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This response time determines, together with the scan speed, the maximum spatial frequency up to which the topographic data is measured faithfully.
The maximum spatial frequency is (q_{max}=N_{x}/{L}=1/Delta x) where (N_{x}) is the number of grid points, Δx is the spatial resolution of the 1-D rod and L is its length, setting the spacing in the q-domain as (Delta q = {1}/{L}).
The maximum spatial frequency sampled, the Nyquist frequency, is f x N ≡ 1/(2Δ x).
As schematically shown in Figure 1b, the limit is on the maximum spatial frequency collected in the diffraction pattern which in principle determines the reconstruction resolution.
Apart from AR, other quantitative markers (also computed from FT images) such as entropy or disorganization parameter [ 12, 21] and the maximum spatial frequency [ 14] have been reported to quantify lamellar organization.
Random undersampling according to CS then requires that a subset of these lines be selected for sampling, with their spacing dictating the field of view of the image and the maximum spatial frequency encoded dictating the spatial resolution.
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When the maximum viewing spatial frequency f imax is higher than f nyq, the higher frequency component over the Nyquist frequency should be removed from the elemental image, and the viewing resolution of an integral image is determined by f nyq.
Driven by the limited dynamic range of the imaging sensor, hereby 15% was selected to be the threshold MTF value and based on Fig. 9 60lp/mm was determined to be the maximum resolvable spatial frequency in the image space.
If the length of road profile is L and the sampling interval is B, the maximum theoretical sampling spatial frequency is nmax = 1/B and the maximum effective sampling spatial frequency is neff = nmax/2 and, within the frequency domain, discretised spatial frequency values ni are equally spaced with an interval of Δn = 1/L.
For Cartesian acquisitions, this could be as simple as increasing the maximum phase-encoded spatial frequency used, leading to a higher effective resolution in the phase encode direction(s).
Figure 6 shows the time series of GPS-derived PWV during the whole campaign (top and middle panels); all the five stations showed consistent time variations over long timespans (i.e., they showed consistent low-frequency signals) with maximum spatial variations (i.e., inter-station PWV differences) ranging from 5 to 10 mm.
Related(20)
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