Calibration Correction Research Articles

A BP neural network-based micro particle parameters calibration and an energy criterion for the application of strength reduction method in MatDEM to evaluate 3D slope stability

To enhance the applicability of discrete element method in 3D slope stability analysis, a BP neural network-based micro parameter calibration method and an energy criterion are proposed by taking MatDEM as an example. Firstly, the relationship between the micro particle parameters and the shear strengths of particle aggregate are represented by using the BP neural network. And then the micro particle parameters are obtained for the given shear strengths by using a correction calibration. Next, the energy conversions are investigated for the stable and instable slope models in MatDEM. From a view of practical application, the abrupt in variation tendency and magnitude of the kinetic energy is selected for indicating the emergence of the limit equilibrium state of a slope. Finally, the effectiveness of the proposed improvements is testified by taking Baijiabao landslide as an example. Results verify that the calibration method established in this study is applicable to provide the micro particle parameters when the shear strength is constantly reduced, and the factor of safety determined by the kinetic energy criterion reflects the landslide stability at the global level.

Calibration Principle and Correction Factor for Flow Calorimeter in RF Medium-Power Measurement

Calibration Principle and Correction Factor for Flow Calorimeter in RF Medium-Power Measurement

Development of a specialised calibration and infra-red emissivity correction to enable the temperature monitoring of intermediate level nuclear waste using thermal imaging

The temperature measurement of intermediate level nuclear waste containers is vital to monitor thermal stability and track temperature trends over time. The use of thermal imaging for this monitoring has numerous advantages compared to using a single spot radiation thermometer, and Sellafield wish to employ this approach for their ‘3 m3 box’ intermediate level waste containers. In order to achieve this objective with confidence a custom temperature calibration is required for low uncertainty temperature measurement. Another key consideration for practical non-contact temperature measurement is the emissivity of the surface being measured at the relevant infrared wavelengths, as such the emissivity of the Sellafield 3 m3 box materials was measured and then corrected for. The implementation of a calibrated instrument and emissivity correction were validated using temperature controlled, 1:10 scale model 3 m3 box containers within a climatic chamber. The surface temperature of the scale containers was determined to an uncertainty of ± 6.5 °C (k = 2.1) for the container walls, ± 3.5 °C (k = 2.1) for the container lid and ± 1.5 °C (k = 2.1) for the container vents. The measurement techniques used to determine the temperature of the 1:10 scale 3 m3 box containers were therefore successful and there is a clear development path to monitoring the containers in storage using thermal imaging.

Method for Accurate Detection of Amino Acids and Mycotoxins in Planetary Atmospheres.

We present a systematic analysis of a large number of mass spectra accumulated as the number of ion fragments recorded in unit mass-to-charge detector channels. The method retrieves the abundances of detected species using an efficient deconvolution algorithm, which relies on fragment pattern recognition, mass calibration, and background correction. The abundance analysis identifies target species, amino acids, and mycotoxins through their characteristic fragmentation patterns in the presence of an increasing number of interfering species. The method offered robust and efficient retrieval of abundances of metabolic molecules in complex mixtures obscured by a wide range of toxic compounds.

HyScreen: A Ground-Based Imaging System for High-Resolution Red and Far-Red Solar-Induced Chlorophyll Fluorescence

Solar-induced chlorophyll fluorescence (SIF) is used as a proxy of photosynthetic efficiency. However, interpreting top-of-canopy (TOC) SIF in relation to photosynthesis remains challenging due to the distortion introduced by the canopy's structural effects (i.e., fluorescence re-absorption, sunlit-shaded leaves, etc.) and sun-canopy-sensor geometry (i.e., direct radiation infilling). Therefore, ground-based, high-spatial-resolution data sets are needed to characterize the described effects and to be able to downscale TOC SIF to the leafs where the photosynthetic processes are taking place. We herein introduce HyScreen, a ground-based push-broom hyperspectral imaging system designed to measure red (F687) and far-red (F760) SIF and vegetation indices from TOC with single-leaf spatial resolution. This paper presents measurement protocols, the data processing chain and a case study of SIF retrieval. Raw data from two imaging sensors were processed to top-of-canopy radiance by dark-current correction, radiometric calibration, and empirical line correction. In the next step, the improved Fraunhofer line descrimination (iFLD) and spectral-fitting method (SFM) were used for SIF retrieval, and vegetation indices were calculated. With the developed protocol and data processing chain, we estimated a signal-to-noise ratio (SNR) between 50 and 200 from reference panels with reflectance from 5% to 95% and noise equivalent radiance (NER) of 0.04 (5%) to 0.18 (95%) mW m-2 sr-1 nm-1. The results from the case study showed that non-vegetation targets had SIF values close to 0 mW m-2 sr-1 nm-1, whereas vegetation targets had a mean F687 of 1.13 and F760 of 1.96 mW m-2 sr-1 nm-1 from the SFM method. HyScreen showed good performance for SIF retrievals at both F687 and F760; nevertheless, we recommend further adaptations to correct for the effects of noise, varying illumination and sensor optics. In conclusion, due to its high spatial resolution, Hyscreen is a promising tool for investigating the relationship between leafs and TOC SIF as well as their relationship with plants' photosynthetic capacity.

Initial Drift Correction and Spectral Calibration of MarSCoDe Laser-Induced Breakdown Spectroscopy on the Zhurong Rover

The Mars Surface Composition Detector (MarSCoDe) carried by the Zhurong rover of China’s Tianwen-1 mission uses Laser-Induced Breakdown Spectroscopy (LIBS) to detect and analyze the material composition on Martian surfaces. As one extraterrestrial remote LIBS system, it is necessary to adopt effective and reliable preprocessing methods to correct the spectral drift caused by the changes in environmental conditions, to ensure the analysis accuracy of LIBS scientific data. This paper focuses on the initial spectral drift correction and estimates the accuracy of on-board wavelength calibration on the LIBS calibration target measured by the MarSCoDe LIBS. There may be two cases during the instrument launch and landing, as well as the long-term operation: (a) the initial wavelength calibration relationship can still apply to the on-board LIBS measurement; and (b) the initial wavelength calibration relationship has been changed, and a new on-board calibration is needed to establish the current relationship. An approach of matching based on global iterative registration (MGR) is presented in respect to case (a). It is also compared with the approach of particle swarm optimization (PSO) for case (b). Furthermore, their accuracy is estimated with the comparison to the National Institute of Standards and Technology (NIST) database. The experimental results show that the proposed approach can effectively correct the drift of the on-board LIBS spectrum. The the root-mean-square error (RMSE) of the internal accord accuracy for three channels is 0.292, 0.223 and 0.247 pixels, respectively, compared with the corrected Ti-alloy spectrum and the NIST database, and the RMSE of the external accord accuracy is 0.232, 0.316 and 0.229 pixels, respectively, for other samples. The overall correction accuracy of the three channels is better than one-third of the sampling interval.

Color Reproduction in LED Wall Virtual Production Stages

Virtual production stages with LED walls utilize illumination, display, and camera equipment which was not designed with this use case in mind. Because the spectral sensitivity of a camera is different from a human observer, a device specific calibration is required. Furthermore, the illumination spectrum emitted by the display contains large gaps in the cyan and yellow wavelength ranges and is dissimilar to the light sources for which cameras are designed. This causes object colors to be reproduced by the camera in an unnatural manner, making cinematographers hesitant to use LED walls as their primary light source. In this paper, a display calibration and camera color correction workflow for LED wall virtual production stages is proposed. A linear color correction matrix and the spectrum of a multi-channel LED fixture are jointly optimized to better reproduce object colors simultaneously illuminated by an LED display and the multi-channel fixture as they would appear under high CRI (Color Rendering Index) light sources. An alternative color correction method using root polynomials is found to further improve color reproduction. It is shown that the camera’s response to the display can be characterized by a linear 3×3 matrix and the display can be calibrated using the inverse of the color correction, allowing for a color accurate reproduction of a virtual environment.

Wavelength calibration and spectral sensitivity correction of luminescence measurements for dosimetry applications: Method comparison tested on the IR-RF of K-feldspar

Spectroscopic investigations provide important insights into the composition of luminescence emissions relevant to trapped-charge dating of sediments. Accurate wavelength calibration and a correction for the wavelength-dependent detection efficiency of the spectrometer system are crucial to ensure the correct spectrum interpretation and allow for its comparison with those obtained from other systems. However, to achieve an accurate detection efficiency correction, it is necessary to obtain the device-specific spectral response function (SRF). Here, we compare two SRF approximation methods by using either a calibration lamp of known irradiance or calculating the product of efficiency curves provided by the manufacturers of all known optical elements. We discuss the results using radiofluorescence (RF) measurements of two K-feldspar samples as an example. Feldspar infra-red (IR) RF spectra are known to be composed of several overlapping emissions, whose variation with sample mineralogy is still poorly understood and requires more extensive investigations. We find that both methods of sensitivity correction yield broadly similar results. However, the observed differences can alter a spectrum's interpretation. For example, we observe that after peak deconvolution the maximum signal wavelength of the IR-RF peak used for dating applications differs by ∼3–13 nm between the two methods, depending on sample and diffraction grating. We recommend using calibration lamps to determine a device's SRF but highlight the need to consider issues such as higher-order signals in the choice of filters to establish the SRF's reliable wavelength range. Additionally, we find that a simple and inexpensive fluorescent white light yields an acceptable wavelength calibration comparable to that obtained from a specialized light source.

Comparison on Quantitative Analysis of Olivine Using MarSCoDe Laser-Induced Breakdown Spectroscopy in a Simulated Martian Atmosphere

A Mars Surface Composition Detector (MarSCoDe) instrument mounted on Zhurong rover of Tianwen-1, adopts Laser-Induced Breakdown Spectroscopy (LIBS), with no sample preparation or dust and coatings ablation required, to conduct rapid multi-elemental analysis and characterization of minerals, rocks and soils on the surface of Mars. To test the capability of MarSCoDe LIBS measurement and quantitative analysis, some methods of multivariate analysis on olivine samples with gradient concentrations were inspected based on the spectra acquired in a Mars-simulated environment before the rover launch in 2020. Firstly, LIBS spectra need preprocessing, including background subtraction, random signal denoising, continuum baseline removal, spectral drift correction and wavelength calibration, radiation calibration, and multi-channel spectra subset merging. Then, the quantitative analysis with univariate linear regression (ULR) and multivariate linear regression (MLR) are performed on the characteristic lines, while principal component regression (PCR), partial least square regression (PLSR), ridge, least-absolute-shrinkage-and-selection-operator (LASSO) and elastic net, and nonlinear analysis with back-propagation (BP) are conducted on the entire spectral information. Finally, the performance on the quantitative olivine analyzed by MarSCoDe LIBS is compared with the mean spectrum and all spectra for each sample and evaluated by some statistical indicators. The results show that: (1) the calibration curve of ULR constructed by the characteristic line of magnesium and iron indicates the linear relationship between the spectral signal and the element concentration, and the limits of detection of forsterite and fayalite is 0.9943 and 2.0536 (c%) analyzed by mean spectra, and 2.3354 and 3.8883 (c%) analyzed by all spectra; (2) the R2 value on the calibration and validation of all the methods is close to 1, and the predicted concentration estimated by these calibration models is close to the true concentration; (3) the shrinkage or regularization technique of ridge, LASSO and elastic net perform better than the ULR and MLR, except for ridge overfitting on the testing sample; the best results can be obtained by the dimension reduction technique of PCR and PLSR, especially with PLSR; and BP is more applicable for the sample measured with larger spectral dataset.

A semi-monolithic detector providing intrinsic DOI-encoding and sub-200ps CRT TOF-capabilities for clinical PET applications.

Current clinical positron emission tomography (PET) systems utilize detectors where the scintillator typically contains single elements of 3-6-mm width and about 20-mm height. While providing good time-of-flight performance, this design limits the spatial resolution and causes radial astigmatism as the depth-of-interaction (DOI) remains unknown. We propose an alternative, aiming to combine the advantages of current detectors with the DOI capabilities shown for monolithic concepts, based on semi-monolithic scintillators (slabs). Here, the optical photons spread along one dimension enabling DOI-encoding with a still small readout area beneficial for timing performance. An array of eight monolithic LYSO slabs of dimensions 3.9×32×19mm3 was read out by a 64-channel photosensor containing digital SiPMs (DPC3200-22-44, Philips Digital Photon Counting). The position estimation in the detector's monolithic and DOI direction was based on a calibration with a fan beam collimator and the machine learning technique gradient tree boosting (GTB). We achieved a positioning performance in terms of mean absolute error (MAE) of 1.44mm for the monolithic direction and 2.12mm for DOI considering a wide energy window of 300-700keV. The energy resolution was determined to be 11.3%, applying a positional-dependent energy calibration. We established both an analytical and machine-learning-based timing calibration approach and applied them for a first-photon trigger. The analytical timing calibration corrects for electronic and optical time skews leading to 240ps coincidence resolving time (CRT) for a pair of slab-detectors. The CRT was significantly improved by utilizing GTB to predict the time difference based on specific training data and applied on top of the analytical calibration. We achieved 209ps for the wide energy window and 198ps for a narrow selection around the photopeak (411-561keV). To maintain the detector's sensitivity, no filters were applied to the data during processing. Overall, the semi-monolithic detector provides attractive performance characteristics. Especially, a good CRT can be achieved while introducing DOI capabilities to the detector, making the concept suitable for clinical PET scanners.

Influence of initial tunneling step on the return energy of high-order harmonic generation

To investigate high-order harmonic generation in a monochromatic laser field, we derive an analytical expression for the return energy of an electron as a function of the time interval between ionization and return. We then expand the expression for kinetic energy to second order with respect to the Keldysh parameter $\ensuremath{\gamma}$. In this expansion, the zero-order term is the return energy in the simple man model and the second-order term corresponds to corrections to this model. The origin of this additional kinetic energy is frequently attributed to the nonzero exit of the initial tunneling step. Here, we show that this commonly used picture is incomplete. We present a framework to fully understand the additional kinetic energy as resulting from additive contributions of zero-order and second-order velocities. Our results show that the nonzero velocity of the initial tunneling step has a quantifiable effect on the cutoff energy measured in high harmonic generation (HHG). This opens the door to experimentally addressing the question of the initial electron velocity at the tunnel exit, with important implications for the correct calibration of the attoclock, as well as our interpretation of the strong field-ionization process more broadly.

Efficiency calibration and self-attenuation correction in radioxenon measurement using β-γ coincidence method

Measurement of the four radioxenon isotopes, namely 131mXe, 133mXe, 133Xe, and 135Xe, play a key role in underground nuclear test monitoring for ensuring compliance with the Comprehensive Nuclear-Test-Ban Treaty (CTBT). To improve detection sensitivity, a β-γ coincidence technique is commonly used. Due to the presence of the gas matrix, such as stable xenon, nitrogen, helium, the self-attenuation effects should be taken into account when measuring different types of sample. In order to improve the accuracy of the measurement, the detection efficiencies of X-rays and γ-rays were derived by using a simulation gas calibration source with low density of sponge matrix. The detection efficiencies of β-particles and conversion electrons (CEs) were calibrated by measuring radioxenon sample. The self-attenuation correction factors of X-rays and γ-rays were determined by Geant4 simulation method. The self-attenuation correction factors of β-particles and CEs were provided by measuring the radioxenon samples with different volumes of xenon, nitrogen and helium.

Central blood pressure estimation in type 1 diabetes: impact and implications of peripheral calibration method.

Peripheral blood pressure (BP) waveforms are used for noninvasive central BP estimation. Central BP could assist in cardiovascular risk assessment in patients with type 1 diabetes mellitus (T1DM). However, correct calibration of peripheral BP waveforms is important to accurately estimate central BP. We examined differences in central BP estimated by radial artery tonometry depending on which brachial BP (SBP/DBP vs. MAP/DBP) is used for calibration of the radial waveforms, for the first time in T1DM. A cross-sectional study in T1DM patients without known cardiovascular disease. Radial artery BP waveforms were acquired using applanation tonometry ( SphygmoCor ) for the estimation of central SBP, central pulse pressure (PP) and central augmentation pressure, using either brachial SBP/DBP or MAP/DBP for the calibration of the radial pressure waveforms. Fifty-four patients (age: 46 ± 9.5 years; T1DM duration: 27 ± 8.8 years) were evaluated. Central BP parameters were significantly higher when brachial MAP/DBP-calibration was used compared with brachial SBP/DBP-calibration (7.5 ± 5.04, 7.5 ± 5.04 and 1.5 ± 1.36 mmHg higher central SBP, central PP and central augmentation pressure, respectively, P < 0.001). In patients with T1DM, there are significant differences in central BP values estimated with radial artery tonometry, depending on the method used for calibration of the radial waveforms. Brachial MAP/DBP-calibration resulted in consistently higher central BP as compared to using brachial SBP/DBP, leading to patient re-stratification. Hence, the accuracy of noninvasive estimation of central BP by radial tonometry is dependent on calibration approach, and this problem must be resolved in validation studies using an invasive reference standard to determine which method best estimates true central BP.

A 64-channel high-time resolution digital waveform sampling electronic system based on DRS4 for positron burst annihilation lifetime measurement

Measurements of the positron burst annihilation lifetime place high demand on the time discrimination of electronics. DRS4 chips based on switched capacitor array technology (SCA) are used to develop an electronic system with a total (2048 + 256)-channel sampling rate up to 5.12 GSPS, which can provide better time resolution and flexible data processing. The electronic system is modular in design and includes a front-end waveform sampling module (WSM) with 32 waveform sampling boards, each with 64 input channels plus 8 additional channels(one per DRS4 chip) for time calibaion, in addition to a back-end data processing module (DPM). The fan-out circuit integrated with the DPM will fan out the T0 signal in multiple stages at the time of positron burst generation and provide a common starting time and trigger signal for every DRS4 chip in the WSM. In this electronic system, the jitter of T0 after three-stage fan-out is 18 ps. After DC offset correction and time interval nonuniformity calibration, the coincidence time resolution with other channels is about 21 ps (σ). In addition, we correct the time difference of different channels of different chips, which is caused by different trace lengths of the multi-level fan-out T0 signal and the different fabrication processes. The electronic system is used to evaluate a 64-pixel detector module, and the time resolution of the detection module is measured to be 44 ps (σ).

Spectral calibration of photon-counting detectors at high photon flux.

Calibration of photon-counting detectors (PCDs) is necessary for quantitatively accurate spectral computed tomography (CT), but the calibration process can be complicated by nonlinear flux-dependent physical factors such as pulsepile-up. This work develops a method for spectral sensitivity calibration of a PCD-based spectral CT system that incorporates nonlinear flux dependence and can thus be employed at high photonflux. A calibration model for the spectral response and polynomial flux dependence is proposed, which incorporates prior x-ray source spectrum and PCD models and that has a small set of parameters for adjusting to the spectral CT system of interest. The model parameters are determined by fitting transmission data from a known object of known composition: a step-wedge phantom composed of different thicknesses of aluminum, a bone equivalent, and polymethyl methacrylate (PMMA), a soft-tissue equivalent. This fitting employs Tikhonov regularization, and the regularization strength and the polynomial order for the intensity modeling are determined by bias and variance analysis. The spectral calibration and nonlinear intensity correction is validated on transmission measurements through a third material, Teflon, at different x-ray photon fluxlevels. The nonlinear intensity dependence is determined to be accurately accounted for with a third-order polynomial. The calibrated spectral CT model accurately predicts Teflon transmission to within 1% for flux levels up to 50% of the detectormaximum. The proposed PCD calibration method enables accurate physical modeling necessary for quantitative imaging in spectral CT. Furthermore, the model applies to high flux settings so that acquisition times will not be limited by restricting the spectral CT system to low fluxlevels.

Prediction of microbial growth via the hyperconic neural network approach

The design and control of biological reactors depends upon the correct calibration and selection of kinetic parameters from the exponential phase in the microbial growth. The kinetic microbial parameters that are reported in the literature of biochemical engineering are obtained based on specific growth conditions, which limits their potential application in a wide variety of dynamic models. In this paper, we propose an adaptive machine-learning approach to predict microbial growth, and provide information on the effect that variations of pH and concentration of the culture media have on the growth rate. We study biological reactions and obtain a set of experimental exploratory data using the Pseudomonas aeruginosa (i.e., P. aeruginosa). The versatile and robust metabolism of P. aeruginosa is responsible for its ability to grow in different environment conditions, even at low nutrient and oxygen levels, in a sample range of temperatures (4∘-42∘C) and polluted sites. Our first contribution is to propose a technique to gather experimental data via measurements of optical density, microbial growth, from the Multiskan™ FC Microplate Photometer, Thermo Scientific. Our second contribution consists of building a surrogate model by successfully adapting the Hyperconic Multilayer Perceptron (HC-MLP), a novel computational and mathematical approach, to predict microbial growth across all the set of conditions of the experimental design. HC-MLP is a state-of-the-art method that is used to define complex non-linear decision boundaries, in the parameters’ space, using a mix of ideas from conformal geometry and neural networks, and focusing on quadratic hyper-surfaces through multiple hidden layers. Consequently, we generate precise surrogates, which can even predict microbial growth in values not evaluated during the experimental stage. Finally, our statistical testing and comparisons validate that the proposed experimental, mathematical and computational framework is robust and capable of predicting the dynamic growth of bacteria P. aeruginosa using two main operation conditions: pH and concentration culture media at pH 7.0. In the future, we plan to apply our proposed methodology to other bacterial strains and advance HC-MLP for forecasting dynamics of other multiple microbial measurements under a wide variety of conditions.

Correction to: Calibration and parameter corrections for the new generation of the TSI monitor on the FY-3E satellite

Correction to: Calibration and parameter corrections for the new generation of the TSI monitor on the FY-3E satellite

Constraints on Future Analysis Metadata Systems in High Energy Physics

In high energy physics (HEP), analysis metadata comes in many forms—from theoretical cross-sections, to calibration corrections, to details about file processing. Correctly applying metadata is a crucial and often time-consuming step in an analysis, but designing analysis metadata systems has historically received little direct attention. Among other considerations, an ideal metadata tool should be easy to use by new analysers, should scale to large data volumes and diverse processing paradigms, and should enable future analysis reinterpretation. This document, which is the product of community discussions organised by the HEP Software Foundation, categorises types of metadata by scope and format and gives examples of current metadata solutions. Important design considerations for metadata systems, including sociological factors, analysis preservation efforts, and technical factors, are discussed. A list of best practices and technical requirements for future analysis metadata systems is presented. These best practices could guide the development of a future cross-experimental effort for analysis metadata tools.

SCC-FRET: single-cell-based calibration of a FRET system

Reliable measurements of calibration parameters are crucial for quantitative three-cube Förster resonance energy transfer (FRET) measurements. Here we have developed a single-cell-based calibration method (SCC-FRET), which can simultaneously obtain spectral crosstalk correction parameters (β and δ) and calibration parameters (G and k) of a quantitative FRET system by imaging a cell expressing one kind of standard FRET plasmid with a known FRET efficiency (E) and the donor-to-acceptor concentration ratio (RC). We performed the SCC-FRET method on a three-cube FRET microscopy for the cells expressing C5V, and obtained β = 0.150 ± 0.000, δ = 0.610 ± 0.000, G = 2.840 ± 0.065, and k = 0.847 ± 0.013. These parameters were used to measure the E and RC values of C17V and C32V constructs in living cells and obtained EC17V = 0.382 ± 0.010 and EC32V = 0.311 ± 0.007, RC17V = 1.010 ± 0.023 and RC32V = 1.050 ± 0.022, consistent with the reported values, demonstrating the effectiveness of the the SCC-FRET method. We also performed the SCC-FRET method for the cells with different S/N levels (S/N > 10, 10 > S/N > 3, 3 > S/N > 1, respectively), and obtained consistent system calibration parameters under different S/N levels, indicating excellent robustness. SCC-FRET requires only imaging a cell expressing one kind of standard FRET plasmid for measuring all calibration parameters under identical imaging conditions, rendering the SCC-FRET method extremely convenient, accurate, and robust. The SCC-FRET provides strong support for expanding the biological application of quantitative FRET analysis in living cells.

Field performance of the GaugeCam image-based water level measurement system

Image-based stage and discharge measuring systems are among the most promising new non-contact technologies available for long-term hydrological monitoring. This article evaluates and reports the long-term performance of the GaugeCam (www.gaugecam.org) image-based stage measuring system in situ. For this we installed and evaluated the system over several months in a tidal marsh to obtain a good stratification of the measured stages. Our evaluation shows that the GaugeCam system was able to measure within about ±5 mm for a 90% confidence interval over a range of about 1 m in a tidal creek in a remote location of North Carolina, USA. Our results show that the GaugeCam system nearly performed to the desired design of ±3 mm accuracy around 70% of the time. The system uses a dedicated target background for calibration and geometrical perspective correction of images, as well as auto-correction to compensate for camera movement. The correction systems performed well overall, although our results show a ‘croissant-shaped’ mean error (-1 to +4 mm,) varying with water stage. We attribute this to the small, yet present, ‘fish-eye’ effect embedded in images, for which our system did not entirely correct in the tested version, and which might affect all image-based water level measurement systems.