Displacement Measurements Using a Michelson Interferometer
A Michelson interferometer is an optical instrument that utilizes interference of light to measure relative displacements with a high resolution. In a minimalist version, such an instrument requires only a few components:
- a coherent light source; monochromatic light with constant phase,
- a means to split the generated light, often a beamsplitter and
- two mirrors.
More specifically, the coherent light is first divided into two beams at the beam splitter. One part is reflected at a fixed reference mirror while the other part hits the target mirror. Then, both reflected beams are guided back to the beamsplitter where interference occurs. Interference is generated by the superposition of both beam intensities, which results in a sinusoidally modulated signal with periodicity equaling half the wavelength of the coherent light source. When projecting this to a screen, one can observe the characteristic ring-shaped interference pattern.
When the amplitude of the interference signal is maximum, constructive interference occurs and both beams are in-phase, while destructive interference happens when the amplitude of the interference signal is zero and both beams are out-of-phase. The phase information, which inherently encodes the interference signal, depends on the optical path length difference between the beam reflected at the reference mirror and the target mirror. When the path length difference is zero, or in other words, when the distance between beamsplitter and the two mirrors is identical, then the signals are in-phase and constructive interference is generated. Once the target mirror is moved, the path length changes, and a succession of constructive and destructive interference is created. The change of intensity of the interference signal can be observed with a photo detector, which generates a flow of current that is proportional to the incident power. Electronic circuitry is then used to filter or process the current change from the photodiode into a clean signal. The below animation shows a simplified version of this signal’s intensity which is analog the mirror’s movement.
Quadrature Detection
The above-described design presents two major flaws. First, the direction of the movement cannot be extracted from the interference signal, since forward and backward movement will create an identical change in intensity. Second, the sensitivity of the method is inconsistent. At the zero crossings, the sensitivity is at maximum, while it is minimum at the extrema. Small displacements will induce vanishingly small changes in intensity, which will be a challenge for the electronic circuitry to record properly.
Both flaws can be overcome by having not one interference signal, but two interference signals with 90°C phase-shift, or in quadrature. These quadrature signals can be represented as a circle, or Lissajous figure, when plotted with respect to each other, and the displacement can then be retrieved by computing the instantaneous phase. This phase signal then has constant sensitivity, but more importantly allows to determine the direction of the movement. If the phase increases, then the path length difference between reference and target mirror increases. If the phase decreases, they drift apart.
Getting signal in quadrature can be achieved in various ways. Often, they require additional components than presented earlier, which is detrimental both in terms of compactness and cost. At SmarAct, we employ state-of-the-art technique, the current modulation of the light source. In a nutshell, the modulation at the laser source with frequency f causes the interference signal to contain harmonics of the modulation frequency: f, 2f, 3f, 4f etc. A pair of harmonics, such as f and 2f, are intrinsically in quadrature, which means that even with a single photo detector, but specific signal processing, it is possible to extract the wanted components. Once extracted, these signals are digitized to a field programmable array (FPGA), which can calculate the corresponding phase, thus displacement.
