scholarly journals Accurate localization microscopy by intrinsic aberration calibration

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Craig R. Copeland ◽  
Craig D. McGray ◽  
B. Robert Ilic ◽  
Jon Geist ◽  
Samuel M. Stavis
Keyword(s):  
Degrees Of Freedom ◽  
Spatial Information ◽  
Three Dimensions ◽  
Optical Aberrations ◽  
Localization Microscopy ◽  
Six Degrees Of Freedom ◽  
Accurate Localization ◽  
Engineering Information ◽  
Testing Accuracy ◽  
Precision Testing

AbstractA standard paradigm of localization microscopy involves extension from two to three dimensions by engineering information into emitter images, and approximation of errors resulting from the field dependence of optical aberrations. We invert this standard paradigm, introducing the concept of fully exploiting the latent information of intrinsic aberrations by comprehensive calibration of an ordinary microscope, enabling accurate localization of single emitters in three dimensions throughout an ultrawide and deep field. To complete the extraction of spatial information from microscale bodies ranging from imaging substrates to microsystem technologies, we introduce a synergistic concept of the rigid transformation of the positions of multiple emitters in three dimensions, improving precision, testing accuracy, and yielding measurements in six degrees of freedom. Our study illuminates the challenge of aberration effects in localization microscopy, redefines the challenge as an opportunity for accurate, precise, and complete localization, and elucidates the performance and reliability of a complex microelectromechanical system.

scholarly journals THE “DUAL” VARIABLES OF YANG-MILLS THEORY AND LOCAL GAUGE-INVARIANT VARIABLES

1996 ◽  
Vol 11 (32) ◽  
pp. 5701-5728 ◽  
Author(s):  
ORI GANOR ◽  
J. SONNENSCHEIN
Keyword(s):  
Degrees Of Freedom ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Six Degrees Of Freedom ◽  
Local Gauge ◽  
Dual Variables ◽  
Topological Part

After adding auxiliary fields and integrating out the original variables, the Yang-Mills action can be expressed in terms of local gauge-invariant variables. This method reproduces the known solution of the two-dimensional SU (N) theory. In more than two dimensions the action splits into a topological part and a part proportional to αs. We demonstrate the procedure for SU (2) in three dimensions where we reproduce a gravitylike theory. We discuss the four-dimensional case as well. We use a cubic expression in the fields as a space-time metric to obtain a covariant Lagrangian. We also show how the four-dimensional SU (2) theory can be expressed in terms of a local action with six degrees of freedom only.

The Qualitative Synthesis of Parallel Manipulators

2004 ◽  
Vol 126 (4) ◽  
pp. 617-624 ◽  
Author(s):  
Jorge Angeles
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Qualitative Reasoning ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Qualitative Synthesis ◽  
Motion Representation ◽  
Six Degrees Of Freedom ◽  
Three Degrees Of Freedom

As shown in this paper, when designing parallel manipulators for tasks involving less than six degrees of freedom, the topology can be laid out by resorting to qualitative reasoning. More specifically, the paper focuses on cases whereby the manipulation tasks pertain to displacements with the algebraic structure of a group. Besides the well-known planar and spherical displacements, this is the case of displacements involving: rotation about a given axis and translation in the direction of the same axis (cylindrical subgroup); translation in two and three dimensions (two- and three-dimensional translation subgroups); three independent translations and rotation about an axis of fixed direction, what is known as the Scho¨nflies subgroup; and similar to the Scho¨nflies subgroup, but with the rotation and the translation in the direction of the axis of rotation replaced by a screw displacement. For completeness, the fundamental concepts of motion representation and groups of displacements, as pertaining to rigid bodies, are first recalled. Finally, the concept of Π-joint, introduced elsewhere, is generalized to two and three degrees of freedom, thereby ending up with the Π2-and the Π3-joints, respectively.

Maximum Norm Error Estimates for Quadratic Block Finite Elements with Twenty-Six Degrees of Freedom

2011 ◽  
Vol 480-481 ◽  
pp. 1388-1392
Author(s):  
Jing Hong Liu ◽  
Gui Hu
Keyword(s):  
Error Estimates ◽  
Degrees Of Freedom ◽  
Elliptic Boundary ◽  
Three Dimensions ◽  
Maximum Norm ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Six Degrees Of Freedom ◽  
Discrete Green’S Function ◽  
Norm Error

For a model elliptic boundary value problem in three dimensions, we give the weak estimates for the quadratic block finite element with twenty-six degrees of freedom (QBFETSDF). Combined with the estimates for discrete Green’s function, we get maximum norm error estimates for the QBFETSDF.

scholarly journals Binocular visual tracking and grasping of a moving object with a 3D trajectory

2009 ◽  
Vol 7 (03) ◽  
Author(s):  
J. Fuentes-Pacheco ◽  
J. Ruiz-Ascencio ◽  
J. M. Rendón-Mancha
Keyword(s):  
Control System ◽  
Visual Servoing ◽  
Degrees Of Freedom ◽  
Vision System ◽  
Moving Object ◽  
Three Dimensions ◽  
Stereo Pair ◽  
Six Degrees Of Freedom ◽  
Linear Predictors ◽  
Server Architecture

This paper presents a binocular eye-to-hand visual servoing system that is able to track and grasp a moving object in real time. Linear predictors are employed to estimate the object trajectory in three dimensions and are capable of predicting future positions even if the object is temporarily occluded. For its development we have used a CRS T475 manipulator robot with six degrees of freedom and two fixed cameras in a stereo pair configuration. The system has a client‐server architecture and is composed of two main parts: the vision system and the control system. The vision system uses color detection to extract the object from the background and a tracking technique based on search windows and object moments. The control system uses the RobWork library to generate the movement instructions and to send them to a C550 controller by means of the serial port. Experimental results are presented to verify the validity and the efficacy of the proposed visual servoing system.

Control of processing at multi-tool two-support setup

2020 ◽  
pp. 67-73
Author(s):  
N.D. YUsubov ◽  
G.M. Abbasova
Keyword(s):  
Degrees Of Freedom ◽  
Factor Model ◽  
Angular Displacement ◽  
Factor Models ◽  
Technological System ◽  
Displacement Control ◽  
Model Accuracy ◽  
Six Degrees Of Freedom ◽  
Angular Displacements ◽  
And Control

The accuracy of two-tool machining on automatic lathes is analyzed. Full-factor models of distortions and scattering fields of the performed dimensions, taking into account the flexibility of the technological system on six degrees of freedom, i. e. angular displacements in the technological system, were used in the research. Possibilities of design and control of two-tool adjustment are considered. Keywords turning processing, cutting mode, two-tool setup, full-factor model, accuracy, angular displacement, control, calculation [email protected]

scholarly journals Design and Calibration of a Hall Effect System for Measurement of Six-Degree-of-Freedom Motion within a Stacked Column

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3740
Author(s):  
Olafur Oddbjornsson ◽  
Panos Kloukinas ◽  
Tansu Gokce ◽  
Kate Bourne ◽  
Tony Horseman ◽  
...  
Keyword(s):  
Hall Effect ◽  
Degrees Of Freedom ◽  
Reactor Core ◽  
Degree Of Freedom ◽  
Life Extension ◽  
Scale Model ◽  
Design Development ◽  
Seismic Safety ◽  
Six Degrees Of Freedom ◽  
Six Degree Of Freedom

This paper presents the design, development and evaluation of a unique non-contact instrumentation system that can accurately measure the interface displacement between two rigid components in six degrees of freedom. The system was developed to allow measurement of the relative displacements between interfaces within a stacked column of brick-like components, with an accuracy of 0.05 mm and 0.1 degrees. The columns comprised up to 14 components, with each component being a scale model of a graphite brick within an Advanced Gas-cooled Reactor core. A set of 585 of these columns makes up the Multi Layer Array, which was designed to investigate the response of the reactor core to seismic inputs, with excitation levels up to 1 g from 0 to 100 Hz. The nature of the application required a compact and robust design capable of accurately recording fully coupled motion in all six degrees of freedom during dynamic testing. The novel design implemented 12 Hall effect sensors with a calibration procedure based on system identification techniques. The measurement uncertainty was ±0.050 mm for displacement and ±0.052 degrees for rotation, and the system can tolerate loss of data from two sensors with the uncertainly increasing to only 0.061 mm in translation and 0.088 degrees in rotation. The system has been deployed in a research programme that has enabled EDF to present seismic safety cases to the Office for Nuclear Regulation, resulting in life extension approvals for several reactors. The measurement system developed could be readily applied to other situations where the imposed level of stress at the interface causes negligible material strain, and accurate non-contact six-degree-of-freedom interface measurement is required.

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