Coherence Length and the White-Light Fringe

Build the Michelson from the previous blueprint, get fringes, then walk one mirror steadily outward. With a laser the fringes go on for ever. With a red LED they fade after a fraction of a millimetre. With white light they appear for about two fringes and then are gone, and no amount of adjustment brings them back except returning to where you were. What you have measured is the source. A perfectly single wavelength would interfere with itself over any distance; a real source has a spread, and the wider the spread the sooner its colours drift out of register. Coherence length is the wavelength squared divided by the linewidth, and it runs from a micrometre for daylight to metres for a good laser. The white-light case looks like the useless extreme and is the most useful of all. Because fringes appear ONLY when the arms are equal to within a micrometre, the white-light fringe marks zero path difference absolutely — it is a unique, unmistakable landmark, where a laser offers millions of identical fringes and no way to know which one you are on. Every instrument that must find a true zero uses it, from the Fourier spectrometer in blueprint 9 to the optical coherence tomography scanners in modern eye clinics. And there is a bonus that took Michelson somewhere unexpected. Watch how the fringe CONTRAST varies as you move, rather than merely when it dies, and you are measuring the Fourier transform of the source's spectrum. He used it in the 1890s to find structure in spectral lines that no prism of the day could resolve.