Review of Electronic Speckle Pattern Interferometry(ESPI) for Three Dimensional Displacement Measurement

Three dimensional（3D） displacements, which can be translated further into 3D strain, are key parameters tor design, manufacturing and quality control. Using different optical setups, phase-shift methods, and algorithms, several different 3D electronic speckle pattern interferometry（ESPl） systems for displacement and strain measurements have been achieved and commercialized. This paper provides a review of the recent developments in ESPI systems for 3D displacement and strain measurement. After an overview of the fundamentals of ESP! theory, temporal phase-shift, and spatial phase-shift techniques, 3D deformation measurements by the temporal phase-shift ESPI system, which is suited well for static measurement, and by the spatial phase-shift ESPI system, which is particularly useful for dynamic measurement, are discussed. For each method, the basic theory, a brief derivation and different optical layouts are presented. The state of art application, potential and limitation of the ESPI systems are shown and demonstrated.

Environmental temperature effect on dimensional measurements of atomic force microscopy

Atomic force microscopy(AFM)is increasingly being used as a fundamental tool for dimensional measurements at the nanoscale in the laboratory and in industry.Since the environmental temperature is not controlled in many measurements,or is even varied on purpose,quantification of its effects on AFM dimensional measurements is needed.In this paper,the influences of the temperature in the entire environment of the AFM(excluding only the controller and computer)and that in the local environment around the tip–sample are investigated.The results show that lateral dimensional measurements are affected mainly by the entire environmental temperature.However,vertical measurements are influenced by the temperature of both the entire environment and the local environment.The effects become significant for temperatures higher than some threshold,here between 35 and 40 XC.

A method for custom measurement of fish dimensions using the improved YOLOv5-keypoint framework with multi-attention mechanisms

Dimensional data directly reflects the growth rate of individual fish,an important economic trait of interest to fish researchers.Efficiently obtaining large-scale fish dimension data would be valuable for both selective breeding and production.To address this,our study proposes a custom dimension measurement method for fish using the YOLOv5-keypoint framework with multi-attention mechanisms.We optimized the YOLOv5 framework,incorporated the SimAM attention mechanism to achieve more accurate and faster fish detection,and added customizable landmarks to the network structure,enabling flexible configuration of the number and location of feature points in the training dataset.This method is applicable to various aquacultural species and other objects.We tested the effectiveness of the method using the economically important grass carp(Ctenopharyngodon idella).The proposed method outperforms pure YOLOv5,Faster R-CNN,and SSD in terms of precision and recall rates,achieving an impressive average precision of 0.9781.Notably,field trials confirmed the method's exceptional measurement accuracy,exceeding 97%compatibility with manual measurements,while demonstrating a realtime speed of 38 frames per second on the NVIDIA RTX A4000.This enables efficient and accurate large-scale surface dimension measurements of economic fish.To facilitate massive measurements in agricultural research,we have implemented this method as an online platform,called Mode-recognition Ruler(MrRuler,http://bioinf o.ihb.ac.cn/mrruler).The platform identifies objects in a single image at an average speed of 0.486±0.005 s,based on a dataset of 10,000 images.MrRuler includes two preset carp models and allows users to upload training datasets for custom models of their targets of interest.

DIMENSIONS OF MEASURE ON GENERAL SIERPINSKI CARPET

Let S = Pi(i=1)(infinity){0, 1, ..., r - 1} and (R) over bar the general Sierpinski carpet, Let mu be the induced probability measure on (R) over bar of <(mu)over tilde> on S by phi, where phi is the natural surjection from S onto (R) over bar and <(mu)over tilde> is the infinite product probability measure corresponding to probability vector (b(0), ..., b(r-1)) with b(i) = a(i)(logn) (m-1)/m(alpha). Authors show that dim(H) mu = (C) under bar(L)(mu) = (C) over bar(L)(mu) = (C) under bar(mu) = (C) over bar C(mu) = alpha.

The Loeb Space of Denumerable Infinite Dimensional Probability Product Measure Spaces

Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.

A NOTE ON MULTIFRACTAL PACKING DIMENSION OF MEASURES

The relations between the multifractal packing dimension of Borel probability measures and the asymptotic behavior of the function Ф＊（x）=limsup logv（B（x,r））-qlogu（B（x,r））/logr are discussed and some applications are given.

A study of making use of computer-aided projection fringe system to measure breast dimension

To measure breast basic dimension by using computer-aided projection fringe system.Methods A system has been developed for measuring breast basic dimension based on computer-aided projection fringe measurement and programming software.Plastic manikins breast’s SN-N (sternal notch to nipple distance),N-ML (nipple to midline distance),N-N (internipple distance),MBW (base width of breast) and N-IMF (nipple to inframammary fold distance) are measured with this system.At the same time,these items are also measured with routine ruler.Results This study indicate that the system has some merits:① non-touching measurement;② it is very rapid,the patient measured need hold his breath only 0.5 second,and all the time it takes is about 2.5 minutes;③ the measurement’s sensitivity is as high as to 0.6 mm,which meets the clinic requirement entirely;④ the measurement’s accuracy of the system is not significantly when comparing to the routine ruler’s.Conclusion Computer-adided projection fringe system for measuring breast basic dimension is feasible and advanced.14 refs,1 fig.

Single Camera 3-D Coordinate Measuring System Based on Optical Probe Imaging

A new vision coordinate measuring system--single camera 3 D coordinate measuring system based on optical probe imaging is presented. A new idea in vision coordinate measurement is proposed. A linear model is deduced which can distinguish six freedom degrees of optical probe to realize coordinate measurement of the object surface. The effects of some factors on the resolution of the system are analyzed. The simulating experiments have shown that the system model is available.

ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION

In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.

THE PACKING MEASURE OF A CLASS OF GENERALIZED SIERPINSKI CARPET

For 1/4< a <(?)/4, let S1(x) =ax, S2(x)=1-a+ax, x∈[0,1]. Ca is the attractor of the iteratedfunction system {S1,S2}, then the packing measure of Ca×Ca isPs(a)(Ca×Ca) = 4·2s(a)(1-a)s(a),where s(a) = -loga4.

NOTE ON THE PAPER “ AN NEGATIVE ANSWER TO A CONJECTURE ON THE SELF-SIMILAR SETS SATISFYING THE OPEN SET CONDITION”

In this paper, we present a more simple and much shorter proof for the main result in the paper ＂ An negative answer to a conjecture on the self-similar sets satisfy- ing the open set condition＂, which was published in the journal Analysis in Theory and Applications in 2009.

Some Results on the Upper Convex Densities of the Self-Similar Sets at the Contracting-Similarity Fixed Points

In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.

3-D Shape Measurement of Complex Objects by Combining Color-Coded Fringe and Neural Networks

A new approach for three dimensional (3-D) shape measurement was proposed based on colorcoded fringe and neural networks. By applying the phase-shift technique to fringe projection, point clouds were generated with high spatial resolution and limited accuracy. The picture element correspondence problem was solved by using projected color-coded fringes with different orientations. Once the high accurate corresponding points were decided, high precision dense 3-D points cloud was calculated by the well trained net. High spatial resolution can be obtained by the phase-shift technique and high accuracy 3-D object point coordinates are achieved by the well trained net, which is not dependent on the camera model and will work for any type of camera. Some experiments verify the performance of this method.

A portable high precision three dimensional trace measuring system for underwater target with high speed

The paper describes a portable high precision three-dimensional trace measuring system for underwater target with high speed. The mathematical model for location, the main error sources, the calibration method for the underwater array and the way to correct its state are discussed. Problems about the distance ambiguity and multi-path interference are also analyzed. Part of experimental results on lake and at sea are given as well.

A NOTE ON THE ASYMPTOTICS OF THE POLYMER MEASURES IN ONE DIMENSION

Given g∈(0,∞), we prove thatfor some constant C∈(0,∞), where (g, T) is the polymer measure defined on C_0([0, T]→R^1), and {W(t)}t∈[0,T] is the corresponding coordinate process.

Hausdorff measure of sets of finite type of one-sided symbolic space

Some estimation formulae and a computation formula for the hausdorff meausre fo the sets of finite type of the one-sided symbolic space are given