Light Diffraction part 2 - Airy Disk
Aa follow up to a previous article I wrote, I wanted to explore further the strange and often inexplicable behavior of focussed light (incandescent, laser and so on). When we focus a flashlight (torch) on a wall, assuming we are fortunate to be able to focus it by rotating a lens (we obviously paid a few extra shekels for the flashlight), we can observe a spectrum of behavior from a cloudy swathe of illumination with no discernible focal point to a defined circular light on a surface with a warm glow or rings of light around the central region.
There area few things we can observe from our cheap flashlight;
- When we shine a flashlight on a wall we tend to see 2 things; a brighter central region and a swathe of light that fades outward from the edge of this central region (it does tend to drop off rather quickly). If we have the ability to rotate a lens in front of the light, we can change the diameter and focus of the central region.
- The light that emanates from the bulb, typically radiates outward in a triangular shape due to a concave shaped reflector behind the bulb. So, the small flashlight (could be an inch in diameter), radiates a circular disk of photons on the wall. The diameter of the disk will mathematically enlarge by a function of the concave nature of the reflector, the size of the lens in relation to the bulb and the distance you are from the illuminated object.
- If our flashlight has no concave reflector or a really poor one, you will not to see a huge change in the diameter of the light over distance (although it will spread), it tends to look funnel like. Indeed a cat laser looks more like this description. Even with a focussed, funneled light, we still see a disk of light on the surface where the light hits, with residual light around it. Thus regardless of what the source of light is, we see a disk with a glow around it.
- Another wonderful characteristic occurs when we point the flashlight toward the ground we see a distortion of the central region into an elliptical shape, and we can also see a similar distortion of the boundary (extra light) away from the source.
- Another thing to ponder is that what we see is function of probability (and only probability). When we see residual light rings or a glow around the central focal point, we are looking at probability in action. Simply speaking, when we shine a light, it can potentially travel in a lot of directions, but based on distance and time, nature determines the most likely position for the photons to bounce off. So when we point our flashlight at a wall, the most likely place it will hit first is straight ahead, but there is also a chance it will hit away from the center. When we see a glow or rings around the focal point we are seeing probability in action, which diminishes the further out you go. You are actually seeing nature deciding the placement of photons based on the probability it could be somewhere other than the most obvious place.
In the diagram created by the great Richard Feynman, we see a source of light (S) and a mirror which is split in segments (A through M). The light can potentially reflect anywhere on the surface, but probability dictates that it is more likely to reflect toward the center (where it's being pointed based on distance and time taken to reflect). The Feynman arrows tend to point in a similar direction toward the center (E through I) and have a higher probability of reflecting in that area. However there is still a chance the light can (and does) bounce off a completely different area. This is what dictates residual light and how we can see it outside where we expect to see it !
- The last observation would be rings around the central area. They exist due to probability. How they get there is a function of light exhibiting waveform characteristics.
In this Image you can see there was a disturbance in the water, and from a central area ripples spill outward. What we are seeing are two things, a peak and a trough (the peaks look brighter and the trough darker). With our light, the rings we see are the peaks of the light waves as they spread out from the center. They fade in unison with probability as we go further from the center.
AIRY DISK
So the humble flashlight is a lot more than a bulb and a battery ! We are observing something quite wonderful and frankly crazy ! Lets take a more detailed look at the structure of what we see. Sir George Biddell Airy in the 19th century was an astronomy who engaged in multiple projects relating to calculating the distance of stars from earth. It was recognized that it was impossible to create a perfectly focussed star (point of light) with even the best lenses. Indeed, observation after observation showed that even with the best lens, you would always see a central disc of light, with a circular rings (patterns) that spread out from the central disc. The disc of light in the center was called the Airy Disk, the
circular patterns or ripples were called the Airy Pattern. The familiar looking phenomena was indeed what we see with our flashlight. The rings of light around the center are called Diffraction. We are seeing the very nature of light, exhibiting waveform properties. These rings being the peaks of the wavelength of the specific light we are observing (from a topographical view). Further still, their position is based solely on mathematical probability and how nature determines where photons should be based on her own logic (why nature decides why one photon goes in specific place, whilst another somewhere else is the greatest of mysteries). With a diffraction limited technology (such as the hubble telescope) where there are no impediments (atmospheric being the most troublesome) to what you can observe through a lens (and an optical resolution), the holy grail is the Airy Disk and pattern. If you see a sharp Airy disk with pattern you have a perfectly focussed lens.
Postscript - Lasers
As a final note, with lasers, this Airy pattern could be problem if the amount of energy in the frequency peaks are extra or unwanted. It is possible to reduce the optic size, but that does not eliminate the quantum mechanical nature of light. The disk and pattern only occur on reflection or interference, like the ocean wave that radiates into a semi circular pattern as it smashes against a rocky inlet. Even the best lasers will exhibit this phenomena.
Nigel Heywood