Interferometry
WHAT IS AN INTERFEROMETER?
An interferometer is a device to make precise measurements using light. Modern interferometers often use laser light because the light is generally a discrete wavelength and the light beam can readily be collimated or expanded.
The name is derived from utilizing the characteristic property of the wave-like nature of light to combine a light beam with another, or often with itself, to cause subtraction or addition to the intensity at a point (interference) measured (metered) by the instrument.
There are many types of interferometers (sometimes call “I-meters” for convenience). They can be used to measure distance, texture of surfaces, step heights, gravitational waves, and several other physical properties. Interferometers have the advantage of being noncontact, and in fact have minimal if any effect on the item being measured.
What Kinds of Interferometers Are There?
There are several well-known interferometers, and many specialized versions that have been developed from the basic principle of light interference. (For an extensive list see here.)
A very famous version is the Michelson interferometer. It was used to measure the speed of light accurately. Michelson did initial attempts to measure the speed of light at the U S Naval Academy in 1877, using a rotating mirror device. Later he was able to get significantly better values using the interferometer design that bears his name, while he taught at what is now Case Western Reserve University in Cleveland, Ohio.
The Michelson interferometer has many variations and has been used for exact measurements of displacement in Computer Numerical Controlled machinery, distance measurements, length standards, gravitational wave detection, and others too numerous to list.
Wavefront Measuring Interferometers
Of greatest interest in the optics manufacturing world are interferometers that detect errors in reflected or transmitted wavefronts from optical elements or assemblies. Light should bounce off a mirror or through a similar element with little or no distortion. Any departure from flatness will be seen in the interference pattern of the reflected beam of a well collimated light that is combined with its undistorted self.
In like manner, light transmitted through an element will be distorted by both surface errors and any inhomogeneity of the substrate material itself.
Again, there are numerous interferometer configurations to detect such errors. There are shearing interferometers, Mach-Zehnder, holographic, Moiré interferometers and others. For the kinds of optics testing in which we are interested there are two; the Fizeau and Twyman-Green types.
Either of these two can be easily assembled from individual optical elements and a coherent light source. The Twyman-Green type requires more and larger elements and is thus more expensive. That makes the Fizeau design more popular. In fact, there are a few manufacturers of assembled, ready to use Fizeau interferometers. These include Davidson, 4D Technology, Trioptics, Wyko Veeco, Zygo, and others. Not all are still making interferometers, but examples of each remain in use. Several manufacturers include detectors and software to analyze the wavefronts.
GAMDAN uses Fizeau interferometers to measure the flatness of surfaces, and transmitted wavefront, which is a functional attribute of our crystals as well as an indication of internal material quality.
Wavefront Calculation
Interference between the wavefronts reflected from a precisely flat beam splitter and the optic being tested results in a pattern of greater and lesser intensity. If the error is great enough, fringe lines will appear. If the error is less than one half wave, fringes may be introduced by tilting one of the optics. Software can display whatever the error is in terms of wavelengths or nanometers since the wavelength of the light source is known. Generally the light source is a monochromatic laser. Helium neon (HeNe) red emitting lasers were an enabling technology for the wavefront measuring interferometer, although diode lasers have replaced them in some instances. Other wavelength sources are available for special cases, such as transmitted wavefront through materials that don’t allow visible light to pass.
There are also manual techniques to calculate wavefront error. These involve displacement or curvature of a fringe pattern, usually translated to waves. Often an eyeball estimation is made when the error is multiple fringes, or down to as little as a tenth wave.
Why Do Intensity Patterns and Fringes Form?
When two identical beams of light combine, they interfere with each other, and can add or subtract in intensity. If they are in phase, they will add to a greater intensity, but if they are exactly 180 degrees out of phase, they will "add" destructively and form a dark area. When multiples of these dark areas or points align, they will form a black fringe line. If not exactly in phase or out of phase they will partially add or subtract intensities. The eye perceives this as dark lines separated by white or bright areas. The gray areas of partial intensity are detected by the sensors in interferometers, but not readily discerned by eye.
A perfect fringe pattern, with only tilt introduced to form the fringes, consists of straight lines, parallel, and evenly spaced. Straightness and parallelism are readily perceived. If only the spacing varies, it won’t be obvious to the eye. Changing the tilt to align the fringes perpendicular to the first pattern will show obvious curvature in that case.
What If You Don't Have an Interferometer?
Before interferometers became readily available, and for in process testing to this day, opticians have formed fringe intensity patterns using a test plate, also known as an optical flat. It is a piece of transparent material, preferably a low expansion one. One side must be polished accurately flat, generally within one twentieth of a wave of visible light. The other side must be polished to good transparency; it may or may not be precisely flat.
It is carefully placed against the optic to be tested after both have been wiped clean and free of lint. There are various techniques used to do this safely without scratching either piece. If the loose “assembly” is positioned under a light with sufficient coherence length, an intensity pattern will appear. If a slight wedge exists between the two pieces, fringe lines will form. The light may be a monochromatic light made for this purpose. Some shops use a bank of ultraviolet fluorescent lamps that include a visible spectrum. Even regular daylight fluorescent lamps will form fringes. They will be rainbow shades, rather than distinct dark and light bands. The key is that the space between the optic and the test flat must be very small.
What Is the Overall Shape of the Optic?
Generally, if it is not flat the optic may be concave (lower in the center; “caved in”) or it may be convex (raised in the center; does your voice get raised when you are vexed?!). Less often it may be cylindrical, saddle shaped like a potato chip, or some combination of concave and convex. Often during polishing a single element may be concave in the center, yet slightly convex near the periphery. Opticians call this pattern “a hole and a roll”. These shapes can be confusing when displayed as fringe patterns, but introducing the computer analyzed display of contour or line drawings has made them intuitive.
This is especially true for phase contrast interferometers, which display many more points than fringe measuring instruments. The continuous pattern of hundreds or thousands of points may be displayed as a color-coded map of high and low regions. Commonly displayed values include peak-to-valley wavefront distortion, RMS wavefront, and residual wavefront after subtracting spherical aberration. Power spectral density (PSD) is also a value important to some applications. The units are commonly expressed in waves, either at the wavelength of the laser used in the interferometer or converted proportionally to some standard wavelength. To accurately evaluate those measurements, the wavelength in question must be known. As an alternative the values may be stated in nanometers, which is an absolute measure that requires no further conversion.
DENNIS J. GARRITY, AUTHOR
Dennis is an engineer with over 45 years of experience in fabrication, testing, and material evaluation for high precision optics, with extensive hands-on experience. More on the author can be found here.