Iterative algorithms for a non-linear inverse problem in atmospheric lidar

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms outperform standard methods in terms of sensitivity to noise and reliability of the estimated profile.Comment: 19 pages, 6 figure

Towards More Precise Survey Photometry for PanSTARRS and LSST: Measuring Directly the Optical Transmission Spectrum of the Atmosphere

Motivated by the recognition that variation in the optical transmission of the atmosphere is probably the main limitation to the precision of ground-based CCD measurements of celestial fluxes, we review the physical processes that attenuate the passage of light through the Earth's atmosphere. The next generation of astronomical surveys, such as PanSTARRS and LSST, will greatly benefit from dedicated apparatus to obtain atmospheric transmission data that can be associated with each survey image. We review and compare various approaches to this measurement problem, including photometry, spectroscopy, and LIDAR. In conjunction with careful measurements of instrumental throughput, atmospheric transmission measurements should allow next-generation imaging surveys to produce photometry of unprecedented precision. Our primary concerns are the real-time determination of aerosol scattering and absorption by water along the line of sight, both of which can vary over the course of a night's observations.Comment: 41 pages, 14 figures. Accepted PAS

Imaging of atmospheric dispersion processes with Differential Absorption Lidar

We consider the inverse problem of fitting atmospheric dispersion parameters based on time-resolved back-scattered differential absorption Lidar (DIAL) measurements. The obvious advantage of light-based remote sensing modalities is their extended spatial range which makes them less sensitive to strictly local perturbations/modelling errors or the distance to the plume source. In contrast to other state-of-the-art DIAL methods, we do not make a single scattering assumption but rather propose a new type modality which includes the collection of multiply scattered photons from wider/multiple fields-of-view and argue that this data, paired with a time dependent radiative transfer model, is beneficial for the reconstruction of certain image features. The resulting inverse problem is solved by means of a semi-parametric approach in which the image is reduced to a small number of dispersion related parameters and high-dimensional but computationally convenient nuisance component. This not only allows us to effectively avoid a high-dimensional inverse problem but simultaneously provides a natural regularisation mechanism along with parameters which are directly related to the dispersion model. These can be associated with meaningful physical units while spatial concentration profiles can be obtained by means of forward evaluation of the dispersion process

2D Signal Estimation for Sparse Distributed Target Photon Counting Data

In this study, we explore the utilization of maximum likelihood estimation for the analysis of sparse photon counting data obtained from distributed target lidar systems. Specifically, we adapt the Poisson Total Variation processing technique to cater to this application. By assuming a Poisson noise model for the photon count observations, our approach yields denoised estimates of backscatter photon flux and related parameters. This facilitates the processing of raw photon counting signals with exceptionally high temporal and range resolutions (demonstrated here to 50 Hz and 75 cm resolutions), including data acquired through time-correlated single photon counting, without significant sacrifice of resolution. Through examination involving both simulated and real-world 2D atmospheric data, our method consistently demonstrates superior accuracy in signal recovery compared to the conventional histogram-based approach commonly employed in distributed target lidar applications

2D velocity and temperature measurements in high speed flows based on spectrally resolved Rayleigh scattering

The use of molecular Rayleigh scattering for measurements of gas velocity and temperature is evaluated. Molecular scattering avoids problems associated with the seeding required by conventional laser anemometry and particle image velocimetry. The technique considered herein is based on the measurement of the spectrum of the scattered light. Planar imaging of Rayleigh scattering using a laser light sheet is evaluated for conditions at 30 km altitude (typical hypersonic flow conditions). The Cramer-Rao lower bounds for velocity and temperature measurement uncertainties are calculated for an ideal optical spectrum analyzer and for a planar mirror Fabry-Perot interferometer used in a static, imaging mode. With this technique, a single image of the Rayleigh scattered light from clean flows can be analyzed to obtain temperature and one component of velocity. Experimental results are presented for planar velocity measurements in a Mach 1.3 air jet

Global Estimation of Range Resolved Thermodynamic Profiles from MicroPulse Differential Absorption Lidar

We demonstrate thermodynamic profile estimation with data obtained using the MicroPulse DIAL such that the retrieval is entirely self contained. The only external input is surface meteorological variables obtained from a weather station installed on the instrument. The estimator provides products of temperature, absolute humidity and backscatter ratio such that cross dependencies between the lidar data products and raw observations are accounted for and the final products are self consistent. The method described here is applied to a combined oxygen DIAL, potassium HSRL, water vapor DIAL system operating at two pairs of wavelengths (nominally centered at 770 and 828 nm). We perform regularized maximum likelihood estimation through the Poisson Total Variation technique to suppress noise and improve the range of the observations. A comparison to 119 radiosondes indicates that this new processing method produces improved temperature retrievals, reducing total errors to less than 2 K below 3 km altitude and extending the maximum altitude of temperature retrievals to 5 km with less than 3 K error. The results of this work definitively demonstrates the potential for measuring temperature through the oxygen DIAL technique and furthermore that this can be accomplished with low-power semiconductor-based lidar sensors

ATMOSPHERIC TEMPERATURE RETRIEVALS FROM LIDAR MEASUREMENTS USING TECHNIQUES OF NON-LINEAR MATHEMATICAL INVERSION

The conventional method of lidar data processing to retrieve atmospheric temperature profiles has some limitations which necessitate the abandonment of the temperatures re­trieved at the uppermost limits of the observational range. The application of mathematical inversion, as a tool to remedy this problem, was investigated in this project. A simple grid search technique was used to develop an alternative way of retrieving atmospheric temper­ature profiles from lidar data. Data obtained from the Purple Crow lidar (PCL) (42.87° N, 81.38° W, 225 m) facility at the University of Western Ontario was used to perform the pre­liminary tests on this technique. PCL data for 12 nights of observation were processed by the new technique. Initial results show that data at the uppermost altitude limits can be reliably retrieved with this method. A numerical scheme to analyze errors in the retrieved tempera­tures was developed. The uncertainties in retrieved temperatures computed using this method are comparable to the corresponding uncertainties in the conventional technique

Robust Bayesian target detection algorithm for depth imaging from sparse single-photon data

This paper presents a new Bayesian model and associated algorithm for depth and intensity profiling using full waveforms from time-correlated single-photon counting (TCSPC) measurements in the limit of very low photon counts (i.e., typically less than 20 photons per pixel). The model represents each Lidar waveform as an unknown constant background level, which is combined in the presence of a target, to a known impulse response weighted by the target intensity and finally corrupted by Poisson noise. The joint target detection and depth imaging problem is expressed as a pixel-wise model selection and estimation problem which is solved using Bayesian inference. Prior knowledge about the problem is embedded in a hierarchical model that describes the dependence structure between the model parameters while accounting for their constraints. In particular, Markov random fields (MRFs) are used to model the joint distribution of the background levels and of the target presence labels, which are both expected to exhibit significant spatial correlations. An adaptive Markov chain Monte Carlo algorithm including reversible-jump updates is then proposed to compute the Bayesian estimates of interest. This algorithm is equipped with a stochastic optimization adaptation mechanism that automatically adjusts the parameters of the MRFs by maximum marginal likelihood estimation. Finally, the benefits of the proposed methodology are demonstrated through a series of experiments using real data.Comment: arXiv admin note: text overlap with arXiv:1507.0251