# Variety of Pinhole Camera_2: Double Slit-Plate

### Principle of the double slit-plate photography

When we put together two plates closely, each of which has a vertical slit and a horizontal slit, respectively, the two plates become one plate with a small rectangular hole with a edge length equal to the width of the original slit.  Though usually the shape of a pinhole used for the pinhole photography is circular, a rectangular hole causes no problem for photographing.  As described in the Aristotle’s problem an image projected by a pinhole is always a similar shape to a photogenic object irrespective of a shape of the pinhole.  As a matte of course, therefore, the “pinhole” camera with this rectangular hole can be used to take a photograph.  Next, we separate the two plates gradually.  Then the pinhole plate with a rectangular hole reverts to the previous two plates with a vertical slit and a horizontal slit, respectively, and an optical system consists of a plate with a vertical slit and a plate with a horizontal slit is obtained.  We call this optical system as a double slit-plate(*).  As imagined easily a photograph taken by a double slit-plate with a small isolation is very similar to a photograph taken by the “rectangular” pinhole camera.  In other words, the pinhole photography is, in a certain sense, a limiting case of the double slit-plate photography.

Double slit-plate
When two slit-plates (the left figure) are put up one over another, a rectangular “pinhole” is obtained (right figure).

How does an image of an object produced by a double slit-plate

*Double slit-plate, double slit, and streak camera
It may be possible to name the optical element explained here as “double slit“.  But in the field of quantum mechanics, “double slit” means one plate with two slits, which is also used for demonstration of the feature of a particle as a wave by using the interference phenomenon.  We have also used this kind of a plate with two slits for explanation of the interference phenomenon appearing in the theory of a zone plate.  Therefore, in order to avoid confusion we call the optical element in this page as “double slit-plate” in which two slits are on two different plates.  Renner uses in his book (Eric Renner, Pinhole Photography Third Edition, Focal Press 2004) generically a word, “slit imaging” which means both single slit and multi-slit photography.  Moreover, there is a completely different “slit camera” in which a slit is set closely to a film and a photograph is taken by feeding a film rapidly.  As in a photograph taken by the slit camera the direction of the film movement is regarded as a temporal axis of the motion of the object this kind of camera was conveniently used for judgement of the order of arrival in the races.  Furthermore, by adjusting the speed of a film appropriately one can take a photograph of a very long train without a perspective distortion.  Correspondingly a panorama camera based on the principle of the slit camera can take a panoramic photograph without a distortion in the angular direction.  A slit camera for high speed photography is a streak camera which was extensively used in the scientific and engineering fields.  There are attempts to use a slit camera for creating artistic photographs (Michio Ohzeki, Aesthetics of After Image<残像の美学>, 1998, in Japanese).  By the way, in the field of medical science this optical element used for a collimator of a SPECT (single photon emission CT) is called as a “Skew Slit“, but this naming seems to restrictive for our purpose and we don’t adopt the name “Skew Slit”.

Interference of waves by a double slit
When a plane wave enters a plate (green) with two slits from beneath waves spread in a circle from the slits and we can see directions where the wave intensity is increased by the interference.

### Features of the double slit-plate photography

The most important feature of the double slit photography is, as a matter of course, the distance between the vertical slit and the image screen is different from the distance between the horizontal slit and the image screen.  By the way the vertical slit determines the angle of view in the horizontal direction, and the horizontal slit determines the vertical angle of view.  In other words, the vertical slit determines the focal length of an image in the horizontal direction and the horizontal slit determines the focal length of an image in the vertical direction.  Therefore, if the front slit is the horizontal slit and the back slit is the vertical slit, the horizontal angle of view is large and the vertical angle of view becomes small, which means that a photograph by this system is wide-angle-like in the horizontal direction and telephoto-like in the vertical direction, and vice-versa.  This state is easily understandable by seeing the following figure.

Arrangement of the double slit-plate and the vertical and horizontal multiplication of an image
Light rays from two points A and B on a circle of the object pass through the vertical slit at the point S2 and those from the points C and D pass through the horizontal slit at the point S1, and reach the points, A’, B’, C’, D’ on the image screen, respectively.  For this reason the image of AB (A’B’) becomes shorter and the image of CD (C’D’) becomes longer.

As shown in the figure when the front slit is vertical and the back slit is horizontal the image of a circle becomes a horizontal ellipse.  Though according to the explanation up to now the two slits are orthogonal each other, an interesting image is obtained by setting two slits intersect non orthogonally.  It is understandable from the figure that unlike in the case of the pinhole photography, naturally, there is no point where all light rays pass in the case of the double slit.  Though presently we use only a double slit system with a simple linear slits we can enjoy various changes in images by using slits with various shapes.