Toward in-cylinder absorption tomography in a production engine

Linear absorption tomography with velocimetry (LATV) for multiparameter measurements in high-speed flows

We present a linear model for absorption tomography with velocimetry (LATV) to reconstruct 2D distributions of partial pressure, temperature, and streamwise velocity in a high-speed flow. Synthetic measurements are generated by multi-beam tunable diode laser absorption spectroscopy (TDLAS). The measurement plane is tilted relative to the streamwise direction and absorbance spectra are Doppler-shifted by the gas flow. Reconstruction comprises two stages. First, the thermodynamic state is obtained by reconstructing two or more integrated absorption coefficients and evaluating local Boltzmann plots. Second, the velocity field is directly reconstructed from absorbance-weighted linecenters. Absorbance data are inferred by Voigt fitting and reconstructions are quickly computed by matrix-vector multiplication. Nonlinear parameter combinations, such as the mass flow, are more accurate when computed by LATV than estimates obtained by assuming uniform gas properties along each beam.

Reconstruction of two-dimensional velocity distribution in scramjet by laser absorption spectroscopy tomography

We propose a method to reconstruct the two-dimensional (2D) velocity distribution of flow fields by laser absorption spectroscopy tomography. A mathematic model is established to reveal the dependence of spectral absorbance on line-of-sight velocity distribution. Then, with multiple laser beams from different angular views covering the region of interest, a nonlinear equation set of 2D velocity distribution is established according to the model. The integrated absorbance coefficient distribution is reconstructed using the Landweber iteration algorithm and substituted into the nonlinear equation set for further simplification. Finally, the velocity distribution is reconstructed by solving the simplified equation group via the interior point algorithm. The proposed method is validated numerically by reconstructing the velocity distribution of water molecules, as calculated by computational fluid dynamics, over a cross section of a double-mode scramjet combustor. The method does not require adding extra tracer particles and avoids issues arising from the short lifetime of molecular tags. It is suitable for diagnosis of high-speed flow fields.

Rapid tomographic reconstruction based on machine learning for time-resolved combustion diagnostics

Optical tomography has attracted surged research efforts recently due to the progress in both the imaging concepts and the sensor and laser technologies. The high spatial and temporal resolutions achievable by these methods provide unprecedented opportunity for diagnosis of complicated turbulent combustion. However, due to the high data throughput and the inefficiency of the prevailing iterative methods, the tomographic reconstructions which are typically conducted off-line are computationally formidable. In this work, we propose an efficient inversion method based on a machine learning algorithm, which can extract useful information from the previous reconstructions and build efficient neural networks to serve as a surrogate model to rapidly predict the reconstructions. Extreme learning machine is cited here as an example for demonstrative purpose simply due to its ease of implementation, fast learning speed, and good generalization performance. Extensive numerical studies were performed, and the results show that the new method can dramatically reduce the computational time compared with the classical iterative methods. This technique is expected to be an alternative to existing methods when sufficient training data are available. Although this work is discussed under the context of tomographic absorption spectroscopy, we expect it to be useful also to other high speed tomographic modalities such as volumetric laser-induced fluorescence and tomographic laser-induced incandescence which have been demonstrated for combustion diagnostics.

Improving chemical species tomography of turbulent flows using covariance estimation

Chemical species tomography (CST) experiments can be divided into limited-data and full-rank cases. Both require solving ill-posed inverse problems, and thus the measurement data must be supplemented with prior information to carry out reconstructions. The Bayesian framework formalizes the role of additive information, expressed as the mean and covariance of a joint-normal prior probability density function. We present techniques for estimating the spatial covariance of a flow under limited-data and full-rank conditions. Our results show that incorporating a covariance estimate into CST reconstruction via a Bayesian prior increases the accuracy of instantaneous estimates. Improvements are especially dramatic in real-time limited-data CST, which is directly applicable to many industrially relevant experiments.

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.

Bayesian approach to the design of chemical species tomography experiments

Reconstruction accuracy in chemical species tomography depends strongly on the arrangement of optical paths transecting the imaging domain. Optimizing the path arrangement requires a scheme that can predict the quality of a proposed arrangement prior to measurement. This paper presents a new Bayesian method for scoring path arrangements based on the estimated a posteriori covariance matrix. This technique focuses on defining an objective function that incorporates the same a priori information about the flow needed to carry out limited data tomography. Constrained and unconstrained path optimization studies verify the predictive capabilities of the objective function, and that superior reconstruction quality is obtained with optimized path arrangements.

Demonstration of temperature imaging by H₂O absorption spectroscopy using compressed sensing tomography

This paper introduces temperature imaging by total-variation-based compressed sensing (CS) tomography of H2O vapor absorption spectroscopy. A controlled laboratory setup is used to generate a constant two-dimensional temperature distribution in air (a roughly Gaussian temperature profile with a central temperature of 677 K). A wavelength-tunable laser beam is directed through the known distribution; the beam is translated and rotated using motorized stages to acquire complete absorption spectra in the 1330-1365 nm range at each of 64 beam locations and 60 view angles. Temperature reconstructions are compared to independent thermocouple measurements. Although the distribution studied is approximately axisymmetric, axisymmetry is not assumed and simulations show similar performance for arbitrary temperature distributions. We study the measurement error as a function of number of beams and view angles used in reconstruction to gauge the potential for application of CS in practical test articles where optical access is limited.

High-resolution bispectral imager at 1000 frames per second

We describe a bispectral, 1000-frames per second imaging instrument working simultaneously in two spectral bands. These bands may be selected for a specific application; however, we implement a pair centered at 4.3 μm and 4.66 μm. Synchronization is accomplished by employing a single focal plane array. To demonstrate the performance of the bispectral imager, we apply it to the methane flame of a Bunsen burner in a near conjugate configuration with flame image length subtending at about 200 pixels. The instrument detects bispectral puffing at 2 Hz, pulsations, and bispectral radiation oscillations, first reported here in two spectral intervals. The period of oscillatory spectral components in two bands is the same, about 3 Hz for this flame, with delay of a quarter period between them, first reported here. With 1-ms integration time, we detect significant formation of turbulence and vortices, especially pronounced in the region where the flame transitions into a plume. We display bispectral ratioed images of flames in near-real time with either the laboratory or the field device.

Spatially resolved and observer-free experimental quantification of spatial resolution in tomographic images

We present a novel framework and experimental method for the quantification of spatial resolution of a tomography system. The framework adopts the "black box" view of an imaging system, considering only its input and output. The tomography system is locally stimulated with a step input, viz., a sharp edge. The output, viz., the reconstructed images, is analysed by Fourier decomposition of their spatial frequency components, and the local limiting spatial resolution is determined using a cut-off threshold. At no point is an observer involved in the process. The framework also includes a means of translating the quantification region in the imaging space, thus creating a spatially resolved map of objectively quantified spatial resolution. As a case-study, the framework is experimentally applied using a gaseous propane phantom measured by a well-established chemical species tomography system. A spatial resolution map consisting of 28 regions is produced. In isolated regions, the indicated performance is 4-times better than that suggested in the literature and varies by 57% across the imaging space. A mechanism based on adjacent but non-interacting beams is hypothesised to explain the observed behaviour. The mechanism suggests that, as also independently concluded by other methods, a geometrically regular beam array maintains maximum objectivity in reconstructions. We believe that the proposed framework, methodology, and findings will be of value in the design and performance evaluation of tomographic imaging arrays and systems.

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.

50-kHz-rate 2D imaging of temperature and H2O concentration at the exhaust plane of a J85 engine using hyperspectral tomography

This paper describes a novel laser diagnostic and its demonstration in a practical aero-propulsion engine (General Electric J85). The diagnostic technique, named hyperspectral tomography (HT), enables simultaneous 2-dimensional (2D) imaging of temperature and water-vapor concentration at 225 spatial grid points with a temporal response up to 50 kHz. To our knowledge, this is the first time that such sensing capabilities have been reported. This paper introduces the principles of the HT techniques, reports its operation and application in a J85 engine, and discusses its perspective for the study of high-speed reactive flows.

Laser-absorption tomography beam arrangement optimization using resolution matrices

Laser-absorption tomography experiments infer the concentration distribution of a gas species from the attenuation of lasers transecting the flow field. Although reconstruction accuracy strongly depends on the layout of optical components, to date experimentalists have had no way to predict the performance of a given beam arrangement. This paper shows how the mathematical properties of the coefficient matrix are related to the information content of the attenuation data, which, in turn, forms a basis for a beam-arrangement design algorithm that minimizes the reliance on additional assumed information about the concentration distribution. When applied to a simulated laser-absorption tomography experiment, optimized beam arrangements are shown to produce more accurate reconstructions compared to other beam arrangements presented in the literature.

Infrared species tomography of a transient flow field using Kalman filtering

In infrared species tomography, the unknown concentration distribution of a species is inferred from the attenuation of multiple collimated light beams shone through the measurement field. The resulting set of linear equations is rank-deficient, so prior assumptions about the smoothness and nonnegativity of the distribution must be imposed to recover a solution. This paper describes how the Kalman filter can be used to incorporate additional information about the time evolution of the distribution into the reconstruction. Results show that, although performing a series of static reconstructions is more accurate at low levels of measurement noise, the Kalman filter becomes advantageous when the measurements are corrupted with high levels of noise. The Kalman filter also enables signal multiplexing, which can help achieve the high sampling rates needed to resolve turbulent flow phenomena.

Validation of temperature imaging by H2O absorption spectroscopy using hyperspectral tomography in controlled experiments

This paper describes a preliminary demonstration and validation of temperature imaging using hyperspectral H2O absorption tomography in controlled experiments. Fifteen wavelengths are monitored on each of 30 laser beams to reconstruct the temperature image in a 381 mm × 381 mm square room-temperature plane that contains a 102 mm × 102 mm square zone of lower or higher temperature. The hyperspectral tomography technique attempts to leverage multispectral information to enhance measurement fidelity. The experimental temperature images exhibit average accuracies of 2.3% or better, with pixel-by-pixel standard deviations of less than 1%. In addition, even when the internal zone is only 4 K cooler than the surroundings, its presence is still detectable; statistical analysis of the associated experimental image reveals a 98% confidence that the internal zone is in fact cooler than the surroundings.

Hyperspectral tomography based on proper orthogonal decomposition as motivated by imaging diagnostics of unsteady reactive flows

A series of previous studies, both numerical and experimental, have demonstrated the advantages of hyperspectral tomography (HT) as a promising technique to measure the two-dimensional distributions of temperature and species concentration in reacting flows. This paper intends to prepare the mathematical groundwork for extended use of the HT technique for three-dimensional and/or time-correlated measurements. Direct application of the methods developed previously encounters both experimental and computational difficulties. Numerical studies reported in this paper suggest that the use of proper orthogonal decomposition (POD) is effective to overcome these difficulties. The use of POD in HT significantly reduces the computational cost, enhances the fidelity of the tomographic reconstructions, and improves the stability of the reconstruction in the presence of measurement noise. Implications of these results for practical applications are also discussed.

Two-color-absorption sensor for time-resolved measurements of gasoline concentration and temperature

A midinfrared absorption sensor for crank-angle-resolved in-cylinder measurements of gasoline concentration and gas temperature for spark-ignition internal-combustion engines is reported, and design considerations and validation testing in the controlled environments of a heated cell and shock-heated gases are discussed. Mid-IR laser light was tuned to transitions in the strong absorption bands associated with C-H stretching vibration near 3.4 microm, and time-resolved fuel vapor concentration and gas temperature were determined simultaneously from the absorption at two different wavelengths. These two infrared laser wavelengths were simultaneously produced by difference-frequency generation, which combines a near-IR signal laser with two near-IR pump lasers in a periodically poled lithium niobate crystal. Injection current modulation of the pump lasers produced intensity modulation of the mid-IR, which allowed the transmitted signals from the two laser wavelengths to be detected on a single detector and separated by frequency demultiplexing. Injection current modulation produced a wavelength modulation synchronous with the intensity modulation for each of the laser wavelengths, and accurate measurement of the gasoline absorption signal required the effects of wavelength modulation to be considered. Validation experiments were conducted for a single-component hydrocarbon fuel (2,2,4-trimethyl-pentane, commonly known as iso-octane) and a gasoline blend in a heated static cell (300 < or = T < or = 600 K) and behind planar shock waves (600 < T < 1100 K) in a shock tube. With a bandwidth of 10 kHz, the measured fuel concentrations agreed within 5% RMS and the measured temperature agreed within 3% RMS to the known values. The 10 kHz bandwidth is sufficient to resolve 1 crank-angle degree at 1600 RPM.

Tomographic imaging of temperature and chemical species based on hyperspectral absorption spectroscopy

A novel technique has been developed to obtain simultaneous tomographic images of temperature and species concentration based on hyperspectral absorption spectroscopy. The hyperspectral information enables several key advantages when compared to traditional tomography techniques based on limited spectral information. These advantages include a significant reduction in the number of required projection measurements, and an enhanced insensitivity to measurements/inversion uncertainties. These advantages greatly facilitate the practical implementation and application of the tomography technique. This paper reports the development of the technique, and the experimental demonstration of a prototype sensor in a near-adiabatic, atmospheric-pressure laboratory Hencken burner. The spatial and temporal resolution enabled by this new sensing technique is expected to resolve several key issues in practical combustion devices.

Determination of the optimal regularization parameters in hyperspectral tomography

In a previous paper, we described a novel technique to exploit hyperspectral absorption spectroscopy to retrieve tomographic imaging of temperature and species concentration simultaneously. This technique casts the tomographic inversion into a nonlinear minimization problem with regularizations. Here a simple and effective method is developed to determine the optimal regularization parameters in the nonlinear optimization problem. This method, combined with the minimization method described previously, provides a robust algorithm for hyperspectral tomography. This method takes advantage of an inherent feature of absorption and is therefore expected to be useful for other sensing techniques based on absorption spectroscopy.

Numerical investigation of hyperspectral tomography for simultaneous temperature and concentration imaging

We investigate the simultaneous tomographic reconstruction of temperature and species concentration using hyperspectral absorption spectroscopy. Previous work on absorption tomography has relied on a small number of wavelengths, resulting in the requirement of a large number of projections and limited measurement capability. Here we develop a tomographic inversion method to exploit the increased spectral information content enabled by recent advancement in laser technologies. The simulation results clearly demonstrate that the use of hyperspectral absorption data significantly reduces the number of projections, enables simultaneous mapping of temperature and species concentration, and provides more stable reconstruction compared with traditional absorption tomographic techniques.

Digitally balanced detection for optical tomography

Analog balanced Photodetection has found extensive usage for sensing of a weak absorption signal buried in laser intensity noise. This paper proposes schemes for compact, affordable, and flexible digital implementation of the already established analog balanced detection, as part of a multichannel digital tomography system. Variants of digitally balanced detection (DBD) schemes, suitable for weak signals on a largely varying background or weakly varying envelopes of high frequency carrier waves, are introduced analytically and elaborated in terms of algorithmic and hardware flow. The DBD algorithms are implemented on a low-cost general purpose reconfigurable hardware (field-programmable gate array), utilizing less than half of its resources. The performance of the DBD schemes compare favorably with their analog counterpart: A common mode rejection ratio of 50 dB was observed over a bandwidth of 300 kHz, limited mainly by the host digital hardware. The close relationship between the DBD outputs and those of known analog balancing circuits is discussed in principle and shown experimentally in the example case of propane gas detection.

Generic-type hierarchical multi digital signal processor system for hard-field tomography

This article introduces the design and implementation of a hierarchical multi digital signal processor system aimed to perform parallel multichannel measurements and data processing of the type widely used in hard-field tomography. Details are presented of a complete tomography system with modular and expandable architecture, capable of accommodating a variety of data processing modalities, configured by software. The configuration of the acquisition and processing circuits and the management of the data flow allow a data frame rate of up to 250 kHz. Results of a case study, guided path tomography for temperature mapping, are shown as a direct demonstration of the system's capabilities. Digital lock-in detection is employed for data processing to extract the information from ac measurements of the temperature-induced resistance changes in an array of 32 noninteracting transducers, which is further exported for visualization.