Modeling and verifying non-linearities in heterodyne displacement interferometry

Cosijns, Sjag Suzanne; Haitjema, Han; Schellekens, Phj Piet

doi:10.1016/s0141-6359(02)00150-2

Cited by 113 publications

(74 citation statements)

References 9 publications

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“…These frequencies may mix (due to "frequency leakage"), resulting in periodic errors that are superimposed on the obtained displacement data. This type of error repeats itself each fraction of a wavelength-hence "periodic"-and is caused by imperfect polarization orthogonality and linearity of the source frequencies combined with imperfect polarizing optics and nonideal alignment [5].There are several approaches for reducing PNL in coaxial interferometer systems. Physically reducing PNL is one of the most costly methods, since it involves expensive high-quality optics and routine individual system alignment.…”

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confidence: 99%

“…This reduction approach is based on the quality of the coaxial beam's source frequency orthogonality together with the quality of the linear polarizations. If these are of high quality, it is also essential that highquality polarized optics are applied for beam splitting, combined with alignment [5][6][7][8][9].A less expensive approach is to digitally compensate for the PNL through analytical modeling [5,[9][10][11]. The advantage of this method is that it typically ensures PNL below 1 nm for small system imperfections, without changing the interferometer configuration.…”

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confidence: 99%

“…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.…”

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Heterodyne displacement interferometer, insensitive for input polarization

Meskers¹,

Spronck²,

Schmidt³

2014

Opt. Lett.

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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 ...

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Heterodyne displacement interferometer, insensitive for input polarization

Meskers¹,

Spronck²,

Schmidt³

2014

Opt. Lett.

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Spin‐Manipulated Photonic Skyrmion‐Pair for Pico‐Metric Displacement Sensing

et al. 2023

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Photonic spin skyrmions with deep‐subwavelength features have aroused considerable interest in recent years. However, the manipulation of spin structure in the skyrmions in a desired manner is still a challenge, while this is crucial for developing the skyrmion‐based applications. Here, an approach of optical spin manipulation by utilizing the spin‐momentum equation is proposed to investigate the spin texture in a photonic skyrmion‐pair. With the benefit of the proposed approach, a unique spin texture with spin angular momentum varying linearly along the line connecting the two skyrmion centers is theoretically designed and experimentally verified. The optimized spin texture is then applied in a displacement‐sensing system, which is capable of attaining pico‐metric sensitivity. Compared with the conventional polarization and phase schemes, the spin‐based manipulation mechanism provides a new pathway for optical modulation, which is of great value in nanophotonics from both fundamental and application.

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Use of adaptive RLS, LMS, and NLMS algorithms for nonlinearity modeling in a modified laser interferometer

Olyaee

Abadi

Hamedi

et al. 2010

Front. Optoelectron. China

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Laser heterodyne interferometer is one kind of nano-metrology systems which has been widely used in industry for high-accuracy displacement measurements. The accuracy of the nano-metrology systems based on the laser heterodyne interferometers can be effectively limited by the periodic nonlinearity. In this paper, we present the nonlinearity modeling of the nano-metrology interferometric system using some adaptive filters. The adaptive algorithms consist of the least mean squares (LMS), normalized least mean squares (NLMS), and recursive least squares (RLS). It is shown that the RLS algorithm can obtain optimal modeling parameters of nonlinearity.

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Modeling and verifying non-linearities in heterodyne displacement interferometry

Cited by 113 publications

References 9 publications

Heterodyne displacement interferometer, insensitive for input polarization

Heterodyne displacement interferometer, insensitive for input polarization

Spin‐Manipulated Photonic Skyrmion‐Pair for Pico‐Metric Displacement Sensing

Use of adaptive RLS, LMS, and NLMS algorithms for nonlinearity modeling in a modified laser interferometer

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