EMA 611, Lab 4a - Michelson interferometer
Advanced Mechanical Testing of Materials
Department of Engineering Physics, Engineering Mechanics Program, University of Wisconsin-Madison
Lab 4 Holographic interferometry; Lab4a, Michelson interferometer
The Michelson interferometer illustrates the formation of interference fringes. Much smaller fringes on the order of a micron (1 μ m) or less generate the images seen in holograms.
The Michelson interferometer is used to measure small displacements. Translation of one of the mirrors by half a wavelength of the laser light causes a motion of the fringe pattern by one fringe. For example, on a precision micrometer, one small division corresponds to 10 μ m. The wavelength of the green laser light from a frequency-doubled YAG laser is 532 nm. So, with half a wavelength per fringe, motion of one small division on the micrometer results in motion of about 37.5 fringes. The wavelength of the helium-neon red laser is 633 nm. Tilt of a mirror causes the fringe spacing to change, proportional to the tilt. If one measures the light intensity with a silicon light detector, sub-fringe measurements of great sensitivity can be made.
Figure 1. Michelson interferometer fringes with high contrast.
The Michelson interferometer is also used to measure the coherence of light. In the image below, displacement of one mirror by several millimeters has caused the fringes to lose contrast.
Contrast of the fringes provides a measure of the coherence of the laser source. A perfectly coherent laser would emit light at a single frequency. Suppose the light is spread uniformly over a band of frequency from zero to ν0. Then, by Fourier transformation [1], there is full contrast for zero path difference, but contrast drops to zero for a path difference Δ = c/2ν0, with c as the speed of light. This path difference, as measured by the Michelson interferometer, is a measure of the coherence length of the laser light. See also [2].
For holography the coherence length should be larger than the object to be imaged.
Figure 2. Michelson interferometer fringes lose contrast after one mirror is moved a few millimeters. This indicates limited coherence.
Figure 3. Michelson interferometer set-up for deformation measurement. A piezoelectric bender element is provided with an electrical signal, resulting in a small deformation measurable using the interferometer. The interferometer is adjusted until one large fringe covers the light detector; the detector converts the light into an electrical signal that is observable on an oscilloscope.
Case study: single mode laser becomes multi-mode
A laser was purchased for the holography portion of class. With a claimed single longitudinal mode, the coherence length exceeded one meter, more than adequate for use in class. The laser was used for about 12 hours of run time that semester, similarly a year later. The following year, holograms made in class showed spurious fringes. Multiple attempts were made to debug the setup, in that spurious fringes can arise from multiple causes. At the end of the spring term, the laser was moved and tested with the Michelson interferometer. The coherence was found to be inadequate for holography. Output had become multi-mode. The home page for Diode Laser Concepts link states "Our diode laser modules are among the most reliable on the market. They are fully customizable and come with a 2 Year Warranty." We used the laser for about 24 hours of run time over about two years. In view of odd fringe patterns seen in class, the laser likely failed to produce adequate coherence in the first two years, but due to use in spring 2012 class (another 12 hours run time) it took a further half year to identify the laser as the cause. We then queried the company on how to regain the promised coherence. They said it was out of warranty and that the warranty for that model was one year. Typical lifetime for this class of laser exceeds 5000 hours run time. We have other single longitudinal mode lasers that have performed well for years.
Tasks for lab
Estimate how many fringes pass when the micrometer screw is advanced 10 μ m. Is your result consistent with the above prediction? Can you easily count the fringes by observation? Is a light detector more appropriate?
What happens to the fringes if you tap on the table? What if you tap on the floor? What are the implications regarding the formation of holograms? Holograms will be made and interpreted in the remaining portion of this lab.
Determine the sensitivity of the piezoelectric device that supports one mirror, in μ m per volt using the Michelson interferometer. Apply a known voltage, evaluate the number of fringes and convert to displacement. How does this sensitivity compare with the intrinsic sensitivity of piezoelectric ceramics (100 to 500 pm/V) ? Explain any difference.
Measure the coherence length of the green solid state laser and the helium neon laser (in service more than 15 years) using the Michelson interferometer. Keep in mind that the coherence length may exceed the travel of the micrometer screw. If that is the case, move one mirror mount by at least 2.5 cm and realign the interferometer. If time permits, another green solid state laser (in service more than 15 years) may be tested.
How might the interferometer be used to measure deformations on the order 5 nm?
Figure 4. Michelson interferometer output from deformation measurement. A piezoelectric bender element is provided with a sinusoidal electrical signal, resulting in a small deformation measurable using the interferometer. The interferometer output is also shown in the figure.
Questions
Can you infer the mode structure of each laser from the change of fringe contrast with mirror motion?
Referring to the case study, if you become a manager in a company, how would you handle such a case of failure of laser performance?
References
[1] Reynolds, G. O., DeVelis, J. B., Parrent, G. B., Thompson B. J., "Physical optics notebook: tutorials in Fourier optics", SPIE, 1989.
[2] R. S. Longhurst, Geometrical and physical optics, third edition, Longman, 1981.
