Topic 9. Introduction to images – the pinhole camera

The relationship between an object and its image

An object can be anything that we observe using an optical system. If it is a physical object, then we imagine that light rays are emitted in all directions from every point on the object. The intensity (and the color) of these rays may vary from point to point. An object may also be virtual. A virtual object is usually the image of a physical object formed by an optical system. An example would be the person that looks back at us when we look in a mirror.

If an optical system forms an image, that means that there is a one-to-one relationship between a point of the object and a point of the image. That is, a point of the image receives light from only one point of the object. The object and the image need not be the same size or have the same orientation. The requirement is only that any given point of the image receive light from only one point of the object.

This one-to-one relationship is usually not realized when light from an object is simply incident on a screen or other target. A single point on a screen usually receives light from many different points on an object, so that there is no unique one-to-one relationship between object and the light that strikes a point on the screen.

We see distinct objects because the lens at the front of our eyes produces an image of the scene on the retina – the light-sensitive “screen” at the back of the eye. This image is really our only connection to the real world, and we can be fooled in interpreting this image if the assumptions that we unconsciously make in evaluating it are not true. This is the basis for “optical illusions,” for our ability to see three-dimensional effects in two-dimensional pictures, etc.

The pinhole camera

The pinhole produces the one-to-one relationship between the object and the image because of its small size

The image is dim because most rays from the object can’t contribute to the image

The image is inverted (both with respect to up/down and right/left) – a feature of many imaging systems

Advantages: cheap and simple; can be used for any wavelength;

objects at any distance produce clear images (great “depth of field”)

Pinhole approximation gets better as hole gets smaller

Image also gets dimmer – fewer rays can get through

Watch out for l/D if pinhole gets too small – requirement for geometrical optics may not be true if pinhole is small enough

There is a simple relationship between the size of the object and the size of the image. This relationship can be seen from the geometrical picture shown below. The object is an arrow on the left that points upward as shown. The image is constructed by drawing straight lines from points on the object to points on the imaging screen, which is shown to the right of the pinhole. Because the pinhole is so small, only one ray from each point on the object reaches any point in the image plane.

The two triangles formed by the object and its two rays and the image and its two rays are similar, and the sides are therefore proportional. If the lengths of the object and image are L_o and L_i respectively, and if the corresponding distances between the pinhole and the object and image are D_o and D_i respectively, then using the properties of similar triangles:

Magnification= L_i/L_o = D_i/D_o

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