Direct-Mapping Cross-Interfaces Computed Tomography

doi:10.21203/rs.3.rs-2454791/v1

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Direct-Mapping Cross-Interfaces Computed Tomography

https://doi.org/10.21203/rs.3.rs-2454791/v1

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published 17 Jul, 2023

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This work reports an optimized tomography method, termed Direct-Mapping Cross-Interfaces Computed Tomography (DMCICT), with enhanced calculation efficiency and accuracy for three-dimensional (3D) reconstruction in confined space. Confined-space tomography methods are designed to correct the image distortion on recorded target images caused by light refraction through optical walls, such as optical engine cylinders. However, past confined-space tomography methods have shortcomings in reconstruction accuracy and time efficiency, since they usually involve time-consuming iterations or numerical interpolation during calculating the mapping relationship from 3D measurement domain to 2D imaging planes. There, DMCICT is developed in this work to directly calculating the mapping relationship by performing reverse ray-tracings originated from imaging planes, then decide the intersection volumes with discretized measurement domain. Numerical and experimental validations of DMCICT are respectively performed based on multiple simulated phantoms and a two-branch laminar flame contained inside an optical cylinder. Compared to past confined-space reconstructions, DMCICT can reduce more than 50% of the computational time in majority of tested cases, while the reconstruction accuracy is also significantly enhanced. Moreover, DMCICT demonstrates the robustness under different spatial resolution conditions and presents solid endurance on measurement errors.

Computed tomography

Mapping relationship

Optimization method

Computational efficiency

Tomography technology has been extensively employed in three-dimensional (3D) optical diagnostics in a wide range of flow and combustion measurements [1–6]. According to the application situations, the tomography technique can be utilized in both open-space and confined-space problems. In open-space problems, all light signals emitted by the target (e.g., flames and flows) signal field are unhindered and can approach the image sensors (e.g., CCD, CMOS cameras and fiber-bundle endoscopes), such as measurements on laboratory burners [7–9], jet nozzles [10], surface flow [11] and so on. The tomography technology and mathematical inversion algorithms for open space have been widely used and developed in flow and combustion diagnostics [17–23]. In contrast, the target signal field of confined-space problems is typically surrounded by facility walls, which are usually made up of transparent materials (e.g., quartz and sapphire) to provide the optical access. Due to the existence of facility walls, the measurement domain can possess high ambient pressure and temperature and develop highly turbulent flows or flames [12, 13], leading to more complicated patterns of the optical signal field compared to the open-space cases. For example, in the measurements of 3D flame topology on optical internal combustion engines [14] and velocity fields in wind and water tunnels [15, 16], the complicated patterns bring great challenges in analyzing the flow or combustion essence.

Moreover, in confined-space tomography problems, the presence of facility transparent wall would refract the light propagating through by the outer and inner surfaces, leading to enormous measurement errors both in 2D projections and 3D reconstructions. To eliminate the influence of refraction, a series of tomography methods have been performed in past researches based on different wall shapes. In details, flat walls cause uniform displacement on every location of recorded 2D projections, thus can be easily corrected by integrally shifting the signal distribution of projections during the calibration process [27]. Practical applications include the ignition dynamics analysis in a Mach 2 combustor [25] and the 3D measurements of fuel/air mixture temperature and fuel vapor/liquid concentration distribution in evaporating sprays contained by an optically accessible rectangular constant volume chamber [26]. Compared to flat surfaces, curved surfaces of facility walls cause not only integral translation but also deformation on projections, which is much harder to be corrected. Such problem appears in the measurements of turbulent flames in optical internal combustion engines [14, 24]. Some researches proposed numerical models to quantify the distortion using polynomial fitting [28–30]. But these models are only suitable for specific-shaped chambers and are not universally applicable. Besides, high-order polynomial fitting usually consumes considerable computing resources. Other studies attempted to revise the ray-tracing method based on pinhole model and Snell’s law to calculate light paths after double-refraction on the facility walls [31, 32]. However, the method requires multiple iterations to accurately determine the correct light path from all possible directions for every location in the measurement domain, thus is practically time consuming. Based on the understanding of past studies, our recent work proposed an improved method, termed Cross-Interfaces Computed Tomography (CICT) [33]. The method revised the mapping relationship based on the traditional reversed ray-tracing method and calculated the one-to-one correspondence from every light source location in the measurement domain and its projection on the cameras without involving iterations.

Although CICT has been validated by both simulation phantoms and experimental flames inside an optical cylinder [33, 34], the method still has nonnegligible shortage in calculation accuracy and efficiency. As for accuracy, CICT discretizes the measurement domain into parallelepiped voxels, which have anisotropic projections in different orientations. That is to say, a voxel would have different projection shape and intensity as viewed from different perspectives, which is contradicted to the physical essence of point light source. As for efficiency, in CICT, the establishment of mapping relationship from discretized voxels in 3D measurement domain to their projections require reverse ray-tracing light paths emitted from all pixels in projections to be calculated in advance. Therefore, the computational time would dramatically grow with the increase of projection numbers (with more pixels) and the refinement of discretized measurement domain (with more voxels). To provide a practical example, if the measurement domain is discretized into 276 voxel × 276 voxel × 105 voxel (i.e., ~ 8 M voxels), and 8 projections are recorded from different perspective, each with a dimension of 850 pixel × 278 pixel (i.e., ~ 0.2 M pixels), the time cost of calculating the mapping relationship would be more than 10 hours using the work station with 576 GB of RAM and Intel(R) Xeon(R) Gold 6130 CPU @ 2.10GHz (double processors).

To further improve calculation accuracy and save computational time, an optimized mapping method from voxel signals to CCD arrays is desired. Enlightened by past studies on tomographic particle image velocimetry [35, 36], it is reasonable to assume the reverse ray-tracing emitted from certain pixel to be magnified into a cylindrical beam after passing the lens group. The cylindrical beam then intersects with voxels in the 3D domain. The fraction of intersecting volume over the total volume of certain voxel can be regarded as the mapping coefficient between the voxel and the pixel. To ensure that the beam-voxel intersection is independent of projection orientations, spherical voxels should be utilized instead of cubic ones in the new method. To the best of our knowledge, such mapping method is only validated by open-space tomo-PIV studies that it is able to calculate the mapping relationship more quickly. Nevertheless, the idea of directly calculating mapping coefficient by beam-voxel intersection is inspiring in effectively solving confined-space tomography problems.

Based on the above understanding of past efforts, this work proposes an optimized tomography approach, termed Direct-Mapping Cross-Interfaces Computed Tomography (DMCICT), to improve the calculation accuracy and efficiency for confined-space tomographic reconstructions. The DMCICT calculates the mapping relationship directly by reverse ray-tracings from projections and their intersections with spherical voxels. The mapping relationship is then utilized by a mature tomographic inversion algorithm (i.e., Algebraic Reconstruction Technique, ART) to reconstruct 3D optical field. In the rest of this paper, Section 2 first describes the mathematical formulation of DMCICT on the basis of the optimization of CICT. Section 3&4 provide numerical and experimental validations of DMCICT based on tomographic reconstructions of three phantoms and two-branch experimental flames inside an optical cylinder. Finally, Section 5 concludes the paper.

This section analyzes the reason for angle restriction existing in CICT then describes the improved imaging model of DMCICT. The detailed algorithm of CICT has been extensively discussed in our past work [34], so only a brief description is provided here to point out its limitation. The CICT method operates in the following five steps: 1) Calculate the reverse ray-tracings from all pixels on image sensors to the measurement domain based on the pinhole model and Snell’s Law; 2) Calculate the distances from an arbitrary point (say point A) in the measurement domain to closest four rays surrounding it, which are emitted by four adjacent pixels on the image plane; 3) Decide the projection point A’ on the image plane by linear interpolation (i.e., the ratio of distances from point A to four closest rays is set equal to that of distances from point A’ to the pixels emitting the rays); 4) Following the same way, the corner points of a parallelepiped voxel are projected on the image plane to determine the cover area of the voxel and then mapping relationship; 5) The 3D voxel intensity distribution is iteratively resolved by ART based on the mapping relationship from voxels to pixels.

The procedure of CICT appears to have shortcomings in accuracy and efficiency during practical applications. First, step 4) of CICT unavoidably leads to inconsistent pixel cover area of the same voxel viewed from different orientations, while the projection of an ideal point source should be isotropic. Therefore, spherical voxels rather than parallelepiped ones are desired to be processed in the program to eliminate anisotropy, which, however, would not be accomplished by CICT since no corner points remains. Second, by tracking the program code operation, it is noticed that steps 2) and 3) consume majority of computational time, which would be unexpectedly prolonged as the numbers of voxels and pixels increases to the level of practical measurements on industry devices. Since both steps are designed to transform the reverse ray-tracings (pixels to voxels) into forward ones (voxels to pixels), it is desired to further optimize such process in a more concise way.

To overcome the limitation of CICT, the DMCICT method is developed in this work to directly resolve the mapping relationship from spherical voxels to pixels. Specifically, the reversed ray-tracing from certain pixel is first magnified by the lenses into a cylindrical beam, then crosses the optical wall and finally intersects with the measurement domain. The intersected spherical voxels would have contribution to the pixel intensity, and the weighting coefficient of each voxel can be represented by the volume of intersection. Following such idea, the mapping relationship would be directly calculated based on each pixel, instead of each voxel. Hence, the direct calculation of reverse ray-tracings from pixels and their intersections with voxels compose the main skeleton of DMCICT. To better illustrate the procedure of DMCICT, Fig. 1 shows the optimized imaging model that establishes mapping relationship from the discretized object in the measurement domain to the imaging plane of camera chip. As shown in Fig. 1, included in the yellow dashed line is an enlarged schematic of a voxel O intersecting with reversed beam R_Q. The reversed beam is originated from pixel Q’, and then magnified by the lens into a cylindrical beam with slightly increasing cross-sectional areas. The magnified cylindrical beam R_Q is then refracted twice by cylinder wall following Snell’s Law [33]. The refracted beam enters the measurement domain and intersects with multiple voxels. The weighting coefficient of voxel O to pixel Q’ is calculated as the fraction of beam volume intersecting the voxel (marked in red). Such calculation is independent from imaging sensor orientations, thus the weighting coefficients are solely related to three variables: 1) the distance b between the voxel center and reversed beam axis; 2) the beam radius R and 3) the voxel radius r. The intersection volume V_inters between a spherical voxel and a beam can be calculated by Eq. (1):

$$\begin{array}{c}{V}_{inters}=\underset{\varOmega }{\iiint }dxdydz,\\ \text{w}\text{h}\text{e}\text{r}\text{e}\text{ }\varOmega =\left\{\left(x,y,z\right)\left|\begin{array}{c}{x}^{2}+{y}^{2}+{z}^{2}\le {r}^{2}, \\ {(x-b)}^{2}+{y}^{2}\le {R}^{2}\end{array}\right.\right\}\end{array}$$

Moreover, while the physical sizes of the voxels and beams are uniquely determined under certain imaging system during specific measurements, the intersecting volume would be only related to b. Hence, for certain calibrated experimental setup (i.e., r and R fixed), we first calculate V_inters by discretizing b from 0 to (r + R) with an increment of 1 micron (10^− 6 m), and then store the results in an array as a prior. Afterwards, during practical measurements through refractive interfaces, the intersection volumes can be easily determined by citing the array. Such processing is much more computationally efficient than repetitively calculating Eq. (1) for every beam and voxel. Eventually, the imaging process of the proposed model can be expressed in Eq. (2):

$$P=\frac{{({D}_{\text{lens}}/f)}^{2}}{16\cdot {l}^{2}}\cdot \frac{{V}_{\text{inters}}}{{V}_{\text{voxel}}}\cdot F$$

where V_voxel is the total volume of a voxel. By applying Eq. (2) to all voxels in the measurement domain, the intensity of each pixel on the camera chip can be calculated as a weighted summation of all voxel signals. During practical measurements, P would be recorded by image sensors, and F would be iteratively solved by ART.

Before moving to detailed simulation and experiments of DMCICT, a simple numerical phantom is reconstructed in Fig. 2 to directly illustrate the performance discrepancy between CICT and DMCICT. As shown in Fig. 2(a). the numerical phantom of a hollow rectangular column is generated in center Z axis the measurement domain with an O-XYZ coordinate system. The phantom intensity is arbitrarily set as unity for all non-zero voxels. The measurement domain is discretized into 184 voxel (X) × 184 voxel (Y) × 70 voxel (Z), with a nominal spatial resolution of 0.5 mm/voxel. The projections from azimuth angles (the angle between the camera axis and the positive X axis) of 45° and 90° are numerically calculated by CICT (in Fig. 2b) and DMCICT (in Fig. 2c). As can be observed in Fig. 2(b), the 45° projection presents irregular curved fringe patterns, and the 90° projection has multiple vertical/horizontal bands with noticeably higher intensity compared to nearby pixels. Comparatively, the projections by DMCICT using spherical voxels have approximately isotropic distribution for both 45° and 90° projections. It is worth noting the tiny grid-like patterns in DMCICT projections are due to the limited size of voxels. With further reduced voxel size, the grid-like patterns would be diminished, and the projection signal distribution tends to become uniform, which is closer to real-life imaging process.

This section reports the numerical validations of DMCICT by reconstructing 3D chemiluminescence distribution of three different phantoms. Figure 3 shows the schematic experimental setup for 3D tomography measurements. All experimental instruments are assembled on an optical platform. The cylinder is made of quartz with uniform refractive index of 1.4, and has a size of 131 mm (outer diameter) × 92 mm (inner diameter) × 42 mm (height). The object coordinate system O-XYZ is defined as follows: the center of the cylinder bottom surface is defined as the origin O; the directions parallel with and normal to the cylinder vertical axis are respectively defined as the X and Y directions; the cylinder vertical axis is defined as the Z direction. Based on the measurement system setup, numerical tomographic reconstructions using DMCICT and CICT on different phantoms are performed prior to any practical experiments.

Three phantoms of different patterns are generated to verify the universality of the DMCICT in Fig. 4. Figure 4(a) shows a simulated flame phantom consisting of a funnel-shaped object and a spindle object, Fig. 5(b) shows a turbulent spray phantom consisted of two branches, and Fig. 5(c) presents a combination of spherical, conical and prismatic shapes. All phantoms have uniform thickness of 2 voxels (i.e., 1 mm). The intensity of phantom voxels is artificially set as unity and the intensity of all other voxels is set as 0. Such intensity distribution simulates a recognizable pattern to help evaluate the quality of tomographic reconstruction. Same as Fig. 2(a), the measurement domain in Fig. 4 is also discretized into 184 voxel (X) × 184 voxel (Y) × 70 voxel (Z). To perform simulation reconstructions, a total of 8 simulated projections are respectively recorded from the azimuth angles of 0°, 30°, 50°, 80°, 100°, 140°, 160° and 180°, and the inclination angle φ is set to 0° for all projections. To ensure all phantoms can be entirely recorded, the pixel resolution of projections is set to be 800 pixels × 300 pixels (with the pixel size of 5.6 µm), and the imaging magnification is set to 15. Besides, the focal length and f number of virtual lens used are 35 mm and 2.8, respectively. To simulate practical experimental uncertainty, 1% of Gaussian noise and 0.1° angle error is added during the imaging process in accordance with our past effort [34]. During the ART iteration, the iteration number is set to 30 with a relaxation factor of 0.7 to ensure convergence for DMCICT.

For variation and comparison purposes, numerical reconstructions by DMCICT and CICT methods are performed for all phantoms. Figure 6(a) shows the calculating reconstruction time for phantom P1, P2 & P3 by both methods. Based on the order of processes, the total calculating time is divided into two parts: 1) the time cost to establish and store the immense mapping relationship matrix, and 2) the time consumed in following ART iterations. As shown in Fig. 5(a), the total calculation time of DMCICT is reduced by more than 50% compared to that of CICT for all phantoms. Such observation reflects that DMCICT has significantly improved calculation efficiency by optimizing the imaging model (explained in Fig. 1). After the tomographic calculation, Fig. 5(b) compares the quality of the reconstruction results by both algorithms. To quantitatively evaluate the reconstructions, a correlation coefficient Corr3 is employed similar to our past tomography approaches [33, 38], which can be calculated using Eq. (3):

$$\begin{array}{c}Corr3({V}_{\text{phan}},{V}_{\text{recon}})=\\ \frac{{\sum }_{\text{j}}\left\{\left[{V}_{\text{phan}}\left(j\right)-\stackrel{-}{{V}_{\text{phan}}}\right]\times \left[{V}_{\text{recon}}\left(j\right)-\stackrel{-}{{V}_{\text{recon}}}\right]\right\}}{\sqrt{{\sum }_{\text{j}}{\left[{V}_{\text{phan}}\left(j\right)-\stackrel{-}{{V}_{\text{phan}}}\right]}^{2}}\times \sqrt{{\sum }_{\text{j}}{\left[{V}_{\text{recon}}\left(j\right)-\stackrel{-}{{V}_{\text{recon}}}\right]}^{2}}}\end{array}$$

where V_phan and V_recon are the 3D signal intensity matrices of the original and reconstructed phantoms, respectively. The overline above a matrix indicates the average of all non-zero values in matrix. Eq. (3) indicates that the closer Corr3 is to 1, the more similar the reconstruction to the original phantom. As shown in Fig. 5(b), for all studied phantoms, the Corr3 values by DMCICT are around 0.9, noticeably higher than those by CICT (~ 0.8). Such observation quantitatively validates the accuracy of DMCICT. Compared to CICT, the DMCICT method is believed to possess the capability of quicker convergence and higher accuracy within limited iterations (i.e., 30 in this work, also an often-used number in practical tomography applications). However, it is necessary to clarify that such comparison does not negate the validity of CICT. Under sufficient number of iterations (e.g., 500 in our previous work [34]), the CICT reconstructions also achieved sufficient accuracy (i.e., Corr3 close to 0.9). Nevertheless, due to significantly enhanced calculation speed in contrast to CICT, the DMCICT method is managed to obtain precise reconstructions more effectively. Hence, the DMCICT is especially preferred when a dynamic target is reconstructed, usually involving hundreds or thousands of frames sequentially recorded.

To evaluate the robustness of DMCICT on practical reconstruction situations, its performance on different voxel sizes is investigated. Besides previously tested discretization (184 voxel × 184 voxel × 70 voxel, namely dim184), the measurement domain are respectively divided into: 92 voxel × 92 voxel × 35 voxel (dim92) and 276 voxel × 276 voxel× 105 voxel (dim276). Figure 6 compares the reconstruction time and accuracy of P3 by DMCICT and CICT under different voxel sizes. As shown in Fig. 6(a), the reconstruction calculation time is significantly reduced when DMCICT is used instead of CICT for all tested voxels sizes. Moreover, the proportion of calculation time saved by DMCICT rises as the voxel size becomes smaller (i.e., the nominal resolution increases). Specially, under dim276 (voxel size: 0.33 mm), the calculating time for DMCICT is reduced to nearly one third of that for CICT. Figure 6(b) shows the reconstruction accuracy of both methods maintains at approximately same level, though Corr3 gradually reduces with smaller voxel size. The method discrepancies in both computational cost and accuracy indicate that DMCICT would be more beneficial for practical tomographic reconstructions desired for higher spatial resolutions.

Figure 7 further evaluates the capacity of DMCICT in withstanding imaging noise. As stated in the simulation setup, the imaging noise is represented by the Gaussian noise and the angle error, set as 1% and 0.1° in previous calculation. Hence, Fig. 7(a) compares the DMCICT reconstructions of all phantoms with Gaussian noise E_gaussian = 1%, 2% and 3% (angle error E_angle = 0.1°), while Fig. 8(b) compares the reconstructions with E_angle = 0.1°, 0.2° and 0.3° (E_gaussian = 1%). As can be observed in Fig. 8, neither Gaussian noise nor angle error has prominent impact on the reconstruction by DMCICT. Specifically, the value of Corr3 maintains above 0.8 under most cases, indicating that the DMCICT method possesses reliable tolerance on imaging noise. The only exception may be the deteriorated reconstruction of P2 with E_gaussian = 3%. This is possibly due to relatively lower signal-to-noise ratio of P2, since P2 is generated from a practical flame reconstruction while others are consisted of basic geometric shapes.

The experimental validation of DMCICT is performed by reconstructing a two-branch laminar cone flame located inside the cylinder, as presented in Fig. 4. An ethylene-air burner is installed at X = -28 mm and Y = -5 mm to produce two-branch premixed laminar cone flames. The height of the burner is set the same as that of the cylinder bottom surface, and the flame height is adjusted to be enclosed in the cylinder inner space. A 1200 mm-diameter circular rail is mounted on the platform and set concentric with the optical cylinder. In total of 8 fiber detectors are installed on the circular rail to deliver 2D projections from different perspectives to two CCD cameras. The fiber detector azimuth angles are calibrated as 3.4°, 29.1°, 53.5°, 78.9°, 105.0°, 137.3°, 158.1° and 182.0°, respectively [8]. The camera exposure time is adjusted to 40 ms to capture the flame fluctuation without image blurring. The recorded flame projections have uniform pixel resolution of 850 pixel × 250 pixel, cropped from the original camera chip. The measurement domain discretization and lens parameters are all set identical as previous simulation.

Figure 8 shows the experimental flame 3D reconstruction results obtained by CICT and DMCICT, respectively. Both reconstructions exhibit similar two-branch cone pattern of the flame. Figure 9 further compares the reconstructed flame intensity by both method in 2D. Figure 10(a) and 10(b) respectively show the 2D flame slice cropped at Y = -5 mm, approximately the center XZ slice. In both panels, the hollow flame front can be clearly observed. Figure 10(c)-10(f) provides quantitative comparison of flame intensity distribution of the center slice at specific heights (i.e., Z = 9, 12, 15 and 18 mm). The averaged signal difference is less than 2% for all tested Z locations. Hence, by quantitatively examining the intensity distribution of reconstructed flame, it is revealed that the DMCICT method can be regarded as reliable as CICT, evaluated from the 3D reconstructions.

Though the intensity variation of 3D reconstructed flame by DMCICT and CICT is not evident, the 2D ray-tracings generated from 3D reconstructions clearly reflect the difference. As shown in Fig. 10, the ray-tracings calculated by CICT have noticeable errors in same of the views. Specifically, in ray-tracing recorded by Fiber 1 and 2, the flame front of both branches is not resolved completely, as circled out. The primary reason is that the reconstruction is not converged under current iteration numbers (i.e., 30). According to past CICT study, the sufficient iteration required by CICT is at least 500. In contrast, the ray-tracings of DMCICT reconstruction present more similar patterns compared to recorded projections. Such comparison demonstrated the superiority of DMCICT for reconstructions under limited iteration rounds.

Furthermore, Fig. 11(a) quantitatively examines the accuracy of DMCICT and CICT reconstructions by calculating the 2D correlation coefficient between measured projections and calculated ray-tracings. The correlation coefficient Corr2 is calculated in the similar way as Corr3, by replacing 3D signal intensity matrices of reconstructions/phantoms with 2D signal matrices of projections/ray-tracings. As shown in Fig. 11(a), the Corr2 of both methods exceeds 0.9 for all views, noticeably higher than Corr3. Specifically, the Corr2 of CICT is around 0.9 for fiber view 1–4, and increases to ~ 0.95 for view 5–8. Meanwhile, the Corr2 of DMCICT exceeds 0.95 for all views, recognizably higher than it of CICT except View 6. Moreover, Fig. 11(b) compares the calculation time of experimental reconstruction by DMCICT and CICT. As shown, the calculating time required by DMCICT is less than half that of CICT. The comparison in Fig. 11 indicates the DMCICT algorithm can significantly improve the calculation efficiency while maintaining sufficient reconstruction accuracy.

This work demonstrates the development and validation of a new tomography method (DMCICT) to efficiently solve 3D reconstructions in confined-space. Different from past approaches that requires multiple steps to resolve the mapping relationship, DMCICT manages to decide the point spread function from voxels to pixels in only one step, thus saves considerable computational cost. Moreover, by comparing the simulated projections from different azimuth angles, the DMCICT projections effectively prevent the artificial noise caused by anisotropic voxel shape in past approaches (represented by CICT). Afterwards, numerical reconstructions are performed to validate the calculation efficiency and reconstruction accuracy of DMCICT based on three different phantoms. By respectively applying DMCICT and CICT, multiple simulated projections (evenly distributed from 0° to 180°) are generated with 1% Gaussian noise and 0.1° angle error added to reconstruct the phantoms. The comparison of reconstructions shows that DMCICT possesses better calculation efficiency, reducing more than 50% of computational time compared to that of CICT for all phantoms. Besides, the DMCICT reconstruction also have noticeably better accuracy, represented by higher 3D correlation coefficient. Moreover, different voxel sizes and imaging noise level are employed to evaluate the robustness of DMCICT under practical reconstruction situations. The investigation shows that DMCICT tends to reduce larger fraction of calculation time as the voxel size decreases (i.e., higher spatial resolution). The DMCICT reconstructions also maintains reasonable accuracy as the Gaussian noise and angle error triples. Finally, the experimental validation of DMCICT is performed by reconstructing a two-branch laminar cone flame. The results show that DMCICT is more efficient compared to CICT in solving practical confined-space problems, by reducing more than half of the computational time. Regarding the reconstruction accuracy, DMCICT is also superior to CICT, proved by 2D simulated ray-tracings more similar to recorded experimental projections.

Author’s contribution YW proposed the main idea. BG and CL have performed the simulation and experiments’ calculation and wrote the main manuscript text. Thorough checking of the paper was done by all authors.

Funding Natural Science Foundation of Beijing (3222041), National Natural Science Foundation of China (51906017), and State Key Laboratory of Engines, Tianjin University (K2021-07)

Data availability statement 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.

Conflict of interest All authors declare that they have no conflict of interest.

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No competing interests reported.

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Direct-Mapping Cross-Interfaces Computed Tomography

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Abstract

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1. Introduction

2. Algorithm Description

3. Numerical Validation Of Dmcict

4. Experimental Validation Of Dmcict

5. Conclusions

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References

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