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.

Spot auto-focusing and spot auto-stigmation methods with high-definition auto-correlation function in high-resolution TEM

Microscopy ◽  
2018 ◽  
Vol 67 (2) ◽  
pp. 75-88
Author(s):  
Shigeto Isakozawa ◽  
Taishi Fuse ◽  
Junpei Amano ◽  
Norio Baba
Keyword(s):  
Thin Film ◽  
Correlation Function ◽  
High Resolution ◽  
High Definition ◽  
Amorphous Thin Film ◽  
Auto Correlation ◽  
Transmission Electron ◽  
Film Images ◽  
Auto Correlation Function ◽  
Auto Focusing

Abstract As alternatives to the diffractogram-based method in high-resolution transmission electron microscopy, a spot auto-focusing (AF) method and a spot auto-stigmation (AS) method are presented with a unique high-definition auto-correlation function (HD-ACF). The HD-ACF clearly resolves the ACF central peak region in small amorphous-thin-film images, reflecting the phase contrast transfer function. At a 300-k magnification for a 120-kV transmission electron microscope, the smallest areas used are 64 × 64 pixels (~3 nm2) for the AF and 256 × 256 pixels for the AS. A useful advantage of these methods is that the AF function has an allowable accuracy even for a low s/n (~1.0) image. A reference database on the defocus dependency of the HD-ACF by the pre-acquisition of through-focus amorphous-thin-film images must be prepared to use these methods. This can be very beneficial because the specimens are not limited to approximations of weak phase objects but can be extended to objects outside such approximations.

Binary collisions in fluids: II: velocity auto correlation function

1983 ◽  
Vol 61 (12) ◽  
pp. 1655-1659 ◽  
Author(s):  
S. Ranganathan
Keyword(s):  
Correlation Function ◽  
Memory Function ◽  
Binary Collision ◽  
Jones Potential ◽  
Auto Correlation ◽  
Wide Range ◽  
Classical Fluids ◽  
Auto Correlation Function ◽  
Molecular Dynamics Results ◽  
Good Agreement

A calculation based on the Zwanzig–Mori formalism and the binary collision expansion is presented for the velocity auto correlation function (VCF) of simple classical fluids. The binary collision expansion is truncated after the second term, thus incorporating exactly all the effects of a single collision between two particles, and this expansion is applied to the memory function associated with the VCF. The only inputs required are the pair distribution function g(r) and a central potential U(r). The potential chosen is the Lennard–Jones potential. It is seen that the approximation of the memory function by the binary force auto correlation function yields results for VCF that are in very good agreement with molecular dynamics results over a wide range of densities from dilute gases to liquids.

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.

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