonstrated an ultra-high-density source-detector (S-D) DOT system scalable to thousands of combinatorial S-D pairs per cm3, and the spatial resolution can reach 100 µm [20]. Compared to CW DOT, FD DOT and TD DOT measure the time information of photon propagation in tissue. The use of FD and TD technologies to obtain path-length information, in combination with model-based iterative reconstruction methods, allows for separation of absorption and scattering properties and improves spatial resolution and contrast [21,22].
The ultrashort pulse and photodetector used for TD DOT usually lead to a high system cost and a complex system. A laser modulated by a pseudo-random bit sequence (PRBS) is used as the light source to detect the target in biological tissues, which calculate the TPSF by cross-correlation of PRBS and solve the problem of the high cost and complexity in TD DOT [23]. The Laplace transform data is obtained directly in the PRBS-based DOT. The negative Laplace parameter can enhance the sensitivity to targets located in the deep region, thus the spatial resolution can be improved [24].
It is important to design a high-quality waveform with correlation characteristics of sharp main peaks and minimal sidelobe. These correlation characteristics are essential to resolve two closely spaced targets in tissue and can achieve a high spatial resolution DOT [25,26]. Chaotic laser has the characteristics of noise-like, broad bandwidth and delta-like auto-correlation. The peak of correlation appears only when the two chaotic signals are completely overlapped, thus the correlation function of chaotic signals is an extremely narrow delta-like function. The correlation technology of chaotic laser can provide the high signal-to-noise ratio (SNR) required for high resolution in DOT [14,27–29]. Based on the above characteristics, cross-correlation of chaotic laser provides the idea for high spatial resolution DOT.
In this paper, chaotic laser is used as the light source for DOT, and a high-density S-D configuration in parallel plate structure is designed for detecting targets in the phantom. The image reconstruction is realized by combining the cross-correlation of chaotic laser with the diffusion theory. The paper is organized as follows. In section II, we introduce the phantom preparation and the proposed DOT system, and build the model of photon propagation with chaotic laser. In section III, we analyze the photon fluence distribution with chaotic laser in phantom, and show the cross-correlation analysis theoretically and experimentally, then show the result of image reconstruction for different phantoms. We evaluate the reconstruction results and the proposed DOT system. Finally, we make the conclusions.
2. Methods and materials
2.1 Phantom preparation
The homogeneous phantom is prepared with a concentration of 7.63% Intralipid as scattering medium and 1% agar powder as curing agent. The size of the phantom is 18 mm in length, 10.6 mm in depth, and 12 mm in height. The required concentration of diluted Intralipid corresponding to the scattering and absorption coefficient can be determined according to the equations derived by David et al. [30], and the scattering and absorption coefficient of the phantom is 1 mm−1 and 0.02 mm−1 at the wavelength of 1070 nm respectively. A three-dimensional (3D) coordinate system is established with the center of the phantom as the origin.
A pair of black spheres with a diameter (d0) of 1.5 mm are submerged in the phantom as targets to evaluate the spatial resolution of the proposed system. The targets in the phantom are invisible under bright ambient illumination. The center-to-center distance (D) of two targets in the x-z plane is set to 5.0 mm, 3.5 mm, and 2.5 mm, respectively, corresponding to the separation distance (d = D - d0) of 3.5 mm, 2.0 mm, and 1.0 mm, respectively. The details of the three phantoms are described in Table 1. The schematic diagram of the phantom 1 is shown in Fig. 1(a) and the image of target after microscope magnification is shown in Fig. 1(b).
Table 1. The details of three phantoms.
2.2 System description
Chaotic laser is generated based on the nonlinear Kerr effect in fiber ring cavity [31]. The time series of chaotic laser shown in Fig. 2(a) is random and noise-like, and its auto-correlation function is a delta-like function shown in Fig. 2(b). The characteristics of the chaotic laser are its intrinsic randomness and correlation properties. The functions of the chaotic laser are measured the scattered signals with high SNR based on the delta-like correlation function.
The proposed DOT system is developed based on cross-correlation of chaotic laser. The experimental setup is displayed in Fig. 3(a). The wavelength is selected in the NIR range of 1070 nm. An optical coupler (OC) guides 10% of the incident signal to the photodetector 1 (PD 1) as the reference signal, and the remaining 90% of the incident signal enters a fiber optic collimator (COL) to irradiate the phantom. The light source and photodetector 2 (PD 2) are respectively fixed on a pair of translation platforms placed opposite each other. The detection signals at different S-D positions are collected by the PD 2 through the movement of the translation platforms. The reference and detection signals collected by PD are displayed in real-time and recorded on the oscilloscope (OSC), and the data processing is performed in the data processing system.
The S-D configuration is described as follows and shown in Fig. 3(b). The positions of 6 sources are arranged in a 2 × 3 matrix with each source position spaced 2 mm both in the x-direction and z-direction. The first row of the source array is 5 mm away from the top edge of the phantom, and the first columns of light sources are 7 mm away from the left edges of the phantom. The positions of 45 photodetectors are arranged in a 3 × 15 matrix, with each detector position spaced 1 mm in the x-direction and 2 mm in the z-direction respectively. The first row of the detector array is 4 mm away from the top edge of the phantom, and the first columns of detector are 2 mm away from the left edges of the phantom. Based on the above S-D configuration, the light source is located at S1 (-2.0, 5.3, 1.0) to irradiate the phantom at first, and the PD 2 is located at D1 (-7.0, -5.3, 2.0) to collect the detection signal. The moving steps of the translation platforms correspond to the spacing in the position matrix of the light source and photodetector respectively. The detection signals at the position of 6S-45D are collected through the movement of a pair of translation platforms. A total of 270 sets of data are collected for each phantom.
2.3 Photon propagation model of chaotic laser in phantom
The forward model of DOT theoretically calculates the photon information emitted from the tissue boundary based on the given S-D configuration and the optical parameter distribution of the tissue [32]. The photon propagation in tissue is calculated by diffusion equation (DE):
The photon propagation in biological tissues can be studied by COMSOL Multiphysics [4,6,7]. The coefficient form partial differential equation in COMSOL Multiphysics is rewritten as Eq. (1) to solve the forward model of the photon propagation of chaotic laser in phantom. The mesh models of three phantoms in Table 1 are shown in Fig. 4. The values of the absorption and diffusion coefficient used to solve Eq. (1) are 0.02 mm−1 and 1.52 mm for the homogeneous background, and 2 mm−1 and 0.17 mm for targets. Chaotic laser is used as light source and the S-D configuration (6S-45D) is described as section 2.1. The photon fluence distribution and probe signals at the position of 6S-45D are calculated using a transient solver.
3. Results
In the proposed DOT system, we reconstruct a 3D absorption distribution in the phantom from the measured peak value of cross-correlation of chaotic laser. First, we describe the relationship between the absorption and photon fluence change in the forward model, and calculate the peak value of cross-correlation of chaotic laser based on the forward model. Then, we reconstruct the absorption distribution based on the measured peak values of cross-correlation of chaotic laser in the inverse model.
3.1 Photon fluence distribution of chaotic laser in phantom
Light source S6 (-2.0, 5.3, -1.0) in the second row and first column of the source array is used as an example for analysis. The photon fluence distribution is given in the 3D slicer and the x-y plane at the center of two targets, respectively. The color bar represents the value of the photon fluence, and the maximum and minimum values are indicated in each image. The 45 probe signals are plotted. The results of three phantoms are shown in Figs. 5, 6, and 7, respectively. A larger photon fluence corresponds to the position closer to the light source. The photon fluence distribution is no longer gradually changing due to the addition of the targets. It can be seen clearly that the photon fluence is minimal at the position of the targets. The target 2-2 is far away from the light source S6 and therefore has the smallest photon fluence at its location. In Figs. 5 and 6, probe D36 closest to the light source S6 has the greatest signal intensity. The signal intensity of probe D35 is slightly greater than that of D36 in Fig. 7 due to the location of the target 3-1. The time series of the probe signal is random. The distribution of probe signals in Figs. 5(c), 6(c), and 7(c) are different, because the intensity of probe signals varies with the location of the targets.
Fig. 5. The photon fluence of phantom 1 under light source S6. (a) 3D slicer. (b) x-y plane with z = 0.2 mm. (c) 45 probe signals.
Fig. 6. The photon fluence of phantom 2 under light source S6. (a) 3D slicer. (b) x-y plane with z = 1.7 mm. (c) 45 probe signals.
Fig. 7. The photon fluence of phantom 3 under light source S6. (a) 3D slicer. (b) x-y plane with z = 0 mm. (c) 45 probe signals.
The probe signals of three phantoms at the positions of 6S-45D are obtained based on the forward model. The probe signals are cross-correlated with the signal of the light source, and the cross-correlation characteristics are analyzed by extracting the peak values of the cross-correlation curve. The peak values of three phantoms based on the forward model are shown in Fig. 8. In phantom 1, targets 1-1 and 1-2 are placed symmetrically so that the peak values shown in Fig. 8(a) under the 6 light sources are evenly distributed. In phantom 2, targets 2-1 and 2-2 are placed on the right side (positive x-axis direction), and in phantom 3, targets 3-1 and 3-2 are placed on the left side (negative x-axis direction). Therefore, the distribution of the peak values under 6 light sources shown in Fig. 8(b) and 8(c) shows an obviously opposite trend. It can be seen that the variation trend of peak values is related to the position of the targets.
Fig. 8. The peak values with 6S-45D of (a) phantom 1, (b) phantom 2, and (c) phantom 3 based on the forward model.
3.2 Image reconstruction
In order to accomplish the image reconstruction, the inverse model of DOT reverses the optical parameters of the tissue according to the measured value under the given S-D configuration [33]. The detection light is measured experimentally at the position of 6S-45D by moving the COL and PD 2 over a constant step, then cross-correlated with the reference light detected by PD 1. The peak values of cross-correlation based on the experimental measurement for three phantoms are shown in Fig. 9. The variation trend of the experimental results for different phantoms is consistent with the theoretical calculation based on the forward model in section 3.1. The 3D distribution of absorption coefficient is reconstructed by using peak values of cross-correlation of chaotic laser and Newton-Raphson nonlinear algorithm [34,35].
Fig. 9. The peak values with 6S-45D of (a) phantom 1, (b) phantom 2, and (c) phantom 3 based on the experimental measurement.
The reconstruction results of phantom 1 are shown in Fig. 10, and the color bar indicates the reconstructed absorption coefficients in mm−1 units. The DOT images are displayed in the x-z plane (Fig. 10(b)), the x-y plane (Fig. 10(c)), and the y-z plane (Fig. 10(d)), respectively. The different slices shown in Fig. 10(e) to 10(g) refer to the reconstructed image for different positions of the y-axis in the x-z plane from y = 1 mm to y = 0 mm, respectively. The reconstruction results show the separation of the two targets at the actual position (y = 0 mm) in the x-z plane. The reconstructed targets become more significant as the position of the y-coordinate in the x-z plane moves toward the actual position (y = 0 mm). The line profiles of µa across the targets are extracted from Fig. 10(g) and shown in Fig. 10(h), where the region of two targets is represented as the red dotted line, and the reconstructed µa is shown as the solid line with scattering. The results indicate that the two targets with a separation distance of d = 3.5 mm can be clearly distinguished.
Fig. 10. Reconstruction for the phantom 1 of two targets with d = 3.5 mm. (a) 3D reconstruction result, and the view of (b) x-z plane, (c) x-y plane, and (d) y-z plane. Reconstruction results in view of x-z planes at (e) y = 1 mm, (f) y = 0.5 mm, and (g) y = 0 mm. (h) The distribution of reconstructed µa at line profiles across the targets.
The reconstruction results of phantom 2 are shown in Fig. 11. The two targets are visible in both views of the x-z plane (Fig. 11(b)) and the x-y plane (Fig. 11(c)). The different slices shown in Fig. 11(e) to 11(g) refer to the reconstructed image for different positions of the y-axis in the x-z plane from y = 0 mm to y = 0.97 mm (actual position), respectively. Figure 11(h) exhibits the line profiles of µa across the targets extracted from Fig. 11(g). The two targets in the reconstruction image are closer with the decrease of the separation distance d. The results indicate that the two targets with a separation distance of d = 2.0 mm still can be distinguished.
Fig. 11. Reconstruction for the phantom 2 of two targets with d = 2.0 mm. (a) 3D reconstruction result, and the view of (b) x-z plane, (c) x-y plane, and (d) y-z plane. Reconstruction results in view of x-z planes at (e) y = 0 mm, (f) y = 0.5 mm, and (g) y = 0.97 mm. (h) The distribution of reconstructed µa at line profiles across the targets.
The reconstruction results of phantom 3 arranged similarly to Fig. 11 are shown in Fig. 12. The different slices shown in Fig. 12(e) to 12(g) refer to the reconstructed image for different positions of the y-axis in the x-z plane from y = 1.5 mm to y = 0.5 mm (actual position), respectively. The two targets with a separation distance of d = 1.0 mm fail to be distinguished.
Fig. 12. Reconstruction for the phantom 3 of two targets with d = 1.0 mm. (a) 3D reconstruction result, and the view of (b) x-z plane, (c) x-y plane, and (d) y-z plane. Reconstruction results in view of x-z planes at (e) y = 1.5 mm, (f) y = 1 mm, and (g) y = 0.5 mm. (h) The distribution of reconstructed µa at line profiles across the targets.
4. Discussion
4.1 Evaluation of reconstruction results
Localization accuracy is quantified by the Euclidean distance between the reconstructed center of the target and its center in the phantom. The reconstruction center is defined as the centroid coordinate corresponding to the maximum µa of the reconstructed target. Since the two targets with a separation distance of d = 1.0 mm cannot be distinguished successfully, localization accuracy is quantified only for the reconstructed results of phantom 1 and 2. The centroid coordinates of four targets are given in Table 2. The results are listed in Table 2 demonstrating that the system achieves satisfactory localization accuracy for the targets, and the localization errors are less than 1 mm in the x-z plane.
Table 2. Localization of the four reconstructed targets.
The quality of reconstructed images is assessed with contrast-noise ratio (CNR). The CNR is defined as:
The interaction between incident light and the target is completely absorbed without scattering, so only localization accuracy and CNR are used to evaluate the reconstruction results. The decreases in the separation distance between the two targets cause the localization accuracy and CNR to deteriorate. This may be due to the small gap between the two targets, which leads to the reflection during photon propagation, and results in a reduction in reconstruction quality.
4.2 Evaluation of the proposed system
To evaluate the spatial resolution of the different data types, a CW laser is used as the light source for the reconstruction of phantom 2. The 3D reconstruction results and the views of the x-z plane at y = 0.97 mm are shown in Fig. 13(a) and 13(b), respectively. It can be seen from Fig. 13(a) and 13(b) that the spatial resolution of the reconstruction results using CW laser is lower than that of the peak values of cross-correlation (as shown in Fig. 11) with the separation distance of d = 2.0 mm.
Fig. 13. Reconstruction for the phantom 2 of two targets with d = 2.0 mm using the intensity of CW laser. (a) 3D DOT reconstruction result. (b) Reconstruction results in view of x-z planes at y = 0.97 mm. (c) The normalized distribution of reconstructed µa at line profiles across the targets in Fig. 11(g) and Fig. 13(b).
Data analysis is used to verify the above results. The line profiles of µa across the targets are also extracted from the reconstructed images and the spatial resolution can be clearly visualized. The reconstructed µa is normalized so that the maximum is unity. Figure 13(c) exhibits the distribution of normalized µa at line profiles across the targets in Figs. 11(g) and 13(b). A metric is used to determine the separation of the two targets [21]. If the minimum of the reconstructed µa of two targets is less than 0.5 (i.e., FWHM), it can be identified. A lower minimum means that the two targets are easier to distinguish, corresponding to a higher spatial resolution. As shown in Fig. 13(c), the minimum of the reconstructed µa using CW laser is closer to the FWHM, that is, it is close to the threshold that cannot distinguish the separation of the two targets with a separation distance of d = 2.0 mm. However, the minimum of the reconstructed µa using peak values of cross-correlation is far away from the FWHM and it indicates that the two targets are easier to distinguish under the same situation.
Table 3 list the relevant results with different techniques for DOT. The reconstructed diameters and separation distances of targets are used to evaluate the spatial resolution. CW DOT usually improves spatial resolution through optimization algorithm [11,12]. The spatial resolution can be improved by structured light illumination and multiple view acquisition [17], and multi-access coded light source in TD DOT [36]. The delta-like cross-correlation function between the reference signal and the detection signal emitted from the phantom can effectively eliminate noise interference. A high SNR measurement can significantly improve image quality and resolution.
Table 3. The relevant results with different techniques for DOT.
Time-of-flight information of the photons in TD DOT is the key to achieve high spatial resolution, and the spatial resolution can be further improved by single photon avalanche diode (SPAD) arrays with high temporal resolution [18,19]. The ultra-high-density S-D configuration also can improve spatial resolution [20]. Therefore, the resolution of 1.5 mm for the proposed system can further be improved by SPAD arrays and ultra-high-density S-D configuration.
5. Conclusion
We propose a parallel plate DOT system for the detection of small targets in phantom based on cross-correlation of chaotic laser. We validate the proposed DOT system on the phantom with two targets embedded with different separation distances and generate high-quality images. The target with a diameter of 1.5 mm is successfully reconstructed in the proposed DOT system. The results show that the proposed DOT system has a spatial resolution of 1.5 mm and localization errors less than 1 mm. The correlation technology of chaotic laser offers significantly better imaging performance than CW DOT. The parallel plane structure similar to X-ray mammography makes it easier to locate the region of the target from the reconstruction results. The proposed technology can achieve the expected results in the real detection of biological tissues by SPAD arrays.
Funding
National Natural Science Foundation of China (61575137, 61675144, 61975141).
Acknowledgments
The authors thank the help of Shanxi 1331 Project Key Innovative Research Team.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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