Image Formation

This chapter offers a physical explanation on how an image is formed. Image formation not only occurs in cameras but also in the eye.

One of the reasons why we can see objects is a phenomenon called reflection. It is a property of light that it spreads radially until it falls on a surface. This surface in turn – in case that it is not fully transparent or entirely light absorbing – reflects light into free space again. However, reflection occurs in various different forms which is the reason why almost every surface has its own look. Any highly polished surface such as smooth metal causes specular reflections. The angle of reflection is always equal to the angle at which the ray is incident to the surface. The secret of mirrors lies in the principle of specular reflections. By contrast, rough and matte surfaces tend to scatter light in all directions. This effect is called diffuse reflection. An incident ray of light is spread into a variety of angles. The intensity of diffusely reflected light depends on the angle of incidence where light vertically incident on the surface produces the brightest diffuse reflection while a decreased angle reduces the intensity of reflected light. By contrast, the intensity of diffusely reflected light is not dependent on the viewing angle and therefore appears with the same brightness from all perspectives. Some other surfaces such as a glossy photo paper or plastics are a combination of texture and smooth polish. Consequently, these produce a reflection that has properties of diffuse reflection but include a directional component like the specular reflection. This hybrid type is called spread reflection. Also, there are colored surfaces that only reflect certain wavelengths of light. This type of color filter produces an effect called selective reflection. The illustration below summarizes the types of reflections.

light surface interactions_part_I

Given that not all subjects consist of solid materials, there are some further types of interactions between light and surfaces. For every transparent or semi-transparent material, transmittance occurs. This effect allows incident light to travel through a subject, but depending on the material, reflection can be inherent with transmittance. Although “full transmittance” and “partial transmittance” appear to be different effects in the illustration, the transmittance of a material is typically expressed in a percentage varying between 0% (opaque) and 100% (fully transparent). The transmittance of a given material can be expressed in a spectral transmittance function where the percentage values are expressed for every wavelengths analyzed. Another phenomenon typical for transparent materials is refraction, however this effect will be described later in the articles on camera lens principles. The illustration below shows the effects of transmittance and refraction.

light surface interactions_part_II

Finally, some materials neither reflect nor transmit light. For many dark colored surfaces, absorption occurs. As the energy of incident light is not released again, this energy typically accumulates within the object in the form of heat. Again, full absorption and partial absorption are not separate phenomena, but can be expressed in percentage values for a given material. In other materials, incident light can excite atoms which absorb the energy and release it later by emitting light in various directions – see diagram below.

light surface interactions_part_III

In addition, every surface can absorb individual wavelenghts and therefore will appear in different colors to an observer. For instance, an object that absorbs short wavelengths (blue light) will appear yellow to the viewer.

In order to form a clear image, rays reflected by any object need to be captured by the camera. Therefore, a lens or an array of various lenses is arranged in front of the camera body. A small section of the reflected light falls on the lens and gets refracted into a converging bundle of rays. The illustration below shows the general image formation principle including a converging (convex) glass lens.

Image Formation

Traces of light rays parallel to the optical axis are passing through the focal point behind the lens. Also, it can be helpful to show both focal points in an optical system as these rays passing through the focal point in front of the lens will be parallel to the optical axis after travelling through the lens. It should be noted that the focal point of a lens usually is not the area where a focused (sharp) image is formed. This only applies for an object located infinitely far away where all its light rays relevant for image formation are incident parallel to the optical axis. For all objects closer to the camera, focus is achieved behind the focal point of the lens. Given that an object reflects light on its entire surface, all points formed in the image plane are combined to a complete image, a virtual reproduction of the object.

The distance between the lens and the projected spot depends on the distance between the lens and the object. More precisely, for thin lenses there is a formula that defines a unique relationship between the focal length of a lens and the position of the object and the image.

The thin lens formula is: 1/o + 1/i = 1/f where o = object distance, i = image distance and f = focal length of the thin lens. It will be shown in the article on the autofocus system how the relationship of these distances is applied in digital cameras.