This section is from the book "Telephotography: An Elementary Treatise On The Construction And Application Of The Telephotographic Lens", by Thomas Rudolphus Dallmeyer. Also available from Amazon: Telephotography and Telephotographic Lens.
Telephotograph of an Encampment taken from a balloon at a height of 800 metres by Captain Mario Moris.
Plate XVII rendering of a square or rectangular object as shown in the figure.
Telephotograph of a Fort taken from a balloon at a height of 900 metres by Captain Mario Moris.
The figure has served to illustrate the manner in which distortion is produced by an uncorrected single lens; the same effects are noticeable in any single positive combination, and arise from the fact that, although adequate correction or defining power may be brought about in the axis of the system, it is impossible to remove spherical aberration, coma, curvature of field, etc, in the eccentrical pencils. These ill effects are reduced by employing a diaphragm which gives rise to the effects of distortion as indicated above.
The distortion of the image is in reality brought about by inherent defects in the lens itself, and not by the diaphragm employed ; for example, if we place a diaphragm either before or behind an optical system which is perfectly corrected, such as a rapid rectilinear, stigmatic lens, etc, it will not bring about distortion in the image, and from this it will be obvious that were we enabled to produce a single combination absolutely free from all aberrations in the eccentrical pencils, the position of the diaphragm with regard to it would have no effect as regards distortion and have no influence in producing it.
From the above remarks it will be evident that the position of the diaphragm with respect to a single negative lens when placed in front of the latter will be to displace the pencils of rays falling upon it outwards from the centre. Hence, if a diaphragm be placed between a single positive and single negative lens, the effect will be to give "pincushion" distortion to the image formed by the positive lens alone, which in its turn will be emphasised by the negative lens in the final image. If we call f1/f2 = m as before, the "pincushion" distortion increases as m increases. A Telephotographic system, then, which has a single positive combination combined with a single negative combination with' a diaphragm placed between must give this form of distortion in an inadmissible degree, even when m is low, except for pencils very near the axis, and in an impossible degree when m is great, or the lens is employed to cover a plate approaching the limits of its circle of illumination.
If the positive element is a single combination with the diaphragm placed in front as in a " single landscape lens," which produces " barrel shaped " distortion per se, it can be combined with a single negative element, and form a Telephotographic system which is non-distorting. The chief drawback to this arrangement is the low intensity of the positive lens and consequently that of the entire system when fine definition is aimed at.*
The "pincushion" distortion involved in a Telephotographic lens composed of a single positive element of high intensity combined with a single negative lens soon led the author to abandon this form of lens, replacing the single front lens by a positive combination of high intensity free from distortion in itself, combining it with a negative combination constructed to give the minimum distortion even when m is very high.
The extra reflecting surfaces of the lenses thus combined constitute a theoretical disadvantage as regards the brilliancy of the image; but this is not found of practical moment. The more complicated system seems to warrant the expenditure of optical means to remove a palpable defect.
On the "Pupils" of a Lens-system. - Professor Abbe has defined these as extending the significance of the diaphragm or stop. We may consider each separate stop of a lens-system as forming an image by the lenses which are in front of it (that is towards the object). The stop whose image thus formed appears under the smallest angle from the object is defined as the " Aperture Stop," and its image is called the "Entrance Pupil" of the lens. Similarly the image of the "Aperture Stop" formed by the lenses succeeding it, that is towards the image, is termed the "Exit Pupil." The "Entrance Pupil" and the " Exit Pupil" bear to one another the same relation as object and image referred to the whole system. (See Notes.) These "Pupils" have a very important and interesting bearing upon the study of optical instruments. Von Rohr points out their bearing upon the correct method of viewing the perspective drawing given by a lens, and also upon the subject of "depth of focus," which is referred to below.
* The author constructed a lens of this form for Mr. J. S. Bergheim to be used in portraiture. As Mr. Bergheim desired to produce " soft" images, the single positive element was made of high intensity, the spherical aberration necessarily introduced giving the softness aimed at, but the combination is free from distortion.
Perspective. - If we put a photographic lens in the orifice of a dark chamber so that it may form an image of any object situated outside, we can take a screen and place it at any distance we choose at (or beyond) the focal point of the lens, and thus receive upon it sharp images of distant objects or nearer objects according to the position in which the screen is placed. In other words, we can only have one plane in the field of the object, or the external field, which is strictly in focus at one time.
On the other hand, when we regard the external field, in order to form a correct idea of the perspective which will be produced in the resulting image upon the screen, we must first select the particular plane in the field of the object for which we shall focus sharply ; we must then consider the appearance of objects situated before or behind this particular plane as projected upon it; we then know, provided that the lens is non-distorting, that the perspective of the image will exactly reproduce the object plane and the projections of objects before or behind it, on to it, in some definite proportion. The perspective, then, is determined by the distance between the entrance pupil of the lens, through which pass all rays from the field of the object, and the chief plane for which we have focused. The entrance pupil and the exit pupil of the lens become the centres of perspective for object and image, and the image itself is an exact facsimile of the perspective produced upon the chief plane in the field of the object; it is usually reduced in size in some proportion n: 1. Now, the size of the image itself does not give us any indication as to the correct point of sight, or distance from which it should be viewed. In order to discover this, we must place the image between the entrance pupil of the lens and the chief plane for which we have focused, in such a position that its projection exactly coincides with the objects in the object field.