To summarize this ray-optics description,

the purpose of the Scheiner-Hartmann-Shack aberrometer is to measure the ray aberration of the eye at multiple pupil locations. This is accomplished with a modified, objective form of the classic Scheiner's Disk in which there are now multiple apertures, as in the Hartmann screen, and each aperture consists of the face of a tiny lenslet in an array of such lenslets, in the manner described by Shack and Platt.