Beautiful Faces

Why can we see a person’s face in great detail in visible light? Hint: think about coherent scattering versus non-coherent scattering of the light. Why is the image of a person’s face blurry in the infrared (IR) and in the ultraviolet (UV)? For simplicity and idealization purposes, assume that we can see equally well in the IR, visible, and UV so that our physiology is not the limiting factor.

Answer

Coherent scattering of light by the atoms in the skin is the reason for our ability to see details of a face. The ambient incident light is scattered by the molecules of the skin. Two factors are significant for this two-step scattering process: the time interval required and the number of coherent scatterers. In the visible region of the electromagnetic spectrum, this scattering process occurs in atoms in less than 10^–8 second over an area of the skin involving about a million atoms within a circle with a radius of about one wavelength of the light. The wavelength of greenish light is about 500 nanometers.

Consider scattering one incident photon at a time. During the scattering time of a single photon by these one million alternative paths there is almost no movement of the scattering atoms in the molecules, so alternative paths have essentially fixed phase relationships. By QM rule 2, ψ = ψ₁ + ψ₂ + ψ₃ + . . . , and ψ = N ψ₁ with probability P = N² |ψ₁|², giving us coherent scattering proportional to N². With incoherent scattering we would not see much detail.

In the UV, both factors are smaller than for light in the visible spectrum the scattering occurs in less time, and the area for each scattering is less and involves fewer atoms because the wavelength is much less. The face seen in the UV would appear grainier with less detail because the adjacent coherent scattering areas are smaller and the shorter time interval means that they will have some effects of almost random phases.

In the IR, most of the scattering involves molecular transitions, which are relatively slow processes, so the scattering process involves a much longer time interval. But each molecule itself is completely involved in the scattering. So even though the wavelength is large, involving many more scattering centers, the molecular scatterers move significantly during the IR scattering process, producing random phases everywhere and a smearing of the image.

Organisms of many different types see in the UV and/or in the IR to find their nourishment, as well as in the visible. However, we humans evolved without being able to see either the UV or the IR, our vision being confined to the visible part of the electromagnetic spectrum. Why our eye-brain system evolved in this way is not known.