Centroid distortion of a wavefront with varying amplitude due to asymmetry in lens diffraction

It is often of interest to measure the centroid of a light intensity pattern in order to deduce physical properties. Examples are the Hartmann-Shack sensor, which measures the wavefront slopes, and position sensors. We investigate whether amplitude changes of the incoming electromagnetic field can affect the location of the centroid, and we show that the effect is strongly dependent on the relative size of the diffraction pattern in relation to the lenslet size. We show that if the phase varies slowly in space-and the focal spot size relative to the centroid integration area approaches zero-this variation does not affect the centroid. This is a consequence of symmetry properties of the Fresnel operator. We then show that when the focal width is not infinitely small, changes in the field amplitude can exacerbate distortion of the centroid results.