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Matlab function to compute the two-dimensional spatial Fast Fourier Transform (FFT) of an input spatially sampled array along x and y (input variables "array_x" and "array_y") given a wavelength ("lambda"), Fourier space sampling "U" and "V", and signal magnitude at each spatial location ("temp"). |
https://data.nist.gov/od/ds/mds2-2595/compute_FFT.m |
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Sparsely sampled lattices on a regular grid introduce grating lobes in the beampattern as demonstrated by this simulated dataset of the beam pattern observed in Fourier space (u=sin(theta)cos(phi), v=sin(theta)sin(phi), where theta is the elevation angle and phi is the azimuth angle) when a regularly sampled sparse array is used to acquire the signal. |
https://data.nist.gov/od/ds/mds2-2595/Fig20_GratingLobesDueToSparseSamplingGrid.csv |
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"Readme" file provided additional information relating to "Grating Lobes and Spatial Aliasing in Sparse Array Beampatterns" simulation dataset. |
https://data.nist.gov/od/ds/mds2-2595/readme.txt |
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Matlab script will generate the exact data provided in "Fig20_GratingLobesDueToSparseSamplingGrid.csv" and will plot the output. This script requires "compute_FFT.m" to be located in the same workspace or directory. To generate the output data given in "Fig22_OptimizedSparseArrayBeamPattern.csv", one can replace "sparse_array_x" (line 20) and "sparse_array_y" (line 21) with the first two columns of "Fig21_SparseArrayBeforeAndAfterOptimization.csv" ("Xposition_m" and "Yposition_m_After"). |
https://data.nist.gov/od/ds/mds2-2595/Code_to_recreate_Figure_20.m |
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A simple approach for mitigating grating lobes in a sparse lattice is to perturb the regularity of the grid spacing by applying a random offset to each spatial sample. These data compare the spatial locations of a regularly sampled sparse array labeled as "Before" to the randomly perturbed sparse array sample locations labeled as "After". |
https://data.nist.gov/od/ds/mds2-2595/Fig21_SparseArrayBeforeAndAfterOptimization.csv |
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Periodicity in the beam pattern, here calculated and reported in Fourier space (u=sin(theta)cos(phi), v=sin(theta)sin(phi), where theta is the elevation angle and phi is the azimuth angle), is eliminated by the use of the randomly perturbed spatial sample locations of the sparse array. These simulated data show the outcome of using the sparse array labeled "After" in dataset "Fig21_SparseArrayBeforeAndAfterOptimization.csv" and provides a comparison to this randomized perturbation to the regular sampling output given in "Fig20_GratingLobesDueToSparseSamplingGrid.csv". |
https://data.nist.gov/od/ds/mds2-2595/Fig22_OptimizedSparseArrayBeamPattern.csv |