Robust Calibration Approach Research Articles

Simple, non-mechanical and automatic calibration approach for axial-scanning microscopy with an electrically tunable lens.

We describe a simple and robust calibration approach for axial-scanning microscopy that realizes axial focus shifts with an electrically tunable lens (ETL). We demonstrate the calibration approach based on a microscope with an ETL placed close to the rear stop of the objective lens. By introducing a target-consisted of repeating lines at one known frequency and placed at a ~45° angle to the imaging path, the calibration method captures multiple images at different ETL currents and calibrates the dependence of the axial focus shift on the ETL current by evaluating the sharpness of the captured images. It calibrates the dependence of the magnification of the microscope on the ETL current by measuring the period of the repeating lines in the captured images. The experimental results show that different from the conventional calibration procedure, the proposed scheme does not involve any mechanical scanning and can simultaneously calibrate the dependence of the axial focus shift and the magnification on the ETL current. This might facilitate imaging studies that require the measurement of fine structures in a 3D volume. We also show the calibration procedure can be used to estimate the radius of a conner-arc sample, fabricated using laser micromachining. We believe that this easy-to-use calibration approach may facilitate use of ETLs for a variety of imaging platforms. It may also provide new insights for the development of novel 3D surface measurement methods. RESEARCH HIGHLIGHTS: The proposed calibration scheme does not involve any mechanical scanning and can simultaneously calibrate the dependence of the axial focus shift and the magnification on the electrically tunable lens (ETL) current. It might facilitate imaging studies that require the measurement of fine structures in a 3D volume, and the use of ETLs for a variety of imaging platforms. It may also provide new insights for the development of novel 3D surface measurement methods.

ORYZA (v3) rice crop growth modeling for MR269 under nitrogen treatments: Assessment of cross-validation on parameter variability

Complex rice crop models are sometimes evaluated with limited data. A one-round validation approach is typically used, in which data is arbitrarily divided into two or more mutually exclusive sets. Some sets are used for calibration, while others are used for validation. It is unknown whether a more structured cross-validation approach would result in variations in the calibrated parameters when applied to the same data sets. The objectives of this paper are (i) to calibrate and evaluate the performance of ORYZA (v3) for simulation of high-yielding MR269 rice variety physiological traits grown in Malaysian rice fields with limited data using a cross-validation approach; and (ii) to assess crop genetic parameter variability that resulted from the cross-validation approach and explore the benefits of the approach with limited data. The cross-validation approach produces six calibrated crop parameter sets (three calibration–validation combinations for two parameter cohorts). Further validation with independent field data sets revealed that two of the six calibrated crop parameter sets produced satisfactory to good fits for the crop dry biomass of green leaves, panicles, and stems, as well as the dry total aboveground biomass of MR269 (NSE ≥ 0.5). This study implies that the plausibility of multiple feasible parameter sets must be acknowledged, and a more robust calibration approach must be considered when working with a complex crop model with limited data. The systematic cross-validation approach as demonstrated in this study allows for a more extensive model evaluation given small data sets.

High-precision laser spectrometer for multiple greenhouse gas analysis in 1 mL air from ice core samples

Abstract. The record of past greenhouse gas composition from ice cores is crucial for our understanding of global climate change. Future ice core projects will aim to extend both the temporal coverage (extending the timescale to 1.5 Myr) and the temporal resolution of existing records. This implies a strongly limited sample availability, increasing demands on analytical accuracy and precision, and the need to reuse air samples extracted from ice cores for multiple gas analyses. To meet these requirements, we designed and developed a new analytical system that combines direct absorption laser spectroscopy in the mid-infrared (mid-IR) with a quantitative sublimation extraction method. Here, we focus on a high-precision dual-laser spectrometer for the simultaneous measurement of CH4, N2O, and CO2 concentrations, as well as δ13C(CO2). Flow-through experiments at 5 mbar gas pressure demonstrate an analytical precision (1 σ) of 0.006 ppm for CO2, 0.02 ‰ for δ13C(CO2), 0.4 ppb for CH4, and 0.1 ppb for N2O, obtained after an integration time of 100 s. Sample–standard repeatabilities (1 σ) of discrete samples of 1 mL STP (Standard Temperature and Pressure) amount to 0.03 ppm, 2.2 ppb, 1 ppb, and 0.04 ‰ for CO2, CH4, N2O, and δ13C(CO2), respectively. The key elements to achieve this performance are a custom-developed multipass absorption cell, custom-made high-performance data acquisition and laser driving electronics, and a robust calibration approach involving multiple reference gases. The assessment of the spectrometer capabilities in repeated measurement cycles of discrete air samples – mimicking the procedure for external samples such as air samples from ice cores – was found to fully meet our performance criteria for future ice core analysis. Finally, this non-consumptive method allows the reuse of the precious gas samples for further analysis, which creates new opportunities in ice core science.

Calibration routine for a telecentric stereo vision system considering affine mirror ambiguity

A robust calibration approach for a telecentric stereo camera system for three-dimensional (3-D) surface measurements is presented, considering the effect of affine mirror ambiguity. By optimizing the parameters of a rigid body transformation between two marker planes and transforming the two-dimensional (2-D) data into one coordinate frame, a 3-D calibration object is obtained, avoiding high manufacturing costs. Based on the recent contributions in the literature, the calibration routine consists of an initial parameter estimation by affine reconstruction to provide good start values for a subsequent nonlinear stereo refinement based on a Levenberg–Marquardt optimization. To this end, the coordinates of the calibration target are reconstructed in 3-D using the Tomasi–Kanade factorization algorithm for affine cameras with Euclidean upgrade. The reconstructed result is not properly scaled and not unique due to affine ambiguity. In order to correct the erroneous scaling, the similarity transformation between one of the 2-D calibration plane points and the corresponding 3-D points is estimated. The resulting scaling factor is used to rescale the 3-D point data, which then allows in combination with the 2-D calibration plane data for a determination of the start values for the subsequent nonlinear stereo refinement. As the rigid body transformation between the 2-D calibration planes is also obtained, a possible affine mirror ambiguity in the affine reconstruction result can be robustly corrected. The calibration routine is validated by an experimental calibration and various plausibility tests. Due to the usage of a calibration object with metric information, the determined camera projection matrices allow for a triangulation of correctly scaled metric 3-D points without the need for an individual camera magnification determination.

Indirect Correspondence-Based Robust Extrinsic Calibration of LiDAR and Camera.

LiDAR and cameras have been broadly utilized in computer vision and autonomous vehicle applications. However, in order to convert data between the local coordinate systems, we must estimate the rigid body transformation between the sensors. In this paper, we propose a robust extrinsic calibration algorithm that can be implemented easily and has small calibration error. The extrinsic calibration parameters are estimated by minimizing the distance between corresponding features projected onto the image plane. The features are edge and centerline features on a v-shaped calibration target. The proposed algorithm contributes two ways to improve the calibration accuracy. First, we use different weights to distance between a point and a line feature according to the correspondence accuracy of the features. Second, we apply a penalizing function to exclude the influence of outliers in the calibration datasets. Additionally, based on our robust calibration approach for a single LiDAR-camera pair, we introduce a joint calibration that estimates the extrinsic parameters of multiple sensors at once by minimizing one objective function with loop closing constraints. We conduct several experiments to evaluate the performance of our extrinsic calibration algorithm. The experimental results show that our calibration method has better performance than the other approaches.

A miniature shoe-mounted orientation determination system for accurate indoor heading and trajectory tracking.

Tracking the position of pedestrian is urgently demanded when the most commonly used GPS (Global Position System) is unavailable. Benefited from the small size, low-power consumption, and relatively high reliability, micro-electro-mechanical system sensors are well suited for GPS-denied indoor pedestrian heading estimation. In this paper, a real-time miniature orientation determination system (MODS) was developed for indoor heading and trajectory tracking based on a novel dual-linear Kalman filter. The proposed filter precludes the impact of geomagnetic distortions on pitch and roll that the heading is subjected to. A robust calibration approach was designed to improve the accuracy of sensors measurements based on a unified sensor model. Online tests were performed on the MODS with an improved turntable. The results demonstrate that the average RMSE (root-mean-square error) of heading estimation is less than 1°. Indoor heading experiments were carried out with the MODS mounted on the shoe of pedestrian. Besides, we integrated the existing MODS into an indoor pedestrian dead reckoning application as an example of its utility in realistic actions. A human attitude-based walking model was developed to calculate the walking distance. Test results indicate that mean percentage error of indoor trajectory tracking achieves 2% of the total walking distance. This paper provides a feasible alternative for accurate indoor heading and trajectory tracking.

Determining sample alignment in x-ray reflectometry using thickness and density from GaAs/AlAs multilayer certified reference materials

X-ray reflectometry (XRR) provides researchers and manufacturers with a non-destructive way to determine thickness, roughness and density of thin films deposited on smooth substrates. Due to the nested nature of equations modeling this phenomenon, the inter-relation between instrument alignment and parameter estimation accuracy is somewhat opaque. In this study, we intentionally shift incident angle information from a high-quality XRR data set and refine a series of shifted data sets using an identical structural model to assess the effect this angle misalignment has on parameter estimation. We develop a series of calibration curves relating angle misalignment to variation in layer thickness and density for a multilayer GaAs/AlAs Certified Reference Material on a GaAs substrate. We then test the validity and robustness of several approaches of using known thickness and density parameters from this structure to calibrate instrument alignment. We find the highest sensitivity to and linearity with, measurement misalignment from buried AlAs and GaAs layers, in contrast to the surface layers, which show the most variability. This is a fortuitous result, as buried AlAs and GaAs exhibit the highest long-term stability in thickness. Therefore, it is indeed possible to use reference thickness estimates to validate XRR angle alignment accuracy. Buried layer mass density information also shows promise as a robust calibration approach. This is surprising, as electron density of buried layers is both a highly-correlated phenomenon and a subtle component within the XRR model.

A robust calibration approach for PM<sub>10</sub> prediction from MODIS aerosol optical depth

Abstract. Investigating the human health effects of atmospheric particulate matter (PM) using satellite data are gaining more attention due to their wide spatial coverage and temporal advantages. Such epidemiological studies are, however, susceptible to bias errors and resulted in poor predictive output in some locations. Current methods calibrate aerosol optical depth (AOD) retrieved from MODIS to further predict PM. The recent satellite-based AOD calibration uses a mixed effects model to predict location-specific PM on a daily basis. The shortcomings of this daily AOD calibration are for areas of high probability of persistent cloud cover throughout the year such as in the humid tropical region along the equatorial belt. Contaminated pixels due to clouds causes radiometric errors in the MODIS AOD, thus causes poor predictive power on air quality. In contrary, a periodic assessment is more practical and robust especially in minimizing these cloud-related contaminations. In this paper, a simple yet robust calibration approach based on monthly AOD period is presented. We adopted the statistical fitting method with the adjustment technique to improve the predictive power of MODIS AOD. The adjustment was made based on the long-term observation (2001–2006) of PM10-AOD residual error characteristic. Furthermore, we also incorporated the ground PM measurement into the model as a weighting to reduce the bias of the MODIS-derived AOD value. Results indicated that this robust approach with monthly AOD calibration reported an improved average accuracy of PM10 retrieval from MODIS data by 50% compared to widely used calibration methods based on linear regression models, in addition to enabling further spatial patterns of periodic PM exposure to be undertaken.

Optimal unemployment insurance in GE: A robust calibration approach

A simple Monte Carlo calibration approach is implemented in a GE model with uninsurable employment risk to quantitatively study the optimal replacement rate of a public unemployment insurance (UI) scheme. The optimal UI sampling distribution is found to be bimodal.

Multi-elemental analysis of solidified mineral melt samples by Laser-Induced Breakdown Spectroscopy coupled with a linear multivariate calibration

Laser-Induced Breakdown Spectroscopy (LIBS) has been successfully applied for multi-elemental analysis of solidified mineral melt samples containing several oxides present in various concentrations. The plasma was generated using a Nd:YAG laser and the spectra were acquired using an Echelle spectrometer, coupled to an ICCD detector, which covers a spectral range from 200 to 780 nm. Using a set of 19 calibration samples, we first established univariate calibration curves for the major elements (Al, Fe, Mg, Ca, Ti and Si). We found out that the presence of matrix effects makes such a model, traditionally used in LIBS, not satisfying for quantitative analysis of such samples. Indeed, no sufficiently linear trends can be extracted from the calibration curves for the elements of interest considering all the samples. Instead, a much more robust calibration approach was obtained by considering a multivariate model. The matrix effects are then taken into account by correcting the spectroscopic signals emitted by a given species due the presence of the others ones. More specifically, we established here a calibration model using a 2nd order polynomial linear multivariate inverse regression. The capability of this approach was then checked using a 2nd set of samples with an unknown composition. A good agreement was observed between the analysis provided by X-ray fluorescence (XRF) and the LIBS measurements coupled to the multivariate model for the unknown samples.