The horizontal derivative is computed for the image in Figure 2.6.5A by application of a simple one-dimensional, "clipped derivative" filter:

value = bin[x +1, y] - bin [x -1, y] % value if value > 0

where b[x,y] is the brightness of the image at coordinate position [x,y], "in" refers to the input, or starting image data and "out" is the output data. This leads to a brightness representation for one line in Figure 2.6.5A as shown in Figure 2.6.6.

The three maxima of the clipped derivative occur at the horizontal positions x = 23, 115, and 211. The distance from the first maximum to the last is known from the stage micrometer specification to be 2 x 10 |m = 20 |m. In pixels this is 211 - 23 = 188 pixels. The sampling frequency in the horizontal direction is 188 pixels/20 |m = 9.4 pixels/|m. The sampling density in the horizontal direction, Ax, is 106 nm/pixel.

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