Axial (Longitudinal) Magnification

As we have seen, a thin lens in air produces a transverse magnification described by the simple equation MT = ν/u. If the source “object” is in fact an assemblage of objects, or an extended object with a palpable axial dimension (measured along the optic axis), the image will also exhibit an axial extent, or apparent thickness. We can show (for example, by differentiating the vergence equation) that the apparent thickness of the image—the axial, or longitudinal, magnification for a refracting system in air—is given by

M L = (MT)²

Figure 1-18 illustrates this relationship.

This effect leads to a substantial distortion of the images seen by direct or indirect ophthalmoscopy. Although it is difficult to appreciate image depth with the monocular view through the direct ophthalmoscope, the aerial image seen with the indirect ophthalmoscope is generally seen stereoscopically. Depending on the power of the condensing lens used, the distortion factor may vary as much as fourfold in changing from a 14-D lens to a 30-D lens. The overall stereoscopic effect is reduced by the small interpupillary distance of the periscopic viewing system but, nevertheless, the perceived shape of fundus features, such as tumors or optic disc excavation, is typically somewhat exaggerated.

Figure 1-18 Ray tracing for a convex lens in air. The source object is the red circle; its image is the ellipse. Notice the considerable distortion caused by the disparity between transverse and axial magnifications.

(Illustration developed by Scott E. Brodie, MD, PhD.)

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.