Quadrature Michelson Interferometer

Introduction

A Quadrature Michelson Interferometer is an optical setup to measure changes in the optical path lengths as small as a fraction of the wavelength. While a "basic" interferometer only provides information about the absolute path length change, the Quadrature Michelson Interferometer also supplies directional information. Therefore, these interferometers utilize two detectors X and Y and from the phase relation between them, the direction of the path length change can be obtained.

These interferometers are extremely useful in a noisy environment where large path length changes in either direction exist (due to vibrations) but the overall net displacement remains very small and centered around an equilibrium point.

Quadrature Michelson Interferometer Designs

Various designs for such interferometers exist. Some utilize either a metallic beam splitter that introduces and additional 90 degree phase shift (like in setup 1) or a mixture of linearly and circularly polarized light (like in interferometers setup 2 and 3). Modulating one of the interferometer arms with an AO cell (not shown) and comparing the phase of the signal from the interferometer with that of the AO cell driver (for example with a high frequency lock-in amplifier) also will yield path length and directional information.

Setup 1: Detailed description of the setup based on: Elsworth and James: "An optical screw with a pitch of one wavelength"

Photograph of a Quadrature Michelson Interferometer cage assembly of Setup 1 to measure the velocity of a Moessbauer drive: the laser enters the left most cube, containing the non-polarized beam splitter through the half wave plate, HWP. One part of the beam is reflected by the mirror in the upper left corner back into the beam splitter; the other part passes twice through a quarter wave plate (QWP, obscured in the picture by the cube) as it is reflected by the mirror on the right. Both beams pass through another quarter wave plate (QWP) to the polarizing beam splitter cube on the right where the horizontal component proceeds to detector X and the vertical to detector Y.

Setup 2: Detailed Description of the setup based on: Doboszy, Usuda and Kurosawa: "Methods for the calibration of vibration pick-ups by laser interferometry"

Setup 3: Detailed Description of the setup based on: Teachspin Metal Film Beam Splitter

Data Analysis

The Data Analysis section uses MATLAB to extract the displacement and velocity as a function of time from the (voltage) data captured by an oscilloscope from the X and Y detectors.