Calculation of the geometrical point-spread function from wavefront aberrations

This report uses the principles of geometrical optics to compute the optical point-spread function (PSF) from the wavefront error function.

Step 1 uses Prentice's rule to determine the spatial form of the PSF established by tracing a field of rays from the eye's exit pupil to the retina. Ray vergence is related to the slope of the wavefront error function, which enables the mapping of light rays to produce a retinal 'spot diagram'. Step 2 completes the PSF by assigning an irradiance value to each ray in the spot diagram.

Spot irradiance is inversely proportional to the Gaussian curvature (i.e. the product of principal curvatures) of each local region of wavefront error surface centered on the corresponding ray. The Gaussian curvature, in turn, may be computed as the determinant of the vergence error matrix associated with each point on the wavefront error surface. Elements of the vergence error matrix consist of sums and differences of the local power vector components M, J₀ and J₄₅ . This method is shown to be equivalent to published derivations of the geometric PSF using the Jacobian of the ray mapping function and equivalent also to the Hessian of the wavefront error function. Examples are presented for the familiar cases of spherical and astigmatic blur as well as for higher order aberrations and the formation of caustics in the retinal image.