Fourier analysis

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Description

What follows is a description of my analysis. First, the FFT that I use is described on the attached pages. Note that the scaling factor for the forward transform is 1/N. I compute the following rms values: rms(original data) = 64.9463 nm; rms(data*hanning) = 55.7723 nm (before renormalization). The use of the hanning filter is accompanied by a renormalization to insure that the rms value is maintained. I also fit to the curvature of the scan. The data corrected for focus gives the following rms values: rms(corrected data) = 56.8835 nm; rms(corrected data*hanning) = 53.2179 nm (before renormalization). The PSD ... continued below

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15 p.

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Lawson, J. March 3, 1997.

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Description

What follows is a description of my analysis. First, the FFT that I use is described on the attached pages. Note that the scaling factor for the forward transform is 1/N. I compute the following rms values: rms(original data) = 64.9463 nm; rms(data*hanning) = 55.7723 nm (before renormalization). The use of the hanning filter is accompanied by a renormalization to insure that the rms value is maintained. I also fit to the curvature of the scan. The data corrected for focus gives the following rms values: rms(corrected data) = 56.8835 nm; rms(corrected data*hanning) = 53.2179 nm (before renormalization). The PSD is shown for various data. The PSD is calculated as: PSD = | FFT(y) | {sup 2} * xl where xl is the length of the x axis, 45.9952. I did find an error in the plot that you were sent. If kx is the frequency axis, i.e., values from (0,Nyquist), then kx(l,Nyquist) is plotted versus PSD(0,Nyquist). This error is corrected in the attached plots. The plot you have appears to be the PSD of the original data with no hanning applied. The removal of the quadratic term appear to have a negligible effect on the PSD. It changes only the first couple of terms (which lie outside of the data valid range). The removal of the center feature has a much stronger effect.

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15 p.

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OSTI as DE97052995

Medium: P; Size: 15 p.

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  • Other Information: PBD: 3 Mar 1997

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  • Other: DE97052995
  • Report No.: UCRL-ID--126849
  • Grant Number: W-7405-ENG-48
  • DOI: 10.2172/522513 | External Link
  • Office of Scientific & Technical Information Report Number: 522513
  • Archival Resource Key: ark:/67531/metadc697073

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  • March 3, 1997

Added to The UNT Digital Library

  • Aug. 14, 2015, 8:43 a.m.

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  • April 7, 2017, 2:50 p.m.

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Lawson, J. Fourier analysis, report, March 3, 1997; California. (digital.library.unt.edu/ark:/67531/metadc697073/: accessed October 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.