If we try to pass light through a very small hole, we will realize that it actually does not go in a straight line, but rather spreads out. This apparent “spreading out beyond the edges” of an aperture or “bending around the corners” of an obstruction, into a region where—using strictly geometric optics reasoning—we would not expect to see it, is referred to as diffraction. Diffraction may be thought of as light, when encountering an obstacle, scattering off in different directions at the edges. What really happens, of course, is light interacts with the electrons in the material, most noticeably with the electrons at the edges.
While a more detailed description of diffraction is beyond the scope of this text, we can appreciate that once light scatters off in different directions, it usually interferes with other parts of the diffracted light. Hence, in classical wave theory, the phenomenon of diffraction of light, as it passes beyond an obstacle of comparable size to its wavelength, is generally described as interference effects of the emerging light.
The consequence of these interference effects created by diffraction on apertures is that it sets a limit on the resolution that can be achieved in any optical instrument, which immediately brings us to applications and clinical relevance in ophthalmology.
Applications and clinical relevance
All apertures produce diffraction to some extent, even an opening as large as the pupil of an eye. Thus, we are constantly aware of its effects in ophthalmology.
With a circular aperture, such as the pupil, in the absence of aberrations, the image of a point source of light formed on the retina—the point spread function (PSF)—takes the form of alternating bright and dark rings surrounding a bright central spot, the Airy disc (Fig 2-11), rather than a point. This pattern is the consequence of diffraction and its associated interference effects. The latter are apparent by the concentric bright and dark rings that are analogous to the fringes observed in Young’s double-slit experiment (see Fig 2-6). Most of the energy is concentrated in the central disk, so the outer rings are usually ignored. The diameter of the Airy disc is given by the equation
where D is the diameter of the aperture (pupil) and f is the focal length—the distance from the aperture to the diffracted image. This equation illustrates that longer wavelengths (eg, red light) have a larger Airy disc than shorter wavelengths (eg, blue light) and therefore diffract more. Similarly, diffraction increases as the pupil size decreases.
Under photopic lighting conditions, the pupil of the human eye is around 2–3 mm in diameter. With pupil sizes less than that (for a person with emmetropia), diffraction effects become visually significant, limiting visual acuity. For an eye with a 3-mm-diameter pupil (and f-number, that is f/D, of about 5), for example, and a 555-nm light source, corresponding to the maximum photopic sensitivity of the retina (see the section Measures of Light), the Airy disc diameter is approximately 7.4 µm, encompassing the outer segments of roughly 11 photoreceptors. The smallest resolvable detail is approximately equal to the Airy disc radius. An Airy disc of 3.7 μm radius corresponds roughly to 20/15 visual acuity.
Figure 2-11 Diffraction pattern produced by a small circular aperture. The central bright spot is called an Airy disc.
(From Campbell, CJ. Physiologic Optics. Hagerstown, MD: Harper & Row; 1974:20.)
Thus, in theory, the larger the pupil size, the smaller the Airy disc and therefore better visual acuity or higher resolution of the image on the retina. However, in practice (as discussed in Chapter 8), higher-order aberrations occur at larger pupil sizes. While there are ways to correct for wavefront aberrations (adaptive optics, discussed in Chapter 8), we cannot suppress diffraction. It sets an absolute limit on the best resolution obtainable with any optical system, including the eye, and is represented by the Airy disc pattern (see Fig 2-11).
Diffraction can also be used to an advantage in ophthalmic optics, in the creation of bifocal or multifocal lenses. For example, etching a specially designed pattern of closely spaced circular steps on one of the surfaces of a contact or intraocular lens can cause light to diffract, such that the resulting interference effects of the diffracted light create a second near focal point for the lens, with the overall curvature of the lens simultaneously providing distance focus.
Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.