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.
In ordinary photographic practice, the camera is usually brought very near to the chief object of interest, so as to give it prominence by obtaining a sufficiently large image. When this takes place, the receding planes of the picture are dwarfed, while the perspective is unsatisfactory; for we do not so view it that its projection from the point of sight coincides with the objects in space. By the use of the pinhole camera it can readily be seen how this may be overcome.
In Fig. 8, where P is at a given distance from the object ab in order that a b may be the required size upon the screen s s, at a fixed distance from p, the objects a b, a' b' are rendered in a certain proportion a b: a' b'; a'b' being considerably smaller than ab. pe is here the correct but inconvenient viewing distance.
If we now remove the camera to a greater distance from a b, the image diminishes in size, and becomes too small for our purpose. But if the screen s s be removed from p, so that the image is received upon s' s' in the same size as in the former case, we shall find the image a' b' of a' b' is now greater than before, or that the proportion ab: a' b' is different in this case. In general, the perspective will be much more satisfactory if the nearest object of interest is not too close to the camera. As already stated, the conditions in the upper drawing in Fig. 8 are very approximately those of an ordinary "positive" lens; whereas in the lower drawing we exhibit the possibilities of the Tele-photographic lens.
* The reader is referred to Dr. P. H. Emerson's " Naturalistic Photography " (Third Edition, Messrs. Dawbarn Ward) for a fuller study of the perspective rendering of lenses.
It is generally held that we ought to view a photograph from a distance equal to the focal length of the lens with which it was taken. This is very approximately true for all lenses irrespective of their construction, when the object is so distant that all rays meeting the lens may be considered parallel; but only under these conditions.
To see the image in true perspective under all conditions we must view it projected towards the object from the "Entrance Pupil" (of the particular optical system with which it was produced), at the position where its projection towards the object will exactly coincide with the object.
There is, then, a definite and correct distance at which every photograph should be viewed, but if we ask ourselves how often we conform to the correct conditions, we shall have to confess that it is very seldom indeed. It is for this reason that many artists are so-severe upon the rendering of perspective by photographic instruments. It is not difficult to see how this comes about. If we look at a painting, a black and white drawing, or a photograph taken by ordinary means, whatever its size may be, we involuntarily take up a position at a distance equal to two, three, or possibly more times the length of its longest side. This standpoint suits the artist's perspective, and it looks right, because he has considered all this in creating his impression; but the poor photograph is terribly handicapped, because we ought to inspect it from a distance equal approximately to the focal length of the lens with which it was produced (generally about the longest side of the print) and when we do not, it looks wrong!
The Telephotographic lens, as will be shown anon, acts as a lens of very considerable focal length, and with its aid photographs are produced that ought to be viewed from a distance equal to three or four times the longer side of the print. We thus conform to our conditions of finding the correct position for true perspective involuntarily, and are not troubled with that apparently false rendering of perspective given by ordinary lenses.
By ordinary reasoning, it might be presumed that the smaller the "pinhole" the finer the definition. This, however, is not the case, as light in passing through the small hole is "diffracted." This "diffraction" interferes with the definition of the image, and for a given distance between screen and pinhole the size of the hole may be either too large or too small to give the best result.
Diffraction is due to the retardation of rays proceeding from the margin of the pinhole as compared with rays proceeding from the centre; to obtain the maximum concentration of light at the focus, the retardation should be half a wave length λ/2. * Lord Rayleigh has shown at any rate that the limit of retardation may be taken as -.
Taking - as the retardation, r as the radius of the pinhole, and d its distance from the plate P, it is easily seen that photographically active, λ=.000017; the radius of the hole should be: -
r2 = (d+λ/2)2 - d2; = d2 + dλ +λ/4- d2; = d λ (as λ/4 is very small) ; r = or d = r2/λ.
Example. - Let the centre of the plate be 10 inches from the hole, and taking the light near the g line of the spectrum as the most or .026, or 1/38 inch, is the best diameter for the hole.
* Captain Abney on "Pinholes," Camera Club Journal, May 1890.
By applying this formula to needles of known diameter (Helic needles of Messrs. Milward & Son, Redditch) the following results may be useful:-
Distance for plate.
We shall presently see that diffraction may also have a disturbing effect upon the definition given by photographic lenses, when the opening of the diaphragm bears too small a relation to its focal length.
It may be convenient now to point out that the "pinhole" camera affords a ready means of ascertaining with some accuracy the focal length of positive lenses or lens-systems. A suitable definite distance between the pinhole and screen being accurately set, a negative is taken of some distant object, the image of which is preferably longitudinally and centrally placed, and of considerable contrast in subject. If this image be very carefully measured in length, its measurement forms a gauge for the determination of the focal length of lenses, by comparison with the images formed by them, a matter of simple proportion - e.g., if the object, a b formed an image, a'b', with a pinhole at the distance d', then two lenses, forming images a b, a" b", would have focal lengths corresponding to the proportion between a' b' and a b, a" b" respectively, or their absolute focal lengths would be d and d".
Taken with an ordinary 10-in. cabinet lens at a distance of 10 ft.; compare with Plate II. and note the exaggerated size of the hand, flower, and foreground, and the dwarfing of the background. (By the Author.)
Taken with an 81/4" c. de v. lens combined with a 4-in. negative lens at a distance of 24 ft. The camera extension was set to render the face in the same scale as Plate I. ; the relative planes of the picture have their proper values in respect of drawing.
(By the Author.)