Numerical and experimental validation of a three-dimensional combustion diagnostic based on tomographic chemiluminescence

Camera spatial arrangement influence on reconstruction accuracy of chemiluminescence tomography

Computed tomography of chemiluminescence (CTC) has been demonstrated to be a powerful tool for three-dimensional (3D) combustion visualization and measurement, in which the number of cameras and their spatial arrangement significantly impact the tomographic reconstruction quality. In this work, the relationship of the camera spatial arrangement and tomographic reconstruction accuracy is theoretically established based on two-dimensional (2D) and 3D Mojette transforms and their accurate reconstruction conditions. Numerical simulations and experiments were conducted to demonstrate the theories. The results suggest that the exact reconstruction conditions of the Mojette transforms can be used to determine the minimum number of cameras required for tomography reconstruction, and its achieved reliability can be used as an indicator to predict the reconstruction quality. Besides, the 2D coplanar semicircular configuration exhibits a better performance than that of the 3D non-coplanar arrangement. When the 3D non-coplanar arrangement is adopted, the cameras should be widely distributed in the hemispherical space. The related research provides a theoretical basis for the establishment of the CTC system and other tomography modalities.

Computed tomography in resolving flame topology with internal optical blockage involved

This work reports the modification and optimization of a computed tomography (CT) algorithm to become capable of resolving an optical field with internal optical blockage (IOB) present. The IOB-practically, the opaque mechanical parts installed inside the measurement domain-prevents a portion of emitted light from transmitting to optical sensors. Such blockage disrupts the line-of-sight intensity integration on recorded projections and eventually leads to incorrect reconstructions. In the modified algorithm developed in this work, the positions of the obstacle are measured a priori, and then the discretized optical fields (i.e., voxels) are classified as those that participate in the CT process (named effective voxels) and those that are expelled, based on the relative positions of the imaging sensors, IOB, and light signal distribution. Finally, the effective voxels can be iteratively reconstructed by combining their projections on sensors that provide direct observation. Moreover, the impact of IOB on reconstruction accuracy is discussed under different sensor arrangements to provide hands-on guidance on sensor orientation selection in practical CT problems. The modified algorithm and sensor arrangement strategy are both numerically and experimentally validated by simulated phantoms and a two-branch premixed laminar flame in this work.

Correlation-based view registration for 3D tomography

This study reports a new, to the best of our knowledge, view registration method that can achieve high-quality tomographic reconstruction in spite of a large view registration (VR) error. The correlation-based view registration (CBVR) method is a directional orientation modification method based on the cross-correlation between measured projections and ray-tracings generated from the reconstruction, which can reduce the gross VR error to moderate levels by iterations. In the CBVR method, a traditional multi-camera VR process is first performed, based on the sensitivity of the projections to the VR error, and are evaluated and quantified for all cameras. Afterward, the orientation of each camera is iteratively updated based on the cross-correlation of the measured projections and the ray-tracings generated from the reconstruction calculated through all other cameras. The CBVR is consecutively validated by numerical and experimental studies. Through a numerical study on a controlled phantom introduced with 2% Gaussian noise, the CBVR method is proved to be able to reduce the large VR error (up to 4.8°) to 0.2° as well as to reduce the reconstruction error to ∼6.7% in 12 rounds of iterations, which is very close to that obtained without any VR error (6% caused by Gaussian noise only). The CBVR method is then demonstrated and validated by reconstructing a two-branch laminar flame. By implementing the method, the initial projection orientations are optimized from traditional multi-camera VR results within a range of ±3^∘, leading to effectively improved tomographic reconstruction of flame chemiluminescence distribution.

Large volume scanning laser induced fluorescence measurement of a bluff-body stabilised flame in an annular combustor

ABSTRACT

This study outlines a variant of three-dimensional OH planar laser-induced fluorescence and its application in characterising a single bluff body stabilised flame inside a 12 burner annular combustor. In this variant of the method a relatively large volume was scanned slowly in order to calculate the full three-dimensional Flame Surface Density (FSD) distribution. The method used a combination of two scanning directions to overcome bias errors associated with laser sheet positions close to the flame edges. The source of this bias error was confirmed numerically through a complimentary synthetic PLIF study, which was also used to refine the experimental setup. The bias error resulted in a reduction of FSD magnitude, although the method was still capable of capturing the flame structure. This was demonstrated by comparing the reconstructions from the two independent scan directions. Combining the data from both directions overcame the bias, and allowed flame asymmetry due to the confinement to be assessed. The FSD was used to determine the heat release rate of the flame with varying local azimuthal angle for different downstream regions. This highlighted the highly asymmetric structure, produced by the asymmetric confinement.

An improved deep learning-based algorithm for 3D reconstruction of vacuum arcs

Extensive attempts have been made to enable the application of deep learning to 3D plasma reconstruction. However, due to the limitation on the number of available training samples, deep learning-based methods have insufficient generalization ability compared to the traditional iterative methods. This paper proposes an improved algorithm named convolutional neural network-maximum likelihood expectation maximization-split-Bergman (CNN-MLEM-SB) based on the combination of the deep learning CNN and an iterative algorithm known as MLEM-SB. This method uses the prediction result of a CNN as the initial value and then corrects it using the MLEM-SB to obtain the final results. The proposed method is verified experimentally by reconstructing two types of vacuum arcs with and without transverse magnetic field (TMF) control. In addition, the CNN and the proposed algorithm are compared with respect to accuracy and generalization ability. The results show that the CNN can effectively reconstruct the arcs between a pair of disk contacts, which has specific distribution patterns: its structural similarity index measurement (SSIM) can reach 0.952. However, the SSIM decreases to 0.868 for the arc between a pair of TMF contacts, which is controlled by the TMF and has complex distribution patterns. Compared with the CNN reconstruction method, the proposed algorithm can achieve a higher reconstruction accuracy for any arc shape. Compared with the iterative algorithm, the proposed algorithm's reconstruction efficiency is higher by 38.24% and 35.36% for the vacuum arc between the disk and the TMF contacts, respectively.

Single-sensor filter-intensified fiber optic 4D tomographic CH* chemiluminesence flame measurements

Chemiluminesence is one of the most common reacting flow visualization techniques, in which a narrowband wavelength associated with species radicals is captured on an image sensor. This technique can provide key insights into flame physics, particularly when a full 3D field can be extracted. Tomographic imaging can capture 3D instantaneous information, but becomes impractical to use when the technique is extended to larger, heavier high-speed imaging equipment. This has resulted in many researchers using fiber-based endoscopes (FBE) to capture multiple views on a single image sensor. However, the introduction of the fiber bundle and corresponding equipment to image specific combustion radicals results in a low SNR imaging environment when captured at high repetition rates. Additionally, when varying equivalence ratios, the signal can become further diminished because the combustion radicals signal weakens at fuel rich and fuel lean conditions. Therefore, this work determines the efficacy of using a filter-intensified FBE approach to capture the CH* radical of a hydrocarbon flame under varying equivalence ratio conditions by comparing the resulting reconstructions to previous quantitative flame measurements.

Learning implicit light propagation from multi-flame projections for computed tomography of chemiluminescence

Classic algorithms for computed tomography of chemiluminescence include two main steps: tomographic weight matrix calculation using imaging models, and inverse calculation using algebraic reconstruction techniques (ARTs). However, pre-calculated weight matrices require a large amount of storage, and accurate voxel weights may not be obtained using a simplified imaging model. In this study, we propose a new, to the best of our knowledge, method named the multi-weight encode reconstruction network (Multi-WERNet) to learn the implicit light propagation physics from the multi-projections of different flames and simultaneously reconstruct the 3D flame chemiluminescence. The reconstructed results from Multi-WERNet are close to those of ART, and no radial streak is found, which is commonly seen in ART-based methods. With the help of information from different flames, the results reconstructed with 5 views using Multi-WERNet outperform the ART method. Moreover, Multi-WERNet successfully learns the implicit light propagation physics as a voxel weight encoder and can be transferred to unseen cases. Finally, Multi-WERNet is found to have higher robustness than ART in reconstruction with imperfect projections, which makes the algorithm more practical.

Adaptive weight matrix and phantom intensity learning for computed tomography of chemiluminescence

Classic algebraic reconstruction technique (ART) for computed tomography requires pre-determined weights of the voxels for the projected pixel values to build the equations. However, such weights cannot be accurately obtained in the application of chemiluminescence measurements due to the high physical complexity and computation resources required. Moreover, streaks arise in the results from ART method especially with imperfect projections. In this study, we propose a semi-case-wise learning-based method named Weight Encode Reconstruction Network (WERNet) to co-learn the target phantom intensities and the adaptive weight matrix of the case without labeling the target voxel set and thus offers a more applicable solution for computed tomography problems. Both numerical and experimental validations were conducted to evaluate the algorithm. In the numerical test, with the help of gradient normalization, the WERNet reconstructed voxel set with a high accuracy and showed a higher capability of denoising compared to the classic ART methods. In the experimental test, WERNet produces comparable results to the ART method while having a better performance in avoiding the streaks. Furthermore, with the adaptive weight matrix, WERNet is not sensitive to the ensemble intensity of the projection which shows much better robustness than ART method.

Linear multispectral absorption tomography based on regularized iterative methods

A regularization approach of iterative algorithms was proposed to reconstruct the two-dimensional temperature and concentration distributions based on linear multispectral absorption tomography (MAT). This method introduces a secondary prior into a classical iterative algorithm via regularization to improve the reconstruction accuracy. Numerical studies revealed that the regularized iteration outperformed the classical and superiorized versions under various noisy conditions and with different number of spectral lines. The algorithms were also tested with the existing experimental data of a premixed flat flame produced by a McKenna burner. The comparison between the reconstructions and the measured temperature profile using thermocouples confirmed the superiority of our proposed regularized iterative method.

3D reconstruction of dynamic behaviors of vacuum arcs under transverse magnetic fields via computer tomography

The transverse magnetic field (TMF) contacts make the vacuum arcs deviate from the axisymmetric structure, so complete spatiotemporal evolution information of the plasma cannot be obtained by adopting one- or two-dimensional (2D) diagnostic methods. To address the issues, computer tomography was introduced in this paper. First, a multi-angle diagnostic imaging system based on split fiber bundles was proposed, which used a high-speed camera to simultaneously acquire eight angles of the arc image over time. In addition, a tomography algorithm called the maximum likelihood expectation maximum with Split Bregman denoising was proposed to reconstruct the dynamic spatiotemporal characteristics of the arc under complex conditions. Then, the three-dimensional (3D) distribution of Cu i and Cr i particles inside the contact gap was obtained by adopting optical filters. The 3D distribution of the vacuum arc had shown an obvious asymmetrical pattern under the TMF contacts, and there was a ring-like aggregation zone inside the arc, which can cause severe ablation on the anode contacts. According to the reconstructed 3D distribution of Cu i and Cr i, it is found that the metal vapor was mainly concentrated near the electrode surface and showed a clear distribution of non-uniform aggregates, while the concentration of particles in the gap was low. Moreover, on the cathode surface, the cathode spots moved in the form of groups driven by the TMF, while the anode surface was ablated by the electric arc, and the metal vapor existed in the form of bands.

Algorithm optimization of cross-interfaces computed tomography into full field

Tomographic approaches in confined space require advanced imaging algorithms that can properly consider the refractive distortion as the imaging rays pass through the optical wall. Our previous work established an algorithm (cross-interfaces computed tomography, CICT) and practically solved tomographic problems in confined space. However, critical restriction was found in CICT, which is that images simulated at small azimuth angles are contaminated with noticeable signal loss and become unusable. Based on this recognition, this work has developed an improved tomography approach, namely, full-field cross-interfaces computed tomography (FCICT), to extend the available view angles to all perspectives. The key to this approach involves the 3D domain discretization using voxel parallelepipeds instead of traditional voxel layers to establish the ray-tracing relationship between imaging planes and the measurement domain. The imaging process of FCICT is first validated by quantitatively comparing the grid imaging locations in measured and simulated projections of a calibration plate. By evenly distributing the view angles in the whole azimuth angle range, the FCICT reconstruction is then numerically validated by reconstructing a simulated double-cone flame phantom. The reconstruction presents a high correlation coefficient of ${\sim}{98}\%$ with the original phantom. Finally, the FCICT is employed to reconstruct an ethylene-air premixed flame. Comparisons show that re-projections generated by the FCICT reconstruction are in accordance with measured flame images, with the mean correlation coefficients of more than 95%.

Sparse regularization-based reconstruction for 3D flame chemiluminescence tomography

Flame chemiluminescence tomography (FCT) is a non-intrusive method that is based on using cameras to measure projections, and it plays a crucial role in combustion diagnostics and measurement. Mathematically, the inversion problem is ill-posed, and in the case of limited optical accessibility in practical applications, it is rank deficient. Therefore, the solution process should ideally be supported by prior information, which can be based on the known physics. In this work, the total variation (TV) regularization has been combined with the well-known algebraic reconstruction technique (ART) for practical FCT applications. The TV method endorses smoothness while also preserving typical flame features such as the flame front. Split Bregman iteration has been adopted for TV minimization. Five different noise conditions and the chosen regularization parameter have been tested in numerical studies. Additionally, for the 12 perspectives, an experimental FCT system is demonstrated, which is utilized to recover the three-dimensional (3D) chemiluminescence distribution of candle flames. Both the numerical and experimental studies show that the typical line artifacts that appear with the conventional ART algorithm when recovering the continuous chemiluminescence field of the flames are significantly reduced with the proposed algorithm.

Development and validation of a reconstruction approach for three-dimensional confined-space tomography problems

This work reports the development and validation of a new tomography approach, termed cross-interfaces computed tomography (CICT), to address confined-space tomography problems. Many practical tomography problems require imaging through optical walls, which may encounter light refractions that seriously influence the imaging process and deteriorate the three-dimensional (3D) reconstruction. Past efforts have primarily focused on developing open-space tomography algorithms, but these algorithms are not extendable to confined-space problems unless the imaging process from the 3D target and its line-of-sight two-dimensional (2D) images (defined as "projections") is properly adjusted. The CICT approach is therefore proposed in this work to establish an algorithm describing the mapping relationship between the optical signal field of the target and its projections. The CICT imaging algorithm is first validated by quantitatively comparing measured and simulated projections of a calibration plate through an optical cylinder. Then the CICT reconstruction is numerically and experimentally validated using a simulated flame phantom and a laminar cone flame, respectively. Compared to reconstructions formed by traditional open-space tomography, the CICT approach is demonstrated to be capable of resolving confined-space problems with significantly improved accuracy.

Quantitative Measurement of OH* and CH* Chemiluminescence in Jet Diffusion Flames

Quantitative measurement of chemiluminescence is a challenging work that limits the development of combustion diagnostics based on chemiluminescence. Here, we present a feasible method to obtain effective quantitative chemiluminescence data with an integrating sphere uniform light source. Spatial distribution images of OH* and CH* radiation from methane laminar diffusion flames were acquired using intensified charge-coupled device (CCD) cameras coupled with multiple lenses and narrow-band-pass filters. After the process of eliminating background emissions by three filters and the Abel inverse transformation, the chemiluminescence intensity was converted to a radiating rate based on the uniform light source. The simulated distributions of OH* and CH* agree well with the experimental results. It has also been found that the distribution of OH* is more extensive and closer to the flame front than that of CH*, demonstrating that OH* is more representative of the flame structure. Based on the change in the reaction rate of different formation reactions, OH* distributions can be divided into three regions: intense section near the nozzle, transition section in the middle of the flame, and secondary section downstream the flame, whereas CH* only exists in the first two regions. In addition, as the velocity ratio of methane and co-flowing air increases, the main reactions become more intense, while the secondary reaction of OH* becomes weaker.

Data-driven three-dimensional super-resolution imaging of a turbulent jet flame using a generative adversarial network

Three-dimensional (3D) computed tomography (CT) is becoming a well-established tool for turbulent combustion diagnostics. However, the 3D CT technique suffers from contradictory demands of spatial resolution and domain size. This work therefore reports a data-driven 3D super-resolution approach to enhance the spatial resolution by two times along each spatial direction. The approach, named 3D super-resolution generative adversarial network (3D-SR-GAN), builds a generator and a discriminator network to learn the topographic information and infer high-resolution 3D turbulent flame structure with a given low-resolution counterpart. This work uses numerically simulated 3D turbulent jet flame structures as training data to update model parameters of the GAN network. Extensive performance evaluations are then conducted to show the superiority of the proposed 3D-SR-GAN network, compared with other direct interpolation methods. The results show that a convincing super-resolution (SR) operation with the overall error of ∼4% and the peak signal-to-noise ratio of 37 dB can be reached with an upscaling factor of 2, representing an eight times enhancement of the total voxel number. Moreover, the trained network can predict the SR structure of the jet flame with a different Reynolds number without retraining the network parameters.

Research on a quantitative method for three-dimensional computed tomography of chemiluminescence

To develop a more advanced 3D computed tomography of the chemiluminescence method, the first quantitative 3D diagnosis was realized. The nonlinearity coefficient, the nonuniformity coefficient of the camera response, and various optical fiber attenuation coefficients were obtained through correction experiments. The conversion relationship between the number of photons released by the target object per unit time and the camera gray value at a specified solid angle was also calibrated. To verify the quantitative reconstruction equation, 3D reconstructions of a methane-air flat flame and a simulated phantom were performed for comparison. The method can overcome artificial distortions caused by uncorrected reconstruction.

Three-dimensional rapid flame chemiluminescence tomography via deep learning

Flame chemiluminescence tomography (FCT) plays an important role in combustion monitoring and diagnostics due to the easy implementation and non-intrusion. However, on account of the high data throughput and the inefficiency of the conventional iteration methods, the 3D reconstructions in FCT are typically conducted off-line and time-consuming. In this work, we present a 3D rapid FCT reconstruction system based on convolutional neural networks (CNN) model for practical combustion measurement, which has the ability to reconstruct 3D flame distribution rapidly after training process. First, the numerical simulation has been performed by creating three cases of phantoms which are designed to mimic the 3D conical flame. Next, after the evaluation of loss function and training time, the optimal CNN architecture has been determined and certificated quantitatively. Finally, a real time FCT system consisting of 12 color CCD cameras is realized and multispectral separation algorithm is adopted to extract CH* and C2* components. Certificated by practical measurements testing, the proposed CNN model is able to reconstruct 3D flame structure from real time captured projections with credible accuracy and structure similarity. Furthermore, compared with conventional iteration reconstruction method, the proposed CNN model shows better performance on obviously improving reconstruction speed and it is expected to achieve 3D rapid monitoring of flames.

High spatial resolution computed tomography of chemiluminescence with densely sampled parallel projections

Computed tomography of chemiluminescence (CTC) is an effective tool for combustion diagnostics by using optical detectors to capture the projections of luminescence from multiple views and realizing the three-dimensional (3D) reconstruction by computed tomography (CT) theories. In the existing CTC, ordinary commodity lenses were employed in the system for imaging, the imaging effects complicate the projection model and the low sampling rate decreases the spatial resolution and reconstruction accuracy. In classical CT techniques, parallel projection based on 2D Radon transform is the simplest model, which has been widely used in CT applications. In this work, double telecentric lens is introduced in CTC to realize the acquisition of parallel projection with high sampling rate. Despite the parallel projection CT theories have been well studied, there are still a few theoretical and technological drawbacks need to be solved when utilizing double telecentric lens in CTC. Firstly, a simple method based on bilinear interpolation is studied to improve the calculation accuracy of the weight matrix. Secondly, the exact reconstruction condition for parallel projections is studied based on the discrete Radon transform theory. It establishes the theoretical relationship of the reconstruction quality and the sampling rate of the projections, the number of views, the range and the spatial resolution of the reconstructed region. In experiment, camera calibration technique for double telecentric lens is studied, and the results of which are used for projection correction. The tomographic reconstructions of an axisymmetric flame demonstrate the feasibility and accuracy of the studies.

Time-resolved laser absorption imaging of ethane at 2 kHz in unsteady partially premixed flames

In this work, laser absorption imaging is expanded in temporal resolution capability to kilohertz measurement rates by coupling sparsely sampled wavelength scanning and digital image postprocessing for diffraction correction. The setup employs an interband cascade laser near 3.34 μm to backlight an unsteady flame for species-specific 2D imaging of ethane (C₂H₆) with a high-speed infrared camera. Injection-current laser tuning is achieved with a high-duty-cycle square wave that involves a sparse number of data samples per scan to recover an integrated absorbance area for the target ethane feature, thereby minimizing the number of camera frames needed. In conjunction, an image-by-image computational diffraction pattern removal scheme is employed based on inverse Fourier transformations with the aim to reject high spatial frequencies associated with diffraction while preserving spatial resolution of the flow field, without averaging in time. These methods are applied to achieve species-specific 2D cinematography of ethane absorption in an unsteady partially premixed flame with a spatial resolution of ∼415  μm and a temporal resolution of 2 kHz.

Development of a modular, high-speed plenoptic-camera for 3D flow-measurement

This paper describes the development of a Modular Plenoptic Adaptor (MPA) for rapid and reversible conversion of high-speed cameras into plenoptic imaging systems, with the primary goal of enabling single-camera, time-resolved 3D flow-measurements. The MPA consists of a regular imaging lens, a microlens array, a tilt-adjustable microlens mount and an optical relay, which are collectively installed onto a high-speed camera through a standard lens mount. Each component within the system is swappable to optimize for specific imaging applications. In this study, multiple configurations of the MPA were tested and they demonstrated the ability to refocus and shift perspectives within high-speed scenes after capture. Additionally, the MPA demonstrated 3D reconstruction of captured scenes with <1% spatial error across a volume spanning approximately 50×30×50mm3. Finally, the MPA also demonstrated reconstruction of a 3D droplets-field with sufficient quality to support qualitatively accurate plenoptic particle image velocimetry (PPIV) calculations.

3D tomography reconstruction improved by integrating view registration

Tomographic measurements involve two steps: view registration (VR) to determine the orientation of the projections and the subsequent tomography reconstruction. Therefore, the practical error in both steps impacts the overall accuracy of the final tomographic measurements. Past work treated these two steps separately. This work shows that the overall tomography accuracy can be enhanced substantially if these two steps are considered holistically because there is an opportunity for each step to leverage the information in the other step to improve the overall accuracy if they are considered holistically. Based on this recognition, this work has developed a new method called the reconstruction integration view registration (RIVR) method to implement such a holistic scheme. The key of this implementation involved the use of the Metropolis criterion to adjust the initial orientation provided by the traditional VR process dynamically. Both controlled experiments and accompanying numerical analyses were conducted to validate the RIVR method. Two sets of controlled experiments were conducted and analyzed, including a static uniform dye solution and turbulent flows, where the RIVR technique was demonstrated to significantly reduce the overall reconstruction error (by ∼37% and ∼35%, respectively) compared to past methods that treated VR and tomography separately.

Numerical and experimental validation of a single-camera 3D velocimetry based on endoscopic tomography

Tomographic velocimetry as a 3D technique has attracted substantial research interests in recent years due to the pressing need for investigations of complex turbulent flows, which are inherently inhomogeneous. However, tomographic velocimetry usually suffers from high experimental costs, especially due to the formidable expenses of multiple high-speed cameras and the excitation laser source. To overcome this limitation, a cost-effective technique called endoscopic tomographic velocimetry has been developed in this work. As a single-camera system, nine projections of the target 3D luminous field at consecutive time instants can be registered from different orientations with one camera and customized fiber bundles, while this is possible only with the same number of cameras in a classical tomographic velocimetry system. Extensive numerical simulations were conducted with three inversion algorithms and two velocity calculation methods. According to RMS error analysis, it was found that the algebraic reconstruction technique outperformed the other two inversion algorithms, and the 3D optical flow method exhibited a better performance than cross correlation in terms of both accuracy and noise immunity. Proof-of-concept experiments were also performed to validate our developed system. The results suggested that an average reconstruction error of the artificially generated 3D velocity field was less than 6%, indicating good performance of the velocimetry system. Although this technique was demonstrated by reconstructing continuous luminous fields, it can be easily extended to discrete ones, which are typically adopted in particle image velocimetry. This technique is promising not only for flow diagnostics but other research areas such as biomedical imaging.

Time-resolved measurements of a swirl flame at 4 kHz via computed tomography of chemiluminescence

Computed tomography of a chemiluminescence (CTC) system was implemented to provide time-resolved 3D measurements of an unconfined turbulent swirl flame. This system was designed in a cost-effective manner and employed three customized view registration assemblies to simultaneously capture eight projections of the target flame at a repetition rate of 4 kHz. Both time-resolved and time-averaged tomographic reconstructions were performed based on data acquired for a duration of 250 ms. Both qualitative and quantitative validations suggested the correctness of our implementation. The time-resolved instantaneous reconstructions successfully captured the evolution of the structural features of the swirl flame such as local extinctions and the helical mode. Based on the reconstructions, the centroids of chemiluminescence for all the layers were calculated. The trajectory of these centroids provided insights into the flow motion and suggested a rotating helical structure of the swirl flame. These results demonstrated the feasibility of resolving the dynamics of turbulent swirl flames with a kHz temporal resolution using the relatively inexpensive CTC system.

Toward real-time volumetric tomography for combustion diagnostics via dimension reduction

Volumetric tomography for combustion diagnostics is experiencing significant progress during the past few years due to its capability of imaging evolving turbulent flows. Such capability facilitates the understanding of the mechanisms behind complicated combustion phenomena such as lean blowout, acoustic oscillations, and formation of soot particles. However, these techniques are not flawless and suffer from high computational cost which prevents them from applications where real-time reconstructions and online monitoring are necessary. In this Letter, we propose a new reconstruction method that can effectively reduce the dimension of the inversion problem, which can then be solved with a minimum computational effort. This method and a classical iterative method were tested against each other using a proof-of-concept experiment in which endoscopic computed tomography of chemiluminescence (CTC) was implemented. The results show that the proposed method can dramatically reduce the computational time and, at the same time, maintain similar reconstruction accuracy, as opposed to the classical approach. Although this Letter was discussed under the context of CTC, it can be applied universally to other modalities of volumetric tomography such as volumetric laser-induced fluorescence.

On the quantification of spatial resolution for three-dimensional computed tomography of chemiluminescence

Three-dimensional computed tomography of chemiluminescence (CTC) for combustion diagnostics is attracting a surged research interest due to recent progress in sensor technologies and reduced costs of high-speed cameras. For example, it has been applied to recover the 3D distributions of intermediate chemical species such as CH* and OH*, heat release rate, and flame topology. Although these applications were demonstrated to be successful, there are still a few drawbacks of this technique that have not be cured. For example, to the best of the authors' knowledge, all the imaging models that have been developed so far ignore the imperfections of cameras such as lens distortion and skewness. However, this will unavoidably introduce errors into the weight matrix. In addition, spatial resolution of a CTC system is a critical performance parameter. However, it has only been studied qualitatively and no quantitative quantification method is reported so far. This work aims to solve these problems by improving the imaging model and developing a method based on edge spread function for the quantification of spatial resolution. Although this work is conducted under the context of CTC for combustion diagnostics, it also provides useful insights for other tomographic modalities such as volumetric laser-induced fluorescence and tomographic laser-induced incandescence.

Demonstration of 3D computed tomography of chemiluminescence with a restricted field of view

Three-dimensional imaging techniques have experienced a surge in research interest during the past few years due to advancements in both hardware, i.e., the sensor arrays and data acquisition systems, and new imaging concepts, such as light field imaging and compressed sensing. Computed tomography of chemiluminescence (CTC) is an intriguing technique for combustion diagnostics due to its ease of implementation, as no excitation source is required in measurements. It has been applied extensively for the retrieval of intermediate species such as CH^*/OH^*, from which the flame topology can be obtained. However, all previous demonstrations or applications were performed under the assumption that a complete field of view is available for all projections. However, this prerequisite cannot be guaranteed for some practical scenarios, such as engine measurements, in which optical access is extremely limited and a portion of the field of view is unavoidably blocked, especially when a considerable number of projections are required. This work aims to develop an improved CTC modality that can handle projections with a restricted field of view, and to suggest the best strategy for tomographic reconstruction under such experimental conditions. Although this technique is discussed under the context of combustion diagnostics, it can also be useful and adapted for other tomographic areas, such as biomedical imaging.

Development of a beam optimization method for absorption-based tomography

Absorption tomography is an imaging technique that has been used simultaneously to image multiple scalar parameters, such as temperature and species concentration for combustion diagnostics. Practical combustors, such as internal combustion engines and gas turbine engines, only allow limited optical access, and typically a few (ca. 20-40) beams are available to probe the domain of interest. With such limited spatial sampling, it is non-trivial to optimize beam arrangement for a faithful reconstruction. Previous efforts on beam optimization rely on either heuristic/empirical methods lacking rigorous mathematical derivation or were derived by assuming certain prior information in the tomographic inversion. This paper aims to develop an approach that is expected to be especially useful when prior information is not easily available or intended to be included in the inversion processes. We demonstrate that the orthogonality between rows of the weight matrix directly correlates with reconstruction fidelity and can be used as an effective predictor for beam optimization. A systematic comparison between our method and the existing ones in the literature suggests the validity of our method. We expect this method to be valuable for not only the absorption tomography but also other tomographic modalities.

Benchmark evaluation of inversion algorithms for tomographic absorption spectroscopy

Tomographic absorption spectroscopy (TAS) is experiencing a surge of interest due to recent progress in laser technology and advanced imaging concepts such as nonlinear tomography and compressed sensing. Nevertheless, even though numerous algorithms have been adapted from other tomographic areas such as medical imaging and engineering process control, and applied in TAS applications, systematic comparison between those methods has not been investigated. In this work, we aim to test major inversion algorithms on both the so-called rank-deficient (RD) and discrete ill-posed (DIP) problems. Comparative studies were performed on extensive cases, and the results for three representative phantoms are reported here. Other important topics such as determination of control parameters and the semiconvergent behavior of iterative methods have also been studied. According to our study, Landweber outperformed other methods for two RD cases and is slightly inferior to the maximum likelihood expectation maximization (MLEM) algorithm for the third one. It has also been found that Landweber and MLEM feature better immunity to semiconvergence than the others; however, since MLEM is sensitive to an initial guess, it is less robust than Landweber. On the other hand, the truncated singular value decomposition (TSVD) method is recommended for DIP problems due to its superior performance as it can effectively suppress detrimental effects from noise, which will be amplified during the inversion procedure. It should be emphasized that even though this study was conducted under the context of TAS, we expect it to provide useful insights for other tomographic modalities.

Three-dimensional dynamic measurements of CH* and C2* concentrations in flame using simultaneous chemiluminescence tomography

The species concentrations of flame chemiluminescence play important role in combustion diagnostics, such as CH* and C2* of hydrocarbon flame, which can provide specific characteristics in combustion control and monitoring. In order to realize both CH* and C2* chemiluminescence intensity detection in propane-air diffusion flame simultaneously, we present three-dimensional dynamic flame detecting method for species concentration determination. Firstly, quantitative flame chemiluminescence multispectral separation technique based on color cameras coupled with double-channel bandpass filters is adopted for dual channel signal division. Next, flame chemiluminescence tomography combining with multi-directional simultaneous capturing is proposed for real time three dimensional observations and detection in flame. Moreover, the proposed technique can quantitatively provide comparison of species intensity between CH* and C2* for further analysis. Considering its credible detecting accuracy and simple requirements, it is believed the proposed technique can be widely used in combustion diagnostics.

Advanced Laser-Based Techniques for Gas-Phase Diagnostics in Combustion and Aerospace Engineering

Gaining information of species, temperature, and velocity distributions in turbulent combustion and high-speed reactive flows is challenging, particularly for conducting measurements without influencing the experimental object itself. The use of optical and spectroscopic techniques, and in particular laser-based diagnostics, has shown outstanding abilities for performing non-intrusive in situ diagnostics. The development of instrumentation, such as robust lasers with high pulse energy, ultra-short pulse duration, and high repetition rate along with digitized cameras exhibiting high sensitivity, large dynamic range, and frame rates on the order of MHz, has opened up for temporally and spatially resolved volumetric measurements of extreme dynamics and complexities. The aim of this article is to present selected important laser-based techniques for gas-phase diagnostics focusing on their applications in combustion and aerospace engineering. Applicable laser-based techniques for investigations of turbulent flows and combustion such as planar laser-induced fluorescence, Raman and Rayleigh scattering, coherent anti-Stokes Raman scattering, laser-induced grating scattering, particle image velocimetry, laser Doppler anemometry, and tomographic imaging are reviewed and described with some background physics. In addition, demands on instrumentation are further discussed to give insight in the possibilities that are offered by laser flow diagnostics.

Implementation of multidirectional moiré computerized tomography: multidirectional affine calibration

To realize three-dimensional (3D) instantaneous diagnoses for flow fields, many multidirectional optical computerized tomographic (optical CT) techniques based on laser interferometry have been proposed. Projections from different directions of these tomographic systems are captured simultaneously to reconstruct the test field. These projections are independent from each other. However, due to the inevitable errors from installation and difference between optical elements, projections will be imaged with different distortion and located at different positions on the sensors. Therefore, a multidirectional calibration should be performed to remap these projections to a unified coordinate system before CT reconstruction. As far as we know, the multidirectional calibration problem for laser interferometric CT techniques has never been discussed in previous research. In this paper, a six-directional moiré tomographic system is designed. Considering the projection characteristics of moiré deflectometry, a multidirectional affine calibration method is proposed to determine the extrinsic and intrinsic parameters of tomographic projections. With the calibration results, projections can be remapped to the unified coordinate system and the 3D distributions of flow field can be reconstructed.

Hybrid algorithm for three-dimensional flame chemiluminescence tomography based on imaging overexposure compensation

Flame tomography of chemiluminescence is a necessary combustion diagnostic technique that provides instantaneous 3D information on flame structure and excited species concentrations. During combustion diagnostics, imaging overexposure always causes missing information, which obviously decreases the accuracy in further reconstructions. In order to compensate imaging overexposure, a hybrid algorithm combining weight correction and Tikhonov's regularization is proposed in this paper. The intensity of the overexposure region can be estimated via the accumulation of weight coefficients. Meanwhile, Tikhonov's regularization is utilized to ameliorate the quality of reconstruction. The numerical simulation quantitatively evaluates the performance of the hybrid algorithm. Additionally, an experiment system consisting of 12 cameras was established to reconstruct the 3D combustion structure of axisymmetric flame with different exposure time settings. This work further investigates dynamic nonaxisymmetric propane diffusion flame. The obtained results show that the hybrid algorithm can effectively reveal the flame structure less influenced by imaging overexposure and achieve better results.

Development and validation of a reconstruction algorithm for three-dimensional nonlinear tomography problems

This work reports the development and experimental validation of a reconstruction algorithm for three-dimensional (3D) nonlinear tomography problems. Many optical tomography problems encountered in practice are nonlinear, for example, due to significant absorption, multiple-scattering, or radiation trapping. Past research efforts have predominately focused on reconstruction algorithms for linear problems, and these algorithms are not readily extendable to nonlinear problems due to several challenges. These challenges include the computational cost caused by the nonlinearity (which was compounded by the large scale of the problems when they are 3D), the limited view angles available in many practical applications, and the measurement uncertainty. A new algorithm was therefore developed to overcome these challenges. The algorithm was validated both numerically and experimentally, and was demonstrated to be able to solve a range of nonlinear tomography problems with significantly enhanced efficiency and accuracy compared to existing algorithms.

Comparison of 2D and 3D flame topography measured by planar laser-induced fluorescence and tomographic chemiluminescence

The goal of this work was to contrast and compare the 2D and 3D flame topography of a turbulent flame. The 2D measurements were obtained using CH-based (methylidyne radical-based) planar laser-induced fluorescence (PLIF), and the 3D measurements were obtained through a tomographic chemiluminescence (TC) technique. Both PLIF and TC were performed simultaneously on a turbulent premixed Bunsen flame. The PLIF measurements were then compared to a cross section of the 3D TC measurements, both to provide a validation to the 3D measurements and also to illustrate the differences in flame structures inferred from the 2D and 3D measurements.

Single-shot volumetric laser induced fluorescence (VLIF) measurements in turbulent flows seeded with iodine

This work reports the experimental demonstration of single-shot visualization of turbulent flows in all three spatial dimensions (3D) based on volumetric laser induced fluorescence (VLIF). The measurements were performed based on the LIF signal of iodine (I2) vapor seeded in the flow. In contrast to established planar LIF (PLIF) technique, the VLIF technique excited the seeded I2 vapor volumetrically by a thick laser slab. The volumetric LIF signals emitted were then simultaneously collected by a total of five cameras from five different orientations, based on which a 3D tomographic reconstruction was performed to obtain the 3D distribution of the I2 vapor in the target flow. Single-shot measurements (with a measurement duration of a few ns) were demonstrated in a 50 mm × 50 mm × 50 mm volume with a nominal spatial resolution of 0.42 mm and an actual resolution of ~0.71 mm in all three dimensions (corresponding to a total of 120 × 120 × 120 voxels).

Multi-directional 3D flame chemiluminescence tomography based on lens imaging

Flame chemiluminescence tomography (FCT) has been widely used in flame diagnostics for three-dimensional (3D), spatially resolved measurements of instantaneous flame geometry and, to some extent, of species concentrations. However, in most studies, tomographic reconstructions are based on a traditional parallel projection model. Due to the light collection characteristics of a lens, a parallel projection model is not appropriate for the practical optical setups that are used for emission imaging, particularly at small F-numbers. Taking the light collection effect of the lens into account, this Letter establishes a complete and novel tomographic theory for a multi-directional tomography system consisting of a lens and CCD cameras. A modified camera calibration method is presented first. It determines the exact spatial locations and intrinsic parameters of the cameras. A 3D projection model based on the lens imaging theory is then proposed and integrated into the multiplicative algebraic reconstruction technique (MART). The new approach is demonstrated with a 12-camera system that is used to reconstruct the emission field of a propane flame, thereby resolving space and time.

3D flame topography obtained by tomographic chemiluminescence with direct comparison to planar Mie scattering measurements

This work reports the measurements of 3D flame topography using tomographic chemiluminescence and its validation by direct comparison against planar Mie scattering measurements. Tomographic measurements of the 3D topography of various well-controlled laboratory flames were performed using projections measured by seven cameras, and a simultaneous Mie scattering measurement was performed to measure a 2D cross section of the 3D flame topography. The tomographic measurements were based on chemiluminescence emissions from the flame, and the Mie scattering measurements were based on micrometer-size oil droplets seeded into the flow. The flame topography derived from the 3D tomographic and the Mie scattering measurement was then directly compared. The results show that the flame topography obtained from tomographic chemiluminescence and the Mie measurement agreed qualitatively (i.e., both methods yielded the same profile of the flame fronts), but a quantitative difference on the order of millimeters was observed between these two methods. These results are expected to be useful for understanding the capabilities and limitations of the 3D tomographic and Mie scattering techniques in combustion diagnostics.

Analysis of four-dimensional Mie imaging using fiber-based endoscopes

This work reports the demonstration and analysis of four-dimensional (4D) imaging measurements in two-phase flows using fiber-based endoscopes (FBEs). Such 4D measurements resolve the droplet distribution in two-phase flows in all three spatial directions and with a temporal resolution of up to 5 kHz. Demonstration measurements were performed in a measurement volume of 85 mm × 85 mm × 85 mm discretized into 64 × 64 × 64 voxels to illustrate FBEs' potential for facilitating practical implementation of 4D tomographic measurements. Mathematical analyses were performed to quantify the fundamental advantage of FBEs to enhance the reconstruction fidelity.

Characterization of linearity and uniformity of fiber-based endoscopes for 3D combustion measurements

This work reports the application of fiber-based endoscopes (FBEs) for instantaneous three-dimensional (3D) flow and combustion measurements, with an emphasis on characterizing the linearity and uniformity of the FBEs and exploring their potential for obtaining quantitative measurements. Controlled experiments were performed using a uniform illuminator to characterize the linearity and uniformity of the FBEs. Based on such characterization, 3D instantaneous measurements of flames were demonstrated by a combined use of FBEs and tomography. To obtain 3D flame measurement, 3D tomographic reconstructions were made from multiple projections of the target flames collected from various orientations by the FBEs. The results illustrate the potential of FBEs to obtain quantitative 3D flow and combustion measurements and also the advantages FBEs offer, including overcoming optical access restrictions and equipment cost.

Experimental demonstration of 4D imaging in two-phase flows based on computed tomography at 5 kHz

Turbulent flows inherently feature 3D spatial structures and temporal dynamics. As a result, 4D experimental techniques have been long desired to fully resolve turbulent flows in all three spatial directions and time. This work describes the demonstration of such 4D measurements in two-phase flows using computed tomography and Mie scattering. Demonstration measurements were performed in airflows seeded with water droplets at a 5 kHz frame rate, with an exposure time of 0.2 ms and a measurement volume of 85  mm×85  mm×85  mm discretized into 128×128×128 voxels. Experimental and computational studies have been conducted, with a focus on comparison and validation of the 3D reconstructions against experiments performed in flows with recognizable patterns.

Volumetric imaging of turbulent reactive flows at kHz based on computed tomography

Diagnostics with three-dimensional (3D) spatial resolution and rapid temporal resolution have been long desired to resolve the complicated turbulence-chemistry interactions. This paper describes a method based on based on tomographic chemiluminescence (TC) to address this diagnostic need. The TC technique used multiple cameras to simultaneously record CH* chemiluminescence emitted by turbulent flames from different view angles. A 3D tomographic algorithm was then applied to reconstruct the instantaneous flame structures volumetrically. Both experimental and computational studies have been conducted to demonstrate and validate the 3D measurements. Experimental results were obtained instantaneously at kHz temporal rate, in a volume of 16 × 16 × 16 cm3, and with a spatial resolution estimated to be 2~3 mm. Computations were conducted to simulate the experimental conditions for comparison and validation.

Practical aspects of implementing three-dimensional tomography inversion for volumetric flame imaging

Instantaneous three-dimensional (3D) measurements have been long desired to resolve the spatial structures of turbulent flows and flame. Previous efforts have demonstrated tomography as a promising technique to enable such measurements. To facilitate the practical application, this work investigated four practical aspects for implementing 3D tomographic under the context of volumetric combustion diagnostics. Both numerical simulations and controlled experiments were performed to study: (1) the termination criteria of the inversion algorithm; (2) the effects of regularization and the determination of the optimal regularization factor; (3) the effects of a number of views; and (4) the impact of the resolution of the projection measurements. The results obtained have illustrated the effects of these practical aspects on the accuracy and spatial resolution of volumetric tomography. Furthermore, all these aspects are related to the complexity and implementing cost (both hardware cost and computational cost). Therefore, the results obtained in this work are expected to be valuable for the design and implementation of practical 3D diagnostics.