scholarly journals Analytical Approximations of Long-Exposure Point Spread Functions and their Use

1989 ◽  
Vol 8 ◽  
pp. 657-661
Author(s):  
O. Bendinelli ◽  
G. Parmeggiani ◽  
F. Zavatti
Keyword(s):  
Gaussian Model ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Point Spread Functions ◽  
Spherical Source ◽  
Analytical Approximations ◽  
Correct Model ◽  
Point Spread ◽  
Surface Image ◽  
Star Images

AbstractThe observed light distribution in long exposure star images (PSF) may be fitted equally well by a variety of models. But dealing with undersainpled star images, only the use of the multi-Gaussian model allows the correct model parameters estimation, taking into account integration on pixel surface, image off-centering and background behaviour. It is also shown that the convolution of a spherical source with the multi-Gaussian and Moffat’s models gives in practice the same result.

scholarly journals Axial localization and tracking of self-interference nanoparticles by lateral point spread functions

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yongtao Liu ◽  
Zhiguang Zhou ◽  
Fan Wang ◽  
Günter Kewes ◽  
Shihui Wen ◽  
...  
Keyword(s):  
Mirror Image ◽  
Excitation Wavelength ◽  
Far Field ◽  
Point Spread Functions ◽  
Microscopy Imaging ◽  
Localization Accuracy ◽  
Field Patterns ◽  
Atomic Force ◽  
Point Spread ◽  
Sensing Technology

AbstractSub-diffraction limited localization of fluorescent emitters is a key goal of microscopy imaging. Here, we report that single upconversion nanoparticles, containing multiple emission centres with random orientations, can generate a series of unique, bright and position-sensitive patterns in the spatial domain when placed on top of a mirror. Supported by our numerical simulation, we attribute this effect to the sum of each single emitter’s interference with its own mirror image. As a result, this configuration generates a series of sophisticated far-field point spread functions (PSFs), e.g. in Gaussian, doughnut and archery target shapes, strongly dependent on the phase difference between the emitter and its image. In this way, the axial locations of nanoparticles are transferred into far-field patterns. We demonstrate a real-time distance sensing technology with a localization accuracy of 2.8 nm, according to the atomic force microscope (AFM) characterization values, smaller than 1/350 of the excitation wavelength.

A COMPARATIVE STUDY OF PHENOMENOLOGICAL MODELS OF MR BRAKE BASED ON NEURAL NETWORKS APPROACH

2013 ◽  
Vol 11 (01) ◽  
pp. 1350009 ◽  
Author(s):  
WITOLD PAWLUS ◽  
HAMID REZA KARIMI
Keyword(s):  
Neural Networks ◽  
Vibration Suppression ◽  
Feedforward Neural Networks ◽  
Active Suspension ◽  
Full Scale ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Systems Identification ◽  
Active Vibration ◽  
Models Validation

In this paper a full-scale commercially available magnetorheological (MR) brake installed in a semi-active suspension (SAS) system is modeled and simulated. Two well-known phenomenological hysteresis models are explored: Bouc–Wen and Dahl ones. In particular, influence of their parameters on the response is evaluated and assessed. The next step is to introduce the artificial neural networks and discuss their application in the field of systems identification. Subsequently, two feedforward neural networks are created and trained to estimate parameters characterizing each of the MR damper models described. The semi-active suspension (SAS) system equipped with a MR brake is described and the detailed procedure for acquisition of the reference data used in the models validation stage is elaborated. The models outputs obtained by simulating them with the values of coefficients as identified by the networks are compared to each other as well as to the reference experimental data. Thanks to that, the comparative analysis between the suggested vibration suppression models and the full-scale MR brake is done and it is concluded which of the discussed models has a better performance. The usability of neural networks in the field of parameters estimation of the mathematical models of the real world phenomena is described as well. The novelty of the presented methodology is the application of artificial intelligence methods to estimate model parameters of a MR brake utilized in a SAS system. The results of this approach have a strong potential to be successfully implemented in the area of model-based control of semi-active vibration suppression systems.

Sharp Analytical Lower Bounds for the Price of a Convertible Bond

2018 ◽  
Keyword(s):  
Finite Difference ◽  
Lower Bounds ◽  
Diffusion Models ◽  
Bond Pricing ◽  
Convertible Bond ◽  
Model Parameters ◽  
Analytical Approximations ◽  
Markov Diffusion

Analytical approximations for the price of a convertible bond within defaultable Markov diffusion models are derived in this article. Because convertible bond pricing requires time-consuming finite difference or tree pricing methods in general, such proxy formulas can help to calibrate model parameters more efficiently. The derivation is based on the idea of “Europeanizing” the American conversion option of the holder. Hence, the quality of the approximations stands and falls with the value of the early conversion premium. In practice, the latter is typically close to zero, which implies that the analytical lower bounds are incredibly sharp.

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