Nonlinear Calibration Research Articles

Representing Camera Response Function by a Single Latent Variable and Fully Connected Neural Network

Modelling the mapping from scene irradiance to image intensity is essential for many computer vision tasks. Such mapping is known as the camera response. Most digital cameras use a nonlinear function to map irradiance, as measured by the sensor to an image intensity used to record the photograph. Modelling of the response is necessary for the nonlinear calibration. In this paper, a new high-performance camera response model that uses a single latent variable and fully connected neural network is proposed. The model is produced using unsupervised learning with an autoencoder on real-world (example) camera responses. Neural architecture searching is then used to find the optimal neural network architecture. A latent distribution learning approach was introduced to constrain the latent distribution. The proposed model achieved state-of-the-art CRF representation accuracy in a number of benchmark tests, but is over twice as fast as the best current models when performing the maximum likelihood estimation during camera response calibration due to the simple yet efficient model representation.

Linear or non-linear multivariate calibration models? That is the question

Concepts from data science, machine learning, deep learning and artificial neural networks are spreading in many disciplines. The general idea is to exploit the power of statistical tools to interpret complex and, in many cases, non-linear data. Specifically in analytical chemistry, many chemometrics tools are being developed. However, they tend to get more complex without necessarily improving the prediction ability, which conspires against parsimony. In this report, we show how non-linear analytical data sets can be solved with equal or better efficiency by easily interpretable modified linear models, based on the concept of local sample selection before model building. The latter activity is conducted by choosing a sub-set of samples located in the neighborhood of each unknown sample in the space spanned by the latent variables. Two experimental examples related to the use of near infrared spectroscopy for the analysis of target properties in food samples are examined. The comparison with seemingly more complex chemometric models reveals that local regression is able to achieve similar analytical performance, with considerably less computational burden.

Electrically Enhanced Sensitivity (EES) of Ion-Selective Membrane Electrodes and Membrane-Based Ion Sensors.

The use of external electronic enforcement in ion-sensor measurements is described. The objective is to improve the open-circuit (potentiometric) sensitivity of ion sensors. The sensitivity determines the precision of analyte determination and has been of interest since the beginning of ion-sensor technology. Owing to the theoretical interpretation founded by W.E. Nernst, the sensitivity is characterized by the slope and numerically predicted. It is empirically determined and validated during calibration by measuring an electromotive force between the ion sensor and the reference electrode. In practice, this measurement is made with commercial potentiometers that function as unaltered “black boxes”. This report demonstrates that by gaining access to a meter’s electrical systems and allowing for versatile signal summations, the empirical slope can be increased favorably. To prove the validity of the approach presented, flow-through ion-sensor blocks used in routine measurements of blood electrolytes (Na+, K+, Li+, Cl−) and multielectrode probes with flat surfaces, similar to those applied previously for monitoring transmembrane fluxes of Na+, K+, Cl− through living biological cells, are used. Several options to serve real-life electroanalytical challenges, including linear calibration for sensors with high-resistance membranes, responses with non-Nernstian slopes, non-linear calibration, and discrimination of nonfunctional sensors, are shown.

Radiometric calibration of a large-array commodity CMOS multispectral camera for UAV-borne remote sensing

• An indoor and outdoor integrated radiometric calibration method for large-array commodity CMOS multispectral cameras. • A nonlinear quantum efficiency calibration model for poor linearity sensors. • A dark target-based empirical line method for low altitude atmospheric correction. • Compared with fitting methods, the lookup table method is a better vignetting effect correction method. To meet the requirement of high-resolution and high-efficiency unmanned aerial vehicle (UAV)-borne multispectral remote sensing, using the miniaturized large-array commodity complementary metal-oxide semiconductor (CMOS) camera is an effective solution. Given the characteristics of the new sensor and platform, almost no systematic and feasible radiometric calibration method has been specifically developed. In this paper, we proposed an indoor and outdoor integrated radiometric calibration method. To develop a systematic indoor calibration method, we explored the optimal methods for dark current offset, vignetting effect correction, and quantum efficiency calibration. According to the comparison results of three different methods, the lookup table (LUT) method was chosen to correct vignetting effect rather than nonlinear regression. Further, we proposed an exponential nonlinear model to replace the traditional linear model for quantum efficiency calibration, which improved the R-squares from around 0.92 to around 0.99. The outdoor calibration included atmospheric path radiance and reflectance correction. We proposed an empirical line method based on the dark target method to correct the atmospheric path radiance before the reflectance correction. Based on our method, the mean absolute percentage errors (MAPE) between the observed reflectance and the true reflectance were around 10%. Moreover, the method can greatly improve the calculated reflectance accuracy of low reflectance targets. Our method can serve as a useful reference for the radiometric calibration of large-array commodity CMOS multispectral cameras. It can also contribute to the application of UAV-borne multispectral remote sensing.

Multi-frequency imaging with non-linear calibration of magnetoresistance sensors for surface and buried defects inspection

Timely inspecting defects has both safety and economic significance in industry. Eddy current testing (ECT) probes with array sensors are widely used for metal structures inspection. However, the sensitivities of array sensors are typically not consistent, resulting in different responses when measuring the same defect signal. Therefore, the array sensors of an array probe are desired to be calibrated. This paper proposes an ECT probe with an array of tunnel magnetoresistance (TMR) sensors and two excitation coils for surface and buried defects inspection. Alternating currents with different frequencies and amplitudes are driven through the two coils simultaneously. The TMR sensors have non-linear resistance vs. magnetic field curves. A non-linear calibration method based on the non-linear characteristic is proposed to calibrate the high frequency signals of the sensors. This calibration method does not need any extra equipment and takes account of the effect of the non-uniformity of the excitation magnetic field to some extent. Experimental result shows that the signal becomes much flatter after the calibration. The relative flat index is reduced from 38.6% to 11% by the calibration process. To validate the detectability of the proposed probe for different kinds of defects, surface and buried defects in aluminum samples are tested by the probe. It is seen that a small surface defect with sizes 1 mm (length) x 0.5 mm (width) x 0.5 mm (height) can be clearly identified from the high-frequency image. Two defects buried 3 mm below the top surface are also inspected. The peak signal values of the two defects are 0.69 V and 0.97 V, respectively, demonstrating that the probe can distinguish the 0.1 mm height difference of the two defects. In addition, a defect buried 10 mm under the surface is imaged by the probe. Thanks to the special probe design and excellent sensitivity of the TMR sensors, the probe has good sensitivity for both surface and buried defects.

Retrieval of Remotely Sensed Sediment Grain Size Evolution Characteristics along the Southwest Coast of Laizhou Bay Based on Support Vector Machine Learning

Grain size is the basic property of intertidal zone sediment. Grain size acts as an indicator of sedimentary processes and geomorphological evolution under human and nature interactions. The remote sensing technique provides an alternative for sediment grain-size parameter monitoring with the advantages of wide coverage and real-time surveying. This paper attempted to map the distributions of three sediment grain size contents and the mean grain size with multitemporal Landsat images along the southwestern coast of Laizhou Bay, China, from 1989 to 2015. Considering the low correlations between the measured reflectance and grain-size parameters, we used a support vector machine (SVM) to develop a nonlinear calibration model by taking several band indices as input variables. Then, the performance of the back propagation neural network (BPNN) was determined and discussed with that of the SVM. The SVM performed better than the BPNN in calibrating the four grain-size parameters based on a comparison of R2 and the root-mean-square error (RMSE). Moreover, an atmospheric correction algorithm originally proposed for case II water enabled the TM\ETM+ images to be precisely atmospherically corrected in this study. The SVM-mapped spatial-temporal grain-size variation showed a coarsening trend, which agreed with that obtained during in situ measurements in a former study. The changes in Yellow River discharge and precipitation associated with the coarsening trend were further analyzed. The yielded results showed that the coarsening trend and reduction in tidal flat area might be aggravated with overutilization. More reasonable planning would be necessary in this case.

Imaging electrochemiluminescence layer to dissect concentration-dependent light intensity for accurate quantitative analysis

As one of most advanced transduction techniques, electrochemiluminescence (ECL), such as that generated by tris(2,2′-bipyridyl)ruthenium (Ru(bpy)32+), has been extensively used in chemical sensing and analysis, but the reaction mechanism has not been fully resolved. Aiming at gaining insightful mechanistic information on the coreactant system involving (Ru(bpy)32+) and tri-n-propylamine (TPrA), herein we investigate the variation of thickness of ECL layer (TEL) with the concentration ratio of (Ru(bpy)32+) to TPrA (cRu/cTPrA) by ECL microscopy. Using carbon fiber as the working electrode, TEL was observed to grow with the increase of cRu/cTPrA remarkably. In conjunction with finite element simulations, the extension of ECL layer was rationalized to be associated with the incremental contribution of so-called “catalytic route”. This route offers an additional channel of generating remote light emission in solution, apart from surface-confined emission produced by the “oxidative-reduction route”. Given the quantitative analysis of coreactant-type analytes is often based on the calibration curve, namely a graph generated by plotting the measured light intensity of a series of standard solutions against their concentrations, the contribution of “catalytic route” particularly at a low concentration of analyte (equivalent to a relatively large cRu/cTPrA) is favorable to the analytical sensitivity. Moreover, the presence and absence of this route will result in a nonlinear and linear calibration curve, respectively, for example in the detection of TPrA and pyruvate. The results highlight the microwire-based imaging approach can provide insightful mechanistic information and help unveil the concentration dependence of measured ECL intensity for precise quantitative analysis.

A 16‐bit, ±10‐V Input Range SAR ADC with a 5‐V Supply Voltage and Mixed‐Signal Nonlinearity Calibration

This paper presents a high-precision, successive approximation register (SAR) analog-to-digital converter (ADC) with resistive analog front-end for low-voltage and wide input range applications. To suppress the serious nonlinearity brought by the voltage coefficients of analog front-end without deteriorating differential nonlinearity performance, a mixed-signal calibration scheme based on piecewise-linear method with calibration digital-to-analog converter is proposed. A compensation current is designed to sink or source from the reference to keep it independent of input signal, which greatly improves the linearity performance. Fabricated in a 0.5-μm CMOS process, the proposed ADC achieves 88-dB signal-to-noise-and-distortion ratio and 103-dB spurious free dynamic range with 5-V supply voltage and 2.5-V reference voltage, and the total power consumption is 37.5 mW.

FBG-based strain monitoring and temperature compensation for composite tank

The composite tank has become the trend and focus for the power system of the new generation aerospace vehicles. However, the evaluation methods and monitoring technologies for composite tanks under cryogenic experiments are still challenging problems. In this paper, fiber Bragg grating (FBG) is used to measure the strain and temperature of the stiffened composite tank under room and cryogenic temperature pressurization experiments. Temperature compensation based on the thermal stratification phenomenon is proposed to increase the reliability and accuracy of strain monitoring in cryogenic environment. A non-linear fitting based calibration method of temperature sensitivity coefficient addresses the non-linear relationship between the FBG wavelength and temperature change from liquid nitrogen temperature to room temperature. The results show that the average absolute error of the nonlinear calibration method in the cryogenic test is less than 50 με. It is also illustrated that the structural features of the sensor location can be qualitatively determined according to the strain changes of different sensors. The comparison of strain increments in the cyclic pressurization illustrated that the different performance degradation phenomena of different regions could be observed. These results provide strong support for the high stability and reliability of FBG-based composite tank strain monitoring.

Potential of visible and near infrared spectroscopy coupled with machine learning for predicting soil metal concentrations at the regional scale

Chemical analytical methods for metal analysis in soils are laborious, time-consuming and costly. This paper aims to evaluate the potential of short-range (SR) and full-range (FR) visible and infrared spectroscopy (vis-NIR) combined with linear and nonlinear calibration methods to estimate concentrations of nickel (Ni), cobalt (Co), cadmium (Cd), lead (Pb) and copper (Cu) in soils. A total of 435 soil samples were collected over agricultural sites, forest (7 %), pasture (5 %) and fallow land across a region in the northern part of Belgium. Generally, better predictions were obtained when using partial least squares regression (PLSR) and nonlinear calibration method [i.e., random forest (RF)] for processing of the spectral data, than when using support vector machine (SVM). FR generally outperformed SR and provided the best prediction results for Ni (R2p = 0.76), Co (R2p = 0.77), Cd (R2p = 0.64) and Pb (R2p = 0.65), when using PLSR and RF. SVM produced the best prediction result only for Pb (R2p = 0.57) using the SR spectra. The metals Ni, Co, Cd and Pb can be predicted successfully (good accuracy) from the FR vis-NIR spectra using PLSR for Co, and RF for Ni, Cd, Pb and Cu. Compared to the FR spectrophotometer, improvement in accuracy was obtained for Cd and Co, using the SR spectra when combined with PLSR and RF, respectively. It is concluded that the SR spectrometer can be used successfully for the prediction of Co with RF (R2p = 0.70), while it best predicted Cd with PLSR with an R2p value of 0.67, which is of value for regional survey.

Robust Calibration of MEMS Accelerometers in the Presence of Outliers

MEMS accelerometers suffer from different problems such as random and systematic errors and the presence of outliers in the measurements. Proper calibration is necessary to obtain accurate results. Various methods exist but very few are designed for robust calibration. This paper explores methods for calibrating MEMS accelerometers in the presence of outliers. Optimization techniques based on Levenberg–Marquardt algorithm and linearization are used to solve the nonlinear calibration equations. Outlier detection methods such as RANSAC (random sample consensus), the Mahalanobis distance, and the median absolute deviation (MAD) are integrated within the optimization algorithm. Outlier scores are calculated and used to eliminate outliers or assign weights. The experimental results show that outlier detection and removal methods allow to achieve substantial improvement in the calibration process compared with non-robust methods. The median absolute deviation is the most effective in detecting outliers. In the presence of outliers, the average error for MAD and model-based method is 0.0136 (a.u.). For non-robust methods, the error is 3.82 (a.u.). For the Mahalanobis distance, the error is 1.8778 (a.u.). The results show that the calibration error is the smallest for the model—based method. The Mahalanobis distance presents higher calibration errors and is less capable of detecting outliers; however, it is still better than non-robust methods. Finally Levenberg–Marquardt algorithm presents slightly better results than linearization.

Mitigating analyte to stable isotope labelled internal standard cross-signal contribution in quantitative liquid chromatography-tandem mass spectrometry

BackgroundUtilising stable isotope labelled internal standards (SIL-IS) in quantitative LC-MS/MS drug analysis is the most widely used approach to normalise for variability during sample quantification processes. However, compounds containing atoms such as Sulphur, Chlorine or Bromine, could potentially cause cross-signal contribution to the SIL-IS from the naturally occurring isotopes, resulting in non-linear calibration curves. A simple, novel method of mitigating the effect is presented here. It entails monitoring of a less abundant SIL-IS isotope, as the precursor ion, of a mass that has no/minimal isotopic contribution from the analyte isotopes. MethodsExperiments were conducted on two LC-MS/MS analysers: Waters Xevo TQ-S and Shimadzu 8050. Flucloxacillin (FLX) was used as an example. Two transitions were selected for FLX (m/z 454 → 160 → 295) and one for each of the SIL-IS isotopes (m/z 458 → 160 for the isotope 457 g/mol and m/z 460 → 160 for the isotope 459 g/mol). Assay biases were assessed at three SIL-IS concentrations: 0.7, 7 and 14 mg/L for each isotope. ResultsWhen using the SIL-IS isotope m/z 458 → 160 at a concentration of 0.7 mg/L, biases were up to 36.9 % on both instruments. Increasing the SIL-IS concentration to 14 mg/L, reduced the bias to 5.8 %. Using the less abundant isotope, m/z 460 → 160, resulted in biases of 13.9 % at an SIL-IS concentration of 0.7 mg/L. ConclusionsApplying this method will mitigate cross-signal contribution from the analyte isotopes to the corresponding SIL-IS, minimise the use of SIL-IS, and, thereby, reduce overall cost.

Methodological Considerations in Development of UV Imaging for Characterization of Intra-Tumoral Injectables Using cAMP as a Model Substance.

A UV imaging release-testing setup comprising an agarose gel as a model for tumorous tissue was developed. The setup was optimized with respect to agarose concentration (0.5% (w/v)), injection procedure, and temperature control. A repeatable injection protocol was established allowing injection into cavities with well-defined geometries. The effective resolution of the SDi2 UV imaging system is 30–80 µm. The linear range of the imaging system is less than that of typical spectrophotometers. Consequently, non-linear cAMP calibration curves were applied for quantification at 280 nm. The degree of deviation from Beer’s law was affected by the background absorbance of the gel matrix. MATLAB scripts provided hitherto missing flexibility with respect to definition and utilization of quantification zones, contour lines facilitating visualization, and automated, continuous data analysis. Various release patterns were observed for an aqueous solution and in situ forming Pluronic F127 hydrogel and PLGA implants containing cAMP as a model for STING ligands. The UV imaging and MATLAB data analysis setup constituted a significant technical development in terms of visualizing behavior for injectable formulations intended for intra-tumoral delivery, and, thereby, a step toward establishment of a bio-predictive in vitro release-testing method.

Predicting the performance of handheld near-infrared photonic sensors from a master benchtop device

Many industries see a shifting focus towards performing on-site analysis using handheld spectroscopic devices. A determining factor for decision-making on the commissioning of these devices is available information on the potential performance of the device for specific applications. By now, myriad handheld solutions with very different specifications and pricing are available on the market. Although specifications are generally available for new devices, this does not directly quantify or predict how available devices will perform for targeted cases. We present a novel chemometric method to estimate the prediction performance of handheld NIR hardware and apply it to estimate the performance of two commercially available handheld NIR technologies in predicting protein content (ranging 120–180 g kg−1) in pig feed from existing data of a benchtop device. Adjusting benchtop data to the wavelength range and resolution of the handheld device lead to over-optimistic estimates of the handheld performances. Our method additionally utilizes information on the error structure of the handheld devices for the estimation. It yielded performance estimates differing less than 1 g kg−1 from the experimentally determined handheld performances and similar model parameters. Our method was effective for linear and nonlinear calibration algorithms, also when estimating performance after averaging multiple scans. Replicate spectra of twenty samples recorded using the handheld were required for replication error estimation to obtain an accurate performance estimation. The error structure could be reported by manufacturers in the future for this approach to be universally employed for predictive quantitative technology assessment. Overall, our method provides estimates of the performance of a handheld device for a specific task with minimal testing required and can thus be used as a device or application screening tool before committing to develop calibrations.

In-situ quantitative monitoring the organic contaminants uptake onto suspended microplastics in aquatic environments

Microplastics act as a source of organic contaminants in aquatic environments and thus affect their environmental fate and toxicity. Because of the weak and reversible interactions between microplastics and organic species, the organic coronas vary with their surrounding environments. Thus, in order to evaluate the possible environmental risks of microplastics, methods for evaluating the dynamic uptake of organic contaminants onto suspended microplastics in aquatic environments are greatly desired. In this work, a UV–vis spectroscopy-based approach was developed for in-situ monitoring organic contaminants uptake onto suspended microplastics after correcting the light scattering interference from microplastics suspensions and establishing the nonlinear relationship between concentration and light absorbance of organic species. The inverse adding-doubling method based on radiative transfer theory was adopted to correct the light scattering effect of suspensions. Then, the resulting mixed absorption spectra were decomposed to calculate the concentrations of the aqueous and adsorbed organic species simultaneously with a nonlinear calibration method. The uptake processes of bisphenol A and p-nitrophenol onto nylon 66 microparticles were monitored with this approach and confirmed by high-performance liquid chromatography analysis. The approach was validated by applying it to natural water samples, and the equilibrium adsorption capacity was found to be interfered mainly by the protein-like substances. This approach has high accuracy, good reproducibility, remarkable universality, and ease of handling, and also provides a potential tool for characterizing the corona formation process on suspended particles both in natural and artificial environments, such as eco-corona formation and engineering surface modification on nano/micro-particles.

A 12-Bit, 100 MS/s SAR ADC Based on a Bridge Capacitor Array with Redundancy and Non-Linearity Calibration in 28 nm CMOS

This paper presents a 12-bit, 100 MS/s successive approximation register (SAR) analog-to-digital converter (ADC) based on a bridge capacitor array with redundancy and non-linearity calibration. The differential non-linearity calibration method was proposed to compensate for the linearity, which is degraded by the parasitic capacitance of the bridge capacitor. To reduce the power dissipation and alleviate the settling error of the DAC capacitor array, a hybrid redundant scheme was proposed. A low-power, high-performance SAR ADC was implemented based on the proposed techniques. This SAR ADC prototype was implemented in 28 nm CMOS technology. Measurement results showed that the proposed SAR ADC could achieve a (signal-to-noise distortion ratio) SNDR of 61.46 dB and 58.82 dB at low and Nyquist input frequencies, respectively, resulting in figure of merits (FOMs) of 8.69 fJ/conversion and 11.8 fJ/conversion step, respectively. The SAR ADC core occupied an active area 0.0227 mm2.

Influence of Formulations on Characteristics of Ruthenium-Based Temperature-Sensitive Paints.

Temperature-sensitive paint (TSP) can optically measure a global temperature distribution using a thermal quenching of dye molecules. The TSP measurement is often used in wind tunnel tests to measure the temperature and flow fields in the aerodynamic field. The measurement accuracy is affected by the characteristics of TSP, such as temperature sensitivity, pressure dependency, luminescent intensity, photostability, and surface condition. The characteristics depend on the formulation of TSP. This study investigates the characteristics of the TSP using dichlorotris (1,10-phenanthroline) ruthenium(II) hydrate (Ru-phen). We compare the characteristics of TSPs using different polymers, solvents, and dye concentrations. The TSPs using polyacrylic acid as a polymer shows linear calibration curves, high luminescent intensity, high photostability, and smooth surface. On the other hand, the TSPs using polymethyl methacrylate have nonlinear calibration curves, low luminescent intensity, strong photodegradation, and a rough surface.

Study on nonlinear error calibration of fiber optical gyroscope scale factor based on LSTM

The calibration accuracy of the inertial navigation system (INS) has a non-negligible effect on its actual navigation performance. As the core component of the INS, the scale factor error of the fiber optical gyroscope (FOG) is one of the main error sources of the INS, which has a vital impact on the navigation accuracy. Generally, the scale factor of FOG is considered to be a constant value, but with the increasing demand for the accuracy of FOG, the scale factor error can not be ignored, how to calibration the FOG scale factor at different input velocity rates and temperature has attracted people's attention. The traditional calibration methods usually select several fixed temperature points and input velocity points, then the scale factor error is compensated by linear fitting or piecewise fitting. In order to improve the calibration accuracy, our paper considers the coupling effect of input velocity rate and temperature and designs a calibration experiment at continuous input velocity rates and temperature, the calibration time is shortened by 30%, then we propose a nonlinear error compensation method based on the LSTM. The experimental result shows that the std error of the FOG scale factor is reduced from 280 ppm to 13 ppm and the angle measurement error is reduced by 70%, which verify the effectiveness of our method.

Automatic Calibration of a Geomechanical Model from Sparse Data for Estimating Stress in Deep Geological Formations

Summary In this study, we demonstrate geomechanical modeling with fully automatic parameter calibration to estimate the full geomechanical stress fields of a prospective US carbon dioxide (CO2) storage site, based on sparse measurement data. The goal is to compute full stress tensor field estimates (principal stresses and orientations) that are maximally compatible with observations within the constraints of the model assumptions, thereby extending pointwise, incomplete partial stress measurement to a simulated full formation stress field, as well as a rough assessment of the associated error. We use the Perch site, located in Otsego County, Michigan, USA, as our case study. The input data consist of partial stress tensor information inferred from in-situ borehole tests, geophysical well logs, and processing of seismic data. A static earth model (SEM) of the site was developed, and geomechanical simulation functionality of the open-source MATLAB Reservoir Simulation Toolbox (MRST) was used to model the stress field. Adjoint-based nonlinear optimization was used to adjust boundary conditions and material properties to calibrate simulated results of observations. Results were interpreted through a Bayesian framework. The focus of this paper is to demonstrate how the fully automatic calibration procedure works and discuss the results obtained; it does not attempt a detailed analysis of the stress field in the context of the proposed CO2 storage initiatives. Our work is part of a larger effort to noninvasively determine in-situ stresses in deep formations considered for CO2 storage. Guided by previously published research on geomechanical model calibration, our work presents a novel calibration approach supporting a potentially large number of linear or nonlinear calibration parameters to produce results optimally agreeing with available measurements and thus extend partial pointwise estimates to full tensor fields compatible with the physics of the site.

T1w/FLAIR ratio standardization as a myelin marker in MS patients

IntroductionCalculation of a T1w/T2w ratio was introduced as a proxy for myelin integrity in the brain of multiple sclerosis (MS) patients. Since nowadays 3D FLAIR is commonly used for lesion detection instead of T2w images, we introduce a T1w/FLAIR ratio as an alternative for the T1w/T2w ratio. ObjectivesBias and intensity variation are widely present between different scanners, between subjects and within subjects over time in T1w, T2w and FLAIR images. We present a standardized method for calculating a histogram calibrated T1w/FLAIR ratio to reduce bias and intensity variation in MR sequences from different scanners and at different time-points. Material and methods207 Relapsing Remitting MS patients were scanned on 4 different 3 T scanners with a protocol including 3D T1w, 2D T2w and 3D FLAIR images. After bias correction, T1w/FLAIR ratio maps and T1w/T2w ratio maps were calculated in 4 different ways: without calibration, with linear histogram calibration as described by Ganzetti et al. (2014), and by using 2 methods of non-linear histogram calibration. The first nonlinear calibration uses a template of extra-cerebral tissue and cerebrospinal fluid (CSF) brought from Montreal Neurological Institute (MNI) space to subject space; for the second nonlinear method we used an extra-cerebral tissue and CSF template of our own subjects. Additionally, we segmented several brain structures such as Normal Appearing White Matter (NAWM), Normal Appearing Grey Matter (NAGM), corpus callosum, thalami and MS lesions using Freesurfer and Samseg. ResultsThe coefficient of variation of T1w/FLAIR ratio in NAWM for the no calibrated, linear, and 2 nonlinear calibration methods were respectively 24, 19.1, 9.5, 13.8. The nonlinear methods of calibration showed the best results for calculating the T1w/FLAIR ratio with a smaller dispersion of the data and a smaller overlap of T1w/FLAIR ratio in the different segmented brain structures. T1w/T2w and T1w/FLAIR ratios showed a wider range of values compared to MTR values. ConclusionsCalibration of T1w/T2w and T1w/FLAIR ratio maps is imperative to account for the sources of variation described above. The nonlinear calibration methods showed the best reduction of between-subject and within-subject variability. The T1w/T2w and T1w/FLAIR ratio seem to be more sensitive to smaller changes in tissue integrity than MTR. Future work is needed to determine the exact substrate of T1w/FLAIR ratio and to obtain correlations with clinical outcome.