On-line electron-optical correlation computing in the CTEM

1978 ◽  
Vol 36 (1) ◽  
pp. 88-89 ◽  
Author(s):  
R. Guckenberger ◽  
W. Hoppe
Keyword(s):  
Fourier Transform ◽  
Correlation Function ◽  
Transfer Function ◽  
Inverse Fourier Transform ◽  
Main Peak ◽  
Optical Correlation ◽  
Auto Correlation ◽  
Auto Correlation Function ◽  
On Line ◽  
The Fourier Transform

Light diffractograms of electron micrographs are frequently used to study the transfer function of the microscope. In order to utilize diffractograms for control operations in the microscope, several attempts have been undertaken to obtain on-line diffractograms /1 - 3/. Alternatively correlation functions (CF) may be used /4-8/. In this paper we describe an electron-optical device for the computation of such CF and its on-line operation in a microscope.The auto-correlation function (ACF) is the inverse Fourier transform of the squared modulus of the Fourier transform (diffractogram) of an image. Therefore it also contains the transfer function. It is its zero peak (main peak) which is of particular interest. In noisy images the main ACF-peak of the noise contributes in an unwanted way to the main ACF-peak of the image. This can be avoided if the ACF will be computed of two images which are identical except for noise /9/ (noise-reduced ACF= NRACF).

Correlation Methods in Electron Image Analysis

1974 ◽  
Vol 32 ◽  
pp. 336-337
Author(s):  
Joachim Frank
Keyword(s):  
Image Analysis ◽  
Fourier Transform ◽  
Correlation Function ◽  
Digital Analysis ◽  
Correlation Matrices ◽  
Auto Correlation ◽  
Correlation Methods ◽  
Auto Correlation Function ◽  
Electron Image ◽  
Crosscorrelation Function

Correlation methods play an important role in the analysis of electron micrographs. Through the development of the Fast Fourier transform algorithms, the computation of correlation matrices of large pictures has become a matter of seconds. In the following, a number of applications of digital analysis using the auto-correlation function (ACF) and the crosscorrelation function (CCF) are outlined.

scholarly journals New Orthogonal Small Set Kasami Code Sequence

2015 ◽  
Vol 14 (1) ◽  
Author(s):  
I Nyoman Pramaita ◽  
I G.A.G.K. Diafari ◽  
DNKP Negara ◽  
Agus Dharma
Keyword(s):  
Correlation Function ◽  
Cross Correlation ◽  
Code Sequence ◽  
Cross Correlation Function ◽  
Auto Correlation ◽  
M Sequence ◽  
Auto Correlation Function ◽  
Small Set

In this paper, the authors propose the design of a new orthogonal small set Kasami code sequence generated using combination of non-orthogonal m-sequence and small set Kasami code sequence. The authors demonstrate that the proposed code sequence has comparable auto-correlation function (ACF), cross- correlation function (CCF), peak cross-correlation values with that of the existing orthogonal small set Kasami code sequence. Though the proposed code sequence has less code sequence sets than that of the existing orthogonal small set Kasami code sequence, the proposed code sequence possesses one more numbers of members in each code sequence set. The members of the same code set of the proposed code sequence are orthogonal to each other.

scholarly journals Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach

2021 ◽  
Author(s):  
Tilo Schwalger
Keyword(s):  
Correlation Function ◽  
Hazard Rate ◽  
Second Order ◽  
Level Crossing ◽  
Input Noise ◽  
Integrate And Fire ◽  
Auto Correlation ◽  
Auto Correlation Function ◽  
Decoupling Approximation ◽  
Crossing Theory

AbstractNoise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate (“escape noise”). While input noise lends itself to modeling biophysical noise processes, the phenomenological escape noise is mathematically more tractable. Using the level-crossing theory for differentiable Gaussian processes, we derive an approximate mapping between colored input noise and escape noise in leaky integrate-and-fire neurons. This mapping requires the first-passage-time (FPT) density of an overdamped Brownian particle driven by colored noise with respect to an arbitrarily moving boundary. Starting from the Wiener–Rice series for the FPT density, we apply the second-order decoupling approximation of Stratonovich to the case of moving boundaries and derive a simplified hazard-rate representation that is local in time and numerically efficient. This simplification requires the calculation of the non-stationary auto-correlation function of the level-crossing process: For exponentially correlated input noise (Ornstein–Uhlenbeck process), we obtain an exact formula for the zero-lag auto-correlation as a function of noise parameters, mean membrane potential and its speed, as well as an exponential approximation of the full auto-correlation function. The theory well predicts the FPT and interspike interval densities as well as the population activities obtained from simulations with colored input noise and time-dependent stimulus or boundary. The agreement with simulations is strongly enhanced across the sub- and suprathreshold firing regime compared to a first-order decoupling approximation that neglects correlations between level crossings. The second-order approximation also improves upon a previously proposed theory in the subthreshold regime. Depending on a simplicity-accuracy trade-off, all considered approximations represent useful mappings from colored input noise to escape noise, enabling progress in the theory of neuronal population dynamics.

Generalized spot auto-focusing method with a high-definition auto-correlation function in transmission electron microscopy

Microscopy ◽  
2019 ◽  
Vol 68 (5) ◽  
pp. 395-412
Author(s):  
Shigeto Isakozawa ◽  
Misuzu Baba ◽  
Junpei Amano ◽  
Shohei Sakamoto ◽  
Norio Baba
Keyword(s):  
Correlation Function ◽  
Yeast Cell ◽  
Thin Section ◽  
High Definition ◽  
Auto Correlation ◽  
Transmission Electron ◽  
Wide Range ◽  
Auto Correlation Function ◽  
Spot Image ◽  
Auto Focusing

Abstract The spot auto-focusing (AF) method with a unique high-definition auto-correlation function (HD-ACF) proposed in the previous paper is improved and is now applicable to general specimens at a wide range of magnifications. According to the definition where the AF is defocused to obtain the highest resolution, the proposed method achieves the sharpest HD-ACF profile in the AF spot image. The relationship where the sharpest HD-ACF profile gives the highest resolution is theoretically explained, and practical AF examples for different specimens and magnifications are experimentally demonstrated. Specimens include a yeast cell thin section at 10-k magnification, a standard grating replica used as a ruler at 50-k, a crystal lattice of graphitized carbon at 400-k and a 60°-tilted thin section (yeast cell) at 10-k. Different procedures are prepared to actively identify the defocus position that gives the sharpest HD-ACF profile. Every AF result demonstrates the highest-resolution image.

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