Emulator-Based Bayesian Calibration of the CISNET Colorectal Cancer Models.

PURPOSE: To calibrate Cancer Intervention and Surveillance Modeling Network (CISNET)'s SimCRC, MISCAN-Colon, and CRC-SPIN simulation models of the natural history colorectal cancer (CRC) with an emulator-based Bayesian algorithm and internally validate the model-predicted outcomes to calibration targets. METHODS: We used Latin hypercube sampling to sample up to 50,000 parameter sets for each CISNET-CRC model and generated the corresponding outputs. We trained multilayer perceptron artificial neural networks (ANNs) as emulators using the input and output samples for each CISNET-CRC model. We selected ANN structures with corresponding hyperparameters (i.e., number of hidden layers, nodes, activation functions, epochs, and optimizer) that minimize the predicted mean square error on the validation sample. We implemented the ANN emulators in a probabilistic programming language and calibrated the input parameters with Hamiltonian Monte Carlo-based algorithms to obtain the joint posterior distributions of the CISNET-CRC models' parameters. We internally validated each calibrated emulator by comparing the model-predicted posterior outputs against the calibration targets. RESULTS: The optimal ANN for SimCRC had 4 hidden layers and 360 hidden nodes, MISCAN-Colon had 4 hidden layers and 114 hidden nodes, and CRC-SPIN had 1 hidden layer and 140 hidden nodes. The total time for training and calibrating the emulators was 7.3, 4.0, and 0.66 h for SimCRC, MISCAN-Colon, and CRC-SPIN, respectively. The mean of the model-predicted outputs fell within the 95% confidence intervals of the calibration targets in 98 of 110 for SimCRC, 65 of 93 for MISCAN, and 31 of 41 targets for CRC-SPIN. CONCLUSIONS: Using ANN emulators is a practical solution to reduce the computational burden and complexity for Bayesian calibration of individual-level simulation models used for policy analysis, such as the CISNET CRC models. In this work, we present a step-by-step guide to constructing emulators for calibrating 3 realistic CRC individual-level models using a Bayesian approach. HIGHLIGHTS: We use artificial neural networks (ANNs) to build emulators that surrogate complex individual-based models to reduce the computational burden in the Bayesian calibration process.ANNs showed good performance in emulating the CISNET-CRC microsimulation models, despite having many input parameters and outputs.Using ANN emulators is a practical solution to reduce the computational burden and complexity for Bayesian calibration of individual-level simulation models used for policy analysis.This work aims to support health decision scientists who want to quantify the uncertainty of calibrated parameters of computationally intensive simulation models under a Bayesian framework.

Proton CT on biological phantoms for x-ray CT calibration in proton treatment planning.

OBJECTIVE: To present and characterize a novel method for X-ray CT (xCT) calibration in proton treatment planning, based on proton CT (pCT) measurements on biological phantoms. Approach: A pCT apparatus was used to perform direct measurements of 3D stopping power relative to water (SPR) maps on stabilized, biological phantoms. Two single-energy xCT calibration curves - i.e. tissue substitutes and stoichiometric - were compared to pCT data. Moreover, a new calibration method based on these data was proposed, and verified against intra- and inter-species variability, dependence on stabilization, beam-hardening conditions, and analysis procedures. Main results: Biological phantoms were verified to be stable in time, with a dependence on temperature conditions, especially in the fat region: (-2.50.5) HU/°C. The pCT measurements were compared with standard xCT calibrations, revealing an average SPR discrepancy within ±1.60% for both fat and muscle regions. In the bone region the xCT calibrations overestimated the pCT-measured SPR of the phantom, with a maximum discrepancy of about +3%. As a result, a new cross-calibration curve was directly extracted from the pCT data. Overall, the SPR uncertainty margin associated with this curve was below 3%; fluctuations in the uncertainty values were observed across the HU range. Cross-calibration curves obtained with phantoms made of different animal species and anatomical parts were reproducible with SPR discrepancies within 3%. Moreover, the stabilization procedure did not affect the resulting curve within a 2.2% SPR deviation. Finally, the cross-calibration curve was affected by the beam-hardening conditions on xCTs, especially in the bone region, while dependencies below 2% resulted from the image registration procedure. Significance: Our results showed that pCT measurements on biological phantoms may provide an accurate method for the verification of current xCT calibrations and may represent a tool for the implementation of a new calibration method for proton treatment planning.

Non-parametric inference on calibration of predicted risks.

Moderate calibration, the expected event probability among observations with predicted probability z being equal to z, is a desired property of risk prediction models. Current graphical and numerical techniques for evaluating moderate calibration of risk prediction models are mostly based on smoothing or grouping the data. As well, there is no widely accepted inferential method for the null hypothesis that a model is moderately calibrated. In this work, we discuss recently-developed, and propose novel, methods for the assessment of moderate calibration for binary responses. The methods are based on the limiting distributions of functions of standardized partial sums of prediction errors converging to the corresponding laws of Brownian motion. The novel method relies on well-known properties of the Brownian bridge which enables joint inference on mean and moderate calibration, leading to a unified "bridge" test for detecting miscalibration. Simulation studies indicate that the bridge test is more powerful, often substantially, than the alternative test. As a case study we consider a prediction model for short-term mortality after a heart attack, where we provide suggestions on graphical presentation and the interpretation of results. Moderate calibration can be assessed without requiring arbitrary grouping of data or using methods that require tuning of parameters.

Chapter 4: Introduction and Getting Ready for Real-Ear Probe Microphone Measures.

Probe microphone measurements are an essential step in an individualized hearing aid fitting. These measurements allow audiologists to account for the individual's hearing and ear canal acoustics when programming hearing aids. An evidence-based hearing aid fitting includes matching the measured output of the hearing aids to targets for each input level and frequency. This allows the audiologist to confidently counsel the patient that the acoustic fitting is accurate, and the next step is for the individual to use the amplification during all waking hours to adapt to the newly amplified sounds. This also avoids mistakes such as overamplification or insufficient gain, which can endanger the patient and/or lead to a compromised fitting.

Aqueous size exclusion chromatography applied to polymer analysis: experimental conditions and molecular weight calibration curves.

Aqueous mode size exclusion chromatography (SEC) was employed for the analysis and construction of molecular weight (MW) calibration curves of three water-soluble polymers, namely, polyethylene glycol, polyethylene oxide, and polyacrylic acid sodium salt. Several calibration curves were obtained, varying chromatographic conditions such as columns arrangement, ionic strength, temperature and pH, in addition trends in polymeric chromatographic behavior were examined. The variation in SEC distribution coefficients at different temperatures was found to be below 10 %, indicating that the studied polymers follow an ideal SEC mechanism under the tested conditions. Thus, differences in chromatographic behavior were ascribed to changes in polymer configuration induced by media and/or temperature. These variations in morphology were consistent with the observed SEC behavior. Regarding MW calibration, polynomial regression models ranging from first to fifth order were applied, and the most adequate ones were selected based on their fit and prediction capabilities. Third order polynomials were the preferred models for polyethylene glycol and polyacrylic acid sodium salt, independently of chromatographic conditions. Meanwhile for polyethylene oxide, either third or fifth-order polynomial models were optimal depending on the chromatographic conditions. All the selected regression models presented coefficients of multiple determination (R2) above 0.990, while achieving relative errors of prediction (REP%) in MW ranging from 0.3 to 4 % for cross-validation.

Chapter 1: Introduction and Getting Ready for Hearing Aid Test Box Measures.

In this chapter you will be introduced to the hearing aid test box equipment and work through how to prepare the equipment so that it is ready to provide the testing you will use to evaluate, fit, and troubleshoot hearing aids and other amplifiers. At the end of this chapter, you will be familiar with terminology associated with hearing aid test box measures and the leveling required with the reference microphone and coupler microphone to ensure that your measurements are accurate and can be interpreted.

Development of a Relative Dosimetric System for Calibration of 32P Eye Applicators Using Radiochromic Films.

Introduction: Beta irradiation after bare scleral surgery of primary pterygium is an effective and safe treatment, which reduces the risk of local recurrence. Purpose: Obtaining the reference dose rate for a radioactive applicator consisting of a plate as a 32P absorber, a steel window and a steel capsule. Methods: Relative dosimetry and dose profile were measured using two types of radiochromic films, HD-810 and EBT1, for the 32P applicator and were compared with Monte Carlo simulation data. Dose uniformity in the 32P applicator was obtained with radiochromic HD-810 film. Results: The measurement depth dose distribution data at distances up to 3.8 mm were compared with calculation data, and the values were not found to differ statistically. Depth dose distribution with a large dose gradient was determined and the dose rate data obtained 0.0053 ± 9.9% in unit of Gy/s.mCi at a 0.1 mm depth distance. Practical results indicated that the dose nonuniformity and the maximum symmetrical for the 32P applicator were 11.5% and 9.2%, respectively. Conclusions: Our experiments show that the use of the radiochromic film to perform the relative dosimetric checks is feasible and the activity value with acceptable error can be determined through this indirect method.

Hepatic-associated vascular morphological assessment to predict overt hepatic encephalopathy before TIPS: a multicenter study.

BACKGROUND: To provide patients the chance of accepting curative transjugular intrahepatic portosystemic shunt (TIPS) rather than palliative treatments for portal hypertension-related variceal bleeding and ascites, we aimed to assess hepatic-associated vascular morphological change to improve the predictive accuracy of overt hepatic encephalopathy (HE) risks. METHODS: In this multicenter study, 621 patients undergoing TIPS were subdivided into training (413 cases from 3 hospitals) and external validation datasets (208 cases from another 3 hospitals). In addition to traditional clinical factors, we assessed hepatic-associated vascular morphological changes using maximum diameter (including absolute and ratio values). Three predictive models (clinical, hepatic-associated vascular, and combined) were constructed using logistic regression. Their discrimination and calibration were compared to test the necessity of hepatic-associated vascular assessment and identify the optimal model. Furthermore, to verify the improved performance of ModelC-V, we compared it with four previous models, both in discrimination and calibration. RESULTS: The combined model outperformed the clinical and hepatic-associated vascular models (training: 0.814, 0.754, 0.727; validation: 0.781, 0.679, 0.776; p < 0.050) and had the best calibration. Compared to previous models, ModelC-V showed superior performance in discrimination. The high-, middle-, and low-risk populations displayed significantly different overt HE incidence (p < 0.001). Despite the limited ability of pre-TIPS ammonia to predict overt HE risks, the combined model displayed a satisfactory ability to predict overt HE risks, both in the low- and high-ammonia subgroups. CONCLUSION: Hepatic-associated vascular assessment improved the predictive accuracy of overt HE, ensuring curative chances by TIPS for suitable patients and providing insights for cirrhosis-related studies.

Effects of IMU sensor-to-segment calibration on clinical 3D elbow joint angles estimation.

Introduction: Inertial Measurement Units (IMU) require a sensor-to-segment calibration procedure in order to compute anatomically accurate joint angles and, thereby, be employed in healthcare and rehabilitation. Research literature proposes several algorithms to address this issue. However, determining an optimal calibration procedure is challenging due to the large number of variables that affect elbow joint angle accuracy, including 3D joint axis, movement performed, complex anatomy, and notable skin artefacts. Therefore, this paper aims to compare three types of calibration techniques against an optical motion capture reference system during several movement tasks to provide recommendations on the most suitable calibration for the elbow joint. Methods: Thirteen healthy subjects were instrumented with IMU sensors and optical marker clusters. Each participant performed a series of static poses and movements to calibrate the instruments and, subsequently, performed single-plane and multi-joint tasks. The metrics used to evaluate joint angle accuracy are Range of Motion (ROM) error, Root Mean Squared Error (RMSE), and offset. We performed a three-way RM ANOVA to evaluate the effect of joint axis and movement task on three calibration techniques: N-Pose (NP), Functional Calibration (FC) and Manual Alignment (MA). Results: Despite small effect sizes in ROM Error, NP displayed the least precision among calibrations due to interquartile ranges as large as 24.6°. RMSE showed significant differences among calibrations and a large effect size where MA performed best (RMSE = 6.3°) and was comparable with FC (RMSE = 7.2°). Offset showed a large effect size in the calibration*axes interaction where FC and MA performed similarly. Conclusion: Therefore, we recommend MA as the preferred calibration method for the elbow joint due to its simplicity and ease of use. Alternatively, FC can be a valid option when the wearer is unable to hold a predetermined posture.

Traceable Calibration of Atmospheric Oxidized Mercury Measurements.

Most previous measurements of oxidized mercury were collected using a method now known to be biased low. In this study, a dual-channel system with an oxidized mercury detection limit of 6-12 pg m-3 was deployed alongside a permeation tube-based automated calibrator at a mountain top site in Steamboat Springs Colorado, USA, in 2021 and 2022. Permeation tubes containing elemental mercury and mercury halides were characterized via an International System of Units (SI)-traceable gravimetric method and gas chromatography/mass spectrometry before deployment in the calibrator. The dual-channel system recovered 97 ± 4 and 100 ± 8% (±standard deviation) of injected elemental mercury and HgBr2, respectively. Total Hg permeation rates and Hg speciation from the gravimetric method, the chromatography system, the dual-channel system, and an independent SI-traceable measurement method performed at the Jozef Stefan Institute laboratory were all comparable within the respective uncertainties of each method. These are the first measurements of oxidized mercury at low environmental concentrations that have been verified against an SI-traceable calibration system in field conditions while sampling ambient air, and they show that accurate, routinely calibrated oxidized mercury measurements are achievable.

On-farm NIR sensor for milk analysis: Exploitation of bias monitoring and bias correction.

Long-term studies have shown a bias drift over time in the prediction performance of near-infrared spectroscopy measurement systems. This bias drift generally requires extra laboratory reference measurements to detect and correct for this bias. Since these reference measurements are expensive and time consuming, there is a need for advanced methodologies for bias drift monitoring and correction without the need for taking extra samples. In this study, we propose and validate a method to monitor the bias drift and two methods to tackle it. The first method requires no extra measurements and uses a modified version of Partial Least Squares Regression to estimate and correct the bias. This method is based on the assumption that the mean concentration of the predicted component remains constant over time. The second method uses regular bulk milk measurements as a reference for bias correction. This method compares the measured concentrations of the bulk milk to the volume-weighted average concentrations of individual milk samples predicted by the sensor. Any difference between the actual and calculated bulk milk composition is then used to perform a bias correction on the predictions by the sensor system. The effectiveness of these methods to improve the component prediction was evaluated on data originating from a custom-built sensor that automatically measures the NIR reflectance and transmittance spectra of raw milk on the farm. We evaluate the practical use case where models for predicting the milk composition are trained upon installation of the sensor at the farm, and later used to predict the composition of subsequent samples over a period of more than 6 months. The effectiveness of the fully unsupervised method was confirmed when the mean concentration of the milk samples remained constant, while the effectiveness reduced when this was not the case. The bulk milk correction method was effective when all relevant samples for the component were measured by the sensor and included in the analyzed bulk milk, but is less effective when samples included in the bulk which are not measured by the sensor system. When the necessary conditions are met, these methods can be used to extend the lifetime of deployed prediction models by significantly reducing the bias on the predicted values.

Comparative analysis of HEC-HMS and SWAT hydrological models for simulating the streamflow in sub-humid tropical region in India.

Assessment of water availability in sub-humid regions is important due to distinct climatic and environmental conditions. In this study, Soil and Water Assessment Tool (SWAT) and Hydrologic Engineering Center-Hydrologic Modeling System (HEC-HMS) models have been assessed in simulating streamflows in the sub-humid tropical Kabini basin in Kerala, India, spanning 1260 km2. Calibration and validation utilized daily weather data from 1997 to 2015 from the Muthankera gauging station. The study investigated the impact of routing methods on runoff simulation in the ArcSWAT, exploring Muskingum and Variable Storage methods. Evaluation metrics encompassed Nash-Sutcliffe Efïciency (NSE), Coefficient of Determination (R2), Percent bias (PBIAS), RMSE-observations standard deviation ratio (RSR), and Peak Percent Threshold Statistics (PPTS) approach for high-flow values. The result indicates that HEC-HMS outperforms SWAT concerning R2 and NSE values during daily calibration and validation. Monthly simulations showed HEC-HMS closely aligning with SWAT (Variable storage), outperforming SWAT (Muskingum). The PPTS approach proved effective in simulating high-flow values. Both models exhibited proficiency in streamflow analysis within the study area, promising predictive potential for future hydrological studies in sub-humid regions.

Wavenumber Calibration Protocol for Raman Spectrometers Using Physical Modelling and a Fast Search Algorithm.

A wavenumber calibration protocol is proposed that replaces polynomial fitting to relate the detector axis and the wavenumber shift. The physical model of the Raman spectrometer is used to derive a mathematical expression relating the detector plane to the wavenumber shift, in terms of the system parameters including the spectrograph focal length, the grating angle, and the laser wavelength; the model is general to both reflection and transmission gratings. A fast search algorithm detects the set of parameters that best explains the position of spectral lines recorded on the detector for a known reference standard. Using three different reference standards, four different systems, and hundreds of spectra recorded with a rotating grating, we demonstrate the superior accuracy of the technique, especially in bands outside of the outermost reference peaks when compared with polynomial fitting. We also provide a thorough review of wavenumber calibration for Raman spectroscopy and we introduce several new evaluation metrics to this field borrowed from chemometrics, including leave-one-out and leave-half-out cross-validation.

Strategy for Ensuring the Metrological Traceability of Nanoparticle Size Measurements by SEM.

The concept of measurement traceability is crucial for ensuring the data reliability and the comparability of measurement results provided by different instruments and operators. In the field of nanoparticle metrology, determining the size of nanoparticles using electron microscopy-based techniques remains a real challenge. In laboratory settings, the establishment of traceability regarding the instrument calibration procedures, the assessment of uncertainties associated with instruments/operators/samples/environments, as well as the complexities related to electron-sample interactions, are often neglected. In this article, we describe the calibration procedure set up at the LNE (Laboratoire National de métrologie et d'Essais) and propose an evaluation method for determining the uncertainties in measuring nanoparticle size by SEM (Scanning Electron Microscopy). This study investigates the impact of the energy of the primary electrons (PEs) generated by the electron beam and accelerating voltage on the reliability of size measurements. The convolution between the signals coming from a nanoparticle and the substrate on which the particle is deposited induces edge effects that can have a negative impact on the measurement results. Finally, a diagram describing the various stages involved in establishing traceability for SEM measurements of nanoparticle size is proposed to facilitate the work of future operators.

Understanding random resampling techniques for class imbalance correction and their consequences on calibration and discrimination of clinical risk prediction models.

OBJECTIVE: Class imbalance is sometimes considered a problem when developing clinical prediction models and assessing their performance. To address it, correction strategies involving manipulations of the training dataset, such as random undersampling or oversampling, are frequently used. The aim of this article is to illustrate the consequences of these class imbalance correction strategies on clinical prediction models' internal validity in terms of calibration and discrimination performances. METHODS: We used both heuristic intuition and formal mathematical reasoning to characterize the relations between conditional probabilities of interest and probabilities targeted when using random undersampling or oversampling. We propose a plug-in estimator that represents a natural correction for predictions obtained from models that have been trained on artificially balanced datasets ("naïve" models). We conducted a Monte Carlo simulation with two different data generation processes and present a real-world example using data from the International Stroke Trial database to empirically demonstrate the consequences of applying random resampling techniques for class imbalance correction on calibration and discrimination (in terms of Area Under the ROC, AUC) for logistic regression and tree-based prediction models. RESULTS: Across our simulations and in the real-world example, calibration of the naïve models was very poor. The models using the plug-in estimator generally outperformed the models relying on class imbalance correction in terms of calibration while achieving the same discrimination performance. CONCLUSION: Random resampling techniques for class imbalance correction do not generally improve discrimination performance (i.e., AUC), and their use is hard to justify when aiming at providing calibrated predictions. Improper use of such class imbalance correction techniques can lead to suboptimal data usage and less valid risk prediction models.

Calibration algorithms for continuous glucose monitoring systems based on interstitial fluid sensing.

Continuous glucose monitoring (CGM) is of great importance to the treatment and prevention of diabetes. As a proven commercial technology, electrochemical glucose sensor based on interstitial fluid (ISF) sensing has high sensitivity and wide detection range. Therefore, it has good promotion prospects in noninvasive or minimally-invasive CGM system. However, since there are concentration differences and time lag between glucose in plasma and ISF, the accuracy of this type of sensors are still limited. Typical calibration algorithms rely on simple linear regression which do not account for the variability of the sensitivity of sensors. To enhance the accuracy and stability of CGM based on ISF, optimization of calibration algorithm for sensors is indispensable. While there have been considerable researches on improving calibration algorithms for CGM, they have still received less attention. This article reviews the problem of typical calibration and presents the outstanding calibration algorithms in recent years. Finally, combined with existing research and emerging sensing technologies, this paper makes an outlook on the future calibration algorithms for CGM sensors.

Development and validation of a lung metastases-predicting nomogram for intermediate- to high-risk differentiated thyroid carcinoma patients.

Aim: This research aimed to construct a clinical model for forecasting the likelihood of lung metastases in differentiated thyroid carcinoma (DTC) with intermediate- to high-risk. Methods: In this study, 375 DTC patients at intermediate to high risk were included. They were randomly divided into a training set (70%) and a validation set (30%). A nomogram was created using the training group and then validated in the validation set using calibration, decision curve analysis (DCA) and receiver operating characteristic (ROC) curve. Results: The calibration curves demonstrated excellent consistency between the predicted and the actual probability. ROC analysis showed that the area under the curve in the training cohort was 0.865 and 0.845 in the validation cohort. Also, the DCA curve indicated that this nomogram had good clinical utility. Conclusion: A user-friendly nomogram was constructed to predict the lung metastases probability with a high net benefit.

[Box: see text].

Dynamic correction of dual-energy x-ray absorptiometry images improves chain speed prediction of lamb composition in abattoirs.

A prototype, on-line Dual Energy X-ray Absorptiometer (DXA) has shown high precision of the prediction of carcass composition for the purpose of improved sheep meat grading in the Australian lamb supply chain, albeit with small inaccuracies over time. These inaccuracies were present across hours, and more significantly across days, which were unacceptable for any accreditation of this device as an objective carcass measurement tool in Australia. This inaccuracy demanded the creation of a novel image-processing algorithm for the prototype DXA. This DXA was tested for repeatability of predictions of lamb carcass composition over minutes, hours, and days, using two developed image processing algorithms. There was high immediate repeatability for both algorithms when predicting lean muscle % in 40 lamb carcasses, with a maximum CV of 0.65% over five repeated scans. There was a decrease in the CV of the prediction of lean muscle % of 30 lambs scanned three times over a 48-h period from 5.93 to 1.19% when the superior algorithm was used. The inaccuracies of lean muscle % predictions were associated with increases in the unattenuated space pixel values in DXA images. Improvements of the current algorithm are required to demonstrate repeatability over time for the purpose of accreditation within the Australian sheep meat industry, and for possible expansion of this technology into international supply chains.

Impact of the measurement conditions and compression paddle on mammography dosimeter response.

The effect of mammography measurement conditions was investigated to evaluate their impact on measurement uncertainties in clinical practice. The most prominent physical X-ray beam quantities i.e., - air kerma, half-value layer, and X-ray tube voltage - were examined by measuring the response of two ionization chambers and six X-ray multimeters (XMMs) of different models. Measurements were performed using several anode/filter combinations and both with and without the compression paddle in the X-ray beam. Maximum differences of higher than 6 % were found for all quantities when the dosimeter displayed value was compared with the reference value or the variation within the clinical anode/filter combinations Mo/Mo and Mo/Rh were considered. The study showed that the calibration procedure with the W/Al anode/filter combination was reliable only for ionization chambers, and the response of XMMs varies in such a way that the calibration coefficient cannot be predicted between various measurement conditions used in calibration and clinical practices. XMM calibrations are typically performed without a compression paddle in the beam, and the response of the XMM changes when radiation quality is slightly altered. If XMM specific data is not available, based on this study, an additional uncertainty of 2 % (k = 1) could be used as a typical estimate, at least for air kerma measurements. XMMs should be used for clinical measurements in mammography only with correct settings. If the correct settings are not available, the XMMs should not be used or used only with extreme caution.

Linearizing the vertical scale of an interferometric microscope and its effect on step-height measurement.

The vertical scale calibration of an interferometric microscope is important for establishing traceability of surface topography measurements to the International System of Units (SI) unit of length, the meter. Building on the calibration procedure for the amplification coefficient developed by de Groot and Beverage [Proc. SPIE 9526, 952610 (2015)], this paper describes a calibration procedure that yields the response curve for the entire vertical scan motion of a coherent scanning interferometric microscope. The method requires only a flat mirror as an artifact, a narrow band spectral filter, an aperture to reduce the effective numerical aperture, and the ability to raise and lower the microscope head so that the center of the interferogram can be varied within the scan range. The local frequency of the interferogram is determined by fitting sections of the interferogram to a sinusoidal function. The nonlinearity determined from the local frequency data can be used to estimate the uncertainty in uncorrected vertical height measurements. We describe how optical profile data can be corrected for nonlinearity due to dynamic effects in the scan motion and show that the correction improves the reproducibility of step height measurements by at least a factor of three and close to that of the repeatability.