Phase recovery from interference fringes by Hilbert transform

2009 ◽  
Author(s):  
Zehra Saraç ◽  
H. Gülay Birkök ◽  
Ahmet Emir ◽  
Ali Dursun
Keyword(s):  
Hilbert Transform ◽  
Phase Recovery ◽  
Interference Fringes

Phase recovery from interference fringes by using S-transform

Measurement ◽  
2008 ◽  
Vol 41 (4) ◽  
pp. 403-411 ◽  
Author(s):  
Ali Dursun ◽  
Zehra Saraç ◽  
Hülya Saraç Topkara ◽  
Serhat Özder ◽  
F. Necati Ecevit
Keyword(s):  
Phase Recovery ◽  
Interference Fringes ◽  
S Transform

Quanitative aspects of electron diffraction using electron holography

1995 ◽  
Vol 53 ◽  
pp. 616-617
Author(s):  
E. Völkl ◽  
L.F. Allard ◽  
B. Frost ◽  
T.A. Nolan
Keyword(s):  
Electron Beam ◽  
Electron Diffraction ◽  
Software Package ◽  
Spatial Coherence ◽  
Electron Holography ◽  
Image Intensity ◽  
Interference Fringes ◽  
Complex Image ◽  
The Difference ◽  
Recorded Image

Off-axis electron holography has the well known ability to preserve the complex image wave within the final, recorded image. This final image described by I(x,y) = I(r) contains contributions from the image intensity of the elastically scattered electrons IeI (r) = |A(r) exp (iΦ(r)) |, the contributions from the inelastically scattered electrons IineI (r), and the complex image wave Ψ = A(r) exp(iΦ(r)) as:(1) I(r) = IeI (r) + Iinel (r) + μ A(r) cos(2π Δk r + Φ(r))where the constant μ describes the contrast of the interference fringes which are related to the spatial coherence of the electron beam, and Φk is the resulting vector of the difference of the wavefront vectors of the two overlaping beams. Using a software package like HoloWorks, the complex image wave Ψ can be extracted.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

A Bayesian View on the Hilbert Transform and the Kramers-Kronig Transform of Electrochemical Impedance Data: Probabilistic Estimates and Quality Scores

2020 ◽  
Author(s):  
Jiapeng Liu ◽  
Ting Hei Wan ◽  
Francesco Ciucci
Keyword(s):  
Power Generation ◽  
Electrochemical Impedance Spectroscopy ◽  
Hilbert Transform ◽  
Electrochemical Impedance ◽  
The Self ◽  
Impedance Data ◽  
The Hilbert Transform ◽  
Validation Tests ◽  
Self Consistency ◽  
Mathematical Relations

<p>Electrochemical impedance spectroscopy (EIS) is one of the most widely used experimental tools in electrochemistry and has applications ranging from energy storage and power generation to medicine. Considering the broad applicability of the EIS technique, it is critical to validate the EIS data against the Hilbert transform (HT) or, equivalently, the Kramers–Kronig relations. These mathematical relations allow one to assess the self-consistency of obtained spectra. However, the use of validation tests is still uncommon. In the present article, we aim at bridging this gap by reformulating the HT under a Bayesian framework. In particular, we developed the Bayesian Hilbert transform (BHT) method that interprets the HT probabilistic. Leveraging the BHT, we proposed several scores that provide quick metrics for the evaluation of the EIS data quality.<br></p>

Silicon Fringe Sample Metrology—A Thickness Measurement Technique

2013 ◽  
Author(s):  
Mark Kimball
Keyword(s):  
Temperature Dependence ◽  
Temperature Coefficient ◽  
Measurement Technique ◽  
Thickness Measurement ◽  
Sample Thickness ◽  
Index Of Refraction ◽  
Interference Fringes ◽  
Noncontact Method ◽  
Thickness Variations

Abstract Silicon’s index of refraction has a strong temperature coefficient. This temperature dependence can be used to aid sample thinning procedures used for backside analysis, by providing a noncontact method of measuring absolute sample thickness. It also can remove slope ambiguity while counting interference fringes (used to determine the direction and magnitude of thickness variations across a sample).

Display of Hilbert Transform Using Polarization Filter

1989 ◽  
Vol 18 (2) ◽  
pp. 48-50
Author(s):  
Kallol Bhattacharya ◽  
D. K. Basu ◽  
Ajay Ghosh ◽  
A. K. Chakrabortt
Keyword(s):  
Hilbert Transform ◽  
Polarization Filter
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