Fig. 22.—Characteristics of focal plane shutter.
In view of the necessity for some distance between shutter and plate it is obviously important to keep a as large as possible, depending for the requisite shutter speed on the velocity of the curtain. Large aperture and high curtain speed are also found to be desirable when we consider the distortion produced by the focal-plane shutter.
Distortions Produced by the Focal-plane Shutter.—While the time of exposure of any point on the plate can, with the focal-plane shutter, easily be made 1
100 second or less, the whole period during which the shutter is moving is much greater than this. For instance, a 1 centimeter opening which gives 1
100 second exposure takes ⅒ second to move across a 10 centimeter plate, or nearly ⅕ second for an 18 centimeter plate. With a moving airplane this means that the point of view at the end of the exposure has moved forward compared to that at the beginning, by the amount of motion of the plane in the interval. If the shutter moves in the direction of motion of the plane the image will be magnified; if in the opposite direction, it will be compressed along the axis of motion. The amount of this distortion is calculated as follows:
Let the velocity of the plane be V, and that of the shutter be v. Let the focal length of the camera be F, and the altitude A. If the camera were stationary, a plate of length l would receive on its surface an image corresponding to a distance A
F × l on the ground. Due to the motion of the shutter the end of the exposure occurs at a time l
v after the start. In this time the plane has moved a distance V × l
v; hence the point photographed at the end of the shutter travel is Vl
v within or beyond the original space covered by the plate, depending on the direction of motion of the curtain. The distortion, D, is given by the ratio of this distance to the length corresponding to the normal stationary field of view:
| V v | × l | VF | ||
| D = | = | |||
| A F | × l | vA | ||
When V = 200 kilometers per hour, v = 100 centimeters per second, F = 50 centimeters, A = 3000 meters, we have—
| 20,000,000 × 50 | 1 | ||
| D = | = approximately | ||
| 3600 × 100 × 300,000 | 100 |
Or if the actual distance error on the ground is desired,
| Vl | |
| = 10.8 meters | |
| v |
As a percentage error this one per cent. is small compared with other uncertainties, such as film shrinkage or the error of level of the camera. As an absolute error in surveying, thirty feet is, of course, excessive.