From recent experiments and reading, I finally have got a grip on coherence, particularly how it works with white light. This might be of use to you guys when some bright kid pops the white light coherence question, preceeded by "Hey, wait a minute!".

Especially helpful to me has been Lipsom and Lipsom, who wrote an Optics text called "Optical Physics" which I bought years ago. There is a copy also in the Weld library, or there was last year when I put it back on the shelf. Somebody had been looking at it, I hope they recognized what they had in their hand, as it is a gem. Check it out.

Many can appreciate how coherence occurs in a laser, stimulated emission being the production mechanism. But white light, from an extended source, like a distant star? How is this possible? Obviously, the light coming from the surface of a star is not organized. How can it be coherent?

Well, here's how it goes, I'm pretty sure now...

When light from a distant source (like a star) arrives at an observer's location and passes through a small opening, a pinhole for example, The light consists of electromagnetic contributions from *billions and billions* of photons, all with random duration, wavelength, phase, polarization and amplitude. At the earth observer's location, this mix of wave energy gets added together in accordance with the superposition principle at every instant. At any one location, (the pinhole in this case) there is a single set of parameters which can accurately describe, for only a very short time, what is coming through the pinhole from the distant star.

Because of the randomness of the parameters which describe the arriving light, the correlation between light arriving at the pinhole at any instant, and light arriving just a bit later cannot be expected to be large. Each photon contributes a brief sinusoidal pulse of energy, modulated in a gaussian manner, the duration of which depends on the atomic transition or collision mechanism which produced it. Considering the bandwidth of white light, this time is roughly how long it takes for just one green wave to pass through the pinhole.

Swithching now from temporal considerations to spacial ones, ask this question: Are the parameters describing white light arriving at an earthly pinhole the same as those for a laterally ajacent pinhole? Well, (and this comes from Lipsom and Lipsom) if the path length difference from all parts of the star to the pinholes is less than a wavelength, approximately, there will be coherence. This is a consequence of the temporal and bandwidth considerations mentioned in the preceeding paragraph. Move the pinholes apart, and if the path difference exceeds a wavelength, the degree of coherence diminishes. So, surprisingly, it is the angular size of the source that determines the size of the coherence region.

Coherence is revealed by setting up the pinholes so that the light coming through them is combined and interference results. High fringe contrast, or fringe visibility, means high coherence in the region where the pinholes are located. As the pinholes are moved apart,

eventually, coherence diminishes. At some separation, the coherence becomes zero. Albert Michelson used these ideas to measure the angular diameter of a distant star for the first time.

The region of coherence gets larger as the angular size of the source gets smaller. The size of the source and the central wavelength determine the size of the coherence region. The exact relation is given in many standard texts. For a disc-like source like a star, the coherence, or correlation function, is a first order Bessel function.

This topic has long been of interest to me because of it's direct application to radio astronomy imaging. Replace the observer's pinholes with a pair of radio telescope dishes. Measure the coherence of the radio signals arriving at the pair of dishes. See how the coherence varies as the dishes are moved apart. (and the earth changes the orientation of the dishes) Use many dishes, in pairs, to map what is called the fringe visibility, the radio astronomy term for coherence, or correlation function. Take the Fourier transform of that, and you have an image of an astronomical object - in the light of radio waves!

When I was at Milton, I never got a chance to talk about this with anyone on the faculty. Too arcane? Too specialized? Not enough time? Somehow it was just never appropriate. But now that I can ponder these issues at length, I feel the need to communicate them. They are fascinating, eh?