Basics of interferometry and interferometers

Basics of interferometry and interferometers

(From: Sam Goldwasser (sam@stdavids.picker.com)).

The dictionary definition goes something like:
"INTERFEROMETER: An instrument designed to produce optical interference fringes for measuring wavelengths, testing flat surfaces, measuring small distances, etc."

As an example of an interferometer for making precise physical measurements, split a beam of monochromatic coherent light from a laser into two parts, bounce the beams around a bit and then recombine them at a screen, optical viewer, or sensor array. The beams will constructively or destructively interfere with each-other on a point-by-point basis depending on the net path-length difference between them. This will result in a pattern of light and dark fringes. If one of the beams is reflected from a mirror or corner reflector mounted on something whose position you need to monitor extremely precisely (like a multi-axis machine tool), then as it moves, the pattern will change. Counting the passage of the fringes can provide measurements accurate to a few nanometers!

A simple version of a Michelson interferometer is shown below:

                                _____ Mirror 1 (Moving)

                                  ^

                                  |

                                  |  Beam

                                  |  Splitter

               +-------+          | /          |

               | Laser |=========>/<---------->| Mirror 2 (Fixed)

               +-------+        / |            |

                                  |

                                  |

                                  |

                                  v    Screen (or optical viewer,

                               -------    magnifier, sensor, etc.)

1.     The laser produces a coherent monochromatic beam which is expanded and collimated by a pair of positive lenses (not shown).

2.     Part of the laser beam is reflected up by the Beam Splitter (half silvered mirror), reflects off of Mirror 1 and back down. A portion of this passes through the Beam Splitter to the Screen.

3.     The remainder of the laser beam passes through the Beam Splitter and is reflected from Mirror 2. Part of this is reflected down by the Beam Splitter to the Screen.

4.     The two beams combine at the Screen resulting in an interference pattern of light and dark fringes. A magnifier, microscope, or other optical system imaging to a human observer or electronic sensor may be provided in place of the screen to view the fringe pattern in more detail or provide input to an electronic measurement system.

5.     A microscopic shift in position or orientation of either mirror will result in a change to the fringe pattern. Presumably, the mirror designated as 'Moving' is mounted on some equipment such as a disk drive head positioner that is being tested or calibrated.

(Yes, about 50 percent of the light gets reflected back toward the laser and is wasted with this particular configuration. This light may also destabilize laser action if it enters the resonator. Both of these problems can be easily dealt with using slightly different optics than what are shown.)

A long coherence length laser producing a TEM00 beam is generally used for this application. HeNe lasers have excellent beam characteristics especially when frequency stabilized to operate in a single longitudinal mode. However, some types of diode lasers (which are normally not thought of as having respectable coherence lengths or stability) may also work. See the section: "Interferometers using inexpensive laser diodes". Even conventional light sources (e.g., gas discharge lamps producing distinct emission lines with narrow band optical filters) have acceptable performance for some types of interferometry.

Such a setup is exceedingly sensitive to EVERYTHING since positional shifts of a small fraction of a wavelength of the laser light (10s of nm - that's nanometers!) will result in a noticeable change in the fringe pattern. This can be used to advantage in making extremely precise position or speed measurements. However, it also means that setting up such an instrument in a stable manner requires great care and isolated mountings. Walking across the room or a bus going by down the street will show up as a fringe shift!

Interferometry techniques can be used to measure vibrational modes of solid bodies, the quality (shape, flattness, etc.) of optical surfaces, shifts in ground position or tilt which may signal the precursor to an earthquake, long term continental drift, shift in position of large suspended masses in the search for gravitational waves, and much much more. Very long base-line interferometry can even be applied at cosmic distances (with radio telescopes a continent or even an earth orbit diameter apart, and using radio emitting stars or galaxies instead of lasers). And, holography is just a variation on this technique where the interference pattern (the hologram) stores complex 3-D information.