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1610 results about "Greek letter epsilon" patented technology

Epsilon (uppercase Ε, lowercase ε or lunate ϵ; Greek: έψιλον) is the fifth letter of the Greek alphabet, corresponding phonetically to a mid front unrounded vowel /e/.

Synchronization and channel response estimation method suitable for OFDM system

The invention relates to a synchronization and channel response estimation method which is applicable to an OFDM system, the technical proposal is as follows: a maximum likelihood criterion ML-based cost function for the symbol timing synchronization, the carrier frequency synchronization and the channel parameter joint estimation is proposed by using an OFDM system model under a frequency selective fading channel and against the requirements on the accuracy of the transmission of high-quality information of the next generation of wireless communication system and the existing OFDM wireless communication system. A system architecture and a strategy of joint estimation symbols of timing offset Theta, carrier frequency offset Epsilon and channel impulse response h are derived from the cost function. The method comprises the following steps of carrying out the coarse synchronization and the channel response estimation and carrying out the fine synchronization and the calculation of a channel estimated value. The method can realize the balance between the calculation precision and the calculation complexity, increase or reduce the times of the iteration of the fine synchronization according to an actual system, reduce the interference during the wireless transmission, further improve the reliability of the system and improve the availability of the system.
Owner:BEIJING JIAOTONG UNIV

Virtual flow cytometry on immunostained tissue-tissue cytometer

The invention provides an automated method of single cell image analysis which determines cell population statistic, applicable in the field of pathology, disease or cancer diagnosis, in a greatly improved manner over manual or prior art scoring techniques. By combining the scientific advantages of computerized automation and the invented method, as well as the greatly increased speed with which population can be evaluated, the invention is a major improvement over methods currently available. The single cells are identified and displayed in an easy to read format on the computer monitor, printer output or other display means, with cell parameter such as cell size and staining distribution at a glance. These output data is an objective transformation of the subjective visible image that the pathologist or scientist relies upon for diagnosis, prognosis, or monitoring therapeutic perturbations. Using our novel proposed technology, we combine the advantages provided by the clinical standard tool of flow cytometry in quantifying single cells and also retain the advantages of microscopy in retaining the capability of visualizing the immunoreactive cells. Unlike flow cytometry however, the invention uses commonly available formalin fixed immunostained tissue and not fresh viable cells. To accomplish this aim, we resort to new and improved advanced image analysis using a unique, useful, and adaptive process as described herein. The method uses multi-stage thresholding and segmentation algorithm based on multiple color channels in RGB and HS I spaces and uses auto-thresholding on red and blue channels in RGB to get the raw working image of all cells, then refines the working image with thresholding on hue and intensity channels in HS I using an adaptive parameter epsilon in entropy mode, and further separates different groups of cells within the same class, by auto-thresholding within the working image region. The Immunohistochemistry Flow cytometry (IHCFLOW) combination results in a new paradigm that is both useful, novel, and provides objective tangible result from a complex color image of tissue.
Owner:CUALING HERNANI D

TD-LTE (Time Division-Long Term Evolution) frequency offset estimation method for relay system

InactiveCN103701733AMake up for the disadvantage of unknown bandwidthSynchronous sending signal frequencyTransmitter/receiver shaping networksTime-Division Long-Term EvolutionEstimation methods
The invention provides a TD-LTE (Time Division-Long Term Evolution) frequency offset estimation method for a relay system and relates to services or facilities suitable for a wireless communication network. The method comprises the following steps: obtaining positions of synchronizing signals and information about cell ID (Identity) number and cell group ID number inside a cell identification group from receiving signals at a relay end, so as to obtain a synchronizing signal sequence received by a relay; secondly, generating a local PSS (Primary Synchronization Signal) and an SSS (Secondary Synchronization Signal) according to the obtained relay-end cell ID number and cell group ID number relay end; thirdly, carrying out an integer-frequency-offset estimation process by using the PPS received at the relay end and the obtained relay locally-generated PSS; and finally, carrying out integer-frequency-offset adjustment on the receiving signals of the PSS/SSS at the relay end by using the obtained result epsilon I of the integer-frequency-offset estimation, and carrying out fine-frequency-offset estimation process by using a corresponding algorithm. Therefore, the problem of the frequency offset estimation at the relay end can be solved, and the sending frequencies of the signals received at the relay end and the signals at a base station end are synchronous.
Owner:HEBEI UNIV OF TECH +1

Interfacial rheological testing method and apparatus by using liquid drop imagery

The invention discloses an interfacial rheological testing method and an interfacial rheological testing apparatus by using liquid drop imagery. According to the invention, after least squares fitting and secondary optimization by using a Newton iteration method are carried out on a discretized Young-lapalace equation theoretical calculated curve and an actual liquid drop contour boundary curve, interfacial chemical properties like surface tension, interfacial tension and a contact angle value, the volume, the area and the wetting line of liquid drops, etc. can be calculated; then interfacial rheological properties like interfacial dilational elasticity Epsilon d and interfacial dilational viscosity Eta d can be obtained through analysis by using an interfacial tension relaxation method; a set of liquid drop sample introduction system and a set of testing apparatus are provided, liquid drop oscillation is realized through corresponding control software so as to increase or reduce the amount of liquid drops and allow oscillation process to accord with sine, cosine, square wave and sawtooth changes. The apparatus provided by the invention enlarges the application field of optical interface chemical analysis apparatuses and meets requirements for high-precision automatic testing of dynamic/static contact angle values, dynamic/static surface tension values, interfacial tension values and interface rheological measurement values.
Owner:上海梭伦信息科技有限公司

Brain MRI (magnetic resonance image) segmentation method based on improved fuzzy C-means clustering algorithm

The invention relates to a brain MRI (magnetic resonance image) segmentation method based on an improved fuzzy C-means clustering algorithm. The method comprises steps that 1, initial classification is carried through utilizing the fuzzy C-means clustering algorithm; 2, the clustering quantity c, a fuzzy factor m, an algorithm iteration stop threshold Epsilon, the maximum iteration times max, a neighborhood window size and other artificial setting parameters are given; 3, a similarity matrix W of two pixels is calculated; 4, similarity rhoki of pixel pair types is calculated; 5, a membership matrix U is updated; 6, if ||U(t+1)-U(t)||<Epsilon, or t=max, iteration stops, U(t+1) is outputted, otherwise t=t+1, and the process turns to the step 4; and 7, for U(t+1), the maximum membership algorithm is employed to carry out deblurring operation, and label distribution is carried out to accomplish image segmentation. Through the method, three-portion optimization including improving a clustering center mode, introducing the partial space information and utilizing the intuitionistic fuzzy set information is accomplished, effects of noise resistance enhancement and segmentation precision improvement are realized, and an actual problem of high-precision segmentation for a brain MRI is solved.
Owner:BEIHANG UNIV

Method for extracting shield tunnel staggered joint and dislocation quantity on basis of three-dimensional scanning technology

The invention discloses a method for extracting shield tunnel staggered joint and dislocation quantity on the basis of a three-dimensional scanning technology. The method includes the following steps that position information of longitudinal joints between adjacent segments is extracted according to a tunnel inner wall orthographic projection obtained through three-dimensional laser scanning, a section S is arranged perpendicular to the center axis of a tunnel lining ring, and tunnel lining ring point sets P1 and P2 on the two sides of the section S of the longitudinal joint between every two adjacent segments in the distance range of epsilon / 2 are extracted; the point sets P1 and P2 on the two sides of the section S are projected on the section S to obtain two section slices; data inspection is performed on segmented arc sections of arcs on the section slices, the two arcs on the section slices are fitted after gross error points are removed, stagger quantity of the adjacent arc sections of each longitudinal joint is calculated in the radius direction, and the stagger quantity is the dislocation quantity on the two sides of each longitudinal joint between every two segments. The method has the advantages that dislocation quantity extraction precision and efficiency are high.
Owner:SHANGHAI GEOTECHN INVESTIGATIONS & DESIGN INST

Prediction method for fatigue life of complex braided structure ceramic-based composite material

The invention discloses a prediction method for the fatigue life of a complex braided structure ceramic-based composite material.The prediction method comprises the steps that the fatigue performance under a cycle number and the fiber failure percentage under the cycle number are calculated; the relationship between the fiber failure percentage and a fiber failure critical value is determined; the unit-cell scale fatigue performance is calculated to obtain the maximum strain epsilon'max under the cycle; the relationship between the maximum strain epsilon'max and the maximum failure strain epsilonmax is determined; a fatigue life curve of the material is obtained.According to the prediction method, a microscale model taking account of fibers, a base body and pores and a unit-cell multi-scale prediction model taking account of warp yarn, weft yarn and holes are presented and overcome the defects that a micromechanical method cannot be directly applied to the braded material with the complex structure, and a macroscopic phenomenological method depends on a large quantity of tests and only can achieve prediction on the fatigue life of a special material, macromechanics and micromechanics are combined, a micromechanical stress strain field of a complex braided structure is supplied, and the application range of the material is widened while the fatigue life curve of the material is precisely predicted.
Owner:NANJING UNIV OF AERONAUTICS & ASTRONAUTICS

Multi-terminal flexible DC power grid line direction pilot protection method

The invention discloses a multi-terminal flexible DC power grid line direction pilot protection method. The method comprises steps: DC current and voltage at two ends of a DC reactor are measured and a DC current mutation rate di/dt and a voltage mutation rate du/dt are calculated; when the di/dt or the du/dt is larger than a threshold value K1-set and K2-set, a protection algorithm is started instantly; fault voltage at two sides of a DC reactor at a protection terminal is measured, and corresponding transient components UM_line and UM_bus (UN_line and UN_bus) are extracted; r1=UM_line/UM_bus (r2=UN_line/UN_bus) is calculated, and a fault direction is judged: if r1>1+epsilon (r2>1+epsilon), epsilon is a reliable margin, positive direction fault is judged and a direction signal RM is equal to 1 (RN=1), or otherwise, reverse direction fault is judged, and a direction signal RM is equal to 0 (RN=0); when RM&RN=1, internal fault is judged; and when RM&RN=0, external fault is judged. The method of the invention has the advantages that data synchronization is not needed; a sampling rate is lowly required; the fault resistance withstanding ability is strong; influences from line distributed capacitance do not exist; engineering implementation is facilitated; and the hardware investment cost is reduced.
Owner:TIANJIN UNIV

Optimization algorithm of micro-grid energy management system based on non-cooperation game

The invention discloses an optimization algorithm of a micro-grid energy management system based on a non-cooperation game. The optimization algorithm includes following steps: 1) acquiring micro-grid meteorological data and load information data; 2) calculating an upper limit value of the allowed output of a photovoltaic array and an upper limit value of the allowed output of a fan at a wind speed; 3) inputting a constraint condition and an objective function, and optimizing a micro-grid; 4) obtaining the marginal cost of the optimization of the micro-grid; 5) dividing a game process of interactive game between the utility function of the micro-grid and the utility function of a user into 24 periods, and regarding the utility functions of an energy side and a user side as the objects for optimization game; and 6) finishing optimization if the deviation between a load curve obtained by the optimization and a load curve obtained by the previous optimization is less than or equal to epsilon, otherwise putting the load data of this time into step 1, and circulating step 1 to step 5 until the deviation is less than epsilon. The optimization algorithm is advantageous in that the optimization of the energy efficiency of the micro-grid is realized, and the feasibility and the adaptability are good.
Owner:SOUTH CHINA UNIV OF TECH

Parameter curve cutter path oriented numerical control system contour error control method

The invention provides a parameter curve cutter path oriented numerical control system contour error control method which comprises the following steps of: 1) calculation of the contour error; 2) calculation and control of the contour error compensation quantity, and is characterized in that: in the step 1), in each sampling period for performing curve interpolation on the parameter curve cutter path, the contour error epsilon is calculated according to the current actual cutter location point and the interpolation point on the tracked parameter curve cutter path, namely the shortest distancefrom the current actual cutter location point to the tracked parameter curve cutter path is calculated; in the step 2), the components of the contour error epsilon along the X axis, Y axis and Z axisare calculated, and the contour error compensation quantities are obtained by proportional control and superposed with the location control quantities for the following error on the X axis, Y axis and Z axis respectively; and then the result is output to a servo execution mechanism to perform contour error compensation control. The method provided by the invention has the advantages that: the contour error calculation precision is high, the contour error compensation method is simple and effective, and the contour precision can be obviously improved.
Owner:SHANDONG UNIV OF TECH

Semi-supervised learning-based multi-gesture facial expression recognition method

The invention relates to a semi-supervised learning-based multi-gesture facial expression recognition algorithm which comprises the steps of acquiring n front expression images and n side expression images of n persons to form a training set X and a testing set S, segmenting face regions of the front expression images and the side expression images, and carrying out illumination compensation on the face regions by using a histogram equalization method; then extracting expression characteristics of the images by adopting a linear discriminant analysis method, carrying out expression recognition on samples in the testing set S; marking each unmarked sample in the training set X by using marked samples in the training set X by adopting an Euclidean distance nearest neighbour method; re-sampling the training set X by adopting a round-robin mode to obtain a new training set Xr; scheduling a basic classifying device to calculate a mark ht of each sample in the training set X at the tth circle by using the new training set Xr, and calculating a mark ft of each sample in the testing set S at the tth circle by using the new training set Xr; and finally, calculating a classifying error rate epsilon t of the basic classifying device to side samples in the training set, and updating weights of all training samples in the training set X until reaching the circle ending condition.
Owner:北京格镭信息科技有限公司

Method for estimating integer multiple frequency deviation with timing error during communication synchronization process

ActiveCN101437005AIdeal autocorrelation propertyGood timing synchronizationMulti-frequency code systemsTime domainPeak value
The invention provides a method for estimating integer frequency offset with timing error during the communication synchronization, which comprises the following steps: a constant-amplitude Chu sequence with ideal autocorrelation characteristics is selected as a frequency domain difference sequence C(k),a first element S(0) in a frequency domain training sequence is defined to be equal to 1, the frequency domain training sequence S(k) with a length of N is obtained according to the recursion formula S(k)=C(k-1)S(k-1), and the S(k) is transformed into a time domain training sequence s(n) through an IFFT; after a receiving sequence finishes the fractional frequency offset compensation, two sections of receiving sequences with a length of N are taken out according to a coarse timing sequence, and two sections of receiving sequences are added to obtain a receiving sequence r(n) with a length of N; the frequency domain of the sequence r(n) is transformed into R(k) through FFT, the formula D(k)=R(k+1)(R(k))<*> is utilized to calculate a receiving frequency domain difference sequence D(k), the cyclic shift correlation is performed through the conjugation of the received sequence D(k) and the sequence C(k), and a related peak value corresponds to the integer frequency offset estimation epsilon int of a system, as shown in the right formula. The method strengthens the frequency offset estimation performance and improves the transmission efficiency of the system on the premise of not affecting the timing synchronous performance.
Owner:COMM ENG COLLEGE SCI & ENGINEEIRNG UNIV PLA

Adaptive terminal sliding-mode controller based mechanical arm trajectory tracking control method

The invention discloses an adaptive terminal sliding-mode controller based mechanical arm trajectory tracking control method. The method includes the following steps: 1, establishing a rigid mechanical arm system dynamics model having n degrees of freedom rotating joints; 2, obtaining the measuring information of each joint angle q and angular velocity which is shown in the description of a mechanical arm through a photoelectric encoder, setting the expected angle q<d> and expected angular velocity which is shown in the description tracked by each joint, and calculating mechanical arm trajectory tracking errors [epsilon]1 = q - q<d> and the first derivative shown in the description of trajectory tracking error versus time; 3, establishing a novel non-singular terminal sliding-mode surface s according to the [epsilon]1 and [epsilon]2; and 4, designing the controlling moment tau of the driving motor of each joint of the mechanical arm according to the sliding-mode surface s, and establishing an adaptive rate which can adjust control gain to dynamically estimate system lumped disturbance upper bound. Under the circumstance that internal and external interference such as parameter perturbation and torque disturbance existing in the mechanical arm system, the method can perform real-time feedback so as to realize the accurate controlling of mechanical arm trajectory tracking based on the measuring information of each joint angle and angular velocity, and the controlling on the robustness of the whole course can be guaranteed.
Owner:SOUTHEAST UNIV

True stress-true strain computation model and test system

InactiveCN101319977AAccurate performance characteristics of mechanical behaviorExpress mechanical behavior characteristicsSpecial data processing applicationsStrength propertiesVisual technologySoftware system
The invention researches the substantive characteristics of material deformation to aim at the practical problem of measuring real stress-real strain and discloses a real stress-real strain calculating model and a practical testing system: 1, based on the analysis on the deformation of a tension specimen, taking a unit body the special part of which is provided with characteristics as the object for the stress-strain analysis, building a unique full-deformation unit model, firstly solving the theory analysis problem of real stress-real strain, establishing a theory foundation and building a novel real stress-real strain calculating formula: Sigma i is equal to 4Fi/Pi d<2>I and Epsilon is equal to (d<2>0/d<2>i) minus 1; 2, adopting a machine visual technology and an image processing method to develop a practical software system and a practical hardware system that are compatible with the machine visual technology and the image processing method, and realizing the direct non-contact real stress-real strain measuring in real meaning; 3, the testing system includes a light source (1), CCD camera (2), an image acquisition card (3), a data acquisition card (4) and a material testing machine (5); 4,the software includes image capturing program, load data acquisition program and comprehensive calculation analysis program.
Owner:HARBIN INST OF TECH

Automatic extraction method for Earth observation laser height measurement satellite elevation control points and data processing method

The invention relates to an automatic extraction method for Earth observation laser height measurement satellite elevation control points and a data processing method. The laser elevation control point extraction method comprises steps that an effective earth observation laser distance value measurement evaluation method is employed, determined cloudless footprint image blocks are kept, and laser elevation data of determined thin-cloud or thick-cloud footprint image blocks are removed; reflectivity Epsilon smaller than 1 of laser footprint points is taken as a screening parameter, laser footprint points of the kept footprint image blocks are screened, Epsilon=reception pulse energy/emission pulse energy, laser footprint points which have only one wave peak, have the peak value greater than the threshold, have the standard deviation sigma not greater than 3.2ns after waveform fitting are selected from an echo waveform, and parameters used for determining the threshold comprise the emission energy and a reception caliber of a laser device. Through the method, influence of clouds on laser distance measurement can be reduced, laser distance measurement precision can be guaranteed, and accuracy of the laser elevation reference data is effectively improved.
Owner:SATELLITE SURVEYING & MAPPING APPL CENTSASMAC NAT ADMINISTATION OF SURVEYING MAPPING & GEOINFORMATION OF CHINANASG

Method for remote sensing estimation of net primary productivity of plants

The invention discloses a method for remote sensing estimation of net primary productivity of plants. The method comprises the steps of performing data pre-processing on remote sensing data; extracting LAI data of an MODIS product in the remote sensing data, and calculating an FPAR; calculating astronomical radiation total Q0 according to geographical location information of a research area including longitude and latitude and date; extracting an empirical coefficient according to conventional global radiation and sunshine percentage data of the research area; using Q0 and the empirical coefficient to calculate solar total radiation quantity SOL; calculating photosynthetically active radiation (APAR) according to the FPAR and the SOL; extracting soil water content and an empirical parameter in the remote sensing data, calculating current leaf water potential, and calculating water stress factor in combination with the previous empirical coefficient; extracting temperature data in the research area in meteorological data, calculating temperature stress factor f1(Ta); calculating solar energy utilization rate epsilon according to f1(Ta), and the maximum solar energy utilization rate; and calculating net primary productivity (NPP) according to the APAR and epsilon. The method has the advantages of being high in estimation precision.
Owner:SOUTH CHINA AGRI UNIV

A training sample data expansion method and device based on a variational auto-encoder

PendingCN109886388ATime-consuming and labor-intensive solution to expansionSolve efficiency problemsNeural architecturesPhysical realisationRegular distributionData expansion
The embodiment of the invention provides a training sample data expansion method and device based on a variational auto-encoder, and relates to the technical field of big data. The method comprises the steps of obtaining an original sample; inputting the original sample into the encoder of the variational autoencoder, wherein the encoder of the variational autoencoder comprises two neural networks, the two neural networks output Mu and sigma respectively, and Mu and sigma are both functions of the original sample; according to the square of the Mu and sigma, namely sigma 2, generating a randomnumber of corresponding Gaussian distribution; randomly sampling the standard normal distribution to obtain a sampling value epsilon, and determining a sampling variable Z according to the sampling value epsilon and the random number of the Gaussian distribution; and inputting the sampling variable Z into a decoder of the variational autoencoder, decoding the sampling variable Z by the decoder ofthe variational autoencoder, and then outputting similar samples of the original samples, and taking the similar samples as extended samples. Therefore, the technical scheme provided by the embodiment of the invention can solve the problems that the time and labor are wasted and the efficiency is low when sample data is manually expanded in the prior art.
Owner:PING AN TECH (SHENZHEN) CO LTD

Improved frequency bias estimation method for wideband MIMO

The invention discloses an improved broadband MIMO intermediate-frequency deviation estimation method. The method comprises the following steps: (1) sending a training sequence, namely sending out the training sequence through each sending antenna according to a designed training sequence sending mode; (2) frequency deviation estimation, namely carrying out frequency deviation estimation by using the combination of an improved SR algorithm and an iteration method, setting initial frequency deviation epsilon, acquiring a frequency deviation estimation value according to the improved SR algorithm and the iteration method on each receiving antenna, while acquiring a final frequency deviation estimation value by adopting a different method, wherein the improved SR algorithm is that after the estimation value of channel frequency domain response H (k) is de-noised, the estimation value is further acquired so as to acquire reconstructed signals; and (3) channel estimation, namely correcting the signals received by the receiving antenna according to the estimated frequency deviation, and estimating the channel. During channel estimation, the method well solves the problem of inaccurate frequency deviation estimation in the premises of considering frequency deviation influence and ensuring the performance of a system.
Owner:SHANDONG UNIV

Three-dimensional space stress-strain measurement method based on fiber bragg grating sensor

ActiveCN103954386AFully reflect the stress situationFully understand the stress statusForce measurement by measuring optical property variationUsing optical meansFiberPrincipal stress
The invention discloses a three-dimensional space stress-strain measurement method based on a fiber bragg grating sensor. The method comprises the following steps: arranging six fiber bragg grating strain sub-sensors on the three principal axes of a space coordinate system and the axes of angular bisectors between every two adjacent principal axes respectively; arranging a temperature sub-sensor on the axis k in the body diagonal direction of a cube; working out the strain in the directions of the six fiber bragg grating strain sub-sensors through a decoupling equation set of the fiber bragg grating sensor based on wavelength, wherein the wavelength is measured by the six fiber bragg grating strain sub-sensors and the temperature sub-sensor; obtaining the values of epsilon x, epsilon y, epsilon z, gama xy, gama yz and gama zx through the plane strain relationship formula of the mechanics of materials; substituting the six quantities into a cubic space principal strain equation to obtain the values of the principal strain epsilon 1, epsilon 2 and epsilon 3; obtaining the values of the principal stress sigma 1, sigma 2 and sigma 3 through a physical equation of the elastic mechanics; obtaining the directions of the principal strain and the principal stress through a space strain relationship equation set of the elastic mechanics and a direction cosine relational expression; obtaining the maximum value taw maximum of shear stress through the maximum shear stress formula; obtaining the direction of the maximum shear stress through the relationship between the principal stress and principal shear stress.
Owner:成都毅莘瑞科技有限公司

Large-scale generator stator winding major insulation aging state test method based on frequency domain spectroscopy

The invention discloses a large-scale generator stator winding major insulation aging state test method based on frequency domain spectroscopy. The method includes the steps: making a generator stop running and be reliably disconnected from a circuit, and cooling the generator to an ambient temperature; testing wiring: connecting a stator winding of the generator with a high-voltage end of a test cable of a dielectric spectrum tester, and connecting a grounding end of a housing of a generator with a grounding end of the test cable of the dielectric spectrum tester; setting a parameter and starting a test; testing a frequency characteristic curve [epsilon]-f of a major insulation complex dielectric constant of the stator winding of the generator, and obtaining the dielectric loss factor increment [delta]tan[delta]N of the current major insulation through calculation by a formula; and evaluating the aging state of the major insulation of the stator winding of the generator according to the obtained dielectric loss factor increment [delta]tan[delta]N. The method is a non-destructive test method, has simple test principles, enables convenient wiring, can accurately determine the dielectric loss factor increment [delta]tan[delta]N of the stator winding of the generator, and thus can effectively evaluate the aging state of the generator.
Owner:ELECTRIC POWER RES INST OF GUANGDONG POWER GRID +1

Aspherical spectacle lens

An aspherical lens by which residual aberration in all of third eye-positions is corrected and which the center or edge thickness can be reduced. Thus, this aspherical lens employs a first or second curved surface represented by the following equation: where (x, y, z) represents the coordinates of a point on an aspherical surface and satisfies (y epsilon [a, b]) &andg& (z epsilon [c. d]); my is an order of a spline function in the direction of the y-axis (in this case, an integer which is not less than 4); mz is an order of the spline function in the direction of the z-axis (in this case, an integer which is not less than 4); ny is the number of inner knots in [a, b] in the direction of the y-axis (in this case, an integer which is not less than 4); nz is the number of inner knots in [c, d] in the direction of the z-axis (in this case, an integer which is not less than 4); Nmy,i (y) represents an ith my-th-order normalized B-spline function in the case that knots in the direction of the y-axis are xi 0, xi 1, xi 2, . . . , xi ny+2my-1 (incidentally, "i" is an integer within [o, nm+my-1] and the position of each knot meets the following condition: xi 0</= xi 1</=. . . </= xi my-1</=a< xi my</=. . . </= xi ny+my-1<b</= xi ny+my</=. . . </= xi ny+my+1; Nmz,i (z) represents an jth mz-th-order normalized B-spline function in the case that knots in the direction of the z-axis are xi 0, xi 1, xi 2, . . . , xi nz+2mz-1 (incidentally, "j" is an integer within [0, nz+mz-1] and the position of each knot meets the following condition: xi 0</= xi 1</=. . . </= xi mz-1</=c< xi mz</=. . . </= xi nz+mz-1<d</= xi nz+mz</=. . . </= xi nz+2mx-1; and ci,j is a coefficient.
Owner:HOYA CORP
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