far as it is governed by chromatic aberration), if a plate of narrow spectral sensitiveness is used, while giving images of different size on panchromatic plates of more extended color sensibility. The choice of the region of the spectrum for which chromatic correction is to be made is thus governed by the color of the photographically effective light. While in ordinary photography the blue of the spectrum is most important, in aerial work where color filters are habitually used with isochromatic plates the green is most important, and color correction centered about this region constitutes a real difference of design peculiar to aerial lenses. Similarly the general use of deep orange or red filters with red sensitive plates, for heavy mist penetration, would call for a shift of correction to that part of the spectrum.
Astigmatism and Covering Power.—Suppose the lens forms at some point off its axis an image of a cross. Suppose one of the elements of the cross to be on a radius from the center of the field, the other element parallel to a tangent. The rays forming the images of these two elements of the cross are subject to somewhat different treatment in their passage through the lens. The curvature of the lens surfaces is on the whole greater with respect to the rays from the radial element than to those from the tangential element. They are therefore refracted more strongly and come to a focus nearer the lens. The arms of the cross are consequently not all in focus at once. This error, termed astigmatism, is rather well shown in Fig. 15, where the images of the outlying concentric circles are sharp in the radial, but blurred in the tangential direction.
Astigmatism can be largely compensated for, and its character controlled. The most usual correction brings the two images in focus together both at the axis, and on a circle at some distance out. This second locus of coincidence may or may not be in the same plane as the first, depending on which disposition produces the best average correction. The mean between the two foci determines the focal plane of the lens, which is in general somewhat curved. The covering power of a lens is given by the size of the field which is sufficiently flat and free from astigmatism for the purpose for which the lens is used. This is largely determined by the astigmatism, but the other aberrations are also important.
Illumination.—The amount of light concentrated by the lens on each elementary area of the image determines its brightness or illumination. The ideal image would, of course, be equally bright over its whole area of good definition, and for lenses of narrow angle this is approximately true. But when it is desired to cover a wide angle the question of illumination becomes serious. The relationship between angle from the axis and illumination is that illumination is proportional to the fourth power of the cosine of the angle. This relationship is shown in the following table:
| Angle | Image brightness |
|---|---|
| 0° | 100 per cent. |
| 10° | 94.1 per cent. |
| 20° | 78.0 per cent. |
| 30° | 56.2 per cent. |
| 40° | 34.4 per cent. |
| 50° | 17.1 per cent. |
If the field of view is 60°, which corresponds to an 18 × 24 centimeter plate with a lens of 25 centimeter focus, the brightness is only 56 per cent., and the necessary exposure at the edge approximately 1.8 times that at the center. This effect is shown in Fig. 15. It is very noticeable if the exposure is so short as to place the outlying areas in the under-exposure period.
Fig. 13.—Barrel and pin-cushion distortion.
Distortion.—Sometimes a lens is relatively free from all the aberrations, mentioned above, so that it gives sharp, clear images on the plate, yet these images may not be exactly similar to the objects themselves as regards their geometrical proportions; in other words, the image will show distortion. Lens distortion assumes two typical forms, illustrated in Fig. 13, which shows the result of photographing a square net-work with lenses suffering in the one case from “barrel” distortion and in the other from “pin-cushion” distortion. In the first the corners are drawn in relative to the sides; in the latter case the sides are drawn in with respect to the corners. Either sort is a serious matter in precision photography, such as aerial photographic mapping aspires to become. It must be reduced to a minimum and its amount must be accurately known if negatives are to be measured for the precise location of photographed objects. In general symmetrical lenses give less distortion than the unsymmetrical (Fig. 14).
Fig. 14.—Arrangement of elements in two lenses suitable for aerial work: a, Zeiss Tessar; two simple and one cemented components (unsymmetrical); b, Hawkeye Aerial; two positive elements of heavy barium crown, two negative of barium flint, uncemented (symmetrical).
Lens Testing and Tolerances for Aerial Work.—Simple and rapid comparative tests of lenses may be made by photographing a test chart, consisting of a large flat surface on which are drawn various combinations of geometrical figures—lines, squares, circles, etc.—calculated to show up any failures of defining power. For testing aerial lenses the chart should be as large as possible, so that it may be photographed at a distance great enough for the performance of the lens to be truly representative of its behavior on an object at infinite distance. This means in practice a chart of 4 or 5 meters side, to be photographed at a distance 20 to 30 times the focal length of the lens.
Fig. 15.—Photograph of a lens testing chart, showing failure in defining power outside area for which the lens is calculated.
A typical photograph of such a chart is shown in Fig. 15. It reveals at a glance the more conspicuous lens errors. At the sides and corners the concentric circles show the lens's astigmatism, by the clear definition of the lines radial to the center of the field and their blurring in the tangential direction. The falling off in illumination with increasing distance from the center is also exhibited; and the blurring of all detail outside the rectangle for which the lens was calculated shows that spherical, chromatic, and other aberrations have become prohibitively large.
But the only complete test of a lens is the quantitative measurement of errors made on an optical bench. A point source of light, which may at will be made of any color of the spectrum, is used as the object and its image formed by the lens in a position where it can be accurately measured for location, size, and shape by a microscope. A chart giving the results of such a test is shown in Fig. 16. In the upper left-hand corner is shown the position of the focus for the different colors of the spectrum. Below this is recorded the lateral chromatism at 21 degrees, in terms of the difference in focus for a red and a blue ray. Below this again comes the distortion, or shift of the image from its proper position, for various angles (plotted at the extreme right) from the lens axis. To the right of this is the image size, at each angle, and finally, to the right of the diagram, are plotted the distances of the two astigmatic foci from the focal plane, together with the mean of the two foci, which practically determines the shape of the field.
An important point to notice is that these data are uniformly plotted in terms of a lens of 100 millimeters focal length irrespective of the actual focal length of the lens measured. Thus this particular chart is for a 50 centimeter lens but would be plotted on the same scale for a 25 or a 100 centimeter lens. Underlying this practice is the assumption that all the characteristics of lenses of the same design and aperture are directly proportional to their focal length. If this were so, then a 50 centimeter lens would give double the size of image that a 25 centimeter does, and so on. As a matter of fact, test shows that the size of the image