Optimized Inversion Algorithm Research Articles

An improved band design framework for atmospheric pollutant detection and its application to the design of satellites for CO2 observation

High-precision atmospheric remote sensing observation is one of the most challenging tasks in the key fields of earth observation. The accurate accounting for technical indicators such as the working spectral band, spectral resolution, and signal-to-noise ratio (SNR) of high-precision atmospheric observation satellites is an urgent research task. To address this need, this paper proposes a band design framework (BDF) that can replace airborne detection experiments to some extent and reduce the workload of satellite design. First, based on the HITRAN database, the absorption spectra of gases in the target gas absorption window are extracted as a band dataset. Then, membership functions are designed based on a trapezoid distribution, the monitoring factor α is introduced according to the importance of strong and weak absorption channels to obtain the improved fuzzy comprehensive evaluation (IFCE) model. Subsequently, the IFCE model is used to screen the band dataset. Finally, the bands are optimized based on the SCIATRAN model, sensitivity analysis and optimal inversion algorithm, and the BDF-IFCE band design method for remote sensing detection of gaseous atmospheric pollutants is established based on the improved fuzzy synthetic evaluation model. The BDF-IFCE method is applied to design the CO2 sensor detection band and two absorption windows are successfully identified (6170–6270 cm−1 and 6290–6380 cm−1). With a restricted range of aerosol AODs, detection accuracy of 3–4 ppm can be achieved with a signal-to-noise ratio of ∼300. The test results are the same as the band setting of existing atmospheric sensors, indicating that this method is effective and feasible in designing the CO2 remote sensor detection band.

Algorithm for Retrieval of Temperature in Mesosphere and Lower Thermosphere from O2 A-Band Night Glow

The O2 A-band night glow can be used to retrieve the temperature in the range of 80–120 km in the mesosphere and lower thermosphere (MLT). From the full spectrum of A-band night glow, the band used to retrieve temperature is selected based on the sensitivity of the emission line on temperature, taking into account the compromise relationship between the spectral band and resolution, inversion efficiency, and inversion accuracy. The non-linear iterative inversion method based on optimization theory is adopted for the retrieval of temperature. Meanwhile, considering the stability of inversion, Tikhonov regularization matrix is added as a constraint, and the optimal estimation inversion algorithm is optimized to suppress the influence of measurement noise on results. Through the recovering simulated noisy spectra from an interferometer, the temperature profile with vertical resolution better than 2 km and an average accuracy better than 2 K is obtained by the optimized inversion method in this paper. In addition, the influence of a priori constraints on the inversion accuracy is studied, and a priori accuracy limits the inversion accuracy. When a priori accuracy is controlled within ±5 K, the average temperature inversion accuracy can be optimized to 1.35 K, which is better than the accuracy of OSIRIS on Odin at 90–105 km.

Time-space united coding spread spectrum single photon counting imaging method

In this paper, we demonstrate a new imaging architecture called time-space united coding spread spectrum single photon counting imaging technique by combining the space coding based single-pixel imaging technology and spread spectrum time coding based scanning imaging technology. This method has the advantages of range ambiguity-free and large time-bandwidth product. Under the interference of noise, this method can accurately restore depth images. In this work, the time-space united correlation nonlinear detection model based on single photon detection, forward imaging model and signal-to-noise ratio model is derived, and the depth image is restored by convex optimization inversion algorithm. The theoretical model and simulation experiments show that compared with the traditional single pixel imaging method based on spatial coding, this method improves the quality of scene reconstruction. Using m-sequence as time coding, imaging has higher noise robustness. In addition, compared with the traditional space coding single pixel imaging technology, the imaging mean square error of the proposed method is reduced by 4/5 and the imaging mean squared error is reduced by 9/10 after introducing the second correlated method. The proposed imaging architecture in this paper may provide a new path for non-scanning lidar imaging methods.

A surrogate-assisted stochastic optimization inversion algorithm: Parameter identification of dams

Dynamic monitoring data plays an essential role in the structural health monitoring of dams. This study presents a surrogate-assisted stochastic optimization inversion (SASOI) algorithm, a novel technique for static and dynamic parameter identification. This algorithm is based on probabilistic finite element simulations and Bayesian inference theory. It combines the advantages of low computational cost in surrogate models and fast convergence in the Bayesian algorithm. Taking four cases of different complexity, this paper verifies the effectiveness of the SASOI algorithm and validates its practicality for large dams. Surrogate models consider several alternatives, including polynomial chaos expansion (PCE), Kriging, polynomial chaos Kriging, and support vector regression. Implementation of the SASOI algorithm on dams shows that PCE outperforms other techniques. This algorithm improves the accuracy and efficiency of the static parameter identification methods by nearly 27 times compared to the classical inversion methods. Furthermore, the accuracy of dynamic parameter identification is higher than that of static one. The SASOI algorithm is applicable to other large-scale infrastructures.

High-Precision Depth Domain Migration Method in Imaging of 3D Seismic Data in Coalfield

Fault structures developed in coal seams, which are often associated with roof collapse, water inrush, gas outburst, and other accidents, are common geological hazards in coal exploration and development. The accurate detection of micro-structures such as small faults has always been a research focus to ensure safety in coalfields. Three-dimensional (3D) seismic research is one of the most efficient methods for obtaining the structural characteristics of coal areas and identify small faults in coal seams, but it is difficult for traditional seismic data imaging technologies to meet the high-precision demand of current coal exploration. Aiming at the characteristics of 3D seismic data in coalfields, we calculated the difference coefficients based on the optimized inversion algorithm and proposed a variable-density acoustic equation optimized with a temporal–spatial staggered-grid finite difference forward algorithm. On this basis, by combining normalized cross-correlation imaging conditions and GPU/CPU collaborative parallel processing technology, we developed an efficient and high-precision 3D reverse time migration method suitable for 3D seismic data in coalfields. Numerical tests verified the accuracy and efficiency of the proposed migration method for the imaging of coal-measure strata with small fault structures and could effectively identify 5 m small faults in the coal seam. The migration test of 3D seismic data in real coalfields showed that our 3D reverse time migration method has good practicability for high-precision imaging of 3D seismic data in coalfields and is an effective method for the precise imaging of small faults in coal measures.

Visco-elastic material characterization by means of full field Lamb waves

In structural design and structural health monitoring (SHM), the identification of the visco-elastic stiffness tensor of composite materials is considered fundamental, however, the reconstruction of the stiffness coefficients is not straightforward due to the inherent presence of anisotropy and heterogeneity. In the current study, an inverse procedure is proposed based on full field wave dispersion curves to characterize the (18) visco-elastic stiffness parameters of an orthotropic composite plate. The procedure is illustrated by means of finite element method simulations conducted with broadband signals. First, the FEM simulation data, consisting of the in-plane and out-of-plane velocities on the 2D top surface of a composite plate, were converted into the frequency-complex wavenumber domain, including information on elasticity and viscosity, by using the matrix pencil method. The converted data set was then considered as input to a surrogate optimization inversion algorithm, using the semi analytical finite element method (SAFE) as the forward model owing to its accuracy, efficiency and robustness. The full tensorial visco-elastic stiffness parameters were calculated and updated by minimizing the error between the simulated and the calculated complex wavenumbers. The final reconstructed stiffness properties in case of an aluminum plate and of a unidirectional composite laminate show good agreement with the exact input stiffness values, with average errors below 5% for all 18 visco-elastic stiffness parameters.

Quantitative evaluation of fracture porosity from dual laterlog based on deep learning method

Fracture porosity is one of the key parameters for characterizing fractured reservoirs. However, fracture porosity calculation is difficult with conventional logging data due to severe anisotropy of the reservoirs. To deal with the problem, the equivalent macroscopic anisotropic formation model based on dual laterolog (DLL) data is adopted to cyclically assign such parameters as bedrock resistivity (RB), fluid resistivity in fractures (RFL), fracture dip angle (FDA) and fracture thickness as well as fracture spacing, and to produce massive data for formation modeling. A large number of training data obtained through three dimensional finite element forward modeling and the functional relationship between DLL responses and fracture parameters that are trained and summarized by deep neural network, are combined to establish a new fast forward model for calculating DLL responses in fractured formations. A new fracture porosity inversion model for fractured reservoirs based on gradient optimization inversion algorithm combined with multi-initial inversion strategy is then proposed. While running the model, formation is divided into eight intervals according to bedrock resistivity and fracture dip angle from 0° to 90° is divided every 0.5° to improve the operation speed and efficiency. The results of numerical verification show that when bedrock resistivity is greater than 1000 Ω m, the mean absolute error (MAE) of fracture porosity inversion is 0.001658% for horizontal fractures, 0.00413% for intermediate fractures and 0.0027% for quasi-vertical fractures. When bedrock resistivity is between 100 Ω m and 1000 Ω m, MAE of fracture porosity inversion is 0.003% for horizontal fractures, 0.0034% for intermediate fractures and 0.00348% for quasi-vertical fractures. Fracture parameters determined by the fracture porosity inversion model with actual data are in good agreement with the results of micro resistivity imaging logging.

A comparison study using particle swarm optimization inversion algorithm for gravity anomaly interpretation due to a 2D vertical fault structure

A new approach to the inversion of gravity data utilizing the Particle Swarm Optimization (PSO) algorithm is used to model 2D vertical faults. The PSO algorithm is stochastic in nature; its development was motivated by the communal in-flight performance of birds looking for food. The birds are represented by particles (or models). Individual particles have a location and a velocity vector. The location vectors represent the parameter value. PSO is adjusted with random particles (models) and searches for targets by updating generations.Herein, the PSO algorithm is applied to three synthetic data sets (residual only with and without noise, residual plus regional, residual plus anomaly generated by a buried cylinder structure) and two field gravity data sets acquired across known faults in Egypt. Assessment of the synthetic data demonstrates that the PSO algorithm generates superior results if a first horizontal gradient (FHG) filter is applied first. The robustness of the PSO inversion algorithm is demonstrated for both synthetic and field gravity data.

H -based selective inversion of nonminimum-phase systems for feedback controls

Stably inverting a dynamic system model is fundamental to subsequent servo designs. Current inversion techniques have provided effective model matching for feedforward controls. However, when the inverse models are to be implemented in feedback systems, additional considerations are demanded for assuring causality, robustness, and stability under closed-loop constraints. To bridge the gap between accurate model approximations and robust feedback performances, this paper provides a new treatment of unstable zeros in inverse design. We provide first an intuitive pole-zero-map-based inverse tuning to verify the basic principle of the unstable-zero treatment. From there, for general nonminimum-phase and unstable systems, we propose an optimal inversion algorithm that can attain model accuracy at the frequency regions of interest while constraining noise amplification elsewhere to guarantee system robustness. Along the way, we also provide a modern review of model inversion techniques. The proposed algorithm is validated on motion control systems and complex high-order systems.

Development of the Inversion Method for Transient Electromagnetic Data

Transient electromagnetic method (TEM) is a geophysical tool to obtain resistivity distribution in the subsurface. Combining with the resistivity property of typical rocks, the TEM method can make inferences of the geological maps underground. The inversion method is the main technique to extract resistivity form the recorded TEM data. There are various inversion methods that have been applied to TEM data, each of which favors different model structures. It is essential to choose the optimal inversion algorithm for a TEM survey in a given geological setting. Thus, this article presents a systematic summary of recent developments of inversion methods for TEM data. We first summarize the basic concept of the TEM inversion theory. Then, the recent developments TEM inverse method are divided into deterministic inversion and stochastic inversion. For the deterministic method, we present the development of constrained inversion and joint inversion. For the stochastic method, we analyze the particle swarm optimization, Bayesian inversion, and TEM pseudo-seismic imaging. Thereafter, we prospect the future research direction of the TEM method.

Susceptibility inversion of near-field magnetic sources and its application

Susceptibility inversion of near-field magnetic sources is of great application significance in the field of magnetic target detections, such as mine clearances and buried pipeline detections. This paper proposes a method of three-dimensional inversion imaging of magnetic sources in near-field with unknown shape, position and magnetization state. The method transforms the total field norm anomaly ΔT on the observation surface into the total field vector anomaly ||Ta|| and then constructs an objective function aiming at minimizing the deviations between the measured and predicted magnetic anomalies. The magnetic dipole equivalence principle is utilized to calculate the kernel matrix. The Gauss-Newton and conjugate gradient algorithms are utilized together to solve the inversion optimization process. The range of the magnetic susceptibility is constrained by using nonlinear transformations. Simulations and measurement experiments demonstrate the proposed method is capable to realize 3D inversions of curved pipes, intersecting pipes, separated magnetic sources, and “L” shaped steel pipes under near-field conditions. Through the actual magnetic field measurement experiments and the implementation of the proposed optimization inversion algorithm, accurate inversion of the magnetic susceptibility distribution and magnetic imaging of the “L” shaped steel tube was realized, testifying that the proposed method is feasible to be applied to the detection of buried pipelines.

Nuclear Magnetic Resonance T1–T2 Spectra in Heavy Oil Reservoirs

Low-field nuclear magnetic resonance (NMR) has been widely used in the petroleum industry for reservoir evaluation. Fluid properties and petrophysical parameters can be determined from NMR spectra, obtained from processing echo data measured from the NMR tool. The more accurate NMR spectra are, the higher the reliability of reservoir evaluation based on NMR logging is. The purpose of this paper is to obtain more precise T1–T2 spectra in heavy oil reservoirs, with focus on the T1–T2 data acquisition and inversion. To this end, four inversion algorithms were tested on synthetic T1–T2 data, their precision was evaluated and the optimal inversion algorithm was selected. Then, the sensitivity to various acquisition parameters (wait time and echo spacing) was evaluated with T1–T2 experiments using a disordered accumulation of glass beads with a diameter of 45 μm saturated with heavy oil and distilled water. Finally, the sensitivity to various inversion parameters (convergence tolerance, maximum number of iterations and regularization parameter) was evaluated using the optimal inversion algorithm. The results showed that the inverted T1–T2 spectra loss some relaxation information when the number of echo train is less than 7. The peak of the heavy oil signal gradually moves along the direction of increase in the T2 and the intensity of the heavy oil signal gradually decreases with increasing echo spacing. The echo spacing should be as small as possible for T1–T2 measurements in heavy oil reservoirs on the premise that the NMR instrument operates normally. A convergence tolerance that is too large or a maximum number of iterations that is too small may result in exiting the iteration prematurely during the inversion. A convergence tolerance of 1 × 10−7 and a maximum number of iterations of 30,000 are recommended for the inversion of the T1–T2 spectra. An appropriate regularization parameter is an important factor for obtaining accurate T1–T2 spectra from the optimal inversion algorithm.

Retrieval of black carbon aerosol surface concentration using satellite remote sensing observations

As an important part of the anthropogenic aerosol, Black Carbon (BC) aerosols in the atmospheric environment have strong impacts on climate change. Recently, most remote sensing studies on aerosol components detection are limited to the inversion of aerosol optical properties, integration of chemistry models or in situ observations. In this paper, an algorithm based on Effective Medium Approximations (EMA) and statistically optimized aerosol inversion algorithm was integrated for retrieving the surface mass concentration of BC aerosols from satellite signals. The sensitivity analyses for the developed forward model proved that the volume fraction of vertical BC is sensitive to the satellite observations and significantly improved especially over bright surface targets or under polluted atmospheric conditions. By updating the forward model and retrieved parameters of the statistically optimized inversion algorithm, three cases of high aerosol loading days were retrieved from Polarization and Anisotropy of Reflectance for Atmospheric Sciences Coupled with Observations from a LiDAR (PARASOL) measurements, which shows a significant ability of BC aerosol detection. Additionally, the validation and closure studies of BC concentration retrievals also indicates an encouraging consistency with correlation (R) of 0.71, mean bias of 3.55, and root-mean-square error (RMSE) of 3.75 when compared against the in-situ observations over South Asia. The accuracy of the retrievals also demonstrates different trends under different levels of aerosol loadings, which shows a higher accuracy in biomass burning seasons (R = 0.75, RMSE = 4.04, Bias = 3.27) while exaggerates the results in the case of clear conditions (R = 0.47, RMSE = 4.83, Bias = 4.00). Finally, the uncertainties of three assumptions, including proposing uniform vertical profile for BC, neglecting light-absorbing aerosols and using spherical EMA models were discussed in our manuscript. The maximum standard deviations caused by these uncertainties on low BC aerosol volume fractions (fBC < 1%) are 0.8%, 0.35% and 0.2% while these deviations will change to 0.25%, 0.05% and 1.5% respectively under higher BC fractions (fBC > 5%). This conclusion confirmed that the proposed algorithm for BC surface concentration retrieval extends the application of satellite remote sensing in monitoring the extreme biomass burning pollution.

An Optimal Estimation Retrieval Algorithm for Microwave Humidity Sounding Channels with Minimal Scan Position Bias

AbstractA flexible and physical optimal estimation-based inversion algorithm for retrieving atmospheric water vapor and cloud liquid water path from passive microwave radiometers over the global oceans is presented. The algorithm’s main strength lies in its ability to explicitly account for forward model errors that depend on the Earth incidence angle (EIA) at which a given radiometer measurement is made. Validation of total precipitable water (TPW) retrieved from Microwave Humidity Sounder (MHS) measurements against near-coincident estimates of TPW from SuomiNet GPS ground stations shows that retrieved TPW values agree closely with SuomiNet estimates, and somewhat better than values from the Microwave Integrated Retrieval System that are retrieved from the same MHS instruments. More importantly, it is found that the inclusion of appropriate forward model error assumptions, which are tailored to the EIA and sea surface temperature of the scene being considered, are able to almost entirely eliminate EIA-dependent biases in retrieved TPW. This result holds true across all satellites currently carrying an MHS instrument, despite the fact that only measurements from one satellite are used to estimate forward model errors. The consistency achieved by the retrieval algorithm across all view angles suggests that other inversion algorithms, particularly those for cross-track-scanning radiometers and potential future constellations of small satellites, would benefit from the inclusion of nuanced error assumptions that consider the effect of EIA.

Revealing small-scale diffracting discontinuities by an optimization inversion algorithm

Revealing small-scale diffracting discontinuities by an optimization inversion algorithm

S-wave velocity profiling from refraction microtremor Rayleigh wave dispersion curves via PSO inversion algorithm

The refraction microtremor method has been increasingly used as an appealing tool for investigating near surface S-wave structure. However, inversion, as a main stage in processing refraction microtremor data, is challenging for most local search methods due to its high nonlinearity. With the development of data optimization approaches, fast and easier techniques can be employed for processing geophysical data. Recently, particle swarm optimization algorithm has been used in many fields of studies. Use of particle swarm optimization in geophysical inverse problems is a relatively recent development which offers many advantages in dealing with the nonlinearity inherent in such applications. In this study, the reliability and efficiency of particle swarm optimization algorithm in the inversion of refraction microtremor data were investigated. A new framework was also proposed for the inversion of refraction microtremor Rayleigh wave dispersion curves. First, particle swarm optimization code in MATLAB was developed; then, in order to evaluate the efficiency and stability of proposed algorithm, two noise-free and two noise-corrupted synthetic datasets were inverted. Finally, particle swarm optimization inversion algorithm in refraction microtremor data was applied for geotechnical assessment in a case study in the area in city of Tabriz in northwest of Iran. The S-wave structure in the study area successfully delineated. Then, for evaluation, the estimated Vs profile was compared with downhole data available around of the considered area. It could be concluded that particle swarm optimization inversion algorithm is a suitable technique for inverting microtremor waves.

Joint Inversion of Atmospheric Refractivity Profile Based on Ground-Based GPS Phase Delay and Propagation Loss

In this paper, we present a new estimation of the atmospheric refractivity profile combining the scattering signal (electromagnetic wave propagation loss) and the direct signal (phase delay). The refractivity profile is modeled using four parameters, i.e., the gradient of the refractivity profile (c1, c2) and the vertical altitude (h1, h2). We apply the NSGA-II (Non-dominated Sorting Genetic Algorithm II), a multiobjective optimization algorithm, to achieve the goals of joint optimization inversion in the inverting process, and compare this method with traditional individual inversion methods. The anti-noise ability of joint inversion is investigated under the noiseless condition and adding noise condition, respectively. The numerical experiments demonstrate that joint inversion is superior to individual inversion. The adding noise test further suggests that this method can estimate synthesized parameters more efficiently and accurately in different conditions. Finally, a set of measured data is tested in the new way and the consequence of inversion shows the joint optimization inversion algorithm has feasibility, effectiveness and superiority in the retrieval of the refractivity profile.

Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations

Abstract. The proposed development is an attempt to enhance aerosol retrieval by emphasizing statistical optimization in inversion of advanced satellite observations. This optimization concept improves retrieval accuracy relying on the knowledge of measurement error distribution. Efficient application of such optimization requires pronounced data redundancy (excess of the measurements number over number of unknowns) that is not common in satellite observations. The POLDER imager on board the PARASOL micro-satellite registers spectral polarimetric characteristics of the reflected atmospheric radiation at up to 16 viewing directions over each observed pixel. The completeness of such observations is notably higher than for most currently operating passive satellite aerosol sensors. This provides an opportunity for profound utilization of statistical optimization principles in satellite data inversion. The proposed retrieval scheme is designed as statistically optimized multi-variable fitting of all available angular observations obtained by the POLDER sensor in the window spectral channels where absorption by gas is minimal. The total number of such observations by PARASOL always exceeds a hundred over each pixel and the statistical optimization concept promises to be efficient even if the algorithm retrieves several tens of aerosol parameters. Based on this idea, the proposed algorithm uses a large number of unknowns and is aimed at retrieval of extended set of parameters affecting measured radiation. The algorithm is designed to retrieve complete aerosol properties globally. Over land, the algorithm retrieves the parameters of underlying surface simultaneously with aerosol. In all situations, the approach is anticipated to achieve a robust retrieval of complete aerosol properties including information about aerosol particle sizes, shape, absorption and composition (refractive index). In order to achieve reliable retrieval from PARASOL observations even over very reflective desert surfaces, the algorithm was designed as simultaneous inversion of a large group of pixels within one or several images. Such multi-pixel retrieval regime takes advantage of known limitations on spatial and temporal variability in both aerosol and surface properties. Specifically the variations of the retrieved parameters horizontally from pixel-to-pixel and/or temporary from day-to-day are enforced to be smooth by additional a priori constraints. This concept is expected to provide satellite retrieval of higher consistency, because the retrieval over each single pixel will be benefiting from coincident aerosol information from neighboring pixels, as well, from the information about surface reflectance (over land) obtained in preceding and consequent observations over the same pixel. The paper provides in depth description of the proposed inversion concept, illustrates the algorithm performance by a series of numerical tests and presents the examples of preliminary retrieval results obtained from actual PARASOL observations. It should be noted that many aspects of the described algorithm design considerably benefited from experience accumulated in the preceding effort on developments of currently operating AERONET and PARASOL retrievals, as well as several core software components were inherited from those earlier algorithms.

Visualization of atherosclerotic plaque mechanical properties using model based intravascular ultrasound elastography.

Cardiovascular disease related deaths occur primarily from fatty plaques inside an artery that rupture and cause clots that disrupt blood flow. The study of arterial plaque mechanics is essential to the monitoring of atherosclerosis and the detection of vulnerable plaques or the likelihood of their rupture. The aim of this work is to measure and image the mechanical behavior of plaques using a clinically available intravascular ultrasound system (IVUS). To test the methods, radial displacements were measured from simulated images and phantom data within two dimensional IVUS rf images using standard elastography techniques. Simulations and phantom experiments were designed to mimic arterial geometries and deformations, which include plaque regions of varying stiffnesses. In addition, an optimization inversion algorithm was used to infer the elastic modulus of the underlying material. This algorithm utilizes a finite element based model and assumes that the deformation is quasi-static, plane strain and that the material is incompressible and linear elastic. The full spatially reconstructed modulus images, with no geometric constraints, are presented and compared to radial strain images. The phantom results are compared to the known modulus contrasts, and the simulated images are compared to contrasts and distributions.

A new technique for retrieval of tropospheric and stratospheric ozone profiles using sky radiance measurements at multiple view angles: Application to a Brewer spectrometer

This paper describes and applies a new technique for retrieving diurnal variability in tropospheric ozone vertical distribution using ground‐based measurements of ultraviolet sky radiances. The measured radiances are obtained by a polarization‐insensitive modified Brewer double spectrometer located at Goddard Space Flight Center, in Greenbelt, Maryland, USA. Results demonstrate that the Brewer angular (0–72° viewing zenith angle) and spectral (303–320 nm) measurements of sky radiance in the solar principal plane provide sufficient information to derive tropospheric ozone diurnal variability. In addition, the Brewer measurements provide stratospheric ozone vertical distributions at least twice per day near sunrise and sunset. Frequent measurements of total column ozone amounts from direct‐sun observations are used as constraints in the retrieval. The vertical ozone profile resolution is shown in terms of averaging kernels to yield at least four points in the troposphere–low stratosphere, including good information in Umkehr layer 0 (0–5 km). The focus of this paper is on the derivation of stratospheric and tropospheric ozone profiles using both simulated and measured radiances. We briefly discuss the necessary modifications of the Brewer spectrometer that were used to eliminate instrumental polarization sensitivity so that accurate sky radiances can be obtained in the presence of strong Rayleigh scattering and aerosols. The results demonstrate that including a site‐specific and time‐dependent aerosol correction, based on Brewer direct‐sun observations of aerosol optical thickness, is critical to minimize the sky radiance residuals as a function of observing angle in the optimal estimation inversion algorithm and improve the accuracy of the retrieved ozone profile.