FIG. 1
Let us now examine how the image, A'B', is formed. The point, A, appears first, and becomes lighter and lighter up to the moment at which all the rays that emanate from the point, A, are unveiled. The point, B', is not yet visible. As the shutter continues its travel the point, B', appears in its turn and becomes illuminated like the point, A'. At this moment the objective is completely uncovered; the image, A'B', is perfect, and possesses its maximum intensity. Then the point, A', gradually becomes obscured and disappears; and the same is the case with all parts of A'B'. The image is developed progressively from A' to B', and makes its impression upon the sensitive plate successively--a fact which, as may be conceived, may have its importance. If, for example, we are photographing a ship that is being tossed about by the sea (and we borrow this example from our colleague, Mr. Davanne), the image of the top of the mast will not be formed at the same instant as that of the base, and if the motion of the mast has sufficient extent it may take on a curved form, due to the fact that it has effected a movement between the moments during which its apex and base were being photographed.
Upon placing the guillotine shutter in the optical center of the objective, what will occur? The shutter will permit the passage of an equal fraction of the rays derived from A and B, that is to say, the image will be complete from the first instant of the exposure. The points, A' and B', will be illuminated precisely at the same moment. As the shutter continues its travel, a fresh quantity of rays coming from A and B will be admitted, and the image will be illuminated more and more up to the moment at which all the rays can pass. It will then possess its maximum intensity. Then a portion of the rays from A and B being intercepted, the image will become darker and darker until complete extinction. The image here, then, is not produced successively as in the former case, but is entire from the beginning. In this case the image of our mast cannot be misshapen, since it has been accurately photographed at the same moment.
The true place for the guillotine shutter, then, from a theoretical standpoint, is in the interior of the objective. Are there any other advantages to be gained by so placing it? Yes; it is easy to understand that for the same time of exposure, and consequently for the same result, the aperture may be so much the smaller in proportion as the optical center is approached.
The luminous rays, in fact, form in the objective a double truncated cone whose upper base is equal to the diaphragm, and the lower one to the diameter of the lenses. If the aperture be equal to any diameter whatever of one of the cones, the result will be the same; but, for the same period of exposure, it will evidently prove advantageous to approach the diaphragm. The ratio of the apertures that give the same results at the optical center or behind the objective is as that of the diaphragm employed to that of the back lens. If the diaphragm is one centimeter and the lenses four centimeters, an aperture of one centimeter in one case and of four in the other will give the same result.
We shall see further along that it is advantageous to employ apertures equal to several times the diameter of the diaphragm or lens. Now, from what we have just said, an aperture, equal for example to four times the diaphragm, will be only 4 centimeters, while the corresponding aperture behind the lens must be 16. The dimensions of the first will be practical, and those of the second will give too cumbersome and too fragile an apparatus. But why must the aperture be larger than the diaphragm employed? This is what we are going to demonstrate. Let us make the aperture equal to the diameter of the objective, and see what occurs at the different periods of the exposure. For the sake of clearness, we shall suppose the velocity uniform.
It is evident, a priori, that a perfect apparatus will be the one that will allow the light to act during the entire exposure with a maximum of intensity. Is it thus, when the aperture is equal to the diameter of the objective? Evidently not. Let us consult Fig. 2. We here see the shutter progressively uncovering the objective. The light will increase from A to C up to the moment when the objective is entirely uncovered, and will then immediately decrease up to B. The objective has operated with a maximum of light for only a short time. We are far from the ideal result in which the maximum of light, CD, should exist during the entire exposure, and form the upper plane precisely equal to AB.
Fig. 2.