<title>Small displacement measurements based on total-internal-reflection heterodyne interferometry</title>

Abstract

A novel method for measuring small displacements based on the total-internal-reflection-heterodyne interferometry is presented. In this method, a common-path heterodyne interferometer is applied to measure the phase differences between s and p polarizations at total-internal reflection. The phase differences depend on the incident angles which are the function of displacements by using the image formula. Hence, small displacements can be evaluated only by measuring the phase differences. In our optical setup, a heterodyne light source with a frequency difference 800 Hz between s and p polarizations is used. A light beam passing through a lens is reflected from a mirror located near the focal plane of the objective lens and is driven by a piezo- electric transducer. If the mirror shifts from the focal plane of the lens, the reflected beam deflects with a small angular deviation to a phase difference measurement system. From Fresnel's equations, the phase difference between s and p polarizations is the function of incident angle and the numbers of TIR at total-internal reflection condition. To compare this test signal with a reference signal using a phase meter, the phase difference can be measured in real- time. Consequently, the displacement also can be calculated.