scholarly journals Laser Safety Calculations for Imaging Sensors

Sensors ◽  
2019 ◽  
Vol 19 (17) ◽  
pp. 3765 ◽  
Author(s):  
Ritt
Keyword(s):  
Closed Form ◽  
Related Concept ◽  
Laser Safety ◽  
Human Eye ◽  
Imaging Sensors ◽  
First Time ◽  
Camera Sensors ◽  
Maximum Permissible Exposure

This publication presents an approach to adapt the well-known classical eye-related concept of laser safety calculations on camera sensors as general as possible. The difficulty in this approach is that sensors, in contrast to the human eye, consist of a variety of combinations of optics and detectors. Laser safety calculations related to the human eye target terms like Maximum Permissible Exposure (MPE) and Nominal Ocular Hazard Distance (NOHD). The MPE describes the maximum allowed level of irradiation at the cornea of the eye to keep the eye safe from damage. The hazard distance corresponding to the MPE is called NOHD. Recently, a laser safety framework regarding the case of human eye dazzling was suggested. For laser eye dazzle, the quantities Maximum Dazzle Exposure (MDE) and the corresponding hazard distance Nominal Ocular Dazzle Distance (NODD) were introduced. Here, an approach is presented to extend laser safety calculations to camera sensors in an analogous way. The main objective thereby was to establish closed-form equations that are as simple as possible to allow also non-expert users to perform such calculations. This is the first time that such investigations have been carried out for this purpose.

scholarly journals A Closed-Form Buckling Formula for Open-Coiled and Properly Supported Circular-Bar Helical Springs

2018 ◽  
Vol 68 (3) ◽  
pp. 33-48
Author(s):  
Yildirim Vebil
Keyword(s):  
Closed Form ◽  
Elementary Theory ◽  
Circular Section ◽  
Helical Springs ◽  
Helix Pitch ◽  
Wide Range ◽  
The Mean ◽  
Artificial Neural Network Ann ◽  
Circular Bar ◽  
First Time

AbstractAs a continuation of the author’s previous studies on the buckling analysis of helical springs, a closed-form formula having been obtained with the help of the artificial neural network (ANN) is proposed and discussed in detail for the first time for a cylindrical close/open-coiled helical spring with fixed ends and having a solid circular section. As far as the author knows there is no such a formula in the open-literature to consider the effects of all stress resultants (torsional and bending moments, axial and shearing forces), large helix pitch angles together with the axial and shear deformations on the buckled state. The present formula may be used in a wide range of the total number of active turns, the ratio of the free axial length to the mean helix diameter, and the spring index. It is yet again revealed that it is not appropriate to use the elementary theory to determine the critical buckling loads for open-coiled springs. The present formula may allow the deeper understanding of spring buckling mechanism and to be used directly and safely in the design processes of such closely/open-coiled springs.

scholarly journals Delay chemical master equation: direct and closed-form solutions

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150049 ◽  
Author(s):  
Andre Leier ◽  
Tatiana T. Marquez-Lago
Keyword(s):  
Master Equation ◽  
Closed Form ◽  
Stochastic Simulation Algorithm ◽  
Chemical Master Equation ◽  
Kolmogorov Equation ◽  
Closed Form Solutions ◽  
Mrna Maturation ◽  
First Time ◽  
Nonlinear Markov Process ◽  
Reaction Schemes

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived.

scholarly journals Estimation of Lens Stray Light with Regard to the Incapacitation of Imaging Sensors

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6308
Author(s):  
Gunnar Ritt ◽  
Bastian Schwarz ◽  
Bernd Eberle
Keyword(s):  
Light Scattering ◽  
Theoretical Model ◽  
Stray Light ◽  
Optical Systems ◽  
Optical Elements ◽  
Laser Safety ◽  
Engineering Software ◽  
Commercial Off The Shelf ◽  
Generic Set ◽  
Imaging Sensors

We present our efforts on estimating light scattering characteristics from commercial off-the-shelf (COTS) camera lenses in order to deduce thereof a set of generic scattering parameters valid for a specific lens class (double Gauss lenses). In previous investigations, we developed a simplified theoretical light scattering model to estimate the irradiance distribution in the focal plane of a camera lens. This theoretical model is based on a 3-parameter bidirectional scattering distribution function (BSDF), which describes light scattering from rough surfaces of the optical elements. Ordinarily, the three scatter parameters of the BSDF are not known for COTS camera lenses, which makes it necessary to assess them by own experiments. Besides the experimental setup and the measurement process, we present in detail the subsequent data exploitation. From measurements on seven COTS camera lenses, we deduced a generic set of scatter parameters. For a deeper analysis, the results of our measurements have also been compared with the output of an optical engineering software. Together with our theoretical model, now stray light calculations can be accomplished even then, when specific scatter parameters are not available from elsewhere. In addition, the light scattering analyses also allow considering the glare vulnerability of optical systems in terms of laser safety.

scholarly journals Baker–Campbell–Hausdorff–Dynkin Formula for the Lie Algebra of Rigid Body Displacements

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1185
Author(s):  
Daniel Condurache ◽  
Ioan-Adrian Ciureanu
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Lie Algebra ◽  
Lie Group ◽  
First Time

The paper proposes, for the first time, a closed form of the Baker–Campbell–Hausdorff–Dynkin (BCHD) formula in the particular case of the Lie algebra of rigid body displacements. For this purpose, the structure of the Lie group of the rigid body displacements S E ( 3 ) and the properties of its Lie algebra s e ( 3 ) are used. In addition, a new solution to this problem in dual Lie algebra of dual vectors is delivered using the isomorphism between the Lie group S E ( 3 ) and the Lie group of the orthogonal dual tensors.

scholarly journals Application of Decomposable Semi-Regenerative Processes to the Study of k-out-of-n Systems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1933
Author(s):  
Vladimir Rykov ◽  
Nika Ivanova ◽  
Dmitry Kozyrev
Keyword(s):  
Closed Form ◽  
Time Dependent ◽  
System State ◽  
Regenerative Processes ◽  
Full System ◽  
Special Cases ◽  
Form Representation ◽  
History Of ◽  
First Time ◽  
Stationary Probabilities

This paper aimed to demonstrate the capabilities of decomposable semi-regenerative processes for the investigation of the k-out-of-n system. Proposed in 1955 by W. Smith, the regeneration idea has come a long way in terms of development and has found widespread applications. First, we briefly recall the history of the development of the regeneration idea and the main results of the theory of regenerative, semi-regenerative, and decomposable semi-regenerative processes. Then, the methods of the theory of decomposable semi-regenerative processes are used for the study of a k-out-of-n renewable system with exponentially distributed life and generally distributed repair times of its components. This system is very important for practice and its special cases have previously been considered (including by the authors); however, only special cases and using other methods are considered herein. In the current paper, two scenarios of system repair after its failure are considered for the first time: the partial and the full system repair scenarios. For both scenarios, the time-dependent system state probabilities are calculated in terms of their Laplace transforms. The closed form representation of the stationary probabilities for both scenarios are also presented. These latest results represent a new contribution to the study of this system.

KINEMATIC ANALYSIS AND PROTOTYPE OF A METAMORPHIC ANTHROPOMORPHIC HAND WITH A RECONFIGURABLE PALM

2011 ◽  
Vol 08 (03) ◽  
pp. 459-479 ◽  
Author(s):  
GUOWU WEI ◽  
JIAN S. DAI ◽  
SHUXIN WANG ◽  
HAIFENG LUO
Keyword(s):  
Closed Form ◽  
Matrix Equation ◽  
Kinematic Analysis ◽  
Structure Design ◽  
Characteristic Matrix ◽  
Robotic Hand ◽  
Closed Form Solutions ◽  
First Time

A novel metamorphic anthropomorphic hand is for the first time introduced in this paper. This robotic hand has a reconfigurable palm that generates changeable topology and augments dexterity and versatility of the hand. Structure design of the robotic hand is presented and based on mechanism decomposition kinematics of the metamorphic anthropomorphic hand is characterized with closed-form solutions leading to the workspace investigation of the robotic hand. With characteristic matrix equation, twisting motion of the metamorphic robotic hand is investigated to reveal both dexterity and manipulability of the metamorphic hand. Through a prototype, grasping and prehension of the robotic hand are tested to illustrate characteristics of the new metamorphic anthropomorphic hand.

scholarly journals Correction: Ritt, G. Laser Safety Calculations for Imaging Sensors. Sensors 2019, 19, 3765

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 1959
Author(s):  
Gunnar Ritt
Keyword(s):  
Laser Safety ◽  
Imaging Sensors

The author wishes to make the following corrections to the paper [...]

scholarly journals Reliability and Risk Controlled by the Simultaneous Presence of Random Events on a Time Interval

2017 ◽  
Vol 4 (2) ◽  
Author(s):  
M. T. Todinov
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Time Interval ◽  
Simultaneous Presence ◽  
Critical Events ◽  
Form Expression ◽  
Expected Time ◽  
Random Events ◽  
First Time ◽  
Unsatisfied Demand

The paper treats the important problem related to risk controlled by the simultaneous presence of critical events, randomly appearing on a time interval and shows that the expected time fraction of simultaneously present events does not depend on the distribution of events durations. In addition, the paper shows that the probability of simultaneous presence of critical events is practically insensitive to the distribution of the events durations. These counter-intuitive results provide the powerful opportunity to evaluate the risk of overlapping of random events through the mean duration times of the events only, without requiring the distributions of the events durations or their variance. A closed-form expression for the expected fraction of unsatisfied demand for random demands following a homogeneous Poisson process in a time interval is introduced for the first time. In addition, a closed-form expression related to the expected time fraction of unsatisfied demand, for a fixed number of consumers initiating random demands with a specified probability, is also introduced for the first time. The concepts stochastic separation of random events based on the probability of overlapping and the average overlapped fraction are also introduced. Methods for providing stochastic separation and optimal stochastic separation achieving balance between risk and cost of risk reduction are presented.

scholarly journals Modelling cascading effects for systemic risk: Properties of the Freund copula

2019 ◽  
Vol 7 (1) ◽  
pp. 24-44
Author(s):  
Sándor Guzmics ◽  
Georg Ch. Pflug
Keyword(s):  
Closed Form ◽  
Systemic Risk ◽  
Copula Function ◽  
Archimedean Copulas ◽  
Economic Agents ◽  
Cascading Effects ◽  
Cascade Effect ◽  
Lifetime Model ◽  
Bivariate Copula ◽  
First Time

AbstractWe consider a dependent lifetime model for systemic risk, whose basic idea was for the first time presented by Freund. This model allows to model cascading effects of defaults for arbitrarily many economic agents. We study in particular the pertaining bivariate copula function. This copula does not have a closed form and does not belong to the class of Archimedean copulas, either.We derive some monotonicity properties of it and show how to use this copula for modelling the cascade effect implicitly contained in observed CDS spreads.

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