Heterodyne displacement interferometer, insensitive for input polarization

Abstract

Periodic nonlinearity (PNL) in displacement interferometers is a systematic error source that limits measurement accuracy. The PNL of coaxial heterodyne interferometers is highly influenced by the polarization state and orientation of the source frequencies. In this Letter, we investigate this error source and discuss two interferometer designs, designed at TU Delft, that showed very low levels of PNL when subjected to any polarization state and/or polarization orientation. In the experiments, quarter-wave plates (qwps) and half-wave plates (hwps) were used to manipulate the polarization state and polarization orientation, respectively. Results from a commercial coaxial system showed first-order PNL exceeding 10 nm (together with higher order PNL) when the system ceased operation at around 15°hwp rotation or 20°qwp rotation. The two "Delft interferometers," however, continued operation beyond these maxima and obtained first-order PNLs in the order of several picometers, without showing higher order PNLs. The major advantage of these interferometers, beside their high linearity, is that they can be fully fiber coupled and thus allow for a modular system buildup. Laser interferometry is an often applied measurement method in several fields of research, since it allows for noncontact measurements. It is especially preferred in the field of metrology, because of its direct traceability to the length standard [1]. Interferometry is also used in lithography machines in the semiconductor industry, gravitational wave detection [2], coordinate measuring machines, and as a calibration tool for other measurement devices, such as capacitive sensors, inductive sensors, and optical encoders. Many types of displacement interferometer systems can be distinguished; this publication deals with heterodyne displacement interferometry using a stabilized He-Ne laser (λ 632.8 nm) combined with two acoustooptic modulators for generating two (fixed-offset) source frequencies.Industrial manufacturing processes currently operate with measurement errors at the subnanometer level and will require even smaller errors in the near future [3]. When operating at this level, a heterodyne interferometer system is hampered by many error sources. The main error sources are the frequency stability of the laser source, noncommon optical pathway variations due to variations in the refractive indices of optical transport media, system alignment (i.e., cosine error, Abbé error), optical wavefront quality combined with beam walkoff [4], and periodic nonlinearity (PNL) in the measured phase [5][6][7][8][9][10]. Operating in vacuum will improve the obtained measurement error. However, PNL in the measurand remains a substantial error source.PNL manifests itself primarily in traditional heterodyne systems with coaxial beams. Such beams contain two linearly polarized frequencies that are orthogonally oriented. These frequencies may mix (due to "frequency leakage"), resulting in periodic errors that are superimposed on the obtained displacement data. This type ...

The Calibration of Displacement Sensors

“…The interaction of the periodic laser interferometer non-linearities with the probe under calibration was further studied by Köning [27] and Sacconi [28]. Also, dedicated laser interferometers been designed that exhibit hardly or no detectable non-linearities [29,30], or systems were designed to compensate these [31][32][33][34]. In that case these may compete for the noise-characteristics with the systems based on Fabry-Pérot interferometers as discussed in the next section.…”

Validation of separated source frequency delivery for a fiber-coupled heterodyne displacement interferometer

“…Frequency leakage (and thereby PNL) can be prevented by spatially separating the source frequencies throughout the interferometer system until detection [11][12][13][14][15][16][17][18]. The main advantage of separated source frequency delivery is that it can take place either free-space as well as via optical fibers, offering a reconfigurable means of optical transport at minimum space consumption and enabling complete fiber-coupled heterodyne displacement interferometers [see Fig.…”

“…The research discussed in this Letter is based upon previous research on the "Delft interferometer" [14][15][16], which reported on its measurement performance when fed with two fiber-delivered source frequencies (using polarization maintaining single-mode fibers) [15]. It did not, however, extensively analyze time variant influences of external disturbances acting on the fiber delivery.…”

“…Note that transport of interference signals from interferometers is less stringent and has already proven itself using optical fibers and external readout (not shown). [15,16]). Note that the tested interferometer was not a monolithic structure as suggested.…”

High-precision measurement of plasmonic phase change in metal nanostructures

“…The heterodyne interferometer uses the dual-frequency beam with a certain frequency difference Δf as a carrier signal. With the rapid development of electronic phase measurement technology, the resolution of the displacement measurement of the heterodyne interferometry has reached subnanometer [37].…”