Figure 8-20 The interference filter transmits mainly those wavelengths for which the internally reflected waves are in
phase with one another. (Redrawn b y C. H. Wooley.)
Optical coherence tomography (OCT) uses Michaelson interferometry to image the retinal layers. The coherence of the light source is crucial; a light source with high temporal coherence (eg, laser) actually decreases the accuracy of OCT thickness measurements. However, a light source with too little coherence limits the thickness that can be measured. To measure the entire retina, OCT uses a superluminous diode, which operates in the near-infrared range and has a 50-nm bandwidth.
Diffraction
Some multifocal intraocular lenses use diffraction (and interference) to produce near and distance images simultaneously. Such lenses have at least one surface that is not smooth but that consists of circular steps that break wavefronts to produce diffraction. Such lenses rely for their effect on interference from the opposite side of each ring and, therefore, should be placed as well centered as possible with respect to the pupil. Consequently, eyes with irregular pupils may not be well suited for such lenses. Corneal astigmatism or IOL tilt also degrades the image quality of diffractive IOLs.
Imaging and the Point Spread Function
Two different but closely related approaches exist to understand the image formation process. (See Chapter 1 for discussions of image formation by lenses, mirrors, or pinholes.) The first approach is the basis for aberration theory, whereas the second is the basis for contrast sensitivity and the measurement of image quality. In the first approach, an object is regarded as a collection of point
sources, each of which radiates light in all directions. Some of the light traverses the lens and focuses at best to a small, irregularly shaped region, never to a perfect point (Fig 8-21). The light from nearby point sources partially overlaps and causes a loss of detail in the formed image. Although no lens focuses perfectly, some focus better than others and produce more detail in the resulting image.
Figure 8-21 Light from a single object point never focuses to a perfect point. Even at best focus, it is usually distributed
over a small, irregularly shaped region in the image. (Illustration developed b y Edmond H. Thall, MD, and Kevin Miller, MD, and rendered b y C. H. Wooley.)
The point spread function (PSF) describes how light from a single point source is distributed in an image and completely describes the imaging characteristics of an optical system. During the design stage of a lens, calculating the PSF precisely is a complex matter that must account for not only refraction and reflection but also diffraction and characteristics such as interference, polarization, light scattering, and dispersion. Even using a computer, calculating a PSF that accounts for all optical variables is difficult. The PSF of a lens can be measured after it is manufactured, but doing so is a time-consuming and costly task requiring specialized equipment and expertise.
Fortunately, most image characteristics, such as location, size, orientation, and brightness, can be calculated or measured without considering PSF. The field of geometric optics greatly simplifies calculations of image characteristics by ignoring most of light’s physical characteristics, especially diffraction. Using only the 3 laws of rectilinear propagation, refraction, and reflection, image characteristics can be determined with sufficient accuracy for most uses. Only when diffraction, interference, or some other physical property is a significant factor in image quality is it necessary to use calculations from physical optics.
The PSF is required only for the analysis of image quality, which in most cases is dominated by aberrations or diffraction. Sir George Airy calculated the PSF for an axial object point imaged by any aberration-free optical system with a circular aperture stop. Airy also assumed temporally coherent light, so the PSF contained interference rings. Airy found that the PSF consisted of a central bright spot (the Airy disc) surrounded by larger rings (Fig 8-22). Most of the energy is in the central disc, so the outer rings are usually ignored. The diameter of the Airy disc is determined according to the equation
where D is the exit pupil diameter and f is the focal length. For an eye with a 3-mm-diameter pupil, the PSF diameter is approximately 6 µm, encompassing the outer segments of roughly 7 photoreceptors.
Figure 8-22 The point spread function of a single monochromatic axial object point produced by an aberration-free optical
system with a circular aperture. (From Campb ell, CJ. Physiologic Optics. Hagerstown, MD: Harper & Row; 1974:20.)
As noted, the Airy disc diameter is the PSF produced solely by diffraction when no aberrations are present. Alternatively, the PSF can be calculated using only the 3 laws of geometric optics, entirely ignoring diffraction. As a rule, diffraction decreases as pupil size increases, but aberrations increase as pupil size increases.
If the geometric PSF value is much larger than the Airy disc diameter, then aberrations dominate and diffraction can be ignored, whereas if the geometric PSF is much smaller, then diffraction dominates and aberrations can be ignored. If values for the geometric PSF and the Airy disc diameter are about the same, then image quality is probably close to optimal for that optical system.