Minimum Error Detection Research Articles

How Does Repetition Coding Enable Reliable and Covert Communications?

This letter tackles whether and how repetition coding enables reliable and covert communications by considering binary phase shift keying. Communication reliability and covertness are analyzed in terms of the bit error rate P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> and the minimum detection error probability ξ*. Our examination shows that, when a warden Willie knows the codeword structure, both P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> and ξ* are determined by the total power nP and do not depend on the codeword length n or the transmit power P individually. However, this conclusion does not hold for the unknown codeword structure, where increasing n can significantly improve the communication reliability under the same covertness constraint, and vice versa.

Carrier Phase-Based Ionospheric Gradient Monitor Under the Mixed Gaussian Distribution

Anomalous ionospheric gradient is a critical risk to be monitored by ground-based augmentation systems (GBASs) utilized for safety-of-life navigation applications. A dual-frequency carrier phase-based ionospheric gradient monitoring method is proposed under the mixed Gaussian distribution. The minimum detection error of the proposed method can be greatly reduced by allowing acceptable ambiguity resolution failure modes, given the required averaging length. The real BeiDou navigation satellite system data were utilized to test the proposed method. The experimental results showed that the minimum detection error (MDE) of the proposed dual-frequency ionospheric gradient monitoring method can be reduced by at least 30% in comparison with the maximum acceptable anomalous ionospheric gradient of category III GBAS. This study demonstrated that the proposed method can be used to protect against the ionospheric gradient for a ground-based augmentation system.

Harvest-and-Opportunistically-Relay: Analyses on Transmission Outage and Covertness

To enhance transmission performance, privacy level, and energy manipulating efficiency of wireless networks, this article initiates a novel simultaneous wireless information and power transfer (SWIPT) full-duplex (FD) relaying protocol, named harvest-and-opportunistically-relay (HOR). Due to the FD characteristics, the dynamic fluctuation of relay’s residual energy is difficult to quantify and track. To solve this problem, the Markov Chain (MC) theory is invoked. Furthermore, to improve the privacy level of the proposed HOR relaying system, covert transmission performance analysis is performed, where closed-form expressions of the optimal detection threshold and minimum detection error probability are derived. Last but not least, with the aid of stationary distribution of the MC, closed-form expression of transmission outage probability is calculated, based on which transmission outage performance is analyzed. Numerical results have validated the correctness of analyses on transmission outage and covertness. The impacts of key system parameters on the performance of transmission outage and covertness are given and discussed. Based on mathematical analysis and numerical results, we showcase that the proposed HOR model can not only reliably enhance the transmission performance via smartly managing residual energy but also efficiently improve the privacy level of the legitimate transmission party via dynamically adjusting the optimal detection threshold.

Probabilistic static foreground elimination for background subtraction

ABSTRACTBackground subtraction is generally used to detect moving objects, because it has low complexity, and it is easy to implement. However, the detection error increases when the background is changing. Therefore, adaptive background subtraction is applied to overcome this problem, and it continuously requires updating the background with a fixed learning rate. The learning rate should be tuned for a consistently evolving background. This paper proposes the Probabilistic Static Foreground Elimination for Background Subtraction (PSFE) algorithm. It consisted of two parameters: the number of frames for static foreground elimination, and the probability of changes in background pixels. These two parameters can tune the learning rate and update background for better detection. The average results of the detection error rate from Wallflower datasets were tested with PSFE and well-known method. They demonstrated that PSFE provides moving object detection with minimum detection error (5.95%), especially in Camouflage, Moved object, and Light switch dataset.

Improved receiver autonomous integrity monitoring algorithm

The integrity monitoring algorithm guarantees that the receiver can get the correct positioning and speed, which has very important theoretical significance and practical application value. It is one of the most important development contents of the satellite navigation system. Based on the introduction of the traditional least square residual method, this paper compares the binomial fitting time-assisted receiver autonomous integrity monitoring (RAIM) algorithm and a grey model time-assisted RAIM algorithm and finds that the latter can well solve the clock error accumulation problem in the binomial fitting time-assisted RAIM algorithm. In the faulty satellite detection experiments with the same pseudo-range error, the minimum detectable pseudo-range error of the grey model time-assisted RAIM algorithm is 15 m, while the binomial fitting time-assisted RAIM algorithm is 28 m. Incidentally, the detection probability of a faulty satellite with 20 m pseudo-range error of the binomial fitting time-assisted RAIM algorithm is 10%, whereas the grey model time-assisted RAIM algorithm is 81%.

Covert Transmission With a Self-Sustained Relay

This work examines the possibility, performance limits, and associated costs for a self-sustained relay to transmit its own covert information to a destination on top of forwarding the source's information. Since the source provides energy to the relay for forwarding its information, the source does not allow the relay's covert transmission and is to detect it. Considering the time switching (TS) and power splitting (PS) schemes for energy harvesting, where all the harvested energy is used for transmission at the self-sustained relay, we derive the minimum detection error probability $\xi^{\ast}$ at the source, based on which we determine the maximum effective covert rate $\Psi^{\ast}$ subject to a given covertness constraint on $\xi^{\ast}$. Our analysis shows that $\xi^{\ast}$ is the same for the TS and PS schemes, which leads to the fact that the cost of achieving $\Psi^{\ast}$ in both the two schemes in terms of the required increase in the energy conversion efficiency at the relay is the same, although the values of $\Psi^{\ast}$ in these two schemes can be different in specific scenarios. For example, the TS scheme outperforms the PS scheme in terms of achieving a higher $\Psi^{\ast}$ when the transmit power at the source is relatively low. If the covertness constraint is tighter than a specific value, it is the covertness constraint that limits $\Psi^{\ast}$, and otherwise it is upper bound on the energy conversion efficiency that limits $\Psi^{\ast}$.

A Speaker Verification Method Based on TDNN–LSTMP

In speaker recognition, a robust recognition method is essential. This paper proposes a speaker verification method that is based on the time-delay neural network (TDNN) and long short-term memory with recurrent project layer (LSTMP) model for the speaker modeling problem in speaker verification. In this work, we present the application of the fusion of TDNN and LSTMP to the i-vector speaker recognition system that is based on the Gaussian mixture model-universal background model. By using a model that can establish long-term dependencies to create a universal background model that contains a larger amount of speaker information, it is possible to extract more feature parameters, which are speaker dependent, from the speech signal. We conducted experiments with this method on four corpora: two in Chinese and two in English. The equal error rate, minimum detection cost function and detection error tradeoff curve are used as criteria for system performance evaluation. The experimental results show that the TDNN–LSTMP/i-vector speaker recognition method outperforms the baseline system on both Chinese and English corpora and has better robustness.

Client-wise cohort set selection by combining speaker- and phoneme-specific I-vectors for speaker verification

This work explores the use of phoneme level information in cohort selection to improve the performance of a speaker verification system. In speaker verification, cohort is used in score normalization to get a better performance. Score normalization is a technique to reduce the undesirable variation arising from acoustically mismatched conditions. Proper selection of cohort significantly improves speaker verification performance. In this paper, we investigate cohort selection based on a speaker model cluster under the i-vector framework that we call the i-vector model cluster (IMC). Two approaches for cohort selection are proposed. First approach utilizes speaker specific properties and called speaker specific cohort selection (SSCS). In this approach, speaker level information is used for cohort selection. The second approach is phoneme specific cohort selection (PSCS). This method improves cohort set selection by using phoneme level information. Phoneme level information is further employed in a late fusion approach that uses a majority voting method on normalized scores to improve the performance of the speaker verification system. Speaker verification experiments were conducted using the TIMIT, HINDI and YOHO databases. An equal error rate improvement of 19.01%, 14.61% and 19.4%is obtained for the proposed method compared to the standard ZT-Norm method for TIMIT, HINDI and YOHO datasets. Reasonable improvements in performance are also obtained in terms of minimum decision cost function (min DCF) and detection error trade-off (DET) curves.

Reliability of GPS/GNSS-based positioning in a forestry environment

The critical environment is one of the main insufficient to positioning. Geodetic observing systems such as the global positioning system (GPS) and the global navigation satellite systems (GNSS) are routinely used to estimate the contaminating effects by critical environment. In an effort to define the accuracy and reliability of GPS/GNSS positioning, we investigated the data having contaminating effects due to forestry environment. Some reliability criteria and geometric concepts were defined and then examined by them. Two sets of data were collected in open sky and closed canopy separately. The analysis of the observed data was performed using the reliability criteria and geometric concepts. The accuracy and reliability of positioning strongly depended on the canopy ratio and satellite availability. The minimum detectable error on baseline was estimated about 2.5 mm under closed canopy. The number of observable satellites and minimal detectable errors were computed for each epoch. The minimal biases on estimated baselines, bias-to-noise ratios for estimating baseline components and probability of success of the integer ambiguity solution were defined in case of forest canopy. Finally, geometric quality could be achieved using the factors of dilution of precision. Thus, the presented accuracy and reliability concepts fulfill the requirement proposed by the global geodetic observing system in forest environment.

The psychometric properties of an Arabic numeric pain rating scale for measuring osteoarthritis knee pain

Purpose: The aims of this study were to translate the numeric rating scale (NRS) into Arabic and to evaluate the test–retest reliability and convergent validity of an Arabic Numeric Pain Rating Scale (ANPRS) for measuring pain in osteoarthritis (OA) of the knee.Methods: The English version of the NRS was translated into Arabic as per the translation process guidelines for patient-rated outcome scales. One hundred twenty-one consecutive patients with OA of the knee who had experienced pain for more than 6 months were asked to report their pain levels on the ANPRS, visual analogue scale (VAS), and verbal rating scale (VRS). A second assessment was performed 48 h after the first to assess test–retest reliability. The test–retest reliability was calculated using the intraclass correlation coefficient (ICC2,1). The convergent validity was assessed using Spearman rank correlation coefficient. In addition, the minimum detectable change (MDC) and standard error of measurement (SEM) were also assessed.Results: The repeatability of ANPRS was good to excellent (ICC 0.89). The SEM and MDC were 0.71 and 1.96, respectively. Significant correlations were found with the VAS and VRS scores (p <0.01).Conclusions: The Arabic numeric pain rating scale is a valid and reliable scale for measuring pain levels in OA of the knee.Implications for RehabilitationThe Arabic Numeric Pain Rating Scale (ANPRS) is a reliable and valid instrument for measuring pain in osteoarthritis (OA) of the knee, with psychometric properties in agreement with other widely used scales.The ANPRS is well correlated with the VAS and NRS scores in patients with OA of the knee.The ANPRS appears to measure pain intensity similar to the VAS, NRS, and VRS and may provide additional advantages to Arab populations, as Arabic numbers are easily understood by this population.

Optimization of Quantum States for Signaling Across an Arbitrary Qubit Noise Channel With Minimum-Error Detection

For discrimination between two signaling states of a qubit, the optimal detector minimizing the probability of error is applied to the situation where detection has to be performed from a noisy qubit affected by an arbitrary quantum noise separately characterized. With no noise, any pair of orthogonal pure quantum states is optimal for signaling as it enables error-free detection. In the presence of noise, detection errors are in general inevitable, and the pairs of signaling states best resistant to such noise are investigated. With an arbitrary quantum noise, modeled as a channel affecting the qubit, and when minimum-error detection is performed from the output, a characterization of the optimal input signaling pairs and of their best detection performance is obtained through a simple maximization of a quadratic scalar criterion in three constrained real variables. This general characterization enables to establish that such optimal signaling pairs are always made of two orthogonal pure quantum states, but that they must be specifically selected to match the noise properties and prior probabilities. The maximization is explicitly solved for several generic quantum noise processes relevant to the qubit, such as the squeezed generalized amplitude damping noise which describes interaction with a thermal bath representing a decohering environment and which includes as special cases both the generalized and the regular amplitude damping noise processes, and such as general Pauli noise processes which include for instance the bit-flip noise and the depolarizing noise. Also, examined is the situation of one imposed (pure or mixed) signaling state, for which the other associated signaling state optimal for noisy detection is determined as a pure state, yet not necessarily orthogonal.

Performance analysis of BDS for regional services with consideration on weighted factors

At the current stage, the service performance analysis of BeiDou satellite navigation system (BDS) can provide important references for BDS applications. Accuracy, integrity, availability, and continuity are important indicators of the service capability of the satellite navigation system. In this paper, the relationships among them are analyzed firstly. Secondly, for describing accuracy, position dilution of precision (PDOP) is selected and the quantitative calculation formulas of its availability and continuity are established. Then PDOP of BDS in Asia-Pacific region is simulated and analyzed, the results show that the average availability and continuity of PDOP in the service area during 24 h are up to 99.60% and 0.9947/h, respectively. Thirdly, this paper has a brief introduction to weighted least square algorithm of receiver autonomous integrity monitoring (RAIM) and analyzes the relationships among the probability of false alert, the probability of missed detection, threshold, the minimum detectable error and the number of visible satellites. The threshold and the minimum detectable error will increase with the increasing number of visible satellites when given the false alert probability and missed detection probability, respectively. Finally, the quantitative calculation formula of RAIM availability and continuity is presented and RAIM availability and continuity are simulated and analyzed as well, the results show that the average availability and continuity in the service area are up to 99.95% and 0.9984/h, respectively.

Orbit Ephemeris Failure Detection in a GNSS Regional Application

To satisfy civil aviation requirements using the Global Navigation Satellite System (GNSS), it is important to guarantee system integrity. In this work, we propose a fault detection algorithm for GNSS ephemeris anomalies. The basic principle concerns baseline length estimation with GNSS measurements (pseudorange, broadcasted ephemerides). The estimated baseline length is subtracted from the true baseline length, computed using the exact surveyed ground antenna positions. If this subtracted value differs by more than a given threshold, this indicates that an ephemeris anomaly has been detected. This algorithm is suitable for detecting Type A ephemeris failure, and more advantageous for use with multiple stations with various long baseline vectors. The principles of the algorithm, sensitivity analysis, minimum detectable error (MDE), and protection level derivation are described and we verify the sensitivity analysis and algorithm availability based on real GPS data in Korea. Consequently, this algorithm is appropriate for GNSS regional implementation.

Bayesian Hypothesis Test Using Nonparametric Belief Propagation for Noisy Sparse Recovery

This paper proposes a low-computational Bayesian algorithm for noisy sparse recovery (NSR), called BHT-BP. In this framework, we consider an LDPC-like measurement matrices which has a tree-structured property, and additive white Gaussian noise. BHT-BP has a joint detection-and-estimation structure consisting of a sparse support detector and a nonzero estimator. The support detector is designed under the criterion of the minimum detection error probability using a nonparametric belief propagation (nBP) and composite binary hypothesis tests. The nonzeros are estimated in the sense of linear MMSE, where the support detection result is utilized. BHT-BP has its strength in noise robust support detection, effectively removing quantization errors caused by the uniform sampling-based nBP. Therefore, in the NSR problems, BHT-BP has advantages over CS-BP which is an existing nBP algorithm, being comparable to other recent CS solvers, in several aspects. In addition, we examine impact of the minimum nonzero value of sparse signals via BHT-BP, on the basis of the results. Our empirical result shows that variation of x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> is reflected to recovery performance in the form of SNR shift.

Effects of Phasor Measurement Uncertainty on Power Line Outage Detection

Phasor measurement unit (PMU) technology provides an effective tool to enhance the wide-area monitoring systems (WAMSs) in power grids. Although extensive studies have been conducted to develop several PMU applications in power systems (e.g., state estimation, oscillation detection and control, voltage stability analysis, and line outage detection), the uncertainty aspects of PMUs have not been adequately investigated. This paper focuses on quantifying the impact of PMU uncertainty on power line outage detection and identification, in which a limited number of PMUs installed at a subset of buses are utilized to detect and identify the line outage events. Specifically, the line outage detection problem is formulated as a multi-hypothesis test, and a general Bayesian criterion is used for the detection procedure, in which the PMU uncertainty is analytically characterized. We further apply the minimum detection error criterion for the multi-hypothesis test and derive the expected detection error probability in terms of PMU uncertainty. The framework proposed provides fundamental guidance for quantifying the effects of PMU uncertainty on power line outage detection. Case studies are provided to validate our analysis and show how PMU uncertainty influences power line outage detection.

반송파 측정값 기반 GNSS 궤도력 고장 검출 알고리즘 성능 분석

본 논문에서는 위성항법시스템의 무결성 저해 요인 중, 항법메시지에 담겨 전송되는 궤도력 (Ephemeris) 정보의 고장 여부를 판단할 수 있는 알고리즘을 분석 및 성능 평가를 수행하였다. 알고리즘은 반송파 측정값과 두 지상 기준국간의 기저벡터 정보가 활용된다. 주요 특징으로 기준국 기저선과 위성이 이루는 기하학적 조건 기저선 길이에 따라 동일 궤도력 고장에 대해 알고리즘의 성능의 편차가 발생할 수 있음을 확인하였다. 또한 알고리즘 적용이 적합한 GBAS의 지상 기준국 안테나 배치 방안 및 제주국제공항에 운용되었을 때의 한계치 및 성능 지표 (MDE : Minimum Detectable Error)를 계산하였다. We analyze fault detection algorithm of ephemeris included in navigation message, which is one of the GNSS risk factors. This algorithm uses carrier-phase measurement and baseline vector of two reference stations and is alternative method for uncertainty condition of previous ephemeris. Even though same ephemeris fault is occurred, the geometry condition, between baseline vector of reference stations and satellites, effects on performance of algorithm. Also, we introduce the suitable geometry of reference stations, threshold and performance index (MDE : Minimum Detectable Error) in jeju international airport.

Measuring Surgical Outcomes in Cervical Spondylotic Myelopathy Patients Undergoing Anterior Cervical Discectomy and Fusion: Assessment of Minimum Clinically Important Difference

ObjectThe concept of minimum clinically important difference (MCID) has been used to measure the threshold by which the effect of a specific treatment can be considered clinically meaningful. MCID has previously been studied in surgical patients, however few studies have assessed its role in spinal surgery. The goal of this study was to assess the role of MCID in patients undergoing anterior cervical discectomy and fusion (ACDF) for cervical spondylotic myelopathy (CSM).MethodsData was collected on 30 patients who underwent ACDF for CSM between 2007 and 2012. Preoperative and 1-year postoperative Neck Disability Index (NDI), Visual-Analog Scale (VAS), and Short Form-36 (SF-36) Physical (PCS) and Mental (MCS) Component Summary PRO scores were collected. Five distribution- and anchor-based approaches were used to calculate MCID threshold values average change, change difference, receiver operating characteristic curve (ROC), minimum detectable change (MDC) and standard error of measurement (SEM). The Health Transition Item of the SF-36 (HTI) was used as an external anchor.ResultsPatients had a significant improvement in all mean physical PRO scores postoperatively (p<0.01) NDI (29.24 to 14.82), VAS (5.06 to 1.72), and PCS (36.98 to 44.22). The five MCID approaches yielded a range of values for each PRO: 2.00–8.78 for PCS, 2.06–5.73 for MCS, 4.83–13.39 for NDI, and 0.36–3.11 for VAS. PCS was the most representative PRO measure, presenting the greatest area under the ROC curve (0.94). MDC values were not affected by the choice of anchor and their threshold of improvement was statistically greater than the chance of error from unimproved patients.ConclusionSF-36 PCS was the most representative PRO measure. MDC appears to be the most appropriate MCID method. When MDC was applied together with HTI anchor, the MCID thresholds were: 13.39 for NDI, 3.11 for VAS, 5.56 for PCS and 5.73 for MCS.

Does gymnastics practice improve vertical jump reliability from the age of 8 to 10 years?

The objective of this study was to confirm whether gymnastics practice from a young age can induce greater vertical jump reliability. Fifty young female gymnasts (8.84 ± 0.62 years) and 42 females in the control group (8.58 ± 0.92 years) performed the following jump tests on a contact mat: squat jump, countermovement jump, countermovement jump with arm swing and drop jump from heights of 40 and 60 cm. The two testing sessions had three trials each and were separated by one week. A 2 (groups) × 2 (sessions) × 3 (trials) repeated measures analysis of variance (ANOVA) and a test-retest correlation analysis were used to study the reliability. There was no systematic source of error in either group for non-plyometric jumps such as squat jump, countermovement jump, and countermovement jump with arm swing. A significant group per trial interaction revealed a learning effect in gymnasts' drop jumps from 40 cm height. Additionally, the test-retest correlation analysis and the higher minimum detectable error suggest that the quick drop jump technique was not fully consolidated in either group. At an introductory level of gymnastics and between the ages of 8–10 years, the condition of being a gymnast did not lead to conclusively higher reliability, aside from better overall vertical jump performance.

Descending Kernel Track of Static and Dynamic Topic Models in Topic Tracking

PDF HTML阅读 XML下载 导出引用 引用提醒 话题跟踪中静态和动态话题模型的核捕捉衰减 DOI: 10.3724/SP.J.1001.2012.04045 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金(61003152, 60970057, 60873105, 90920004, 60970056); 国家高技术研究发展计划(863)(2012AA011102); 国家教育部博士点基金(200932011 10006); 苏州市应用基础研究计划基金(SYG201030) Descending Kernel Track of Static and Dynamic Topic Models in Topic Tracking Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:话题跟踪是一项针对新闻话题进行相关信息识别、挖掘和自组织的研究课题,其关键问题之一是如何建立符合话题形态的统计模型.话题形态的研究涉及两个问题,其一是话题的结构特性,其二是话题变形.对比分析了现有词包式、层次树式和链式这3 类主流话题模型的形态特征,尤其深入探讨了静态和动态话题模型拟合话题脉络的优势和劣势,并提出一种基于特征重叠比的核捕捉衰减评价策略,专门用于衡量静态和动态话题模型追踪话题发展趋势的能力.在此基础上,分别给出突发式增量式学习方法和时序事件链的更新算法,借以提高动态话题模型的核捕捉性能.实验基于国际标准评测语料TDT4,采用NIST(National Institute of Standards and Technology)提出的最小检测错误权衡系数评测法,并结合所提出的核捕捉衰减评价方法,对各类主要话题模型进行测试.实验结果显示,结构化的动态话题模型具有最佳的跟踪性能,且突发式增量式学习和时序事件链的更新算法分别给予动态话题模型0.4%和3.3%的性能改进. Abstract:Topic tracking is a task in research on identifying, mining and self-organizing relevant information to news topics. Its key issue is to establish statistical models that adapt the kind of news topic. This includes two aspects: one is topical structure; the other is topic evolution. This paper focuses on comparing and analyzing the features of three main kinds of topic models including words bag, hierarchical tree and chain. Different performances of static and dynamic topic models are deeply discussed, and a term overlapping rate based evaluation method, namely descending kernel track, is proposed to evaluate the abilities of static and dynamic topic models on tracking the trend of topic development. On this basis, this paper respectively proposes two methods of burst based incremental learning and temporal event chain to improve the performance of capturing topic kernels of dynamic topic models. Experiments adopt the international-standard corpus TDT4 and minimum detection error tradeoff evaluation method proposed by NIST (National Institute of Standards and Technology), along with descending kernel track method to evaluate the main topic models. The results show that structural dynamic models have the best tracking performance, and the burst based incremental learning algorithm and temporal event chain achieve 0.4% and 3.3% improvement respectively. 参考文献 相似文献 引证文献

Lens Sag Measurement of Microlens Array Using Optical Interferometric Microscope

This study attempted to develop a detection system for lens sag of the microlens array in real time using an optical automatic inspection framework to link with the computer through a camera. An image processing technique was applied to detect the spherical microlens array, and then, the results were compared. The system light source used laser light and applied CCD to collocate with the microscope array to form an automatic optical detection system for an optical interferometric microscope. It applied the principle of the Fizeau interferometer, illuminated the surface of microlens array, and formed the phase difference required by the interference of two lights through the laser light reflected by the reference plane and the surface of the microlens array, thus, forming an interference fringe. When the sag of the microlens was much longer than the wave length of the detection light source, the fringe would be densely distributed, thus, only a few central fringes were clear in the microscopic image. An image processing method was used to search the center of the interference fringe and a creative algorithm was utilized to obtain the lens sag of the microlens. As proved by the experiment, lens sag of 4 microlens arrays were detected in real time, with a minimum detection error of 0.08 μm, and a maximum detection error of 4 μm (error value 1 ~ 9%), according to different sample processes. This system featured a simple structure and is applicable to non-contact detection and detection of different-sized microlens arrays.