Basics of Gratings (sinewave and square-wave)

A grating is a repeating sequence of light and dark bars. One adjacent pair of a light and a dark bar makes up one cycle. These cycles repeat over and over in a grating. Typically, we think of these gratings as having sharp edges like the bars shown in Figure 1 below.
Figure 1. A grating composed of black and white bars that is typically called a square-wave grating.

These gratings have become known as square-wave gratings because they have characteristics like a square such as sharp edges. This square-like nature of the light levels (or luminance), as it falls across different positions along the surface of an object can be seen in Figure 2. Clicking on Figure 2 will bring down the square-wave grating so that you can more easily compare the actual grating to the graph of the grating.
Figure 2. A graph of the luminance of a square-wave as a function of position for one cycle.

However, there is no reason that light has to vary in a square-wave fashion. What if the light varied in a sinewave fashion? Figure 3 shows one cycle of a sinewave. Clicking on Figure 3 will bring down a sinewave grating with four cycles just as Figure 1 showed a square-wave grating with four cycles.
Figure 3. A graph of the luminance of a sinewave as a function of position for one cycle.

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