Quadric wavefront aberrations in phase-type images of binary amplitude gratings with small opening ratios

We discuss the quadric wavefront aberration of a fractional Talbot imaging ray which distorts the phase-type image of a binary amplitude grating with a small value of the opening ratio. When the opening ratio is equal to 1/2 or 1/3, the imaging rays are shown to have no quadric wavefront aberrations. For the opening ratios of 1/4 and 1/5, two different types of quadric wavefront aberrations are responsible for the three-level phase images. If the opening ratio gets to 1/6, we find that three different types of quadric wavefront aberrations distort the fractional Talbot image. The quadric wavefront aberration formulated here may be used in evaluating the phase-type image of a binary amplitude grating with an arbitrary value of the opening ratio.