Residual errors in laser interferometry from air turbulence and nonlinearity

Abstract

Laser displacement interferometry is used extensively in precision equipment for semiconductor manufacture. In these applications it is often necessary to introduce a high velocity airflow to the measurement environment to minimize the density of airborne particulate contaminants. The performance of the heterodyne interferometer is degraded by the resulting fluctuations in the index of refraction along the beam path. The magnitude, correlation length, and probability distribution of the optical path length (OPL) fluctuations are measured for several airflow conditions. The data are interpreted in terms of the path length errors for some common interferometric configurations. The OPL fluctuations are generally less significant than the systematic sources of measurement error. A more fundamental limit on the accuracy of the heterodyne Michelson interferometer is the periodic nonlinearity caused by leakage of the frequency components in the beamsplitter. The effect is discussed in detail. A direct observation of the nonlinearity is reported. The magnitude of the effect is about lambda/64 for the beam splitters used in this experiment. A simple technique which indicates the presence and magnitude of the nonlinearity is described.

Precision comparison of the lattice parameters of silicon monocrystals

“…Heterodyne Michelson interferometers are prone to sub-periodic nonlinearity resulting from imperfect separation of the two frequencies by the primary beam splitter [26,27]. The periodic nonlinearity can be evaluated by pressure scanning the interferometer and recording the fringe advance vs pressure increa.se.…”

Distance Measurements Using Mode-Locked Lasers: A Review

“…The underlying principle is to measure the phase variation of a single light wavelength with distance by employing homodyne [9][10][11][12] or heterodyne phase-measuring electronics [13][14][15][16]. This single wavelength method leads to incremental displacement measurement with nanometer-region sub-wavelength resolutions over extensive ranges up to several meters.…”

The effect of laser source and PBS on the nonlinearity in heterodyne interferometer

“…In heterodyne interferometer systems, periodic nonlinearities occurs as a consequence of optical mixing(polarization mixing or frequency mixing) and errors in the electronic phase meter [1][2][3][4][5][6][7][8][9]. Under unfavorable circumstances these errors may exceed 20 nm peak-to-peak.…”

“…Under unfavorable circumstances these errors may exceed 20 nm peak-to-peak. The nonlinearity of heterodyne interferometers is caused not only by polarization ellipticity or nonorthogonality of the laser beams, the imperfect optical parts can also contribute [1,2]. Hou [3] has proposed that the optical arrangement of interferometer could influence the nonlinearity.…”

“…Non-orthogonality of the frequency states produced by the laser is one of the causes of nonlinerity [8,9]. Theoretically, the nonlinearity error due to the leakage of the PBS could be generally neglected, because the laser beam has to pass the PBS at least two times and its leakage component is mostly filtered before being mixed at the receiver [1,3]. In this paper, we have experimentally proved that the nonlinearity error due to the leakage of the PBS is very small compare to the nonlinearity error due to the polarization ellipticity or nonorthogonality of the laser beams.…”