Cosmological power spectrum in a noncommutative spacetime

We study how the noncommutative spacetime affects inflation. First we obtain the noncommutative power spectrum of the curvature perturbations produced during inflation in the slow-roll approximation. This is the explicit k-dependent power spectrum up to first order in slow-roll parameters ε1, δ1 including the noncommutative parameter μ. In order to test the role of μ further, we calculate the noncommutative power spectrum using the slow-roll expansion. We find corrections which arise from the change of pivot scale and the slowly varying nature of μ. It turns out that the noncommutative parameter μ could be considered as a zero order slow-roll parameter and the noncommutative spacetime effect provides a negatively large running spectral index.

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The on-line use of histogram data for high-speed correction and alignment of electron microscope images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100112713 ◽

1984 ◽

Vol 42 ◽

pp. 556-557

Author(s):

William Krakow

Keyword(s):

Power Spectrum ◽

High Speed ◽

Direct Memory Access ◽

Digital Television ◽

Contrast Transfer Function ◽

The Past ◽

High Resolution Tem ◽

On Line ◽

Correction Of Astigmatism ◽

The Fourier Transform

In the past few years on-line digital television frame store devices coupled to computers have been employed to attempt to measure the microscope parameters of defocus and astigmatism. The ultimate goal of such tasks is to fully adjust the operating parameters of the microscope and obtain an optimum image for viewing in terms of its information content. The initial approach to this problem, for high resolution TEM imaging, was to obtain the power spectrum from the Fourier transform of an image, find the contrast transfer function oscillation maxima, and subsequently correct the image. This technique requires a fast computer, a direct memory access device and even an array processor to accomplish these tasks on limited size arrays in a few seconds per image. It is not clear that the power spectrum could be used for more than defocus correction since the correction of astigmatism is a formidable problem of pattern recognition.

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Log-log scale roughness spectroscopy of surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100146965 ◽

1993 ◽

Vol 51 ◽

pp. 224-225

Author(s):

P. Fraundorf ◽

B. Armbruster

Keyword(s):

Power Spectrum ◽

Autocorrelation Function ◽

Power Spectra ◽

Scanning Force Microscopy ◽

Scanning Tunneling ◽

Tunneling Microscopy ◽

Force Microscopy ◽

Scanning Force ◽

Lateral Structure ◽

Scale Roughness

Optical interferometry, confocal light microscopy, stereopair scanning electron microscopy, scanning tunneling microscopy, and scanning force microscopy, can produce topographic images of surfaces on size scales reaching from centimeters to Angstroms. Second moment (height variance) statistics of surface topography can be very helpful in quantifying “visually suggested” differences from one surface to the next. The two most common methods for displaying this information are the Fourier power spectrum and its direct space transform, the autocorrelation function or interferogram. Unfortunately, for a surface exhibiting lateral structure over several orders of magnitude in size, both the power spectrum and the autocorrelation function will find most of the information they contain pressed into the plot’s origin. This suggests that we plot power in units of LOG(frequency)≡-LOG(period), but rather than add this logarithmic constraint as another element of abstraction to the analysis of power spectra, we further recommend a shift in paradigm.

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