Sensor Response Function Research Articles

Fusion neutron diagnostics with CVD diamond detectors

The measurement of Deuterium–Deuterium (DD) and Deuterium–Tritium (DT)-fusion neutrons is crucial for plasma diagnostics at nuclear fusion facilities, such as ITER. Elevated temperatures and high radiation levels challenge radiation detectors. Chemical Vapour Deposition (CVD) diamond withstands harsh environments and is a distinguished candidate for reliable plasma instrumentation (Angelone et al., 2021 and Passeri et al., 2021). Neutron-induced nuclear reactions on Carbon nuclei of diamond substrates are the basis for fusion neutron detection with CVD diamond detectors. DD-fusion neutrons have an energy of 2.45 MeV. The corresponding response function of diamond sensors is purely elastic scattering and has a characteristic shape. DT-fusion neutrons have 14.1 MeV kinetic energy, and their response function reveals different nuclear reactions. The 12C(n, α)9Be peak is the most prominent structure in this response function. The principles of neutron diagnostics with CVD diamond detectors are discussed in this paper and the measured response functions of diamond sensors for 2.45 MeV and 14.1 MeV neutrons are presented, as well as the fusion neutron measurement using a proton-recoil telescope.

Validation of EMI-2 Radiometric Performance with TROPOMI over Dome C Site in Antarctica

(1) The Environmental Trace Gases Monitoring Instrument-2(EMI-2) is a high-quality spaceborne imaging spectrometer that launched in September 2021. To evaluate its radiometric calibration performance in-flight, the UV2 and VIS1 bands of EMI-2 were cross-calibrated by the corresponding bands (band3 and band4) of TROPOMI over the pseudo-invariant calibration site Dome C. (2) After angle limitation and cloud filtering of the Earth radiance data measured by EMI-2 and TROPOMI over Dome C, the top of atmosphere (TOA) reflectance time series were calculated. The spectral adjustment factors (SAF) were derived from the solar spectrum measured by the sensor to minimize the uncertainties caused by the different spectral response functions (SRF) of sensors. In addition, a correction method based on the radiative transfer model (RTM) SCIATRAN was used to suppress unaccounted angular dependence of atmospheric scattering. The radiation performance of EMI-2 is evaluated using the TOA reflectance ratio of EMI-2 and TROPOMI, combining the SAF correction and RTM-based correction methods. (3) It was shown that the time series trending of the TOA reflectance ratio between EMI-2 measurements and TROPOMI demonstrate flat characteristics and strong correlation. The mean reflectance ratios range from 0.998 to 1.09. The standard deviation of the reflection ratio is less than 3%. For 328 nm, 335 nm, 340 nm, 460 nm, and 490 nm, the mean values are close to one, and the relative radiometric bias estimated through EMI-2 and TROPOMI intercalibration is less than 3%, and for other wavelengths, the biases are less than 6%, except for 416 nm, which behaves higher than 7%. The cross-calibration results show that the radiometric calibration of EMI-2 is within the relative accuracy requirement.

Optical Inline-Sagnac Current Sensor, Part II: Performance and Applications

The performance and applications of the optical inline-Sagnac current sensor/transducer in utility high voltage alternating current measurements (metering and protection) and high voltage direct current measurements (control, metering, and protection) are presented. New measurements of commercially available sensors are presented for a 216 kA <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">peak</sub> transient current, scale factor linearity for alternating currents from 5 mA <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rms</sub> to 32 kA <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rms</sub> and for direct currents from 100 mA to 27 kA, and temperature performance of ±0.11% over the temperature range of −60 °C to +65 °C. New properties of polarizer temperature-wavelength effects on the scale factor of the sensor are presented. Power quality measurements are discussed over the frequency range of 16.66 Hz to 5 kHz. A discussion of the limitations of optical noise on low current measurements is given. The experimental and calculated sensor response functions are compared. The limitations for low current measurements due to the IEC 61869 standard digital output are presented.

A novel method to simulate AVIRIS-NG hyperspectral image from Sentinel-2 image for improved vegetation/wildfire fuel mapping, boreal Alaska

• - Vegetation mapped from simulated AVIRIS-NG image offers greater details and accuracy. • − 33% improvement in the new vegetation map accuracy. • - A novel approach to generate improved vegetation maps for Alaska’s boreal domain. Detailed vegetation maps are one of the primary inputs for forest and wildfire management. Hyperspectral remote sensing is a proven technique for detailed and accurate vegetation mapping. However, the availability of recent hyperspectral imagery in Alaska is limited because of the logistics and high cost involved in its acquisition. In this study, we simulated AVIRIS-NG (Airborne Visible InfraRed Imaging Spectrometer - Next Generation) hyperspectral data from widely available Sentinel-2 multispectral data using the Universal Pattern Decomposition Method (UPDM). The UPDM is a spectral unmixing technique that uses detailed ground spectra of vegetation classes and the Spectral Response Functions of AVIRIS-NG and Sentinel-2 sensors to simulate imagery with the same number of bands and spectral resolution as an AVIRIS-NG image. We simulated three images (each covering an area of 100 km × 100 km) from two ecoregions to test portability of the approach. We collected ground spectra of vegetation and bare ground during summers (2019–2021) using a PSR+ 3500 hand-held spectroradiometer and created a spectral library for this study. The Iterative Endmember Selection (IES) algorithm was used to optimize the spectral library and to select the most representative endmembers for simulation: birch, spruce, and gravel. We validated the simulated hyperspectral imagery by comparing it with available AVIRIS-NG images. The simulated image was visually and spectrally similar to the AVIRIS-NG image (RMSE of 0.03 and 0.02 for birch and spruce spectra, respectively). We applied the Random Forest image classification model to derive detailed vegetation maps from the simulated images. Our vegetation map showed an improvement of 33% in the map accuracy compared to the LANDFIRE EVT map. This study demonstrated an efficient and cost-effective approach to derive detailed vegetation maps at the Sentinel scene scale by simulating hyperspectral images in Google’s cloud environment. It offers a novel pathway to generate detailed vegetation and fuel maps for the whole boreal region of Alaska to aid effective forest and fire management.

Source parameter estimation of acoustic emissions induced by hydraulic fracturing in the laboratory

SUMMARYThe hydraulic fracturing technique is used for resource production, such as in shale gas/oil extraction and enhanced geothermal systems. The effects of fracturing are often monitored via induced earthquakes, and obtaining as much information as possible from those earthquakes is desirable. The stress drop—calculated from the seismic moment Mo and corner frequency fc—is an earthquake-related parameter that can help identify additional characteristics of the seismicity. To investigate the relationship between stress drops and hydraulically induced seismic events, we estimated the Mo and fc of acoustic emission (AE) events during hydraulic fracturing experiments performed in the laboratory in previous studies using 2 Eagle Ford shale and 10 Kurokami-jima granite samples. We estimated Mo by fitting the theoretical spectra to the observed spectra after correcting for the following effects: (1) frequency response of AE transducers under the installation method used in the fracturing experiment, including differences in sensitivity across every transducer used in each experiment; and (2) the difference in radiation pattern coefficients, which depends on the focal mechanisms of each AE event. This analysis used 46 857 focal mechanisms obtained from moment tensor solutions estimated using a deep learning technique. The range of the resultant Mo was found to be 2.8 × 10–5 ≤ Mo ≤ 4.5 × 10–1 [N·m], corresponding to −9.1 ≤ Mw ≤ −6.3, where Mw is the moment magnitude. We also estimated fc using the multiple-empirical Green's function method, reducing the influence of modelling errors in the AE sensor response and transfer function of the medium. Out of the 1053 events whose Mo and fc were estimated, 465 events (44.2 per cent)—regardless of their focal mechanisms—were found to have Mo and fc values consistent with the constant stress drop scaling of shear failure (i.e. shear failures have 0.1–100 MPa stress drops independent of their magnitude) that has been repeatedly confirmed in many previous studies. The remaining events showed lower fc values than those expected from the scaling law. This indicates that high pore pressure in a source region induced by fluid stimulation contributes to the occurrence of low-frequency earthquakes. Overall, we demonstrated that source parameter estimation was possible for laboratory AEs induced by hydraulic fracturing, which can improve our understanding of the characteristics of fluid-induced earthquakes.

Calculation of Capacitive-Based Sensors of Rotating Shaft Vibration for Fault Diagnostic Systems of Powerful Generators.

This paper presents the results of research and development of capacitive-based sensors of rotating shaft vibration for fault diagnostic systems of powerful turbines and hydro generators. It showed that diagnostic systems with special sensors are the key to increasing the reliability of powerful turbines and hydro generators. The application of sensors in monitoring systems was considered, and the requirements for the sensors used were analyzed. Structures of concentric capacitive-based sensors of rotating shaft vibration based on the measurement of the capacitance value from the distance to the metal surface were proposed. The design scheme was created for determining electrode dimensions of the rotating shaft vibration capacitive-based sensors with concentric electrodes, and analytical dependences were obtained. The calculation results allow the selection of optimal parameters of the active and guard electrodes. Analytical and computer simulation methods determined the response functions of the capacitive sensors. Analytical calculations and simulation results using 3D FEM were used to find the response functions of the sensors. The calculation of the characteristics of the capacitive-based sensors of rotating shaft vibration is presented. The study of the influence of fringe effects was carried out using the obtained results of the modeling and analytical calculations.

Hyperspectral Microwave Sensors—Advantages and Limitations

Temperature and humidity soundings form the bedrock of modern data assimilation due to their ability to directly constrain the atmospheric state variables. Because of their ability to penetrate clouds and work in all weather conditions, microwave sounders have very large impacts on constraining numerical weather prediction models. Recent advancements in integrated microwave assembly, space-grade high speed analog to digital converters, gigabit-per-second data interconnects, and field programmable gate arrays have enabled a transition from traditional analog detector-based demodulators to digitally channelized systems that allow for hyperspectral, or fine spectral resolution microwave sounders to be viable replacements to the current operational instruments. This article demonstrates that retrievals of temperature and moisture soundings can be improved by as much as 50% when 60–80 appropriately chosen pseudochannels are employed. While the current simulations were limited to cloud free oceans, perhaps even greater benefits can be realized over land and cloud conditions where additional channels can help constrain the surface and clouds. The article also demonstrated the advantages of hyperspectral sensors as a way to detect radio frequency interference in the few Kelvin range, as well as its ability to improve intercalibration efforts due to its ability to match frequency response functions of target sensors.

Passively biased inline Sagnac interferometer-optical current sensor: theoretical review

A full theoretical analysis of the performance of passive inline Sagnac interferometric optical current sensor with component errors has been completed. A mathematical model was developed to show how nonideal components affect the overall performance of the sensor. The Faraday rotator element is a critical component in this passively biased optical current sensor. The analysis indicates that errors in the rotation element in the assembly can cause a ∼10 % / deg nonlinear error with current. Another source of nonlinearity in the response of the sensor is the 45-deg splices to the polarization maintaining fiber (PMF) link between the rotator element and the sensing head assembly. The analysis indicates a ∼0.2 % / deg error for the splice between the rotator and PMF link to the sensing head and a ∼0.1 % / deg error for the splice between the PMF and the quarter waveplate fiber at the sensing head. All quarter waveplate errors in the rotator assembly have linear effects to the sensor response function which can be calibrated out of the final sensor assembly. Temperature response data are presented for an uncompensated sensor over the +40 ° C to −30 ° C temperature range and the sensor shows a ±1.5 % accuracy.

Empirical models on urban surface emissivity retrieval based on different spectral response functions: A field study

Thermal emissivity is a prerequisite for retrieving the land surface temperature (LST) and estimating the land surface budget based on data from remote sensing. Despite the availability of empirical models on emissivity retrieval on the meso-scales, their incompatibility for complex surfaces of the micro-scale leads to errors in emissivity retrieval, thus compromising thermal assessments of urban environments. To minimize such errors, this paper proposed a method to retrieve pixel-scale emissivity on the micro-scale. To measure reflectance spectra and emissivity spectra in the field, a PSR+3500 handheld spectrometer and a 102F portable Fourier transform infrared spectrometer were respectively used. Upon resampling these spectra to spectral response functions (SRF) of drone-derived and satellite-derived sensors, diverse reflectance and emissivity values were obtained to establish empirical models characterizing correlations between the normalized difference vegetation index (NDVI) and emissivity. Then, these models were applied to the low-altitude hyperspectral image from the Nano-Hyperspec imager on a drone. The results show that the model established by the SRF of a thermal camera achieved a root mean square error (RMSE) of 0.0129, and the accuracy of emissivity retrieval was within 0.010. For satellite applications, the model founded by the SRF of Aster was the most accurate for retrieving the emissivity of urban surfaces, with a RMSE of 0.0082 and an average accuracy of 0.003. The model based on SRFs of Landsat 8 registered a RMSE of 0.0155 alongside an average accuracy of 0.012, while that based on Modis registered a RMSE of 0.1210, alongside an average accuracy of 0.007.

Performance of Radiative Transfer Models in the Microwave Region

AbstractWe compared two fast radiative transfer models, Community Radiative Transfer Model (CRTM) and Radiative Transfer for TIROS Operational Vertical Sounder (RTTOV), with the LBL model Atmospheric Radiative Transfer Simulator (ARTS). We used the measurements from Advanced Technology Microwave Sounder (ATMS) and the Global Precipitation Measurement Microwave Imager (GMI) for evaluation of the radiative transfer models. The models in comparison with the observations and each other performed very well with a mean difference less than 0.5 K for the temperature sounding channels operating near the oxygen absorption band at 60 GHz. There was a difference of up to 1 K among the models as well as compared with the observations for humidity sounding channels operating around water vapor absorption line at 183 GHz. The mean difference between the simulations and observations was up to 6 K for surface sensitive channels. Water vapor and surface sensitive channels also showed to be more sensitive than the temperature sounding channels to the spectroscopy models used to calculate the absorption coefficients. There was a small difference, less than 0.1 K, between brightness temperatures calculated using traditional boxcar and actual Sensor or Spectral Response Functions, except for a difference of 0.25 K for ATMS Channel 6. Double difference technique showed about 1 K difference between water vapor channels from ATMS instruments onboard N20 and National Polar‐orbiting Partnership (NPP). However, comparison of a new version of ATMS/NPP observations recently generated using an enhanced calibration algorithm with ATMS/N20 observations showed that the differences between the two instruments are less than 0.5 K after improving the ATMS/NPP calibration.

A Sensitivity Study of the 4.8 µm Carbon Dioxide Absorption Band in the MWIR Spectral Range

The measurements of gas concentrations in the atmosphere are recently developed thanks to the availability of gases absorbing spectral channels in space sensors and strictly depending on the instrument performances. In particular, measuring the sources of carbon dioxide is of high interest to know the distribution, both spatial and vertical, of this greenhouse gas and quantify the natural/anthropogenic sources. The present study aims to understand the sensitivity of the CO2 absorption band at 4.8 µm to possibly detect and measure the spatial distribution of emissions from point sources (i.e., degassing volcanic plumes, fires, and industrial emissions). With the aim to define the characteristics of future multispectral imaging space radiometers, the performance of the CO2 4.8 µm absorption band was investigated. Simulations of the “Top of Atmosphere” (TOA) radiance have been performed by using real input data to reproduce realistic scenarios on a volcanic high elevation point source (&gt;2 km): actual atmospheric background of CO2 (~400 ppm) and vertical atmospheric profiles of pressure, temperature, and humidity obtained from probe balloons. The sensitivity of the channel to the CO2 concentration has been analyzed also varying surface temperatures as environmental conditions from standard to high temperature. Furthermore, response functions of operational imaging sensors in the middle wave infrared spectral region were used. The channel width values of 0.15 µm and 0.30 µm were tested in order to find changes in the gas concentration. Simulations provide results about the sensitivity necessary to appreciate carbon dioxide concentration changes considering a target variation of 10 ppm in gas column concentration. Moreover, the results show the strong dependence of at-sensor radiance on the surface temperature: radiances sharply increase, from 1 Wm−2sr−1µm−1 (in the “standard condition”) to &gt;1200 Wm−2sr−1µm−1 (in the warmest case) when temperatures increase from 300 to 1000 K. The highest sensitivity has been obtained considering the channel width equal to 0.15 µm with noise equivalent delta temperature (NEDT) values in the range from 0.045 to 0.56 K at surface temperatures ranging from 300 to 1000 K.

Spectral Adjustment Model's Analysis and Application to Remote Sensing Data

Differences in the relative spectral response functions of sensors lead to data inconsistencies that should be harmonized before multisensor exploitation. In this paper, we use spectral libraries to simulate satellite data and build models to correct them. We then explore and compare different models for coarse and medium spatial resolution optical sensors, including moderate resolution imaging spectroradiometer, advanced very high resolution radiometer (AVHRR), visible infrared imaging radiometer suite, multispectral instrument aboard Sentinel-2, and Operational Land Imager aboard Landsat 8. We found that optimal correction of different bands depends on the model used. For the green and near infrared bands, a multilinear land cover dependent regression improves the accuracy by up to 80.9%. For the red band, a novel exponential dependence of the spectral band adjustment factor with the normalized difference vegetation index (NDVI) provides an accuracy improvement of up to 72.8%. The best way to correct the NDVI value is to use the corrected NIR and red bands using these models. We apply the proposed methods to 445 BELMANIP2 sites using AVHRR data from the long-term data record from 1982–2017. High NDVI pixels result in 30-year trends varying up to 0.06 when comparing uncorrected to spectrally adjusted NDVI. Further application of these methods to NASA's Harmonized Landsat and Sentinel 2 product shows that for the red band and NDVI, our proposed method provides improved accuracy (54.6% and 62.5%) over the linear spectral adjustment currently used.

Are Paleomagnetic Records From U-Channels Appropriate for Studies of Reversals and Excursions?

Sampling of sediment cores using plastic U‐channels has made possible the acquisition of detailed records of paleomagnetic secular variation, geomagnetic polarity, environmental magnetic studies, and relative paleointensity over the past several million years. U‐channel measurements provide the great advantage of rapid measurements of long sediment cores, but the signal resolution is attenuated by the response function of the magnetometer sensors, which therefore restrains the recovery of rapid and large‐amplitude field changes. Here we focus on the suitability of the dynamics of reversals and excursions derived from U‐channel measurements. We compare successive individual paleomagnetic directions of 1.5 cm × 1.5 cm × 1.5 cm cubic discrete samples with those of a 1.5‐m equivalent U‐channel sample train obtained by placing the samples adjacent to each other. We use varying excursion and transition lengths and generate transitional directions that resemble those of the most detailed paleomagnetic records. Excursions with opposite polarity directions recorded over less than 7.5 cm are barely detected in U‐channel measurements. Regarding reversals, U‐channel measurements smooth the signal of low‐resolution records and generate artificial transitional directions. Despite producing misleading similarities with the overall structure of transition records, longer transitional intervals fail also to reproduce the complexity of field changes. Finally, we test the convolution of magnetization by different response functions. The simulation reveals that even small response function changes can generate significant differences in results.

Genetic circuit characterization and debugging using RNA‐seq

Genetic circuits implement computational operations within a cell. Debugging them is difficult because their function is defined by multiple states (e.g., combinations of inputs) that vary in time. Here, we develop RNA‐seq methods that enable the simultaneous measurement of: (i) the states of internal gates, (ii) part performance (promoters, insulators, terminators), and (iii) impact on host gene expression. This is applied to a three‐input one‐output circuit consisting of three sensors, five NOR/NOT gates, and 46 genetic parts. Transcription profiles are obtained for all eight combinations of inputs, from which biophysical models can extract part activities and the response functions of sensors and gates. Various unexpected failure modes are identified, including cryptic antisense promoters, terminator failure, and a sensor malfunction due to media‐induced changes in host gene expression. This can guide the selection of new parts to fix these problems, which we demonstrate by using a bidirectional terminator to disrupt observed antisense transcription. This work introduces RNA‐seq as a powerful method for circuit characterization and debugging that overcomes the limitations of fluorescent reporters and scales to large systems composed of many parts.

Effect of propagation distance on acoustic emission fracture mode classification in textile reinforced cement

Textile reinforced cement (TRC) is a composite material being increasingly used for load bearing applications. Damage in TRC as in all cementitious materials is an important issue in civil engineering. Acoustic emission (AE) exhibits promising outcomes in laboratory and in in-situ monitoring applications. Evaluation of the fracture mode is crucial as generally, shearing phenomena occur later than tensile (bending) cracking and indicate more severe damage. The acoustic signatures of the damage modes influence most of AE parameters including the average frequency AF and RA-value. However, there are no universal classification boundaries between tensile and shear signals mainly due to geometric effects, material properties, as well as sensor location and response function. In order to highlight this problem and discuss the possibility of a solution, the study occupies not only with the evaluation of the damage mode based on AE parameters but in addition uses multiple sensors to investigate the effect of the wave propagation distance. This is crucial in thin cementitious laminates since damping, scattering, reflections and plate wave dispersion seriously distort the signal having a strong effect on the classification result. It is seen that the classification boundaries between tensile and shear fracture should incorporate the information of propagation distance.

Endocrine functions of the renal interstitium.

This review aims to summarize the knowledge about the sensor and endocrine response functions of resident interstitial cells of the kidney. By the production of renin, erythropoietin and arachidonate metabolites (medullipin) subsets of renal interstitial fibroblasts and pericytes in different kidney zones play a central role in salt, blood pressure and oxygen homeostasis of the body. Common to these endocrine functions is that their regulation mainly occurs by (de)recruitment of active cells.

Model-guided combinatorial optimization of complex synthetic gene networks.

Constructing gene circuits that satisfy quantitative performance criteria has been a long‐standing challenge in synthetic biology. Here, we show a strategy for optimizing a complex three‐gene circuit, a novel proportional miRNA biosensor, using predictive modeling to initiate a search in the phase space of sensor genetic composition. We generate a library of sensor circuits using diverse genetic building blocks in order to access favorable parameter combinations and uncover specific genetic compositions with greatly improved dynamic range. The combination of high‐throughput screening data and the data obtained from detailed mechanistic interrogation of a small number of sensors was used to validate the model. The validated model facilitated further experimentation, including biosensor reprogramming and biosensor integration into larger networks, enabling in principle arbitrary logic with miRNA inputs using normal form circuits. The study reveals how model‐guided generation of genetic diversity followed by screening and model validation can be successfully applied to optimize performance of complex gene networks without extensive prior knowledge.

Unsteady heat-flux measurements of second-mode instability waves in a hypersonic flat-plate boundary layer.

In this paper, we report on the application of the atomic layer thermopile (ALTP) heat-flux sensor to the measurement of laminar-to-turbulent transition in a hypersonic flat-plate boundary layer. The centerline of the flat-plate model was instrumented with a streamwise array of ALTP sensors, and the flat-plate model was exposed to a Mach 6 freestream over a range of unit Reynolds numbers. Here, we observed an unstable band of frequencies that are associated with second-mode instability waves in the laminar boundary layer that forms on the flat-plate surface. The measured frequencies, group velocities, phase speeds, and wavelengths of these instability waves are consistent with data previously reported in the literature. Heat flux time series, and the Morlet wavelet transforms of them, revealed the wave-packet nature of the second-mode instability waves. In addition, a laser-based radiative heating system was used to measure the frequency response functions (FRF) of the ALTP sensors used in the wind tunnel test. These measurements were used to assess the stability of the sensor FRFs over time and to correct spectral estimates for any attenuation caused by the finite sensor bandwidth.

EMCCD color correction based on spectral sensitivity analysis

The sensor response function of a color camera is very essential to understand an overall camera imaging pipeline and to process captured images. It is also true when we characterize underlying imaging behaviors of the electron multiplying charge coupled device (EMCCD) camera, which was recently proposed to acquire color images in low-light-level conditions. Unlike existing CCD cameras, the EMCCD camera contains partially uni-modal spectral sensitivity functions (SSFs), some of which consists of two base (bi-modal) functions, thus often leading to a serious color distortion in existing characterization techniques. To address this problem, we propose a novel method that corrects output colors of the EMCCD camera by analyzing its partially uni-modal characteristics. Specifically, our goal is to correct such color distortion by adjusting bi-modal SSFs to be uni-modal. We remove the secondary region of bi-modal channels using a pre-calculated spectral sensitivity of the EMCCD camera. Experimental results demonstrate that the proposed method reduces the color distortion as well as enlarges a color gamut, which is crucial to color reproduction.

Analytical Sensor Response Function of Viscosity Sensors Based on Layered Piezoelectric Thickness Shear Resonators

Resonant piezoelectric sensors based on bulk acoustic wave (BAW) thickness shear resonators are promising for the inline measurement of fluid viscosity, e.g., in industrial processes. The sensor response function can be derived from the general rigorous transfer matrix description of one-dimensional layered structures consisting of piezoelectric and non-piezoelectric layers of arbitrary number. This model according to Nowotny et al. provides a complete analytical description of the electrical and mechanical behaviour of such structures with two electrodes and arbitrary acoustic termination impedances (Rig-1d-Model). We apply this model to derive the sensor response functions and the mechanical displacement curves of the following configurations appropriate for viscosity sensors:(a)An AT cut quartz crystal plate in contact with vacuum at the backside plane and with the liquid under investigation at the front side plane (QL).(b)An AT cut quartz crystal in contact with the liquid under investigation at both sides (LQL).It is shown that in the QL case the originally only heuristically introduced and well established sensor response function according to Kanasawa can be derived from the Rig-1d-Model by introducing minor approximations. Experimental results are presented for the LQL configuration using an N1000 viscosity reference oil as test fluid.