This chapter calls on maths, but the maths is relatively elementary. The first four sections only require simple geometry. The final sections refer to Fourier transforms, but only at a descriptive level.

Sight is the most complete of our senses. Our eyes detect light. So our eyes are photon detectors. There's more: our eyes distinguish light of different colours. So our eyes are spectrometers. There's more: our eyes tell the direction the light is coming from. So our eyes are imaging devices. There's more: between them, our eyes let us build up a three-dimensional image of the scene we are viewing.

We extend our vision using instruments. For example, the telescope lets us see the distant; the microscope, the small.

We can extend our vision to other parts of the electromagnetic spectrum. To do this, we need an instrument sensitive to invisible radiation that converts it to something we can see. X-rays are an example. An x-ray viewer records x-rays arriving from different places and presents this in a way the eye can see. At first, photographic film was used to display x-rays. Now a computer monitor is standard. In principle, the x-rays could be separated according to frequency, but this is not usually done in practice. By taking multiple x-ray images from different angles, a three-dimensional x-ray image may be built up. This process is called computer-axial tomography or computer-aided tomography (CAT) or simply computer tomography (CT).