Centroid Error Research Articles

Comparison of the Accuracy Between the Z CALC2 Calculator and Barrett Toric Calculator in Toric IOL Calculation.

To compare the accuracy of the Z CALC2 calculator and Barrett toric calculator in toric intraocular lens (IOL) calculation. Eighty-five eyes of 85 patients who underwent uneventful cataract surgery with toric IOL implantation were included. The accuracy was compared between the Z CALC2 calculator and Barrett toric calculator under two calculation modes: using simulated keratometry (SimK) from the IOLMaster 700 (Carl Zeiss Meditec AG) for posterior corneal astigmatism (PCA) prediction and employing total corneal astigmatism (total corneal refractive power [TCRP] or measured PCA) obtained from the Pentacam (Oculus Optikgeräte GmbH). The centroid of prediction errors, percentage of eyes with prediction errors within ±0.50 diopter (D), mean prediction error, and mean absolute prediction error were calculated. Subgroup analysis was conducted based on the orientation and magnitude of anterior corneal astigmatism and axial length. When using SimK, the two calculators with predicted PCA showed comparable accuracy. When employing total corneal astigmatism, the Barrett toric calculator with measured PCA showed a lower centroid error (0.15 vs 0.38 D), a higher percentage of eyes with prediction errors within ±0.50 D (47.1% vs 32.9%, P = .018), and a lower mean prediction error (0.57 vs 0.71 D, P = .033) compared to the Z CALC2 calculator with TCRP in the 4-mm zone. In subgroup analysis, when employing total corneal astigmatism, the Barrett toric calculator with measured PCA exhibited superior accuracy, especially in the with-the-rule and anterior corneal astigmatism of 2.00 D or less subgroups. When using SimK, the Z CALC2 calculator and Barrett toric calculator yield comparable accuracy. The Barrett toric calculator with measured PCA may be more recommended when employing total corneal astigmatism. [J Refract Surg. 2024;40(10):e681-e691.].

Accuracy of Toric Intraocular Lens Formulas With Measured Posterior Corneal Astigmatism of Different Orientations

PurposeTo assess whether the use of measured posterior corneal astigmatism (PCA) values improves the prediction accuracy of toric intraocular lens power formulas, compared to predicted PCA values, when the orientation of the steep axis of PCA is non-vertical. DesignRetrospective observational cohort study Methods418 eyes of 344 patients were included in the study. Prediction errors (PE) for postoperative refractive astigmatism at 4 weeks postoperatively were determined using vector analysis and compared for the following toric intraocular lens power formulas: Barrett Toric with predicted posterior corneal astigmatism (PPCA); Barrett Toric with measured posterior corneal astigmatism (MPCA); EVO Toric PPCA; EVO Toric MPCA; Holladay I with Abulafia-Koch regression. Subgroup analysis compared PEs for eyes with a vertically orientated steep axis of PCA (60-120o) to eyes with a non-vertically orientated steep axis of PCA. SettingCathedral Eye Clinic, Belfast, United Kingdom and Tan Tock Seng Hospital, Singapoore. ResultsStandard keratometry was with-the-rule in 48% of eyes, while the steep PCA axis was vertically orientated in 91% of eyes. For all eyes, EVO PPCA had a smaller mean absolute error than Barrett-MPCA, Barrett-PPCA and Abulafia-Koch (p < 0.01 for all). EVO-PPCA had the highest percentage of eyes within 0.50D of predicted postoperative astigmatism for eyes with vertical PCA (61%), while EVO-MPCA had the highest percentage for eyes with non-vertical PCA (54%). EVO-MPCA had the smallest centroid error for all eyes, and the subgroups (p < 0.01 for all). Eyes with non-vertical PCA had a lower percentage within 0.50D than eyes with vertical PCA when using PPCA (43% vs 61%, p = 0.034), but there was no significant difference between these groups when MPCA is used for eyes with non-vertical PCA (54% vs 61%, p = 0.40). ConclusionsWhen the steep axis of posterior corneal astigmatism is not vertically orientated, the use of measured posterior keratometry values improves prediction accuracy.

Lidar signal processing method for atmospheric coherence length measurement based on the WD-ADMF

A denoising method applied to atmospheric coherent length lidar is proposed. Wavelet decomposition (WD) and the adaptive median filter (ADMF) are combined in this method. In this research, the effectiveness of the WD-ADMF has been verified through simulation and measurement. The results show that this filter algorithm, when applied to lidar data, improves the average peak signal-to-noise ratio (PSNR) and centroid error while maintaining data integrity such that the measurement of coherence length or the inference of C n 2 from coherence length more closely matches simulated truth and measured data.

Fusion of a priori information and energy distribution for the centroiding method of the star sensor

The star sensor is the most accurate measurement instrument in the spacecraft attitude measurement system, and the accurate centroid of the star point is the basis for ensuring the performance of the star sensor. Currently, the centroid of the gray method is the most widely used centroid extraction method in practice. Systematic errors caused by the centroid of the gray method and random noise in the detector imaging process are the main factors contributing to the deviation of the star centroiding coordinates. Considering the relationship between the point spread function and the pixel gray value, this paper proposes a centroiding method to reduce the star point centroiding error by fusing a priori information and energy distribution. The star charts are first preprocessed using a curvature filter and Gaussian blur to reduce the random noise. Then the complexity of the point spread function is considered, and the pixel gray values are corrected based on a priori information and gray value fuzzy processing. Finally, the symmetry of the one-dimensional energy distribution is used to quickly determine the sub-pixel deviation to get the star centroid coordinates. Through simulation and physical simulation experiments, the method was verified to be effective, and the extraction accuracy met the requirements of high-precision star sensors. The night sky observation test results demonstrate that the method in this paper can improve the measurement accuracy of the star sensors.

An OpenSim-Based Closed-Loop Biomechanical Wrist Model for Subject-Specific Pathological Tremor Simulation.

A pathological tremor (PT) is an involuntary rhythmic movement of varying frequency and amplitude that affects voluntary motion, thus compromising individuals' independence. A comprehensive model incorporating PT's physiological and biomechanical aspects can enhance our understanding of the disorder and provide valuable insights for therapeutic approaches. This study aims to build a biomechanical model of pathological tremors using OpenSim's realistic musculoskeletal representation of the human wrist with two degrees of freedom. We implemented a Matlab/OpenSim interface for a forward dynamics simulation, which allows for the modeling, simulation, and design of a physiological H∞ closed-loop control. This system replicates pathological tremors similar to those observed in patients when their arm is extended forward, the wrist is pronated, and the hand is subject to gravity forces. The model was individually tuned to five subjects (four Parkinson's disease patients and one diagnosed with essential tremor), each exhibiting distinct tremor characteristics measured by an inertial sensor and surface EMG electrodes. Simulation agreement with the experiments for EMGs, central frequency, joint angles, and angular velocities were evaluated by Jensen-Shannon divergence, histogram centroid error, and histogram intersection. The model emulated individual tremor statistical characteristics, including muscle activations, frequency, variability, and wrist kinematics, with greater accuracy for the four Parkinson's patients than the essential tremor. The proposed model replicated the main statistical features of subject-specific wrist tremor kinematics. Our methodology may facilitate the design of patient-specific rehabilitation devices for tremor suppression, such as neural prostheses and electromechanical orthoses.

Способ подбора данных кератометрии для расчета торичности ИОЛ

Purpose. To elaborate the customized principle of determining the actual zone of the corneal astigmatism based on keratotopographic data and compare the accuracy of calculating the toric IOL according to the actual zone and conventional keratometry. Material and methods. The study included 48 patients (48 eyes) who underwent toric IOL implantation. 3–6 months (5.1±0.6) after surgery, all patients were measured the residual refractive astigmatism. The toric IOL was retrospectively calculated according to the data of the actual keratotopographic zone determined by the proposed method (1st group) and according to conventional keratometry (2nd group). Vector and centroid analyses were used to estimate the error in calculating the IOL toricity. Results. The principles of determining the actual zone are based on the assumption that maximum visual acuity and visual quality can be achieved when the regularity of astigmatism in the central parts of the cornea corresponds to the regularity of toric IOL. The mean diameter of the selected actual zone was 2.93±0.61 (from 2.0 to 4.3 mm respectively). The average vector error of toricity calculation in 1st group was 0.30±0.31, in 2nd group – 0.42±0.30 (p=0.006). Centroid analysis showed similar values of centroid error in 1st group and 2nd group (0.09 and 0.08), while the dispersion was higher in 2nd group (0.42 and 0.51, respectively). Conclusion. The customized principle of selecting the actual zone according to topographic maps of the cornea showed a more accurate calculation of the IOL toricity compared with the use of conventional keratometry data. Key words: toric IOL, corneal astigmatism, IOL calculation accuracy, keratometry, keratotopography

Comparison of toric intraocular lens calculation with the integrated K method and three single biometric devices.

To compare astigmatic outcomes using the Integrated K method and anterior surface keratometry from 3 different biometric devices. Lions Eye Institute, Perth, Australia. Retrospective case series. Eyes of patients who underwent uneventful cataract surgery were analyzed. Predicted postoperative astigmatism was calculated for Integrated K method, IOLMaster 700, Lenstar and Pentacam. The mean centroid error in predicted postoperative refractive astigmatism (PE), mean absolute PE and percentage of eyes within 0.5 diopter (D), 0.75 D and 1 D of absolute magnitude of PE were compared. A subset analysis was done where the difference in cylinder magnitude between the 2 methods was more than 0.25 D. Spherical prediction outcomes were also analyzed. 241 eyes of 139 patients were included in the study. The mean centroid PE of Integrated K method (-0.07 @ 69) was significantly different from IOLMaster and Pentacam. The mean absolute PE with Integrated K method (0.33 ± 0.17) was significantly lower than all 3 devices. The percentage of eyes within 0.5 D and 0.75 D of absolute magnitude of PE was 82% and 99% for Integrated K method, 76% and 95% for IOLMaster and Lenstar, and 60% and 86% for Pentacam. In the subset analysis, the improvement in accuracy of the Integrated K method compared with a single device was greater in terms of the percentage of eyes predicted within 0.5 D. The Integrated K method did not impact the spherical prediction outcomes. The integrated K method is more accurate and precise than anterior surface keratometry from a single biometric device.

Improved active-tracking performance through Hadamard speckle contrast reduction.

We report wave-optics simulation results and benchtop experimental findings that demonstrate reduced centroiding error through a Hadamard speckle contrast reduction (HSCR). The method involves projecting multiple orthogonal phase patterns onto an actively imaged object within a single camera resolution cell and integration time. Ideally, performance improves in proportion to the square root of the number of such phase realizations applied. Using 16 subpixels per camera pixel, our simulated track performance consistently meets this expectation with a decent experimental agreement, particularly at smaller object sizes. This outcome has promising implications for active tracking and wavefront sensing, extending the utility of HSCR beyond its known benefits to coherent image quality.

Calculation of envelope area between grinding tool and curved surface

Typical aerospace curved surface parts have high contour accuracy, which directly affects the working performance and service life of the equipment. To improve the contour accuracy of these parts, the freestyle abrasive belt grinding technology can be employed, where the size of the envelope area determines the material removal volume. However, due to the complex contour of the curved surface and large contact deformation of the belt, the envelope area between the flexible belt and curved surface parts is complex and time-varying. The accurate calculation of the envelope area is still an open problem. To this end, a novel locally approximate distance fields-mass spring systems (LADF-MSS) method is proposed. Firstly, the improved distance field is established accurately: the octree is applied to search for the reference point where the curved surface is a local quadric approximation, and then the projection point is calculated based on the reference point. Secondly, the locally approximate distance field is combined with efficient mass-spring systems to extract the envelope area. The experimental results of grinding the curved surface show that the average area error and average centroid error of the envelope area are 0.7 mm2 and 1.08 mm respectively, and the average computing time is 7.5 min. Compared with the finite element method (FEM), the average calculation errors through utilizing the LADF-MSS method are reduced by 40.3% and 76.4% respectively, and calculation efficiency is increased by 166%. These results demonstrate that the proposed method offers both higher calculation accuracy and efficiency.

Influence of Image Processing Method on Wavefront Reconstruction Accuracy of Large-Aperture Laser

In order to improve the wavefront reconstruction accuracy of a large-aperture laser, this paper proposed an adaptive window preprocessing algorithm based on the threshold center of gravity method (AW-TCoG). The effects of median filtering and mean filtering on spot image processing and wavefront reconstruction accuracy are simulated and analyzed. The results show that the mean filtering method has a better effect on noise elimination and can further improve the accuracy of wavefront reconstruction. In addition, the centroid detection errors of large-aperture laser wavefront reconstruction through the center of gravity (CoG), the threshold center of gravity (T-CoG), and the Windowing method were studied. The analysis shows that, due to the influence of noise, the wavefront reconstruction accuracy is poor when the CoG and Windowing methods are used to calculate centroid parameters, while the wavefront reconstruction accuracy of the threshold centroid method is better and can reach 0.2λ. When using the AW-TCoG proposed in this paper, the wavefront reconstruction accuracy can be maintained within 0.1λ for different incident wavefront RMS values and spot images with different signal-to-noise ratio (SNR) levels. Compared with the traditional threshold centroid method, the wavefront reconstruction accuracy of this method is significantly improved.

Feasibility of 4D HDR brachytherapy source tracking using x-ray tomosynthesis: Monte Carlo investigation.

High dose rate (HDR) brachytherapy rapidly delivers dose to targets with steep dose gradients. This treatment method must adhere to prescribed treatment plans with high spatiotemporal accuracy and precision, as failure to do so may degrade clinical outcomes. One approach to achieving this goal is to develop imaging techniques to track HDR sources in vivo in reference to surrounding anatomy. This work investigates the feasibility of using an isocentric C-arm x-ray imager and tomosynthesis methods to track Ir-192 HDR brachytherapy sources in vivo over time (4D). A tomosynthesis imaging workflow was proposed and its achievable source detectability, localization accuracy, and spatiotemporal resolution were investigated in silico. An anthropomorphic female XCAT phantom was modified to include a vaginal cylinder applicator and Ir-192 HDR source (0.5 × 0.5 × 5.0 mm3 ), and the workflow was carried out using the MC-GPU Monte Carlo image simulation platform. Source detectability was characterized using the reconstructed source signal-difference-to-noise-ratio (SDNR), localization accuracy by the absolute 3D error in its measured centroid location, and spatiotemporal resolution by the full-width-at-half-maximum (FWHM) of line profiles through the source in each spatial dimension considering a maximum C-arm angular velocity of 30° per second. The dependence of these parameters on acquisition angular range (θtot = 0°-90°), number of views, angular increment between views (Δθ = 0°-15°), and volumetric constraints imposed in reconstruction was evaluated. Organ voxel doses were tallied to derive the workflow's attributable effective dose. The HDR source was readily detected and its centroid was accurately localized with the proposed workflow and method (SDNR: 10-40, 3D error: 0-0.144 mm). Tradeoffs were demonstrated for various combinations of image acquisition parameters; namely, increasing the tomosynthesis acquisition angular range improved resolution in the depth-encoded direction, for example from 2.5 mm to 1.2 mm between θtot = 30o and θtot = 90o , at the cost of increasing acquisition time from 1 to 3 s. The best-performing acquisition parameters (θtot = 90o , Δθ = 1°) yielded no centroid localization error, and achieved submillimeter source resolution (0.57 × 1.21 × 5.04 mm3 apparent source dimensions, FWHM). The total effective dose for the workflow was 263 µSv for its required pre-treatment imaging component and 7.59 µSv per mid-treatment acquisition thereafter, which is comparable to common diagnostic radiology exams. A system and method for tracking HDR brachytherapy sources in vivo using C-arm tomosynthesis was proposed and its performance investigated in silico. Tradeoffs in source conspicuity, localization accuracy, spatiotemporal resolution, and dose were determined. The results suggest this approach is feasible for localizing an Ir-192 HDR source in vivo with submillimeter spatial resolution, 1-3 second temporal resolution and minimal additional dose burden.

Realistic CT data augmentation for accurate deep-learning based segmentation of head and neck tumors in kV images acquired during radiation therapy.

Using radiation therapy (RT) to treat head and neck (H&N) cancers requires precise targeting of the tumor to avoid damaging the surrounding healthy organs. Immobilisation masks and planning target volume margins are used to attempt to mitigate patient motion during treatment, however patient motion can still occur. Patient motion during RT can lead to decreased treatment effectiveness and a higher chance of treatment related side effects. Tracking tumor motion would enable motion compensation during RT, leading to more accurate dose delivery. The purpose of this paper is to develop a method to detect and segment the tumor in kV images acquired during RT. Unlike previous tumor segmentation methods for kV images, in this paper a process for generating realistic and synthetic CT deformations was developed to augment the training data, and make the segmentation method robust to patient motion. Detecting the tumor in 2D kV images is a necessary step towards 3D tracking of the tumor position during treatment. In this paper a conditional generative adversarial network (cGAN) is presented that can detect and segment the gross tumor volume (GTV) in kV images acquired during H&N RT. Retrospective data from 15 H&N cancer patients obtained from the Cancer Imaging Archive were used to train and test patient-specific cGANs. The training data consisted of digitally reconstructed radiographs (DRRs) generated from each patient's planning CT and contoured GTV. Training data was augmented by using synthetically deformed CTs to generate additional DRRs (in total 39600 DRRs per patient or 25200 DRRs for nasopharyngeal patients) containing realistic patient motion. The method for deforming the CTs was a novel deformation method based on simulating head rotation and internal tumor motion. The testing dataset consisted of 1080 DRRs for each patient, obtained by deforming the planning CT and GTV at different magnitudes to the training data. The accuracy of the generated segmentations was evaluated by measuring the segmentation centroid error, Dice similarity coefficient (DSC) and mean surface distance (MSD). This paper evaluated the hypothesis that when patient motion occurs, using a cGAN to segment the GTV would create a more accurate segmentation than no-tracking segmentations from the original contoured GTV, the current standard-of-care. This hypothesis was tested using the 1-tailed Mann-Whitney U-test. The magnitude of our cGAN segmentation centroid error was (mean ± standard deviation) 1.1 ± 0.8 millimeters and the DSC and MSD values were 0.90 ± 0.03 and 1.6 ± 0.5 millimeters respectively. Our cGAN segmentation method reduced the segmentation centroid error (p<0.001), and MSD (p = 0.031) when compared to the no-tracking segmentation, but did not significantly increase the DSC (p = 0.294). The accuracy of our cGAN segmentation method demonstrates the feasibility of this method for H&N cancer patients during RT. Accurate tumor segmentation of H&N tumors would allow for intrafraction monitoring methods to compensate for tumor motion during treatment, ensuring more accurate dose delivery and enabling better H&N cancer patient outcomes. This article is protected by copyright. All rights reserved.

Total Keratometry Measured With a Swept-Source Optical Biometer Versus Anterior Keratometry: From Planning to Postoperative Results.

To compare the influence of total keratometry (TK) versus anterior keratometry (K) measured with the swept-source optical biometer IOLMaster 700 (Carl Zeiss Meditec AG) on the planning of toric intraocular lenses (IOLs), and the error in predicted residual astigmatism (PRA). This single-center retrospective study included 247 eyes of 180 patients. In eyes undergoing cataract surgery, the optimal toric IOL was calculated based on K or TK measured with the IOLMaster 700. Two formulas were used to estimate IOL power: Holladay and Barrett Toric. Optimal cylinder power and alignment axis change induced by using TK versus K were reported. PRA by each calculation method was compared with manifest refractive astigmatism. Postoperative refractive astigmatism prediction error was calculated using vector analysis. The optimal toric IOL based on TK compared with K was different in 39.3% of cases with the Holladay formula and 31.6% of cases with the Barrett Toric formula. The use of TK rather than K reduced the centroid error in PRA when calculated with the Holladay formula (P < .001), but not when calculated with the Barrett Toric formula (P = .19). The against-the-rule astigmatism subgroup analysis with the Barrett Toric formula showed a statistically significant decrease of centroid error in PRA with the use of TK compared with K (P = .01). TK compared with K measured with the IOL-Master 700 resulted in a change of optimal toric IOL in almost one-third of cases and decreased the error in PRA in patients with against-the-rule astigmatism. [J Refract Surg. 2023;39(4):257-264.].

Impact of Total Corneal Astigmatism Estimated With the Abulafia-Koch Formula Versus Measured With a SS-OCT Biometer on the Refractive Outcomes of a Toric Intraocular Lens in Cataract Surgery.

To compare the impact of total corneal astigmatism (TCA) estimated with the Abulafia-Koch formula (TCAABU) versus measured by Total Keratometry (TK), swept-source optical coherence tomography (OCT) coupled with telecentric keratometry (TCATK) on the refractive outcomes after cataract surgery with toric intraocular lens (IOL) implantation. Two hundred one eyes of 146 patients who underwent cataract surgery with toric IOL implantation (XY1AT; HOYA Corporation) were included in this single-center, retrospective study. For each eye, TCAABU (estimated from the anterior keratometry values measured with the IOLMaster 700 [Carl Zeiss Meditec AG]) and TCATK (measured using TK IOLMaster 700) were entered into the HOYA Toric Calculator. Patients were operated on based on TCAABU. For each eye, centroid and mean absolute error in predicted residual astigmatism (EPA) were calculated according to TCA used (TCAABU or TCATK). The cylinder power and the axis of the posterior chamber IOL were compared. The mean uncorrected distance visual acuity was 0.07 ± 0.12 logMAR, the mean spherical equivalent was 0.11 ± 0.40 D, and mean residual astigmatism was 0.35 ± 0.36 D. Mean centroid EPA was 0.28 D at 132° with TCAABU and 0.35 D at 148° with TCATK (P(x) < .001; P(y) < .01). Mean absolute EPA was 0.46 ± 0.32 D with TCAABU and 0.50 ± 0.37 D with TCATK (P < .01). In the with-the-rule astigmatism subgroup, a deviation from the target of less than 0.50 D was achieved in 68% of eyes with TCAABU versus 50% of eyes with TCATK. The proposed posterior chamber IOL was different depending on the calculation methods used in 86% of cases. Both calculation methods showed excellent results. However, the predictability error was significantly reduced when TCAABU was used compared to TCATK measured with the IOLMaster 700 in the whole cohort. Finally, TCA was overestimated by TK in the with-the-rule astigmatism subgroup. [J Refract Surg. 2023;39(3):171-179.].

Self-Triggered Coverage Control for Mobile Sensors

The deployment and coordination of mobile sensor networks for coverage control applications can present several practical challenges, including how to efficiently share limited communication resources and how to reduce the use of localization devices (e.g., radars and lidars). One potential solution to these challenges is to reduce the frequency at which agents communicate or sample each other's position. In this article, we present a distributed asynchronous self-triggered control policy for centroidal Voronoi coverage control that is shown to decrease the sampling or communication instants among agents without degrading the performance of the mobile sensor network. Each agent independently decides when to sample the position of nearby agents and uses outdated information of its neighbors until new information is required. We prove that the locational cost function describing the distribution of agents monotonically decreases everywhere outside of a bounded neighborhood around the group's optimal configuration and that the agents asymptotically converge to their Voronoi centroids if the data-sampled centroid errors approach zero. In addition, we show that the sampling intervals are always positive and lower bounded and, as illustrated by simulations and experiments, they tend to stabilize at a large value as the mobile sensor network comes to a steady state. Simulations and experiments with ground vehicles validate the control strategy and show that the proposed policy can achieve similar level of performance as a continuous or fast periodic implementation.

Research on the Pose Error Compensation Technology for the Mass and Centroid Measurement of Large-Sized Aircraft Based on Kinematics

The accurate measurement of mass and centroid is indispensable for accurate control of aircraft. In order to eliminate the influence of assembly error and product pose error on the measurement results, a multi-station measurement idea that can self-compensate for the geometric parameter error is proposed in this paper based on. At the same time, the kinematic model of the mechanical structure of the measurement equipment is established to prove the effectiveness of the structure in error compensation theoretically, and the experimental verification of the standard part and aircraft is carried out. The test results show that the measurement results using the idea of the multi-station compensation measurement are significantly better than those of the more common methods, with the mass measurement accuracy of 0.03% and the centroid error within ±0.15 mm, meeting the requirement of high precision measurement for the mass properties.

Сравнительная оценка хирургической коррекции роговичного астигматизма торическими ИОЛ с использованием различных кератометрических данных и методов расчета

Purpose. Compare the effectiveness of regular corneal astigmatism correction with toric monofocal IOL using various keratometric data and calculation methods. Material and methods. The study included 28 patients (31 eyes) with age-related cataracts and regular corneal astigmatism who underwent phacoemulsification (n=31) with implantation of a monofocal toric IOL (EnVista Toric). Two groups were formed according to the type of calculation and possible options of keratometric data: 1) keratometric data of IOL-master 500 + online manufacturer's calculator; 2) keratometric data of the anterior and posterior corneal surfaces (Pentacam HR) + Barrett's toric calculator. Results. The mean absolute deviation of the predicted residual astigmatism from the actual one was distributed as follows: 1st group – 0.62±0.62 D, 2nd group – 0.41 ± 0.71 D. The values of the mean absolute vector and mean centroid error in diopters were: 0.80±0.59 D and 0.06 D in 1st group, 0.48±0.65 D and 0.02 D in 2nd group, respectively. Conclusion. When using the measured astigmatism of the anterior and posterior surface of the cornea, Barrett's toric calculator showed the best result. The most accurate forecast of residual astigmatism was obtained using the Barrett calculator in combination with Pentacam keratometry data (Axial\Sagittal (Front), Axial\Sagittal (Back)). Key words: corneal astigmatism, posterior corneal astigmatism, toric IOL, centroid analysis, keratometry, cataract surgery

Star centroid error compensation based on the star triangle internal angles for celestial navigation with aero-optical degradation

In this paper, to solve the correction problem of star vector error induced by the aero-optic effect under hypersonic conditions, and to improve the navigation accuracy further, a novel method of star centroid error correction is proposed. The method is based on the star triangle internal angles, which can effectively use the prior information to estimate the aero-optical star centroid error. The method is verified by the Monte Carlo simulation and Hardware-In-Loop simulation. According to Hardware-In-Loop simulation, the star centroid error can be reduced by approximately 27%, and the attitude error can be reduced by approximately 14%. Therefore, the presented method is significant for the application of celestial navigation with hypersonic conditions.

Analysis and Correction of the Rolling Shutter Effect for a Star Tracker Based on Particle Swarm Optimization

The rolling shutter effect decreases the accuracy of the attitude measurement of star trackers when they work in rolling shutter exposure mode, especially under dynamic conditions. To solve this problem, a rolling shutter effect correction method based on particle swarm optimization is proposed. Firstly, a collinear reverse installation method between the star tracker and the satellite is proposed, which simplifies the relationship between the velocity of the star centroid and the star tracker angular velocity. Next, the centroid error model is obtained by the star centroid velocity. Based on the centroid error model and angular distance invariance, the loss function of the centroid error is proposed. Then, the particle swarm optimization algorithm is used to determine the star tracker angular velocity by minimizing the loss function. Finally, the simulation and experiments are carried out to verify the proposed method. The experimental results show that the convergence times of the algorithm are less than 50 and the root mean square error (RMSE) of the angular velocity is better than 0.02°/s when the angular velocity of the star tracker is no more than 5°/s.

Research on achromatic Risley prism in normal tracing angle measurement system

The normal tracing angle measurement system based on Risley prisms can eliminate the influence of aberrations other than the dispersion of Risley prisms on the angle measurement accuracy. Although the traditional dispersion optimization method based on the extreme point can make the beam directions of different wavelengths more consistent after passing through the Risley prisms, the light intensity distribution that deviates from the extreme point wavelength causes the spot centroid to deviate from the target position, thus introducing the angle measurement error. In this paper, we propose a highly symmetry-glued achromatic Risley prisms optimization method for the needs of a normal tracing angle measurement system. Our method not only realizes the beam direction as closely as possible after the deflection of the Risley prisms but also compensates for the centroid error caused by the beam deviating from the central wavelength. ZEMAX simulation shows that, in the normal tracing angle measurement system, within the angle measurement range of ±700 ″ and the light source wavelength range of 600 to 700 nm, the angle measurement error introduced by the dispersion of the optimized Risley prisms is not >0.01 ″ .