ophthalmoscope is focused to compensate for the refractive error of the examiner and that of the patient, the 2 retinas are conjugate (Fig 1-8). An image of the patient’s retina is present on the examiner’s retina and vice versa. However, the patient does not “see” the examiner’s retina, because it is not illuminated by the ophthalmoscope light and because this light is so bright.
Figure 1-8 Conjugacy in direct ophthalmoscopy. (Illustration developed b y Kevin M. Miller, MD, and rendered b y C. H. Wooley.)
Object Characteristics
Objects may be characterized by their location with respect to the imaging system and by whether they are luminous. If an object point such as a candle flame produces its own light, it is called luminous. If it does not produce its own light, it can be imaged only if it is reflective and illuminated.
Image Characteristics
Images are described by characteristics such as magnification, location, quality, and brightness. Some of these features will be discussed briefly.
Magnification
Three types of magnification are considered in geometric optics: transverse, angular, and axial. The ratio of the height of an image to the height of the corresponding object is transverse magnification (Fig 1-9):
Figure 1-9 Object height (O) and image height (I) may be measured from any pair of off-axis conjugate points. (Illustration
developed b y Edmond H. Thall, MD, and Kevin M. Miller, MD, and rendered b y C. H. Wooley.)
To calculate transverse magnification, we compare the height of an object (ie, the distance an object extends above or below the optical axis) to that of its conjugate image (ie, the distance its image extends above or below the axis). Object and image heights are measured perpendicularly to the optical axis and, by convention, are considered positive when the object or image extends above the optical axis and negative when below the axis.
An image is a scale model of the object. If the object or image is upright (extending above the optical axis), a positive (+) sign is used; an object or image that is inverted (extending below the optical axis) is indicated by a minus (–) sign. The transverse magnification represents the size of the image in relation to that of the object. For instance, in Figure 1-9 the object height is +4 cm and the image height –2 cm; thus, the transverse magnification is –0.5, meaning that the image is inverted and half as large as the object. A magnification of +3 means the image is upright and 3 times larger than the object.
Transverse magnification can be confused with linear magnification. Linear magnification refers to the magnification of the area of an image relative to that of an object located perpendicular to the optical axis. For example, a 4 cm × 6 cm object imaged with a magnification of 2 produces an 8 cm × 12 cm image. Both width and length double, yielding a fourfold increase in image area. The reader should also not confuse transverse magnification with axial magnification, which is measured along the optical axis and is discussed at the end of this section. Generally, the multiplication sign, ×, is used to indicate magnification. The transverse magnification of microscope objectives, for example,
is sometimes expressed by this convention.
The word power is sometimes used synonymously with transverse magnification. This is unfortunate because power has several different meanings, and confusion often arises. Other uses of the word include the terms refracting power, resolving power, prism power, and light-gathering power.
Most optical systems have a pair of nodal points (Fig 1-10). Occasionally, the nodal points overlap, appearing as a single point, but technically they remain a pair of overlapping nodal points. The nodal points are always on the optical axis and have an important property. From any object point, a unique ray passes through the anterior nodal point. This ray emerges from the optical system along the line connecting the posterior nodal point to the conjugate image point. These rays form 2 angles with the optical axis. The essential property of the nodal points is that these 2 angles are equal for any selected object point. Because of this feature, nodal points are useful for establishing a relationship among transverse magnification, object distance, and image distance. (See Appendix 1.1, Quick Review of Angles, Trigonometry, and the Pythagorean Theorem, at the end of the chapter.)
Figure 1-10 The anterior and posterior nodal points (N and N′, respectively) of an optical system. The angle subtended by
the object (α) is equal to the angle subtended by the image. (Illustration developed b y Kevin M. Miller, MD, and rendered b y C. H. Wooley.)
Regardless of the location of an object, the object and the image subtend equal angles with respect to their nodal points.
Therefore,
Angular magnification is the ratio of the angular height subtended by an object viewed by the eye
through a magnifying lens to the angular height subtended by the same object viewed without the magnifying lens. By convention, the standard viewing distance for this comparison is 25 cm. For small angles, the angular magnification (M) provided by a simple magnifier (P) is independent of the actual object size:
More will be said about simple magnifiers later.
Axial magnification, also known as longitudinal magnification, is measured along the optical axis. For small distances around the image plane, axial magnification is the square of the transverse magnification.
Axial Magnification = (Transverse Magnification)2
For example, if an object 4 cm in height (perpendicular to the optical axis) and 0.5 cm in length along the optical axis is imaged with a transverse magnification of 2×, the axial magnification is 4×. This produces an 8 cm × 2 cm image (4 × 2 = 8 cm height perpendicular to the optical axis and 0.5 × 4 = 2 cm length along the optical axis). This concept will be discussed in greater detail in Chapter 7.
Image Location
Another important characteristic of an image is its location. Refractive errors result when images formed by the eye’s optical system are in front of or behind the retina. Image location is specified as the distance (measured along the optical axis) between a reference point associated with the optical system and the image.
The reference point depends on the situation. It is often convenient to use the back surface of a lens as a reference point. The back lens surface is usually not at the same location as the posterior nodal point, but it is easier to locate.
Frequently, image distance is measured from the posterior principal point to the image. The principal points (discussed later in the chapter), like the nodal points, are a pair of useful reference points on the optical axis. The nodal points and principal points often overlap.
Whatever reference point is used to measure image distance, the sign convention is always the same:
By convention, when the image is to the right of the reference point, image distance is positive; when the image is to the left of the reference point, the distance is negative.
Depth of Focus
If we perform a basic imaging demonstration with a lens and focus an image of a light source on a paper, we notice that if the paper is moved forward or backward within a range of a few millimeters, the image remains relatively focused. With the paper positioned outside this region, the image appears blurred. The size of this region represents the depth of focus, which may be small or large depending on several factors. (See Clinical Example 1-2.) In the past, depth of focus was of concern