Transport Equation for Calculating Power Spectra of Schroedinger Waves: Application to Exchange-Narrowing and Environmental Isomers

1995 ◽  
Vol 99 (16) ◽  
pp. 6199-6207 ◽  
Author(s):  
F. F. Knudsen ◽  
K. Razi Naqvi
Keyword(s):  
Transport Equation ◽  
Power Spectra ◽  
Exchange Narrowing

Image formation analysis of thick biological specimens using three-dimensional power-spectra of through focus series

1994 ◽  
Vol 52 ◽  
pp. 124-125
Author(s):  
Karen F. Han
Keyword(s):  
Inelastic Scattering ◽  
Imaging Techniques ◽  
Mass Density ◽  
Relative Proportion ◽  
Three Dimensional ◽  
Power Spectra ◽  
Image Formation ◽  
Energy Filtering ◽  
Ewald Sphere ◽  
Nonlinear Imaging

The primary focus in our laboratory is the study of higher order chromatin structure using three dimensional electron microscope tomography. Three dimensional tomography involves the deconstruction of an object by combining multiple projection views of the object at different tilt angles, image intensities are not always accurate representations of the projected object mass density, due to the effects of electron-specimen interactions and microscope lens aberrations. Therefore, an understanding of the mechanism of image formation is important for interpreting the images. The image formation for thick biological specimens has been analyzed by using both energy filtering and Ewald sphere constructions. Surprisingly, there is a significant amount of coherent transfer for our thick specimens. The relative amount of coherent transfer is correlated with the relative proportion of elastically scattered electrons using electron energy loss spectoscopy and imaging techniques.Electron-specimen interactions include single and multiple, elastic and inelastic scattering. Multiple and inelastic scattering events give rise to nonlinear imaging effects which complicates the interpretation of collected images.

Log-log scale roughness spectroscopy of surfaces

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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