E3 Diffraction Optics and Resolution Limit

Topic

Although the optical ray model describes light traveling in a straight line and refracting at each interface, light also behaves as a wave; this wave nature becomes evident when light passes through a finite aperture such as the pupil—the circular opening through which light enters the eye. Upon passing through the pupil, light does not converge to a single, infinitesimally small point on the retina—not even if the cornea and lens refracted the light without any aberration. Because the pupil is an aperture of finite size, it causes the light to spread slightly as it passes through—a phenomenon known as diffraction. In this instance, it specifically corresponds to the Fraunhofer diffraction regime, observed when the point of observation (the retina, in this case) is sufficiently far from the pupil that the incoming rays can be treated as parallel to one another.

Light emanating from a single point on the object and passing through the pupil does not form a single point on the retina due to diffraction; instead, it creates a diffraction pattern consisting of a central spot of light surrounded by much fainter rings. The smaller the pupil through which the light passes, the wider the diffraction pattern on the retina becomes, because a smaller aperture causes greater spreading of the light; conversely, the larger the pupil, the narrower the diffraction pattern, because a larger aperture causes less spreading of that same light.

When light from two distinct points on the object passes through the same pupil, each point forms its own diffraction pattern on the retina; if the two object points are sufficiently far apart, their respective diffraction patterns will also be sufficiently separated on the retina to be distinguished as two distinct points. The Rayleigh criterion establishes the exact limit of this separation: according to the criterion, two diffraction patterns remain distinguishable as separate points when the center of the central spot of one pattern falls exactly upon the first faint ring surrounding the central spot of the other; if the two object points are closer together than this, their diffraction patterns overlap excessively and can no longer be distinguished as separate points, appearing instead as a single point.

The minimum angular separation between two object points that still satisfies the Rayleigh criterion defines the eye's theoretical resolution limit—the smallest minimum angle of resolution the eye can achieve, determined solely by diffraction at the pupil rather than by any other ocular imperfection. This theoretical resolution limit depends on pupil size in the same way the diffraction pattern itself does: the larger the pupil, the narrower the diffraction pattern for each point, and the smaller—that is, the better—the eye's theoretical resolution limit becomes.

This theoretical resolution limit imposed by diffraction at the pupil serves as the starting point for calculating the maximum theoretical visual acuity achievable by a perfectly focused, aberration-free eye—a "best-case scenario" against which the actual visual acuity measured by an eye chart is compared. Similarly, diffraction at the pupil limits the optical transfer function of the entire eye—even in the absence of other imperfections. Within this context, the modulation transfer function—which describes image degradation caused by cataracts—represents only the component measuring the contrast retained in specific details; even a perfect eye cannot achieve a perfect modulation transfer function for all fine details, because diffraction at the pupil imposes a physical limit before any other ocular imperfections even come into play.

ID:4311