Linearity of the pyramid wavefront sensor

The pyramid wavefront sensor is very similar to the Fourier knife-edge test, but employs dynamic modulation to quantify the phase derivative. For circular modulation, we compare approximate geometrical optics calculations, more exact diffraction calculations, and experimental results. We show that both the sinusoidal and the approximate linear relationship between wavefront derivative and wavefront sensor response can be derived rigorously from diffraction theory. We also show that geometrical, diffraction and experimental results are very similar, and conclude that the approximate geometrical predictions can be used in place of the more complex diffraction results.