The accuracy of a heterodyne interferometer is often limited by the periodic nonlinearity that arises mainly from imperfect separation of the two optical frequencies. This paper describes a new method for compensation of the nonlinearity in the heterodyne laser interferometer using the quadrature mixing technique for the phase measurement. The compensation technique is based on the elliptical fitting of two phase-quadrature signals obtained by a lock-in amplifier. The brief analysis and compensation scheme of the nonlinearity in the heterodyne interferometer, and the experimental result using a Zeeman stabilized He-Ne laser, have been presented. The results show that the suggested method can compensate for the nonlinearity of the heterodyne interferometer with sub-nanometre accuracy.

We have proposed and demonstrated a novel method that can determine both the geometrical thickness and refractive index of a silicon wafer at the same time using an optical comb. The geometrical thickness and refractive index of a silicon wafer was determined from the optical thickness using phase information obtained in the spectral domain. In a feasibility test, the geometrical thickness and refractive index of a wafer were measured to be 334.85 microm and 3.50, respectively. The measurement uncertainty for the geometrical thickness was evaluated as 0.95 microm (k = 1) using a preliminary setup.

We developed an accurate and efficient method for measuring the refractive indices of a transparent plate by analyzing the transmitted intensity versus angle of incidence. By using two different wavelengths, we resolved the 2pi-ambiguity inherent to the phase measurement involving a thick medium, leading to independent determination of the absolute index of refraction and the thickness with a relative uncertainty of 10(-5). The validity and the accuracy of our method were confirmed with a standard reference material. Furthermore, our method is insensitive to environmental perturbations, and simple to implement, compared to the conventional index measurement methods providing similar accuracy.

This note presents a digital signal processing module for the real-time nonlinearity compensation of a homodyne interferometer. The nonlinearity is corrected by using the parameter values describing two phase-quadrature signals, through simple arithmetic calculation of the quadrature signals at specific phases, which are multiples of π/4. A field-programmable gate array was employed for the real-time implementation of a processing module since it has reconfigurable input/output and high precision synchronization. The developed module has a minimum loop time of 4.4 µs and can compensate the nonlinearity error less than ±0.5 nm, which is comparable with the elliptical fitting method. We also proved the performance of the module by examining the convergence and the stability of parameter values under various operational conditions.

A phase-encoding electronics capable of compensating for the nonlinearity error in a heterodyne laser interferometer is described. The system consists of the phase demodulating electronics and the nonlinearity compensating electronics. For phase demodulation, we use the phase-quadrature mixing technique. For nonlinearity compensation, the offsets, the amplitudes and the phase of two output signals from the demodulator are adjusted electrically so that their Lissajous figure is a circle. As a result, the correct phase can be obtained. An analysis of the nonlinearity in the heterodyne interferometer and the design of the phase-encoding electronics are presented. The experiment was performed in a Michelson-type interferometer using a transverse Zeeman stabilized He-Ne laser. We demonstrate that this method can encode the phase of a heterodyne interferometer with sub-nanometer accuracy.