Properties of Light

emerging from the instrument, instead of being parallel, appears to diverge from a point 40 to 80 inches in front of the eyelens. A telescope so focused is more readily adaptable to the eye of the average observer than one focused so that the rays of light are parallel. A fixed-focus instrument is much simplified and can be made entirely waterproof. However, if the power of the telescope is greater than 3.5 or 4, the accommodation of the average eye is not sufficient to permit its use.

Section VII

ABERRATIONS AND OTHER OPTICAL DEFECTS

39. GENERAL.

a. An aberration is a lens or prism imperfection resulting in an image that is not a true reproduction of the object.

b. In designing an instrument, correction is usually made for optical defects with special attention being given to the use to which the instrument is to be put. Correction is achieved by using lenses or prisms made of two or more kinds of glass (called compound lenses or compound prisms), by eliminating rays which would be refracted through the outer edges of lenses (called marginal rays), and by equipping the instrument with a suitable eyepiece.

c.

There are six general types of aberrations-spherical and chromatic aberration, astigmatism, coma, curvature of field, and distortion. Other factors which may affect the operation of the optical system of an instrument are resolving power, Newton's rings, light loss, and parallax.

40. SPHERICAL ABERRATION.

a.

Light rays refracted through a spherical lens near its center and those refracted through the outer portion or margin do not intersect the axis at a single point. The outer rays of a convergent lens intersect the axis closer to the lens than the more central ones (fig. 53), and the opposite is true of a divergent lens (fig. 54). The result is a blurred image. This fault is common to all single spherical lenses and is termed spherical aberration.

b. The thickness of a lens and its focal length influence the amount of spherical aberration. Spherical aberration is least in thin lenses of long focal length.

C. If the lens were ground with constantly flattening curves to the edge (parabolic), instead of being ground with each refracting surface as a true portion of a sphere, the rays would be caused to cross the axis at a single point and a sharp image would result. Such lenses, however, would be too difficult and costly to manufacture. Instead, two other methods are utilized either singly or together, which satisfactorily eliminate spherical aberration.

d. Field Stop or Diaphragm. Spherical aberration can be reduced by using a field stop or diaphragm. The central portion of a lens is most free of spherical aberration. Tests of a lens will show how much of the area around the axis may be safely used to form a sharp image. This area is called the least circle of aberrations. The usual practice is to mask out all rays passing through the lens beyond this circle (fig. 55). The mask used for this purpose is called a field stop. It is a flat ring or diaphragm of metal or other opaque material covering the outer portion of the lens. It stops the rays from entering the margin of the lens but, as it cuts down the effective size of the lens, it limits the amount of light passing through the lens.

e. Compound Lens. In fire control instruments, spherical aberration is commonly eliminated by the use of a convergent and a divergent lens cemented together to form a single element known as a compound lens (par. 64). The compound lens approximately corrects spherical aberration because the concave curves of the divergent lens neutralizes the positive aberration of the convex curves. The refractive power of the combination is retained by the proper choice of indices of refraction for each of the two lenses. A lens in which spherical aberration has been minimized or eliminated is said to be aplanatic.

41. CHROMATIC (COLOR) ABERRATION.

a. Upon being refracted through a prism, light rays of different wave lengths are dispersed into bundles of rays of the same wave length, forming a spectrum of various colors (par. 29). The rays of different colors are refracted to different extents, red undergoing the least refraction and violet the most. Inasmuch as a lens is composed of an infinite number of prisms, this dispersion also exists where light is refracted through a lens. This produces an optical defect, present in every uncorrected single lens, known as chromatic aberration or

Figure 55-Effect of Field Stop on Spherical Figure 56-Effect of Compound Lens on
Aberration
Spherical Aberration

chromatism. The violet rays focus nearer the lens than the red rays (fig. 57), and the rays of the other colors focus at intermediate points. Thus, such a lens would have a different focal length for each color, and the image would be fringed with color.

b. Correction of Chromatic Aberration of Lens. Like spherical aberration, chromatic aberration is corrected by making a compound lens of two separate lenses, one positive (convergent) and one negative (divergent). The positive lens is made of crown glass while *the negative lens is made of flint glass (fig. 58). The high color dispersion of the flint glass negative lens is sufficient to compensate for the lower color dispersion of the crown glass positive lens, without entirely neutralizing its refractive power. A compound lens so designed is said to be achromatic. Construction of a lens of this type is described in paragraph 64 b.

C. Spherical and chromatic aberrations usually are corrected by the same two elements of a compound lens. In some lenses, the negative element is plano-concave (only one surface ground spherically). In this case, the adjacent surfaces are ground to compensate for these two defects. In others, the inner curves of the lenses are calculated to eliminate chromatic aberration and the outer curves to remove spherical and other types of aberration.

d. Correction of Chromatic Aberration of Prism. The majority of prisms employed in fire control equipment are used to reflect light; some are used to refract light. When light is reflected by a prism, there is no chromatic aberration because the light rays are not divided up or dispersed. Only when light is refracted by a prism, as through a measuring wedge of a range or height finder, is the light affected by chromatic aberration.

e. Chromatic aberration in a refracting prism is corrected in much the same manner that it is in a lens. Two prisms made of different kinds of glass are cemented together (fig. 59). The prism having the larger refracting angle and which is to be the means of refracting the image from its normal path is made of crown glass. The prism having the smaller refracting angle is made of heavy flint glass which has a large dispersion of colors. The flint prism, by reason of its large dispersion, neutralizes the dispersion caused by the crown prism without entirely neutralizing the deviation of the path of the image. This compound prism is known as an achromatic prism.

a. Astigmatism is a lens aberration which makes it impossible to get images of lines equally sharp when these lines run at angles to one another. This optical defect is found in practically all but relatively complex lenses known as anastigmats which are particularly designed to eliminate this condition.

b. A perfect lens refracts all the rays from a point of light to a sharply defined point of light on the image. The rays which form each point of light of the image are refracted as a cone (fig. 60). Each cross section of one of these cones is circular in form, each successive circle becoming smaller until the focal point is reached.

C. In the grinding process, one or both refracting surfaces may become partly cylindrical instead of entirely spherical. The unequal curvature gives the lens two different focal planes. One of these brings lines in one direction into sharp focus; the second sharply focuses lines at right angles to the other lines.

d. A lens with spherical or plane faces properly ground will not show astigmatism for points near the axis, but will show astigmatism for points off the axis. The face of the lens is then presented

obliquely to the incoming light rays. Cross sections of the cone of light refracted by the lens become successively narrow ovals until they become a line in the vertical focal plane; then they become broader ovals until they are circular; and then they again become a line in the horizontal focal plane, at right angles to the first line (fig. 61). Between the two focal planes is an area known as the circle of least confusion. It is in this plane that the most satisfactory image is secured.

e. Correction for Astigmatism. Astigmatism is eliminated in the same manner as spherical and other aberrations. Lenses are made of optical glasses possessing different degrees of refraction, ground to different curvatures, so that the aberrations of all types cancel each other.

43. COMA.

a.

Coma is due to unequal refracting power of the various zones or concentric ring surfaces of a lens. It is caused by the rays from the various zones coming to a focus at slightly different points so that they are not exactly superimposed. It appears as blurring of the images at the edges of the field.

b. The image of a point of light is formed by a cone of light rays refracted through a relatively wide portion of a lens. The lens may be considered to be divided into concentric circular zones or rings of varying thickness. To form a sharply defined point of light, the rays from each zone must come to a focus at exactly the same place in the focal plane.

C. In a lens producing coma, rays of light refracted through the inner zone form a well-defined image of the point. Rays refracted through the next zone form a larger, less-defined image of the point