On Tue, Jun 30, 2009 at 06:02:34PM -0700, Scott Webster wrote: > I'm wondering about the units of the "y-axis" of the PSDF tool. In > gwyddion they are length^3. I have thought about this, and seem to > think that it should be length^4. Is this just some convention that > gwyddion has chosen? Is there a rationale or does anyone know of a > reference that explains it? I have a paper here that also seems to > suggest length^4 (DOI:10.1117/12.823844).
I cannot access the paper (well, no surprise at my university), however, the difference might be as follows. PSDF in Gwyddion is based on the concept of an infinite (rough) surface. The measured data is a finite-resolution measurement on a finite area which is assumed to have the same statistical properties as the entire surface. The total energy of an infinite surface is infinite so, a meaningful quantity is the energy per unit interval. The PSDF displayed in Gwyddion can be then imagined as this function. It is sampled in certain points given by the discrete nature of the whole business, nevertheless, the values should be approximations of W₁(k) that results from contignuous FT of the entire infinite surface. This has the following nice consequences: - PSDF of a part of the scan is identical to PSDF of the entire scan (as long as they are still statistically equivalent). - PSDF of a resampled scan is identical to PSDF of the original scan (sans the lost high frequency information, of course). Regards, Yeti ------------------------------------------------------------------------------ Enter the BlackBerry Developer Challenge This is your chance to win up to $100,000 in prizes! For a limited time, vendors submitting new applications to BlackBerry App World(TM) will have the opportunity to enter the BlackBerry Developer Challenge. See full prize details at: http://p.sf.net/sfu/blackberry _______________________________________________ Gwyddion-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/gwyddion-users
