The Sine Grating

Topics Covered:

  • On the nature of Edges and Boundaries
  • The Sine Grating

The eye altering, alters all – William Blake

There are no sharp edges in the absolute sense. If you zoom in close, even the sharpest edge will become smooth at some point. If you zoom out far enough, even the smoothest of edges will appear sharp. Therefore, it is clear that the mathematical representation of edges is better served by a sine wave, rather than a square wave:

Edges behave like sine waves.

This is why sine waves are used almost exclusively in the measurement of optical devices, and the pattern that represents a sine wave in visual terms is a Sine Grating.

Sine Grating

What we expect:

What we get:

The sine wave grating has two critical properties. One is contrast, the difference between the darkest point (the line), and the brightest point (the white space between the lines). The other is spatial frequency, which we’ll deal with next.

Takeaways:

  • Edges behave like sine waves.
  • A Sine grating is a chart that uses sine patterns instead of square, lines or other patterns for a more accurate mathematical representation of reality.

Links for further study:

Next: Spatial Frequency
Previous: The First Phone Call