Full Calibration Research Articles

Polarization upgrade of specMACS: calibration and characterization of the 2D RGB polarization-resolving cameras

Abstract. The spectrometer of the Munich Aerosol Cloud Scanner (specMACS) is a high-spatial-resolution hyperspectral and polarized imaging system. It is operated from a nadir-looking perspective aboard the German High Altitude and LOng range (HALO) research aircraft and is mainly used for the remote sensing of clouds. In 2019, its two hyperspectral line cameras, which are sensitive to the wavelength range between 400 and 2500 nm, were complemented by two 2D RGB polarization-resolving cameras. The polarization-resolving cameras have a large field of view and allow for multi-angle polarimetric imaging with high angular and spatial resolution. This paper introduces the polarization-resolving cameras and provides a full characterization and calibration of them. We performed a geometric calibration and georeferencing of the two cameras. In addition, a radiometric calibration using laboratory calibration measurements was carried out. The radiometric calibration includes the characterization of the dark signal, linearity, and noise as well as the measurement of the spectral response functions, a polarization calibration, vignetting correction, and absolute radiometric calibration. With the calibration, georeferenced, absolute calibrated Stokes vectors rotated into the scattering plane can be computed from raw data. We validated the calibration results by comparing observations of the sunglint, which is a known target, with radiative transfer simulations of the sunglint.

Ultra-simplified diffraction-based computational spectrometer

Miniaturizing spectrometers for compact and cost-effective mobile platforms is a major challenge in current spectroscopy research, where conventional spectrometers are impractical due to their bulky footprint. Existing miniaturized designs primarily rely on precalibrated response functions of nanophotonic structures to encode spectral information captured in a snapshot by detector arrays. Accurate spectrum reconstruction is achieved through computational techniques, but this requires precise component design, high-precision fabrication, and calibration. We propose an ultra-simplified computational spectrometer that employs a one-to-broadband diffraction decomposition strategy facilitated by a numerical regularized transform that depends only on the spectrum of the diffracted radiation. The key feature of our design is the use of a simple, arbitrarily shaped pinhole as the partial disperser, eliminating the need for complex encoding designs and full spectrum calibration. Our spectrometer achieves a reconstructed spectral peak location accuracy of better than 1 nm over a 200 nm bandwidth and excellent resolution for peaks separated by 3 nm in a bimodal spectrum, all within a compact footprint of under half an inch. Notably, our approach also reveals a breakthrough in broadband coherent diffractive imaging without requiring any prior knowledge of the broadband illumination spectrum, assumptions of non-dispersive specimens, or correction for detector quantum efficiency.

Experimental full calibration of quantum devices in a semi-device-independent way

Semi-device-independent (SDI) methods offer a credible way to calibrate preparation and measurement devices simultaneously in quantum information processing, using only prior knowledge such as the Hilbert space dimension. To date, the SDI method is restricted to a few state paradigms, which impedes its broader applications. Recently, Tavakoli [Phys. Rev. Lett. 125, 150503 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.150503] proposed an SDI scheme to certify t-designs with discrete and symmetric structures. In this work, we bridge the gap between discrete and continuous structures with a concept termed “covering angle,” while maintaining the SDI feature. This concept enables us to evaluate a quantum device’s ability to generate arbitrary quantum states in a Hilbert space via calibrating a certain t-design. This so-called full calibration method is further tailored to be tolerant of errors in realistic state production. We demonstrate this full calibration scheme for a qubit system with various t-designs and show that it renders SDI certificates for quantum key distribution, quantum random number generation, and magic state distillability.

Overall elastic characterization of equivalent FE models for aluminum foams through computational homogenization approach and genetic algorithm optimization

Aluminum foams are gaining increasing interest because of their widespread set of functional attributes combined with highly specific structural properties and affordable manufacturing processes. The finite element analysis of foam materials is typically performed with complex and time-consuming 3D models. Here, a beam FE model strategy is utilized to obtain a precise and time-saving simulation instrument for open-cell aluminum foams. The beam FE modeling is based on the Kelvin cell as a fundamental unit and provides a simplified geometrical description of the intersection node between ligaments whose elastic properties need to be adjusted through a calibration procedure. The beam FE model elastic properties are measured through a homogenization procedure that evaluates the elastic constants of an equivalent material. The issue of model calibration is formulated as an optimization problem exploiting the NSGA-II genetic algorithm. This procedure allows obtaining the full elastic calibration of the beam FE model, reproducing the orthotropic elastic behavior of the aluminum foams with reduced computational efforts.

Predictive maturity of non-linear concrete constitutive models for impact simulation

This paper explores the concept of predictive maturity for non-linear concrete constitutive models employed in the computational prediction of the structural response of reinforced concrete structures to impact from free-flying missiles. Such concrete constitutive models are widely varied in complexity. Three constitutive models were utilized within the same finite element structural model to simulate the response of the IRIS III experiment. Each of the models were individually calibrated with available material testing data and also re-calibrated assuming limited availability of test data. When full calibration is possible, more sophisticated constitutive models appear to provide more predictive maturity; however, when this data is not available (e.g. for an existing structure where representative test specimens may not be available), the expected maturity is reduced. Indeed, this hypothesis is supported by the simulations that indicate good agreement with measured experimental response quantities from the IRIS III tests with complex constitutive models and full calibration, and accordingly poor predictions when less complex models are used or when the more sophisticated models are poorly calibrated. Thus, predictions of structural response where complete material testing data is not obtainable should be understood as less predictive.

Online Self-Calibration for Visual-Inertial Navigation: Models, Analysis, and Degeneracy

As sensor calibration plays an important role in visual-inertial sensor fusion, this article performs an in-depth investigation of online self-calibration for robust and accurate visual-inertial state estimation. To this end, we first conduct complete observability analysis for visual-inertial navigation systems (VINS) with full calibration of sensing parameters, including inertial measurement unit (IMU)/camera intrinsics and IMU-camera spatial-temporal extrinsic calibration, along with readout time of rolling shutter (RS) cameras (if used). We study different inertial model variants containing intrinsic parameters that encompass most commonly used models for low-cost inertial sensors. With these models, the observability analysis of linearized VINS with full sensor calibration is performed. Our analysis theoretically proves the intuition commonly assumed in the literature—that is, VINS with full sensor calibration has four unobservable directions, corresponding to the system's global yaw and position, while all sensor calibration parameters are observable given fully excited motions. Moreover, we, for the first time, identify degenerate motion primitives for IMU and camera intrinsic calibration, which, when combined, may produce complex degenerate motions. We compare the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">online</i> self-calibration on commonly used IMUs against the state-of-art <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">offline</i> calibration toolbox Kalibr, showing that the proposed system achieves better consistency and repeatability. Based on our analysis and experimental evaluations, we also offer practical guidelines to effectively perform online IMU-camera self-calibration in practice.

Modeling of Fatigue Cracking in Asphalt Materials Based on the Paris Law with an Initialization Term—Calibration from Notched and Unnotched Specimens

Abstract This article aims at presenting a thermo-mechanical model dedicated to fatigue cracking in bituminous material. The model calibration based on two-point bending (2PB) fatigue tests performed on specimens of bitumen-bound sand is also detailed. In the model, crack growth is handled by the Paris law considering the initialization term Nini. This parameter represents the number of loading cycles required to initiate a short macrocrack of length a0 from which the Paris law can be applied. The tests utilized for calibration and comparison with the numerical simulations are performed on notched and unnotched trapezoidal samples, for different levels of imposed displacement amplitude. The parameters of the Paris law are determined using the notched specimens (a0 being assimilated to the notch depth) except for Nini, which is deduced from the difference in lifetime duration between the tests carried out on notched and unnotched specimens. The full calibration procedure described thereafter has the advantage to not depend on the choice of a0. It is shown that the simulations run for the calibrated model are globally in good agreement with the test results obtained for both types of samples and for all the imposed displacement amplitudes. Finally, the model is used to predict the response of four-point bending tests carried out on the same bitumen-bound sand, considering the input parameters determined from the 2PB tests. The intrinsic nature of the model is evaluated through its ability to simulate both types of tests using the same set of material parameters.

Integration of numerical models to simulate 2D hydrodynamic/water quality model of contaminant concentration in Shatt Al-Arab River with WRDB calibration tools

Abstract The hydrodynamic model is essential for building a water quality model for rivers, lakes, estuaries, and other water systems. Most model software, such as HEC-RAS, can perform a complex hydrodynamic surface water body and limitations to represent water quality for the corresponding area. In contrast, other models, like WASP, can simulate a wide range of contaminants in a multidimensional geometry of rivers, estuaries, lakes, and reservoirs. Still, it requires flow information from separate hydrodynamic models. This article aims to develop a comprehensive water quality model of the Shatt Al Arab River south of Iraq by linking HEC-RAS with WASP. A variety of software techniques has sequentially been used. This software includes GIS for DEM modification, HEC-RAS for the hydrodynamic model, Python code with PyCharm to run the external coupler, WASP software for advective and dispersive contaminant transport, and finally, WRDB software for full calibration process and results display. The results showed successful transportation of flow information had been achieved. Moreover, the article described an effective calibration process by plotting comparison graphs and statistical summaries to make the appropriate decision. Another goal of this work is to collect the equations and associated reaction rates of source/sink kinetic for eutrophication’s state variables.

LC-MS/MS Analysis of Cyanotoxins in Bivalve Mollusks-Method Development, Validation and First Evidence of Occurrence of Nodularin in Mussels (Mytilus edulis) and Oysters (Magallana gigas) from the West Coast of Sweden.

In this paper, an LC-MS/MS method for the simultaneous identification and quantification of cyanotoxins with hydrophilic and lipophilic properties in edible bivalves is presented. The method includes 17 cyanotoxins comprising 13 microcystins (MCs), nodularin (NOD), anatoxin-a (ATX-a), homoanatoxin (h-ATX) and cylindrospermopsin (CYN). A benefit to the presented method is the possibility for the MS detection of MC-LR-[Dha7] and MC-LR-[Asp3] as separately identified and MS-resolved MRM signals, two congeners which were earlier detected together. The performance of the method was evaluated by in-house validation using spiked mussel samples in the quantification range of 3.12-200 µg/kg. The method was found to be linear over the full calibration range for all included cyanotoxins except CYN for which a quadratic regression was used. The method showed limitations for MC-LF (R2 = 0.94), MC-LA (R2 ≤ 0.98) and MC-LW (R2 ≤ 0.98). The recoveries for ATX-a, h-ATX, CYN, NOD, MC-LF and MC-LW were lower than desired (<70%), but stable. Despite the given limitations, the validation results showed that the method was specific and robust for the investigated parameters. The results demonstrate the suitability of the method to be applied as a reliable monitoring tool for the presented group of cyanotoxins, as well as highlight the compromises that need to be included if multi-toxin methods are to be used for the analysis of cyanotoxins with a broader range of chemical properties. Furthermore, the method was used to analyze 13 samples of mussels (Mytilus edulis) and oysters (Magallana gigas) collected in the 2020-2022 summers along the coast of Bohuslän (Sweden). A complementary qualitative analysis for the presence of cyanotoxins in phytoplankton samples collected from marine waters around southern Sweden was performed with the method. Nodularin was identified in all samples and quantified in bivalve samples in the range of 7-397 µg/kg. Toxins produced by cyanobacteria are not included in the European Union regulatory monitoring of bivalves; thus, the results presented in this study can be useful in providing the basis for future work including cyanotoxins within the frame of regulatory monitoring to increase seafood safety.

Comparison of generic Tenax and specialized PAH tubes for monitoring polycyclic aromatic hydrocarbons in the ambient air

The thermal desorption (TD) technique has potential advantages for monitoring polycyclic aromatic hydrocarbons (PAHs) in the air, e.g., no need for sample preparation. This study aims to compare the performance of two types of TD tubes: the generic Tenax TA tube and a proprietary PAH tube specifically designed for PAH sampling. Full calibrations were performed on a TD-gas chromatography/mass spectrometry (GC/MS) system for 16 priority PAHs. Co-located field samples were collected with two tubes at a flow rate of 200 mL/min for 24 h in eight rounds. In the laboratory, blank Tenax and PAH tubes had trace-level PAHs ranging from 0 to 0.35 ng/tube and 0−0.83 ng/tube, respectively, after 2-hr conditioning at 330 °C. The calibration with Tenax tubes showed an average precision of 7.5%, R2 from 0.9959 to 1.0000, and method detection limits (MDLs) from 0.056 to 3.64 ng/m3. The calibration of PAH tubes showed an average precision of 7.5%, R2 from 0.9945 to 1.0000, and MDLs from 0.065 to 5.91 ng/m3. In the field, blank Tenax and PAH tubes had trace PAH levels of 0.01–0.34 ng/tube and 0.01−0.42 ng/tube, respectively. Both tubes had negligible breakthroughs (<4%) and good precisions (<20%). Co-located Tenax and PAH tubes displayed a good agreement for light PAHs (differences mostly <30%) but high uncertainty for heavy PAHs (difference 35−70%). Both tubes are applicable for PAH monitoring, but the proprietary PAH tube does not outperform the generic Tenax TA tube. More work is still needed to improve the sensitivity of TD methods for heavy PAHs, e.g., selecting appropriate sorbents and adopting advanced instruments.

Exploring the construction of an all-round cost management system for investment control in university engineering construction

Abstract In recent years, the investment amount of university engineering construction has been increasing significantly, and the establishment of scientific and reasonable cost management system has become particularly important in the investment control of engineering construction. This paper explores the investment control of university engineering construction and designs the basic framework based on three parts: whole process cost control, full caliber cost audit and full gradient grading management. With the help of BIM, we build a cost management system, which is divided into the planning stage, bidding stage, mid-construction, until the completion of the collation of cost data, extraction and preservation of cost indicators. After establishing a full range of cost management systems, the adjacency matrix X algorithm and functions are used to calculate. The experiment proves that: the investment estimate before the project construction affects more than 75% of the overall investment, and the all-round cost management system built based on BIM can make the investment estimate accurate and stable at 75%, and the negotiation change rule based on this is to save nearly 25% of the investment funds. The comprehensive cost management system has a comprehensive and detailed grasp of the cost process of specific construction projects and specific issues during construction, fully protecting the university’s investment interests.

Energy management strategy of Battery Energy Storage Station (BESS) for power grid frequency regulation considering battery SOX

In recent years, the application of BESS in power system has been increasing. If lithium-ion batteries are used, the greater the number of batteries, the greater the energy density, which can increase safety risks. Considering the state of charge (SOC), state of health (SOH) and state of safety (SOS), this paper proposes a BESS real-time power allocation method for grid frequency regulation. This method establishes the battery charge criterion table, selects the required action unit, and finally solves it through the planning solver. It can realize the safety management of BESS and deal with extreme situations. It can complete a full charge calibration without disconnecting the battery from BESS, so that the SOC of each battery is consistent. The effectiveness of this method is proved by the model based on 50 MW/100 MWh BESS in Qinghai Golmud.

Covariance dependent kernels, a Q-affine GARCH for multi-asset option pricing

This paper introduces a class of multivariate GARCH models that extends the existing literature by explicitly modeling correlation dependent pricing kernels. A large subclass admits closed-form recursive solutions for the moment generating function under the risk-neutral measure, which permits efficient pricing of multi-asset options. We perform a full calibration to three bivariate series of index returns and their corresponding volatility indexes in a joint maximum likelihood estimation. The results empirically confirm the presence of correlation dependance in addition to the well known variance dependance in the pricing kernel. The model improves both the overall likelihood and the VIX-implied likelihoods, with a better fitting of marginal distributions, e.g., 15% less error on one-asset option prices. The new degree of freedom is also shown to significantly impact the shape of marginal and joint pricing kernels, and leads to up to 53% differences for out-of-the-money two-asset correlation option prices.

Experimental Study and 3-D Meso-Scale Discrete Element Modeling on the Compressive Behavior of Foamed Concrete

The relationships between the mechanical properties of foam concrete and its pore structure and cement slurry properties have been confirmed, but these relationships cannot be directly reflected just through experimental research. Thus, experiments and the discrete element method (DEM) were used to reveal the relationship between pore structure, cement slurry characteristics, and mechanical properties in foam concrete in this paper. In order to ensure the authenticity and accuracy of numerical simulation, tests of foam concrete were carried out first, such as X-ray computed tomography (CT), the uniaxial compression test, and the three-point flexural test. On this basis, the failure process of foamed concrete was reflected by numerical simulation. The results show that the bearing capacity of foam concrete increases significantly with its increased density. In 750 kg/m3 foam concrete, the stress is mainly borne by the cement matrix. The ability of the cement matrix around the pores to resist tensile failure is weak, and the failure of foamed concrete is mainly caused by tensile failure. Moreover, when the loading rate is low, it takes a long time for the foamed concrete to break, and the cracks generated by the force expand along the weakest area around the pores to form a rough failure section. At higher loading rates, cracks tend to develop directly through the cement matrix along a straight line. The crack development process inside foam concrete is accurately presented by DEM. The density of foam concrete increases, the number of internal cracks decreases, and the cracks are dispersed. The crack development of foam concrete can be divided into the following stages: First, the microcracks are generated near the supports. Following that, the cracks are caused by tensile stress and gradually extend with increasing loading until the foamed concrete fails. Under full calibration, the engineering design of foam concrete can be completed by DEM.

Temperature dependent performance of Schmidt-Boelter heat flux sensors.

The total heat flux sensors for NASA's Mars Entry, Descent, and Landing Instrumentation 2 (MEDLI2) sensor suite on the Mars 2020 vehicle and the Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) technology demonstration mission are passively cooled Schmidt-Boelter gauges. The output of these sensors has been experimentally demonstrated to be dependent on the temperature of the sensing element. The experimental results are shown to align with a model that assumes temperature-dependent material properties, specifically the Seebeck coefficient. The MEDLI2 and LOFTID flight total heat flux sensors did not undergo a full thermal calibration prior to being installed on the flight vehicles since the temperature dependence was unknown ahead of time. Additionally, the material properties are not known due to the designs being proprietary. For these reasons, an approximate correction factor was derived. The applicability and associated uncertainty of this temperature-dependent correction factor are presented. The error that would be introduced into the measurement if temperature effects were not accounted for would be as high as 9.5% and 16% for the MEDLI2 and LOFTID total heat flux sensors, respectively. As a best practice for future flight missions and ground-based applications that employ similar passively cooled heat flux sensors, it is recommended to individually calibrate each sensor across all applicable use temperatures to account for sensor-to-sensor variations and minimize measurement uncertainty.

A recalibrated prediction model can identify level-1 trauma patients at risk of nosocomial pneumonia

IntroductionNosocomial pneumonia has poor prognosis in hospitalized trauma patients. Croce et al. published a model to predict post-traumatic ventilator-associated pneumonia, which achieved high discrimination and reasonable sensitivity. We aimed to externally validate Croce’s model to predict nosocomial pneumonia in patients admitted to a Dutch level-1 trauma center.Materials and methodsThis retrospective study included all trauma patients (≥ 16y) admitted for > 24 h to our level-1 trauma center in 2017. Exclusion criteria were pneumonia or antibiotic treatment upon hospital admission, treatment elsewhere > 24 h, or death < 48 h. Croce’s model used eight clinical variables—on trauma severity and treatment, available in the emergency department—to predict nosocomial pneumonia risk. The model’s predictive performance was assessed through discrimination and calibration before and after re-estimating the model’s coefficients. In sensitivity analysis, the model was updated using Ridge regression.Results809 Patients were included (median age 51y, 67% male, 97% blunt trauma), of whom 86 (11%) developed nosocomial pneumonia. Pneumonia patients were older, more severely injured, and underwent more emergent interventions. Croce’s model showed good discrimination (AUC 0.83, 95% CI 0.79–0.87), yet predicted probabilities were too low (mean predicted risk 6.4%), and calibration was suboptimal (calibration slope 0.63). After full model recalibration, discrimination (AUC 0.84, 95% CI 0.80–0.88) and calibration improved. Adding age to the model increased the AUC to 0.87 (95% CI 0.84–0.91). Prediction parameters were similar after the models were updated using Ridge regression.ConclusionThe externally validated and intercept-recalibrated models show good discrimination and have the potential to predict nosocomial pneumonia. At this time, clinicians could apply these models to identify high-risk patients, increase patient monitoring, and initiate preventative measures. Recalibration of Croce’s model improved the predictive performance (discrimination and calibration). The recalibrated model provides a further basis for nosocomial pneumonia prediction in level-1 trauma patients. Several models are accessible via an online tool.Level of evidenceLevel III, Prognostic/Epidemiological Study.

Residual correlation and ensemble modelling to improve crop and grassland models

Multi-model ensembles are becoming increasingly accepted for the estimation of agricultural carbon-nitrogen fluxes, productivity and sustainability. There is mounting evidence that with some site-specific observations available for model calibration (with vegetation data as a minimum requirement), median outputs assimilated from biogeochemical models (multi-model medians) provide more accurate simulations than individual models. Here, we evaluate potential deficiencies in how model ensembles represent (in relation to climatic factors) the processes underlying biogeochemical outputs in complex agricultural systems such as grassland and crop rotations including fallow periods. We do that by exploring the correlation of model residuals. We restricted the distinction between partial and full calibration to the two most relevant calibration stages, i.e. with plant data only (partial) and with a combination of plant, soil physical and biogeochemical data (full). It introduces and evaluates the trade-off between (1) what is practical to apply for model users and beneficiaries, and (2) what constitutes best modelling practice. The lower correlations obtained overall with fully calibrated models highlight the centrality of the full calibration scenario for identifying areas of model structures that require further development.

Eliminating or Shortening the Calibration for a P300 Brain-Computer Interface Based on a Convolutional Neural Network and Big Electroencephalography Data: An Online Study.

A brain-computer interface (BCI) measures and analyzes brain activity and converts it into computer commands to control external devices. Traditional BCIs usually require full calibration, which is time-consuming and makes BCI systems inconvenient to use. In this study, we propose an online P300 BCI spelling system with zero or shortened calibration based on a convolutional neural network (CNN) and big electroencephalography (EEG) data. Specifically, three methods are proposed to train CNNs for the online detection of P300 potentials: (i) training a subject-independent CNN with data collected from 150 subjects; (ii) adapting the CNN online via a semisupervised learning/self-training method based on unlabeled data collected during the user's online operation; and (iii) fine-tuning the CNN with a transfer learning method based on a small quantity of labeled data collected before the user's online operation. Note that the calibration process is eliminated in the first two methods and dramatically shortened in the third method. Based on these methods, an online P300 spelling system is developed. Twenty subjects participated in our online experiments. Average accuracies of 89.38%, 94.00% and 93.50% were obtained by the subject-independent CNN, the self-training-based CNN and the transfer learning-based CNN, respectively. These results demonstrate the effectiveness of our methods, and thus, the convenience of the online P300-based BCI system is substantially improved.

Thromboplastin calibration revisited to look for possible revision of the World Health Organization recommendations

BackgroundThromboplastin calibration is essential to determine the international sensitivity index required to calculate the international normalized ratio (INR). The procedure for calibration recommended by the World Health Organization (WHO) calls for the selection of patients on stable anticoagulation in the range of 1.5 to 4.5 INR. These patients are difficult to be recruited as the conventional therapeutic interval for warfarin is 2.0 to 3.0. A possible solution could be including patients with less intense anticoagulation in the calibration. ObjectivesWe sought to investigate the impact of this amended procedure on the parameters of calibration. MethodsEight data sets from previous calibrations of a rabbit thromboplastin that included patients on anticoagulation as required by WHO were used for this pilot study. Parameters of calibration as determined by the full data sets are identified as “full calibrations” and are considered reference. Each of the data sets were used to recalculate the calibration parameters after including patients with INRs of <4.0, <3.5, or <3.0, which were identified as “trimmed calibrations” and compared with those from the full calibrations. ResultsThere was marginal variation of the international sensitivity index, CV, and INR that can be hardly of practical significance. CV was the most affected parameter, which increased from the full to the trimmed <3.0 calibration, but never exceeded the 3% cutoff value recommended by WHO. ConclusionsShould the results of this pilot study be confirmed for the calibration of other thromboplastins, revision of the WHO recommendations to include patients with INR from 1.5 to 4.0 is warranted.

Sample balancing of curves for lens distortion modeling and decoupled camera calibration

State-of-the-art camera calibration methods usually estimate the pinhole model and lens distortion together by strict point correspondence. However, in many applications, only part of the full calibration result is required. Simpler calibration patterns like straight lines are studied in many works to calibrate only the lens distortion but lack precision compared with conventional methods. In this paper, we study the geometric invariants of line straightness and proposed a method to accurately estimate the normal vector of the original line from the distorted curve. We discovered that unbalanced samples have a significant influence on estimation accuracy. We proposed a sample balancing method and linear COD determination methods based on normal geometry. The proposed method requires little positioning restrictions of the camera or the calibration pattern, and lines are very easily found or established patterns. The proposed method is demonstrated with both synthetic data and real images. We show by experiment that camera calibration can be decoupled, and more flexible calibration patterns can be used for each stage.