Surface Tilt Research Articles

Retinal magnification factors at the fixation locus derived from schematic eyes with four individualized surfaces.

Retinal magnification factors (RMFs) allow the conversion of angles to lengths in retinal images. In this work, we propose paraxial and non-paraxial RMF calculation methods that incorporate the individual topography and separation of the anterior and posterior surfaces of the cornea and crystalline lens, assuming homogeneous ocular media. Across 34 eyes, the two RMF methods differ by 0.1% on average, due to surface tilt, decenter, and lack of rotational symmetry in the non-paraxial modeling, which results in up to 2.2% RMF variation with retinal meridian. Differences with widely used individualized RMF calculation methods are smallest for eyes with ∼24 mm axial length, and as large as 7.5% in a 29.7 mm long eye (15D myope). To better model the capture of retinal images, we propose the tracing of chief rays, instead of the scaling of posterior nodal or principal distances often used in RMF definitions. We also report that RMF scale change is approximately proportional to both refractive error and axial separation between the ophthalmoscope's exit pupil and the eye's entrance pupil, resulting in RMF changes as large as 13% for a 1cm displacement in a 15D myopic eye. Our biometry data shows weak correlation and statistical significance between surface radii and refractive error, as well as axial length, whether considering all eyes in the study, or just the high myopes, defined as those with refractive error sphere equivalent ≤ -4D. In contrast, vitreous thicknesses show a strong correlation (r ≤ -0.92) and significance (p ≤ 10-13) with refractive error when considering all eyes or just high myopes (r ≤ -0.95; p ≤ 10-5). We also found that potential RMF change with depth of cycloplegia and/or residual accommodation is smaller than 0.2%. Finally, we propose the reporting of individual ocular biometry data and a detailed RMF calculation method description in scientific publications to facilitate the comparison of retinal imaging biomarker data across studies.

A BUILDING CHANGE DETECTION METHOD BASED ON A SINGLE ALS POINT CLOUD AND A HRS IMAGE

Abstract. For common remote sensing image change detection based on different time phases, it is difficult to solve the problem of surface tilt caused by the different shooting angle and time, which makes it difficult to complete the accurate registration. Some scholars utilized three-dimensional data for change detection to avoid registration problem, however, it costs very high for using 3D data to detect changes. Aim at this problem, this paper proposes a method of combining a single phase of ALS (Airborne Laser Scanning) data and HRS (High Resolution Satellite) image. It is composed of the following four steps: (1) Extracting the shadow area of the new-phase optical image, and superimposing it with the classified old-time point cloud data, and then the disappeared building area and the approximate building area are obtained according to the associated relationship between the shadow area and buildings. (2) Determining the unchanged building areas as positive samples, and taking the remaining area and vegetation area after removing the approximate buildings from the image as negative samples, and then GrabCut algorithm is used to segment new-phase HRS images to obtain building areas. (3) Comparing between building areas obtained in the previous step and the registered old-time ALS data to obtain a new building area with noise. (4) Denoising the results of the previous step to obtain the final new building area. Two datasets are used to verify the method. The detection accuracy of the disappeared buildings is over 85%, and the detection accuracy of the newly added buildings is over 70%.

The direction of landscape erosion

Abstract. The rate of erosion of a landscape depends largely on local gradient and material fluxes. Since both quantities are functions of the shape of the catchment surface, this dependence constitutes a mathematical straitjacket, in the sense that – subject to simplifying assumptions about the erosion process, and absent variations in external forcing and erodibility – the rate of change of surface geometry is solely a function of surface geometry. Here we demonstrate how to use this geometric self-constraint to convert a gradient-dependent erosion model into its equivalent Hamiltonian, and explore the implications of having a Hamiltonian description of the erosion process. To achieve this conversion, we recognize that the rate of erosion defines the velocity of surface motion in its orthogonal direction, and we express this rate in its reciprocal form as the surface-normal slowness. By rewriting surface tilt in terms of normal slowness components and deploying a substitution developed in geometric mechanics, we extract what is known as the fundamental metric function of the model phase space; its square is the Hamiltonian. Such a Hamiltonian provides several new ways to solve for the evolution of an erosion surface: here we use it to derive Hamilton's ray-tracing equations, which describe both the velocity of a surface point and the rate of change of the surface-normal slowness at that point. In this context, gradient-dependent erosion involves two distinct directions: (i) the surface-normal direction, which points subvertically downwards, and (ii) the erosion ray direction, which points upstream at a generally small angle to horizontal with a sign controlled by the scaling of erosion with slope. If the model erosion rate scales faster than linearly with gradient, the rays point obliquely upwards, but if erosion scales sublinearly with gradient, the rays point obliquely downwards. This dependence of erosional anisotropy on gradient scaling explains why, as previous studies have shown, model knickpoints behave in two distinct ways depending on the gradient exponent. Analysis of the Hamiltonian shows that the erosion rays carry boundary-condition information upstream, and that they are geodesics, meaning that surface evolution takes the path of least erosion time. Correspondingly, the time it takes for external changes to propagate into and change a landscape is set by the velocity of these rays. The Hamiltonian also reveals that gradient-dependent erosion surfaces have a critical tilt, given by a simple function of the gradient scaling exponent, at which ray-propagation behaviour changes. Channel profiles generated from the non-dimensionalized Hamiltonian have a shape entirely determined by the scaling exponents and by a dimensionless erosion rate expressed as the surface tilt at the downstream boundary.

Development of an Optical Sensor Capable of Measuring Distance, Tilt, and Contact Force

Depth, proximity, and tactile sensors are often used in robotic object manipulation. The three types of sensors are combined to address each sensor limitation: Depth use is limited by blind spots and measurable range, proximity sensor is limited to millimetric distances, and the tactile sensor requires direct contact with the object. Here we present a novel sensor that can simultaneously measure millimetric distance and surface tilt, as well as contact force. We demonstrated the advantage of this novel sensor during a contact task. There, we implemented an admittance control and succeeded in achieving smooth transition from zero- to infinite-impedance contact condition and vice-versa. This novel sensor affords the realization of advanced interactions between robot and objects and contrary to previous approaches—limited by distance, blind spots, and impact force during initial contact—demonstrated good performance at all times with smooth and continuous measurements during contact.

No Difference in the Acute Effects of Randomization vs. Blocking of Units of Lower-Extremity Proprioceptive Training on Balance and Postural Control in Young Healthy Male Adults.

Random practice is a form of differential learning and its favorable acute effects on motor performance are well described when visual tasks are practiced. However, no study to date has investigated the acute effects of differential learning using variable proprioceptive stimuli instead of the visual cues. The aim of the present study was to compare the acute effects of randomized versus blocked lower-extremity proprioceptive training stimuli on balance and postural adjustments. In two conditions, healthy young males (n = 15, age = 23 years) performed 16 one-legged landings on a board tilted in four directions: 1) tilt direction unknown and randomized and 2) tilt direction known with order of presentation blocked. Multi-segmental angular sway while balancing on an unstable surface and postural responses to perturbation stimulus by surface tilts were measured before and 4 min after training. Overall frontal-plane postural sway on the unstable surface decreased (p < 0.05, η2 = 0.022) in both conditions, while sagittal-plane postural sway remained unchanged. When the surface was toes-up tilted in the perturbation test, the sagittal-plane shank-thigh-pelvis alignment improved in both conditions (p < 0.05, η2 = 0.017), but the direction of the segmental positioning was non-uniform across participants. We conclude that randomization vs. blocking of units of lower-extremity proprioceptive training did not affect balance and postural control in our cohort of healthy young adults but the improvements were test-specific.

Spontaneous charging affects the motion of sliding drops

Water drops moving on surfaces are not only an everyday phenomenon seen on windows but also form an essential part of many industrial processes. Previous understanding is that drop motion is dictated by viscous dissipation and activated dynamics at the contact line. Here we demonstrate that these two effects cannot fully explain the complex paths of sliding or impacting drops. To accurately determine the forces experienced by moving drops, we imaged their trajectory when sliding down a tilted surface, and applied the relevant equations of motion. We found that drop motion on low-permittivity substrates is substantially influenced by electrostatic forces. Our findings confirm that electrostatics must be taken into consideration for the description of the motion of water, aqueous electrolytes and ethylene glycol on hydrophobic surfaces. Our results are relevant for improving the control of drop motion in many applications, including printing, microfluidics, water management and triboelectric nanogenerators.

Percutaneous k-wiring versus closed reduction and cast application for the management of extra-articular distal end radius fractures: A comparative study

Introduction: In extra-articular distal radius fractures, closed reduction and casting have been the mainstay of treatment, difficulty lies in predicting and maintaining the proper reduction at the final union. Percutaneous K-wire stabilization is also a widely accepted treatment option, but there is no consensus on its outcome compared to closed reduction and casting. Aim: To evaluate the results of closed reduction and casting versus closed reduction with percutaneous K wire fixation and casting in the treatment of the distal radius extra-articular fracture with reference to the restoration of radial height, radial inclination, a volar tilt of the distal articular surface and to assess the functional outcome of the same measured by the Gartland and Werley demerit scoring system. Materials and Methods: Prospective study was conducted on 60 patients attending the Department of Orthopaedics, from December 2013 to May 2015 with extra-articular fractures (AO type 23-A2 and 23-A3) of the distal radius and fulfilling all the inclusion and exclusion criteria. The cases were randomly divided into two equal groups of 30 patients, the first group was treated by closed reduction and below elbow cast application, while the second group was treated by closed reduction percutaneous K-wire application and below elbow cast application. The radiological outcome of both groups were evaluated by measuring the Volar inclination, Radial inclination and Radial height, while the functional outcome was evaluated by the demerit scoring system of Gartland and Werley.Results: The Cast application group had 13 excellent, 9 good, 7 fair and 1 poor result the mean outcome score of the group was 5.2. The K wiring group had 11 excellent, 13 good, 5 fair and 1 poor result, the mean score of the group was 5.17. The unpaired student’s t-test on the values obtained from both groups yielded a p-value of 0.9816. The mean radial height in the Cast application group was 8.033mm while the mean in the k wiring group was 11.783mm. The mean volar tilt was 4.867 degrees and 7.5 degrees respectively. The mean radial inclination was 14.23 degrees and 19.1respectively. Unpaired student’s t-test on the values revealed a p-value of 0.0001 for all three.Conclusion: We concluded that closed reduction with percutaneous K-wire fixation under C-arm for treatment of extra articular fractures of distal radius gives statistically significantly better radiological outcome than treatment with closed reduction and casting alone, but there is no statistically significant difference in functional outcome.

Investigation of measurement data of low-coherence interferometry at tilted surfaces in the 3D spatial frequency domain

Abstract The 3D transfer characteristics of interference microscopes and their effect on the interference signals occurring at surface slopes are studied. The interference image stacks acquired during a depth scan are 3D Fourier transformed. This allows a comprehensive frequency domain analysis of the interferograms. The double foil model introduced in a previous publication enables the interpretation of the signal spectra and the underlying transfer behavior of the interferometer using the concept of the Ewald sphere, which is limited by the numerical aperture (NA) of the imaging system. Analysis in the 3D spatial frequency domain directly discloses that the lateral dimensions of the transfer function depend on the axial spatial frequency. In this contribution we investigate measuring objects produced by Nanoimprint-Lithography. The corresponding signal spectra bear information that can be utilized to optimize the subsequent signal processing algorithms. These include envelope and phase evaluation procedures of the interference signals. A narrow bandpass filter is used to actively select certain frequency components in order to improve the robustness of the estimation of the envelope position. Although the shape and width of the envelope are affected, this procedure increases the reliability of the evaluation process and improves the accuracy of the measured topography especially at steeper surface slopes.

Making the Urban Sky View Factor With Numerical Models Consistent With Radiation Heat Transfer Theory

Abstract This work proposes a method for removing the inconsistency between the numerical models used for determining the sky view factor (SVF) in an urban environment and fundamental radiation heat transfer theory. For this purpose, a transformation of the coordinate system from global to surface was developed, which corrected the measurement of the angular coordinates of the elements in the discretized sky vault. The transformation was deployed in a published numerical model and was validated in a non-urban environment with a widely used analytical expression for the SVF, with which it was found to be in excellent agreement. The method was subsequently applied to an urban scenario, and the results were compared with the original numerical model. The proposed method provides a better determination of the SVF as a function of the surface azimuth and tilt angle.

Dynamic characteristics of drops on tilted hydrophobic ratchet surfaces

Asymmetric ratchet surfaces are used to manipulate drops, which have received extensive attention due to their wide potential applications. In this study, using aluminum sheets as substrates, some hydrophobic ratchet surfaces with different geometric parameters were prepared. The dynamic behavior of drops in the initial movement stage on the tilted surfaces was captured by a high-speed camera. Compared with the behavior on the flat tilted aluminum sheet, the velocity and acceleration of the drop on the tilted ratchet surfaces exhibit non-linear characteristics. The forces acting on the drop were analyzed, and a theoretical model was proposed to elucidate the dynamic behavior, which was in agreement with the experimental results. Moreover, by changing the tilt angle of the substrate, the geometric parameters of ratchets and the size of the drops, the factors that affect the drop movement were investigated.

Liquid bridges between particles and the hydrophobic or hydrophilic surfaces of solar photovoltaic glass

Photovoltaic (PV) power generation technology is one of the most important methods for reaching the carbon peak and achieving carbon neutralization. Dust accumulation on the surface of PV glass greatly reduces the working performance and power generation efficiency of PVs. The hydrophobic or hydrophilic surfaces on the PV glass have substantial self-cleaning potential. In this study, the liquid bridges formed between particles and the hydrophobic or hydrophilic surfaces of solar PV glass are investigated. The effects of the liquid bridge force and the influencing factors for these two surfaces on particle dynamics behaviours are studied. Furthermore, the self-cleaning abilities of these two surfaces are also discussed. The results indicate that the liquid bridges formed between a particle and a hydrophilic PV glass placed horizontally or obliquely exhibit similar saddle shapes, but the liquid bridges wrap the particle on the surface of hydrophobic PV glass. The influence of the liquid bridges causes particles to adhere to the tilted hydrophilic or hydrophobic surfaces at liquid bridge volumes (VL) < 6 μL, making initially moving particles stay on these two tilted surfaces with 6 μL ≤ VL ≤ 20 μL and even achieving self-cleaning properties at VL > 20 μL. Both hydrophobic and hydrophilic surfaces increase the self-cleaning forces resulting from the liquid bridge formation with increasing VL, thus completing the self-cleaning process. Increasing the self-cleaning forces and decreasing the friction force and the liquid bridge force improves the self-cleaning abilities of the surface. These research findings have important theoretical significance and commercial engineering value in preventing and reducing dust accumulation on glass.

A novel hybrid model for predicting hourly global solar radiations on the tilted surface

A novel hybrid model for predicting hourly global solar radiations on the tilted surface

Electrostatic tweezer for droplet manipulation

Various physical tweezers for manipulating liquid droplets based on optical, electrical, magnetic, acoustic, or other external fields have emerged and revolutionized research and application in medical, biological, and environmental fields. Despite notable progress, the existing modalities for droplet control and manipulation are still limited by the extra responsive additives and relatively poor controllability in terms of droplet motion behaviors, such as distance, velocity, and direction. Herein, we report a versatile droplet electrostatic tweezer (DEST) for remotely and programmatically trapping or guiding the liquid droplets under diverse conditions, such as in open and closed spaces and on flat and tilted surfaces as well as in oil medium. DEST, leveraging on the coulomb attraction force resulting from its electrostatic induction to a droplet, could manipulate droplets of various compositions, volumes, and arrays on various substrates, offering a potential platform for a series of applications, such as high-throughput surface-enhanced Raman spectroscopy detection with single measuring time less than 20 s.

Comparative Valuation of Global Solar Radiation on Horizontal and Tilt Surfaces in Owerri, Nigeria

Comparative valuation of global solar radiation on horizontal and tilt surfaces with the use of Angstrom-Page and four isotropic models for Owerri has been carried out in this paper. Angstrom linear regression model is developed from thirty years (1992-2022) of sunshine hour and average monthly global solar radiation sourced from NIMET and NASA, respectively. The Angstrom regression coefficients 𝑎 and 𝑏determined for Owerri is 0.210 and 0.696, respectively. The developed model is used to estimate average monthly global solar radiation on horizontal surface and consequently, the amount of incident solar radiation received on tilt surface by the isotropic models. The MBE, RMSE and MPE values are estimated to be 0.0083, 0.0029 and -0.0041%, respectively, for the developed Angstrom-Page model. A strong coefficient of determination of 76.6% was obtained and Analysis of Variance (ANOVA) significant of 100% was observed, which shows the goodness of fitness of the model. Among the isentropic models studied, one of the models poorly estimated solar radiation on horizontal and tilt surfaces for the study location

Machine Learning Approach for Solar Irradiance Estimation on Tilted Surfaces in Comparison with Sky Models Prediction

In this study, two supervised machine learning models (Extreme Gradient Boosting and K-nearest Neighbour) and four isotropic sky models (Liu and Jordan, Badescu, Koronakis, and Tian) were employed to estimate global solar radiation on daily data measured for one year period at the National Center for Energy, Research and Development (NCERD) at the University of Nigeria, Nsukka. Two solarimeters were employed to measure solar radiation: one measured solar radiation on a tilted surface at a 15° angle of tilt, facing south, and the other measured global horizontal solar radiation. The measured global horizontal solar radiation and the time and day number were used as input for the prediction process. Python computational software was used for model prediction, and the performance of each model was assessed using statistical methods such as mean bias error (MBE), mean absolute error (MAE), and root mean square error (RMSE) (RMSE). Compared to the measured data, it was discovered that the Extreme Gradient Boosting (XGBoost) algorithm offered the best performance with the least inaccuracy to sky models.

Operating Temperatures and Diurnal Temperature Variations of Modules Installed in Open-Rack and Typical BIPV Configurations

Because of building skin integration with restricted or reduced rear-side ventilation, elevated operating temperatures are expected in building-integrated photovoltaics (BIPV) modules and systems, which may impact their long performance and reliability. This article reports an analysis of operating temperatures and diurnal (day–night) temperature variations of the modules in open-rack and some BIPV mounting configurations (BIPV-ventilated and BIPV-insulated) monitored over a period of 2–5 years in Southern Switzerland. The modules in BIPV configurations operated at 20°C–30°C higher temperatures than the same modules installed in an open-rack configuration. In the worst-case, the temperature of the BIPV modules reached values slightly above 90°C. In addition, the modules installed in BIPV configurations were confronted with considerably greater diurnal (day–night) temperature variations compared with the same modules with an open-rack mounting (on average 18°C–25°C more). This demonstrates that these modules can suffer from higher thermo-mechanical stresses, potentially leading to accelerated degradation rates, and shorter lifetimes. The suitability of the indoor qualification and safety tests in IEC 61215 and IEC 61730 were evaluated according to the threshold set at the 98th percentile real-life operating module temperature (as defined in the IEC TS 63126 guideline for qualifying PV modules operating at elevated temperatures). This study shows that according to IEC TS 63126, BIPV modules on a tilted surface in Southern Switzerland may need to be tested at harsher environmental conditions (e.g., higher temperatures) in a selection of indoor qualification and safety tests.

A Comprehensive Study of Solar Energy Components by Using Various Models on Horizontal and Inclined Surfaces for Different Climate Zones

The main objective of this research is to analyze the monthly average daily of global (H), beams (B) and diffuses (D) solar irradiance on a horizontal surface at four selected sites (El-Kharga, Hurghada in Egypt and Dammam, Hail in Saudi Arabia) during the period time from 1980 to 2020. The empirical models between (H/Ho) and meteorological parameters along with the values of (MBE), (RMSE), MPE, R2 and the t-Test statics are discussed. The results in this study indicate good agreement between observed and calculated values of total solar energy and diffuse solar fraction. The results for south facing surfaces of the (RMSE) for different slope at different models in the present research are discussions. Nine different models between isotropic and anisotropic used to estimate the diffuse solar radiation on a tilted surface at selected sites in this study. The absolute relative values of RMSE for the south-facing surface ranges from 7 to 41.3 at El-Kharga and Hurghada sites, Egypt in the present study for Koronakis and Stevenand Unsworth (SU) models respectively. The values of (RMSE), for the south-facing surface ranges from 9.3 to 39.7 at Dammam and Hail sites, Saudi Arabia in the present research for Koronakis and Klucher models respectively. For west-facing surface the values of RMSE range from 11.2 to 47.3 for Badescu and Koronakis models at El-Kharga and Hurghada sites, Egypt respectively, while values of RMSE range from 6.5 to 38.5 for Klucher and Reindl et al. models at Dammam and Hail sites, Saudi Arabia. The models Koronakis, Klucher and Stevenand Unsworth (SU) models are given the most accurate estimate for the south-facing surface, and Badescu, Koronakis, Klucher and Reindl et al. models are good performs better estimated for the west-facing surface.

Evaluation of 12 Transposition Models Using Observations of Solar Radiation and Power Generation

This article evaluates the performance of 12 solar transposition models according to the measured data in Zhangbei of Northern China, including four isotropic models, Liu&Jordan, Koronakis, Badescu, and Tian, and eight anisotropic models, Willmot, Bugler, Hay, Skartveit−Olseth, Stevenand−Unsworth, Reindl, Temps−Coulson, and Klucher. We measured global horizontal irradiance, beam global horizontal irradiance, and diffuse horizontal irradiance. Open circuit voltage and short circuit current data of tilted photovoltaic panels are also surveyed. The radiation data of tilted surface estimated by the transposition models are fitted with the power generation data calculated by open circuit voltage and short circuit current. The different transposition models are evaluated by three error indicators, which are, respectively, root mean square error RMBE, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The relationship between radiation and power generation is explored. In Zhangbei, the best performing anisotropic model is Reindl model. The unit area power generation of PV panels in this region is about 0.03−0.05 times of the value of unit area received radiation. We compare measured power generation with power generation estimated by the Reindl model. For most of data, the absolute errors of power generation are less than 0.1 kWh/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , and relative errors of power generation are not more than 20%.

Toward Terrain Effects on GNSS Interferometric Reflectometry Snow Depth Retrievals: Geometries, Modeling, and Applications

Accurate and high temporal-spatial resolution snow depth retrieval using the Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) has become a popular topic. The terrain is a significant issue affecting GNSS-IR snow depth retrieval. This study explores detailed information about the problems and new solutions to this issue. The main conclusions include but are not limited to the following aspects: 1) Reflections from Below the Antenna (RBA) is the primary geometrical relationship of the GNSS multipath signal for snow depth retrieval; 2) The proposed GSnow_TERR model considers the terrain effects by incorporating the surface tilt angle (γ) into the derivative of the multipath relative phase (φ) with respect to the satellite elevation angle ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> ). Unlike the previous region-by-region solutions, the new model has a definite physical meaning which considers the γ as an independent non-negligible variable; 3) The new model performs well for repeatable and non-repeatable GNSS tracks. The former agrees with the PBO H2O product with r <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.97 and a slightly 1 ~ 2 cm improvement in the RMSE. The latter agrees with the baseline two-step clustering method for GLONASS, Galileo, and BDS, with r <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.96 and RMSD = 1.11 cm. The rate of data utilization increases by a mean value of 38.21% for non-repeatable tracks. The performance of the model in practical applications is consistent with theoretical analysis. The findings of this study provide a valuable reference for future GNSS-IR snow depth research and applications.

Solar Transposition Modeling via Deep Neural Networks With Sky Images

This article presents a notable advance toward the development of a new method of increasing the single-axis tracking photovoltaic (PV) system power output by improving the determination and near-term prediction of the optimum module tilt angle. The tilt angle of the plane receiving the greatest total irradiance changes with Sun position and atmospheric conditions including cloud formation and movement, aerosols, and particulate loading, as well as varying albedo within a module's field of view. In this article, we present a multi-input convolutional neural network that can create a profile of plane-of-array irradiance versus surface tilt angle over a full 180 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\circ }$</tex-math></inline-formula> arc from horizon to horizon. As input, the neural network uses the calculated solar position and clear-sky irradiance values, along with sky images. The target irradiance values are provided by the multiplanar irradiance sensor (MPIS). In order to account for varying irradiance conditions, the MPIS signal is normalized by the theoretical clear-sky global horizontal irradiance. Using this information, the neural network outputs an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -dimensional vector, where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the number of points to approximate the MPIS curve via Fourier resampling. The output vector of the model is smoothed with a Gaussian kernel to account for error in the downsamping and subsequent upsampling steps, as well as to smooth the unconstrained output of the model. These profiles may be used to perform near-term prediction of angular irradiance, which can then inform the movement of a PV tracker.