as the focal length; so that while the image size for a 25 centimeter lens would be, say, .05 millimeters per 100 millimeters focal length, it will be only .03 or .04 millimeters per 100 millimeters focal length for a 50 centimeter lens. The actual size of a point image will therefore be greater, though not proportionately greater.
Fig. 16.—Chart recording measurements of lens characteristics.
The chart presents tests on a good quality lens, and so gives a good idea of the permissible magnitude of the various errors. In many ways the most important figure is that for image size, including as it does the result of all the aberrations. In the example given, this varies from .075 to .15 mm. actual size. For the same type of lens of 25 centimeters focus this range will be from .05 to .10 mm. Since these are commonly used focal lengths, a good average figure for image size, commonly used in aerial photographic calculations, is ⅒ mm. In regard to astigmatic tolerances, the two astigmatic foci should not be separated at any point by more than 6 to 7 millimeters, and the mean of these should not deviate from the true flat field by more than ½ millimeter, in each case the figures being based on the conventional 100 millimeters focal length. Distortion should not be over .08 millimeter at 18° or .20 millimeter at 24° from the axis (per 100 millimeters focal length).
Lens Aperture.—In the simple lens the aperture is merely the diameter. In compound lenses the aperture is not the linear opening but the effective opening of an internal diafram. Photographically, however, aperture has come to have a more extensive meaning. While in the telescope the actual diameter of an objective is perhaps the most important figure, and in the microscope the focal length, in photography the really important feature is the amount of light or illumination. This is determined by lens opening and focal length together; specifically, by the ratio of the lens area to the focal length. The common system of representing photographic lens aperture is by the ratio of focal length to lens diameter, the lens being assumed to be circular. Thus F/5 (often written F.5) indicates that the diameter is one-fifth the focal length.
Two points are to be constantly borne in mind in connection with this system of representation. First, all lenses of the same aperture (as so represented) give the same illumination of the plate (except for differences due to loss of light by absorption and reflection in the lens system). This follows simply from the fact that the illumination of the plate is directly proportional to the square of the lens diameter, and inversely as the square of the focal length. Secondly, the illumination of the plate is inversely as the square of the numerical part of the expression for aperture. That is, lenses of aperture F/4.5 and F/6 give images of relative brightness (6 4.5)2 = 1.78.
What lens aperture, and therefore what image brightness, is feasible, is determined chiefly by the angular field that must be covered with any given excellence of definition. The largest aperture ordinarily used for work requiring good definition and flat field free from distortion is F/4.5. Anastigmatic lenses of this aperture cover an angle of 16° to 18° from the axis satisfactorily, which corresponds to an 18 × 24 centimeter plate with a lens of 50 centimeters focus. Lenses with aperture as large as F/3.5 were used to some extent in German hand cameras of 25 centimeters focal length, with plates of 9 × 12 centimeters. English and American lenses of this latter focal length were commonly of aperture F/4.5, designed to cover a 4 × 5 inch plate.
As a general rule the greater the focal length the smaller the aperture—a relationship primarily due to the difficulty of securing optical glass in large pieces. Thus while 50 centimeter lenses of aperture F/4.5 are reasonably easy to manufacture, the practicable aperture for quantity production is F/6, and for 120 centimeter lenses, F/10. This means that a very great sacrifice of illumination must be faced to secure these greater focal lengths. As is to be expected from the state of the optical glass industry, the German lenses were of generally larger aperture for the same focal lengths than were those of the Allies. Besides the F/3.5 lenses already mentioned, their 50 centimeter lenses were commonly of aperture F/4.8, their 120 centimeter lenses of aperture F/7, or of about double the illuminating power of the French lenses of the same size.
Demands for large covering power also result in smaller aperture. The 26 centimeter lenses used on French hand cameras utilizing 13 × 18 centimeter plates were commonly of aperture F/6 or F/5.6. The lens of largest covering power decided on for use in the American service was of 12 inch focus, to be used with an 18 × 24 centimeter plate (extreme angle 26°); the largest satisfactory aperture for this lens is F/5.6.
Ordinarily the question of aperture is closely connected with that of diaframs, whereby the lens aperture may be reduced at will. Diaframs have been very little used in aerial photography. All the aperture that can be obtained and more is needed to secure adequate photographic action with the short exposures required under the conditions of rapid motion and vibration peculiar to the airplane. Any excess of light, over the minimum necessary to secure proper photographic action, is far better offset by increase of shutter speed or by introduction of a color filter. For this reason American aerial lenses were made without diaframs. In the German cameras, however, adjustable diaframs are provided (Fig. 43), controlled from the top of the camera by a rack and pinion. In the camera most used in the Italian service an adjustable diafram is provided, but this is occasioned by the employment of a between-the-lens shutter of fixed speed, so that the only way exposure can be regulated is by aperture variation, a method which has little to recommend it.
The Question of Focal Length.—In aerial photography the lens is invariably used at fixed, infinity, focus. Under these conditions the simple relationship holds that the size of the image is directly proportional to the focal length and inversely proportional to the altitude. If any chosen scale is desired for the picture the choice of focal length is determined by the height at which it is necessary to fly. This at least would be the case were there no limitation to the practicable focal length—which means camera size—and were one limited to the original size of the picture as taken; that is, were the process of enlargement not available. But the possibility of using the enlarging process brings in other questions: Is the defining power of a short focus lens as good in proportion to its focal length as that of a long focus lens? If so a perfect enlargement from a negative made by a short focus lens would be identical with a contact print from a negative made with a lens of longer focus. Is defining power lost in the enlarging process with its necessary employment of a lens which has its own errors of definition and which must be accurately focussed?
Certain factors which enter into comparisons of this sort in other lines of work, such as astronomical photography, play little part here. These are, first, the optical resolving power of the lens, which is conditioned by the phenomena of diffraction, and is directly as the diameter; and, second, the size of the grain of the plate emulsion. The first of these does not enter directly, because the size of a point image on the axis of the lens, due merely to diffraction, is very much less than that given by any photographic lens which has been calculated to give definition over a large field, instead of the minute field of the telescope. Yet it may contribute toward somewhat better definition with a long focus lens because of the actually larger diameter of such lenses. The second factor is not important, because, as will be seen later, the resolving power of the plates suitable for aerial photography is considerably greater than that of the lens. The emulsion grain is in fact only a quarter or a fifth the size of the image as given by a 25 centimeter lens, and enlargements of more than two or three times are rarely wanted.
A series of experiments was made for the U. S. Air Service to test out these questions, using a number of representative lenses of all focal lengths, both at their working apertures and at identical apertures for all. With regard to lens defining power, as shown by the size of a point image, the answer has already been reported in a previous section. Lenses of long focus give a relatively smaller image than lenses of the same design of short focus. In regard to the whole process of making a small negative and enlarging it, the loss of definition is quite marked, as compared to the pictures of the same scale made by contact printing from negatives taken with longer focus lenses.
This answer is clear-cut only for lenses calculated to give the same angular field. Thus a 10 inch lens covering a 4 × 5 inch plate has about the same angle as a 50 centimeter lens