its aperture stop and opens in dim conditions to allow broader pencils of light to enter.
The field of view of a multi-element optical system is the visible extent of the image plane. For example, a typical pair of binoculars might have a field of view of 7 degrees—objects outside that field cannot be seen without turning the binoculars toward them. When a 2× condensing lens is used with the indirect ophthalmoscope, the field of view is 2 times larger in degrees than with a 4× condensing lens of the same diameter. Twice the diameter of the field viewed gives 4 times as much area.
When you look at someone’s pupil through the cornea and aqueous, the pupil appears to be larger and closer than it truly is. What you are seeing is the entrance pupil of the eye’s optical system—the image of the eye’s aperture stop, the pupil, viewed through the optical elements that precede it in the system. Rays that do not pass through the eye’s entrance pupil cannot reach the retina because they are unable to pass the aperture stop, which is the pupil of the eye.
For an observer to see the entire field of view of an optical instrument, his or her entrance pupil needs to be located at the instrument’s exit pupil, which is the image of its aperture stop formed by the optical elements following it in the system. The distance from the last surface of the eyepiece to that exit pupil is called the eye relief of the instrument.
In the preceding section, we discussed the adjustment of working distance to form a loupe. Suppose an object is well focused on the loupe’s image plane; how much closer or farther away can we move the object without noticeable blurring of the image? The distance the object can be moved is the system’s depth of field. Depth of focus, on the other hand, is the amount of leeway on the image side of the system; for example, it refers to how near or far you can move a screen relative to a focused projector before the image becomes noticeably out of focus.
Measurements of Performance of Optical Systems
The f-stop of a lens, familiar to photographers, and a related concept, the numerical aperture, are measures of light gathering. Light gathering is important not only in generating a bright image of a dim source; it is also related to the resolving power of an instrument—how close together 2 points can be on an object before they become indistinguishable in the image. If a higher-power instrument does not take in a wide-angled pencil of light from each of the 2 nearby points, no matter how carefully the instrument is constructed, the diffraction patterns coming from the 2 points will overlap too much to be distinguished from each other. For example, the oil immersion objective of a microscope has a higher numerical aperture than a dry objective, which means that it can gather a wider angle of light from each point source and therefore have the potential for better resolution.
Light beginning at a point source and passing through a focused optical system does not all focus to the same image point because of aberrations and diffraction. The spread-out luminance that is detected is called the point spread function. The modulation transfer function (MTF) of an optical system is a measure of its ability to preserve an object’s contrast, such as that of a sinusoidal pattern of light and dark, in the image that comes out of the system. This ability varies with the spatial frequency of the pattern being imaged, and the MTF helps a designer choose the best optical elements for the purpose at hand.
Optical Instruments and Techniques Used in Ophthalmic Practice
Direct Ophthalmoscope
Suppose you want to look at my retina and that we both have eyes that are emmetropic and not accommodating. A pencil of rays coming from a point on my retina leaves my eye with zero vergence, and the pencil continues to have no vergence until it reaches your eye, which focuses it exactly on your retina. When you look through the peephole of a direct ophthalmoscope with no lenses in place, just past the edge of a mirror that reflects light into my eye, almost coaxial to your view, you will see an upright, virtual, magnified image of a small portion of my retina; our retinas are on conjugate planes. The optics of the eye are approximately +60 D, so the magnification is 60/4, or 15×, as we have defined magnification for a simple magnifier. In case either of us has an uncorrected spherical refractive error, a wheel of spherical lenses is available to dial into the path. If the subject eye is myopic, the extra plus power of the eye’s optics and the minus power dialed into place in the ophthalmoscope together form a Galilean telescope, increasing magnification and decreasing the field of view. Similarly, the retina of a hyperopic eye will be magnified less than 15× because of the reverse Galilean telescope created by the optics of the eye and the lens of the direct ophthalmoscope. A retinal lesion elevated 1 mm will be approximately 3 D out of focus when viewed with the direct ophthalmoscope (Fig 7-6).
Figure 7-6 Viewing system of a direct ophthalmoscope. A, A bundle of light rays emerges from the emmetropic eye with zero vergence. B, A bundle of light rays emerges converging from the myopic eye with positive vergence; the corrective lens is minus. C, A bundle of rays with negative vergence diverges coming out of the hyperopic eye; the corrective lens is
plus. (Developed b y Neal H. Ateb ara, MD. Redrawn b y C. H. Wooley.)
Indirect Ophthalmoscope
In an indirect ophthalmoscope, mirrors direct a bright light toward the subject’s retina through, for instance, a 20 D lens and the subject’s eye. The lens has an aspheric design on one side and antireflective coatings to minimize aberrations and glare. Assuming that the subject eye is emmetropic, a pencil of light coming from an illuminated point on the retina leaves the eye with zero vergence (Fig 7-7A). The pencil of light is gathered and refracted by the large +20 D “condensing” lens to focus to a point one-twentieth of a meter (5 cm) closer to the observer, who therefore sees an optically real, inverted aerial image of the retina that appears to be 5 cm closer to her eye than the 20 D lens in her hand (Fig 7-7B). If the aerial image is 50 cm from her eye, she will have to accommodate 2 D to see it, so a 2 D lens is added on the front of the ophthalmoscope (Fig 7-8).
Figure 7-7 Fundus image formation. A, A retinal image is formed at optical infinity. B, A condensing lens focuses a bundle of parallel rays to a place closer to the viewer than his or her hand. (Developed b y Neal H. Ateb ara, MD. Redrawn b y C. H. Wooley.)
Figure 7-8 The “aerial” image. The light rays focus and diverge, and they are brought to a new focus on the observer’s retina by a condensing lens and the optics of the observer’s eye. (Developed b y Neal H. Ateb ara, MD. Redrawn b y C. H. Wooley.)
Mirrors are used in the binocular instrument to bring an image to each of the observer’s eyes, adjusting as needed for the observer’s interpupillary distance. To avoid glare, it is important that the observer’s pupils be conjugate with the pupil of the patient’s eye, so that the illuminating and 2 viewing paths pass through the pupils of both people (Figs 7-9, 7-10). If the patient’s pupil is small, the ingoing path and the 2 outgoing paths can be brought closer by varying the positions of mirrors (Fig 7-11).
Figure 7-9 Conjugacy of pupils. A, In indirect ophthalmoscopy, the observer’s pupil (O) and patient’s pupil (P) are
conjugate to avoid “wasting” light. B, If the condensing lens is too close to the patient’s eye, the peripheral retina will not be illuminated. C, If the condensing lens is too far from the patient’s eye, light from the patient’s peripheral retina will not reach
the observer’s eye. (Developed b y Neal H. Ateb ara, MD. Redrawn b y C. H. Wooley.)
Figure 7-10 Indirect ophthalmoscope: illumination. (Developed b y Neal H. Ateb ara, MD. Redrawn b y C. H. Wooley.)
Figure 7-11 Indirect ophthalmoscope: mirrors used for binocular viewing. A, Binocular observation. B, To achieve binocularity when viewing through a small pupil, one can bring the light paths closer together by moving the triangular mirror closer to the observer. C, Alternatively, when viewing through a patient’s small pupil, one can bring the light paths closer together by moving the eyepieces as far apart as the observer’s interpupillary distance allows, or by moving the observer’s head farther from the patient. Orange circles represent viewing paths, and yellow circles represent illumination