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512 barrier systems ABSTRACT Microstructural images actual grain actual mean grain amplitude ASTM components corresponds directly components per area cycle tone pulse density of frequency density of length DETERMINATION OF GRAIN digital 512 point enhanced image Equation 18 fast Fourier transform Figure 1(a Figure 3(a Figure 5(b Fourier transform theory frequency components fundamental frequency grain boundary grain size distribution grain width grains having widths gray level line hardwired histogram image analyzer image contained image Figure 4(a length components corresponds length distribution function level line scan mean grain shape minicomputer negligible or incoherent noise number of components number of cycles percent uncertainty Performing Organization photomicrographs PULSE ENCODED IMAGES rde dr reciprocal variable represents the density shape and orientation shown in Figure subsequently Fourier transformed three cycle tone tone pulse encoded transformed to determine TRANSFORMS OF TONE two-dimensional Fourier transform value tone code video digitizer vidicon x-axis x-direction yield zero value tone